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1

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

2

Buckling of a sublaminate in a quasi-isotropic composite laminate  

NASA Technical Reports Server (NTRS)

The buckling of an elliptic delamination embedded near the surface of a thick quasi-isotropic laminate was predicted. The thickness of the delaminated ply group (the sublaminate) was assumed to be small compared to the total laminate thickness. Finite-element and Rayleigh-Ritz methods were used for the analyses. The Rayleigh-Ritz method was found to be simple, inexpensive, and accurate, except for highly anisotropic delaminated regions. Effects of delamination shape and orientation, material anisotropy, and layup on buckling strains were examined. Results show that: (1) the stress state around the delaminated region is biaxial, which may lead to buckling when the laminate is loaded in tension; (2) buckling strains for multi-directional fiber sublaminates generally are bounded by those for the 0 deg and 90 deg unidirectional sublaminates; and (3) the direction of elongation of the sublaminate that has the lowest buckling strain correlates with the delamination growth direction.

Shivakumar, K. N.; Whitcomb, J. D.

1984-01-01

3

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

4

Experimental data on single-bolt joints in quasi isotropic graphite/polyimide laminates  

NASA Technical Reports Server (NTRS)

Sixteen ply, quasi-isotropic laminates of Celanese Celion 6000/PMR-15 and Celion 6000/LARC-160 with a fiber orientation of (0/45/90/-45) sub 2S were evaluated. Tensile and open hole specimens were tested at room temperature to establish laminate tensile strength and net tensile strength at an unloaded bolt hole. Double lap joint specimens with a single 4.83-mm (0.19 in.) diameter bolt torqued to 1.7 N-m (15 lbf-in.) were tested in tension at temperatures of 116 K (-250F), 297 K (75F), and 589 K (600F). The joint ratios of w/d (specimen width to hole diameter) and e/d (edge distance to hole diameter) were varied from 4 to 6 and from 2 to 4, respectively. The effect of joint geometry and temperature on failure mode and joint stresses are shown. Joint stresses calculated at maximum load for each joint geometry and test temperature are reported. Joint strength in net tension, bearing, and shear out at 116 K (-250F), 297 K (75F), and 589 K (600F) are given for the Celion 6000/PMR-15 and Celion 6000/LARC-160 laminates.

Wichorek, G. R.

1982-01-01

5

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 20-100įC 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

6

The effect of resin toughness and modulus on compressive failure modes of quasi-isotropic graphite/epoxy laminates  

NASA Technical Reports Server (NTRS)

Compressive failure mechanisms in quasi-isotropic graphite/epoxy laminates were characterized for both unnotched and notched specimens and also following damage by impact. Two types of fibers (Thornel 300 and 700) and four resin systems (Narmco 5208, American Cyanamid BP907, and Union Carbide 4901/MDA and 4901/mPDA) were studied. For all material combinations, failure of unnotched specimens was initiated by kinking of fibers in the 0-degree plies. A major difference was observed, however, in the mode of failure propagation after the 0-degree ply failure. The strength of quasi-isotropic laminates in general increased with increasing resin tensile modulus. The laminates made with Thornel 700 fibers exhibited slightly lower compressive strengths than did the laminates made with Thornel 300 fibers. The notch sensitivity as measured by the hole strength was lowest for the BP907 resin and highest for the 5208 resin. For the materials studied, however, the type of fiber had no effect on the notch sensitivity.

Hahn, H. Thomas; Williams, Jerry G.; Sohi, Ohsen M.

1987-01-01

7

The effect of resin toughness and modulus on compressive failure modes of quasi-isotropic graphite/epoxy laminates  

NASA Technical Reports Server (NTRS)

Compressive failure mechanisms in quasi-isotropic graphite/epoxy laminates were characterized for both unnotched and notched specimens and also following damage by impact. Two types of fibers (Thornel 300 and 700) and four resin systems (Narmco 5208, American Cyanamid BP907, and Union Carbide 4901/MDA and 4901/mPDA) were studied. For all material combinations, failure of unnotched specimens was initiated by kinking of fibers in the 0-degree plies. A major difference was observed, however, in the mode of failure propagation after the 0-degree ply failure. The strength of quasi-isotropic laminates in general increased with increasing resin tensile modulus. The laminates made with Thornel 700 fibers exhibited slightly lower compressive strengths than did the laminates made with Thornel 300 fibers. The notch sensitivity as measured by the hole strength was lowest for the BP907 resin and highest for the 5208 resin. For the materials studied, however, the type of fiber had no effect on the notch sensitivity.

Sohi, M. M.; Hahn, H. T.; Williams, J. G.

1986-01-01

8

Effects of partial interlaminar bonding on impact resistance and loaded-hole behavior of graphite/epoxy quasi-isotropic laminates  

NASA Technical Reports Server (NTRS)

A partial-bonding interlaminar toughening concept was evaluated for resistance to impact and for behavior of a loaded hole. Perforated Mylar sheets were interleaved between all 24 plies of a graphite/epoxy quasi-isotropic lay-up. Specimens were impacted by aluminum spheres while under tensile or compressive loads. Impact-failure thresholds and residual strengths were obtained. Loaded-hole specimens were tested in three configurations that were critical in bearing, shear, or tension. Partial bonding reduced the tensile and compressive strengths of undamaged specimens by about one-third. For impact, partial bonding did not change the threshold for impact failure under tensile preload. However, under compressive preload, partial bonding caused serious degradation of impact resistance. Partial bonding reduced the maximum load-carrying capacity of all three types of loaded-hole specimens. Overall, partial bonding degraded both impact resistance and bearing strength of holes.

Illg, W.

1986-01-01

9

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

10

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

11

Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact  

NASA Technical Reports Server (NTRS)

A geometrically nonlinear finite-element analysis was developed to calculate the strain energy released by delamination plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, G sub I, and shear sliding, G sub II, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding (G sub II) was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, G sub I, for a near-surface delamination can be as high as 0.5G sub II and can contribute significantly to the delamination growth.

Shivakumar, K. N.; Elber, W.

1984-01-01

12

Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact  

NASA Technical Reports Server (NTRS)

A geometrically nonlinear finite-element analysis has been developed to calculate the strain energy released by delaminating plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, GI, and shear sliding, GII, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow first before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, GI, for a near-surface delamination can be as high as 0.5GII, and can contribute significantly to the delamination growth.

Shivakumar, K. N.; Elber, W.

1984-01-01

13

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

14

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 Sparma√?nahme Anhang √?berblick Einleitung: `Alles ist Zahl' am Digitalcomputer Archimedes und

Auzinger, Winfried

15

Interpolation and Approximation Theory.  

ERIC Educational Resources Information Center

Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH)

Kaijser, Sten

1991-01-01

16

Durability-Based Design Criteria for a Quasi-Isotropic Carbon-Fiber-Reinforced Thermoplastic Automotive Composite  

SciTech Connect

This report provides recommended durability-based design properties and criteria for a quais-isotropic carbon-fiber thermoplastic composite for possible automotive structural applications. The composite consisted of a PolyPhenylene Sulfide (PPS) thermoplastic matrix (Fortron's PPS - Ticona 0214B1 powder) reinforced with 16 plies of carbon-fiber unidirectional tape, [0?/90?/+45?/-45?]2S. The carbon fiber was Hexcel AS-4C and was present in a fiber volume of 53% (60%, by weight). The overall goal of the project, which is sponsored by the U.S. Department of Energy's Office of Freedom Car and Vehicle Technologies and is closely coordinated with the Advanced Composites Consortium, is to develop durability-driven design data and criteria to assure the long-term integrity of carbon-fiber-based composite systems for automotive structural applications. This document is in two parts. Part 1 provides design data and correlations, while Part 2 provides the underlying experimental data and models. The durability issues addressed include the effects of short-time, cyclic, and sustained loadings; temperature; fluid environments; and low-energy impacts (e.g., tool drops and kickups of roadway debris) on deformation, strength, and stiffness. Guidance for design analysis, time-independent and time-dependent allowable stresses, rules for cyclic loadings, and damage-tolerance design guidance are provided.

Naus, Dan J [ORNL; Corum, James [ORNL; Klett, Lynn B [ORNL; Davenport, Mike [ORNL; Battiste, Rick [ORNL; Simpson, Jr., William A [ORNL

2006-04-01

17

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; Kšll, Mikael

2014-09-23

18

May 1, 2001 / Vol. 26, No. 9 / OPTICS LETTERS 605 Polarization competition in a quasi-isotropic CO2 laser  

E-print Network

the emission line P20 and the cavity detuning. The discharge tube is 68 cm long and has an inside diameter of 20 mm. The cavity length is L 1.3 m. The medium is pumped by a dc discharge, which in our experiments state is imposed by anisotropies of the cavity. For instance, in gas lasers it is usual to introduce in

Rey Juan Carlos, Universidad

19

On Approximate Calculations.  

ERIC Educational Resources Information Center

The ability to undertake approximate calculations and to get a rough feel for data is an important skill which should not be overlooked. Presents some ideas for teaching and assessing approximate calculation. Contains 13 references. (Author/ASK)

Jolliffe, Flavia

1999-01-01

20

Approximate flavor symmetries  

SciTech Connect

We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.

Rasin, A.

1994-04-01

21

Approximation through Multicommodity Flow  

Microsoft Academic Search

The first approximate max-flow-min-cut theorem for general multicommodity flow is proved. It is used to obtain approximation algorithms for minimum deletion of clauses of a 2-CNF?formula, via minimization problems, and other problems. Also presented are approximation algorithms for chordalization of a graph and for register sufficiency that are based on undirected and directed node separators

Philip N. Klein; Ajit Agrawal; R. Ravi; Satish Rao

1990-01-01

22

Surfaces: Representation and approximation  

NASA Technical Reports Server (NTRS)

Schemes for the representation and approximation of surfaces, based on Coon's and triangular patches and blending are discussed. The necessary criteria/characteristics for resulting spaces are outlined.

Barnhill, R. E.

1982-01-01

23

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

24

Approximation theory for matrices  

NASA Astrophysics Data System (ADS)

We review the theory of optimal polynomial and rational Chebyshev approximations, and Zolotarev's formula for the sign function over the range ? < ? z? < 1. We explain how rational approximations can be applied to large sparse matrices efficiently by making use of partial fraction expansions and multi-shift Krylov space solvers.

Kennedy, A. D.

2004-02-01

25

Extended Limber Approximation  

E-print Network

We develop a systematic derivation for the Limber approximation to the angular cross-power spectrum of two random fields, as a series expansion in 1/(\\ell+1/2). This extended Limber approximation can be used to test the accuracy of the Limber approximation and to improve the rate of convergence at large \\ell's. We show that the error in ordinary Limber approximation is O(1/\\ell^2). We also provide a simple expression for the second order correction to the Limber formula, which improves the accuracy to O(1/\\ell^4). This correction can be especially useful for narrow redshift bins, or samples with small redshift overlap, for which the zeroth order Limber formula has a large error. We also point out that using \\ell instead of (\\ell+1/2), as is often done in the literature, spoils the accuracy of the approximation to O(1/\\ell).

Marilena LoVerde; Niayesh Afshordi

2008-09-30

26

Extended Limber Approximation  

E-print Network

We develop a systematic derivation for the Limber approximation to the angular cross-power spectrum of two random fields, as a series expansion in 1/(\\ell+1/2). This extended Limber approximation can be used to test the accuracy of the Limber approximation and to improve the rate of convergence at large \\ell's. We show that the error in ordinary Limber approximation is O(1/\\ell^2). We also provide a simple expression for the second order correction to the Limber formula, which improves the accuracy to O(1/\\ell^4). This correction can be especially useful for narrow redshift bins, or samples with small redshift overlap, for which the zeroth order Limber formula has a large error. We also point out that using \\ell instead of (\\ell+1/2), as is often done in the literature, spoils the accuracy of the approximation to O(1/\\ell).

LoVerde, Marilena

2008-01-01

27

Extended Limber approximation  

SciTech Connect

We develop a systematic derivation for the Limber approximation to the angular cross-power spectrum of two random fields, as a series expansion in (l+1/2){sup -1}. This extended Limber approximation can be used to test the accuracy of the Limber approximation and to improve the rate of convergence at large l's. We show that the error in ordinary Limber approximation is O(l{sup -2}). We also provide a simple expression for the 2nd order correction to the Limber formula, which improves the accuracy to O(l{sup -4}). This correction can be especially useful for narrow redshift bins, or samples with small redshift overlap, for which the 0th order Limber formula has a large error. We also point out that using l instead of l+1/2, as is often done in the literature, spoils the accuracy of the approximation to O(l{sup -1})

LoVerde, Marilena [Institute for Strings, Cosmology and Astro-particle Physics (ISCAP), Department of Physics, Columbia University, New York, New York 10027 (United States); Afshordi, Niayesh [Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada)

2008-12-15

28

Approximations to toroidal harmonics  

SciTech Connect

Toroidal harmonics P/sub n-1/2/ (cosh ) and Q/sub n-1/2/ (cosh ) are useful in solutions to Maxwell's equations in toroidal coordinates. In order to speed their computation, a set of approximations has been developed that is valid over the range 0 < < infinity. The functional form used for these approximations is dictated by their behavior as 0 and as infinity, and is similar to that used by Hastings in his approximations to the elliptic integrals K and E. This report lists approximations of several mathematical forms with varying numbers of terms; approximations to the above Legendre functions are given for n = 0 through 6. Coefficients of each expansion have been adjusted to distribute the relative error in equi-amplitude peaks over some range, typically .05 < < 5, and in the best cases these peaks are less than 10 . The simple method used to determine the approximations is described. Relative error curves are also presented, obtained by comparing approximations to the more accurate values computed by direct summation of the hypergeometric series.

Pribyl, P.A.

1985-10-01

29

Fourier Series Approximation  

NSDL National Science Digital Library

This site includes a Java applet that displays Fourier series approximations and corresponding magnitude and phase spectra of a periodic continuous-time signal. Select from provided signals, or draw a signal with the mouse.

2012-08-14

30

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

31

Approximation and invariant measures  

Microsoft Academic Search

We prove certain approximation theorems for the class of invertible, measurable, and non-singular transformations of the unit interval. The main results concern the approximation of such transformations by those having no a-finite invariant measure absolutely continuous with respect to Lebesgue measure. We are indebted to A. ION~SCTJ TULC~A for making available to us a preprint of her paper [6] which

R. V. Chacon; N. Friedman

1965-01-01

32

Diophantine Approximations on Fractals  

Microsoft Academic Search

We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove\\u000a that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure)\\u000a contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0, 1]2, possessing some

Manfred Einsiedler; Lior Fishman; Uri Shapira

2011-01-01

33

Approximating Markov chains.  

PubMed

A common framework of finite state approximating Markov chains is developed for discrete time deterministic and stochastic processes. Two types of approximating chains are introduced: (i) those based on stationary conditional probabilities (time averaging) and (ii) transient, based on the percentage of the Lebesgue measure of the image of cells intersecting any given cell. For general dynamical systems, stationary measures for both approximating chains converge weakly to stationary measures for the true process as partition width converges to 0. From governing equations, transient chains and resultant approximations of all n-time unit probabilities can be computed analytically, despite typically singular true-process stationary measures (no density function). Transition probabilities between cells account explicitly for correlation between successive time increments. For dynamical systems defined by uniformly convergent maps on a compact set (e.g., logistic, Henon maps), there also is weak continuity with a control parameter. Thus all moments are continuous with parameter change, across bifurcations and chaotic regimes. Approximate entropy is seen as the information-theoretic rate of entropy for approximating Markov chains and is suggested as a parameter for turbulence; a discontinuity in the Kolmogorov-Sinai entropy implies that in the physical world, some measure of coarse graining in a mixing parameter is required. PMID:11607293

Pincus, S M

1992-05-15

34

Approximate kernel competitive learning.  

PubMed

Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. PMID:25528318

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

2015-03-01

35

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

36

Science/Mathematics Approximation  

E-print Network

: : : : : : 9 Lecture 2 11 2.1 Four MoreWays to Skin a Cat: Approximation Algorithms for Set Cover 11 2 : : : : : : : : : : : : : : : : : : : : : : : 46 6.1.1 A Dumb Randomized Algorithm for MAX CUT : : : : : : : : 46 6.1.2 MAX CUT in Dense Graphs : : : : : : : : : : : : : : : : : : : : : 60 7.1.3 Graph Coloring : : : : : : : : : : : : : : : : : : : : : : : : : : 62 Lecture 8 67 8

Sgall, Jiri

37

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

38

Approximating Integrals Using Probability  

ERIC Educational Resources Information Center

As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches ofÖ

Maruszewski, Richard F., Jr.; Caudle, Kyle A.

2005-01-01

39

Living Expenses (includes approximately  

E-print Network

Students Fall 2014 - Spring 2015 Summer Estimated Expenses -- See Footnote #3 All figures cited are broad approximately $800 for fees) $43,700 $19,600 $55,200 $21,300 $20,900 3 SUMMER 2014-2015 ESTIMATES - Full ) Altoona, Berks, Erie, and Harrisburg 12-Month Estimated Expenses and Financial Guarantee for International

Yener, Aylin

40

Rough approximation quality revisited  

Microsoft Academic Search

In rough set theory, the approximation quality is the traditional measure to evaluate the clas- sification success of attributes in terms of a numerical evaluation of the dependency properties generated by these attributes. In this paper we re-interpret the classical in terms of MZ and PRE measures, and exhibit infinitely many possibilities to define -like measures which are meaning- ful

Gunther Gediga; Ivo Duntsch

2001-01-01

41

APPROXIMATE - A Query Processor that Produces Monotonically Improving Approximate Answers  

Microsoft Academic Search

APPROXIMATE, a query processor that makes approximate answers available if part of the database is unavailable, or if there is not enough time to produce an exact answer, is described. The processor implements approximate query processing, and the accuracy of the approximate result produced improves monotonically with the amount of data retrieved to produce the result. The monotone query processing

Susan V. Vrbsky; Jane W.-S. Liu

1993-01-01

42

Approximate Bayesian Computation  

PubMed Central

Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology). PMID:23341757

SunnŚker, Mikael; Corander, Jukka; Foll, Matthieu; Dessimoz, Christophe

2013-01-01

43

Approximate nonlinear self-adjointness and approximate conservation laws  

E-print Network

In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed by means of the method. As an application, a class of perturbed nonlinear wave equations is considered to illustrate the effectiveness.

Zhi-Yong Zhang

2011-10-31

44

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

45

Approximation Bayesian Computation  

PubMed Central

Approximation Bayesian computation [ABC] is an analysis approach that has arisen in response to the recent trend to collect data that is of a magnitude far higher than has been historically the case. This has led to many existing methods become intractable because of difficulties in calculating the likelihood function. ABC circumvents this issue by replacing calculation of the likelihood with a simulation step in which it is estimated in one way or another. In this review we give an overview of the ABC approach, giving examples of some of the more popular specific forms of ABC. We then discuss some of the areas of most active research and application in the field, specifically, choice of low-dimensional summaries of complex datasets and metrics for measuring similarity between observed and simulated data. Next, we consider the question of how to do model selection in an ABC context. Finally, we discuss an area of growing prominence in the ABC world, use of ABC methods in genetic pathway inference.

Marjoram, Paul

2014-01-01

46

Approximation by hinge functions  

SciTech Connect

Breiman has defined {open_quotes}hinge functions{close_quotes} for use as basis functions in least squares approximations to data. A hinge function is the max (or min) function of two linear functions. In this paper, the author assumes the existence of smooth function f(x) and a set of samples of the form (x, f(x)) drawn from a probability distribution {rho}(x). The author hopes to find the best fitting hinge function h(x) in the least squares sense. There are two problems with this plan. First, Breiman has suggested an algorithm to perform this fit. The author shows that this algorithm is not robust and also shows how to create examples on which the algorithm diverges. Second, if the author tries to use the data to minimize the fit in the usual discrete least squares sense, the functional that must be minimized is continuous in the variables, but has a derivative which jumps at the data. This paper takes a different approach. This approach is an example of a method that the author has developed called {open_quotes}Monte Carlo Regression{close_quotes}. (A paper on the general theory is in preparation.) The author shall show that since the function f is continuous, the analytic form of the least squares equation is continuously differentiable. A local minimum is solved for by using Newton`s method, where the entries of the Hessian are estimated directly from the data by Monte Carlo. The algorithm has the desirable properties that it is quadratically convergent from any starting guess sufficiently close to a solution and that each iteration requires only a linear system solve.

Faber, V.

1997-05-01

47

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 32and 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.

1985-01-01

48

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

49

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

50

Approximating Functions with Exponential Functions  

ERIC Educational Resources Information Center

The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"Ö

Gordon, Sheldon P.

2005-01-01

51

Uniform approximations for fermionic densities  

E-print Network

Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many non-interacting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the leading corrections to Thomas-Fermi theory, involve neither sums nor derivatives, are spatially uniform approximations, and are exceedingly accurate.

Raphael F. Ribeiro; Donghyung Lee; Attila Cangi; Peter Elliott; Kieron Burke

2014-09-24

52

Approximation Capabilities of Folding Networks  

E-print Network

on inputs with restricted height, but the resources necessarily increase at least ex­ ponentially. If the maximum in­ put height is restricted any mapping can be approximated, but the resources increase in the input height. In general, approximation on arbitrary inputs is not possible in the maximum norm. 1

Hammer, Barbara

53

Approximating Directed Multicuts Joseph Cheriyan  

E-print Network

multicommodity flow network, and give the first non- trivial upper bounds on the max flow-to-min multicut ratio and Rao (1988) and subsequent papers presented approximate min- max theorems relating multicommodity flow approximation algorithms, and generated novel tools for utilizing linear programming relaxations. Yet, despite

Cheriyan, Joseph

54

INDEXING THE APPROXIMATE NUMBER SYSTEM Indexing the Approximate Number System  

E-print Network

; Pica, Lemer, Izard, & Dehaene, 2004). Some researchers have hypothesised that the ANS is the cognitive, suggesting that an ANS deficit may #12;INDEXING THE APPROXIMATE NUMBER SYSTEM 4 be the cause of mathematical

Inglis, Matthew

55

Transient approximations in queueing networks  

E-print Network

that provides accurate results while executing much faster than a traditional Monte Carlo simulation. Two closure approximations for the M/1lf/J queue were extended to a Jackson network. These approximations were compared to a Monte Carlo simulation of a... network. Average relative error values of less than 5% were obtained for the mean queue size for all test cases. The closure approximations provided these results in as little as 1/100 of the CPU time required for the Monte Carlo simulation to obtain...

Andrewartha, John Michael

1989-01-01

56

Mathematical algorithms for approximate reasoning  

NASA Technical Reports Server (NTRS)

Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away from the conclusion. These algorithms allow one to reason accurately with uncertain data. The above environment can replicate state-f-the-art expert system environments which provides a continuity between the current expert systems which cannot be validated or verified and future expert systems which should be both validated and verified

Murphy, John H.; Chay, Seung C.; Downs, Mary M.

1988-01-01

57

Holography, Pade Approximants and Deconstruction  

E-print Network

We investigate the relation between holographic calculations in 5D and the Migdal approach to correlation functions in large N theories. The latter employs Pade approximation to extrapolate short distance correlation functions to large distances. We make the Migdal/5D relation more precise by quantifying the correspondence between Pade approximation and the background and boundary conditions in 5D. We also establish a connection between the Migdal approach and the models of deconstructed dimensions.

Adam Falkowski; Manuel Perez-Victoria

2006-10-25

58

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 ďclassicalĒ 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 ďhardĒ 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 ďlandscapeĒ 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.; Lšuchli, A. M.; Moessner, R.; Sondhi, S. L.

2013-06-01

59

Wavelet Sparse Approximate Inverse Preconditioners  

NASA Technical Reports Server (NTRS)

There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.

Chan, Tony F.; Tang, W.-P.; Wan, W. L.

1996-01-01

60

Gadgets, approximation, and linear programming  

SciTech Connect

We present a linear-programming based method for finding {open_quotes}gadgets{close_quotes}, i.e., combinatorial structures reducing constraints of one optimization problems to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method we present a number of new, computer-constructed gadgets for several different reductions. This method also answers a question posed by on how to prove the optimality of gadgets-we show how LP duality gives such proofs. The new gadgets improve hardness results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 60/61 and 44/45 respectively is N P-hard. We also use the gadgets to obtain an improved approximation algorithm for MAX 3SAT which guarantees an approximation ratio of .801. This improves upon the previous best bound of .7704.

Trevisan, L. [Universita degli Studi Di Roma La Sapienza, Rome (Italy); Sudan, M.; Sorkin, G.B.; Williamson, D.P. [IBM T.J. Watson Research Center, Yorktown Heights, NY (United States)

1996-12-31

61

Approximations to camera sensor noise  

NASA Astrophysics Data System (ADS)

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

Jin, Xiaodan; Hirakawa, Keigo

2013-02-01

62

Scattering in the quenched approximation  

E-print Network

We study, in the quenched approximation, Luescher's relation between pion scattering lengths and the finite-volume energy of two pions at rest. The quenched relation is drastically different from the full theory one; in particular, ``enhanced finite-volume corrections" of order $L^0=1$ and $L^{-2}$ occur at one loop ($L$ is the linear size of the box), due to the special properties of the $\\eta'$ in the quenched approximation. Numerical examples show that the size of these effects can be substantial.

Claude Bernard; Maarten Golterman

1995-09-11

63

Approximating spatially exclusive invasion processes  

NASA Astrophysics Data System (ADS)

A number of biological processes, such as invasive plant species and cell migration, are composed of two key mechanisms: motility and reproduction. Due to the spatially exclusive interacting behavior of these processes a cellular automata (CA) model is specified to simulate a one-dimensional invasion process. Three (independence, Poisson, and 2D-Markov chain) approximations are considered that attempt to capture the average behavior of the CA. We show that our 2D-Markov chain approximation accurately predicts the state of the CA for a wide range of motility and reproduction rates.

Ross, Joshua V.; Binder, Benjamin J.

2014-05-01

64

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

65

Speech Compression by Polynomial Approximation  

Microsoft Academic Search

Methods for speech compression aim at reducing the transmission bit rate while preserving the quality and intelligibility of speech. These objectives are antipodal in nature since higher compression presupposes preserving less information about the original speech signal. This paper presents a method for compressing speech based on polynomial approximations of the trajectories in time of various speech features (i.e., spectrum,

Sorin Dusan; James L. Flanagan; Amod Karve; Mridul Balaraman

2007-01-01

66

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 numbersÖ

Peralta, Javier

2008-01-01

67

ARE FUZZY SYSTEMS UNIVERSAL APPROXIMATORS?  

Microsoft Academic Search

This paper is a critical reflection on various results in lileralure claiming that fuzzy systems are universal approximators. For this purpose the most specific features of fuzzy systems are outlined and it is discussed to which extent they are incorporated in the formal definition of a Tuzzy system in literature. It is argued that fuzzy systems can only be universal

ERICH PETER KLEMENT; LASZLO T. KOCZY; BERNHARD MOSER

1999-01-01

68

Optimization, Approximation, and Complexity Classes  

Microsoft Academic Search

We define a natural variant of NP, MAX NP, and also a subclass called MAX SNP. These are classes of optimization problems, and in fact contain several natural, well-studied ones. We show that problems in these classes can be approximated with some bounded error. Furthermore, we show that a number of common optimization problems are complete under a kind of

Christos H. Papadimitriou; Mihalis Yannakakis

1991-01-01

69

Heat pipe transient response approximation  

Microsoft Academic Search

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

2001-01-01

70

Heat pipe transient response approximation  

Microsoft Academic Search

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

Robert S. Reid

2002-01-01

71

Approximate Query Processing Using Wavelets  

Microsoft Academic Search

Approximate query processing has emerged as a cost-effective approach for dealing with the huge data volumes and stringent response-time requirements of today's decision support systems (DSS). Most work in this area, however, has so far been limited in its query processing scope, typically fo- cusing on specific forms of aggregate queries. Furthermore, conventional approaches based on sampling or histograms ap-

Kaushik Chakrabarti; Minos N. Garofalakis; Rajeev Rastogi; Kyuseok Shim

2000-01-01

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

1973-01-01

73

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

74

Transient and impulse response approximations  

Microsoft Academic Search

Electromagnetic field waveforms produced by scattering of transient plane waves from finite objects are related to those produced by an impulsive plane wave. Properties of the impulse response waveforms at great distances from the target, particularly in the backscattering direction, are discussed. Various methods for approximation of impulse response waveforms using time and frequency domain concepts are suggested and illustrated.

E. M. Kennaugh; D. L. Moffatt

1965-01-01

75

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

76

Testing the frozen flow approximation  

NASA Technical Reports Server (NTRS)

We investigate the accuracy of the frozen-flow approximation (FFA), recently proposed by Matarrese, et al. (1992), for following the nonlinear evolution of cosmological density fluctuations under gravitational instability. We compare a number of statistics between results of the FFA and n-body simulations, including those used by Melott, Pellman & Shandarin (1993) to test the Zel'dovich approximation. The FFA performs reasonably well in a statistical sense, e.g. in reproducing the counts-in-cell distribution, at small scales, but it does poorly in the crosscorrelation with n-body which means it is generally not moving mass to the right place, especially in models with high small-scale power.

Lucchin, Francesco; Matarrese, Sabino; Melott, Adrian L.; Moscardini, Lauro

1993-01-01

77

Surprises in approximating Levenshtein distances  

Microsoft Academic Search

The Levenshtein distance is an important tool for the comparison of symbolic\\u000asequences, with many appearances in genome research, linguistics and other\\u000aareas. For efficient applications, an approximation by a distance of smaller\\u000acomputational complexity is highly desirable. However, our comparison of the\\u000aLevenshtein with a generic dictionary-based distance indicates their\\u000astatistical independence. This suggests that a simplification along this

Michael Baake; Uwe Grimm; Robert Giegerich

2006-01-01

78

Generalized Gradient Approximation Made Simple  

Microsoft Academic Search

Generalized gradient approximations (GGA's) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91

John P. Perdew; Kieron Burke; Matthias Ernzerhof

1996-01-01

79

Nonlinear surface approximation using photogammetry  

E-print Network

December 2005 Major Subject: Aerospace Engineering iii ABSTRACT Nonlinear Surface Approximation Using Photogammetry. (December 2005) Elizabeth Osgood, B.S., Embry-Riddle Aeronautical University Chair of Advisory Committee: Dr. John L. Junkins... accurately and, although more complex, offers advantages and addresses the desire for a family of designs wherein higher accuracy is achievable by further optimization. v ACKNOWLEDGEMENTS I would like to thank Dr. John L. Junkins for his constant...

Osgood, Elizabeth

2006-04-12

80

Polynomial Compensation, Inversion, And Approximation  

NASA Technical Reports Server (NTRS)

New criterion introduced for design of discrete-time compensator. Method devised for polynomial compensation, inversion, and approximation of discrete-time linear systems. Involves quadratic measure of difference between response of compensated system and desired response. Impulse response of compensated system improves as degree of polynomial increases. Compensator emphasizes matching of large initial response. Compensators used in variety of applications, including navigation systems for spacecraft, aircraft, ships, and automated manufacturing equipment.

Baram, Yoram

1990-01-01

81

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

82

Improved non-approximability results  

SciTech Connect

We indicate strong non-approximability factors for central problems: N{sup 1/4} for Max Clique; N{sup 1/10} for Chromatic Number; and 66/65 for Max 3SAT. Underlying the Max Clique result is a proof system in which the verifier examines only three {open_quotes}free bits{close_quotes} to attain an error of 1/2. Underlying the Chromatic Number result is a reduction from Max Clique which is more efficient than previous ones.

Bellare, M.; Sudan, M.

1994-12-31

83

Approximating Metal-Insulator Transitions  

E-print Network

We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate metal-insulator transitions (MIT) at the finite iteration steps. We also report evidence on mobility edges which are at variance to the celebrated Aubry-Andre model. The dynamics near the MIT shows a critical slowing down of the ballistic group velocity in the metallic phase similar to the divergence of the localization length in the insulating phase.

C. Danieli; K. Rayanov; B. Pavlov; G. Martin; S. Flach

2014-05-06

84

Generalized Gradient Approximation Made Simple  

SciTech Connect

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

Perdew, J.P.; Burke, K.; Ernzerhof, M. [Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118 (United States)] [Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118 (United States)

1996-10-01

85

Indexing the approximate number system.  

PubMed

Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects. PMID:24361686

Inglis, Matthew; Gilmore, Camilla

2014-01-01

86

Analytical approximations for spiral waves  

SciTech Connect

We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency ? and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent ?(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.

LŲber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald [Institut fŁr Theoretische Physik, Technische Universitšt Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin (Germany)] [Institut fŁr Theoretische Physik, Technische Universitšt Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin (Germany)

2013-12-15

87

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.

Heinšsmški, Sami

2012-02-01

88

Approximating Stellar Orbits: Improving on Epicycle Theory  

E-print Network

Already slightly eccentric orbits, such as those occupied by many old stars in the Galactic disk, are not well approximated by Lindblad's epicycle theory. Here, alternative approximations for flat orbits in axisymmetric stellar systems are derived and compared to results from numeric integrations. All of these approximations are more accurate than Lindblad's classical theory. I also present approximate, but canonical, maps from ordinary phase-space coordinates to a set of action-angle variables. Unfortunately, the most accurate orbit approximation leads to non-analytical R(t). However, from this approximation simple and yet very accurate estimates can be derived for the peri- and apo-centers, frequencies, and actions integrals of galactic orbits, even for high eccentricities. Moreover, further approximating this approximation allows for an analytical R(t) and still an accurate approximation to galactic orbits, even with high eccentricities.

Walter Dehnen

1999-06-04

89

Partial equilibrium approximations in Apoptosis  

E-print Network

Apoptosis is one of the most basic biological processes. In apoptosis, tens of species are involved in many biochemical reactions with times scales of widely differing orders of magnitude. By the law of mass action, the process is mathematically described with a large and stiff system of ODEs (ordinary differential equations). The goal of this work is to simplify such systems of ODEs with the PEA (partial equilibrium approximation) method. In doing so, we propose a general framework of the PEA method together with some conditions, under which the PEA method can be justified rigorously. The main condition is the principle of detailed balance for fast reactions as a whole. With the justified method as a tool, we made many attempts via numerical tests to simplify the Fas-signaling pathway model due to Hua et al. (2005) and found that nine of reactions therein can be well regarded as relatively fast. This paper reports our simplification of Hua at el.'s model with the PEA method based on the fastness of the nine ...

Huang, Ya-Jing

2012-01-01

90

Approximate Noether gauge symmetries of Bardeen model  

E-print Network

We investigate the approximate Noether gauge symmetries of the geodesic Lagrangian for the Bardeen spacetime model. This is accommodated by a set of new approximate Noether gauge symmetry relations for the perturbed geodesic Lagrangian in the spacetime. A detailed analysis to the spacetime of Bardeen model up to third-order approximate Noether gauge symmetries is presented.

U. Camci

2014-10-28

91

Closure Approximations for Passive Scalar Turbulence  

E-print Network

Closure Approximations for Passive Scalar Turbulence: A Comparative Study on an Exactly Solvable running head: "Closure approximations: A Comparative Study" Corresponding author: Peter Kramer 301 Amos Sciences, New York University, New York, NY 1 #12;Abstract Some standard closure approximations used

Kramer, Peter

92

Closure Approximations for Passive Scalar Turbulence  

E-print Network

Closure Approximations for Passive Scalar Turbulence: A Comparative Study on an Exactly Solvable Suggested running head: "Closure approximations: A Comparative Study" Corresponding author: Peter Kramer 301 Sciences, New York University, New York, NY 1 #12;Abstract Some standard closure approximations used

Van Den Eijnden, Eric

93

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

94

How Accurate Is the Steady State Approximation  

NSDL National Science Digital Library

The steady-state approximation is commonly used in enzyme catalysis kinetics calculations, but how much error does the approximation introduce? This Java applet allows you to visually determine the accuracy of the steady-state and pre-equilibrium approximations.

95

Approximations of Matrices and Tensors Shmuel Friedland  

E-print Network

Approximations of Matrices and Tensors Shmuel Friedland Univ. Illinois at Chicago Colloquium at Kansas University, December 11, 2008 Shmuel Friedland Approximations of Matrices and Tensors #12;Overview­III Simulations Conclusions Shmuel Friedland Approximations of Matrices and Tensors #12;Statement of the problem

Friedland, Shmuel

96

DIMACS Technical Report 9513 APPROXIMATE MINIMUMCOST MULTICOMMODITY  

E-print Network

DIMACS Technical Report 95­13 May 1995 APPROXIMATE MINIMUM­COST MULTICOMMODITY FLOWS IN ~ O('' 02, an approximate minimum­ cost multicommodity flow can be computed in ~ O('' 02 KNM) running time, where). #12; APPROXIMATE MINIMUM­COST MULTICOMMODITY FLOWS IN ~ O('' 02 KNM) TIME* Michael D. Grigoriadis

97

Rational Approximation on the Complex Plane  

E-print Network

Rational Approximation on the Complex Plane A Thesis submitted for the degree of Master of Science and thinness . . . . 10 2 Rational Approximation Theory 11 2.1 Introduction properties of finely holomorphic functions 18 3.2 Rational approximation of finely holomorphic functions

Geest, Harm G. van der

98

Comparative Accuracy of Selected Multiple Scattering Approximations.  

NASA Astrophysics Data System (ADS)

Computational results have been obtained for the plane albedo, total transmission and fractional absorption of plane-parallel atmospheres composed of cloud droplets. These computations, which were obtained using the doubling method, are compared with comparable results obtained using selected radiative transfer approximations. Both the relative and absolute accuracies of asymptotic theory for thick layers and delta-Eddington, Meador-Weaver and Coakley-Chżlek approximations are compared as a function of optical thickness, solar zenith angle and single scattering albedo. Asymptotic theory is found to be accurate to within 5% for all optical thickness greater than about 6. On the other hand, the Coakley-Chżlek approximation is accurate to within 5% for thin atmospheres having optical thickness less than about 0.2 for most values of the solar zenith angle. Though the accuracies of delta-Eddington and Meador-Weaver approximations are less easily summarized it can generally be concluded that the delta-Eddington approximation is the most accurate for conservative scattering when the solar zenith angle is small, while the Meador-Weaver approximation is the most accurate for nonconservative scattering (0 0.9). Selected results from the Eddington approximation are presented to illustrate the effect of delta function scaling in the delta-Eddington approximation. In addition, selected results from the single scattering approximation and asymptotic theory are presented in order to help explain the strengths and limitations of the various approximations.

King, Michael D.; Harshvardhan

1986-04-01

99

Rational Approximations to Category Learning 1 Running head: RATIONAL APPROXIMATIONS TO CATEGORY LEARNING  

E-print Network

Rational Approximations to Category Learning 1 Running head: RATIONAL APPROXIMATIONS TO CATEGORY LEARNING Rational approximations to rational models: Alternative algorithms for category learning Adam N@gatsby.ucl.ac.uk #12;Rational Approximations to Category Learning 2 Abstract Rational models of cognition typically

Cottrell, Garrison W.

100

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...

Yunes, N

2006-01-01

101

Approximate Actions for Lattice QCD Simulation  

E-print Network

We describe a systematic approach to generating approximate actions for the lattice simulation of QCD. Three different tuning conditions are defined to match approximate with true actions, and it is shown that these three conditions become equivalent when the approximate and true actions are sufficiently close. We present a detailed study of approximate actions in the lattice Schwinger model together with an exploratory study of full QCD at unphysical parameter values. We find that the technicalities of the approximate action approach work quite well. However, very delicate tuning is necessary to find an approximate action which gives good predictions for all physical observables. Our best view of the immediate applicability of the methods we describe is to allow high statistics studies of particular physical observables after a low statistics full fermion simulation has been used to prepare the stage.

Alan C. Irving; James C. Sexton

1996-08-28

102

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

103

Sensitivity approximation for robust stability and tracking  

E-print Network

Major Subject: Electrical Engineering Sensitivity Approximation For Robust Stability and Tracking A Thesis by Chris Steven McLean Approved as to style and content by: alph K. Cavin, III (Chairman of Committee) Shankar P. Bhattacharyya (Member... Figure 13. Constrained Optimization, Kt ?? Kq ? 20, p = 100 43 Figure 14. The Quadratic Approximation vs. the Desired Response Figure 15. Error of the Quadratic Approximation 47 48 I. Introduction As in most engineering problems, the design...

McLean, Chris Steven

2012-06-07

104

An arc spline approximation to a clothoid  

NASA Astrophysics Data System (ADS)

The clothoid is a spiral used in highway and railway route design. Clothoids are transcendental functions and so have been approximated by polynomials, by power series and continued fractions, and by rational functions. Here the clothoid is approximated by an arc spline. The chief advantage in doing so is that arc splines are very easy to lay out and to offset. Examples show that the approximation is of extremely high accuracy. It is proved that if the arc spline has n arcs, then the error in the approximation is of order O(1/n2).

Meek, D. S.; Walton, D. J.

2004-09-01

105

Degree of Simultaneous Coconvex Polynomial Approximation  

E-print Network

] change its convexity finitely many times in the interval, say s times, at Y s : \\Gamma1 ! y s ! \\Delta \\Delta \\Delta ! y 1 ! 1. We estimate the degree of simultane­ ous approximation of f and its derivative that provided n is sufficiently large, depending on the location of the points Y s , the rate of approximation

Leviatan, Dany

106

Approximate Euclidean Ramsey theorems Adrian Dumitrescu  

E-print Network

an arbitrary long approximate arithmetic progression, if L is large enough. (ii) every dense separated set condition is needed in this case. Keywords: Euclidean Ramsey theory, approximate arithmetic progression of a geometric nature is Van der Waerden's theorem on arithmetic progressions: Theorem 2 (Van der Waerden [31

Dumitrescu, Adrian

107

Blood Management Using Approximate Linear Programming  

E-print Network

Blood Management Using Approximate Linear Programming Marek Petrik and Shlomo Zilberstein January 13th, 2009 Marek Petrik and Shlomo Zilberstein () Blood Management Using Approximate Linear ProgrammingJanuary 13th, 2009 1 / 36 #12;Blood Inventory Management Problem Regional blood banks: Aggregate

Shenoy, Prashant

108

Spline approximations for nonlinear hereditary control systems  

NASA Technical Reports Server (NTRS)

A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

Daniel, P. L.

1982-01-01

109

Inversion and approximation of Laplace transforms  

NASA Technical Reports Server (NTRS)

A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.

Lear, W. M.

1980-01-01

110

SPECTRAL VISCOSITY APPROXIMATIONS TO HAMILTONJACOBI SOLUTIONS  

E-print Network

SPECTRAL VISCOSITY APPROXIMATIONS TO HAMILTON­JACOBI SOLUTIONS OLGA LEPSKY SIAM J. NUMER. ANAL. c. The spectral viscosity approximate solution of convex Hamilton­Jacobi equations with periodic boundary bounded, formally spectral accurate, and converge to the unique viscosity solution. The L1-convergence

Tadmor, Eitan

111

February 13, 2012 Diophantine approximation and  

E-print Network

;Diophantus of Alexandria (250 ¬Ī50) #12;Rational approximation The rational numbers are dense in the real : starting from the rational numbers, compute the maximal number of digits of x with the minimum;Rational approximation The rational numbers are dense in the real numbers : For any x in R and any > 0

Waldschmidt, Michel

112

Semantics by lub's of Approximations fact  

E-print Network

Semantics by lub's of Approximations fact :: Int -> Int fact = \\x -> if x fact(x-1) * x Regard non-recursively defined approximations fact0 = \\x -> bot fact1 = \\x -> if x else fact0(x - 1) x fact2 = \\x -> if x fact1(x - 1) x . . . Thus: facti+1 = ff facti

√Ābrah√°m, Erika

113

AN APPROXIMATION ALGORITHM FOR COUNTING CONTINGENCY TABLES  

E-print Network

AN APPROXIMATION ALGORITHM FOR COUNTING CONTINGENCY TABLES Alexander Barvinok, Zur Luria, Alex, the permanent approximation algo¬≠ rithm, and an integral representation for the number of contingency tables. 1 # i=1 r i = n # j=1 c j = N. A contingency table with margins (R, C) is an m √? n non¬≠negative integer

Yong, Alexander

114

Efficient Real Root Approximation Michael Kerber  

E-print Network

Efficient Real Root Approximation Michael Kerber IST (Institute of Science and Technology) Austria real roots of a square- free polynomial f . Given isolating intervals, our algorithm refines each of them to a width at most 2-L, that is, each of the roots is approximated to L bits after the binary

115

Efficient Real Root Approximation Michael Kerber  

E-print Network

Efficient Real Root Approximation Michael Kerber IST (Institute of Science and Technology) Austria real roots of a square- free polynomial f. Given isolating intervals, our algorithm refines each of them to a certain width 2-L, that is, each of the roots is approximated to L bits after the binary

116

Nonlinear Wavelet Approximation in Anisotropic Besov Spaces  

E-print Network

video camera. Here x and y ...... Cp,? . Let Sn = ?n j=1 aj??. J(j) be an n-term approximation to f. The integer n will be specified later. .... P. Petrushev and V. Popov, Rational Approximation of Real Functions, Cambridge. University Press, 1987.

1910-10-62

117

Polynomial approximation of functions in Sobolev spaces  

Microsoft Academic Search

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

Todd Dupont; Ridgway Scott

1980-01-01

118

Quirks of Stirling's Approximation  

ERIC Educational Resources Information Center

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

Macrae, Roderick M.; Allgeier, Benjamin M.

2013-01-01

119

Rational approximation to Thomas-Fermi equations  

E-print Network

We show that a simple and straightforward rational approximation to the Thomas-Fermi equation provides the slope at origin with unprecedented accuracy and that relatively small Pad\\'e approximants are far more accurate than more elaborate approaches proposed recently by other authors. We consider both the Thomas-Fermi equation for isolated atoms and for atoms in strong magnetic fields.

Francisco M. Fernandez

2009-04-07

120

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 theirÖ

Goldberg, Mayer

2012-01-01

121

Frankenstein's glue: transition functions for approximate solutions  

NASA Astrophysics Data System (ADS)

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 analytic solutions together. In particular, we propose certain sufficient conditions on these functions and prove that these conditions guarantee that the joined solution still satisfies the Einstein equations analytically 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, then 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.

Yunes, NicolŠs

2007-09-01

122

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

2007-08-17

123

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

124

Approximating Light Rays in the Schwarzschild Field  

NASA Astrophysics Data System (ADS)

A short formula is suggested that approximates photon trajectories in the Schwarzschild field better than other simple prescriptions from the literature. We compare it with various "low-order competitors," namely, with those following from exact formulas for small M, with one of the results based on pseudo-Newtonian potentials, with a suitably adjusted hyperbola, and with the effective and often employed approximation by Beloborodov. Our main concern is the shape of the photon trajectories at finite radii, yet asymptotic behavior is also discussed, important for lensing. An example is attached indicating that the newly suggested approximation is usableóand very accurateófor practically solving the ray-deflection exercise.

SemerŠk, O.

2015-02-01

125

Stochastic Approximation Approach to Stochastic Programming  

E-print Network

Monte Carlo sampling techniques, namely, the Stochastic Approximation (SA) and the Sample. Average ... than 5. The aim of this paper is to compare two computational approaches based on Monte. Carlo sampling ..... does not exceed M2.

2007-10-03

126

Approximate inference in Gaussian graphical models  

E-print Network

The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a ...

Malioutov, Dmitry M., 1981-

2008-01-01

127

Approximate Confidence Intervals for Effect Sizes.  

ERIC Educational Resources Information Center

Investigated the approximate confidence intervals for effect sizes developed by K. Bird (2002) and proposed a more accurate method developed through simulation studies. The average coverage probability for the new method was 0.959. (SLD)

Algina, James; Keselman, H. J.

2003-01-01

128

Approximate Dynamic Programming -II: Warren B. Powell  

E-print Network

Approximate Dynamic Programming - II: Algorithms Warren B. Powell December 8, 2009 #12;Abstract the property of making decisions over time under different types of uncertainty. In Powell (2010), a modeling

Powell, Warren B.

129

Treecodes for Potential and Force Approximations  

E-print Network

clearly expensive for large values of N. There have been some approximation algorithmslike the Barnes-Hut Method and the Fast Multipole Method (FMM) proposedfor these problems to reduce the complexity. However, the applicability of these algorithmsare...

Kannan, Kasthuri Srinivasan

2009-05-15

130

A fresh look at the adhesion approximation  

E-print Network

I report on a systematic derivation of the phenomenological ``adhesion approximation'' from gravitational instability together with a brief evaluation of the related status of analytical modeling of large-scale structure.

Thomas Buchert

1997-11-04

131

A Sample Approximation Approach for Optimization with ...  

E-print Network

We study approximations of optimization problems with probabilistic constraints ... supply chain management [17], production planning [21], optimization of chemical ... that it will be violated if doing so would sufficiently decrease the cost of the.

2008-05-02

132

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

133

New Approximation Schemes for General Variational Inequalities  

Microsoft Academic Search

In this paper, we suggest and consider a class of new three-step approximation schemes for general variational inequalities. Our results include Ishikawa and Mann iterations as special cases. We also study the convergence criteria of these schemes.

Muhammad Aslam Noor

2000-01-01

134

A Monte-Carlo AIXI Approximation  

E-print Network

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. Our approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement ...

Silver, David

135

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

136

An analytical approximation of a pendulum trajectory  

NASA Astrophysics Data System (ADS)

An analytical approximation of a pendulum trajectory is developed for large initial angles. Instead of using a perturbation method, a succession of just two polynomials is used in order to get simple integrals. By obtaining the approximated period, the result is compared with the Kidd-Frogg and Hite formulas for the period which are very close to the exact solution for the considered angle.

Salinas-HernŠndez, E.; Ares de Parga, G.; DomŪnguez-HernŠndez, S.; MuŮoz-Vega, R.

2014-07-01

137

Shannon wavelet approximations of linear differential operators  

Microsoft Academic Search

Recent works emphasized the interest of numerical solution of PDE's with wavelets. In their works, A.Cohen, W.Dahmen and R.DeVore focussed on the non linear approximation aspect of the wavelet approximation of PDE's to prove the relevance of such methods. In order to extend these results, we focuss on the convergence of the iterative algorithm, and we consider different possibilities offered

Erwan Deriaz

2007-01-01

138

ShannonĖGabor wavelet distributed approximating functional  

Microsoft Academic Search

The Shannon sampling theorem is critically reviewed from a physical point of view. An approximate sampling formula is proposed, combining Shannon sampling with a Gabor-distributed approximating functional (DAF) window function, which results in new ShannonĖGabor wavelet DAFs (SGWDs). They are extremely smooth, decay rapidly, have simultaneous time-frequency localization, and are also generalized delta sequences (reducing to the Dirac delta function

D. K. Hoffman; G. W. Wei; D. S. Zhang; D. J. Kouri

1998-01-01

139

[Problems of overhanging approximate amalgam fillings].  

PubMed

The authors summarize findings pertaining to overhanging approximate amalgam fillings and associated problems. They describe the most frequent causes of incorrect preparation of amalgam fillings, Black's class II, and their incidence in common dental practice. From data in the literature ensues that overhanging fillings on molars and premolars are an important secondary factor in inflammation of the periodontium. Insertion of an adequate approximate amalgam filling and its finish after hardening is one of the basic preventive measures in marginal periodontopathies. PMID:2640716

Balazic, V; Durovic, E

1989-10-01

140

The closure approximation in the hierarchy equations.  

NASA Technical Reports Server (NTRS)

The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the ?self-consistent field' approximation in nonequilibrium statistical mechanics are clarified. The error at any level of the hierarchy can be given and can be avoided by the use of the iterative method.

Adomian, G.

1971-01-01

141

Classical and hyperbolic approximation of hysteresis loops  

NASA Astrophysics Data System (ADS)

Analytical approximation of symmetrical and unsymmetrical hysteresis loops is based on the general description of magnetization consisting of the slow reversible process and more violent irreversible process. The coercivity term in the irreversible component generates symmetrical hysteresis loops, which are used for the approximation of first-order reversal curves and their distribution. Model has been applied to materials with typical S-shaped and rectangular hysteresis loops.

W?odarski, Zdzis?aw

2007-02-01

142

Rough Sets Approximations for Learning Outcomes  

NASA Astrophysics Data System (ADS)

Discovering dependencies between students' responses and their level of mastering of a particular skill is very important in the process of developing intelligent tutoring systems. This work is an approach to attain a higher level of certainty while following students' learning progress. Rough sets approximations are applied for assessing students understanding of a concept. Consecutive responses from each individual learner to automated tests are placed in corresponding rough sets approximations. The resulting path provides strong indication about the current level of learning outcomes.

Encheva, Sylvia; Tumin, Sharil

143

Polynomial approximation of functions in Sobolev spaces  

NASA Technical Reports Server (NTRS)

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

Dupont, T.; Scott, R.

1980-01-01

144

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

145

Generalizing the finite element method: Diffuse approximation and diffuse elements  

Microsoft Academic Search

This paper describes the new ďdiffuse approximationĒ method, which may be presented as a generalization of the widely used ďfinite element approximationĒ 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

146

Behaviour of Lagrangian Approximations in Spherical Voids  

E-print Network

We study the behaviour of spherical Voids in Lagrangian perturbation theories L(n), of which the Zel'dovich approximation is the lowest order solution L(1). We find that at early times higher order L(n) give an increasingly accurate picture of Void expansion. However at late times particle trajectories in L(2) begin to turnaround and converge leading to the {\\em contraction} of a Void, a sign of pathological behaviour. By contrast particle trajectories in L(3) are well behaved and this approximation gives results in excellent agreement with the exact top-hat solution as long as the Void is not too underdense. For very underdense Voids, L(3) evacuates the Void much too rapidly leading us to conclude that the Zel'dovich approximation L(1), remains the best approximation to apply to the late time study of Voids. The behavior of high order approximations in spherical voids is typical for asymptotic series and may be generic for Lagrangian perturbation theory.

V. Sahni; S. F. Shandarin

1995-10-27

147

Approximate solutions to NP-optimization problems  

SciTech Connect

Most combinatorial optimization problems are NP-hard, and thus unlikely to be solvable to optimality in polynomial time. This tutorial is concerned with polynomial-time algorithms for the approximate solution of such problems. Such an algorithm is said to solve a problem within F(n) if, for every problem instance, it determines the optimal value within a multiplicative error of at most F(n). It has long been known that the knapsack and bin packing problems can be approximated within 1 + a for any positive a. We discuss recent advances in the construction of approximation algorithms for graph partitioning, multicommodity flow and Steiner tree problems. We also discuss negative results, showing that, unless P = NP, it is impossible to approximate the clique number or the chromatic number of a graph within the ratio n{sup b}, where b is a certain small positive number. These negative results stem from an unexpected connection between approximation algorithms and the theory of probabilistically checkable proofs, a branch of theoretical computer science related to cryptography. We also discuss problems such as vertex cover and maximum 2-sat that can be solved within a constant ratio, but not within an arbitrarily small constant ratio (unless P = NP).

Karp, R.

1994-12-31

148

Optical pulse propagation with minimal approximations  

SciTech Connect

Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations--including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first-order propagation equation using a minimum of approximations and a straightforward 'factorization' mathematical scheme. The approach generates exact coupled bidirectional equations, after which it is clear that the description can be reduced to a single unidirectional first-order wave equation by means of a simple 'slow evolution' approximation, where the optical pulse changes little over the distance of one wavelength. It also allows a direct term-to-term comparison of an exact bidirectional theory with the approximate unidirectional theory.

Kinsler, Paul [Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ (United Kingdom)

2010-01-15

149

Faddeev random-phase approximation for molecules  

SciTech Connect

The Faddeev random-phase approximation is a Green's function technique that makes use of Faddeev equations to couple the motion of a single electron to the two-particle-one-hole and two-hole-one-particle excitations. This method goes beyond the frequently used third-order algebraic diagrammatic construction method: all diagrams involving the exchange of phonons in the particle-hole and particle-particle channel are retained, but the phonons are now described at the level of the random-phase approximation, which includes ground-state correlations, rather than at the Tamm-Dancoff approximation level, where ground-state correlations are excluded. Previously applied to atoms, this paper presents results for small molecules at equilibrium geometry.

Degroote, Matthias; Van Neck, Dimitri [Center for Molecular Modeling, Technologiepark 903, B-9052 Zwijnaarde (Belgium); Barbieri, Carlo [Department of Physics, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford GU2 7XH (United Kingdom)

2011-04-15

150

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

151

Parallel computations and complex analytic approximations: From diophantine approximations to quantum mechanics  

SciTech Connect

High precision solution of extremal and (complex analytic) approximations problems that can be represented in terms of multiple integrals or integral equations involving hypergeornetric functions are examined. Fast algorithms of computations of (approximate) solutions are presented that are well suited for parallelization. Among problems considered are: WKB and adelic asymptotics of multidimensional hypergeometric Pade approximations to classical functions, and high accuracy computations of high order eigenvalues and eigenstates for 2D and 3D domains of complex geometry.

Chudnovsky, D.V.; Chudnovsky, G.V. [Columbia Univ., New York, NY (United States)

1995-12-01

152

Shannon Gabor wavelet distributed approximating functional  

NASA Astrophysics Data System (ADS)

The Shannon sampling theorem is critically reviewed from a physical point of view. An approximate sampling formula is proposed, combining Shannon sampling with a Gabor-distributed approximating functional (DAF) window function, which results in new Shannon-Gabor wavelet DAFs (SGWDs). They are extremely smooth, decay rapidly, have simultaneous time-frequency localization, and are also generalized delta sequences (reducing to the Dirac delta function under the limit of a zero window width). Shannon's sampling theorem is recovered exactly when the window is infinitely wide.Finally, SGWDs are well-behaved L2( R) kernels, and thus can be used for solving differential equations.

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

1998-04-01

153

Extending the Eikonal Approximation to Low Energy  

E-print Network

E-CDCC and DEA, two eikonal-based reaction models are compared to CDCC at low energy (e.g. 20AMeV) to study their behaviour in the regime at which the eikonal approximation is supposed to fail. We confirm that these models lack the Coulomb deflection of the projectile by the target. We show that a hybrid model, built on the CDCC framework at low angular momenta and the eikonal approximation at larger angular momenta gives a perfect agreement with CDCC. An empirical shift in impact parameter can also be used reliably to simulate this missing Coulomb deflection.

Pierre Capel; Tokuro Fukui; Kazuyuki Ogata

2014-11-21

154

Selfconsistent approximations, symmetries and choice of representation  

E-print Network

In thermal field theory selfconsistent (Phi-derivable) approximations are used to improve (resum) propagators at the level of two-particle irreducible diagrams. At the same time vertices are treated at the bare level. Therefore such approximations typically violate the Ward identities connected to internal symmetries. Examples are presented how such violations can be tamed by a proper choice of representation for the fields which describe the system under consideration. These examples cover the issue of massless Goldstone bosons in the linear sigma model and the Nambu--Jona-Lasinio model and the problem of current conservation in theories with massive vector mesons.

Stefan Leupold

2006-10-26

155

Approximate Minimum-Cost Multicommodity Flows In  

Microsoft Academic Search

We show that an \\\\epsilon-approximate solution of the cost-constrained K-commodity flow problem on an N-node M-arc network G can be computed by sequentially solving O(K(\\\\epsilon^{-2} log K) log M log(\\\\epsilon^{-1}K) single-commodity minimum-cost flow problems on the same network. In particular, an approximate minimumcost multicommodity flow can be computed in O^~(\\\\epsilon^{-2}KNM) running time, where the notation O^~(.) means "up to logarithmic

Michael D. Grigoriadis; Leonid G. Khachiyan

1995-01-01

156

The pseudopotential approximation in electronic structure theory.  

PubMed

A short review is presented on one of the most successful theories for electronic structure calculations, the pseudopotential approximation, originally introduced by Hans G. A. Hellmann in 1934. Recent developments in relativistic quantum theory allow for the accurate adjustment of pseudopotential parameters to valence spectra, producing results for properties of atoms, molecules, and the solid-state in excellent agreement with more accurate all-electron results if a small-core definition is used. Thus the relativistic pseudopotential approximation is now the most widely applied method for systems containing heavy elements. PMID:21809427

Schwerdtfeger, Peter

2011-12-01

157

Approximation Algorithms for Hamming Clustering Problems  

E-print Network

Approximation Algorithms for Hamming Clustering Problems Leszek G#24;asieniec 1 , Jesper Jansson 2.Lingasg@cs.lth.se Abstract. We study Hamming versions of two classical clustering prob- lems. The Hamming radius p that minimize the maximum Hamming distance between a string in S and the closest of the p strings; this minimum

Gasieniec, Leszek

158

Wavelet approximations for computationally efficient FM demodulation  

NASA Astrophysics Data System (ADS)

We present a framework for the use of stationary phase approximations to a Morlet wavelet transform as a device to generate computationally efficient algorithms for extracting modulation information in frequency modulated (FM) signals. Presented here are two specific FM estimators generated from this approach that may be implemented in terms of filter banks with very few filters.

Teolis, Anthony; Scheper, Richard; Frankpitt, Bernard A.

2001-03-01

159

Texture descriptor based on local approximations  

NASA Astrophysics Data System (ADS)

This paper proposes a novel texture descriptor based indices of degrees of local approximating polynomials. An input image is divided into non-overlapping patches which are reshaped into a one-dimensional source vectors. These vectors are approximated using local polynomial functions of various degrees. For each element of the source vector, these approximations are ranked according to the difference between the original and approximated values. A set of indices of polynomial degrees form a local feature. This procedure is repeated for every pixel. Finally, a proposed texture descriptor is obtained from the frequency histogram of all obtained local features. A nearest neighbor classifier utilizing distance metric is used to evaluate a performance of the introduced descriptor on the following datasets: Brodatz, KTH-TIPS, KTH-TIPS2b, UCLA and Columbia-Utrecht (CUReT) with respect to different methods of texture analysis and classification. A proper parameter setup of the proposed texture descriptor is discussed. The results of this comparison demonstrate that the proposed method is competitive with the recent statistical approaches such as local binary patterns (LBP), local ternary patterns, completed LBP, Weber's local descriptor, and VZ algorithms (VZ-MR8 and VZ-Joint). At the same time, on KTH-TIPS2-b and KTH-TIPS datasets, the proposed method is slightly inferior to some of the state-of-the-art methods.

Sherstobitov, A. I.; Marchuk, V. I.; Timofeev, D. V.; Voronin, V. V.; Egiazarian, K. O.; Agaian, Sos S.

2014-05-01

160

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

161

An Approximate Lagrange Multiplier Rule 1 Introduction  

E-print Network

sary tools that we require from nonsmooth analysis and we shall also present the approximate ... condition in many cases would allow us to work with gradient information, a luxury which .... move away from convexity in an interesting way. One can ...... The interesting thing to be observed is that we are using only gradient.

2009-06-04

162

Adaptive joint fuzzy sets for function approximation  

Microsoft Academic Search

This paper presents a new method to create and tune joint fuzzy sets. Multidimensional fuzzy sets define the if-part fuzzy sets of rules in feedforward fuzzy function approximators. These joint set functions do not factor into a product of scalar fuzzy sets (such as triangles or bell curves) and so they do not ignore the correlation structure among the input

Sanya Mitaim; Bart Kosko

1997-01-01

163

An Approximate Theory of Order in Alloys  

Microsoft Academic Search

Short-range order parameters alphai are defined to express the interaction of a given atom in an alloy with the atoms of the ith shell of atoms surrounding it. From simple thermodynamic reasoning, involving a certain degree of approximation, equations relating the alphai with energy terms and the temperature are derived. Equations for the long-range order parameter, S, are obtained by

J. M. Cowley

1950-01-01

164

Interference-Driven Adaptation in Sparse Approximation  

E-print Network

, the representations produced by iterative descent methods, such as orthogonal matching pursuit (OMP), will contain and less a reflection of the decomposition process. I. INTRODUCTION Recent works on signal processing and data analysis con- tinue to demonstrate the benefits of sparse approximation (see, e.g., [1

California at Santa Barbara, University of

165

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

166

Forest Stewardship? Approximately six million acres of  

E-print Network

What is Forest Stewardship? Approximately six million acres of private forest land exists in Colorado. Like all natural resources, forests require proper management to be healthy and productive. By managing your forest you can protect water quality, increase habitat diversity for wildlife, and increase

167

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

168

Numerical methods for solving approximating kinetic equations  

Microsoft Academic Search

The paper considers the numerical solution of the kinetic equation of the incomplete third successive approximation for a pseudo-Maxwellian gas. The solution to the equation must incorporate the following features: (1) a method for computing the collision term, (2) a rule for computing velocity space integrals, (3) an iterative procedure, and (4) a numerical scheme for solving the kinetic equation

E. M. Shakhov

1975-01-01

169

Approximation space for intelligent system design patterns  

Microsoft Academic Search

This article introduces an approximation space for graded acceptance of proposed models for intelligent system design relative to design patterns that conform to a design standard. A fundamental problem in system design is that feature values extracted from experimental design models tend not to match exactly patterns associated with standard design models. It is not generally known how to measure

James F. Peters

2004-01-01

170

OPTIMAL APPROXIMATION RATE OF CERTAIN STOCHASTIC INTEGRALS  

E-print Network

. We are interested in the minimal quadratic risk under the constraint that one trades only n times, iOPTIMAL APPROXIMATION RATE OF CERTAIN STOCHASTIC INTEGRALS HEIKKI SEPP ň? AL ň? A Abstract. Given of integrability properties of H. These results are applied to the approxi¬≠ mation of certain stochastic integrals

Jyväskylä, University of

171

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

172

Pixel Approximation Errors in Common Watershed Algorithms  

E-print Network

Pixel Approximation Errors in Common Watershed Algorithms Hans Meine1 , Peer Stelldinger1 algorithms are among the most important approaches to image seg- mentation. This is in large part due caused by common watershed discretization schemes. This investigation reveals a number of interesting

Hamprecht, Fred A.

173

Approximate Convolution Using DCT Coe cient Multipliers  

E-print Network

Approximate Convolution Using DCT Coe cient Multipliers Neri Merhav and Renato Kreschy November 4, 1997 Abstract We develop a method for designing DCT coe cient multipliers in order to approxi- mate formats of DCT-based compression methods (JPEG, MPEG, H.261) by using decoding quantization tables

Merhav, Neri

174

BRDF approximation and estimation for Augmented Reality  

Microsoft Academic Search

In Augmented Reality applications it is important to have a good description of the surfaces of real objects if a consistent shading between real and virtual object is required. If such a description of a surface is not available it has to be estimated or approximated. In this paper several methods are presented that deal with the bi-directional reflectance distribution

Patrick Kuhtreiber; Martin Knecht; Christoph Traxler

2011-01-01

175

Auxiliary basis sets to approximate Coulomb potentials  

Microsoft Academic Search

We demonstrate accuracy and computational efficiency resulting from an approximate treatment of Coulomb operators which is based on the expansion of molecular electron densities in atom-centered auxiliary basis sets. This is of special importance in density functional methods which separate the treatment of Coulomb and exchange-correlation terms. Auxiliary basis sets are optimized as much as possible for isolated atoms and

Karin Eichkorn; Oliver Treutler; Holger ÷hm; Marco Hšser; Reinhart Ahlrichs; Marco Ser

1995-01-01

176

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

177

Rapid Approximate Silhouette Rendering Of Implicit Surfaces  

Microsoft Academic Search

We describe a method for rapidly producing a nonphotorealistic rendering of an implicit surface. The rendering includes silhouettes and some shading near silhouettes to help indicate curvature. The method identi es silhouettes probabilistically, but we include strategies to make it likely that we nd all silhouette curves, especially in multiple-frame sequences. The method is approximate, in the sense that the

David Bremer; John F. Hughes

1998-01-01

178

Characterizing Conclusive Approximations by Logical Formulae  

E-print Network

proofs of s R t, were done on crypto- graphic protocols [18, 12, 4] where protocols and intruders an initial set of terms E, a rewriting relation R and a goal set of terms Bad, reachability analysis in term to this approximation. Recently, reachability analysis turned out to be a very efficient verification technique

Paris-Sud XI, Université de

179

Approximate l -fold Cross-Validation  

E-print Network

Approximate l -fold Cross-Validation with Least Squares SVM and Kernel Ridge Regression Dr. Richard Networks · (Non-)Linear Regression · Self-Organizing Maps · C/K-Means · Ensemble Learning #12;9 Presentation name Big Data Opportunities · EnergyPlus - Whole building energy sim ­ 600k lines Fortran · Input

Wang, Xiaorui "Ray"

180

Truth Revelation in Approximately Ecient Combinatorial Auctions  

E-print Network

Truth Revelation in Approximately E√?cient Combinatorial Auctions Daniel Lehmann School of Computer). Traditional analysis of these mechanisms - in partic- ular, their truth revelation properties - assumes payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does

Lehmann, Daniel

181

FRACTAL STRUCTURES IN DYADIC DIOPHANTINE APPROXIMATION  

E-print Network

FRACTAL STRUCTURES IN DYADIC DIOPHANTINE APPROXIMATION JOHAN NILSSON Faculty of Engineering Centre prove that the set {x S : 2nx c, n > 0} is a fractal set whose Hausdorff dimension depends continuously on c and is constant on intervals which form a set of Lebesgue measure 1. Hence it has a fractal

Nilsson, Johan

182

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

183

AN APPROXIMATION ALGORITHM FOR COUNTING CONTINGENCY TABLES  

E-print Network

AN APPROXIMATION ALGORITHM FOR COUNTING CONTINGENCY TABLES Alexander Barvinok, Zur Luria, Alex algo- rithm, and an integral representation for the number of contingency tables. 1. Introduction Let R = N. A contingency table with margins (R, C) is an m √? n non-negative integer matrix D = (dij

Barvinok, Alexander

184

Progressive Image Coding by Hierarchical Linear Approximation.  

ERIC Educational Resources Information Center

Proposes a scheme of hierarchical piecewise linear approximation as an adaptive image pyramid. A progressive image coder comes naturally from the proposed image pyramid. The new pyramid is semantically more powerful than regular tessellation but syntactically simpler than free segmentation. This compromise between adaptability and complexityÖ

Wu, Xiaolin; Fang, Yonggang

1994-01-01

185

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

186

An adiabatic approximation for grain alignment theory  

NASA Astrophysics Data System (ADS)

The alignment of interstellar dust grains is described by the joint distribution function for certain `internal' and `external' variables, where the former describe the orientation of the axes of a grain with respect to its angular momentum, J, and the latter describe the orientation of J relative to the interstellar magnetic field. I show how the large disparity between the dynamical time-scales of the internal and external variables - which is typically 2-3 orders of magnitude - can be exploited to simplify calculations of the required distribution greatly. The method is based on an `adiabatic approximation' which closely resembles the Born-Oppenheimer approximation in quantum mechanics. The adiabatic approximation prescribes an analytic distribution function for the `fast' dynamical variables and a simplified Fokker-Planck equation for the `slow' variables which can be solved straightforwardly using various techniques. These solutions are accurate to O(epsilon), where epsilon is the ratio of the fast and slow dynamical time-scales. As a simple illustration of the method, I derive an analytic solution for the joint distribution established when Barnett relaxation acts in concert with gas damping. The statistics of the analytic solution agree with the results of laborious numerical calculations which do not exploit the adiabatic approximation.

Roberge, W. G.

1997-10-01

187

An Adiabatic Approximation for Grain Alignment Theory  

NASA Astrophysics Data System (ADS)

The alignment of interstellar dust grains is described by the joint distribution function for certain ``internal'' and ``external'' variables, where the former describe the orientation of a grain's axes with respect to its angular momentum, J, and the latter describe the orientation of J relative to the interstellar magnetic field. I show how the large disparity between the dynamical timescales of the internal and external variables--- which is typically 2--3 orders of magnitude--- can be exploited to greatly simplify calculations of the required distribution. The method is based on an ``adiabatic approximation'' which closely resembles the Born-Oppenheimer approximation in quantum mechanics. The adiabatic approximation prescribes an analytic distribution function for the ``fast'' dynamical variables and a simplified Fokker-Planck equation for the ``slow'' variables which can be solved straightforwardly using various techniques. These solutions are accurate to cal {O}(epsilon ), where epsilon is the ratio of the fast and slow dynamical timescales. As a simple illustration of the method, I derive an analytic solution for the joint distribution established when Barnett relaxation acts in concert with gas damping. The statistics of the analytic solution agree with the results of laborious numerical calculations which do not exploit the adiabatic approximation.

Roberge, W. G.

1997-12-01

188

Approximate Multicommodity Flow for WDM Networks Design  

E-print Network

algorithm constructing a multicommodity flow based on the randomized rounding of the linear relaxation of theApproximate Multicommodity Flow for WDM Networks Design M. Bouklit D. Coudert§ J-F. Lalande§ C- proximations of the fractional multicommodity flow problem which is the central part of a complex randomized

Bermond, Jean-Claude

189

Multidimensional stochastic approximation using locally contractive functions  

NASA Technical Reports Server (NTRS)

A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.

Lawton, W. M.

1975-01-01

190

Impulse noise removal using polynomial approximation  

E-print Network

Impulse noise removal using polynomial approximation Dapeng Zhang Zhou Wang City University of Hong. A novel filtering algorithm is presented to restore images cor- rupted by impulsive noise. As a preprocessing procedure of the noise cancellation filter, an improved impulse detector is used to generate

Wang, Zhou

191

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

192

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

193

Thin groups and superstrong approximation MSRI Publications  

E-print Network

Thin groups and superstrong approximation MSRI Publications Volume 61, 2013 Constructing thin. Following Sarnak [25], a subgroup of is called thin if has infinite index in , but is Zariski dense, in addition insist that a thin group is finitely generated and does not decompose as a free product

Bigelow, Stephen

194

Improved Error Estimate for the Valence Approximation  

E-print Network

We construct a systematic mean-field-improved coupling constant and quark loop expansion for corrections to the valence (quenched) approximation to vacuum expectation values in the lattice formulation of QCD. Terms in the expansion are evaluated by a combination of weak coupling perturbation theory and a Monte Carlo algorithm.

W. Lee; D. Weingarten

1998-04-10

195

Fast Approximation of the Shape Diameter Function  

Microsoft Academic Search

In this paper we propose an optimization of the Shape Diameter Function (SDF) that we call Accelerated SDF (ASDF). We discuss in detail the advantages and disadvantages of the original SDF definition, proposing theoretical and practical approaches for speedup and approximation. Using Poisson-based interpolation we compute the SDF value for a small subset of randomly distributed faces and ...

Fabio Guggeri; Stefano Marras; Riccardo Scateni

2010-01-01

196

Optimizing the Zel'dovich Approximation  

E-print Network

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 we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that the ``truncated Zel'dovich approximation" (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear ($\\sigma \\sim 3$) regimes. TZA sets Fourier amplitudes equal to zero for {\\it all} wavenumbers greater than $k_{n\\ell}$, where $k_{n\\ell}$ marks the transition to the nonlinear regime. Here, we study crosscorrelation of generalized TZA with a group of $n$--body simulations for three shapes of window function: sharp $k$--truncation (as in CMS), tophat in coordinate space, or a Gaussian. We also study the crosscorrelation as a function of initial scale within each window type. We find $k$--truncation, which was so much better than other things tried in CMS, is the {it worst} of these three window shapes. We find that a Gaussian window $e^{-k^2/2k_G^2}$ applied to the intial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation all cases we studied. The optimum choice of $k_G$ for the Gaussian window is (spectrum-- dependent) 1--1.5 times $k_{n\\ell}$, with $k_{n\\ell}$ defined by (3). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, phase agreement with the $n$--body simulation is better for the Gaussian window. We ascribe Gaussian window success to its superior treatment of phase evolution.

A. L. Melott; T. F. Pellman; S. F. Shandarin

1993-12-18

197

Counting independent sets using the Bethe approximation  

SciTech Connect

The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques.

Chertkov, Michael [Los Alamos National Laboratory; Chandrasekaran, V [MIT; Gamarmik, D [MIT; Shah, D [MIT; Sin, J [MIT

2009-01-01

198

Approximating Mathematical Semantic Web Services Using Approximation Formulas and Numerical Methods  

E-print Network

Approximating Mathematical Semantic Web Services Using Approximation Formulas and Numerical Methods.andreica@cs.pub.ro) Abstract: Mathematical semantic web services are very useful in practice, but only a small number of a mathematical semantic web service, from its semantic description, using existing mathematical semantic web

Paris-Sud XI, Université de

199

Approximation Via CostSharing: A Simple Approximation Algorithm for the Multicommodity RentorBuy Problem  

E-print Network

Approximation Via Cost¬≠Sharing: A Simple Approximation Algorithm for the Multicommodity Rent¬≠or¬≠Buy Problem Anupam Gupta #3; Amit Kumar y Martin P‚??al z Tim Roughgarden z Abstract We study the multicommodity We study the multicommodity rent¬≠or¬≠buy (MRoB) prob¬≠ lem. In this problem, we are given an undirected

Kumar, Amit

200

Approximation Via CostSharing: A Simple Approximation Algorithm for the Multicommodity RentorBuy Problem  

E-print Network

Approximation Via Cost­Sharing: A Simple Approximation Algorithm for the Multicommodity Rent the multicommodity rent­or­buy problem, a type of network design problem with economies of scale. In this problem­98­1­0589. Email: fmpal,timrg@cs.cornell.edu. #12; 1 Introduction We study the multicommodity rent­or­buy (MRo

P√°l, Martin

201

An Origami Approximation to the Cosmic Web  

E-print Network

The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in 'polygonal' or 'polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls ...

Neyrinck, Mark C

2014-01-01

202

Phase Transitions for Greedy Sparse Approximation Algorithms  

E-print Network

A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many such algorithms have now been proven to have optimal-order uniform recovery guarantees using the ubiquitous Restricted Isometry Property (RIP). However, it is unclear when the RIP-based sufficient conditions on the algorithm are satisfied. We present a framework in which this task can be achieved; translating these conditions for Gaussian measurement matrices into requirements on the signal's sparsity level, length, and number of measurements. We illustrate this approach on three of the state-of-the-art greedy algorithms: CoSaMP, Subspace Pursuit (SP), and Iterative Hard Thresholding (IHT). Designed to allow a direct comparison of existing theory, our framework implies that, according to the best known bounds, IHT requires the fewest number of compressed sensing measuremen...

Blanchard, Jeffrey D; Tanner, Jared; Thompson, Andrew

2010-01-01

203

Zel'dovich approximation and General Relativity  

E-print Network

We show how the Zel'dovich approximation and the second order displacement field of Lagrangian perturbation theory can be obtained from a general relativistic gradient expansion in \\Lambda{}CDM cosmology. The displacement field arises as a result of a second order non-local coordinate transformation which brings the synchronous/comoving metric into a Newtonian form. We find that, with a small modification, the Zel'dovich approximation holds even on scales comparable to the horizon. The corresponding density perturbation is not related to the Newtonian potential via the usual Poisson equation but via a modified Helmholtz equation. This is a consequence of causality not present in the Newtonian theory. The second order displacement field receives relativistic corrections that are subdominant on short scales but are comparable to the second order Newtonian result on scales approaching the horizon. The corrections are easy to include when setting up initial conditions in large N-body simulations.

Cornelius Rampf; Gerasimos Rigopoulos

2012-12-13

204

Second derivatives for approximate spin projection methods.  

PubMed

The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical second derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives. PMID:25662635

Thompson, Lee M; Hratchian, Hrant P

2015-02-01

205

Numerical and approximate solutions for plume rise  

NASA Astrophysics Data System (ADS)

Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585-590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).

Krishnamurthy, Ramesh; Gordon Hall, J.

206

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

207

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

208

JIMWLK evolution in the Gaussian approximation  

NASA Astrophysics Data System (ADS)

We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors N c . This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it re-produces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite N c . Any higher n-point function with n ? 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.

Iancu, E.; Triantafyllopoulos, D. N.

2012-04-01

209

OBNER BASES, PAD E APPROXIMATION, AND DECODING  

E-print Network

GR ň? OBNER BASES, PAD ‚?? E APPROXIMATION, AND DECODING OF LINEAR CODES JEFFREY B. FARR AND SHUHONG of functions on V with values in F q . Thus, f(P i ) # F q for all i and for f # L. Define C = {(f(P 1 ), . . . , f(P n )) : f # L}; that is, C is the image of L under evaluation at the points in V . Then C

Gao, Shuhong

210

Scalable and fast approximate excess rate detection  

Microsoft Academic Search

An important requirement in high speed network monitoring is the fast and scalable identification of heavy-hitters, traffic flows whose generation rate exceeds some pre-established peak or mean rate conditions. This problem has been addressed in the past through the design of approximate counters, derived from counting Bloom filters, capable of performing this task without the need to keep per-flow state.

G. Bianchi; S. Teofili; E. Boschi; B. Trammell; C. Greco

2010-01-01

211

The Gibbs phenomenon bounds in wavelet approximations  

Microsoft Academic Search

Typical Gibbs phenomenon manifests itself by appearance of overshoots and undershoots around the jump discontinuities. It is well known that the first maximum and minimum of approximation of the signum function by the truncated Fourier integral is 1.17898 and 0.9028 respectively, which divided to the jump discontinuity correspond to 8.95% the Gibbs overshoot and to 4.86% undershoot. We proved that

Algirdas Bastys

2003-01-01

212

Approximate active fault detection and control  

NASA Astrophysics Data System (ADS)

This paper deals with approximate active fault detection and control for nonlinear discrete-time stochastic systems over an infinite time horizon. Multiple model framework is used to represent fault-free and finitely many faulty models. An imperfect state information problem is reformulated using a hyper-state and dynamic programming is applied to solve the problem numerically. The proposed active fault detector and controller is illustrated in a numerical example of an air handling unit.

äkach, Jan; Pun?ochŠ?, Ivo; äimandl, Miroslav

2014-12-01

213

Approximation methods for stochastic petri nets  

NASA Technical Reports Server (NTRS)

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists.

Jungnitz, Hauke Joerg

1992-01-01

214

Multipole decomposition in discrete dipole approximation  

NASA Astrophysics Data System (ADS)

In the framework of discrete dipole approximation, multipole decomposition of extinction and scattering spectra by nanoparticles of arbitrary shape is discussed. The method is applied to cubic Si nanoparticles with resonant multipole responses in the visible spectral range. It is demonstrated that there is a spectral band where Si cubic nanoparticles support a magnetic quadruple mode and scatter light as a point-like magnetic quadrupole.

Evlyukhin, Andrey B.; Reinhardt, Carsten; Chichkov, Boris N.

2012-09-01

215

Quantum adiabatic approximation and the geometric phase  

Microsoft Academic Search

A precise definition of an adiabaticity parameter nu of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(tau)=?lU(l)(tau) with U(l)(tau) being at least of the order nul. In particular, U(0)(tau) corresponds to the adiabatic approximation and yields Berry's adiabatic phase. It is shown that this

Ali Mostafazadeh

1997-01-01

216

Viscosity approximation methods for nonexpansive mappings  

Microsoft Academic Search

Viscosity approximation methods for nonexpansive mappings are studied. Consider a nonexpansive self-mapping T of a closed convex subset C of a Banach space X. Suppose that the set Fix(T) of fixed points of T is nonempty. For a contraction f on C and t?(0,1), let xt?C be the unique fixed point of the contraction x?tf(x)+(1?t)Tx. Consider also the iteration process

Hong-Kun Xu

2004-01-01

217

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

218

Fast Approximate Wavelet Tracking on Streams  

Microsoft Academic Search

Recent years have seen growing interest in effective algorithms for summarizing and querying massive, high-speed data streams. Randomized sketch synopses provide accurate approximations for general-purpose summaries of the streaming data distribution (e.g., wavelets). The focus of existing work has typi- cally been on minimizing space requirementsof the maintained synopsis ó how- ever, to effectively support high-speed data-stream analysis, a crucial

Graham Cormode; Minos N. Garofalakis; Dimitris Sacharidis

2006-01-01

219

Strong Washout Approximation to Resonant Leptogenesis  

E-print Network

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 $\\varepsilon=X\\sin(2\\varphi)/(X^2+\\sin^2\\varphi)$, where $X=8\\pi\\Delta/(|Y_1|^2+|Y_2|^2)$, $\\Delta=4(M_1-M_2)/(M_1+M_2)$, $\\varphi=\\arg(Y_2/Y_1)$, and $M_{1,2}$, $Y_{1,2}$ are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where $|Y_{1,2}|^2\\gg \\Delta$, {\\it 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.

Bjorn Garbrecht; Florian Gautier; Juraj Klaric

2014-09-18

220

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, BjŲrn; Gautier, Florian; Klaric, Juraj

2014-09-01

221

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

222

Proportional damping approximation using the energy gain and simultaneous perturbation stochastic approximation  

NASA Astrophysics Data System (ADS)

The design of vector second-order linear systems for accurate proportional damping approximation is addressed. For this purpose an error system is defined using the difference between the generalized coordinates of the non-proportionally damped system and its proportionally damped approximation in modal space. The accuracy of the approximation is characterized using the energy gain of the error system and the design problem is formulated as selecting parameters of the non-proportionally damped system to ensure that this gain is sufficiently small. An efficient algorithm that combines linear matrix inequalities and simultaneous perturbation stochastic approximation is developed to solve the problem and examples of its application to tensegrity structures design are presented.

Sultan, Cornel

2010-10-01

223

Approximations for crossing two nearby spin resonances  

NASA Astrophysics Data System (ADS)

Solutions to the Thomas-Bargmann-Michel-Telegdi spin equation for spin 1 /2 particles have to date been confined to the single-resonance crossing. However, in reality, most cases of interest concern the overlapping of several resonances. While there have been several serious studies of this problem, a good analytical solution or even an approximation has eluded the community. We show that this system can be transformed into a Hill-like equation. In this representation, we show that, while the single-resonance crossing represents the solution to the parabolic cylinder equation, the overlapping case becomes a parametric type of resonance.

Ranjbar, V. H.

2015-01-01

224

Shear viscosity in the postquasistatic approximation  

SciTech Connect

We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of anisotropic nonadiabatic radiating and dissipative distributions in general relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in noncomoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the nonadiabatic and adiabatic limit. In both cases, the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity.

Peralta, C.; Rosales, L.; Rodriguez-Mueller, B.; Barreto, W. [Deutscher Wetterdienst, Frankfurter Str. 135, 63067 Offenbach (Germany); Laboratorio de Fisica Computacional, Universidad Experimental Politecnica 'Antonio Jose de Sucre', Puerto Ordaz (Venezuela, Bolivarian Republic of); Computational Science Research Center, College of Sciences, San Diego State University, San Diego, California (United States); Centro de Fisica Fundamental, Facultad de Ciencias, Universidad de Los Andes, Merida (Venezuela, Bolivarian Republic of)

2010-05-15

225

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

226

Virial expansion coefficients in the harmonic approximation  

NASA Astrophysics Data System (ADS)

The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated to reproduce ground-state properties at low temperature and the noninteracting high-temperature limit of constant virial coefficients. This resembles the smearing of shell effects in finite systems with increasing temperature. Numerical results are discussed for the second and third virial coefficients as functions of dimension, temperature, interaction, and transition temperature between low- and high-energy limits.

Armstrong, J. R.; Zinner, N. T.; Fedorov, D. V.; Jensen, A. S.

2012-08-01

227

Approximate Bogomol'nyi-Prasad-Sommerfield states.  

PubMed

We consider dimensionally reduced three-dimensional supersymmetric Yang-Mills-Chern-Simons theory. Although the N=1 supersymmetry of this theory does not allow local massive Bogomol'nyi-Prasad-Sommerfield (BPS) states, we find approximate BPS states which have nonzero masses that are almost independent of the Yang-Mills coupling constant and which are a reflection of the massless BPS states of the underlying N=1 super-Yang-Mills theory. The masses of these states at large Yang-Mills coupling are exactly at the n-particle continuum thresholds. This leads to a relation between their masses at zero and large Yang-Mills coupling. PMID:12398590

Hiller, J R; Pinsky, S S; Trittmann, U

2002-10-28

228

[Bond selective chemistry beyond the adiabatic approximation  

SciTech Connect

The adiabatic Born-Oppenheimer potential energy surface approximation is not valid for reaction of a wide variety of energetic materials and organic fuels; coupling between electronic states of reacting species plays a key role in determining the selectivity of the chemical reactions induced. This research program initially studies this coupling in (1) selective C-Br bond fission in 1,3- bromoiodopropane, (2) C-S:S-H bond fission branching in CH[sub 3]SH, and (3) competition between bond fission channels and H[sub 2] elimination in CH[sub 3]NH[sub 2].

Butler, L.J.

1993-02-28

229

Fast Approximate Analysis Of Modified Antenna Structure  

NASA Technical Reports Server (NTRS)

Abbreviated algorithms developed for fast approximate analysis of effects of modifications in supporting structures upon root-mean-square (rms) path-length errors of paraboloidal-dish antennas. Involves combination of methods of structural-modification reanalysis with new extensions of correlation analysis to obtain revised rms path-length error. Full finite-element analysis, usually requires computer of substantial capacity, necessary only to obtain responses of unmodified structure to known external loads and to selected self-equilibrating "indicator" loads. Responses used in shortcut calculations, which, although theoretically "exact", simple enough to be performed on hand-held calculator. Useful in design, design-sensitivity analysis, and parametric studies.

Levy, Roy

1991-01-01

230

Fast Approximation Algorithms for Multicommodity Flow Problems  

Microsoft Academic Search

All previously known algorithms for solving the multicommodity flow problem with capacities are based on linear programming. The best of these algorithms uses a fast matrix multiplication algorithm and takes O(k3.5n3m0.5 log(nDU)) time for the multicommodity flow problem with integer demands and at least O(k2.5n2m0.5 log(n??1DU)) time to find an approximate solution, where k is the number of commodities, n

Frank Thomson Leighton; Fillia Makedon; Serge A. Plotkin; Clifford Stein; …va Stein; Spyros Tragoudas

1995-01-01

231

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

232

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

233

Geometric spectral inversion by the WKB approximation  

NASA Astrophysics Data System (ADS)

A particle moves in one spatial dimension in an attractive symmetric potential vf(x) and obeys nonrelativistic quantum mechanics. If Fn(v) is the trajectory function which describes how the nth energy eigenvalue depends on the coupling parameter, and Gn(u)=uFn(1/u), then an approximation f~n(x) for the potential is given by the general inversion formula x=?f~nGn(0)Pn(z)dz/(f~n-z)1/2, where Pn(z)=2n+1/4G'n(G-1n(z))[G-1n(z)]1/2. Specific inversion formulas are derived for power-law potentials and also for the sech-squared potential. Every energy trajectory of the harmonic oscillator inverts to x2 exactly. In the other cases studied, limn-->?f~n(x)=f(x). These results obtained by the WKB approximation suggest that for attractive symmetric potentials, ``geometric spectral inversion'' Fn(v)-->f(x) exists generally for every state n.

Hall, Richard L.

1995-03-01

234

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

235

Approximate discrete dynamics of EMG signal  

E-print Network

Approximation of a continuous dynamics by discrete dynamics in the form of Poincare map is one of the fascinating mathematical tool, which can describe the approximate behaviour of the dynamics of the dynamical system in lesser dimension than the embedding diemnsion. The present article considers a very rare biomedical signal like Electromyography (EMG) signal. It determines suitable time delay and reconstruct the attractor of embedding diemnsion three. By measuring its Lyapunov exponent, the attractor so reconstructed is found to be chaotic. Naturally the Poincare map obtained by corresponding Poincare section is to be chaotic too. This may be verified by calculation of Lyapunov exponent of the map. The main objective of this article is to show that Poincare map exists in this case as a 2D map for a suitable Poincare section only. In fact, the article considers two Poincare sections of the attractor for construction of the Poincare map. It is seen that one such map is chaotic but the other one is not so, both are verified by calculation of Lyapunov exponent of the map.

Sayan Mukherjee; Sanjay Kumar Palit; D. K. Bhattacharya

2014-09-23

236

An approximation algorithm for counting contingency tables  

E-print Network

We present a randomized approximation algorithm for counting contingency tables, mxn non-negative integer matrices with given row sums R=(r_1, ..., r_m) and column sums C=(c_1, ..., c_n). We define smooth margins (R,C) in terms of the typical table and prove that for such margins the algorithm has quasi-polynomial N^{O(ln N)} complexity, where N=r_1+...+r_m=c_1+...+c_n. Various classes of margins are smooth, e.g., when m=O(n), n=O(m) and the ratios between the largest and the smallest row sums as well as between the largest and the smallest column sums are strictly smaller than the golden ratio (1+sqrt{5})/2 = 1.618. The algorithm builds on Monte Carlo integration and sampling algorithms for log-concave densities, the matrix scaling algorithm, the permanent approximation algorithm, and an integral representation for the number of contingency tables.

Barvinok, Alexander; Samorodnitsky, Alex; Yong, Alexander

2008-01-01

237

The validity of the Background Field Approximation  

E-print Network

In the absence of a tractable theory of quantum gravity, quantum matter field effects have been so far computed by treating gravity at the Background Field Approximation. The principle aim of this paper is to investigate the validity of this approximation which is not specific to gravity. To this end, for reasons of simplicity and clarity, we shall compare the descriptions of thermal processes induced by constant acceleration (i.e. the Unruh effect) in four dynamical frameworks. In this problem, the position of the ``heavy'' accelerated system plays the role of gravity. In the first framework, the trajectory is treated at the BFA: it is given from the outset and unaffected by radiative processes. In the second one, recoil effects induced by these emission processes are taken into account by describing the system's position by WKB wave functions. In the third one, the accelerated system is described by second quantized fields and in the fourth one, gravity is turned on. It is most interesting to see when and why transitions amplitudes evaluated in different frameworks but describing the same process do agree. It is indeed this comparison that determines the validity of the BFA. It is also interesting to notice that the abandonment of the BFA delivers new physical insights concerning the processes. For instance, in the fourth framework, the ``recoils'' of gravity show that the acceleration horizon area acts as an entropy in delivering heat to accelerated systems.

R. Parentani

1997-10-10

238

The Background Field Approximation in (quantum) cosmology  

E-print Network

We analyze the Hamilton-Jacobi action of gravity and matter in the limit where gravity is treated at the background field approximation. The motivation is to clarify when and how the solutions of the Wheeler-DeWitt equation lead to the Schr\\"odinger equation in a given background. To this end, we determine when and how the total action, solution of the constraint equations of General Relativity, leads to the HJ action for matter in a given background. This is achieved by comparing two neighboring solutions differing slightly in their matter energy content. To first order in the change of the 3-geometries, the change of the gravitational action equals the integral of the matter energy evaluated in the background geometry. Higher order terms are governed by the ``susceptibility'' of the geometry. These classical properties also apply to quantum cosmology since the conditions which legitimize the use of WKB gravitational waves are concomitant with those governing the validity of the background field approximation.

R. Parentani

1998-03-12

239

Fast approximate hierarchical clustering using similarity heuristics  

PubMed Central

Background Agglomerative hierarchical clustering (AHC) is a common unsupervised data analysis technique used in several biological applications. Standard AHC methods require that all pairwise distances between data objects must be known. With ever-increasing data sizes this quadratic complexity poses problems that cannot be overcome by simply waiting for faster computers. Results We propose an approximate AHC algorithm HappieClust which can output a biologically meaningful clustering of a large dataset more than an order of magnitude faster than full AHC algorithms. The key to the algorithm is to limit the number of calculated pairwise distances to a carefully chosen subset of all possible distances. We choose distances using a similarity heuristic based on a small set of pivot objects. The heuristic efficiently finds pairs of similar objects and these help to mimic the greedy choices of full AHC. Quality of approximate AHC as compared to full AHC is studied with three measures. The first measure evaluates the global quality of the achieved clustering, while the second compares biological relevance using enrichment of biological functions in every subtree of the clusterings. The third measure studies how well the contents of subtrees are conserved between the clusterings. Conclusion The HappieClust algorithm is well suited for large-scale gene expression visualization and analysis both on personal computers as well as public online web applications. The software is available from the URL PMID:18822115

Kull, Meelis; Vilo, Jaak

2008-01-01

240

Investigating Material Approximations in Spacecraft Radiation Analysis  

NASA Technical Reports Server (NTRS)

During the design process, the configuration of space vehicles and habitats changes frequently and the merits of design changes must be evaluated. Methods for rapidly assessing astronaut exposure are therefore required. Typically, approximations are made to simplify the geometry and speed up the evaluation of each design. In this work, the error associated with two common approximations used to simplify space radiation vehicle analyses, scaling into equivalent materials and material reordering, are investigated. Over thirty materials commonly found in spacesuits, vehicles, and human bodies are considered. Each material is placed in a material group (aluminum, polyethylene, or tissue), and the error associated with scaling and reordering was quantified for each material. Of the scaling methods investigated, range scaling is shown to be the superior method, especially for shields less than 30 g/cm2 exposed to a solar particle event. More complicated, realistic slabs are examined to quantify the separate and combined effects of using equivalent materials and reordering. The error associated with material reordering is shown to be at least comparable to, if not greater than, the error associated with range scaling. In general, scaling and reordering errors were found to grow with the difference between the average nuclear charge of the actual material and average nuclear charge of the equivalent material. Based on this result, a different set of equivalent materials (titanium, aluminum, and tissue) are substituted for the commonly used aluminum, polyethylene, and tissue. The realistic cases are scaled and reordered using the new equivalent materials, and the reduced error is shown.

Walker, Steven A.; Slaba, Tony C.; Clowdsley, Martha S.; Blattnig, Steve R.

2011-01-01

241

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

242

On spectral approximations in elliptical geometries using Mathieu functions  

NASA Astrophysics Data System (ADS)

We consider in this paper approximation properties and applications of Mathieu functions. A first set of optimal error estimates are derived for the approximation of periodic functions by using angular Mathieu functions. These approximation results are applied to study the Mathieu-Legendre approximation to the modified Helmholtz equation and Helmholtz equation. Illustrative numerical results consistent with the theoretical analysis are also presented.

Shen, Jie; Wang, Li-Lian

2009-06-01

243

Animal models and integrated nested Laplace approximations.  

PubMed

Animal models are generalized linear mixed models used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast, nonsampling-based Bayesian inference for hierarchical Gaussian Markov models. In this article, we demonstrate that the INLA methodology can be used for many versions of Bayesian animal models. We analyze animal models for both synthetic case studies and house sparrow (Passer domesticus) population case studies with Gaussian, binomial, and Poisson likelihoods using INLA. Inference results are compared with results using Markov Chain Monte Carlo methods. For model choice we use difference in deviance information criteria (DIC). We suggest and show how to evaluate differences in DIC by comparing them with sampling results from simulation studies. We also introduce an R package, AnimalINLA, for easy and fast inference for Bayesian Animal models using INLA. PMID:23708299

Holand, Anna Marie; Steinsland, Ingelin; Martino, Sara; Jensen, Henrik

2013-08-01

244

Approximate Bayesian inference for complex ecosystems  

PubMed Central

Mathematical models have been central to ecology for nearly a century. Simple models of population dynamics have allowed us to understand fundamental aspects underlying the dynamics and stability of ecological systems. What has remained a challenge, however, is to meaningfully interpret experimental or observational data in light of mathematical models. Here, we review recent developments, notably in the growing field of approximate Bayesian computation (ABC), that allow us to calibrate mathematical models against available data. Estimating the population demographic parameters from data remains a formidable statistical challenge. Here, we attempt to give a flavor and overview of ABC and its applications in population biology and ecology and eschew a detailed technical discussion in favor of a general discussion of the advantages and potential pitfalls this framework offers to population biologists. PMID:25152812

2014-01-01

245

Animal Models and Integrated Nested Laplace Approximations  

PubMed Central

Animal models are generalized linear mixed models used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast, nonsampling-based Bayesian inference for hierarchical Gaussian Markov models. In this article, we demonstrate that the INLA methodology can be used for many versions of Bayesian animal models. We analyze animal models for both synthetic case studies and house sparrow (Passer domesticus) population case studies with Gaussian, binomial, and Poisson likelihoods using INLA. Inference results are compared with results using Markov Chain Monte Carlo methods. For model choice we use difference in deviance information criteria (DIC). We suggest and show how to evaluate differences in DIC by comparing them with sampling results from simulation studies. We also introduce an R package, AnimalINLA, for easy and fast inference for Bayesian Animal models using INLA. PMID:23708299

Holand, Anna Marie; Steinsland, Ingelin; Martino, Sara; Jensen, Henrik

2013-01-01

246

Heat flow in the postquasistatic approximation  

SciTech Connect

We apply the postquasistatic approximation to study the evolution of spherically symmetric fluid distributions undergoing dissipation in the form of radial heat flow. For a model that corresponds to an incompressible fluid departing from the static equilibrium, it is not possible to go far from the initial state after the emission of a small amount of energy. Initially collapsing distributions of matter are not permitted. Emission of energy can be considered as a mechanism to avoid the collapse. If the distribution collapses initially and emits one hundredth of the initial mass only the outermost layers evolve. For a model that corresponds to a highly compressed Fermi gas, only the outermost shell can evolve with a shorter hydrodynamic time scale.

Rodriguez-Mueller, B. [Computational Science Research Center, College of Sciences, San Diego State University, San Diego, California (United States); Peralta, C. [Deutscher Wetterdienst, Frankfurter Strasse 135, 63067 Offenbach (Germany); School of Physics, University of Melbourne, Parkville, VIC 3010 (Australia); Barreto, W. [Centro de Fisica Fundamental, Facultad de Ciencias, Universidad de Los Andes, Merida (Venezuela, Bolivarian Republic of); Rosales, L. [Laboratorio de Fisica Computacional, Universidad Experimental Politecnica, 'Antonio Jose de Sucre', Puerto Ordaz (Venezuela, Bolivarian Republic of)

2010-08-15

247

Exact and Approximate Probabilistic Symbolic Execution  

NASA Technical Reports Server (NTRS)

Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.

Luckow, Kasper; Pasareanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem

2014-01-01

248

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

249

Nonlocal gravity: The general linear approximation  

NASA Astrophysics Data System (ADS)

The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field equations is derived. The linear approximation of nonlocal gravity is thoroughly examined and the solutions of the corresponding field equations are discussed. It is shown that nonlocality, with a characteristic length scale of order 1 kpc, simulates dark matter in the linear regime while preserving causality. Light deflection in linearized nonlocal gravity is studied in connection with gravitational lensing; in particular, the propagation of light in the weak gravitational field of a uniformly moving source is investigated. The astrophysical implications of the results are briefly mentioned.

Mashhoon, B.

2014-12-01

250

Approximate spacetime symmetries and conservation laws  

E-print Network

A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincare and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these objects are discussed for both geodesics and extended matter distributions. One example is a generalized Komar integral that may be taken to define the linear and angular momenta of a spacetime volume as seen by a particular observer. This is evaluated explicitly for a gravitational plane wave spacetime.

Abraham I Harte

2008-05-28

251

Heat flow in the postquasistatic approximation  

E-print Network

We apply the postquasistatic approximation to study the evolution of spherically symmetric fluid distributions undergoing dissipation in the form of radial heat flow. For a model which corresponds to an incompressible fluid departing from the static equilibrium, it is not possible to go far from the initial state after the emission of a small amount of energy. Initially collapsing distributions of matter are not permitted. Emission of energy can be considered as a mechanism to avoid the collapse. If the distribution collapses initially and emits one hundredth of the initial mass only the outermost layers evolve. For a model which corresponds to a highly compressed Fermi gas, only the outermost shell can evolve with a shorter hydrodynamic time scale.

B. RodrŪguez-Mueller; C. Peralta; W. Barreto; L. Rosales

2010-08-05

252

A numerical approximation to distribution function  

E-print Network

g(Qi) & lrt ? sl & c6 h + o(h ). 2 2 We will now use Lemma 2 to show that, for a given Q , G. (y) is 1 i 2 n ? 1 an order h ~ h approximation to F (Y) LEMMA 3: Let f(x) f c [Q ], 0 & m &~3f(x)/gx ~& H for all x p Q 2 n n G (Y) = mess (x f Q. ( g(x..., 2) where c is between t, and x, . This gives us it 1/2 Similarly, Substituting the bounds (5) and (6) into (4), and simplifying we get Ia'(x. +I/2)) Itt ? cI c3 h + cih + 2, (a" (?. +I/2)~ c4 h +o(h ) 2 2 I ?2 2 and hence Z(Q ) = )n -t~ & c&h +o(h...

Tuttle, Keith Allan

2012-06-07

253

An approximate Riemann solver for hypervelocity flows  

NASA Technical Reports Server (NTRS)

We describe an approximate Riemann solver for the computation of hypervelocity flows in which there are strong shocks and viscous interactions. The scheme has three stages, the first of which computes the intermediate states assuming isentropic waves. A second stage, based on the strong shock relations, may then be invoked if the pressure jump across either wave is large. The third stage interpolates the interface state from the two initial states and the intermediate states. The solver is used as part of a finite-volume code and is demonstrated on two test cases. The first is a high Mach number flow over a sphere while the second is a flow over a slender cone with an adiabatic boundary layer. In both cases the solver performs well.

Jacobs, Peter A.

1991-01-01

254

Spline Approximation of Thin Shell Dynamics  

NASA Technical Reports Server (NTRS)

A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material nonhomogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method.

delRosario, R. C. H.; Smith, R. C.

1996-01-01

255

Dark energy from approximate U(1 symmetry  

NASA Astrophysics Data System (ADS)

The PLANCK observation strengthens the argument that the observed acceleration of the Universe is dominated by the invisible component of dark energy. We address how this extremely small DE density can be obtained in an ultraviolet complete theory. From two mass scales, the grand unification scale MG and the Higgs boson mass, we parametrize the scale of dark energy (DE). To naturally generate an extremely small DE term, we introduce an almost flat DE potential of a pseudo-Goldstone boson of an approximate global symmetry U(1 originating from some discrete symmetries allowed in an ultraviolet complete theory, as e.g. obtained in string theory constructions. For the DE potential to be extremely shallow, the pseudo-Goldstone boson is required not to couple to the QCD anomaly. This fixes uniquely the nonrenormalizable term generating the potential suppressed by MG7 in supergravity models.

Kim, Jihn E.; Nilles, Hans Peter

2014-03-01

256

Approximate Particle Spectra in the Pyramid Scheme  

E-print Network

We construct a minimal model within the general class of Pyramid Schemes, which is consistent with both supersymmetry breaking and electroweak symmetry breaking. In order to do computations, we make unjustified approximations to the low energy K\\"ahler potential. The phenomenological viability of the resultant mass spectrum is then examined and compared with current collider limits. We show that, for certain regimes of parameters, the Pyramid Scheme can accommodate the current collider mass constraints on physics beyond the standard model with a tree-level light Higgs mass near 125 GeV. However, in this regime the model exhibits a little hierarchy problem, and one must permit fine-tunings that are generically 5%.

Banks, Tom

2012-01-01

257

Approximate Particle Spectra in the Pyramid Scheme  

E-print Network

We construct a minimal model within the general class of Pyramid Schemes, which is consistent with both supersymmetry breaking and electroweak symmetry breaking. In order to do computations, we make unjustified approximations to the low energy K\\"ahler potential. The phenomenological viability of the resultant mass spectrum is then examined and compared with current collider limits. We show that, for certain regimes of parameters, the Pyramid Scheme can accommodate the current collider mass constraints on physics beyond the standard model with a tree-level light Higgs mass near 125 GeV. However, in this regime the model exhibits a little hierarchy problem, and one must permit fine-tunings that are generically 5%.

Tom Banks; T. J. Torres

2012-07-21

258

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

259

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 discovered last year, by Arora [1] and by Mitchell [9, 10]. This paper represents a continuation of our

Mitchell, Joseph S.B.

260

AABC: Approximate approximate Bayesian computation for inference in population-genetic models.  

PubMed

Approximate Bayesian computation (ABC) methods perform inference on model-specific parameters of mechanistically motivated parametric models when evaluating likelihoods is difficult. Central to the success of ABC methods, which have been used frequently in biology, is computationally inexpensive simulation of data sets from the parametric model of interest. However, when simulating data sets from a model is so computationally expensive that the posterior distribution of parameters cannot be adequately sampled by ABC, inference is not straightforward. We present "approximate approximate Bayesian computation" (AABC), a class of computationally fast inference methods that extends ABC to models in which simulating data is expensive. In AABC, we first simulate a number of data sets small enough to be computationally feasible to simulate from the parametric model. Conditional on these data sets, we use a statistical model that approximates the correct parametric model and enables efficient simulation of a large number of data sets. We show that under mild assumptions, the posterior distribution obtained by AABC converges to the posterior distribution obtained by ABC, as the number of data sets simulated from the parametric model and the sample size of the observed data set increase. We demonstrate the performance of AABC on a population-genetic model of natural selection, as well as on a model of the admixture history of hybrid populations. This latter example illustrates how, in population genetics, AABC is of particular utility in scenarios that rely on conceptually straightforward but potentially slow forward-in-time simulations. PMID:25261426

Buzbas, Erkan O; Rosenberg, Noah A

2015-02-01

261

An improved estimate of PSWF approximation and approximation by Mathieu functions  

Microsoft Academic Search

In this paper, an error estimate of spectral approximations by prolate spheroidal wave functions (PSWFs) with explicit dependence on the bandwidth parameter and optimal order of convergence is derived, which improves the existing result in [Chen et al., Spectral methods based on prolate spheroidal wave functions for hyperbolic PDEs, SIAM J. Numer. Anal. 43 (5) (2005) 1912Ė1933]. The underlying argument

Li-Lian Wang; Jing Zhang

2011-01-01

262

Approximate von Neumann entropy for directed graphs  

NASA Astrophysics Data System (ADS)

In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks.

Ye, Cheng; Wilson, Richard C.; Comin, Cťsar H.; Costa, Luciano da F.; Hancock, Edwin R.

2014-05-01

263

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

264

Approximate forms of daytime ionospheric conductance  

NASA Astrophysics Data System (ADS)

The solar zenith angle (SZA) dependence of the conductance is studied and a simple theoretical form for the Hall-to-Pedersen conductance ratio is developed, using the peak plasma production height. The European Incoherent Scatter (EISCAT) radar observations at TromsÝ (67 MLAT) on 30 March 2012 were used to calculate the conductance. The daytime electric conductance is associated with plasma created by solar extreme ultraviolet radiation incident on the neutral atmosphere of the Earth. However, it has been uncertain whether previous conductance models are consistent with the ideal Chapman theory for such plasma productions. We found that the SZA dependence of the conductance is consistent with the Chapman theory after simple modifications. The Pedersen conductance can be understood by approximating the plasma density height profile as being flat in the topside E region and by taking into account the upward gradient of atmospheric temperature. An additional consideration is necessary for the Hall conductance, which decreases with increasing SZA more rapidly than the Pedersen conductance. This rapid decrease is presumably caused by a thinning of the Hall conductivity layer from noon toward nighttime. We expressed this thinning in terms of the peak production height in the Chapman theory.

Ieda, A.; Oyama, S.; Vanhamški, H.; Fujii, R.; Nakamizo, A.; Amm, O.; Hori, T.; Takeda, M.; Ueno, G.; Yoshikawa, A.; Redmon, R. J.; Denig, W. F.; Kamide, Y.; Nishitani, N.

2014-12-01

265

Femtolensing: Beyond the Semi-Classical Approximation  

E-print Network

Femtolensing is a gravitational lensing effect in which the magnification is a function not only of the positions and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of $(10^{-13}-10^{-16} M_{\\sun})$ dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculations in general potentials. The physical-optics results presented here differ at low frequencies from the semi-classical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semi-classical 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 $10^{-11}$ solar masses, much larger than previously believed. Additionally, we discuss the possibility of a search for femtolensing of white dwarfs in the LMC at optical wavelengths.

A. Ulmer; J. Goodman

1994-06-16

266

Approximations for acoustically excited bubble cluster dynamics  

NASA Astrophysics Data System (ADS)

In this paper the effect of interaction on the expansion of a bubble in a regular monodisperse cluster is investigated. By a geometric construction a two-dimensional ordinary differential equation with an exact expression for first-order bubble interactions is derived for an n-bubble model. An approximate equation is derived for the rapid expansion of the bubble which can be solved yielding an analytic expression for the collapse of a bubble which undergoes inertial cavitation. It is then demonstrated that the maximum volume of a bubble in a cluster is considerably less than that of a single bubble. This result is of significance as typically the dispersion relationship, the wave speed and the co-efficient of attenuation are calculated using a single bubble model and summed for the total number of bubbles to yield the void fraction. Furthermore it is shown that the maximum radius of a bubble in the cluster is considerably smaller than that of a single bubble, yet the duration of the collapse phase is only weakly dependent on the number of bubbles. Hence, it is conjectured that the likelihood of fragmentation due to Rayleigh-Taylor instability is reduced. The results from the analysis are in good agreement with full numerical simulations of multi-bubble dynamics, as well as experimental observations

Sinden, D.; Stride, E.; Saffari, N.

2012-03-01

267

Adaptive approximation of higher order posterior statistics  

SciTech Connect

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, E-mail: leew@maths.ox.ac.uk

2014-02-01

268

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 networksópolitical weblogs and student friendshipsóand 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

269

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%Ė30% 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

270

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

271

Difference equation state approximations for nonlinear hereditary control problems  

NASA Technical Reports Server (NTRS)

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

Rosen, I. G.

1984-01-01

272

Difference equation state approximations for nonlinear hereditary control problems  

NASA Technical Reports Server (NTRS)

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Rosen, I. G.

1982-01-01

273

VISCOSITY AND RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS  

E-print Network

VISCOSITY AND RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS Athanasios E. Tzavaras Abstract. These lecture notes deal with the approximation of conservation laws via viscosity criteria is discussed. The problem of constructing entropy weak solutions for hyperbolic conservation laws

Tzavaras, Athanasios E.

274

Approximate truncated balanced realizations for infinite dimensional systems  

NASA Technical Reports Server (NTRS)

This paper presents an approximate method for obtaining truncated balance realizations of systems represented by non-rational transfer functions, that is infinite dimensional systems. It is based on the approximation to the Hankel operator.

Hartley, Tom T.; Deabreu-Garcia, J. Alex

1991-01-01

275

Complex Padť approximant operators for wide-angle beam propagation  

NASA Astrophysics Data System (ADS)

The conventional rational Hadley( m, n) approximant of wide-angle beam propagator based on real Padť approximant operators incorrectly propagates the evanescent modes. In order to overcome this problem, two complex Padť approximants of wide-angle beam propagator are presented in this paper. The complex propagators of the first approach are obtained by using the same recurrence formula from the scalar Helmholtz equation of the conventional approximant method with a different initial value while those of the second method derived from Hadley( m, n) approximant of a square-root operator that has been rotated in the complex plane. These resulting approaches allow more accurate approximations to the Helmholtz equation than the well-known real Padť approximant. Furthermore, our proposed complex Padť approximant operators give the evanescent modes the desired damping.

Le, Khai Q.

2009-04-01

276

On the complexity of approximating a nash equilibrium  

E-print Network

We show that computing a relative---that is, multiplicative as opposed to additive---approximate Nash equilibrium in two-player games is PPAD-complete, even for constant values of the approximation. Our result is the first ...

Daskalakis, Constantinos

2011-01-01

277

Approximation Algorithms for Multicommodity Flow and Shop Scheduling Problems  

E-print Network

Approximation Algorithms for Multicommodity Flow and Shop Scheduling Problems by Clifford Stein B Students #12; #12; Approximation Algorithms for Multicommodity Flow and Shop Scheduling Problems problems: multicommodity flow problems and shop scheduling problems. The algo­ rithms we develop

Yang, Junfeng

278

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

279

Collisionless magnetic reconnection under anisotropic MHD approximation  

NASA Astrophysics Data System (ADS)

We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless magneto-hydro-dynamic (MHD) simulations based on the double adiabatic approximation, which is an important step to 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 observation. According to our results, a pair of slow shocks does form in the reconnection layer. The resultant shock waves, however, are quite weak compared with those in an isotropic MHD from the point of view of the plasma compression and the amount of the magnetic energy released across the shock. Once the slow shock forms, the downstream plasma are heated in highly anisotropic manner and a firehose-sense (P_{||}>P_{?}) pressure anisotropy arises. The maximum anisotropy is limited by the marginal firehose criterion, 1-(P_{||}-P_{?})/B(2) =0. In spite of the weakness of the shocks, the resultant reconnection rate is kept at the same level compared with that in the corresponding ordinary MHD simulations. It is also revealed that the sequential order of propagation of the slow shock and the rotational discontinuity, which appears when the guide field component exists, changes depending on the magnitude of the guide field. Especially, when no guide field exists, the rotational discontinuity degenerates with the contact discontinuity remaining at the position of the initial current sheet, while with the slow shock in the isotropic MHD. Our 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, Kota; Hoshino, Masahiro

280

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

281

Laplace approximation for Bessel functions of matrix argument  

Microsoft Academic Search

We derive Laplace approximations to three functions of matrix argument which arise in statistics and elsewhere: matrix Bessel A?; matrix Bessel B?; and the type II confluent hypergeometric function of matrix argument, ?. We examine the theoretical and numerical properties of the approximations. On the theoretical side, it is shown that the Laplace approximations to A?, B? and ? given

Ronald W. Butler; Andrew T. A. Wood

2003-01-01

282

Test of dilute gas approximation in quantum mechanical model  

Microsoft Academic Search

The validity of dilute gas approximation is explored by making use of the large-sized instanton in quantum mechanical model. It is shown that the Euclidean probability amplitude derived through a dilute gas approximation not only cannot explain the result of the linear combination of atomic orbitals approximation, but also does not exhibit a proper limiting case when the size of

D. K. Park; Soo-Young Lee; Jae-Rok Kahng; Sahng-Kyoon Yoo; C. H. Lee; Chang Soo Park; Eui-Soon Yim

1996-01-01

283

Real space Dynamical Super Cell Approximation for interacting disordered systems  

Microsoft Academic Search

Effective medium super-cell approximation method which is introduced for disordered systems is extended to a general case of interacting disordered systems. We found that the dynamical cluster approximation (DCA) and also the non local coherent potential approximation (NLCPA) are two simple case of this technique. Whole equations of this formalism derived by using the effective medium theory in real space.

Rostam Moradian

2004-01-01

284

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

285

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials  

NASA Technical Reports Server (NTRS)

Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

Freund, Roland

1989-01-01

286

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

287

Minimax principle and lower bounds in H2 -rational approximation  

E-print Network

. Classification numbers (AMS): 31B05, 35J25, 42B35, 46E20, 47B35. 1. Introduction Rational approximationMinimax principle and lower bounds in H2 -rational approximation Laurent Baratcharta,1, Sylvain University of Macao Abstract We derive some lower bounds in rational approximation of given degree

Paris-Sud XI, Université de

288

Open-channel flow model approximation for controller design  

Microsoft Academic Search

In this paper, open-channel flow is analyzed using the linearized St. Venant equations. A method is presented to derive an approximation model for an open channel with backwater effects; the approximation model consists of functions that allow the application of effective control synthesis methods. The accuracy of the approximation models is demonstrated by two examples.

R. Brouwer

1995-01-01

289

Approximate Equality is no Fuzzy Equality Martine De Cock  

E-print Network

Approximate Equality is no Fuzzy Equality Martine De Cock Dept. of Applied Mathematics and Computer, and in particular fuzzy equalities, in general are not suitable to model approximate equality due to the notion the problem by choosing resemblance rela- tions. Keywords: fuzzy equivalence, fuzzy equality, approximate

De Cock, Martine

290

Approximation Refinement for Interpolation-Based Model Checking  

Microsoft Academic Search

Model checking using Craig interpolants provides an effec- tive method for computing an over-approximation of the set of reachable states using a SAT solver. This method requires proofs of unsatisfiabil- ity from the SAT solver to progress. If an over-approximation leads to a satisfiable formula, the computation restarts using more constraints and the previously computed approximation is not reused. Though

Vijay DíSilva; Mitra Purandare; Daniel Kroening

2008-01-01

291

Measurement of anomalous cosmic ray oxygen at heliolatitudes approximately 25 deg to approximately 64 deg  

NASA Astrophysics Data System (ADS)

We report measurements of the oxygen component (0.5 - 22 MeV/nucl) of the interplanetary cosmic ray flux as a function of heliolatitude. The measurements reported here were made with the Wart telescope of the Heliosphere Instrument for Spectra, Composition, and Anisotropy at Low Energies (HI-SCALE) low energy particle instrument on the Ulysses spacecraft as the spacecraft climbed from approximately 24 deg to approximately 64 deg south solar heliolatitude during 1993 and early 1994. As a function of heliolatitude, the O abundance at 2-2.8 MeV/nucl drops sharply at latitudes above the heliospheric current sheet. The oxygen spectrum obtained above the current sheet has a broad peak centered at an energy of approximately 2.5 MeV/nucl that is the anomalous O component at these latitudes. There is little evidence for a latitude dependence in the anomalous O fluxes as measured above the current sheet. Within the heliospheric current sheet, the O measurements are composed of both solar and anomalous origin particles.

Lanzerotti, L. J.; Maclennan, C. G.; Gold, R. E.; Armstrong, T. P.; Roelof, E. C.; Krimigis, S. M.; Simnett, G. M.; Sarris, E. T.; Anderson, K. A.; Pick, M.

1995-02-01

292

Four-Stream Isosector Approximation for Solar Radiative Transfer.  

NASA Astrophysics Data System (ADS)

For radiative transfer in a thin atmosphere, an analytical four-stream isosector approximation for solar radiative transfer is presented. This approximation method is based on the assumption of four spherical sectors of isotropic intensities. Calculations show that the four-stream isosector approximation model substantially improves the accuracy in reflection, transmission, and absorption with respect to the Coakley-Chżlek model. For an optical thickness less than unity, the four-stream isosector approximation has errors mostly under 5%, in contrast to errors up to 20% or higher for the Coakley-Chżlek model. This four-stream isosector approximation can be applied to atmospheric aerosol layers or thin cirrus clouds.

Li, J.; Dobbie, J. S.

1998-02-01

293

An analogue of Fabry's theorem for generalized Pade approximants  

SciTech Connect

The current theory of Pade approximation emphasises results of an inverse character, when conclusions about the properties of the approximated function are drawn from information about the behaviour of the approximants. In this paper Gonchar's conjecture is proved; it states that analogues of Fabry's classical 'ratio' theorem hold for rows of the table of Pade approximants for orthogonal expansions, multipoint Pade approximants and Pade-Faber approximants. These are the most natural generalizations of the construction of classical Pade approximants. For these Gonchar's conjecture has already been proved by Suetin. The proof presented here is based, on the one hand, on Suetin's result and, on the other hand, on an extension of Poincare's theorem on recurrence relations with coefficients constant in the limit, which is obtained in the paper. Bibliography: 19 titles.

Buslaev, Viktor I [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2009-08-31

294

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 RĮ(Z) and lower approximation set R_(Z)) are presented, respectively. The disadvantages of using upper-approximation set RĮ(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

295

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=1nRiĮ,?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

296

LCAO approximation for scaling properties of the Menger sponge fractal.  

PubMed

The electromagnetic eigenmodes of a three-dimensional fractal called the Menger sponge were analyzed by the LCAO (linear combination of atomic orbitals) approximation and a first-principle calculation based on the FDTD (finite-difference time-domain) method. Due to the localized nature of the eigenmodes, the LCAO approximation gives a good guiding principle to find scaled eigenfunctions and to observe the approximate self-similarity in the spectrum of the localized eigenmodes. PMID:19529555

Sakoda, Kazuaki

2006-11-13

297

Beyond the Born approximation in one-dimensional profile reconstruction  

NASA Astrophysics Data System (ADS)

A new method of one-dimensional profile reconstruction is presented. The method is based on an extension to the Born approximation and relates measurements of the scattered field to the Fourier transform of the slab profile. Since the Born and our new approximations are most valid at low frequency, we utilize superresolution to recover high-frequency information and then invert for the slab profile. Finally, we vary different parameters and examine the resulting reconstructions. approximation, profile reconstruction, superresolution.

Trantanella, Charles J.; Dudley, Donald G.; Nabulsi, Khalid A.

1995-07-01

298

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

299

Bioluminescence tomography based on the phase approximation model  

PubMed Central

A reconstruction method of bioluminescence sources is proposed based on a phase approximation model. Compared with the diffuse approximation, this phase approximation model more correctly predicts bioluminescence photon propagation in biological tissues, so that bioluminescence tomography can accurately locate and quantify the distribution of bioluminescence sources. The compressive sensing (CS) technique is applied to regularize the inverse source reconstruction to enhance numerical stability and efficiency. The numerical simulation and phantom experiments demonstrate the feasibility of the proposed approach. PMID:20126228

Cong, W.; Wang, G.

2010-01-01

300

Approximate analysis of postbuckled through-width delaminations  

NASA Technical Reports Server (NTRS)

An approximate analysis was developed to analyze the postbuckling behavior of through-width delaminations in a laminated coupon. The analysis contains two parameters which are determined using a finite element analysis. After calculating the parameters for a few configurations, the approximate analysis was used to analyze many other configurations. Lateral deflections and mode I strain-energy release rates obtained with the approximate analysis were compared with results from the finite element analysis. For the configurations analyzed, the approximate analysis agreed very well with the finite element results.

Whitcomb, J. D.

1981-01-01

301

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

302

Bethe free-energy approximations for disordered quantum systems  

E-print Network

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.

I. Biazzo; A. Ramezanpour

2014-07-08

303

Differential equation based method for accurate approximations in optimization  

NASA Technical Reports Server (NTRS)

This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new 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 msot 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 displacement are used to approximate bending stresses.

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

304

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

305

Approximation of Real Numbers by Rationals: Some Metric Theorems  

Microsoft Academic Search

Letxbe a real number in [0,†1], Fnbe the Farey sequence of ordernand?n(x) be the distance betweenxand Fn. The first result concerns the average rate of approximation:[formula]The second result states that any badly approximable number is better approximable by rationals than all numbers in average. Namely, we show that ifx?[0,†1] is a badly approximable number thenc1?n2?n(x)?c2for all integersn?1 and some constantsc1>0,c2>0.

Pavel Kargaev; Anatoly Zhigljavsky

1996-01-01

306

The Need for Champions for Approximate Social Search  

E-print Network

-and- paper system involving time-critical approximate social search. In particular, participants' goal participants. In the absence of technological networks, time- critical social search poses two The Need for Champions for Approximate Social Search Yves-Alexandre de Montjoye, Jesika Haria

307

A Faster, Better Approximation Algorithm for the Minimum Latency Problem  

E-print Network

A Faster, Better Approximation Algorithm for the Minimum Latency Problem Aaron Archer # Asaf Levin­MST with a performance guarantee of 2. We are able to obtain the same approximation ratio that would be given by Goemans for some values of k that we are not able to specify in advance. 1 Introduction Given a metric space with n

Williamson, David P.

308

Interacting distributed approximating functions for real-time quantum dynamics  

Microsoft Academic Search

The distributed approximating function (DAF) approach to quantum real-time dynamics is generalized to include the effects of the potential. The ĎĎinteractingíí DAF (IDAF) is introduced as the identity for a certain class of functions that can be chosen to approximate as closely as desired any wave packet of interest. Free propagation of the IDAF yields the free propagator for the

David K. Hoffman; Mark Arnold; Wei Zhu; Donald J. Kouri

1993-01-01

309

Polylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity  

E-print Network

) emerged to be edit distance (aka Levenshtein distance) [Lev65], defined as the minimum number of characterPolylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity Alexandr Andoni We present a near-linear time algorithm that approximates the edit distance between two strings

Goldreich, Oded

310

Polylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity  

E-print Network

the Levenshtein distance) [25], defined as the mini- mum number of character insertions, deletions, and subPolylogarithmic Approximation for Edit Distance and the Asymmetric Query Complexity Alexandr Andoni--We present a near-linear time algorithm that approximates the edit distance between two strings within

Krauthgamer, Robert

311

Understanding Cloud Data Using Approximate String Matching and Edit Distance  

E-print Network

) than Damerau-Levenshtein edit distance and preserves all approximate matches. Our method creates precision (as low as 33%) [4][5]. We replaced the Soundex with the Damerau- Levenshtein (DL) edit distanceUnderstanding Cloud Data Using Approximate String Matching and Edit Distance Joseph Jupin, Justin Y

Obradovic, Zoran

312

Static Approximation of Dynamically Generated Web Pages Yasuhiko Minamide  

E-print Network

by checking the approximation against the specifications of safe or unsafe strings. For example, Web pagesStatic Approximation of Dynamically Generated Web Pages Yasuhiko Minamide Department of Computer to generate Web pages dynamically according to a user's request and to customize pages for each user. However

Minamide, Yasuhiko

313

Approximating Convex Functions Via Non-Convex Oracles Under ...  

E-print Network

when given a black box access to an L-approximation oracle ė? of ? (the oracle value is always within a multiplicative .... (E.g., consider the domain D = [10,20], the identity function. ?(x) := x ... The cash management problem studied ...... We leave the approximability status of the other classes to be studied in future work.

2014-06-12

314

Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks  

Microsoft Academic Search

We consider multiclass feedforward queueing networks under first in first out and priority service disciplines driven by long-range dependent arrival and service time processes. We show that in critical loading the normalized workload, queue length and sojourn time processes can converge to a multi-dimensional reflected fractional Brownian motion. This weak heavy traffic approximation is deduced from a deterministic pathwise approximation

Kurt Majewski

2005-01-01

315

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

316

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

317

GRASS: Trimming Stragglers in Approximation Analytics Ganesh Ananthanarayanan1  

E-print Network

GRASS: Trimming Stragglers in Approximation Analytics Ganesh Ananthanarayanan1 , Michael Chien. In this paper, we present GRASS, which carefully uses speculation to mitigate the impact of stragglers in approximation jobs. GRASS's design is based on first principles analysis of the impact of speculation. GRASS

Govindan, Ramesh

318

Feature selection for best mean square approximation of class densities  

NASA Technical Reports Server (NTRS)

A criterion for linear feature selection is proposed which is based on mean square apporximation of class density functions. It is shown that for the widest possible class of approximants, the criterion reduces to Devijver's Bayesian distance. For linear approximants the criterion is equivalent to well known generalized Fisher criteria.

Peters, C.

1978-01-01

319

A note on smooth approximation capabilities of fuzzy systems  

Microsoft Academic Search

Modeling and prediction in some systems requires the simultaneous approximation of mappings and their derivatives to a certain finite order. In this paper, universal approximation capabilities of fuzzy systems are extended to this situation, by showing the denseness of some general classes of fuzzy models in appropriate function spaces where distance between functions is defined in terms of their derivatives.

Manuel Landajo; MarŪa J. RŪo; Rigoberto Pťrez

2001-01-01

320

Laplace approximations for hypergeometric functions with matrix argument  

Microsoft Academic Search

In this paper we present Laplace approximations for two functions of matrix argument: the Type I confluent hypergeometric function and the Gauss hypergeometric function. Both of these functions play an important role in distribution theory in multivariate analysis, but from a practical point of view they have proved challenging, and they have acquired a reputation for being difficult to approximate.

Roland W. Butler; Andrew T. A. Wood

2002-01-01

321

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 procedureÖ

Oud, Johan H. L.; Folmer, Henk

2011-01-01

322

Antinoise approximation of the lidar signal with wavelet neural networks  

E-print Network

wavelet approximation property but also to make a neural network that has a self-learning and adaptive of the WNN for antinoise approximation of lidar signals by simultaneously addressing simulated and real lidar the atmosphere temperature profile with the real signal processed by the WNN. To show the contrast, we also

Hefei Institute of Intelligent Machines

323

The approximate controllability of a model for mutant selection  

E-print Network

: parabolic system, population genetics, evolutionary selec- tion, approximate controllability AMS with population control to evolve in a re- actor with impenetrable walls is approximately controllable. 1 that the model contains no population control, which makes it unrealistic. In fact it was shown by T. Malthus

Weinberger, Hans

324

Pade Approximations in Inverse Homogenization and Numerical Simulation of Electromagnetic  

E-print Network

Pad¬īe Approximations in Inverse Homogenization and Numerical Simulation of Electromagnetic Fields and in numerical simulation of time- domain electromagnetic fields in composites. It is assumed that the scale governing the electromagnetic fields are of convolution type. We use rational Pad¬īe approximation to derive

Cherkaev, Elena

325

2007 Warren B. Powell Slide 1 Approximate Dynamic Programming for  

E-print Network

·Design and evaluation of approximation strategies ·Design of advanced approximation strategies #12;© 2007 and municipalities. ·Design of sensor networks and communication systems to manage responses to major weather events. Powell Slide 12 Energy management Applications ·Jet fuel hedging ­ Designing strategies to hedge against

Powell, Warren B.

326

Multidimensional rational approximations with an application to linear transforms  

Microsoft Academic Search

We discuss two new algorithms for the calculation of simultaneous rational approximations with specific computational characteristics. These approximations are used for efficient calculation of linear transforms. We develop an application in compression using the discrete cosine transform (DCT); however, the methods are also applicable to other integer transforms. To facilitate efficient multiplierless implementation for small field programmable gate arrays (FPGAs)

Jennifer Q. Trelewicz; Timothy J. Trenary

2004-01-01

327

Greedy Construction of 2-Approximation Minimum Manhattan Network  

E-print Network

suffices to get 2-approximation network. Key words: Minimum Manhattan Network, approximation algorithm point set T , the Minimum Manhattan Network (MMN) Problem is to find a Manhattan network G between the MMN problem and planar t-spanners. For t 1, if there exists a planar graph G

328

Approximate N-View Stereo Kiriakos N. Kutulakos  

E-print Network

Approximate N-View Stereo Kiriakos N. Kutulakos Department of Computer Science & Department@cs.rochester.edu Abstract. This paper introduces a new multi-view reconstruction problem called approximate N -view stereo discrete scenes (i.e., for unknown, arbitrarily-shaped Lambertian scenes that are defined by a finite set

Jepson, Allan D.

329

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 factÖ

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

330

Transport approximations in partially diffusive media Guillaume Bal  

E-print Network

Transport approximations in partially diffusive media Guillaume Bal Department of Applied Physics concerns the analysis of approximations of transport equations in diffusive media. Firstly, we consider a variational formulation for the first-order transport equation that has the correct diffusive behavior

Bal, Guillaume

331

POINTWISE ERROR ESTIMATES FOR RELAXATION APPROXIMATIONS TO CONSERVATION LAWS  

E-print Network

POINTWISE ERROR ESTIMATES FOR RELAXATION APPROXIMATIONS TO CONSERVATION LAWS EITAN TADMOR AND TAO that the maximum principle can be applied. Key words. conservation laws, error estimates, relaxation method@fisher.math.hkbu.edu.hk). 870 #12;RELAXATION APPROXIMATIONS TO CONSERVATION LAWS 871 dissipative mechanism for discontinuities

Soatto, Stefano

332

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

333

Atomic Structure Schrdinger equation has approximate solutions for multi-  

E-print Network

Atomic Structure Schrödinger equation has approximate solutions for multi- electron atoms, which indicate that all atoms are like hydrogen Atomic Structure Schrödinger equation has approximate solutions 3s 3p 3d Energy hydrogen multi-electron #12;Atomic Structure · orbitals are populated by electrons

Zakarian, Armen

334

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 the Gopher Fast Fourier Transform (GFFT), of the more recently developed sparse Fourier transform techniques

335

Some approximate treatments of fracture statistics for polyaxial tension  

Microsoft Academic Search

A frequently used approximate treatment of fracture statistics for polyaxial stress states assumes that the probability of survival is the product of the probabilities of survival of the structure for the principal stresses applied individually. The present paper shows that this assumption is generally unconservative and therefore the approximation serves as a lower bound to the failure probability. A simple

S. B. Batdorf

1984-01-01

336

Some approximate treatments of fracture statistics for polyaxial tension  

Microsoft Academic Search

A frequently used approximate treatment of fracture statistics for polyaxial stress states assumes that the probability of survival is the product of the probabilities of survival of the structure for the principal stresses applied individually. The present paper shows that this assumption is generally unconservative and therefore the approximation serves as a lower bound to the failure probability. A simple

S. B. Batdorf

1977-01-01

337

Sensitivity, Approximation and Uncertainty in Power System Dynamic Simulation  

E-print Network

1 Sensitivity, Approximation and Uncertainty in Power System Dynamic Simulation Ian A. Hiskens sensitivities can be used to generate accurate first-order approximations of trajecto- ries that arise from perturbed parameter sets. The computational cost of obtaining the sensitivities and perturbed trajectories

338

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.

339

COMSATS IIT, Lahore Campus March 12, 2013 Diophantine approximation  

E-print Network

approximation The set of rational numbers is dense in the set of real numbers : For any x in R and any > 0, there exists p/q Q such that x - p q rational numbers, compute the maximal number of digits of x with the minimum of operations. Rational approximation : given x and , find

Waldschmidt, Michel

340

Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models  

Microsoft Academic Search

In this paper we propose fast approximate methods for computing posterior marginals in spatial generalized linear mixed models. We consider the common geostatistical special case with a high dimensional latent spatial variable and observations at only a few known registration sites. Our methods of inference are deterministic, using no random sampling. We present two methods of approximate inference. The first

JO EIDSVIK; SARA MARTINO; HŇVARD RUE

2008-01-01

341

Approximate Counting Scheme for m n Contingency Tables  

E-print Network

Approximate Counting Scheme for m √? n Contingency Tables Shuji Kijima and Tomomi Matsui METR 2003-01 JANUARY 2003 #12;Approximate Counting Scheme for m √? n Contingency Tables Shuji Kijima and Tomomi Matsui. In this paper, we propose a new counting scheme for m √? n contingency tables. Our scheme is a modification

Yamamoto, Hirosuke

342

Adaptive Encoding Strongly Improves Function Approximation with CMAC  

Microsoft Academic Search

The Cerebellar Model Arithmetic Computer (CMAC) (Albus 1981) is well known as a good function approximator with local generalization abilities. Depending on the smoothness of the function to be approximated, the resolution as the smallest distinguishable part of the input domain plays a crucial role. If the binary quantizing functions in CMAC are dropped in favor of more general, continuous-valued

Martin Eldracher; Alexander Staller; Renť Pompl

1997-01-01

343

Fast Approximation Algorithms for Multicommodity Flow Problems \\Lambda  

E-print Network

Fast Approximation Algorithms for Multicommodity Flow Problems \\Lambda Tom Leighton y Fillia, UTD proposal #870049. 0 #12; Proposed running head: Approximating multicommodity flow Contact Author Clifford.Stein@dartmouth.edu 1 #12; Abstract All previously known algorithms for solving the multicommodity

Yang, Junfeng

344

A combinatorial approximation algorithm for the multicommodity ow problem ?  

E-print Network

A combinatorial approximation algorithm for the multicommodity #29;ow problem ? David Coudert Hervé is motivated by the need for approximation al- gorithms for the integral multicommodity #29;ow problem which multicommodity #29;ow by using an incremental approach. This approach is validated by exper- imental results

Bermond, Jean-Claude

345

Fast Approximation Algorithm for Minimum Cost Multicommodity Flow  

E-print Network

Fast Approximation Algorithm for Minimum Cost Multicommodity Flow Anil Kamath \\Lambda Omri Palmon y Serge Plotkin z Abstract Minimum­cost multicommodity flow problem is one of the classical optimization deterministic approximation algorithm, which given that there exists a multicommodity flow of cost B

Plotkin, Serge

346

Approximating Fractional Multicommodity Flow Independent of the Number of Commodities  

Microsoft Academic Search

We describe fully polynomial time approximation schemes for various multicom- modity ow problems in graphs with m edges and n vertices. We present the rst approximation scheme for maximum multicommodity ow that is independent of the number of commodities k, and our algorithm improves upon the runtime of previous algorithms by this factor of k, running inO ( 2m2) time.

Lisa K. Fleischer

1999-01-01

347

Faster Approximation Schemes for Fractional Multicommodity Flow George Karakostas y  

E-print Network

Faster Approximation Schemes for Fractional Multicommodity Flow Problems #3; George Karakostas y Abstract We present fully polynomial approximation schemes for concurrent multicommodity ow problems; k (multicommodity ow). In general one would like to calculate ows f i from s i to t i that would

Karakostas, George

348

Practical Approximation Algorithms for Separable Packing Linear Programs ?  

E-print Network

approximation schemes for gen­ eralized multicommodity flow problems arising in VLSI applications such as Global polynomial time approximation scheme for edge capacitated multicommodity flows to multiterminal multicommodity flows in graphs with capacities on vertices and subsets of vertices. In addition, our prob­ lem

Zelikovsky, Alexander

349

A Perceptual Study of Approximated Cantonese Tone Contours  

Microsoft Academic Search

This paper describes a perceptual study on approximated Cantonese tone contours. It is found that Cantonese tone contours and tone transitions can be approximated by a limited number of linear movements, without creating any noticeable perceptual difference. The slopes of these linear movements are analyzed. They are found to be related with two thresholds of pitch movement perception. The results

Yujia Li; Tan Lee

2008-01-01

350

Space-angle approximations in the variational nodal method  

Microsoft Academic Search

The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2)

E. E. Lewis; G. Palmiotti; T. Taiwo

1999-01-01

351

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

352

Fast Polygonal Approximation of Terrains and Height Fields  

E-print Network

Fast Polygonal Approximation of Terrains and Height Fields Michael Garland and Paul S. Heckbert. #12; Abstract Several algorithms for approximating terrains and other height fields using polygonal meshes are described, compared, and optimized. These algorithms take a height field as input, typically

Garland, Michael

353

Fast Polygonal Approximation of Terrains and Height Fields  

E-print Network

Fast Polygonal Approximation of Terrains and Height Fields Michael Garland and Paul S. Heckbert Several algorithms for approximating terrains and other height fields using polygonal meshes are described, compared, and optimized. These algorithms take a height field as input, typically a rectangular grid

Garland, Michael

354

Analysis of spectral approximations using prolate spheroidal wave functions  

Microsoft Academic Search

In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of non-periodic functions in Sobolev spaces. These results serve as an indispensable tool for the analysis of PSWF spectral methods. A PSWF spectral-Galerkin method is proposed and analyzed for

Li-Lian Wang

2010-01-01

355

Continuous meshless approximations for nonconvex bodies by diffraction and transparency  

Microsoft Academic Search

Continuous meshless approximations are developed for domains with non-convex boundaries, with emphasis on cracks. Two techniques are developed in the context of the element-free Galerkin method: a transparency method wherein smooth approximations are generated by making boundaries partially transparent, and a diffraction method, where the domain of influence wraps around a concave boundary. They are compared to the original method

D. Organ; M. Fleming; T. Terry; T. Belytschko

1996-01-01

356

Rational TransformApproximation via the LaguerreSpectrum  

E-print Network

Rational TransformApproximation via the LaguerreSpectrum by KENNETH STEIGLITZ Department for determination of an n th order rational transform approximation for a time function, given at least n + 1 of its with a rational generating function. The method does not require predetermination of the poles; and allows the use

Steiglitz, Kenneth

357

The shape of fuzzy sets in adaptive function approximation  

Microsoft Academic Search

The shape of if-part fuzzy sets affects how well feedforward fuzzy systems approximate continuous functions. We explore a wide range of candidate if-part sets and derive supervised learning laws that tune them. Then we test how well the resulting adaptive fuzzy systems approximate a battery of test functions. No one shape emerges as the best. The sine function often does

Sanya Mitaim; Bart Kosko

2001-01-01

358

Approximation of boundary conditions for mimetic finite-difference methods  

Microsoft Academic Search

The numerical solution of partial differential equations solved with finite-difference approximations that mimic the symmetry properties of the continuum differential operators and satisfy discrete versions of the appropriate integral identities are more likely to produce physically faithful results. Furthermore, those properties are often needed when using the energy method to prove convergence and stability of a particular difference approximation. Unless

J. M. Hyman; M. Shashkov

1998-01-01

359

Laplace approximation for Bessel functions of matrix argument  

NASA Astrophysics Data System (ADS)

We derive Laplace approximations to three functions of matrix argument which arise in statistics and elsewhere: matrix Bessel A[nu]; matrix Bessel B[nu]; and the type II confluent hypergeometric function of matrix argument, [Psi]. We examine the theoretical and numerical properties of the approximations. On the theoretical side, it is shown that the Laplace approximations to A[nu], B[nu] and [Psi] given here, together with the Laplace approximations to the matrix argument functions 1F1 and 2F1 presented in Butler and Wood (Laplace approximations to hyper-geometric functions with matrix argument, Ann. Statist. (2002)), satisfy all the important confluence relations and symmetry relations enjoyed by the original functions.

Butler, Ronald W.; Wood, Andrew T. A.

2003-06-01

360

Adaptive and anisotropic finite element approximation : Theory and algorithms  

E-print Network

Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of scientific computing. The use of anisotropic triangles allows to improve the efficiency of the procedure by introducing long and thin triangles that fit in particular the directions of the possible curves of discontinuity. Given a norm X of interest and a function f to be approximated, we formulate the problem of optimal mesh adaptation, as minimizing the approximation error over all (possibly anisotropic) triangulations of prescribed cardinality. We address the four following questions related to this problem: I. How does the approximation error behave in the asymptotic regime when the number of triangles N tends to infinity, when f is a smooth function ? II. Which classes of functions govern the rate of decay of the approximation error as N grows, and are in that sense natu...

Mirebeau, Jean-Marie

2011-01-01

361

Approximate number word knowledge before the cardinal principle.  

PubMed

Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge. PMID:25462030

Gunderson, Elizabeth A; Spaepen, Elizabet; Levine, Susan C

2015-02-01

362

Light scattering by large spheroids in the Physical Optics Approximation: numerical comparison with other approximate and exact results  

Microsoft Academic Search

Physical Optics Approximation is used to compute scattering efficiency factors forward- and back-scattering intensities, angular distributions of intensity and depolarization by large dielectric or absorbing spheroids. The results are compared with those obtained by exact theories or other approximate calculations. If the radius of curvature at any point of the illuminated part of the scatterer is greater than about a

J. C. Ravey; P. Mazeron

1983-01-01

363

Approximation Via Cost-Sharing: A Simple Approximation Algorithm for the Multicommodity Rent-or-Buy Problem  

E-print Network

Approximation Via Cost-Sharing: A Simple Approximation Algorithm for the Multicommodity Rent-or-Buy Problem Anupam Gupta¬£ Amit Kumar√Ě Martin P¬īal √? Tim Roughgarden√? Abstract We study the multicommodity rent We study the multicommodity rent-or-buy (MRoB) prob- lem. In this problem, we are given an undirected

Gupta, Anupam

364

Approximation Via Cost-Sharing: A Simple Approximation Algorithm for the Multicommodity Rent-or-Buy Problem  

E-print Network

Approximation Via Cost-Sharing: A Simple Approximation Algorithm for the Multicommodity Rent-or-Buy Problem Anupam Gupta Amit Kumar Martin P¬īal Tim Roughgarden Abstract We study the multicommodity rent We study the multicommodity rent-or-buy (MRoB) prob- lem. In this problem, we are given an undirected

Roughgarden, Tim

365

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

366

A Test of the Adhesion Approximation for Gravitational Clustering  

E-print Network

We quantitatively compare a particle implementation of the adhesion approximation to fully non--linear, numerical nbody simulations. Our primary tool, cross--correlation of nbody 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 nbody 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. Subject Heading: Galaxies, formation, clustering--large--scale structure of the Universe

A. L. Melott; S. F. Shandarin; D. H. Weinberg

1993-11-30

367

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 nonlinear, 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 that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that 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 F.; Weinberg, David H.

1994-01-01

368

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

369

Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers  

NASA Technical Reports Server (NTRS)

Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method used in conjunction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used.

Wong, Yau Shu; Jiang, Hong

1987-01-01

370

Approximate Quantum Cloaking and Almost-Trapped States  

SciTech Connect

We describe potentials which act as approximate cloaks for matter waves. These potentials are derived from ideal cloaks for the conductivity and Helmholtz equations. At most energies E, if a potential is surrounded by an approximate cloak, then it becomes almost undetectable and unaltered by matter waves originating externally to the cloak. For certain E, however, the approximate cloaks are resonant, supporting wave functions almost trapped inside the cloaked region and negligible outside. Applications include dc or magnetically tunable ion traps and beam switches.

Greenleaf, Allan [Department of Mathematics, University of Rochester, Rochester, New York 14627 (United States); Kurylev, Yaroslav [Department of Mathematical Sciences, University College London, London, WC1E 6BT (United Kingdom); Lassas, Matti [Institute of Mathematics, Helsinki University of Technology, FIN-02015 (Finland); Uhlmann, Gunther [Department of Mathematics, University of Washington, Seattle, Washington 98195 (United States)

2008-11-28

371

Efficient Approximation for Structural Optimization Under Multiple Constraints  

NASA Technical Reports Server (NTRS)

The cooperative agreement covered work between August 1995 and August 1997. The focus of the work was efficient approximations of structural response and sensitivity. The effort proceeded in three directions as follows: (1) Development of an approximation extended to efficient sensitivity approximations and demonstrated for structural models for the High Speed Civil Transport; (2) Preliminary development of the adjoint method for calculating sensitivity derivatives; and (3) A review of method for fast exact reanalysis. Attachments of papers which were submitted during this period are included.

Haftka, Raphael T.

1997-01-01

372

Analytic Approximate Solution for Falkner-Skan Equation  

PubMed Central

This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration. PMID:24883417

Marinca, Bogdan

2014-01-01

373

Convergence of multipoint Pade approximants of piecewise analytic functions  

SciTech Connect

The behaviour as n{yields}{infinity} of multipoint Pade approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Pade approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Pade approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points. Bibliography: 11 titles.

Buslaev, Viktor I [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)] [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2013-02-28

374

Investigation of the nonlocal coherent-potential approximation  

NASA Astrophysics Data System (ADS)

Recently the nonlocal coherent-potential approximation (NLCPA) has been introduced by Jarrell and Krishnamurthy for describing the electronic structure of substitutionally disordered systems. The NLCPA provides systematic corrections to the widely used coherent-potential approximation (CPA) whilst preserving the full symmetry of the underlying lattice. Here an analytical and systematic numerical study of the NLCPA is presented for a one-dimensional tight-binding model Hamiltonian, and comparisons with the embedded cluster method (ECM) and molecular coherent potential approximation (MCPA) are made.

Rowlands, D. A.

2006-03-01

375

Dynamical systems - A unified colored-noise approximation  

NASA Astrophysics Data System (ADS)

An adiabatic elimination procedure and a particular time scaling are used to derive a novel colored-noise approximation in the form of a Smoluchowski dynamics which is exact both for correlation times of colored noise (tau) equal to zero and to infinity. This dynamics combines the advantageous features of a recent decoupling theory that does not restrict the value of tau with those occurring in the small-correlation-time theory of Fox (1986). The approximative theory is applied to a nonlinear model for a dye laser driven by multiplicative noise. Excellent agreement for the stationary probability is obtained between the numerically exact solution and the novel approximative theory.

Jung, Peter; Hanggi, Peter

1987-05-01

376

``Thin-wall'' approximations to vacuum decay rates  

NASA Astrophysics Data System (ADS)

We examine the validity of Coleman's ``thin-wall'' approximation to the euclidean action of the bounce solution by comparing its predictions with exact numerically integrated actions for potentials which yield thin-and thick-wall bubbles. In both cases, the original thin-wall approximation is found to be poor, rapidly diverging from the exact action as the difference in energy of the two vacuum states is increased from zero. We introduce a new approximation scheme, calculationally similar to the original thin-wall scheme, which gives greatly improved accuracy.

Samuel, David A.; Hiscock, William A.

1991-05-01

377

Some approximations in the linear dynamic equations of thin cylinders  

NASA Technical Reports Server (NTRS)

Theoretical analysis is performed on the linear dynamic equations of thin cylindrical shells to find the error committed by making the Donnell assumption and the neglect of in-plane inertia. At first, the effect of these approximations is studied on a shell with classical simply supported boundary condition. The same approximations are then investigated for other boundary conditions from a consistent approximate solution of the eigenvalue problem. The Donnell assumption is valid at frequencies high compared with the ring frequencies, for finite length thin shells. The error in the eigenfrequencies from omitting tangential inertia is appreciable for modes with large circumferential and axial wavelengths, independent of shell thickness and boundary conditions.

El-Raheb, M.; Babcock, C. D., Jr.

1981-01-01

378

Improved approximate formulas for flux from cylindrical and rectangular sources  

SciTech Connect

This report provides two new approximate formulas for the flux at detector points outside the radial and axial extensions of a homogeneous cylindrical source and improved approximate formulas for the flux at points opposite rectangular surface sources. These formulas extend the range of geometries for which analytic approximations may be used by shield design engineers to make rapid scoping studies and check more extensive calculations for reasonableness. These formulas can be used to support skeptical, independent evaluations and are also valuable teaching tools for introducing shield designers to complex shield analyses.

Wallace, O.J.; Bokharee, S.A.

1993-03-01

379

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. II. Semi-infinite cylindrical approximations  

NASA Astrophysics Data System (ADS)

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (?), convectivity (V), and damping (?) in a cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based upon the heat equation in a semi-infinite cylindrical domain. The approximations are based upon continued fractions, asymptotic expansions, and multiple harmonics. The relative error for the different derived approximations is presented for different values of frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can yield good approximations over a wide parameter space for different cases, such as no convection and damping, only damping, and both convection and damping. This paper is the second part (Part II) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part III, cylindrical approximations are treated for heat waves traveling towards the center of the plasma.

van Berkel, M.; Hogeweij, G. M. D.; Tamura, N.; Zwart, H. J.; Inagaki, S.; de Baar, M. R.; Ida, K.

2014-11-01

380

CORC REPORT 19991 Approximately solving largescale linear programs. I.  

E-print Network

relaxations. Our implementation produces fast approximate solu­ tions to large pure multicommodity flow multicommodity flow problems and large LP­relaxations of network design problems. This paper is organized

Bienstock, Daniel

381

Approximating the ground state of gapped quantum spin systems  

E-print Network

We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset, X, of V the ground state projector can be approximated by the product of two projections, one supported on X and one supported on X^c, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue.

Eman Hamza; Spyridon Michalakis; Bruno Nachtergaele; Robert Sims

2009-04-29

382

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

383

High-Order Approximation of the Talbot Distance for Lithography  

NASA Astrophysics Data System (ADS)

The Talbot distance is investigated for the application of fine patterning by self-imaging in semiconductor lithography. Talbot distances were derived from 2nd- and 4th-order approximations, and the finite difference time domain (FDTD) optical simulation. Until now, the Talbot distance has been derived from the 2nd-order approximation; however, this was found to be insufficient for the self-imaging of a pattern pitch close to the illumination light source. However, the 4th order approximation is close to the FDTD results. The 4th-order approximation is required for estimating the Talbot distance for self-imaging obtained from +/-1st- and 0th-order diffraction beams.

Sato, Takashi

2012-09-01

384

On the mathematical treatment of the Born-Oppenheimer approximation  

E-print Network

Motivated by a paper by B.T. Sutcliffe and R.G. Woolley, we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigourous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by B.T. Sutcliffe and R.G. Woolley. The paper neither contains mathematical statements nor proofs. Instead we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

Thierry Jecko

2014-04-24

385

Orthogonal Polynomial Approximation in Higher Dimensions: Applications in Astrodynamics  

E-print Network

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...

Bani Younes, Ahmad H.

2013-08-05

386

Bayesian approximation error approach in full-wave ultrasound tomography.  

PubMed

In ultrasound tomography, the spatial distribution of the speed of sound in a region of interest is reconstructed based on transient measurements made around the object. The computation of the forward problem (the full-wave solution) within the object is a computationally intensive task and can often be prohibitive for practical purposes. The purpose of this paper is to investigate the feasibility of using approximate forward solvers and the partial recovery from the related errors by employing the Bayesian approximation error approach. In addition to discretization error, we also investigate whether the approach can be used to reduce the reconstruction errors that are due to the adoption of approximate absorbing boundary models. We carry out two numerical studies in which the objective is to reduce the computational times to around 3% of the time that would be required by a numerically accurate forward solver. The results show that the Bayesian approximation error approach improves the reconstructions. PMID:25265173

Koponen, Janne; Huttunen, Tomi; Tarvainen, Tanja; Kaipio, Jari P

2014-10-01

387

Polynomial Time Approximation Schemes for Dense Instances of NPHard Problems  

E-print Network

Polynomial Time Approximation Schemes for Dense Instances of NP­Hard Problems Sanjeev Arora \\Lambda ap­ proximation ratio---the worst­case ratio of the value \\Lambda Princeton University. arora in general, b

388

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

389

Randomized accuracy-aware program transformations for efficient approximate computations  

E-print Network

Despite the fact that approximate computations have come to dominate many areas of computer science, the field of program transformations has focused almost exclusively on traditional semantics-preserving transformations ...

Misailovic, Sasa

390

Approximating the ground state of gapped quantum spin systems  

SciTech Connect

We consider quantum spin systems defined on finite sets V equipped with a metric. In typical examples, V is a large, but finite subset of Z{sup d}. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset {chi} {contained_in} V the ground state projector can be approximated by the product of two projections, one supported on {chi} and one supported on {chi}{sup c}, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue.

Michalakis, Spyridon [Los Alamos National Laboratory; Hamza, Eman [NON LANL; Nachtergaele, Bruno [NON LANL; Sims, Robert [NON LANL

2009-01-01

391

Irrational approximations and their applications to partial differential ...  

E-print Network

nal projections related to partial differential equations in unbounded domains are established. As an example of applications, a Galerkin approximation using the ...... of ordinary differential equations with the unknown functions cl,m(r): ?. 1 r2 d.

2006-12-05

392

Contextual classification of multispectral image data: Approximate algorithm  

NASA Technical Reports Server (NTRS)

An approximation to a classification algorithm incorporating spatial context information in a general, statistical manner is presented which is computationally less intensive. Classifications that are nearly as accurate are produced.

Tilton, J. C. (principal investigator)

1980-01-01

393

Approximate penetration factors for nuclear reactions of astrophysical interest  

NASA Technical Reports Server (NTRS)

The ranges of validity of approximations of P(l), the penetration factor which appears in the parameterization of nuclear-reaction cross sections at low energies and is employed in the extrapolation of laboratory data to even lower energies of astrophysical interest, are investigated analytically. Consideration is given to the WKB approximation, P(l) at the energy of the total barrier, approximations derived from the asymptotic expansion of G(l) for large eta, approximations for small values of the parameter x, applications of P(l) to nuclear reactions, and the dependence of P(l) on channel radius. Numerical results are presented in tables and graphs, and parameter ranges where the danger of serious errors is high are identified.

Humblet, J.; Fowler, W. A.; Zimmerman, B. A.

1987-01-01

394

Approximate Flavour Symmetries and See-Saw Mechanism  

E-print Network

We study the approximate flavour symmetries imposed on the lepton sector assuming see-saw mechanism as the neutrino mass structure. We apply the symmetry to various neutrino phenomenologies and obtain constraints on neutrino masses and mixings.

Kang Young Lee; Jae Kwan Kim

1995-07-07

395

Approximating Digital 3D Shapes by Rational Gaussian Surfaces  

Microsoft Academic Search

Abstract: this paper, a surface recovery method is describedthat approximates a digital 3-D shape by a rational Gaussian (RAG) surface. The obtainedsurface, which is obtained from coarse to fine, enables efficient transmission, rendering, andediting of the shape

Marcel Jackowski; Martin Satter; A. Ardeshir Goshtasby

2003-01-01

396

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

397

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

398

VIEW INLAND (MAUKA) FROM BEACH ROAD. NOTE THE APPROXIMATE 46' ...  

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

VIEW INLAND (MAUKA) FROM BEACH ROAD. NOTE THE APPROXIMATE 46' DISTANCE BETWEEN RESIDENCES 26 AND 28 WORCHESTER AVENUE. VIEW FACING NORTHEAST. - Hickam Field, Fort Kamehameha Historic Housing, Along Worchester Avenue & Hope Street, Honolulu, Honolulu County, HI

399

MAX-PLANCK-INSTITUT Approximate and Exact Deterministic  

E-print Network

K _ _ _ _ _ _ _ _ __ Im Stadtwald W 6600 Saarbr√ľcken Germany #12;Approximate and Exact Deterministic-Planck-Institut f√ľr Informa.tik, Im Stadtwald, W-6600 Germany 2 UMIACS, University of Maryland, College Park, MD 20742

400

Validity of pair approximations for nuclei in open shells  

NASA Astrophysics Data System (ADS)

We study the validity of pair approximations of the nuclear shell model (SM) for a few realistic nuclei (130-131Te and 132I here) in open shells (i.e., nuclei with both valence protons and valence neutrons). We take a phenomenological shell model Hamiltonian, which includes the single-particle energy term, monopole and quadrupole pairing interactions for like particles, and quadrupole-quadrupole interactions between all valence nucleons. We make comparisons of energy levels and B(E2) values calculated by pair approximations with those in the SM calculations. The overlaps between wave functions of the nucleon pair approximation (NPA) and those of the SM are presented explicitly for the low-lying states. Our calculated results demonstrate that the NPA is a remarkable approximation of the SM for these nuclei. The important role played by pairs with negative parity in some low-lying states is discussed.

Lei, Y.; Zhao, Y. M.; Arima, A.

2011-10-01

401

Feature-based image patch approximation for lung tissue classification.  

PubMed

In this paper, we propose a new classification method for five categories of lung tissues in high-resolution computed tomography (HRCT) images, with feature-based image patch approximation. We design two new feature descriptors for higher feature descriptiveness, namely the rotation-invariant Gabor-local binary patterns (RGLBP) texture descriptor and multi-coordinate histogram of oriented gradients (MCHOG) gradient descriptor. Together with intensity features, each image patch is then labeled based on its feature approximation from reference image patches. And a new patch-adaptive sparse approximation (PASA) method is designed with the following main components: minimum discrepancy criteria for sparse-based classification, patch-specific adaptation for discriminative approximation, and feature-space weighting for distance computation. The patch-wise labelings are then accumulated as probabilistic estimations for region-level classification. The proposed method is evaluated on a publicly available ILD database, showing encouraging performance improvements over the state-of-the-arts. PMID:23340591

Song, Yang; Cai, Weidong; Zhou, Yun; Feng, David Dagan

2013-04-01

402

Recycling Authorizations: Toward Secondary and Approximate Authorizations Model  

E-print Network

1 Recycling Authorizations: Toward Secondary and Approximate Authorizations Model (SAAM) Konstantin 2005 Abstract: In large and complex enterprises, obtaining authorizations could be communicationally. This paper establishes the concept of recycling previously made authorizations for serving new authorization

403

Comparison of the Padť Approximation Method to Perturbative QCD Calculations  

NASA Astrophysics Data System (ADS)

We present a method of estimating perturbative coefficients in quantum field theory using Padť approximants. We test this method on various known quantum chromodynamics (QCD) results, and find that the method works very well.

Samuel, Mark A.; Ellis, John; Karliner, Marek

1995-05-01

404

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

405

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

406

Approximate Self-Consistent Models for Tidally Truncated Star Clusters  

E-print Network

This paper generalises King's models for tidally truncated star clusters by including approximately the non-spherical symmetry of the tidal field and the resulting non-spherical distortion of the cluster.

D. C. Heggie; N. Ramamani

1993-03-19

407

Simple Linear Time Approximation Algorithm for Betweenness Yury Makarychev  

E-print Network

Simple Linear Time Approximation Algorithm for Betweenness Yury Makarychev Toyota Technological will appear in Operations Research Letters (2012), doi:10.1016/j.orl.2012.08.008. 1 #12;there is at least one

Collar, Juan I.

408

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.

409

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

410

Approximating max-min linear programs with local algorithms  

E-print Network

to the global problem? 9 / 24 #12;Local algorithms Definition: (e.g., Naor and Stockmeyer 1995) Distributed: Locally checkable labellings (Naor and Stockmeyer 1995) Dominating set, randomised approximations (Kuhn

Suomela, Jukka

411

Perspective view looking from the northeast, from approximately the same ...  

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

Perspective view looking from the northeast, from approximately the same vantage point as in MD-1109-K-12 - National Park Seminary, Japanese Bungalow, 2801 Linden Lane, Silver Spring, Montgomery County, MD

412

Practical limits of the parabolic approximation for focused ultrasound beams  

NASA Astrophysics Data System (ADS)

Applying the parabolic approximation to the wave equation results in a far simpler and more tractable model for ultrasound propagation. The approximate (Kuznetsov)model assumes that sound propagates predominantly in the axial direction and that the pressure amplitude is a slowly varying function of the axial coordinate. Since the terms "predominantly" and "slowly" ar far from quantitative descriptors, and since recent work shows excellent agreement between simulation and experiment at surprisingly low F-numbers, the presentwork seeks tomore firmly establish the region of validity of this approximation for focused ultrasound sources. To this end, the focused beam of a flat panel transducer is modeled using both the full wave equation and its parabolic approximation. The simulation results are compared as a function of focusing depth and beam steering angle.

Soneson, Joshua E.

2012-10-01

413

Approximation algorithms for combinatorial auctions with complement-free bidders  

Microsoft Academic Search

We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items $m$ and in the number of bidders n, even though the \\

Shahar Dobzinski; Noam Nisan; Michael Schapira

2005-01-01

414

Rational approximation to the Thomas--Fermi equation  

E-print Network

We show that a simple and straightforward rational approximation to the Thomas--Fermi equation provides the slope at origin with unprecedented accuracy. We compare present approach with other available ones.

Francisco M. Fernandez

2008-05-28

415

Applied and computational aspects of nonlinear wavelet approximation  

E-print Network

then study the rate of approximation, i.e. the range of r ‚?? 0 for which there exists C ? 0 such that oe N (f ], j = 0; \\Delta \\Delta \\Delta ; N \\Gamma 1. 3) Linear approximation in a basis: given a basis (e k ) k‚??0 in a Banach space, SN := Span(e 0 ; \\Delta \\Delta \\Delta ; e N ). In all these situations, N

Cohen, Albert

416

Sparse approximate inverse smoothers for geometric and algebraic multigrid  

Microsoft Academic Search

Sparse approximate inverses are considered as smoothers for geometric and algebraic multigrid methods. They are based on the SPAI-Algorithm [M.J.†Grote, T.†Huckle, SIAM J. Sci. Comput. 18 (1997) 838Ė853], which constructs a sparse approximate inverse M of a matrix A, by minimizing I?MA in the Frobenius norm. This leads to a new hierarchy of inherently parallel smoothers: SPAI-0, SPAI-1, and SPAI(?).

Oliver BrŲker; Marcus J. Grote

2002-01-01

417

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

418

Stability analysis of an approximate scheme for moving horizon estimation.  

SciTech Connect

We analyze the stability properties of an approximate algorithm for moving horizon estimation (MHE). The strategy provides instantaneous state estimates and is thus suitable for large-scale feedback control. In particular, we study the interplay between numerical approximation errors and the convergence of the estimator error. In addition, we establish connections between the numerical properties of the Hessian of the MHE problem and traditional observability definitions. We demonstrate the developments through a simulation case study.

Zavala, V. M. (Mathematics and Computer Science)

2010-01-01

419

A Parallel Algorithm for Approximating the Minimum Cycle Cover  

Microsoft Academic Search

We address the problem of approximating a minimum cycle cover in parallel.We give the first efficient parallel algorithm for finding an approximation to aminimum cycle cover. Our algorithm finds a cycle cover whose size is withina factor of O(1 +n log nm+n ) of the minimum sized cover using O(log2n) time on(m + n)= log n processors.1 IntroductionIn this paper

Philip N. Klein; Clifford Stein

1993-01-01

420

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

421

Accurate and monotone approximations of some transcendental functions  

Microsoft Academic Search

A technique for computing monotonicity preserving approximations Fa(x) of a function F(x) is presented. This technique involves computing an extra precise approximation of F(x) that is rounded to produce the value of Fa(x). For example, only a few extra bits of precision are used to make the accurate transcendental functions found on the Cyrix FasMath line of 80387 compatible math

Warren E. Ferguson; T. Brightman

1991-01-01

422

Approximate large N method for lattice chiral models  

NASA Astrophysics Data System (ADS)

An approximation is used that permits one to explicitly solve the two-point Schwinger-Dyson equations of the U(N) lattice chiral models. The approximate solution correctly predicts a phase transition for dimensions d greater than two. For d<=2, the system is in a single disordered phase with a mass gap. The method reproduces known N=? results well for d=1. For d=2, there is a moderate difference with N=? results only in the intermediate coupling constant region.

Samuel, Stuart

1997-08-01

423

A Simple Local-Control Approximation Algorithm for Multicommodity Flow  

Microsoft Academic Search

In this paper, we describe a very simple (1 + ")-approximation algorithm for the multicommodityflow problem. The algorithm runs in time that ispolynomial in N (the number of nodes in the network)and ffl\\\\Gamma1(the closeness of the approximation tooptimal). The algorithm is remarkable in that it ismuch simpler than all known polynomial time flowalgorithms (including algorithms for the special caseof one-commodity

Baruch Awerbuch; Frank Thomson Leighton

1993-01-01

424

Analysis of spectral approximations using prolate spheroidal wave functions  

NASA Astrophysics Data System (ADS)

In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of non-periodic functions in Sobolev spaces. These results serve as an indispensable tool for the analysis of PSWF spectral methods. A PSWF spectral-Galerkin method is proposed and analyzed for elliptic-type equations. Illustrative numerical results consistent with the theoretical analysis are also presented.

Wang, Li-Lian

2010-04-01

425

Problems with the quenched approximation in the chiral limit  

SciTech Connect

In the quenched approximation, loops of the light singlet meson (the [eta][prime]) give rise to a type of chiral logarithm absent in full QCD. These logarithms are singular in the chiral limit, throwing doubt upon the utility of the quenched approximation. In previous work, I summed a class of diagrams, leading to non-analytic power dependencies such as [l angle][anti [psi

Sharpe, S.R.

1992-01-01

426

Approximate models for broken clouds in stochastic radiative transfer theory  

NASA Astrophysics Data System (ADS)

This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called "internal mixing" models assume a combination of the optical properties of the cloud and the clear sky, while the "external mixing" models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum.

Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas

2014-09-01

427

Cluster-enhanced sparse approximation of overlapping ultrasonic echoes.  

PubMed

Ultrasonic pulse-echo methods have been used extensively in non-destructive testing of layered structures. In acoustic measurements on thin layers, the resulting echoes from two successive interfaces overlap in time, making it difficult to assess the individual echo parameters. Over the last decade sparse approximation methods have been extensively used to address this issue. These methods employ a large dictionary of elementary functions (atoms) and attempt to select the smallest subset of atoms (sparsest approximation) that represent the ultrasonic signal accurately. In this paper we propose the cluster-enhanced sparse approximation (CESA) method for estimating overlapping ultrasonic echoes. CESA is specifically adapted to deal with a large number of signals acquired during an ultrasonic scan. It incorporates two principal algorithms. The first is a clustering algorithm, which divides a set of signals comprising an ultrasonic scan into groups of signals that can be approximated by the same set of atoms. The second is a two-stage iterative algorithm, which alternates between update of the atoms associated with each cluster, and re-clustering of the signals according to the updated atoms. Because CESA operates on clusters of signals, it achieves improved results in terms of approximation error and computation time compared with conventional sparse methods, which operate on each signal separately. The superior ability of CESA to approximate highly overlapping ultrasonic echoes is demonstrated through simulation and experiments on adhesively bonded structures. PMID:25643086

Mor, Etai; Aladjem, Mayer; Azoulay, Amnon

2015-02-01

428

A quantum algorithm for additive approximation of Ising partition functions  

E-print Network

We investigate quantum computational complexity of calculating partition functions of Ising models. We construct a quantum algorithm for an additive approximation of Ising partition functions on square lattices. To this end, we utilize the overlap mapping developed by Van den Nest, D\\"ur, and Briegel [Phys. Rev. Lett. 98, 117207 (2007)] and its interpretation through measurement-based quantum computation (MBQC). We specify an algorithmic domain, on which the proposed algorithm works, and an approximation scale, which determines the accuracy of the approximation. We show that the proposed algorithm does a nontrivial task, which would be intractable on any classical computer, by showing the problem solvable by the proposed quantum algorithm are BQP-complete. In the construction of the BQP-complete problem coupling strengths and magnetic fields take complex values. However, the Ising models that are of central interest in statistical physics and computer science consist of real coupling strengths and magnetic fields. Thus we extend the algorithmic domain of the proposed algorithm to such a real physical parameter region and calculate the approximation scale explicitly. We found that the overlap mapping and its MBQC interpretation improves the approximation scale exponentially compared to a straightforward constant depth quantum algorithm. On the other hand, the proposed quantum algorithm also provides us a partial evidence that there exist no efficient classical algorithm for a multiplicative approximation of the Ising partition functions even on the square lattice. This result supports that the proposed quantum algorithm does a nontrivial task also in the physical parameter region.

Akira Matsuo; Keisuke Fujii; Nobuyuki Imoto

2014-05-12

429

Validity of the Aluminum Equivalent Approximation in Space Radiation Shielding  

NASA Technical Reports Server (NTRS)

The origin of the aluminum equivalent shield approximation in space radiation analysis can be traced back to its roots in the early years of the NASA space programs (Mercury, Gemini and Apollo) wherein the primary radiobiological concern was the intense sources of ionizing radiation causing short term effects which was thought to jeopardize the safety of the crew and hence the mission. Herein, it is shown that the aluminum equivalent shield approximation, although reasonably well suited for that time period and to the application for which it was developed, is of questionable usefulness to the radiobiological concerns of routine space operations of the 21 st century which will include long stays onboard the International Space Station (ISS) and perhaps the moon. This is especially true for a risk based protection system, as appears imminent for deep space exploration where the long-term effects of Galactic Cosmic Ray (GCR) exposure is of primary concern. The present analysis demonstrates that sufficiently large errors in the interior particle environment of a spacecraft result from the use of the aluminum equivalent approximation, and such approximations should be avoided in future astronaut risk estimates. In this study, the aluminum equivalent approximation is evaluated as a means for estimating the particle environment within a spacecraft structure induced by the GCR radiation field. For comparison, the two extremes of the GCR environment, the 1977 solar minimum and the 2001 solar maximum, are considered. These environments are coupled to the Langley Research Center (LaRC) deterministic ionized particle transport code High charge (Z) and Energy TRaNsport (HZETRN), which propagates the GCR spectra for elements with charges (Z) in the range I <= Z <= 28 (H -- Ni) and secondary neutrons through selected target materials. The coupling of the GCR extremes to HZETRN allows for the examination of the induced environment within the interior' of an idealized spacecraft as approximated by a spherical shell shield, and the effects of the aluminum equivalent approximation for a good polymeric shield material such as genetic polyethylene (PE). The shield thickness is represented by a 25 g/cm spherical shell. Although one could imagine the progression to greater thickness, the current range will be sufficient to evaluate the qualitative usefulness of the aluminum equivalent approximation. Upon establishing the inaccuracies of the aluminum equivalent approximation through numerical simulations of the GCR radiation field attenuation for PE and aluminum equivalent PE spherical shells, we Anther present results for a limited set of commercially available, hydrogen rich, multifunctional polymeric constituents to assess the effect of the aluminum equivalent approximation on their radiation attenuation response as compared to the generic PE.

Badavi, Francis F.; Adams, Daniel O.; Wilson, John W.

2009-01-01

430

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations  

NASA Astrophysics Data System (ADS)

In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (?), convectivity (V), and damping (?) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of ? under the influence of V and ? based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate ? well in cylindrical geometry, the relationships between heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate ?, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which ?, V, and ? can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and ? in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and ? based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.

van Berkel, M.; Zwart, H. J.; Tamura, N.; Hogeweij, G. M. D.; Inagaki, S.; de Baar, M. R.; Ida, K.

2014-11-01

431

A matching pursuit method for approximating overlapping ultrasonic echoes.  

PubMed

Ultrasonic pulse-echo methods have been used extensively in measuring the thickness of layered structures as well as those of thin adhesive interface layers. When acoustically measuring thin layers, the resulting echoes from two successive interfaces overlap in time, limiting the minimum thickness that can be resolved using conventional pulse-echo techniques. In this paper, we propose a method, named support matching pursuit (SMP), for resolving the individual echoes. The method is based on the concept of sparse signal approximation in an overcomplete dictionary composed of Gabor atoms (elementary functions). Although the dictionary enables highly flexible approximations, it is also overcomplete, which implies that the approximation is not unique. We propose a method for approximation in which each ultrasonic echo is principally represented by a single atom and therefore has a physical interpretation. SMP operates similarly to the sparse matching pursuit (MP) method. It iteratively improves the approximation by adding, at each iteration, a single atom to the solution set. However, our atom selection criterion utilizes the time localization nature of ultrasonic echoes, which causes portions of a multi-echo ultrasonic signal to be composed mainly from a single echo. This leads to accurate approximations in which each echo is characterized by a set of physical parameters that represent the composing ultrasonic echoes. In the current research we compare SMP to other sparse approximation methods such as MP and basis pursuit (BP). We perform simulations and experiments on adhesively bonded structures which clearly demonstrate the superior performance of the SMP method over the MP and BP methods. PMID:20875989

Mor, Etai; Azoulay, Amnon; Aladjem, Mayer

2010-09-01

432

An optimized semiclassical approximation for vibrational response functions  

PubMed Central

The observables of multidimensional infrared spectroscopy may be calculated from nonlinear vibrational response functions. Fully quantum dynamical calculations of vibrational response functions are generally impractical, while completely classical calculations are qualitatively incorrect at long times. These challenges motivate the development of semiclassical approximations to quantum mechanics, which use classical mechanical information to reconstruct quantum effects. The mean-trajectory (MT) approximation is a semiclassical approach to quantum vibrational response functions employing classical trajectories linked by deterministic transitions representing the effects of the radiation-matter interaction. Previous application of the MT approximation to the third-order response function R(3)(t3, t2, t1) demonstrated that the method quantitatively describes the coherence dynamics of the t3 and t1 evolution times, but is qualitatively incorrect for the waiting-time t2 period. Here we develop an optimized version of the MT approximation by elucidating the connection between this semiclassical approach and the double-sided Feynman diagrams (2FD) that represent the quantum response. Establishing the direct connection between 2FD and semiclassical paths motivates a systematic derivation of an optimized MT approximation (OMT). The OMT uses classical mechanical inputs to accurately reproduce quantum dynamics associated with all three propagation times of the third-order vibrational response function. PMID:23556706

Gerace, Mallory; Loring, Roger F.

2013-01-01

433

Variational principles with Padť approximants for tearing mode analysis  

SciTech Connect

Tearing modes occur in several distinct physical regimes, and it is often important to compute the inner layer response for these modes with various effects. There is a need for an approximate and efficient method of solving the inner layer equations in all these regimes. In this paper, we introduce a method of solving the inner layer equations based on using a variational principle with Padť approximants. For all the regimes considered, the main layer equations to be solved are inhomogeneous, and Padť approximants give a convenient and efficient method of satisfying the correct asymptotic behavior at the edge of the layer. Results using this variational principleóPadť approximant method in three of these regimes is presented. These regimes are the constant-? resistive-inertial (RI) regime, the constant-? viscoresistive regime, and the non-constant-? inviscid tearing regime. The last regime includes the constant-? RI regime and the inertial regime. The results show that reasonable accuracy can be obtained very efficiently with Padť approximants having a small number of parameters.

Cole, Andrew J. [Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 (United States)] [Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 (United States); Finn, John M. [Applied Mathematics and Plasma Physics, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87544 (United States)] [Applied Mathematics and Plasma Physics, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87544 (United States)

2014-03-15

434

Efficient solution of parabolic equations by Krylov approximation methods  

NASA Technical Reports Server (NTRS)

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Gallopoulos, E.; Saad, Y.

1990-01-01

435

Exact and Approximate Radiative Transfer in Differentially Moving Media  

NASA Astrophysics Data System (ADS)

Models of the central engines in bright galactic X-ray sources and in active galactic nuclei require accurate solutions of the radiative transfer problem. Full solutions, that accommodate both diffusive and streaming photon transport through differentially moving gas, are usually too time-consuming to be used in radiation hydrodynamic simulations, and modelers therefore resort to approximate transfer schemes such as flux-limited diffusion. Exact solutions are needed to establish the accuracy and reliability of these schemes. In this paper we present exact solutions to the spherically symmetric, time-independent radiative transfer problem in differentially moving media. We compare these with solutions of truncated transfer equations, in which only terms of low order in the flow speed ? = ?c have been retained. We find that for mildly relativistic inflows, solutions of the O(?2) radiative transfer equation closely approximate the exact solutions, but that the O(?) transfer equation fails to provide a good approximation, since it cannot adequately describe radiation trapping. Exact solutions are also compared with approximate solutions obtained through flux-limited diffusion and variable Eddington factor approaches to the transfer problem. We find that both methods provide good approximations to the exact solutions but only if they are derived from transfer equations in which terms of order ?2 or higher have been retained. The O(?2) stationary-frame flux-limited diffusion method we present here is thus valid over a much wider range of conditions than existing O(?) stationary-frame methods.

Yin, Wei-Wei; Miller, Guy S.

1995-08-01

436

Rational trigonometric approximations using Fourier series partial sums  

NASA Technical Reports Server (NTRS)

A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented.

Geer, James F.

1993-01-01

437

?-convergence Approximation of Fracture and Cavitation in Nonlinear Elasticity  

NASA Astrophysics Data System (ADS)

Our starting point is a variational model in nonlinear elasticity that allows for cavitation and fracture that was introduced by Henao and Mora-Corral (Arch Rational Mech Anal 197:619-655, 2010). The total energy to minimize is the sum of the elastic energy plus the energy produced by crack and surface formation. It is a free discontinuity problem, since the crack set and the set of new surface are unknowns of the problem. The expression of the functional involves a volume integral and two surface integrals, and this fact makes the problem numerically intractable. In this paper we propose an approximation (in the sense of ?-convergence) by functionals involving only volume integrals, which makes a numerical approximation by finite elements feasible. This approximation has some similarities to the Modica-Mortola approximation of the perimeter and the Ambrosio-Tortorelli approximation of the Mumford-Shah functional, but with the added difficulties typical of nonlinear elasticity, in which the deformation is assumed to be one-to-one and orientation-preserving.

Henao, Duvan; Mora-Corral, Carlos; Xu, Xianmin

2014-12-01

438

Beam normal spin asymmetry in the quasi-RCS approximation  

E-print Network

The two-photon exchange contribution to the single spin asymmetries with the spin orientation normal to the reaction plane is discussed for elastic electron-proton scattering in the equivalent photon approximation. In this case, hadronic part of the two-photon exchange amplitude describes real Compton scattering (RCS). We show that in the case of the beam normal spin asymmetry, this approximation selects only the photon helicity flip amplitudes of RCS. At low energies, we make use of unitarity and estimate the contribution of the $\\pi N$ multipoles to the photon helicity flip amplitudes. In the Regge regime, QRCS approximation allows for a contribution from two pion exchange, and we provide an estimate of such contributions. We furthermore discuss the possibility of the quark and gluon GPD's contributions in the QRCS kinematics.

Mikhail Gorchtein

2005-12-16

439

Beam normal spin asymmetry in the quasireal Compton scattering approximation  

SciTech Connect

The two-photon exchange contribution to the single spin asymmetries with the spin orientation normal to the reaction plane is discussed for elastic electron-proton scattering in the equivalent photon approximation. In this case, the hadronic part of the two-photon exchange amplitude describes real Compton scattering (RCS). We show that in the case of the beam normal spin asymmetry this approximation selects only the photon helicity flip amplitudes of RCS. At low energies, we make use of unitarity and estimate the contribution of the {pi}N multipoles to the photon helicity flip amplitudes. In the Regge regime, the quasi-RCS (QRCS) approximation allows for a contribution from two-pion exchange, and we provide an estimate of such contributions.

Gorchtein, M. [Genoa University, Department of Physics, I-16146 Genoa, Italy and California Institute of Technology, Pasadena, California 91125 (United States)

2006-05-15

440

Integral approximants for functions of higher monodromic dimension  

SciTech Connect

In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.

Baker, G.A. Jr.

1987-01-01

441

Natural orbit approximations in single power-law potentials  

E-print Network

In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here I explore several extensions of these approximations to improve accuracy, especially for nearly radial orbits. 1) It is found that moderately improved orbital fits can be achieved with higher order perturbation expansions (in eccentricity), with the addition of `harmonic' terms to the solution. 2) Alternately, a matching of the extreme radial excursions of an orbit can be imposed, and a more accurate estimate of the eccentricity parameter is obtained. However, the error in the precession frequency is usually increased. 3) A correction function of small magnitude corrects the frequency problem. With this correction, even first order approximations yield excellent fits at quite high eccentricity over a range of potential indices that includes flat and falling rotation curve cases. 4) Adding a first harmonic term to fit the breadt...

Struck, Curtis

2014-01-01

442

Corrections to Eikonal Approximation for Nuclear Scattering at Medium Energies  

E-print Network

The upcoming Facility for Rare Isotope Beams (FRIB) at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University has reemphasized the importance of accurate modeling of low energy nucleus-nucleus scattering. Such calculations have been simplified by using the eikonal approximation. As a high energy approximation, however, its accuracy suffers for the medium energy beams that are of current experimental interest. A prescription developed by Wallace \\cite{Wallace:1971zz,Wallace:1973iu} that obtains the scattering propagator as an expansion around the eikonal propagator (Glauber approach) has the potential to extend the range of validity of the approximation to lower energies. Here we examine the properties of this expansion, and calculate the first-, second-, and third-order corrections for the scattering of a spinless particle off of a ${}^{40}$Ca nucleus, and for nuclear breakup reactions involving ${}^{11}$Be. We find that, including these corrections extends the lower bound of th...

Buuck, Micah

2014-01-01

443

Dual methods and approximation concepts in structural synthesis  

NASA Technical Reports Server (NTRS)

Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins.

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

444

Fourth-post-Newtonian exact approximation to general relativity  

SciTech Connect

An approximation to general relativity is presented that agrees with the Einstein field equations up to and including the fourth post-Newtonian (PN) order. This approximation is formulated in a fully constrained scheme: all involved equations are explicitly elliptic except the wave equation that describes the two independent degrees of freedom of the gravitational field. The formalism covers naturally the conformal-flat condition approach by Isenberg, Wilson, and Mathews and the improved second PN-order exact approach conformal-flat condition plus. For stationary configurations, like Kerr black holes, agreement with general relativity is achieved even through 5PN order. In addition, a particularly interesting 2PN-exact waveless approximation is analyzed in detail, which results from imposing more restrictive conditions. The proposed scheme can be considered as a further development on the waveless approach suggested by Schaefer and Gopakumar.

Brizuela, David; Schaefer, Gerhard [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet, Max-Wien-Platz 1, 07743 Jena (Germany)

2010-04-15

445

Value Function Approximation in Zero-Sum Markov Games  

E-print Network

This paper investigates value function approximation in the context of zero-sum Markov games, which can be viewed as a generalization of the Markov decision process (MDP) framework to the two-agent case. We generalize error bounds from MDPs to Markov games and describe generalizations of reinforcement learning algorithms to Markov games. We present a generalization of the optimal stopping problem to a two-player simultaneous move Markov game. For this special problem, we provide stronger bounds and can guarantee convergence for LSTD and temporal difference learning with linear value function approximation. We demonstrate the viability of value function approximation for Markov games by using the Least squares policy iteration (LSPI) algorithm to learn good policies for a soccer domain and a flow control problem.

Michail G. Lagoudakis; Ronald Parr

2002-01-01

446

Computer-generated hologram using an approximate Fresnel integral  

NASA Astrophysics Data System (ADS)

We propose a fast calculation method of a computer-generated hologram (CGH) using an approximate Fresnel integral. Calculating a Fresnel integral requires the calculation of a numerical integral, which consumes computational time. When generating a CGH using a Fresnel integral, it is difficult to calculate it in real-time. Instead of a Fresnel integral, we use an approximate Fresnel integral without a numerical integral. In addition, we use an look-up table with small memory and multi-thread technology on a CPU in order to accelerate the generation of the approximate Fresnel integral. We show a numerical experiment that enables a CGH from a simple scene consisting of rectangular patches to be calculated in real-time on a PC.

Oikawa, Minoru; Shimobaba, Tomoyoshi; Masuda, Nobuyuki; Ito, Tomoyoshi

2011-07-01

447

Approximation Methods Applied to the Pullen-Edmonds Hamiltonian  

NASA Astrophysics Data System (ADS)

In this work we have studied the Hamburger theorem sequence which uses the moments of the Hamiltonian evaluated for a particular state, as well as a variety of approximation schemes derivable from the t-expansion and also a Lanczos tridiagonalization scheme. Each of these calculational schemes has been applied to the well-studied Pullen-Edmonds Hamiltonian for the representation of a 2D isotropic harmonic oscillator with an interaction potential of the form x^2y^2. We further investigate truncated approximations from moments, matrix truncations relative to the natural 2D simple harmonic oscillator states |nxny>, and a class of analytic truncations in the spirit of Feenberg perturbation theory. Each of these different approximation schemes will be compared with respect to effort, accuracy, and calculational problems.

Murawski, R. K.; Erickson, J.; Bowen, S. P.; Fessatidis, V.; Mancini, J. D.

2010-03-01

448

Space-angle approximations in the variational nodal method.  

SciTech Connect

The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared.

Lewis, E. E.; Palmiotti, G.; Taiwo, T.

1999-03-12

449

Calculation of Tensor Susceptibility Beyond Rainbow-Ladder Approximation  

NASA Astrophysics Data System (ADS)

In this paper, we extend the calculation of tensor vacuum susceptibility in the rainbow-ladder approximation of the Dyson-Schwinger (DS) approach in Shi et al. (Phys Lett B 639:248, 2006) to that of employing the Ball-Chiu (BC) vertex. The dressing effect of the quark-gluon vertex on the tensor vacuum susceptibility is investigated. Our results show that compared with its rainbow-ladder approximation value, the tensor vacuum susceptibility obtained in the BC vertex approximation is reduced by about 10%. This shows that the dressing effect of the quark-gluon vertex is not large in the calculation of the tensor vacuum susceptibility in the DS approach.

Shi, Yuan-Mei; Zhu, Hui-Xia; Sun, Wei-Min; Zong, Hong-Shi

2010-08-01

450

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems  

NASA Technical Reports Server (NTRS)

An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

451

Antihydrogen production and accuracy of the equivalent photon approximation  

NASA Astrophysics Data System (ADS)

The production of antihydrogen in flight in pĮ-nucleus collisions is calculated theoretically in the plane wave Born approximation (which is equivalent to the straight line semiclassical approximation). Antihydrogen has been produced in this way at CERN LEAR and is presently studied at Fermilab at various pĮ energies. Dirac wave functions for the leptons are used, taking first order (Z?) corrections into account. Analytical results are obtained for differential cross sections. Total cross sections are obtained by numerical integration. The dependence on the transverse momentum transfer is studied and the accuracy of the equivalent photon approximation and a recent variant by Munger, Brodsky, and Schmidt is discussed as a function of beam energy.

Bertulani, C. A.; Baur, G.

1998-08-01

452

Approximate Multi-Parameter Inverse Scattering Using Pseudodifferential Scaling  

NASA Astrophysics Data System (ADS)

I propose a computationally efficient method to approximate the inverse of the normal operator arising in the multi-parameter linearized inverse problem for reflection seismology in two and three spatial dimensions. Solving the inverse problem using direct matrix methods like Gaussian elimination is computationally infeasible. In fact, the application of the normal operator requires solving large scale PDE problems. However, under certain conditions, the normal operator is a matrix of pseudodifferential operators. This manuscript shows how to generalize Cramer's rule for matrices to approximate the inverse of a matrix of pseudodifferential operators. Approximating the solution to the normal equations proceeds in two steps: (1) First, a series of applications of the normal operator to specific permutations of the right hand side. This step yields a phase-space scaling of the solution. Phase space scalings are scalings in both physical space and Fourier space. Second, a correction for the phase space scaling. This step requires applying the normal operator once more. The cost of approximating the inverse is a few applications of the normal operator (one for one parameter, two for two parameters, six for three parameters). The approximate inverse is an adequately accurate solution to the linearized inverse problem when it is capable of fitting the data to a prescribed precision. Otherwise, the approximate inverse of the normal operator might be used to precondition Krylov subspace methods in order to refine the data fit. I validate the method on a linearized version of the Marmousi model for constant density acoustics for the one-parameter problem. For the two parameter problem, the inversion of a variable density acoustics layered model corroborates the success of the proposed method. Furthermore, this example details the various steps of the method. I also apply the method to a 1D section of the Marmousi model to test the behavior of the method on complex two-parameter layered models.

Nammour, Rami

453

Quantum algorithm for an additive approximation of Ising partition functions  

NASA Astrophysics Data System (ADS)

We investigate quantum-computational complexity of calculating partition functions of Ising models. We construct a quantum algorithm for an additive approximation of Ising partition functions on square lattices. To this end, we utilize the overlap mapping developed by M. Van den Nest, W. DŁr, and H. J. Briegel [Phys. Rev. Lett. 98, 117207 (2007), 10.1103/PhysRevLett.98.117207] and its interpretation through measurement-based quantum computation (MBQC). We specify an algorithmic domain, on which the proposed algorithm works, and an approximation scale, which determines the accuracy of the approximation. We show that the proposed algorithm performs a nontrivial task, which would be intractable on any classical computer, by showing that the problem that is solvable by the proposed quantum algorithm is BQP-complete. In the construction of the BQP-complete problem coupling strengths and magnetic fields take complex values. However, the Ising models that are of central interest in statistical physics and computer science consist of real coupling strengths and magnetic fields. Thus we extend the algorithmic domain of the proposed algorithm to such a real physical parameter region and calculate the approximation scale explicitly. We found that the overlap mapping and its MBQC interpretation improve the approximation scale exponentially compared to a straightforward constant-depth quantum algorithm. On the other hand, the proposed quantum algorithm also provides partial evidence that there exist no efficient classical algorithm for a multiplicative approximation of the Ising partition functions even on the square lattice. This result supports the observation that the proposed quantum algorithm also performs a nontrivial task in the physical parameter region.

Matsuo, Akira; Fujii, Keisuke; Imoto, Nobuyuki

2014-08-01

454

Approximation in control of flexible structures, theory and application  

NASA Technical Reports Server (NTRS)

The sense in which the feedback control law based on an approximate finite dimensional model of a continuous structure approximates a control law which is optimal for the distributed, or infinite dimensional, model of the structure is studied. From the analysis of the various control and stability issues associated with this basis question, useful information for designing finite dimensional compensators which produce near-optimal performance in infinite dimensional systems is gained. Some of the important predictions that can be made about large-order finite dimensional control laws, using the theory of infinite dimensional Riccati equations are indicated.

Gibson, J. S.

1983-01-01

455

On the approximation of crack shapes found during inservice inspection  

SciTech Connect

This paper addresses the characterization of axial internal flaw found during inservice inspection of a pipe. J-integral distribution for various flaw shapes is obtained using line spring finite, element method. The peak J-value and its distribution across the crack is found to be characteristic feature of each shape. The triangular shape yields peak J-value away from the center, the point of depth. The elliptic approximation results in large overestimate of J-value for unsymmetric flaws. Triangular approximation is recommended for such flaws so that further service can be obtained from the component.

Bhate, S.R.; Chawla, D.S.; Kushwaha, H.S. [Bhabha Atomic Research Centre, Bombay (India)] [and others

1997-04-01

456

Compressibility Corrections to Closure Approximations for Turbulent Flow Simulations  

SciTech Connect

We summarize some modifications to the usual closure approximations for statistical models of turbulence that are necessary for use with compressible fluids at all Mach numbers. We concentrate here on the gradient-flu approximation for the turbulent heat flux, on the buoyancy production of turbulence kinetic energy, and on a modification of the Smagorinsky model to include buoyancy. In all cases, there are pressure gradient terms that do not appear in the incompressible models and are usually omitted in compressible-flow models. Omission of these terms allows unphysical rates of entropy change.

Cloutman, L D

2003-02-01

457

Delta-function Approximation SSC Model in 3C 273  

NASA Astrophysics Data System (ADS)

We obtain an approximate analytical solution using ? approximate calculation on the traditional one-zone synchrotron self-Compton (SSC) model. In this model, we describe the electron energy distribution by a broken power-law function with a sharp cut-off, and non-thermal photons are produced by both synchrotron and inverse Compton scattering of synchrotron photons. We calculate the radiation energy spectrum of electrons by the ? function. We apply this model to the multi-wavelength Spectral Energy Distributions (SED) of the 3C 273 in different states, and obtain excellent fits to the observed spectra of this source.

Kang, S. J.; Zheng, Y. G.; Wu, Q.

2014-12-01

458

Semigroup theory and numerical approximation for equations in linear viscoelasticity  

NASA Technical Reports Server (NTRS)

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Fabiano, R. H.; Ito, K.

1990-01-01

459

Nonlinear acoustic behavior at a caustic - An approximate analytical solution  

NASA Technical Reports Server (NTRS)

The present paper discusses an approximate analytical solution to the nonlinear behavior of a discontinuous acoustic signal near a caustic. The Seebass transformation (1970) is refined to provide results which satisfy the governing equation to any prescribed accuracy, except across the shock wave produced by reflection of the simple wave at the caustic. The solution is approximate in the sense that the basic equation is satisfied wherever the solution is continuous but can satisfy only one of the two jump conditions at the reflected shock. The results give essential geometric features of the exact solution and provide a quantitative estimate of the strength of the so-called superboom.

Gill, P. M.; Seebass, A. R.

1975-01-01

460

Approximated maximum likelihood estimation in multifractal random walks  

NASA Astrophysics Data System (ADS)

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.64.026103 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the r computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.

LÝvsletten, O.; Rypdal, M.

2012-04-01

461

Exponentially accurate approximations to piece-wise smooth periodic functions  

NASA Technical Reports Server (NTRS)

A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.

Greer, James; Banerjee, Saheb

1995-01-01

462

Approximations to large amplitude solitary waves on nonlinear electrical lattices  

NASA Astrophysics Data System (ADS)

In this paper we describe an approximate method to characterise solitary wave solutions of nonlinear lattice equations. It is based upon one and two point Padť approximations to a series of the real exponential travelling wave solutions of the underlying dispersive system. The theory is applied to an example of a lattice system which models an experimental nonlinear transmission line and the results obtained are consistent with numerical simulations even for relatively large amplitude solitary waves. The speed-amplitude relation is investigated and compared with the derived using quasi-continuum methods.

Hicks, Andrew C.; Common, Alan K.; Sobhy, Mohanned I.

463

Intermediate boundary conditions for LOD, ADI and approximate factorization methods  

NASA Technical Reports Server (NTRS)

A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.

Leveque, R. J.

1985-01-01

464

Some special series in ultraspherical polynomials and their approximation properties  

NASA Astrophysics Data System (ADS)

Using the explicit form of a limiting ultraspherical series \\sumk=0^? f_k-1\\widehat P_k-1(x), which was established by us in [1], we consider new, more general, special series in ultraspherical Jacobi polynomials and their approximation properties. We show that as an approximation tool, these series compare favourably with Fourier series in Jacobi polynomials. At the same time, they admit a simple construction, which in important particular cases enables one to use the fast Fourier transform for the numerical realization of their partial sums.

Sharapudinov, I. I.

2014-10-01

465

Approximate thresholds of interval mapping tests for QTL detection.  

PubMed

A general method is proposed for calculating approximate thresholds of interval mapping tests for quantitative trait loci (QTL) detection. Simulation results show that this method, when applied to backcross and F2 populations, gives good approximations and is useful for any situation. Programs which calculate these thresholds for backcross, recombinant inbreds and F2 for any given level and any chromosome with any given distribution of codominant markers were written in Fortran 77 and are available under request. The approach presented here could be used to obtain, after suitable calculations, thresholds for most segregating populations used in QTL mapping experiments. PMID:8001790

RebaÔ, A; Goffinet, B; Mangin, B

1994-09-01

466

Rational-spline approximation with automatic tension adjustment  

NASA Technical Reports Server (NTRS)

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline.

Schiess, J. R.; Kerr, P. A.

1984-01-01

467

Decoupling approximation design using the peak to peak gain  

NASA Astrophysics Data System (ADS)

Linear system design for accurate decoupling approximation is examined using the peak to peak gain of the error system. The design problem consists in finding values of system parameters to ensure that this gain is small. For this purpose a computationally inexpensive upper bound on the peak to peak gain, namely the star norm, is minimized using a stochastic method. Examples of the methodology's application to tensegrity structures design are presented. Connections between the accuracy of the approximation, the damping matrix, and the natural frequencies of the system are examined, as well as decoupling in the context of open and closed loop control.

Sultan, Cornel

2013-04-01

468

Dynamical nonlocal coherent-potential approximation for itinerant electron magnetism.  

PubMed

A dynamical generalisation of the nonlocal coherent-potential approximation is derived based upon the functional integral approach to the interacting electron problem. The free energy is proven to be variational with respect to the self-energy provided a self-consistency condition on a cluster of sites is satisfied. In the present work, calculations are performed within the static approximation and the effect of the nonlocal physics on the formation of the local moment state in a simple model is investigated. The results reveal the importance of the dynamical correlations. PMID:25351678

Rowlands, D A; Zhang, Yu-Zhong

2014-11-26

469

Approximate minimum-cost multicommodity flows in( ? ?2 KNM ) timetime  

Microsoft Academic Search

We show that an ?-approximate solution of the cost-constrainedK-commodity flow problem on anN-nodeM-arc network,G can be computed by sequentially solving O(K(?\\u000a ?2+logGK) logGM log (G?\\u000a ?1\\u000a GK)) single-commodity minimum-cost flow problems on the same network. In particular, an approximate minimum-cost multicommodity\\u000a flow can be computed in\\u000a $$\\\\tilde O$$\\u000a (G?\\u000a ?2\\u000a GKNM) running time, where the notation ’(∑) means ďup to

Michael D. Grigoriadis; Leonid G. Khachiyan

1996-01-01

470

Univariate approximate integration via nested Taylor multivariate function decomposition  

NASA Astrophysics Data System (ADS)

This work is based on the idea of nesting one or more Taylor decompositions in the remainder term of a Taylor decomposition of a function. This provides us with a better approximation quality to the original function. In addition to this basic idea each side of the Taylor decomposition is integrated and the limits of integrations are arranged in such a way to obtain a universal [0;1] interval without losing from the generality. Thus a univariate approximate integration technique is formed at the cost of getting multivariance in the remainder term. Moreover the remainder term expressed as an integral permits us to apply Fluctuationlessness theorem to it and obtain better results.

GŁrvit, Ercan; Baykara, N. A.

2014-12-01

471

Improved Approximations for Guarding 1.5-Dimensional Terrains  

E-print Network

We present a 4-approximation algorithm for the problem of placing a fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the currently best approximation factor of 5. Our method is based on rounding the linear programming relaxation of the corresponding covering problem. Besides the simplicity of the analysis, which mainly relies on decomposing the constraint matrix of the LP into totally balanced matrices, our algorithm, unlike previous work, generalizes to the weighted and partial versions of the basic problem.

Elbassioni, K; Mestre, J; Severdija, D

2008-01-01

472

Ternary approximating non-stationary subdivision schemes for curve design  

NASA Astrophysics Data System (ADS)

In this paper, an algorithm has been introduced to produce ternary 2m-point (for any integer m ? 1) approximating non-stationary subdivision schemes which can generate the linear spaces spanned by {1; cos( ?.); sin( ?.)}. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the schemes. The proposed algorithm can be consider as the non-stationary counter part of the 2-point and 4-point existing ternary stationary approximating schemes, for different values of m. Moreover, the proposed algorithm has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines.

Siddiqi, Shahid S.; Younis, Muhammad

2014-12-01

473

Exact and approximate arithmetic in an Amazonian indigene group.  

PubMed

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukķ, an Amazonian language with a very small lexicon of number words. Although the Mundurukķ lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. PMID:15486303

Pica, Pierre; Lemer, Cathy; Izard, Vťronique; Dehaene, Stanislas

2004-10-15

474

Approximate Coverage in Wireless Sensor Networks Yuzhen Liu Weifa Liang  

E-print Network

1 Approximate Coverage in Wireless Sensor Networks Yuzhen Liu Weifa Liang Department of Computer and inexpensive wireless sensors. Sensor networks have received significant attention due to their potential it possible to construct compact and inexpensive wireless sensors. Networks formed by such sensors, termed

Liang, Weifa

475

PERSISTENCE APPROXIMATION PROPERTY AND CONTROLLED OPERATOR K-THEORY  

E-print Network

PERSISTENCE APPROXIMATION PROPERTY AND CONTROLLED OPERATOR K-THEORY HERV¬īE OYONO-OYONO AND GUOLIANG of quantitative K-theory 4 1.2. Quantitative objects 6 1.3. Controlled morphisms 7 1.4. Control exact sequences 8 1.5. KK-theory and controlled morphisms 11 1.6. Quantitative assembly maps 13 2. Persistence

Paris-Sud XI, Université de

476

Effects of Global Illumination Approximations on Material Appearance (Supplementary Material)  

E-print Network

of the test object was approximately 1.2 metres. A 3ds Max model of the scene is included with the auxiliary an unobstructed view of the interior. Note that this image was rendered in 3ds Max using a different rendering material (file stimulus2.max). A view of the scene from the outside of the room is shown in Figure 1

Bala, Kavita

477

An Approximative Criterion for the Potential of Energetic Reasoning  

E-print Network

An Approximative Criterion for the Potential of Energetic Reasoning Timo Berthold1, Stefan Heinz1 jschulz@math.tu-berlin.de Abstract. Energetic reasoning is one of the most powerful propagation algorithms present an implementation of energetic reasoning that employs this condition and that can

Nabben, Reinhard

478

Gluon Condensate in Pion Superfluid beyond Mean Field Approximation  

E-print Network

We study gluon condensate in a pion superfluid, through calculating the equation of state of the system in the Nambu-Jona-Lasinio model. While in mean field approximation the growing pion condensate leads to an increasing gluon condensate, meson fluctuations reduce the gluon condensate and the broken scalar symmetry can be smoothly restored at finite isospin density.

Yin Jiang; Pengfei Zhuang

2010-12-10

479

SESHADRI CONSTANTS, DIOPHANTINE APPROXIMATION, AND ROTH'S THEOREM FOR ARBITRARY VARIETIES  

E-print Network

Spec(k). The Bombieri-Lang conjecture predicts that if X is of general type then the k-points of X = 2 for irrational algebraic x R. The invariant x(L). In §2 we generalize the approximation exponent

Roth, Mike

480

Combinatorial Approximation Algorithms for Generalized Flow Problems \\Lambda  

E-print Network

, the multicommodity maximum­flow, and the multicommodity nonnegative­cost minimum­cost flow problems. For all multipliers' representation. Also, the gener­ alized concurrent flow and the generalized multicommodityCombinatorial Approximation Algorithms for Generalized Flow Problems \\Lambda Jeffrey D. Oldham y

Pratt, Vaughan

481

An approximation formula for a class of Markov reliability models  

NASA Technical Reports Server (NTRS)

A way of considering a small but often used class of reliability model and approximating algebraically the systems reliability is shown. The models considered are appropriate for redundant reconfigurable digital control systems that operate for a short period of time without maintenance, and for such systems the method gives a formula in terms of component fault rates, system recovery rates, and system operating time.

White, A. L.

1984-01-01

482

Managing Approximate Models in Evolutionary Aerodynamic Design Optimization  

E-print Network

algorithm to a wrong solution. To address this problem, individual and generation based evolution control correctly. A framework for managing approximate models in generation­based evo­ lution control is proposed optimiza­ tion problems such as preliminary turbine design [3], turbine blade design [4] and multi

Coello, Carlos A. Coello

483

APPROXIMATIVE METHOD FOR THE INVERSION OF THE RIESZ POTENTIAL OPERATOR  

E-print Network

(·)(Rn) with variable exponent p(x), the method of hypersingular integrals for the same goals was used in [1] where of hypersingular integrals works for complex values of only in the case 0 of the approximation in- version, in comparison with the direct inversion by hypersingular integrals, is in a different

Samko, Stefan

484

Triangulation Based Approximation Model for Agent Positioning Problem  

NASA Astrophysics Data System (ADS)

In this paper, we propose a triangulation based function approximation model for agent positioning problem in the dynamic environments. In many problems of the real-world multi-agent/robot domain, a position of each agent is an important factor to affect agents' performance. Because the real-world problem is generally dynamic, a suitable position for each agent should be determined according to the current status of the environment. First, we formalized this issue as a function approximation that maps from state variables to a desirable position of each agent, and proposed a function approximation model using Delaunay triangulation. This method is simple, fast and accurate, so that it can be implemented for real-time and scalable problems. In our previous works, our model showed very high approximation accuracy and good generalization capability for two-dimensional input. However, two-dimensional input is insufficient for more generic problems. Therefore, we extend our previous model so that multi-dimensional input can be taken. The extended model forms tree structure that each node represents a local input space. This structure enables us to maintain the multi-dimensional input space flexibly. The previous model is directly used in each local input space. Therefore, each local input space keeps high accuracy and generalization capability. We implemented the extended model and performed the experiments to evaluate its performance. The result shows our extended model can take the multi-dimensional input adequately.

Akiyama, Hidehisa; Noda, Itsuki

485

The Quenched Approximation in Health and in Sickness  

E-print Network

We present results for physical quantities computed in quenched chiral perturbation theory and compare them with the corresponding unquenched expressions. We also point out an apparent theoretical problem of the quenched approximation. latex, file espcrc2.sty needed (appended at the end: search for espcrc2.sty).

Claude Bernard; Maarten Golterman

1992-11-06

486

Approximating Edit Distance Efficiently Ziv Bar-Yossef  

E-print Network

Levenshtein distance), which is the minimum number of character insertions, deletions, and substitutionsApproximating Edit Distance Efficiently Ziv Bar-Yossef T. S. Jayram Robert Krauthgamer Ravi Kumar Abstract Edit distance has been extensively studied for the past several years. Nevertheless, no linear

Krauthgamer, Robert

487

Approximate Approaches to the One-Dimensional Finite Potential Well  

ERIC Educational Resources Information Center

The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (m[subscript i]) is taken to be distinct from mass outside (m[subscript o]). A relevant parameter is the massÖ

Singh, Shilpi; Pathak, Praveen; Singh, Vijay A.

2011-01-01

488

A 2-Approximation for the Minimum Duplication Speciation Problem  

E-print Network

A 2-Approximation for the Minimum Duplication Speciation Problem AI¨DA OUANGRAOUA,1 KRISTER M trees, spanning a given set of species, find a first speciation which splits these species into two subsets and minimizes the number of gene duplications that happened before this speciation. We call

Chauve, Cedric

489

On Approximation Preserving Reductions: Complete Problems and Robust Measures  

E-print Network

, s is a corresponding optimal solution, and c is the cost function, the quality of s is taken to be ¬Ķr(s) = c(s) - c(s) c(s) (for definiteness, we assume we are dealing with a minimization problem). An approximation

Orponen, Pekka

490

Ecient Approximation Algorithms for the Hamming Center Problem  

E-print Network

E√?cient Approximation Algorithms for the Hamming Center Problem Leszek G#24;asieniec #3; Jesper Jansson y Andrzej Lingas z Abstract The Hamming center problem for a set S of k binary strings, each of length n, asks for a binary string #12; of length n that minimizes the maximum Hamming distance between

491

A Simple Geometric Approach to Approximating the Gini Coefficient  

ERIC Educational Resources Information Center

The author shows how a quick approximation of the Lorenz curve's Gini coefficient can be calculated empirically using numerical data presented in cumulative income quintiles. When the technique here was used to estimate 621 income quintile/Gini coefficient observations from the Deninger and Squire/World Bank data set, this approach performedÖ

Kasper, Hirschel; Golden, John

2008-01-01

492

On the mathematical treatment of the Born-Oppenheimer approximation  

NASA Astrophysics Data System (ADS)

Motivated by the paper by Sutcliffe and Woolley ["On the quantum theory of molecules," J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

Jecko, Thierry

2014-05-01

493

An Equivalence Between Sparse Approximation And Support Vector Machines  

Microsoft Academic Search

Abstract This paper shows a relationship between two di?erent approximation techniques: the Support Vector Machines (SVM), proposed by V Vapnik (1995), and a sparse ap - proximation scheme that resembles the Basis Pursuit De - Noising algorithm (Chen, 1995; Chen, Donoho and Saunders, 1995) SVM is a technique which can be derived from the Structural Risk Minimization Principle (Vapnik, 1982)

Federico Girosi

1998-01-01

494

Third Order Asymptotic Model: Exponential And Location Type Approximations  

Microsoft Academic Search

This paper develops some basic asymptotictheory for such a simple statistical model. For this special case we determine canonical versions of thebest approximation at a data point, by an exponential type or location type model. We also examinethe standard parameterization-invariant test quantities for these models and determine the connectionsamong them. The results lead to some simple proofs for key inference

F. Abebe; S. Cakmak; P. k. Cheah; D. a. s. Fraser

1995-01-01

495

Sensitivity, Approximation, and Uncertainty in Power System Dynamic Simulation  

Microsoft Academic Search

Parameters of power system models, in particular load models, are seldom known exactly, yet dynamic security assessment relies upon simulation of those uncertain models. This paper proposes a computationally feasible approach to assessing the influence of uncertainty in simulations of power system dynamic behavior. It is shown that trajectory sensitivities can be used to generate accurate first-order approximations of trajectories

Ian A. Hiskens; J. Alseddiqui

2006-01-01

496

Self Assembly of Soft Matter Quasicrystals and Their Approximants  

NASA Astrophysics Data System (ADS)

The discovery of soft-matter quasicrystals (QCs) and their approximants [1-4] hints at a unique thermodynamic mechanism underlying their stability. In the past, specific interaction potentials have been contrived to stabilize QCs and their approximants in computer simulations, but such interactions are difficult to achieve in colloidal systems. Here, we use molecular simulation to demonstrate an alternative approach for assembling dodecagonal QCs and their approximants based solely on particle functionalization and shape [5]. Our approach replaces complex energetic interactions with simpler-to-achieve bonded and excluded-volume interactions, encouraging the formation of structures with low surface contact area, including non-close-packed and polytetrahedral structures. We argue that this mechanism can be widely exploited to assemble QCs and approximants in colloidal systems, and may further elucidate the formation of soft matter QCs in experiment [1-4]. [4pt] [1] G. Ungar, et al., Science 299 (2003) [0pt] [2] X. Zeng, et al., Nature 428, (2004) [0pt] [3] S. Lee, M.J. Bluemle, F.S. Bates, Science, 330 (2010) [0pt] [4] S. Fischer, et al. Proc. Natl. Acad. Sci., 108, (2011) [0pt] [5] C.R. Iacovella, A.S. Keys, S.C. Glotzer, Proc. Natl. Acad. Sci., in press (2011) arXiv:1102.5589

Iacovella, Christopher; Keys, Aaron; Glotzer, Sharon

2012-02-01

497

1. ONTARIO MINE IS LOCATED ALONG FAR RIGHT ROADWAY APPROXIMATELY ...  

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

1. ONTARIO MINE IS LOCATED ALONG FAR RIGHT ROADWAY APPROXIMATELY 100 YARDS FROM CAMERA POSITION. TAILING PILE DOWN SLOPE AND WEST OF CAMERA POSITION IN ID-31-C-44. - Florida Mountain Mining Sites, Ontario Mine, Northwest side of Florida Mountain, Silver City, Owyhee County, ID

498

2. UPPER NOTTINGHAM MINE, WOODEN BOXES. BOXES ARE LOCATED APPROXIMATELY ...  

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

2. UPPER NOTTINGHAM MINE, WOODEN BOXES. BOXES ARE LOCATED APPROXIMATELY 10 YARDS TO THE RIGHT AND DOWNSLOPE OF THE ADIT IN ID-31-F-1. CAMERA IS POINTED EAST-SOUTHEAST. - Florida Mountain Mining Sites, Upper Nottingham Mine, West face of Florida Mountain, head of Jacobs Gulch, Silver City, Owyhee County, ID

499

On Exact and Approximate Interpolation of Sparse Rational Functions*  

E-print Network

On Exact and Approximate Interpolation of Sparse Rational Functions* Erich Kaltofen Department vector recovery itself. Finally, one can deploy the sparse rational function interpolation algorithm the numerator from the denominator of a multivariate rational function can be combined with sparse multivariate

Kaltofen, Erich

500

Stochastic Approximation Methods for Latent Regression Item Response Models  

ERIC Educational Resources Information Center

This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariatesÖ

von Davier, Matthias; Sinharay, Sandip

2010-01-01