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1

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

NASA Astrophysics Data System (ADS)

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

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

2008-03-01

2

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

SciTech Connect

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

Kravtsov, Yu. A. [Space Research Institute, Profsoyuznaya St. 82/34, Moscow 117997 (Russian Federation); Institute of Physics, Maritime University of Szczecin, Waly Chrobrego 1/., 70-500 Szczecin (Poland); Bieg, B. [Institute of Physics, Maritime University of Szczecin, Waly Chrobrego 1/., 70-500 Szczecin (Poland); Bliokh, K. Yu. [Institute of Radio Astronomy, 4 Krasnoznamyonnaya St., Kharkov 61002 (Ukraine); Optical Engineering Laboratory, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000 (Israel); Hirsch, M. [Max Planck Institute for Plasma Physics, Greifswald, Wendelsteinstrasse D-17491 (Germany)

2008-03-19

3

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

NASA Astrophysics Data System (ADS)

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

Kravtsov, Yury A.; Bieg, Bohdan

2008-09-01

4

Fatigue Degradation in Centrally Notched Quasi-Isotropic Laminates  

Microsoft Academic Search

The aim of this research is first to model the degradation of the elastic modulus of quasi-isotropic [0\\/90\\/ ±45]2s graphite\\/epoxy centrally notched composite lam inates subjected to tension-tension (T-T) fatigue tests. Then we can predict the fatigue life in terms of elastic modulus as a non-destructive parameter of failure criterion and express the residual strength by using the elastic modulus

Ming-Hwa R. Jen; J. M. Hsu; D. G. Hwang

1990-01-01

5

Stability of polarized modes in a quasi-isotropic laser  

NASA Astrophysics Data System (ADS)

The polarization states of quasi-isotropic lasers are highly sensitive to residual cavity anisotropies and to weak (parasitic) anisotropic feedback. Internal anisotropies are usually constant, whereas the effective mirror anisotropy produced by feedback is strongly frequency (phase) dependent. A model for such a laser is developed, and analytic steady-state solutions are obtained for the case when both anisotropies are parallel. The linear stability analysis is also analytic. For the 3.39-micron He-Ne laser, the theory explains the previously observed variations with frequency of the intensity of the laser, the regions of monostable linear polarization, and in the bistable region the inverse dependence of the width of the hysteresis loop on the low-signal net gain. In contrast to Lamb's (964) theory, the calculations show that the polarization flip arises from an instability in the relative phase between the vector components of a mode.

May, A. D.; Stephan, G.

1989-12-01

6

Effect of Multiple Delamination on Free Vibration Behaviour of Quasi-Isotropic Composite Conical Shells  

NASA Astrophysics Data System (ADS)

In this paper, a finite element method is employed to investigate the free vibration characteristics of single and multiple delaminated graphite-epoxy quasi-isotropic composite conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The formulation is based on Mindlin's theory considering eight-noded isoparametric plate bending element. The multipoint constraint algorithm is employed to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The QR iteration algorithm is utilized for solution of standard eigen value problem. Finite element codes are developed to obtain the natural frequencies of single and multiple delaminated quasi-isotropic composite conical shells. The mode shapes for a typical laminate configuration are also depicted. Numerical results obtained are the first known values which could serve as reference solutions for the future investigators.

Dey, S.; Karmakar, A.

2013-01-01

7

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

Microsoft Academic Search

This report provides recommended durability-based design properties and criteria for a quasi-isotropic carbon-fiber composite for possible automotive structural applications. The composite, which was made by a rapid molding process suitable for high-volume automotive applications, consisted of continuous Thornel T300 fibers (6K tow) in a Baydur 420 IMR urethane matrix. The reinforcement was in the form of four {+-}45{sup o} stitch-bonded

J. M. Corum; R. L. Battiste; M. B. Ruggles-Wrenn

2002-01-01

8

Guided waves in anisotropic and quasi-isotropic aerospace composites: Three-dimensional simulation and experiment.  

PubMed

Three-dimensional (3D) elastic wave simulations can be used to investigate and optimize nondestructive evaluation (NDE) and structural health monitoring (SHM) ultrasonic damage detection techniques for aerospace materials. 3D anisotropic elastodynamic finite integration technique (EFIT) has been implemented for ultrasonic waves in carbon fiber reinforced polymer (CFRP) composite laminates. This paper describes 3D EFIT simulations of guided wave propagation in undamaged and damaged anisotropic and quasi-isotropic composite plates. Comparisons are made between simulations of guided waves in undamaged anisotropic composite plates and both experimental laser Doppler vibrometer (LDV) wavefield data and dispersion curves. Time domain and wavenumber domain comparisons are described. Wave interaction with complex geometry delamination damage is then simulated to investigate how simulation tools incorporating realistic damage geometries can aid in the understanding of wave interaction with CFRP damage. In order to move beyond simplistic assumptions of damage geometry, volumetric delamination data acquired via X-ray microfocus computed tomography is directly incorporated into the simulation. Simulated guided wave interaction with the complex geometry delamination is compared to experimental LDV time domain data and 3D wave interaction with the volumetric damage is discussed. PMID:23769180

Leckey, Cara A C; Rogge, Matthew D; Raymond Parker, F

2013-05-28

9

EVIDENCE FOR QUASI-ISOTROPIC MAGNETIC FIELDS FROM HINODE QUIET-SUN OBSERVATIONS  

SciTech Connect

Some recent investigations of spectropolarimetric observations of the Zeeman effect in the Fe I lines at 630 nm carried out with the Hinode solar space telescope have concluded that the strength of the magnetic field vector in the internetwork regions of the quiet Sun is in the hG regime and that its inclination is predominantly horizontal. We critically reconsider the analysis of such observations and carry out a complete Bayesian analysis with the aim of extracting as much information as possible from them, including error bars. We apply the recently developed BAYES-ME code that carries out a complete Bayesian inference for Milne-Eddington atmospheres. The sampling of the posterior distribution function is obtained with a Markov Chain Monte Carlo scheme and the marginal distributions are analyzed in detail. The Kullback-Leibler divergence is used to study the extent to which the observations introduce new information in the inference process resulting in sufficiently constrained parameters. Our analysis clearly shows that only upper limits to the magnetic field strength can be inferred, with fields in the kG regime completely discarded. Furthermore, the noise level present in the analyzed Hinode observations induces a substantial loss of information for constraining the azimuth of the magnetic field. Concerning the inclination of the field, we demonstrate that some information is available to constrain it for those pixels with the largest polarimetric signal. The results also point out that the field in pixels with small polarimetric signals can be nicely reproduced in terms of a quasi-isotropic distribution.

Asensio Ramos, A. [Instituto de AstrofIsica de Canarias, 38205, La Laguna, Tenerife (Spain)], E-mail: aasensio@iac.es

2009-08-20

10

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

SciTech Connect

This report provides recommended durability-based design properties and criteria for a quasi-isotropic carbon-fiber composite for possible automotive structural applications. The composite, which was made by a rapid molding process suitable for high-volume automotive applications, consisted of continuous Thornel T300 fibers (6K tow) in a Baydur 420 IMR urethane matrix. The reinforcement was in the form of four {+-}45{sup o} stitch-bonded mats in the following layup: [0/90{sup o}/{+-}45{sup o}]{sub S}. This material is the second in a progression of three candidate thermoset composites to be characterized and modeled as part of an Oak Ridge National Laboratory project entitled Durability of Carbon-Fiber Composites. The overall goal of the project, which is sponsored by the U.S. Department of Energy's Office of Advanced Automotive Technologies and is closely coordinated with the industry Automotive Composites Consortium, is to develop durability-driven design data and criteria to assure the long-term integrity of carbon-fiber-based composite systems for large automotive structural components. This document is in two parts. Part I provides the design criteria, and Part 2 provides the underlying experimental data and models. The durability issues addressed include the effects on deformation, strength, and stiffness of cyclic and sustained loads, operating temperature, automotive fluid environments, and low-energy impacts (e.g., tool drops and kickups of roadway debris). Guidance is provided for design analysis, time-dependent allowable stresses, rules for cyclic loadings, and damage tolerance design guidance, including the effects of holes. Chapter 6 provides a brief summary of the design criteria.

Corum, J.M.

2002-04-17

11

The static indentation behavior of composite sandwich panels with thin quasi-isotropic skins  

NASA Astrophysics Data System (ADS)

The quasi-static normal indentation of sandwich panels with quasi-isotropic laminated composite skins and honeycomb or foam cores, by spherical indentors, has been investigated using experiments and finite element analysis. The experimental program emphasized the effects of indentor size on the resulting load indentation responses, failure mechanisms in the skin and the core, and the measurement of contact areas between indentor and the target. The sandwich panels were indented up to the initiation of skin fracture and the resulting contact data was used to characterize contact power laws. A non-linear finite element model was developed based on the experimental observations to systematically explore the indentation behavior of diverse sandwich configurations and to investigate the contact pressure distributions. The finite element model was used as an experimental tool in the development of a simple non-dimensional semi-empirical model that was based on the Graeco-Latin-square factorial plan. The indentation experiments revealed the strong dependence of the indentation response and the failure mechanism on the indentor size and the core type. A characteristic network of contact induced delaminations was observed to form in honeycomb core sandwich panels. A decreasing stiffness type loading response was observed for smaller indentors, while the opposite was observed for larger indentors, the transition indentor size being governed by the relative stiffnesses of the skin and the core. The parameter characterizing the non-linearity in the unloading behavior was observed to be a function of the point from which unloading occurred, contrary to previous observations. The contact pressure distributions obtained from the finite element analysis indicated the presence of a saddle type distribution at smaller indentations while approaching a uniformly distributed pressure as the indentations increased. The peak contact pressure was observed to translate from the edge of the contact zone towards the center as the indentations increased. An increase in compressive stiffness of the core beyond a certain limit was found to decrease the indentation loads for a given crush stress. The load-indentation response predictions of the semi-empirical non-dimensional model compared satisfactorily with the finite element and experimental data for similar sandwich configurations. A conceptual guideline for developing semi-empirical models for the contact radius and pressures has also been presented. Additional scope exists for the improvisation of the empirical model for increased accuracy and range of variables in the future.

Keshavanarayana, Suresh Raju

12

Effects of Hole-size and Environment on the Mechanical Behaviour of a Quasi-isotropic AS4/3501-6 Laminate in Tension, Compression and Bending.  

National Technical Information Service (NTIS)

This report describes the results of open-hole-tension (OHT), open- hole-compression (OHC) and open-hole-four-point-bend (OHB) tests conducted on AS4/3501-6 quasi-isotropic (45/0/- 45/90)2s laminates in the room temperature dry (RTD) and elevated temperat...

P. J. Callus

2007-01-01

13

Moisture effects on the toughness, mode-I and mode-II of particles filled quasi-isotropic glass–fibre reinforced polyester resin composites  

Microsoft Academic Search

An experimental programme is presented for the effect of moisture on the toughness, mode-I and mode-II of aluminium tri-hydrate and polyethylene filled and unfilled quasi-isotropic glass–fibre reinforced epoxy–vinylester resin (GFRP) composites. Specimens were exposed in water at room temperature (20°C) for a period of 8 months and the effect of moisture content on toughness, GIc and GIIc values were obtained

V. K. SRIVASTAVA; P. J. HOGG

1998-01-01

14

Multistage fatigue life monitoring on quasi-isotropic carbon fibre reinforced polymers enhanced with multi-wall carbon nanotubes: parallel use of electrical resistance, acoustic emission, and acousto-ultrasonic techniques  

Microsoft Academic Search

In this study, CNTs were used as modifiers of the epoxy matrix of quasi-isotropic carbon fibre reinforced laminates. The prepared laminates were subjected to tensile loading and tension-tension fatigue and, the changes in the longitudinal resistance were monitored via a digital multimeter. In addition, Acoustic Emission and Acousto-Ultrasonic techniques were used for monitoring the fatigue process of the laminates. The

V. Kostopoulos; A. Vavouliotis; T. Loutas; P. Karapappas

2009-01-01

15

Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates  

SciTech Connect

The Kerr metric outside the ergosphere is transformed into Arnowitt-Deser-Misner coordinates up to the orders 1/r{sup 4} and a{sup 2}, respectively, in radial coordinate r and reduced angular momentum variable a, starting from the Kerr solution in quasi-isotropic as well as harmonic coordinates. The distributional source terms for the approximate solution are calculated. To leading order in linear momenta, higher-order-in-spin interaction Hamiltonians for black hole binaries are derived.

Hergt, Steven; Schaefer, Gerhard [Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, 07743 Jena (Germany)

2008-05-15

16

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

17

Electro-mechanical fatigue behavior of a quasi-isotropic laminate with an embedded piezoelectric actuator  

SciTech Connect

This study primarily investigated the electro-mechanical fatigue behavior of the embedded piezoelectric actuators in graphite/epoxy laminate with a lay-up of 0/ {+-} 45 / 90s. A secondary focus was the investigation of the mechanical fatigue effects of the 0 / 0 / {+-} 45 / 0 / 0 / 90s laminate with embedded PZT under tensile loading. All the fatigue tests were conducted with a triangular loading waveform which had a frequency of 10 Hz and with R = 0.1. In the electro-mechanical testing, the embedded actuator was excited by a {minus}10 V to {minus}100 V or a 10 V to 100 V voltage input, which resulted in either in-phase or out-of-phase electrically induced strain waveform with respect to the mechanical loading or strain. It was found that the embedded PZTs performed very well during the out-of-phase electro-mechanical and low stress fatigue conditions when the applied strain was within the operating range of PZT. Beyond the upper strain limit, the voltage output of the PZT was primarily influenced by the mechanical fatigue loading. Results from the high stress fatigue tests showed that the embedded piezoelectric actuators did not have significant effect on the tensile strength of the laminates.

Hsu, T.L.

1998-09-01

18

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

19

Improved Toeplitz Approximation Method.  

National Technical Information Service (NTIS)

This reprint suggests a modification of the Toeplitz approximation method for estimating frequencies of multiple sinusoids from covariance measurements. The method constructs a state-feedback matrix following a low-rank approximation of the Toeplitz covar...

B. D. Rao K. S. Arun

1988-01-01

20

Approximating Labeled Markov Processes  

Microsoft Academic Search

We study approximate reasoning about continuous-state labeled Markov processes. We show how to approximate a labeled Markov process by a family offinite-state labeled Markov chains. We show that the collection of labeled Markov processes carries a Polish space structure with a countable basis given by finite state Markov chains with ra- tional probabilities. The primary technical tools that we develop

Josee Desharnais; Vineet Gupta; Radha Jagadeesan; Prakash Panangaden

2000-01-01

21

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

Microsoft Academic Search

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%

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

2006-01-01

22

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

23

2-D Biaxial Testing and Failure Predictions of IM7/977-2 Carbon/Epoxy Quasi-Isotropic Laminates.  

National Technical Information Service (NTIS)

In previous research, a series of a thickness-tapered cruciform specimen configurations have been used to determine the biaxial (two- dimensional, in-plane) and triaxial (three-dimensional) strength of several carbon/epoxy and glass/vinyl-ester laminate c...

A. C. Biskner J. S. Mayes J. S. Welsh

2006-01-01

24

Finite Element Simulation of Low Velocity Impact Damage Morphology in Quasi_Isotropic Composite Panels Under Variable Shape Impactors  

Microsoft Academic Search

This study was aimed at improving the understanding of the barely visible internal impact damage (BVID), its initiation, growth and tolerance in fibrous composites under low velocity impact through developing a computational model to perform damage assessment, and visualize the damage morphology. Instead of inducing damage in the form of ply the selected areas equal to the size of the

Umar Farooq; Karl Gregory

25

Relativistic Eikonal Approximation.  

National Technical Information Service (NTIS)

The authors earlier claims in support of the eikonal approximation to generalized ladder graph amplitudes are withdrawn -- for the case of scalar-scalar interactions. Justification of the eikonal formula is provided, however, for the more interesting situ...

G. Tiktopoulos S. B. Treiman

1970-01-01

26

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

27

Optimizing the Zeldovich Approximation.  

National Technical Information Service (NTIS)

We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1...

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

1994-01-01

28

Anomalous diffraction approximation limits  

NASA Astrophysics Data System (ADS)

It has been reported in a recent article [Liu, C., Jonas, P.R., Saunders, C.P.R., 1996. Accuracy of the anomalous diffraction approximation to light scattering by column-like ice crystals. Atmos. Res., 41, pp. 63-69] that the anomalous diffraction approximation (ADA) accuracy does not depend on particle refractive index, but instead is dependent on the particle size parameter. Since this is at odds with previous research, we thought these results warranted further discussion.

Videen, Gorden; Chýlek, Petr

29

Approximately intertwining mappings  

NASA Astrophysics Data System (ADS)

Let be a Banach algebra, and let E be a weak Banach -bimodule. An approximately intertwining mapping corresponding to a functional equation is a mapping with f(0)=0 such that and for each the mappingsfa(x)=f(ax)-af(x), are continuous at a point. In this paper, we show that every approximately intertwining mapping corresponding to Cauchy, generalized Jensen or Trif functional equation can be estimated by an intertwining mapping.

Moslehian, Mohammad Sal

2007-08-01

30

Quantifiers and approximation  

Microsoft Academic Search

We investigate tile relationship between logical expressibility of NP optimization problems and their approximation properties. First sucll attempt was made by Papadimitriou and Yannakakis, who defined the class of NPO problems MAX NP. We show that many importaut optimization problems do not belong to MAX NP and that in fact there are problems in P which are not ill lk'IAX

Alessandro Panconesi; Desh Ranjan

1990-01-01

31

Approximating Latin Square Extensions  

Microsoft Academic Search

In this paper, we consider the following question: what is the maximum number of entriesthat can be added to a partially filled latin square? The decision version of this question isknown to be NP-complete. We present two approximation algorithms for the optimizationversion of this question. We first prove that the greedy algorithm achieves a factor of 1\\/3. Wethen use insights

Ravi Kumar; Alexander Russell; Ravi Sundaram

1996-01-01

32

Multidimensional Stochastic Approximation Methods  

Microsoft Academic Search

Multidimensional stochastic approximation schemes are presented, and conditions are given for these schemes to converge a.s. (almost surely) to the solutions of $k$ stochastic equations in $k$ unknowns and to the point where a regression function in $k$ variables achieves its maximum.

Julius R. Blum

1954-01-01

33

Multicriteria approximation through decomposition  

SciTech Connect

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

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

1997-12-01

34

Multicriteria approximation through decomposition  

SciTech Connect

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

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

1998-06-01

35

Approximate Inclusion-Exclusion  

Microsoft Academic Search

The Inclusion-Exclusion formula expresses the size of a union of a family of sets in terms of the sizes of intersections of all subfamilies. This paper considers approximating the size of the union when intersection sizes are known for only some of the subfamilies, or when these quantities are given to within some error, or both.

Nathan Linial; Noam Nisan

1990-01-01

36

Approximate portfolio analysis  

Microsoft Academic Search

This paper presents a portfolio selection model based on the idea of approximation. The model describes a portfolio by its decumulative distribution curve and a preference structure by a family of convex indifference curves. It prescribes the optimal portfolio as the one whose decumulative curve has the highest tangent indifference curve. The model extends the mean–variance model in the sense

Liping Liu

1999-01-01

37

Optimizing the Zeldovich approximation  

NASA Astrophysics Data System (ADS)

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

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

38

An improved saddlepoint approximation.  

PubMed

Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm. PMID:17306841

Gillespie, Colin S; Renshaw, Eric

2006-09-09

39

Approximating Latin Square Extensions  

Microsoft Academic Search

.    In this paper we investigate the problem of computing the maximum number of entries which can be added to a partially filled\\u000a latin square. The decision version of this question is known to be NP-complete. We present two approximation algorithms for the optimization version of this question. We first prove that the\\u000a greedy algorithm achieves a factor of

Ravi Kumar; Alexander Russell; Ravi Sundaram

1999-01-01

40

Approximating labelled Markov processes  

Microsoft Academic Search

Labelled Markov processes are probabilistic versions of labelled transition systems. In general, the state space of a labelled Markov process may be a continuum. In this paper, we study approximation techniques for continuous-state labelled Markov processes.We show that the collection of labelled Markov processes carries a Polish-space structure with a countable basis given by finite-state Markov chains with rational probabilities;

Josee Desharnais; Vineet Gupta; Radha Jagadeesan; Prakash Panangaden

2003-01-01

41

Approximate Probabilistic Model Checking  

Microsoft Academic Search

\\u000a Symbolic model checking methods have been extended recently to the verification of probabilistic systems. However, the representation\\u000a of the transition matrix may be expensive for very large systems and may induce a prohibitive cost for the model checking\\u000a algorithm. In this paper, we propose an approximation method to verify quantitative properties on discrete Markov chains.\\u000a We give a randomized algorithm

Thomas Hérault; Richard Lassaigne; Frédéric Magniette; Sylvain Peyronnet

2004-01-01

42

Approximate IBM-2 calculations  

NASA Astrophysics Data System (ADS)

An approximate method for calculations in the neutron-proton interacting boson model (IBM-2) is investigated. An additional quadrupole q-boson, identified with the antisymmetric neutron-proton state, is added to the IBM-1 space of s- and d-bosons. The states in the (s, d, q)-space with nq = 0, l,... are related to the IBM-2 states with the value of F-spin F = Fmax, Fmax-1,... Equating the matrix elements between corresponding states in the IBM-2 space and the (s, d, q)-space we map the IBM-2 operators onto the operators in the (s, d, q)-space. Comparison of exact IBM-2 calculations and approximate calculations in the (s, d, q)-space shows that the latter reproduces quite well the IBM-2 results for low-lying states. Application of mean field techniques to the approximate (s, d, q)-space method allows a transparent interpretation of the mixed symmetry states and provides simple formulas for their characteristics.

Dobeš, J.

1987-08-01

43

Optimizing the Zeldovich Approximation  

NASA Astrophysics Data System (ADS)

We have recently learned that the Zel'dovich 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 by Coles, Melott & Shandarin (hereafter CMS) the accuracy of several analytic approximations to gravitational clustering was studied in the mildly non-linear regime. We found that what was called the `truncated Zel'dovich approximation' (TZA) was better than any other (except, in one case, the ordinary Zel'dovich approximation) over a wide range from linear to mildly non-linear (? ~ 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k_nl_, where k_nl_ marks the transition to the non-linear regime. Here we study the cross-correlation of generalized TZA with a group of N-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a top-hat in coordinate space, and a Gaussian. We also study the variation in the cross-correlation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window exp (-k^2^/2k_G_^2^) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved cross- correlation in those cases that most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of k_G_ for the Gaussian window is (somewhat spectrum-dependent) 1 to 1.5 times k_nl_, where k_nl_ is defined by equation (3). Although all three windows produce similar power spectra and density distribution functions after application of the Zel'dovich approximation, the agreement of the phases of the Fourier components with the N-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment of phases in the non-linear regime. We also report on the accuracy of particle positions and velocities

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

1994-08-01

44

Approximate option pricing  

SciTech Connect

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

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

1996-04-08

45

Sublinear approximation of signals  

NASA Astrophysics Data System (ADS)

It has recently been observed that sparse and compressible signals can be sketched using very few nonadaptive linear measurements in comparison with the length of the signal. This sketch can be viewed as an embedding of an entire class of compressible signals into a low-dimensional space. In particular, d-dimensional signals with m nonzero entries (m-sparse signals) can be embedded in O(m log d) dimensions. To date, most algorithms for approximating or reconstructing the signal from the sketch, such as the linear programming approach proposed by Candes-Tao and Donoho, require time polynomial in the signal length. This paper develops a new method, called Chaining Pursuit, for sketching both m-sparse and compressible signals with O(m polylog d) nonadaptive linear measurements. The algorithm can reconstruct the original signal in time O(m polylog d) with an error proportional to the optimal m-term approximation error. In particular, m-sparse signals are recovered perfectly and compressible signals are recovered with polylogarithmic distortion. Moreover, the algorithm can operate in small space O(m polylog d), so it is appropriate for streaming data.

Gilbert, Anna C.; Strauss, Martin J.; Tropp, Joel A.; Vershynin, Roman

2006-06-01

46

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).

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

2013-01-01

47

Approximation by Hill Functions: II.  

National Technical Information Service (NTIS)

The problem of the approximation in Sobolev spaces by piecewise smooth function is considered. This approach deals with the problems of approximation on less dimensional manifolds and simultaneous approximation on manifolds of different dimensions.

I. Babuska

1971-01-01

48

The fuzzy rough approximation decomposability  

Microsoft Academic Search

In this paper, we propose the definition of fuzzy rough approximation decomposability, discuss the properties of several fuzzy rough approximations and give several decision theorems for fuzzy rough approximation decomposability.

Xiong Fenglan; Ding Xiangqian; Yuhai Liu

2003-01-01

49

Trapezoidal approximations of fuzzy numbers  

Microsoft Academic Search

The problem of the trapezoidal approximation of fuzzy numbers is discussed. A set of criteria for approximation operators is formulated. These constraints can be used for direct operator derivation. A new nearest trapezoidal approximation operator preserving expected interval is suggested.

Przemyslaw Grzegorzewski; Edyta Mrówka

2005-01-01

50

Sequences, Series, and Function Approximation  

Microsoft Academic Search

Sequences are important in approximation: the usual representation of real numbers using decimals is in fact the process of giving a sequence of rational numbers approximation the real number in question successively better as more decimal places are given. These decimal approximation sequences are actually rather special: successive decimal approximations never get smaller (so the sequence is monotone nondecreasing) and

Lawrence N. Stout

2006-01-01

51

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

52

Weak Copositive and Intertwining Approximation  

Microsoft Academic Search

It is known that shape preserving approximation has lower rates than unconstrained approximation. This is especially true for copositive and intertwining approximations. Forf?Lp, 1?papproximations and conclude that the most sensible way is the

Y. K. Hu; K. A. Kopotun; X. M. Yu

1999-01-01

53

Approximate convex decomposition of polygons  

Microsoft Academic Search

We propose a strategy to decompose a polygon, containing zero or more holes, into ``approximately convex'' pieces. For many applications, the approximately convex components of this decomposition provide similar benefits as convex components, while the resulting decomposition is significantly smaller and can be computed more efficiently. Moreover, our approximate convex decomposition (ACD) provides a mechanism to focus on key structural

Jyh-Ming Lien; Nancy M. Amato

2004-01-01

54

Flexible lognormal sum approximation method  

Microsoft Academic Search

A simple and novel method is presented to approximate the distribution of the sum of independent, but not necessarily identical, lognormal random variables, by the lognormal distribution. It is shown that matching a short Gauss-Hermite approximation of the moment generating function of the lognormal sum with that of the lognormal distribution leads to an accurate lognormal sum approximation. The advantage

Jingxian Wu; Neelesh B. Mehta; Jin Zhang

2005-01-01

55

Noncommutative lattices as finite approximations  

Microsoft Academic Search

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

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

1996-01-01

56

Structural optimization using Kriging approximation  

Microsoft Academic Search

An optimization method using Kriging approximation is applied to a structural optimization problem. The method involves two main processes. The first is a space estimation process that uses the Kriging method, and the second is an optimization process. The use of the Kriging method makes it easier to perform the approximation optimization. As an example of the estimation performed as

S. Sakata; F. Ashida; M. Zako

2003-01-01

57

Validity of the Rytov Approximation.  

National Technical Information Service (NTIS)

The limitations on the applicability of the Rytov approximation are examined in this paper. It is shown that (1) the singular behavior of the perturbation series of which the Rytov approximation is the first term cannot be removed by adding a 'constant' a...

W. P. Brown

1967-01-01

58

Approximate Genealogies Under Genetic Hitchhiking  

PubMed Central

The rapid fixation of an advantageous allele leads to a reduction in linked neutral variation around the target of selection. The genealogy at a neutral locus in such a selective sweep can be simulated by first generating a random path of the advantageous allele's frequency and then a structured coalescent in this background. Usually the frequency path is approximated by a logistic growth curve. We discuss an alternative method that approximates the genealogy by a random binary splitting tree, a so-called Yule tree that does not require first constructing a frequency path. Compared to the coalescent in a logistic background, this method gives a slightly better approximation for identity by descent during the selective phase and a much better approximation for the number of lineages that stem from the founder of the selective sweep. In applications such as the approximation of the distribution of Tajima's D, the two approximation methods perform equally well. For relevant parameter ranges, the Yule approximation is faster.

Pfaffelhuber, P.; Haubold, B.; Wakolbinger, A.

2006-01-01

59

Approximate Controllability and Weak Stabilizability.  

National Technical Information Service (NTIS)

A necessary and sufficient condition for the stabilizability of semigroups which are similar to contractions is given in terms of the approximate controllability of the infinite dimensional system dx/dt = Ax + Bu. (Author)

C. D. Benchimol

1977-01-01

60

Computer Experiments for Function Approximations.  

National Technical Information Service (NTIS)

This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineeri...

A. Chang C. Tong I. Izmailov O. Alexandrov S. Rizzo S. Wynter

2007-01-01

61

Approximate invariant using Lie algebra.  

National Technical Information Service (NTIS)

An approximate invariant is found for sextupole transverse dynamics. It is represented in terms of the elements of a Lie algebra associated with a sextupole contribution to the time-dependent Hamiltonian for transverse dynamics.

T. Garavaglia

1992-01-01

62

Normed likelihood as saddlepoint approximation  

Microsoft Academic Search

Barndorff-Nielsen's formula (normed likelihood with constant-information metric) has been proffered as an approximate conditional distribution for the maximum-likelihood estimate, based on likelihood functions. Asymptotic justifications are available and the formula coincides with the saddlepoint approximation in full exponential models. It is shown that the formula has wider application than is presently indicated, that in local analysis it corresponds to Laplace's

D. A. S. Fraser

1988-01-01

63

Approximate coloring of uniform hypergraphs  

Microsoft Academic Search

Abstract We consider an algorithmic problem,of coloring r-uniform hypergraphs. The problem,of finding the exact value of the chromatic number of a hypergraph is known to be NP-hard, so we discuss approximate,solutions to it. Using a simple construction and known,results on hardness of graph coloring, we show that for any r 3 it is impossible to approximate in polynomial time the

Michael Krivelevich; Benny Sudakov

2003-01-01

64

The complexity of approximating entropy  

Microsoft Academic Search

(MATH) We consider the problem of approximating the entropy of a discrete distribution under several models. If the distribution is given explicitly as an array where the i-th location is the probability of the i-th element, then linear time is both necessary and sufficient for approximating the entropy.We consider a model in which the algorithm is given access only to

Tu?kan Batu; Sanjoy Dasgupta; Ravi Kumar; Ronitt Rubinfeld

2002-01-01

65

Approximate entropy of network parameters.  

PubMed

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches. PMID:22680542

West, James; Lacasa, Lucas; Severini, Simone; Teschendorff, Andrew

2012-04-19

66

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

67

Rational approximations for tomographic reconstructions  

NASA Astrophysics Data System (ADS)

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

Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas

2013-06-01

68

Adaptive approximation models in optimization  

SciTech Connect

The paper proposes a method for optimization of functions of several variables that substantially reduces the number of objective function evaluations compared to traditional methods. The method is based on the property of iterative refinement of approximation models of the optimand function in approximation domains that contract to the extremum point. It does not require subjective specification of the starting point, step length, or other parameters of the search procedure. The method is designed for efficient optimization of unimodal functions of several (not more than 10-15) variables and can be applied to find the global extremum of polymodal functions and also for optimization of scalarized forms of vector objective functions.

Voronin, A.N.

1995-05-01

69

Quantum tunneling beyond semiclassical approximation  

Microsoft Academic Search

Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies

Rabin Banerjee; Bibhas Ranjan Majhi

2008-01-01

70

Approximate Spatial Reasoning (Abstract Only).  

National Technical Information Service (NTIS)

Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alter...

S. Dutta

1988-01-01

71

Approximate factorization for incompressible flow  

Microsoft Academic Search

For computational solution of the incompressible Navier-Stokes equations, the approximate factorization (AF) algorithm is used to solve the vectorized momentum equation in delta form based on the pressure calculated in the previous time step. The newly calculated velocities are substituted into the pressure equation (obtained from a linear combination of the continuity and momentum equation), which is then solved by

R. S. Bernard

1981-01-01

72

Approximations to wire grid inductance.  

SciTech Connect

By using a multipole-conformal mapping expansion for the wire currents we examine the accuracy of approximations for the transfer inductance of a one dimensional array of wires (wire grid). A simple uniform fit is constructed by introduction of the decay factor from bipolar coordinates into existing formulas for this inductance.

Warne, Larry Kevin; Johnson, William Arthur; Merewether, Kimball O.

2004-06-01

73

Best Approximation with Walsh Atoms.  

National Technical Information Service (NTIS)

The authors consider the approximation of L2(R) of a given function using finite linear combinations of Walsh atoms, which are Walsh functions localized to dyadic intervals, also called Haar-Walsh wavelet packets. It is shown that up to a constant factor,...

L. F. Villemoes

1995-01-01

74

Pythagorean Approximations and Continued Fractions  

ERIC Educational Resources Information Center

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

Peralta, Javier

2008-01-01

75

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

76

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

77

Approximation properties of haplotype tagging  

PubMed Central

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

Vinterbo, Staal A; Dreiseitl, Stephan; Ohno-Machado, Lucila

2006-01-01

78

Approximations to optimal nonlinear filters  

Microsoft Academic Search

Let the signal and noise processes be given as solutions to nonlinear stochastic differential equations. The optimal filter for the problem, derived elsewhere, is usually infinite dimensional. Several methods of obtaining possibly useful finite dimensional approximations are considered here, and some of the special problems of simulation are discussed. The numerical results indicate a number of useful features of the

H. Kushner

1967-01-01

79

Weak Approximations for Wiener functionals  

Microsoft Academic Search

In this paper we introduce a simple space-filtration discretization scheme on Wiener space which allows us to study weak decompositions and smooth explicit approximations for a large class of Wiener functionals. We show that any Wiener functional has an underlying robust semimartingale skeleton which under mild conditions converges to it. The discretization is given in terms of discrete-jumping filtrations which

Dorival Leao; Alberto Ohashi

2009-01-01

80

Exact and approximate membership testers  

Microsoft Academic Search

In this paper we consider the question of how much space is needed to represent a set. Given a finite universe U and some subset V (called the vocabulary), an exact membership tester is a procedure that for each element s in U determines if s is in V. An approximate membership tester is allowed to make mistakes: we require

Larry Carter; Robert W. Floyd; John Gill; George Markowsky; Mark N. Wegman

1978-01-01

81

Approximation theory of output statistics  

Microsoft Academic Search

Given a channel and an input process we study the minimum randomness of those input processes whose output statistics approximate the original out- put statistics with arbitrary accuracy. We introduce the notion of resolva- bility of a channel, defined as the number of random bits required per channel use in order to generate an input that achieves arbitrarily accu- rate

Te Sun Han; Sergio Verdii

1993-01-01

82

Normal Approximation to Poisson Distribution  

NSDL National Science Digital Library

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

Dinov, Ivo

2009-01-14

83

Quantitative measurement of variational approximations  

Microsoft Academic Search

Variational problems have long been used to mathematically model physical systems. Their advantage has been the simplicity of the model as well as the ability to deduce information concerning the functional dependence of the system on various parameters embedded in the variational trial functions. However, the only method in use for estimating the error in a variational approximation has been

D. J. Kaup; T. K. Vogel

2007-01-01

84

Incremental Approximation of Optimal Allocations.  

National Technical Information Service (NTIS)

The paper concerns the approximation of optimal allocations by delta allocations. Delta allocations are obtained by fixing an increment delta of effort and deciding at each step upon a single cell in which to allocate the entire increment. It is shown tha...

L. D. Stone

1972-01-01

85

Analytic Approximations for Spread Options  

Microsoft Academic Search

This paper expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new analytic approximation for the price of a European spread option, and

Carol Alexander; Aanand Venkatramanan

2007-01-01

86

Chemical Laws, Idealization and Approximation  

NASA Astrophysics Data System (ADS)

This paper examines the notion of laws in chemistry. Vihalemm ( Found Chem 5(1):7-22, 2003) argues that the laws of chemistry are fundamentally the same as the laws of physics they are all ceteris paribus laws which are true "in ideal conditions". In contrast, Scerri (2000) contends that the laws of chemistry are fundamentally different to the laws of physics, because they involve approximations. Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34-50, 2000) agree that the laws of chemistry are operationally different to the laws of physics, but claim that the distinction between exact and approximate laws is too simplistic to taxonomise them. Approximations in chemistry involve diverse kinds of activity and often what counts as a scientific law in chemistry is dictated by the context of its use in scientific practice. This paper addresses the question of what makes chemical laws distinctive independently of the separate question as to how they are related to the laws of physics. From an analysis of some candidate ceteris paribus laws in chemistry, this paper argues that there are two distinct kinds of ceteris paribus laws in chemistry; idealized and approximate chemical laws. Thus, while Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34--50, 2000) are correct to point out that the candidate generalisations in chemistry are diverse and heterogeneous, a distinction between idealizations and approximations can nevertheless be used to successfully taxonomise them.

Tobin, Emma

2013-07-01

87

Approximate Symmetries of a Viscoelastic Model  

NASA Astrophysics Data System (ADS)

Approximate symmetries of a mathematical model describing one-dimensional motion in a viscoelastic medium with a small viscosity coefficient are studied. An approximate invariant solution is obtained through the approximate generator of the first-order approximate symmetries.

Valenti, Antonino

2008-04-01

88

Waveless Approximation Theories of Gravity  

NASA Astrophysics Data System (ADS)

The analysis of a general multibody physical system governed by Einstein's equations is quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties — many coupled degrees of freedom, dynamic instability — are associated with the presence of gravitational waves. We have developed a number of "waveless approximation theories" (WAT's) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.

Isenberg, James A.

89

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

90

Simulating bioterrorism through epidemiology approximation  

Microsoft Academic Search

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

Ryan Layfield; Murat Kantarcioglu; Bhavani M. Thuraisingham

2008-01-01

91

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

92

Finite approximations in fluid mechanics  

Microsoft Academic Search

This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for

Hirschel

1986-01-01

93

Finding All Approximate Gapped Palindromes  

Microsoft Academic Search

We study the problem of finding all maximal approximate gapped palindromes in a string. More specifically, given a string S of length n, a parameter q???0 and a threshold k?>?0, the problem is to identify all substrings in S of the form uvw such that (1) the Levenshtein distance between u and w\\u000a \\u000a r\\u000a is at most k, where w

Ping-hui Hsu; Kuan-yu Chen; Kun-mao Chao

2009-01-01

94

Computer Experiments for Function Approximations  

SciTech Connect

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

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

2007-10-15

95

Padé approximants and resonance poles  

NASA Astrophysics Data System (ADS)

Based on the mathematically well defined Padé theory, a theoretically safe new procedure for the extraction of the pole mass and width of a resonance is proposed. In particular, thanks to the Montessus de Ballore theorem we are able to unfold the second Riemann sheet of an amplitude to search for the position of the resonance pole in the complex plane. The method is systematic and provides a model-independent treatment of the prediction and the corresponding errors of the approximation. Likewise, it can be used in combination with other well-established approaches to improve future determinations of resonance parameters.

Masjuan, Pere; Sanz-Cillero, Juan José

2013-10-01

96

Communication: The distinguishable cluster approximation.  

PubMed

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

Kats, Daniel; Manby, Frederick R

2013-07-14

97

Inverse closedness of approximation algebras  

NASA Astrophysics Data System (ADS)

We prove the inverse closedness of certain approximation algebras based on a quasi-Banach algebra X using two general theorems on the inverse closedness of subspaces of quasi-Banach algebras. In the first theorem commutative algebras are considered while the second theorem can be applied to arbitrary X and to subspaces of X which can be obtained by a general K-method of interpolation between X and an inversely closed subspace Y of X having certain properties. As application we present some inversely closed subalgebras of and C[-1,1]. In particular, we generalize Wiener's theorem, i.e., we show that for many subalgebras S of , the property {ck(f)}[set membership, variant]S (ck(f) being the Fourier coefficients of f) implies the same property for 1/f if vanishes nowhere on .

Almira, J. M.; Luther, U.

2006-02-01

98

Saddlepoint Approximations to the Trimmed Mean.  

National Technical Information Service (NTIS)

Saddlepoint approximations for the trimmed mean and the studentized trimmed mean are established. Some numerical evidence on the quality of our saddlepoint approximations is also included. These approximations can be applied to the bootstrap for the stude...

B. Y. Jing G. Qin R. Helmers W. Zhou

2002-01-01

99

Adiabatic approximations to internal rotation.  

PubMed

A number of subtle and confusing issues are addressed concerning large amplitude motion (LAM) coordinates (chi) for internal molecular motions, using the methyl rotation in acetaldehyde (CH(3)CHO) as a model problem. If the LAM coordinate is chosen to be one of the H-C-C-O dihedral angles rho(1), rho(2), or rho(3), it lacks the required 2pi3 periodicity, and its use is thus undesirable. An excellent local internal coordinate for this model problem is tau(3)=13(rho(1)+rho(2)+rho(3)-2pi). A similarly good but nonlocal coordinate for the adiabatic approximation of internal rotation is provided by the intrinsic reaction coordinate s. Comparison of the mass-independent V(0)(tau(3)) and the mass-dependent V(0)(s) internal rotation curves shows that the two are virtually identical for the parent isotopolog of acetaldehyde. A unified internal coordinate projection scheme for determining complementary vibrational frequencies and subsequently V(ZPVE)(chi) along a path for LAM has been formulated, where V(ZPVE)(chi) is the zero-point vibrational energy correction to the internal rotation curve. In addition to its simplicity, the projection scheme developed for a distinguished reaction path generated by constrained optimizations is appealing because the vibrational frequencies along the LAM path are invariant to chemically meaningful choices of the internal coordinates for the complementary modes. PMID:16784277

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

2006-06-14

100

Semiclassics beyond the diagonal approximation  

NASA Astrophysics Data System (ADS)

The statistical properties of the energy spectrum of classically chaotic closed quantum systems are the central subject of this thesis. It has been conjectured by O.Bohigas, M.-J.Giannoni and C.Schmit that the spectral statistics of chaotic systems is universal and can be described by random-matrix theory. This conjecture has been confirmed in many experiments and numerical studies but a formal proof is still lacking. In this thesis we present a semiclassical evaluation of the spectral form factor which goes beyond M.V.Berry's diagonal approximation. To this end we extend a method developed by M.Sieber and K.Richter for a specific system: the motion of a particle on a two-dimensional surface of constant negative curvature. In particular we prove that these semiclassical methods reproduce the random-matrix theory predictions for the next to leading order correction also for a much wider class of systems, namely non-uniformly hyperbolic systems with f>2 degrees of freedom. We achieve this result by extending the configuration-space approach of M.Sieber and K.Richter to a canonically invariant phase-space approach.

Turek, Marko

2004-05-01

101

Padé approximants for the q -elementary functions  

Microsoft Academic Search

We give a simple construction of the Padé approximants toq analogues of exp and log. The construction is based on the functional relations they satisfy. The Padé approximants for the ordinary exp and log are then limiting cases.

Peter B. Borvein

1988-01-01

102

Planetary Ephemerides Approximation for Radar Astronomy.  

National Technical Information Service (NTIS)

The planetary ephemerides approximation for radar astronomy is discussed, and, in particular, the effect of this approximation on the performance of the programmable local oscillator (PLO) used in Goldstone Solar System Radar is presented. Four different ...

R. Sadr M. Shahshahani

1991-01-01

103

Lecture Notes on Approximation Algorithms. Volume 1.  

National Technical Information Service (NTIS)

These lecture notes are based on the course CS351 (Dept. of Computer Science, Stanford University) offered during the academic year 1991-92. The notes correspond to the first half of the course. Topics include: Approximation Algorithms; Approximations Sch...

R. Motwani

1992-01-01

104

Validity of the Relativistic Eikonal Approximation.  

National Technical Information Service (NTIS)

The relativistic eikonal formula for high-energy scattering, discussed recently by a number of authors, rests on a certain technical approximation concerning the high-energy behavior of sums of generalized ladder graphs. This approximation is shown to be ...

G. Tiktopoulos S. B. Treiman

1970-01-01

105

Stabilized approximations of strongly continuous semigroups  

NASA Astrophysics Data System (ADS)

This paper introduces stabilization techniques for intrinsically unstable, high accuracy rational approximation methods for strongly continuous semigroup. The methods not only stabilize the approximations, but improve their speed of convergence by a magnitude of up to 1/2.

McAllister, Sarah; Neubrander, Frank

2008-06-01

106

Approximate analytical method for groundwater modelling.  

National Technical Information Service (NTIS)

The approximate analytical method described in this report is a combined analytical and numerical analysis method for obtaining an approximate solution to a groundwater model which usually consists of partial differential equation(s). The attractive featu...

G. L. Moltyaner

1988-01-01

107

Nearest interval approximation of a fuzzy number  

Microsoft Academic Search

The problem of the interval approximation of fuzzy numbers is discussed. A new interval approximation operator, which is the best one with respect to a certain measure of distance between fuzzy numbers, is suggested.

Przemyslaw Grzegorzewski

2002-01-01

108

Trapezoidal approximations of fuzzy numbers - revisited  

Microsoft Academic Search

Fuzzy number approximation by trapezoidal fuzzy numbers which preserve expected interval is discussed. The previously proposed approximation operator is improved so as to always produce a well formed trapezoidal fuzzy number.

Przemyslaw Grzegorzewski; Edyta Mrówka

2007-01-01

109

Linear radiosity approximation using vertex radiosities.  

National Technical Information Service (NTIS)

Using radiosities computed at vertices, the radiosity across a triangle can be approximated by linear interpolation. We develop vertex-to-vertex form factors based on this linear radiosity approximation, and show how they can be computed efficiently using...

N. Max M. Allison

1990-01-01

110

Analysis of an Approximate Decorrelating Detector  

Microsoft Academic Search

In this paper an approximate decorrelating detector is analyzed on the basis of a first order approximation to the inverse crosscorrelation matrix of signature waveforms. The approximation is fairly accurate for systems with low crosscorrelations and is exact in the two-user synchronous case. We present an exact as well as approximate analysis of the bit-error-rate performance of this detector on

Narayan B. Mandayam; Sergio Verdú

1998-01-01

111

Approximation of Functions Using Digital Nets  

Microsoft Academic Search

In analogy to a recent paper by Kuo, Sloan, and Wo?niakowski, which studied lattice rule algorithms for approximation in weighted\\u000a Korobov spaces, we consider the approximation problem in a weighted Hilbert space of Walsh series. Our approximation uses\\u000a a truncated Walsh series with Walsh coefficients approximated by numerical integration using digital nets. We show that digital\\u000a nets (or more precisely,

Josef Dick; Peter Kritzer; Prances Y. Kuo

112

Uniform approximation of a modified Bessel function  

Microsoft Academic Search

The calculation of mathematical functions on computers can be hastened by using their uniform spline approximation (an approximation with the same maximum error on each segment). Each segment of a spline is the best Chebyshev approximation by a polynomial (by a rational expression) [1]. To choose the degree of a polynomial (a segment) of a spline and the number of

S. B. Kostenko; B. O. Popov

1994-01-01

113

Approximation by the Riemann zeta-function  

Microsoft Academic Search

Any meromorphic function having at most simple poles can be approximated by linear combinations of translates of the Riemann zeta-function. In particular, an arbitrary holomorphic function can be so approximated. If derivatives of the zeta-function are allowed, then arbitrary meromorphic functions can be approximated.

P. M. Gauthier; N. Tarkhanov

2005-01-01

114

Approximate plasma dispersion functions at relativistic temperatures  

Microsoft Academic Search

Analytic approximations to relativistic plasma dispersion functions are derived in terms of the exponential integral function, Ei(x), for relativistic temperatures T⪆ m_ec(2) (where m_ec(2) is the electron rest energy). It is shown that a simpler, useful approximation to these functions can be obtained based on known approximations to the exponential integral function.

Q. Luo; D. B. Melrose

2004-01-01

115

An approximation to the plasma dispersion function  

Microsoft Academic Search

A closed expression for an approximation to the plasma dispersion function is obtained by replacing the Gaussian by a triangular function. The approximation is particularly good in regions where the evaluation of the plasma dispersion function is difficult. The range of validity of the approximation is discussed for both the function and its derivative. The results are used to obtain

J. Jimenez-Mier

2001-01-01

116

A new clustering technique for function approximation  

Microsoft Academic Search

To date, clustering techniques have always been oriented to solve classification and pattern recognition problems. However, some authors have applied them unchanged to construct initial models for function approximators. Nevertheless, classification and function approximation problems present quite different objectives. Therefore it is necessary to design new clustering algorithms specialized in the problem of function approximation. This paper presents a new

Jesús González; H. Rojas; J. Ortega; A. Prieto

2002-01-01

117

High order approximation method for curves  

Microsoft Academic Search

In this paper, an approximation procedure for space curves is described, which significantly improves the standard approximation rate via parametric Taylor's approximations. The method takes advantages of the freedom in the choice of the parametrization and yields the order (m + 1) + [(m + 1)(2d - 1)] for a curve in Rd, where m is the degree of the

Abedallah Rababah

1995-01-01

118

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.

119

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-Chýlek 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-Chýlek 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

120

Cross approximation in electron density computations  

Microsoft Academic Search

Abstract We propose,new,tensor approximation,algorithms,for certain discrete functions related with the Hartree-Fock equation. Given a canonical,tensor representation for the electron density function (for example, produced by some packages such as MOLPRO), we obtain its Tucker approximation with much fewer parameters than the input data and Tucker approximation for the cubic root of this function, which is part of the Kohn-Sham exchange,operator.

I. V. Oseledets; D. V. Savostyanov; E. E. Tyrtyshnikov

121

An Optimal Approximation Algorithm for Bayesian Inference  

Microsoft Academic Search

Approximating the inference probability Pr[X = xjE = e] in any sense, even fora single evidence node E, is NP-hard. This result holds for belief networks that areallowed to contain extreme conditional probabilities---that is, conditional probabilitiesarbitrarily close to 0. Nevertheless, all previous approximation algorithms have failedto approximate efficiently many inferences, even for belief networks without extremeconditional probabilities.We prove that we

Paul Dagum; Michael Luby

1997-01-01

122

Multiresolution Approximations of Generalized Voronoi Diagrams  

Microsoft Academic Search

\\u000a A framework to support multiresolution approximations of planar generalized Voronoi diagrams is presented. Our proposal is:\\u000a (1) A multiresolution model based on a quadtree data structure which encodes approximations of a generalized Voronoi diagram\\u000a at different levels of detail. (2) A user driven refinement strategy which generates from the quadtree a continuous polygonal\\u000a approximation of the Voronoi diagram.

Imma Boada; Narcís Coll; Joan Antoni Sellarès

2004-01-01

123

Comparison of Approximate Methods for Handling Hyperparameters  

Microsoft Academic Search

I examine two approximate methods for computational implementation of Bayesianhierarchical models, that is, models which include unknown hyperparameters such asregularization constants and noise levels. In the `evidence framework\\

David J. C. Mackay

1999-01-01

124

Adiabatic approximation for weakly open systems  

SciTech Connect

We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is 'physically reasonable' as under wide conditions it leads to a completely positive evolution, if the original master equation can be written on a time-dependent Lindblad form. We demonstrate the approximation for a non-Abelian holonomic implementation of the Hadamard gate, disturbed by a decoherence process. We compare the resulting approximate evolution with numerical simulations of the exact equation.

Thunstroem, Patrik; Aaberg, Johan; Sjoeqvist, Erik [Department of Quantum Chemistry, Uppsala University, Box 518, SE-751 20 Uppsala (Sweden)

2005-08-15

125

On Approximation Complexity of Metric Dimension Problem  

NASA Astrophysics Data System (ADS)

We study the approximation complexity of the Metric Dimension problem in bounded degree, dense as well as in general graphs. For the general case, we prove that the Metric Dimension problem is not approximable within ( 1 - ? ) ln n for any ? > 0, unless NP subseteq DTIME( n^{log log n} ), and we give an approximation algorithm which matches the lower bound. Even for bounded degree instances it is APX-hard to determine (compute) the exact value of the metric dimension which we prove by constructing an approximation preserving reduction from the bounded degree Vertex Cover problem.

Hauptmann, Mathias; Schmied, Richard; Viehmann, Claus

126

Approximation and data fitting methods: Part 1, Introduction to numerical approximation methods  

SciTech Connect

After a general statement of the numerical approximation problem and a discussion of the existence and uniqueness of best approximations, these notes treat polynomial interpolation, piecewise polynomial interpolation (including shape preserving methods and B-splines), parametric interpolation, multivariate interpolation, and functional approximation (including uniform and least squares approximation by polynomials). 4 refs.

Fritsch, F.N.

1986-12-01

127

Novel moment closure approximations in stochastic epidemics.  

PubMed

Moment closure approximations are used to provide analytic approximations to non-linear stochastic population models. They often provide insights into model behaviour and help validate simulation results. However, existing closure schemes typically fail in situations where the population distribution is highly skewed or extinctions occur. In this study we address these problems by introducing novel second- and third-order moment closure approximations which we apply to the stochastic SI and SIS epidemic models. In the case of the SI model, which has a highly skewed distribution of infection, we develop a second-order approximation based on the beta-binomial distribution. In addition, a closure approximation based on mixture distribution is developed in order to capture the behaviour of the stochastic SIS model around the threshold between persistence and extinction. This mixture approximation comprises a probability distribution designed to capture the quasi-equilibrium probabilities of the system and a probability mass at 0 which represents the probability of extinction. Two third-order versions of this mixture approximation are considered in which the log-normal and the beta-binomial are used to model the quasi-equilibrium distribution. Comparison with simulation results shows: (1) the beta-binomial approximation is flexible in shape and matches the skewness predicted by simulation as shown by the stochastic SI model and (2) mixture approximations are able to predict transient and extinction behaviour as shown by the stochastic SIS model, in marked contrast with existing approaches. We also apply our mixture approximation to approximate a likelihood function and carry out point and interval parameter estimation. PMID:15893556

Krishnarajah, Isthrinayagy; Cook, Alex; Marion, Glenn; Gibson, Gavin

2004-12-15

128

An Approximation Algorithm for #k-SAT  

Microsoft Academic Search

We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k >= 3 within a running time that is not only non-trivial, but also significantly better than that of the currently fastest exact algorithms

Marc Thurley

2011-01-01

129

Dynamic diffusion as approximation of quantum behavior  

Microsoft Academic Search

The approximation of quantum unitary dynamics of a particle by a swarm of point wise classical samples of this particle is proposed. Quantum mechanism of speedup rests on the creation and annihilation of absolutely rigid bons, which join samples in dot wise symplexes so that the density of swarm approximate the quantum probability. This mechanism does not require differentiation of

Yuri Ozhigov

2010-01-01

130

Optimal stopping and strong approximation theorems†  

Microsoft Academic Search

Strong approximation theorems known also as (strong) invariance principles provide uniform (in time) almost sure or in average approximations (as opposed to the convergence in distribution) in the central limit theorem type results which is done by redefining in certain ways corresponding random variables or vectors on one probability space without changing their distributions. Three methods are known at present

Yuri Kifer

2007-01-01

131

The Second-Order Rytov Approximation.  

National Technical Information Service (NTIS)

An explicit and useful formulation of the solution for the second-order Rytov approximation is given. From this solution a condition of validity for the Rytov solution is obtained. It is concluded that, in general, both the Born and Rytov approximations h...

H. T. Yura

1969-01-01

132

Diagonal Pade approximations for initial value problems  

SciTech Connect

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

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

1987-06-01

133

On Approximating the Depth and Related Problems  

Microsoft Academic Search

We study the question of nding a deepest point in an arrangement of regions, and provide a fast algorithm for this problem using random sampling, showing it sucient to solve this problem when the deepest point is shallow. This implies, among other results, a fast algorithm for solving linear programming with violations approximately. We also use this technique to approximate

Boris Aronov; Sariel Har-Peled

134

Computing Nash Equilibria: Approximation and Smoothed Complexity  

Microsoft Academic Search

We advance significantly beyond the recent progress on the algorithmic complexity of Nash equilibria by solving two major open problems in the approximation of Nash equilibria and in the smoothed analysis of algorithms. • We show that no algorithm with complexity poly(n, 1 ? ) can compute an ? -approximate Nash equilibrium in a two-player game, in which each player

Xi Chen; Xiaotie Deng; Shang-Hua Teng

2006-01-01

135

Approximation for nonresonant beam target fusion reactivities  

SciTech Connect

The beam target fusion reactivity for a monoenergetic beam in a Maxwellian target is approximately evaluated for nonresonant reactions. The approximation is accurate for the DD and TT fusion reactions to better than 4% for all beam energies up to 300 keV and all ion temperatures up to 2/3 of the beam energy. 12 refs., 1 fig., 1 tab.

Mikkelsen, D.R.

1988-11-01

136

Covariance sequence approximation for parametric spectrum modeling  

Microsoft Academic Search

Parametric methods of spectrum analysis are founded on finite-dimensional models for covariance sequences. Rational spectrum approximants for continuous spectra are based on autoregressive (AR), moving average (MA), or autoregressive moving average (ARMA) models for covariance sequences. Line spectrum approximants to discrete spectra are based on cosinusoidal models for covariance sequences. In this paper we make the point that a wide

A. Beex; L. Scharf

1981-01-01

137

Approximate Bayesian Computation in Population Genetics  

Microsoft Academic Search

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

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

2002-01-01

138

Tree Approximations of Dynamic Stochastic Programs  

Microsoft Academic Search

We consider a tree-based discretization technique utilizing conditional transporta- tion distance, which is well suited for the approximation of multi-stage stochastic programming problems, and investigate corresponding convergence properties. We explain the relation between the approximation quality of the probability model and the quality of the solution. 1. Introduction. Dynamic stochastic optimization models are an up to date tool of modern

Radoslava Mirkov; Georg Ch. Pflug

2007-01-01

139

Momentum translation approximation in accelerated beta decay  

Microsoft Academic Search

The MTA (momentum translation approximation) is a nonperturbative analytical method to describe the dressing of a bound quantum state by a low frequency field which may be of very high intensity. The approximation is limited to those cases where the low frequency field in itself cannot contribute enough energy to cause transitions, but acts as an assisting field to some

H. R. Reiss; A. Shabaev; H. Wang

1997-01-01

140

Rough Vague Sets in an Approximation Space  

Microsoft Academic Search

In this paper we propose that a vague set can be approximated by two vague sets in Pawlak's approximation space. Consequently we define rough vague set and study their properties. Some propositions on rough vague sets are proved. Copyright c ? 2008 Yang's Scientific Research Institute, LLC. All rights reserved.

Ahmad A. Al-Rababah; Ranjit Biswas

2008-01-01

141

APPROXIMATING SWITCHED CONTINUOUS SYSTEMS BY RECTANGULAR AUTOMATA  

Microsoft Academic Search

An approximation procedure is presented for a class of hybrid systems in which switching occurs only when the continuous state trajectory crosses thresholds defined by a rectangular partitioning of the state space. The result of the approximation are rectangular automata, a class of hybrid automata for which a numerically robust approx- imative analysis algorithm exists. Thus, the approxima- tion procedure

O. Stursberg; S. Kowalewski

1999-01-01

142

A Theory of Mean Field Approximation  

Microsoft Academic Search

I present a theory of mean field approximation based on information ge- ometry. This theory includes in a consistent way the naive mean field approximation, as well as the TAP approach and the linear response the- orem in statistical physics, giving clear information-theoretic interpreta- tions to them.

Toshiyuki Tanaka

1998-01-01

143

Algebraic Approximation of Event Tree Sequences.  

National Technical Information Service (NTIS)

An event tree sequence XY bar is often approximated by X, i.e., by retaining only system failure events in the sequence. This paper describes a decomposition of the formula for X that produces an approximation X sub 2 to XY bar. It is shown that XY bar le...

R. B. Worrell

1982-01-01

144

Normal Approximation to the Binomial Distribution  

NSDL National Science Digital Library

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

Lane, David M.

2009-07-07

145

Approximation and Radial-Basis-Function Networks  

Microsoft Academic Search

This paper concerns conditions for the approximation of functions in certain general spaces using radial-basis-function networks. It has been shown in recent papers that certain classes of radial-basis-function networks are broad enough for universal approximation. In this paper these results are considerably extended and sharpened.

Jooyoung Park; Irwin W. Sandberg

1993-01-01

146

Finding approximate tandem repeats in genomic sequences  

Microsoft Academic Search

An efficient algorithm is presented for detecting approximate tandem repeats in genomic sequences. The algorithm is based on a flexible statistical model which allows a wide range of definitions of approximate tandem repeats. The ideas and methods underlying the algorithm are described and examined and its effectiveness on genomic data is demonstrated.

Ydo Wexler; Zohar Yakhini; Yechezkel Kashi; Dan Geiger

2004-01-01

147

Approximating Unknown Mappings: An Experimental Evaluation  

Microsoft Academic Search

Different methodologies have been introduced in recent years with the aim of approximating unknown functions. Basically, these methodologies are general frameworks for representing non-linear mappings from several input variables to several output variables. Research into this problem occurs in applied mathematics (multivariate function approximation), statistics (nonparametric multiple regression) and computer science (neural networks). However, since these methodologies have been proposed

Rafael Martí; Francisco Montes; Abdellah El-fallahi

2005-01-01

148

Techniques for Assessing Polygonal Approximations of Curves  

Microsoft Academic Search

Given the enormous number of available methods for finding polygonal approximations to curves techniques are required to assess different algorithms. Some of the standard approaches are shown to be unsuitable if the approximations contain varying numbers of lines. Instead, we suggest assessing an algorithm's results relative to an optimal polygon, and describe a measure which combines the relative fidelity and

Paul L. Rosin

1997-01-01

149

Approximate error conjugation gradient minimization methods  

DOEpatents

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

Kallman, Jeffrey S

2013-05-21

150

Stochastic population dynamics: The Poisson approximation  

NASA Astrophysics Data System (ADS)

We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics of the populations is then the result of the projection from the space of events into the space of populations that determine the state of the system (phase space). The properties of the Poisson approximation are studied in detail. Especially, error bounds for the moment generating function and the generating function receive particular attention. The deterministic approximation for the population fractions and the Langevin-type approximation for the fluctuations around the mean value are recovered within the framework of the Poisson approximation as particular limit cases. However, the proposed framework allows to treat other limit cases and general situations with small populations that lie outside the scope of the standard approaches. The Poisson approximation can be viewed as a general (numerical) integration scheme for this family of problems in population dynamics.

Solari, Hernán G.; Natiello, Mario A.

2003-03-01

151

Adiabatic approximation for nucleus-nucleus scattering  

SciTech Connect

Adiabatic approximations to few-body models of nuclear scattering are described with emphasis on reactions with deuterons and halo nuclei (frozen halo approximation) as projectiles. The different ways the approximation should be implemented in a consistent theory of elastic scattering, stripping and break-up are explained and the conditions for the theory's validity are briefly discussed. A formalism which links few-body models and the underlying many-body system is outlined and the connection between the adiabatic and CDCC methods is reviewed.

Johnson, R.C. [Department of Physics, School of Electronics and Physical Sciences, University of Surrey, Guildford, Surrey, GU2 7XH (United Kingdom)

2005-10-14

152

Tailored Testing, An Application of Stochastic Approximation.  

National Technical Information Service (NTIS)

Some stochastic approximation procedures are considered in connection with the following problem. How shall one choose a sequence of test questions in order to estimate as accurately as possible a given examinee's standing on some psychological dimension....

F. M. Lord

1971-01-01

153

Approximate Structural Analysis Techniques Employing Undetermined Parameters.  

National Technical Information Service (NTIS)

A unified approach for the approximate solution of boundary value problems by undetermined parameters is presented. It is demonstrated how the general technique reduces to the well known method or Ritz, Galerkin, least-squares, collocations, Mikhlin, and ...

I. U. Ojalvo R. F. Russell

1966-01-01

154

Matrix rank in variational nodal approximations  

Microsoft Academic Search

Diffusion and transport variational nodal methods are being used increasingly for two and three-dimensinal fast reactor calculations in both Cartesian and hexagonal geometries. This report is concerned with matrix rank in variational nodal approximations.

C. B. Carrico; G. Palmoitti; E. E. Lewis

1994-01-01

155

Cubic approximation neural network for multivariate functions.  

PubMed

This paper introduces a novel neural network architecture-cubic approximation neural network (CANN), capable of local approximation of multivariate functions. It is particularly simple in concept and in structure. Its simplicity enables a quantitative evaluation of its approximation capabilities, namely, for a desired error bound the size of the needed network can be calculated. In addition, if a training session is used, a thorough analysis of the learning process performance is performed. The trade-off between the rate of learning and the steady-state performance is clearly demonstrated. On the other hand, this approach suffers from the problem common to all local approximation networks-the number of neurons grows exponentially with the dimension of the input vector. PMID:12662834

Stein, D; Feuer, A

1998-03-01

156

Inhomogeneous Diophantine approximation of some Hurwitzian numbers  

NASA Astrophysics Data System (ADS)

We continue the work of Takao Komatsu, and consider the inhomogeneous approximation constant L(?,?) for Hurwitzian ? and ??Q(?)+Q. The current work uses a compactness theorem to relate such inhomogeneous constants to the homogeneous approximation constants. Among the new results are: a characterization of such pairs ?,? for which L(?,?) = 0, consideration of small values of n2L(e2/s,?) for ? = (r?+m)/n, and the proof of a conjecture of Komatsu.

Bumby, Richard T.; Flahive, Mary E.

2008-01-01

157

On Approximating the TSP with Intersecting Neighborhoods  

Microsoft Academic Search

In the TSP with neighborhoods problem we are given a set of n regions (neighborhoods) in the plane, and seek to find a minimum length TSP tour that goes through all the regions. We give\\u000a two approximation algorithms for the case when the regions are allowed to intersect: We give the first O(1)-factor approximation algorithm for intersecting convex fat objects

Khaled M. Elbassioni; Aleksei V. Fishkin; René Sitters

2006-01-01

158

Space-efficient approximate Voronoi diagrams  

Microsoft Academic Search

(MATH) Given a set $S$ of $n$ points in $\\\\IR^d$, a {\\\\em $(t,\\\\epsilon)$-approximate Voronoi diagram (AVD)} is a partition of space into constant complexity cells, where each cell $c$ is associated with $t$ representative points of $S$, such that for any point in $c$, one of the associated representatives approximates the nearest neighbor to within a factor of $(1+\\\\epsilon)$. Like

Sunil Arya; Theocharis Malamatos; David M. Mount

2002-01-01

159

Local linear approximations of jump diffusion processes  

Microsoft Academic Search

Local linear approximations have been the main component in the\\u000aconstruction of a class of effective numerical integrators and\\u000ainference methods for diffusion processes. In this note, two local\\u000alinear approximations of jump diffusion processes are introduced\\u000aas a generalization of the usual ones. Their rate of uniform\\u000astrong convergence is also studied.

J. C. Jimenez; F. Carbonell

2006-01-01

160

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

161

Legendre-tau Approximation for Functional Differential Equations. Part 3: Eigenvalue Approximations and Uniform Stability.  

National Technical Information Service (NTIS)

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the un...

K. Ito

1984-01-01

162

Calculus rules for global approximate minima and applications to approximate subdifferential calculus  

Microsoft Academic Search

We provide calculus rules for global approximate minima concerning usual operations on functions. The formulas we obtain are then applied to approximate subdifferential calculus. In this way, new results are presented, for example on the approximate subdifferential of a deconvolution, or on the subdifferential of an upper envelope of convex functions.

M. Volle

1994-01-01

163

Approximation techniques in strongly correlated electron systems  

NASA Astrophysics Data System (ADS)

This dissertation details the study and application of three approximation techniques for strongly correlated electron systems. These techniques are the dynamical mean field approximation (DMFA), dynamical cluster approximation (DCA) and cellular dynamical mean field theory (CDMFT). The DMFA is a local approximation in which electron-electron correlations are only dynamical in time and all non-local correlations in space are suppressed. This technique becomes exact in the limit of infinite dimensions. The DCA and CDMFT are both approaches to systematically add non-local correlations to the DMFA. The DCA is a cluster technique in reciprocal space while the CDMFT is a cluster technique in real space. Both techniques become exact when the cluster size, diverges. Two chapters of this dissertation have been dedicated to the DCA, its combination with a perturbation theory technique called the fluctuation exchange approximation (FLEX) to study the Hubbard model and a microscopic theory that uniquely prescribes how to implement the DCA in terms of Feynman diagrammatics for the thermodynamic potential. A comparison between the convergence behaviors of the DCA and CDMFT is the topic of another chapter. Lastly, the DMFA is employed to study ferromagnetism in III--V dilute magnetic semiconductors with the particular example of Ga1-xMn xAs. The last chapter summarizes the results and conclusions presented in individual chapters and outlines prospective future developments.

Aryanpour, Karan

164

Mimetic difference approximations of partial differential equations  

SciTech Connect

Goal was to construct local high-order difference approximations of differential operators on nonuniform grids that mimic the symmetry properties of the continuum differential operators. Partial differential equations solved with these mimetic difference approximations automatically satisfy discrete versions of conservation laws and analogies to Stoke`s theorem that are true in the continuum and therefore more likely to produce physically faithful results. These symmetries are easily preserved by local discrete high-order approximations on uniform grids, but are difficult to retain in high-order approximations on nonuniform grids. We also desire local approximations and use only function values at nearby points in the computational grid; these methods are especially efficient on computers with distributed memory. We have derived new mimetic fourth-order local finite-difference discretizations of the divergence, gradient, and Laplacian on nonuniform grids. The discrete divergence is the negative of the adjoint of the discrete gradient, and, consequently, the Laplacian is a symmetric negative operator. The new methods derived are local, accurate, reliable, and efficient difference methods that mimic symmetry, conservation, stability, the duality relations and the identities between the gradient, curl, and divergence operators on nonuniform grids. These methods are especially powerful on coarse nonuniform grids and in calculations where the mesh moves to track interfaces or shocks.

Hyman, J.M.; Shashkov, M.; Staley, M.; Kerr, S. [Los Alamos National Lab., NM (United States); Steinberg, S. [New Mexico Univ., Albuquerque, NM (United States); Castillo, J. [San Diego State Univ., CA (United States)

1997-08-01

165

Application of the GW Approximation to Trans -  

NASA Astrophysics Data System (ADS)

The emphasis of the work described in this dissertation is the application of a many-body Greens function technique called the GW approximation. Pilot calculations have been performed implementing this technique on the quasi-one -dimensional system, trans-polyacetylene. Until recently, standard procedures for band structure calculations have been limited to approximations such as the Hartree-Fock or local density approximation in which electrons are assumed to feel an effective one-electron potential. These techniques do not rigorously address the long-range coulomb interaction (correlation effects) between the electrons, hence the single-particle eigenvalues associated with them have no formal justification as being quasiparticle in nature and as a result, cannot accurately describe the spectra in a solid. Although both techniques are widely used, band gap discrepancies remain problematic. The present approach requires solving the Dyson equation, which contains a non-local, non-Hermitian, energy -dependent operator called the self-energy. Included in this operator are all the effects of exchange and correlation among the electrons which are not completely accounted for in the Hartree-Fock or local density approximations. Electronic spectra and energy-loss calculations were obtained using the first-order approximation, the GW method, which models the self-energy operator as the product of a single-particle Greens function and a Coulomb interaction screened by the dielectric response of the system.

Ethridge, Elana Chris

166

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

167

On the Gaussian Approximation for Master Equations  

NASA Astrophysics Data System (ADS)

We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach (the fact that the probability distribution is Gaussian at first order). We analyze the scaling of the error with a large parameter of the system and compare it with van Kampen's method. Our theoretical analysis and the study of several examples shows that the Gaussian approximation turns out to be more accurate than van Kampen's expansion at first order. This could be specially important for problems involving stochastic processes in systems with a small number of particles.

Lafuerza, Luis F.; Toral, Raul

2010-09-01

168

New approximate formula for Arrhenius temperature integral  

Microsoft Academic Search

In this paper a more precise approximate formula for Arrhenius temperature integral, i.e., ?lnP(u)=0.37773896+1.89466100lnu+1.00145033u, is proposed, by using two-step linearly fitting process: (i) the linear dependence of dlnp(u)\\/du on 1\\/u and (ii) the linear dependence of (lnp(u)?clnu) on u. Values of p(u) at different u were directly obtained from numerical integration of temperature integral without derivation from any approximating infinite

Wanjun Tang; Yuwen Liu; Hen Zhang; Cunxin Wang

2003-01-01

169

ANALOG QUANTUM NEURON FOR FUNCTIONS APPROXIMATION  

SciTech Connect

We describe a system able to perform universal stochastic approximations of continuous multivariable functions in both neuron-like and quantum manner. The implementation of this model in the form of multi-barrier multiple-silt system has been earlier proposed. For the simplified waveguide variant of this model it is proved, that the system can approximate any continuous function of many variables. This theorem is also applied to the 2-input quantum neural model analogical to the schemes developed for quantum control.

A. EZHOV; A. KHROMOV; G. BERMAN

2001-05-01

170

Approximate average deployments versus defense parameters  

SciTech Connect

Calculations of the number of reentry vehicles (RVs) killed as a function of missile and defense parameters can be well approximated by analytic expressions that are valid for all numbers of missiles and interceptors. The approximation uniformly underestimates the effectiveness of boost-phase defenses: the discrepancies in kill rates are about 10%. If if is used to size the boost phase of two-layer defenses, the uncertainties would at worst double the demands on the midcourse layer, which is generally a minor part of the total. 4 refs., 3 figs.

Canavan, G.H.

1991-12-01

171

Number-operator approximation for pairing  

SciTech Connect

Conservation of particle number in the number-operator approximation of Otsuka and Arima is shown to require a particular normalization for the pair-creation operator. Even with this normalization, two difficulties arise: (a) the average number of particles in a shell can easily violate the Pauli principle, and (b) the mean square fluctuation of the particle number can be negative. As a consequence of the tendency to Pauli violation, the approximate ground-state expectation of the single-particle energy per particle is too low and fails to increase with the number of particles.

Vincent, C.M.

1983-01-01

172

Analytic approximation of matrix functions in Lp  

Microsoft Academic Search

We consider the problem of approximation of matrix functions of class Lp on the unit circle by matrix functions ana- lytic in the unit disk in the norm of Lp, 2 p < 1. For an m n matrix function in Lp, we consider the Hankel operator H : Hq(Cn) ! H2 (C m), 1=p + 1=q = 1=2. It

Laurent Baratchart; F. L. Nazarov; V. V. Peller

2009-01-01

173

Environmental stress: Approximate entropy approach revisited  

Microsoft Academic Search

Radiotelemetred male Wistar outbrad rats and borderline hypertensive rats (BHR) were exposed to acute and chronic environmental stress. Approximate entropy (ApEn) approach is applied in order to investigate the pulse interval (PI) response to two different types of environmental stress: shaker and restrain stress. The performance of ApEn method was evaluated from the parameter selection point of view. The purpose

Tatjana Loncar-Turukalo; Dragana Bajic; Olivera Sarenac; Nina Japundzic-Zigon; A. Boskovic

2009-01-01

174

Spline Approximation of Thin Shell Dynamics.  

National Technical Information Service (NTIS)

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 sh...

R. C. H. Delrosario R. C. Smith

1996-01-01

175

Analytic Approximations for Moist Convectively Adjusted Regions  

Microsoft Academic Search

Solutions are obtained for convective regions in a continuously stratified, linearized primitive equation model using a smoothly posed moist convective adjustment parameterization of cumulus convection. In the approximation in which the convective adjustment time is fast compared to other processes, the vertical structure of the temperature field is constrained to be close to the quasi-equilibrium structure determined by the convective

Jia-Yuh Yu; J. David Neelin

1997-01-01

176

Approximate Time-Parallel Cache Simulation  

Microsoft Academic Search

In time-parallel simulation, the simulation time axis is de- composed into a number of slices which are assigned to parallel processes for concurrent simulation. Although a promising parallelization technique, it is difficult to be ap- plied. Recently, using approximation with time-parallel simulation has been proposed to extend the class of suit- able models and to improve the performance of existing

Tobias Kiesling

2004-01-01

177

Local Graph Partitions for Approximation and Testing  

Microsoft Academic Search

We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of bounded-degree graphs with an excluded minor, and in general, for any hyperfinite class o f bounded-degree graphs. These oracles utilize only local compu- tation to consistently answer queries about a global partition that breaks the graph into

Avinatan Hassidim; Jonathan A. Kelner; Huy N. Nguyen; Krzysztof Onak

2009-01-01

178

Classical approximation to quantum cosmological correlations  

Microsoft Academic Search

We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. We study, as a toy model, phi3 theory on a de Sitter background for a massless minimally coupled scalar field phi. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be

Meindert van der Meulen; Jan Smit

2007-01-01

179

On approximating the depth and related problems  

Microsoft Academic Search

In this paper, we study the problem of finding a disk covering the largest number of red points, while avoiding all the blue points. We reduce it to the question of finding a deepest point in an arrangement of pseudodisks and provide a near-linear expected-time randomized approximation algorithm for this problem. As an application of our techniques, we show how

Boris Aronovt; Sariel Har-Peled

2005-01-01

180

An Approximate Minimum Degree Ordering Algorithm  

Microsoft Academic Search

An Approximate Minimum Degree ordering algorithm (AMD) for preordering a symmetric sparse matrix prior to numerical factorization is presented. We use techniques based on the quotient graph for matrix factorization that allow us to obtain computationally cheap bounds on the minimum degree. We show that these bounds are often equal to the actual degree. The resulting algorithm is typically much

P. r. Amestoy; T. a. Davis; I. s. Duff

1994-01-01

181

Brownian approximations to first passage probabilities  

Microsoft Academic Search

By direct probabilistic argument one term of an Edgeworth type asymptotic expansion is obtained for certain first passage distributions for random walks. These results provide partial justification for and extensions of approximations suggested earlier as a heuristic consequence of Laplace transform calculations.

D. Siegmund; Yih-Shyh Yuh

1982-01-01

182

An experimental approximation of thought reform  

Microsoft Academic Search

Thought reform processes were simulated in the laboratory with 96 Ss. The Ss were required to evolve an extended series of alternative responses from their own behavior repertoire, in successive approximation to the criterion demanded by the E, which remained unknown to the Ss. This study sought to achieve the abandonment of a basic behavior pattern and the adoption of

O. Henry Harsch; Herbert Zimmer

1965-01-01

183

Randomized Self-assembly for Approximate Shapes  

Microsoft Academic Search

In this paper we design tile self-assembly systems which assemble arbitrarily close approximations to target squares with arbitrarily high probability. This is in contrast to previous work which has only considered deterministic assemblies of a single shape. Our technique takes advantage of the ability to assign tile concentrations to each tile type of a self-assembly system. Such an assignment yields

Ming-yang Kao; Robert T. Schweller

2008-01-01

184

Audiovisual Content in Europe: Transnationalization and Approximation  

Microsoft Academic Search

This article is concerned with the development of television in Europe in the context of commercialization and the complex global–local nexus defining contemporary cultural spheres. It is argued that since the mid 1980s the trajectory of European television, notwithstanding local particularities, has been defined by an underlying trend towards transnationalization and approximation. The aim of this article is to demonstrate

Andrea Esser

2007-01-01

185

Gauss-Newton approximation to Bayesian learning  

Microsoft Academic Search

This paper describes the application of Bayesian regularization to the training of feedforward neural networks. A Gauss-Newton approximation to the Hessian matrix, which can be conveniently implemented within the framework of the Levenberg-Marquardt algorithm, is used to reduce the computational overhead. The resulting algorithm is demonstrated on a simple test problem and is then applied to three practical problems. The

F. Dan Foresee; Martin T. Hagan

1997-01-01

186

Eikonal Approximation in Partial Wave Version.  

National Technical Information Service (NTIS)

The eikonal approximation is formulated in a partial wave version. This makes it possible to evaluate the electron scattering from many-electron atomic systems in a direct manner with a formal procedure similar to the Coulomb-Born and distorted wave appro...

W. Qian H. Narumi

1989-01-01

187

Segmentation Using Locally Optimal Piecewise Approximations.  

National Technical Information Service (NTIS)

This note deals with a method of segmenting one-dimensional patterns. It is based on a scheme for detecting natural 'sides' (= maximal intervals of approximately constant slope) on a simple closed curve. Analogously, the method described in this note dete...

A. Rosenfeld A. F. Blumenthal L. S. Davis

1975-01-01

188

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 Öhm; Marco Häser; Reinhart Ahlrichs; Marco Ser

1995-01-01

189

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

190

Positive Linear Programming, Parallel Approximation and PCP's  

Microsoft Academic Search

. Several sequential approximation algorithms are based onthe following paradigm: solve a linear or semidefinite programming relaxation,then use randomized rounding to convert fractional solutions of therelaxation into integer solutions for the original combinatorial problem.We demonstrate that such a paradigm can also yield parallel approximationalgorithms by showing how to convert certain linear programmingrelaxations into essentially equivalent positive linear programming [18]...

Luca Trevisan

1996-01-01

191

Approximate Frequency Counts over Data Streams  

Microsoft Academic Search

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

Gurmeet Singh Manku; Rajeev Motwani

2002-01-01

192

Pose Calibration using Approximately Planar Urban Structure  

Microsoft Academic Search

We introduce an algorithm that automatically aligns images with partial wireframe models to compute extrinsic camera parameters with respect to the model reference frame. Aligned imagery is fused with the model to incorporate high-resolution textures and to facilitate context sensitive image processing. The technique is designed to exploit the approximately planar structure commonly found in human-made environments such as building

Christopher Jaynes; Mike Partington

193

Approximation for the Effect of Working Overtime.  

National Technical Information Service (NTIS)

This paper presents a two-moment approximation for the amount of work at the beginning of each period in a production or service system with overtime by exploiting the similarity with the D(G)1 queue. The approach is based on the one presented in De Kok (...

J. van der Wal

1996-01-01

194

Approximate theory for radiation from mesh reflectors  

Microsoft Academic Search

Reconfigurable shaped reflector antennas have potential applications in satellite communications and satellite broadcasting. When a metallic mesh is employed pillowing occurs between the points at which the reflector is constrained. This paper describes an approximate theory to explain this behavior, and results are obtained which are in good agreement with exact analysis. The effect of pillowing is found to produce

G. T. Poulton; H. Zhou; P. J. B. Clarricoats

1988-01-01

195

Approximate Blast Theory: Application to Solids  

NASA Astrophysics Data System (ADS)

A method for analyzing strong shock waves in solids is developed for one-dimensional geometries. An approximation to classical Taylor-Sedov theory is applied to materials described by a Mie-Grueneisen equation of state. This methodology is then extended to the near-field case where source mass is not negligible. Example solution results are given.

Hutchens, Gregory J.

2002-07-01

196

Approximate blast theory: Application to solids  

NASA Astrophysics Data System (ADS)

A method for analyzing strong shock waves in solids is developed for one-dimensional geometry. An approximation to classical Taylor-Sedov theory is applied to materials described by the Mie-Gruneisen equation of state. This methodology is then extended to the near-field case where source mass is not negligible. Example solution results are given.

Hutchens, Gregory

2001-06-01

197

Searching for approximate description of decision classes  

Microsoft Academic Search

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

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

1996-01-01

198

A simple, approximate model of parachute inflation  

Microsoft Academic Search

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

Macha

1992-01-01

199

Thermally stimulated depolarizations: disclosing an approximate universality  

NASA Astrophysics Data System (ADS)

This paper presents an approximate universality displayed by thermally stimulated depolarization currents ruled by stretched exponential relaxations when properly re-scaled. A visually perfect universality occurs especially when the energy and the heating rate are varied. It becomes somewhat poorer when the frequency factor or the stretched exponent changes. Empirical relations between the half widths and other pertinent parameters are given.

Leal Ferreira, G. F.; Moreno Alfaro, R. A.; Figueiredo, M. T.

1996-12-01

200

Real-time creased approximate subdivision surfaces  

Microsoft Academic Search

We present an extension of recently developed Loop and Schaefer's approximation of Catmull-Clark surfaces (ACC) for surfaces with creases and corners which are essential for most applications. We discuss the integration of ACC into Valve's Source game engine and analyze performance of our implementation.

Denis Kovacs; Jason Mitchell; Shanon Drone; Denis Zorin

2009-01-01

201

Nuclear optical potential in first born approximation  

NASA Astrophysics Data System (ADS)

We calculate nuclear scalar and vector optical potentials in the first Born approximation (FBA) using ?, ?, ?, ?, ?, and ? meson exchanges. We obtain strong attractive scalar and repulsive vector optical potentials which are the characteristics of relativistic approaches based upon Dirac phenomenology. Research supported in part by the Department of Energy.

Iqbal, M. J.

1985-05-01

202

Quantization of fractional systems using WKB approximation  

NASA Astrophysics Data System (ADS)

The Caputo’s fractional derivative is used to quantize fractional systems using (WKB) approximation.The wave function is build such that the phase factor is the same as the Hamilton’s principle function “S”. The energy eigenvalue is found to be in exact agreement with the classical case. To demonstrate our approach an example is investigated in details.

Rabei, Eqab M.; Muslih, Sami I.; Baleanu, Dumitru

2010-04-01

203

Approximate String Matching in DNA Sequences  

Microsoft Academic Search

Approximate string matching on large DNA sequences data is very important in bioinformatics. Some studies have shown that suffix tree is an efficient data structure for ap- proximate string matching. It performs better than suffix array if the data structure can be stored entirely in the mem- ory. However, our study find that suffix array is much bet- ter than

Lok-lam Cheng; David Wai-lok Cheung; Siu-ming Yiu

2003-01-01

204

On Rational Approximations of Groups of Operators.  

National Technical Information Service (NTIS)

Stability and convergence of rational approximations r to the n power (hA), nh = t, of a strongly continuous semigroup e to the tA power on a Banach space X, when the absolute value r(Z) is less than or equal to 1 for Re Z is less than or equal to 0, is o...

P. Brenner V. Thomee

1978-01-01

205

The complexity of approximating the entropy  

Microsoft Academic Search

The Shannon entropy is a measure of the randomness of a distribution, and plays a central role in statistics, information theory, and data compression. Knowing the entropy of a random source can shed light on the compressibility of data produced by such a source. We consider the complexity of approximating the entropy under various different assumptions on the way the

T. Batu; S. Dasgupta; R. Kumar; R. Rubinfeld

2002-01-01

206

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

207

Strong Approximation on LOG Dense Sets.  

National Technical Information Service (NTIS)

Extensions of classical probability limit theorems involving log average and log density are considered. The purpose is to extend Fisher's approximation theorem to i.i.d. sequences the set X(n) with EX (upper bound 2, lower bound 1) + infinity belonging t...

I. Berkes H. Dehling

1991-01-01

208

Closed Form Approximations for Spread Options  

Microsoft Academic Search

This article expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new closed form approximation for the price of a European spread option

Aanand Venkatramanan; Carol Alexander

2011-01-01

209

Neuro-fuzzy systems for function approximation  

Microsoft Academic Search

We present a neuro-fuzzy architecture for function approximation based on supervised learning. The learning algorithm is able to determine the structure and the parameters of a fuzzy system. The approach is an extension to our already published NEFCON and NEFCLASS models which are used for control or classification purposes. The proposed extended model, which we call NEFPROX, is more general

Detlef Nauck; Rudolf Kruse

1999-01-01

210

Speech synthesis using approximate matching of syllables  

Microsoft Academic Search

In this paper we propose a technique for a syllable based speech synthesis system. While syllable based synthesizers produce better sounding speech than diphone and phone, the coverage of all syllables is a non-trivial issue. We address the issue of coverage of syllables through approximating the syllable when the required syllable is not found. To verify our hypothesis, we conducted

E. Veera Raghavendra; B. Yegnanarayana; Kishore Prahallad

2008-01-01

211

Approximate Formulas for Photoelectric Counting Distributions.  

National Technical Information Service (NTIS)

The validity of a simple approximate formula for the photoelectric counting probability in a thermal optical field, which was proposed by one of us (L.M.) in 1959, is investigated. The formula is based on a generalization of the Bose-Einstein distribution...

G. Bedard J. C. Chang L. Mandel

1967-01-01

212

Approximately vanishing of topological cohomology groups  

NASA Astrophysics Data System (ADS)

In this paper, we establish the pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers-Ulam stability of some functional equations. We prove that for each Banach algebra A, Banach A-bimodule X and positive integer n,Hn(A,X)=0 if and only if the nth cohomology group approximately vanishes.

Moslehian, M. S.

2006-06-01

213

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

214

Testing the Frozen-Flow Approximation  

NASA Astrophysics Data System (ADS)

We investigate the accuracy of the frozen-flow approximation (FFA), recently proposed by Matarrese et al., for tracing of the non-linear 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 Melon, Pellman & Shandarin to test the Zel'dovich approximation. The FFA performs reasonably well in a statistical sense (for example, in reproducing the counts-in-cells distribution) at small scales, but it does poorly in the cross-correlation with N-body simulations, which means that it is generally not moving mass to the right place, especially in models with high small-scale power.

Melott, A. L.; Lucchin, F.; Matarrese, S.; Moscardini, L.

1994-05-01

215

Momentum translation approximation in accelerated beta decay  

NASA Astrophysics Data System (ADS)

The MTA (momentum translation approximation) is a nonperturbative analytical method to describe the dressing of a bound quantum state by a low frequency field which may be of very high intensity. The approximation is limited to those cases where the low frequency field in itself cannot contribute enough energy to cause transitions, but acts as an assisting field to some other interaction. We examine the limits of applicability of the MTA as it relates to the treatment of the acceleration of forbidden beta decay by intense external fields. The electric field F of any practicable applied field cannot possibly be large enough to cause transitions, but we find that validity of the MTA depends on F/? , where ? is the frequency. In those terms we show that the MTA should work well for the beta decay application.

Reiss, H. R.; Shabaev, A.; Wang, H.

1997-04-01

216

Approximate gauge symmetry of composite vector bosons  

NASA Astrophysics Data System (ADS)

It can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.

Suzuki, Mahiko

2010-08-01

217

The approximability of the String Barcoding problem  

PubMed Central

The String Barcoding (SBC) problem, introduced by Rash and Gusfield (RECOMB, 2002), consists in finding a minimum set of substrings that can be used to distinguish between all members of a set of given strings. In a computational biology context, the given strings represent a set of known viruses, while the substrings can be used as probes for an hybridization experiment via microarray. Eventually, one aims at the classification of new strings (unknown viruses) through the result of the hybridization experiment. In this paper we show that SBC is as hard to approximate as Set Cover. Furthermore, we show that the constrained version of SBC (with probes of bounded length) is also hard to approximate. These negative results are tight.

Lancia, Giuseppe; Rizzi, Romeo

2006-01-01

218

The approximability of the String Barcoding problem.  

PubMed

The String Barcoding (SBC) problem, introduced by Rash and Gusfield (RECOMB, 2002), consists in finding a minimum set of substrings that can be used to distinguish between all members of a set of given strings. In a computational biology context, the given strings represent a set of known viruses, while the substrings can be used as probes for an hybridization experiment via microarray. Eventually, one aims at the classification of new strings (unknown viruses) through the result of the hybridization experiment. In this paper we show that SBC is as hard to approximate as Set Cover. Furthermore, we show that the constrained version of SBC (with probes of bounded length) is also hard to approximate. These negative results are tight. PMID:16895600

Lancia, Giuseppe; Rizzi, Romeo

2006-08-08

219

Approximate gauge symmetry of composite vector bosons  

SciTech Connect

It can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.

Suzuki, Mahiko [Lawrence Berkeley National Laboratory and Department of Physics, University of California, Berkeley, California 94720 (United States)

2010-08-15

220

Evolutionary Algorithm in Approximation of Defuzzification Functional  

NASA Astrophysics Data System (ADS)

The space of ordered fuzzy numbers (OFN) forms a normed space on which defuzzification functionals can be defined. They play the main role when dealing with fuzzy controllers and fuzzy inference systems. An approximation formula for a general nonlinear functional is given. If a training set is given which describes an action of the functional on OFN then a dedicated evolutionary algorithm can be presented to determine its form. Genotypes composed of chromosomes are proposed together with the fitness function and genetic operators. Some numerical experiments are also performed in the case when ordered fuzzy numbers are given in terms of step functions. For the comparison an approximation procedure with the use of artificial neural networks is also implemented.

W?grzyn-Wolska, Katarzyna; Borzymek, Piotr; Kosi?ski, Witold

2010-09-01

221

Validity of the energy sudden approximation  

SciTech Connect

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

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

1983-03-15

222

Approximate Euclidean shortest path in 3-space  

Microsoft Academic Search

Papadimitriou's approximation approach to the Euclidean shortest path (ESP) problem in 3-space is revisited. As this problem is NP-hard, his approach represents an important step towards practical algorithms. Unfortunately, there are non-trivial gaps in the original description. Besides giving a complete treatment, we also give an alternative to his subdivision method which has some nice properties. Among the tools needed

Joonsoo Choi; Jürgen Sellen; Chee-Keng Yap

1994-01-01

223

Approximating the Permanent via Nonabelian Determinants  

Microsoft Academic Search

Celebrated work of Jerrum, Sinclair, and Vigoda has established that the\\u000apermanent of a {0,1} matrix can be approximated in randomized polynomial time\\u000aby using a rapidly mixing Markov chain. A separate strand of the literature has\\u000apursued the possibility of an alternate, purely algebraic, polynomial-time\\u000aapproximation scheme. These schemes work by replacing each 1 with a random\\u000aelement of

Cristopher Moore; Alexander Russell

2009-01-01

224

Improved Approximation of Linear Threshold Functions  

Microsoft Academic Search

Abstract We prove two main results on how arbitrary linear threshold functions f(x) = sign(w ¢ x ¡ µ) over the n-dimensional Boolean hypercube can be approximated by simple threshold functions. Our flrst result shows that every n-variable threshold function f is †-close to a threshold function depending only on Inf(f)A preliminary version of this work appeared in the Proceedings

Ilias Diakonikolas; Rocco A. Servedio

2009-01-01

225

Effective Computation of Rational Approximants and Interpolants  

Microsoft Academic Search

This paper considers the problem of efiective algorithms for some problems having structured co- e-cient matrices. Examples of such problems include rational approximation and rational interpolation. The corresponding coe-cient matrices include Hankel, Toeplitz and Vandermonde-like matrices. Efiective implies that the algorithms studied are suitable for implementation in either a numeric environment or else a symbolic environment. The paper includes two

Bernhard Beckermann; George Labahn

2000-01-01

226

A Approximation Algorithm for MAX 3SAT?  

Microsoft Academic Search

We describe a randomized approximation algorithm which takes an instance of MAX 3SAT as input. If the instance—a collection of clauses each of lengthat most three—is satisfi- able, then the expected weight of the assignment found is at least of optimal. We provide strong evidence (but not a proof) that the algorithm performs equally well on arbitrary MAX 3SAT instances.

Howard Karloff; Uri Zwick

227

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

228

On Approximate Range Counting and Depth  

Microsoft Academic Search

We improve the previous results by Aronov and Har-Peled (SODA’05) and Kaplan and Sharir (SODA’06) and present a randomized\\u000a data structure of O(n) expected size which can answer 3D approximate halfspace range counting queries in \\u000a \\u000a expected time, where k is the actual value of the count. This is the first optimal method for the problem in the standard decision tree

Peyman Afshani; Timothy M. Chan

2009-01-01

229

On approximate range counting and depth  

Microsoft Academic Search

We improve the previous results by Aronov and Har-Peled (SODA'05) and Kaplan and Sharir (SODA'06) and present a randomized data structure of O(n) expected sizewhich can answer 3D approximate halfspace range counting queries in O(log n\\/k) expected time, where k is the actual value of the count. This is the first optimal method for the problem in the standard decision

Peyman Afshani; Timothy M. Chan

2007-01-01

230

Residual Algorithms: Reinforcement Learning with Function Approximation  

Microsoft Academic Search

A number of reinforcement learning algorithms have been developed that are guaranteed to converge to the optimal solution when used with lookup tables. It is shown, however, that these algorithms can easily become unstable when implemented directly with a general function-approximation system, such as a sigmoidal multilayer perceptron, a radial-basis- function system, a memory-based learning system, or even a linear

Leemon C. Baird III

1995-01-01

231

Bubble and Hermite Natural Element Approximations  

Microsoft Academic Search

In this paper, new natural element approximations are proposed, in order to address issues associated with incompressibility\\u000a as well as to increase the accuracy in the Natural Element Method (NEM). The NEM exhibits attractive features such as interpolant\\u000a shape functions or auto-adaptive domain of influence, which alleviates some of the most common difficulties in meshless methods.\\u000a Nevertheless, the shape functions

J. Yvonnet; P. Villon; F. Chinesta

232

Trigonometric approximation in Lp-norm  

NASA Astrophysics Data System (ADS)

We shall weaken the conditions of monotonicity given by Chandra [J. MathE Anal. Appl. 275 (2002) 13-26], where he investigated trigonometrical polynomials associated with f[set membership, variant]Lip([alpha],p) (0<[alpha][less-than-or-equals, slant]1, p[greater-or-equal, slanted]1) to approximate f in Lp-norm to the degree of O(n-[alpha]) (0<[alpha][less-than-or-equals, slant]1).

Leindler, László

2005-02-01

233

The logarithmic discretization embedded cluster approximation  

SciTech Connect

This work proposes a new approach to study transport properties of highly correlated local structures. The method, dubbed the logarithmic discretization embedded cluster approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson s idea of a logarithmic discretization of the representation of the band. A many-body formalism provides a solid theoretical foundation to the method.

Anda, E. V. [Pontificia Universidade, Brazil; Chiappe, G. [Universidad de Alicante; Busser, C. A. [Oakland University, Rochester, MI; Davidovich, M. A. [Pontificia Universidad Catolica-Rio de Janerio, Brazil; Martins, G. B. [Oakland University, Rochester, MI; Heidrich-Meisner, F. [Institut fur Physikalische Chemie der RWTH; Dagotto, Elbio R [ORNL

2009-01-01

234

The concept of the approximants of quasicrystals  

SciTech Connect

The study of quasicrystals has always been associated with the research of related crystalline phases. Quasicrystalline alloys are rarely single phase and the secondary phases are usually crystalline. For example, in melt-spun ribbons of Ti{sub 2}Fe alloys, the following phases are observed: an icosahedral phase, Ti{sub 2}Fe (Ti{sub 2}Ni type), {alpha}-Ti{sub 2}Fe ({alpha}-AlMnSi type), TiFe (CsCl type, or B2 structure) and {beta}-Ti (W type, or A3 structure). Similar phases were also observed in Ti-Ni alloys. In Al-Cu-Fe quasicrystalline alloys, one finds {lambda}-Al{sub 13}Fe{sub 4}, a cubic phase (a B2 superstructure), {omega}-Al{sub 7}Cu{sub 2}Fe, {phi}-Al{sub 10}Cu{sub 10}Fe, {theta}-Al{sub 2}Cu, etc. Valence electron concentration has been proposed as a new criterion to define the approximants to quasicrystals: these should satisfy two basic requirements: (1) they possess approximately the same valence electron concentration as that of the corresponding quasicrystal; (2) they arise from the projection of a hyper crystal along rational directions. The first criterion indicates that the approximants are Hume-Rothery phases existing in an e/a-constant band in the phase diagrams; the second implies that their atomic structures are related to those of quasicrystals. According to their positions in the phase diagrams, they can be classified into two groups: the phases to the left of quasicrystal composition are complex approximants retaining some local quasi-periodic structure; those to the right include B2 and its superstructures.

Dong, C. [Beijing Lab. of Electron Microscopy, Beijing (China)]|[Dalian Univ. of Technology (China). Dept. of Materials Engineering

1995-07-15

235

On Surface Approximation Using Developable Surfaces  

Microsoft Academic Search

We introduce a method for approximating a given surface by a developablesurface. It will be either a G1surface consisting of pieces of cones or cylindersof revolution or a GrNURBS developable surface. Our algorithm will also dealproperly with the problems of reverse engineering and produce robust approximationof given scattered data. The presented technique can be applied incomputer aided manufacturing, e.g. in

H.-Y. Chen; I.-K. Lee; Stefan Leopoldseder; Helmut Pottmann; Thomas Randrup; Johannes Wallner

1999-01-01

236

Largescale Structure and the Adhesion Approximation  

NASA Astrophysics Data System (ADS)

The adhesion approximation, introduced by Gurbatov, Saichev & Shandarin, greatly extends the useful range of the Zel'dovich (quasi-linear) approximation by using artificial viscosity to mimic some of the effects of non-linear gravity. We describe a fast, three-dimensional implementation of the adhesion approximation, compare adhesion simulations to N-body calculations with identical initial conditions, and present results from large scale-free and cold dark matter (CDM) initial conditions. The adhesion approximation is generally quite accurate on scales >~2h^-1^Mpc it is most successful for the biased CDM and hot-matter models, while for models with more small-scale power it underestimates the fragmentation of structure into dense clumps. Adhesion simulations with scale-free initial conditions develop a network of filaments, walls, tunnels and cells, with a characteristic size that depends on the amplitude and slope of the power spectrum. Simulated redshift samples drawn from biased CDM simulations show empty voids 20-50 h^-1^Mpc across and walls and filaments up to 150 h^-1^Mpc in length. Unbiased CDM models also show giant superclusters, but their underdense regions typically contain a sprinkling of isolated galaxies. Non-linear gravitational evolution resembles, in some respects, a 'smoothing' process that acts on the initial density fluctuations. As time increases, larger scale modes of the density field come to dominate the evolved structure; finer details are washed away by merging, and gravitational collapse transfers energy from ordered motions into virial velocity dispersions. Sheets and filaments develop directly from features present in the initial conditions. The combination of gravitational instability and biasing in hierarchical models like cold dark matter creates a network of structure with a remarkable resemblance to the observed galaxy distribution.

Weinberg, D. H.; Gunn, J. E.

1990-11-01

237

Pentaquarks in the Jaffe-Wilczek approximation  

Microsoft Academic Search

The masses of $uudd\\\\bar s $, $uudd\\\\bar d$ and $uuss\\\\bar d$ pentaquarks are evaluated in a framework of both the Effective Hamiltonian approach to QCD and spinless Salpeter using the Jaffe--Wilczek diquark approximation and the string interaction for the diquark--diquark--antiquark system. The pentaquark masses are found to be in the region above 2 GeV. That indicates that the Goldstone boson

I. M. Narodetskii; C. Semay; B. Silvestre-Brac; Yu. A. Simonov; M. A. Trusov

2005-01-01

238

Approximation by superpositions of a sigmoidal function  

Microsoft Academic Search

In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of\\u000a affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results\\u000a settle an open question about representability in the class of single hidden

G. Cybenko

1989-01-01

239

Variational Bayesian Approximation methods for inverse problems  

NASA Astrophysics Data System (ADS)

Variational Bayesian Approximation (VBA) methods are recent tools for effective Bayesian computations. In this paper, these tools are used for inverse problems where the prior models include hidden variables and where where the estimation of the hyper parameters has also to be addressed. In particular two specific prior models (Student-t and mixture of Gaussian models) are considered and details of the algorithms are given.

Mohammad-Djafari, Ali

2012-09-01

240

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

241

Numerical Approximation to the Thermodynamic Integrals  

NASA Astrophysics Data System (ADS)

We approximate boson thermodynamic integrals as polynomials in two variables chosen to give the correct limiting expansion and to smoothly interpolate into other regimes. With 10 free parameters, an accuracy of better than 0.009% is achieved for the pressure, internal energy density, and number density. We also revisit the fermion case, originally addressed by Eggleton, Faulkner, & Flannery (1973), and substantially improve the accuracy of their fits.

Johns, S. M.; Ellis, P. J.; Lattimer, J. M.

1996-12-01

242

Numerical approximation to the thermodynamic integrals  

SciTech Connect

We approximate boson thermodynamic integrals as polynomials in two variables chosen to give the correct limiting expansion and to smoothly interpolate into other regimes. With 10 free parameters, an accuracy of better than 0.009{percent} is achieved for the pressure, internal energy density, and number density. We also revisit the fermion case, originally addressed by Eggleton, Faulkner, & Flannery (1973), and substantially improve the accuracy of their fits. {copyright} {ital 1996 The American Astronomical Society.}

Johns, S.M. [School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455-012 (United States)]|[Department of Physics, Cornell University, Ithaca, New York 14853 (United States); Ellis, P.J. [School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455-012 (United States); Lattimer, J.M. [Department of Earth and Space Sciences, SUNY at Stony Brook, Stony Brook, New York 11794-2100 (United States)

1996-12-01

243

Approximation Algorithms for some Routing Problems  

Microsoft Academic Search

Several polynomial time approximation algorithms for some NP-complete routing problems are presented, and the worst-case ratios of the cost of the obtained route to that of an optimal are determined. A mixed-strategy heuristic with a bound of 9\\/5 is presented for the Stacker-Crane problem (a modified Traveling Salesman problem). A tour-splitting heuristic is given for k-person variants of the Traveling

Greg N. Frederickson; Matthew S. Hecht; Chul E. Kim

1976-01-01

244

Singular perturbation approximation of balanced systems  

Microsoft Academic Search

This paper relates the singular perturbation approximation technique for model reduction to the direct truncation technique if the system model to be reduced is stable, minimal and internally balanced. It shows that these two methods constitute two fully compatible model-reduction techniques for a continuous-time system, and both methods yield a stable, minimal and internally balanced reduced-order system with the same

YI LIU; BRIAN D. O. ANDERSON

1989-01-01

245

WKB approximation to the power wall  

NASA Astrophysics Data System (ADS)

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

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

2013-05-01

246

The spinor Boltzmann equation beyond gradient approximation  

NASA Astrophysics Data System (ADS)

In this paper, we generalize the spinor Boltzmann equation in order to describe the spin-polarized transport in magnetic multilayers beyond gradient approximation, because the usual gradient approximation, hence the quantum Boltzmann equation based on it, is only suitable for the systems whose potentials vary slowly with respect to time and position. In our derivation, we do not adopt the gradient approximation to simplify those convolutions concerning with Fourier transformations, we just deal with them by the way given by Wigner [E. Wigner, Phys. Rev. 40, 749 (1932)], which assures the final quantum Boltzmann equation can be applied to the system with rapid varying potential. Then we illustrate it by the spin-polarized transport in magnetic multilayers in which the potential have sudden jumps at the interfaces, and apply the generalized spinor Boltzmann equation to the entire magnetic multilayers, it avoids to connect the distribution functions of different layers by matching conditions as usual. We also study the quantum corrections for the distribution function, the equations satisfied by the zero-order distribution function and the first order quantum correction are exhibited.

Wang, Zheng-Chuan

2013-05-01

247

The simplified P{sub 3} approximation  

SciTech Connect

The simplified P{sub 3} (SP{sub 3}) approximation to the multigroup neutron transport equation in arbitrary geometries is derived using a variational analysis. This derivation yields the SP{sub 3} equations along with material interface and Marshak-like boundary conditions. The multigroup SP{sub 3} approximation is reformulated as a system of within-group problems that can be solved iteratively. An explicit iterative algorithm for solving the within-group problems that can be solved iteratively. An explicit iterative algorithm for solving the within-group problem is described. Fourier analyzed, and shown to be more efficient than the traditional FLIP implicit algorithm. Numerical results compare diffusion (P{sub 1}), simplified P{sub 2} (SP{sub 2}), and simplified P{sub 3} calculations of a mixed-oxide (MOX) fuel benchmark problem to a reference transport calculation. The SP{sub 3} approximation can eliminate much of the inaccuracy in the diffusion and SP{sub 2} calculations of MOX fuel problems.

Brantley, P.S.; Larsen, E.W.

2000-01-01

248

An approximate projection method for incompressible flow  

NASA Astrophysics Data System (ADS)

This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139-1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40-65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency.A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake.

Stevens, David E.; Chan, Stevens T.; Gresho, Phil

2002-12-01

249

Shear viscosity in the postquasistatic approximation  

NASA Astrophysics Data System (ADS)

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.; Rodríguez-Mueller, B.; Barreto, W.

2010-05-01

250

An approximate factorisation explicit method for CFD  

NASA Astrophysics Data System (ADS)

An approximate factorization explicit (AFE) algorithm for solving tridiagonal systems of equations iteratively on parallel processors is combined with a group finite element multigrid auxiliary potential solver for the incompressible Navier-Stokes equations. In scalar mode one iteration of the AFE algorithm requires 2.5 times as many operations as a direct tridiagonal solver and typically four AFE iterations are required to achieve efficient convergence of the overall algorithm. Applied to a forward-facing corner flow and a ventilated room flow the auxiliary potential algorithm is only 2 to 3 times more expensive in scalar mode when based on the AFE algorithm rather than on a direct tridiagonal solver.

Fletcher, C. A. J.; Bain, J. G.

251

Multi-compartment linear noise approximation  

NASA Astrophysics Data System (ADS)

The ability to quantify the stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally expensive. Building on previous work, a linear noise approximation is developed for biochemical models with many compartments, for example cells. The procedure is then implemented in the software package COPASI. This technique is illustrated with two simple examples and is then applied to a more realistic biochemical model. Expressions for the noise, given in the form of covariance matrices, are presented.

Challenger, Joseph D.; McKane, Alan J.; Pahle, Jürgen

2012-11-01

252

Rational approximation in linear systems and control  

NASA Astrophysics Data System (ADS)

In this paper we want to describe some examples of the active interaction that takes place at the border of rational approximation theory and linear system theory. These examples are mainly taken from the period 1950-1999 and are described only at a skindeep level in the simplest possible (scalar) case. We give comments on generalizations of these problems and how they opened up new ranges of research that after a while lived their own lives. We also describe some open problems and future work that will probably continue for some years after 2000.

Bultheel, A.; Moor, B. De

2000-09-01

253

Pentaquarks in the Jaffe-Wilczek approximation  

Microsoft Academic Search

The masses of \\u000a $$uudd\\\\bar s,{\\\\text{ }}uudd\\\\bar d$$\\u000a , and \\u000a $$uuss\\\\bar d$$\\u000a pentaquarks are evaluated in a framework of both the effective Hamiltonian approach to QCD and the spinless Salpeter equation\\u000a using the Jaffe-Wilczek diquark approximation and the string interaction for the diquark-diquark-antiquark system. The pentaquark\\u000a masses are found to be in the region above 2 GeV. That indicates that the

I. M. Narodetskii; C. Semay; B. Silvestre-Brac; Yu. A. Simonov; M. A. Trusov

2005-01-01

254

Spectral approximations of unbounded nonselfadjoint operators  

NASA Astrophysics Data System (ADS)

We consider the operator A=S+B, where S is an unbounded normal operator in a separable Hilbert space H, having a compact inverse one and B is a linear operator in H, such that BS^{-1} is compact. Let \\{e_k\\}_{k=1}^infty be the normalized eigenvectors of S and B be represented in \\{e_k\\}_{k=1}^infty by a matrix (b_{jk})_{j,k=1}^infty . We approximate the eigenvalues of A by a combination of the eigenvalues of S and the eigenvalues of the finite matrix {(b_{jk})}_{j,k=1}n. Applications of to differential operators are also discussed.

Gil', Michael

2013-03-01

255

Relativistic Random Phase Approximation At Finite Temperature  

SciTech Connect

The fully self-consistent finite temperature relativistic random phase approximation (FTRRPA) has been established in the single-nucleon basis of the temperature dependent Dirac-Hartree model (FTDH) based on effective Lagrangian with density dependent meson-nucleon couplings. Illustrative calculations in the FTRRPA framework show the evolution of multipole responses of {sup 132}Sn with temperature. With increased temperature, in both monopole and dipole strength distributions additional transitions appear in the low energy region due to the new opened particle-particle and hole-hole transition channels.

Niu, Y. F. [State Key Laboratory for Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871 (China); Physics Department, Faculty of Science, University of Zagreb (Croatia); Paar, N.; Vretenar, D. [Physics Department, Faculty of Science, University of Zagreb (Croatia); Meng, J. [State Key Laboratory for Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871 (China)

2009-08-26

256

Asphericity and approximation properties of crossed modules  

SciTech Connect

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

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

2007-04-30

257

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

258

The simplified P{sub 2} approximation  

SciTech Connect

The simplified P{sub 2} (SP{sub 2}) approximation to the transport equation is derived by a formal procedure and by a variational analysis. The variational analysis yields the SP{sub 2} equations, together with interface and Marshak-like boundary conditions. Numerical calculations show that the resulting SP{sub 2} solution is generally more accurate than the P{sub 1} solution for both integral quantities and detailed flux distributions, except near material interfaces, where the SP{sub 2} solution is discontinuous.

Tomasevic, D.I.; Larsen, E.W. [Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Nuclear Engineering and Radiological Sciences

1996-03-01

259

Relativistic mean field approximation to baryons  

SciTech Connect

We stress the importance of the spontaneous chiral symmetry breaking for understanding the low-energy structure of baryons. The Mean Field Approximation to baryons is formulated, which solves several outstanding paradoxes of the naive quark models, and which allows to compute parton distributions at low virtuality in a consistent way. We explain why this approach to baryons leads to the prediction of relatively light exotic pentaquark baryons, in contrast to the constituent models which do not take seriously the importance of chiral symmetry breaking. We briefly discuss why, to our mind, it is easier to produce exotic pentaquarks at low than at high energies.

Dmitri Diakonov

2005-02-01

260

Probabilistic Approximations of Signaling Pathway Dynamics  

NASA Astrophysics Data System (ADS)

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

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

261

Analytic approximate radiation effects due to Bremsstrahlung  

SciTech Connect

The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R&D Energy Recovery Linac.

Ben-Zvi I.

2012-02-01

262

Decoupling with unitary approximate two-designs  

NASA Astrophysics Data System (ADS)

Consider a bipartite system, of which one subsystem, A, undergoes a physical evolution separated from the other subsystem, R. One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and R, i.e. decouples the subsystems. A quantitative answer to this question is provided by decoupling theorems, which have been developed recently in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling is achieved if the evolution on A consists of a typical unitary, chosen with respect to the Haar measure, followed by a process that adds sufficient decoherence. Here, we prove a generalized decoupling theorem for the case where the unitary is chosen from an approximate two-design. A main implication of this result is that decoupling is physical, in the sense that it occurs already for short sequences of random two-body interactions, which can be modeled as efficient circuits. Our decoupling result is independent of the dimension of the R system, which shows that approximate two-designs are appropriate for decoupling even if the dimension of this system is large.

Szehr, Oleg; Dupuis, Frédéric; Tomamichel, Marco; Renner, Renato

2013-05-01

263

Iterative Sparse Approximation of the Gravitational Potential  

NASA Astrophysics Data System (ADS)

In recent applications in the approximation of gravitational potential fields, several new challenges arise. We are concerned with a huge quantity of data (e.g. in case of the Earth) or strongly irregularly distributed data points (e.g. in case of the Juno mission to Jupiter), where both of these problems bring the established approximation methods to their limits. Our novel method, which is a matching pursuit, however, iteratively chooses a best basis out of a large redundant family of trial functions to reconstruct the signal. It is independent of the data points which makes it possible to take into account a much higher amount of data and, furthermore, handle irregularly distributed data, since the algorithm is able to combine arbitrary spherical basis functions, i.e., global as well as local trial functions. This additionaly results in a solution, which is sparse in the sense that it features more basis functions where the signal has a higher local detail density. Summarizing, we get a method which reconstructs large quantities of data with a preferably low number of basis functions, combining global as well as several localizing functions to a sparse basis and a solution which is locally adapted to the data density and also to the detail density of the signal.

Telschow, R.

2012-04-01

264

Nonobservability of Born Approximation Structures in GOSs.  

NASA Astrophysics Data System (ADS)

We explain the unfeasibility of observing experimentally the complicated structure of Generalized oscillator strengths (GOS's), which are calculated in the first Born approximation (FBA), demonstrating that FBA calculations are not valid in the vicinity of the minima even at very high non-relativistic electron impact energies. The differences between the FBA and CCC numerical results for the 6s ? 6p ^1P0 transition in Ba have been accounted for through examination of the real and imaginary parts of the scattering amplitude, as a function of momentum transfer, for different electron impact energies. Our calculations of the scattering amplitude demonstrate that, while with increasing energy of the initial electron the imaginary part of the amplitude rapidly converges to the amplitude obtained in FBA, the real part does not diminish significantly, giving a big increase of GOS in comparison with the plane wave approximation predictions. An exception is the region of small momentum transfer, which however are usually in an experimentally inaccessible nonphysical region of the scattering angle.

Avdonina, N. B.; Pratt, R. H.; Fursa, D.; Msezane, A. Z.

2003-05-01

265

On some applications of diophantine approximations.  

PubMed

Siegel's results [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1] on the transcendence and algebraic independence of values of E-functions are refined to obtain the best possible bound for the measures of irrationality and linear independence of values of arbitrary E-functions at rational points. Our results show that values of E-functions at rational points have measures of diophantine approximations typical to "almost all" numbers. In particular, any such number has the "2 + epsilon" exponent of irrationality: Theta - p/q > q(-2-epsilon) for relatively prime rational integers p,q, with q >/= q(0) (Theta, epsilon). These results answer some problems posed by Lang. The methods used here are based on the introduction of graded Padé approximations to systems of functions satisfying linear differential equations with rational function coefficients. The constructions and proofs of this paper were used in the functional (nonarithmetic case) in a previous paper [Chudnovsky, D. V. & Chudnovsky, G. V. (1983) Proc. Natl. Acad. Sci. USA 80, 5158-5162]. PMID:16593441

Chudnovsky, G V

1984-03-01

266

Approximate solutions to fractional subdiffusion equations  

NASA Astrophysics Data System (ADS)

The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer). The prescribed profile satisfies the boundary conditions imposed by the boundary layer that allows its coefficients to be expressed through its depth as unique parameter. The integral approach to the fractional subdiffusion equation suggests a replacement of the real distribution function by the approximate profile. The solution was performed with Riemann-Liouville time-fractional derivative since the integral approach avoids the definition of the initial value of the time-derivative required by the Laplace transformed equations and leading to a transition to Caputo derivatives. The method is demonstrated by solutions to two simple fractional subdiffusion equations (Dirichlet problems): 1) Time-Fractional Diffusion Equation, and 2) Time-Fractional Drift Equation, both of them having fundamental solutions expressed through the M-Wright function. The solutions demonstrate some basic issues of the suggested integral approach, among them: a) Choice of the profile, b) Integration problem emerging when the distribution (profile) is replaced by a prescribed one with unknown coefficients; c) Optimization of the profile in view to minimize the average error of approximations; d) Numerical results allowing comparisons to the known solutions expressed to the M-Wright function and error estimations.

Hristov, J.

2011-03-01

267

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

268

Mathematical approximation of fibular malleolus curvature.  

PubMed

While there are several manuscripts describing the articular surfaces of the ankle joint and the fibula itself, there is no study describing the outer surface and the degree of curvature of the fibular malleolus. This paper aims to approximate the sagital curvature of the outer surface of the lateral malleolus mathematically. Such data would facilitate the design of the anatomic plate that can be used for the ostheosynthesis of the fibular malleolus fracture. 30 males who were examined in the emergency department due to ankle sprains, where they underwent a standard anteroposterior x-ray of the ankle in the neutral position were recruited. The radiographs which revealed no bony injury were digitized and statistically processed. A mathematical function for each separate fibula was obtained through the processing of the digitized x-rays. When all the functions were applied to one graph, common traits of all fibulas were noted. The mean value of all functions was obtained and it corresponds to the polynomial function of degree 6. Mathematical approximation of the curvature is a simple and reliable method that can be applied to other ellipsoid human bone structures besides the ankle, thus being a valuable method in anthropometric, radiological and virtual geometric calculations. PMID:24060013

Haluzan, Damir; Ehrenfreund, Tin; Simek, Zeljko; Labidi, May; Dobric, Ivan; Augustin, Goran; Davila, Slavko; Slaus, Mario

2013-09-01

269

Chiral Magnetic Effect in Hydrodynamic Approximation  

NASA Astrophysics Data System (ADS)

We review derivations of the chiral magnetic effect (ChME) in hydrodynamic approximation. The reader is assumed to be familiar with the basics of the effect. The main challenge now is to account for the strong interactions between the constituents of the fluid. The main result is that the ChME is not renormalized: in the hydrodynamic approximation it remains the same as for non-interacting chiral fermions moving in an external magnetic field. The key ingredients in the proof are general laws of thermodynamics and the Adler-Bardeen theorem for the chiral anomaly in external electromagnetic fields. The chiral magnetic effect in hydrodynamics represents a macroscopic manifestation of a quantum phenomenon (chiral anomaly). Moreover, one can argue that the current induced by the magnetic field is dissipation free and talk about a kind of "chiral superconductivity". More precise description is a quantum ballistic transport along magnetic field taking place in equilibrium and in absence of a driving force. The basic limitation is the exact chiral limit while temperature—excitingly enough—does not seemingly matter. What is still lacking, is a detailed quantum microscopic picture for the ChME in hydrodynamics. Probably, the chiral currents propagate through lower-dimensional defects, like vortices in superfluid. In case of superfluid, the prediction for the chiral magnetic effect remains unmodified although the emerging dynamical picture differs from the standard one.

Zakharov, Valentin I.

270

Bogoliubov approximation as a second-order approximation in the spectral-density method.—II  

Microsoft Academic Search

Summary  We discuss a method, based on the second-order approximation in the spectral-density approach, which avoids the difficulties\\u000a which appear in the Bogoliubov approximation for an interacting Bose system. We indicate the prescriptions under which, starting\\u000a from the original number-conserving Hamiltonian, the known Bogoliubov results and the possibility to obtain corrections to\\u000a those results emerge in a natural way. Explicit calculations

A. Caramico D'Auria; L. De Cesare; U. Esposito; F. Esposito

1980-01-01

271

Approximation diophantienne et approximants de Hermite-Pad\\\\'e de type I de fonctions exponentielles  

Microsoft Academic Search

En utilisant des approximants de Hermite-Pad\\\\'e de fonctions exponentielles, ainsi que des d\\\\'eterminants d'interpolation de Laurent, nous minorons la distance entre un nombre alg\\\\'ebrique et l'exponentielle d'un nombre alg\\\\'ebrique non nul. ----- We use Hermite-Pad\\\\'e approximants of exponential functions along with Laurent's interpolation determinants to obtain lower bounds for the distance between an algebraic number and the exponential of another

Samy Khémira; Paul Voutier

2010-01-01

272

Approximating MIN 2SAT and MIN 3SAT  

Microsoft Academic Search

Abstract We obtain substantially improved approximation algorithms for the MIN - SAT problem, for More specifically, we obtain a 1 - approximation algorithm for the MIN 2 - SAT problem, improving a previous - approximation algorithm, and a 1 - approximation algorithm for the MIN 3 - SAT problem, improving a previous 1 - approximation algorithm for the problem These

Adi Avidor; Uri Zwick

2005-01-01

273

On the approximation of smooth functions using generalized digital nets  

Microsoft Academic Search

Abstract In this paper we study an approximation algorithm which firstly approximates certain Walsh coefficients of the function under consideration and consequently uses a Walsh polynomial to approximate the function. A similar approach has previously been used for approximating periodic functions, using lattice rules (and Fourier polynomials), and for approximating functions in Walsh Korobov spaces, using digital nets. Here, the

Jan Baldeaux; Josef Dick; Peter Kritzer

2009-01-01

274

On the Approximation of Smooth Functions Using Generalized Digital Nets  

Microsoft Academic Search

In this paper we study an approximation algorithm which firstly approximates certain Walsh coefficients of the function under consideration and consequently uses a Walsh polynomial to approximate the function. A similar approach has previously been used for approximating periodic functions, using lattice rules (and Fourier polynomials), and for approximating functions in Walsh Korobov spaces, using digital nets. Here, the key

Jan Baldeauxa; Josef Dick; Peter Kritzer

275

Biophysics of the cochlea: linear approximation.  

PubMed

Several deficiencies affecting previous "box" models of the cochlea are overcome in this paper. Both mechanical and hydrodynamical aspects are treated at a level adequate to the complexity of realistic cochlear structures. The dynamics of the cochlea as a passive physical system, in the linear approximation, is described by an integral equation. It is further shown that this equation describes the properties of the working cochlea, provided a force term that accounts for hair cell motility is included. Numerical solutions for different degrees of outer hair cells activity, obtained by matrix methods in the frequency domain, are presented. Amplitudes and phases of the computer-simulated traveling waves are in fair agreement with basilar membrane responses to tones measured in various experimental conditions. PMID:8326060

Mammano, F; Nobili, R

1993-06-01

276

Random dispersion approximation for the Hubbard model  

NASA Astrophysics Data System (ADS)

We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard transition in the Hubbard model at half band filling. The RDA becomes exact for the Hubbard model in infinite dimensions. We implement the RDA on finite chains and employ the Lanczos exact diagonalization method in real space to calculate the ground-state energy, the average double occupancy, the charge gap, the momentum distribution, and the quasi-particle weight. We find a satisfactory agreement with perturbative results in the weak- and strong-coupling limits. A straightforward extrapolation of the RDA data for L ? 14 lattice results in a continuous Mott-Hubbard transition at Uc?W. We discuss the significance of a possible signature of a coexistence region between insulating and metallic ground states in the RDA that would correspond to the scenario of a discontinuous Mott-Hubbard transition as found in numerical investigations of the Dynamical Mean-Field Theory for the Hubbard model.

Ejima, S.; Gebhard, F.; Noack, R. M.

2008-11-01

277

Approximate truncation robust computed tomography-ATRACT.  

PubMed

We present an approximate truncation robust algorithm to compute tomographic images (ATRACT). This algorithm targets at reconstructing volumetric images from cone-beam projections in scenarios where these projections are highly truncated in each dimension. It thus facilitates reconstructions of small subvolumes of interest, without involving prior knowledge about the object. Our method is readily applicable to medical C-arm imaging, where it may contribute to new clinical workflows together with a considerable reduction of x-ray dose. We give a detailed derivation of ATRACT that starts from the conventional Feldkamp filtered-backprojection algorithm and that involves, as one component, a novel original formula for the inversion of the two-dimensional Radon transform. Discretization and numerical implementation are discussed and reconstruction results from both, simulated projections and first clinical data sets are presented. PMID:23941816

Dennerlein, Frank; Maier, Andreas

2013-08-14

278

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

279

Approximate particle spectra in the pyramid scheme  

NASA Astrophysics Data System (ADS)

We construct a minimal model inspired by the general class of pyramid schemes [T. Banks and J.-F. Fortin, J. High Energy Phys. 07 (2009) 046JHEPFG1029-8479], which is consistent with both supersymmetry breaking and electroweak symmetry breaking. In order to do computations, we make unjustified approximations to the low energy Kähler 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 model, and thus generically 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 of order 5%.

Banks, Tom; Torres, T. J.

2012-12-01

280

Gutzwiller approximation in strongly correlated electron systems  

NASA Astrophysics Data System (ADS)

Gutzwiller wave function is an important theoretical technique for treating local electron-electron correlations nonperturbatively in condensed matter and materials physics. It is concerned with calculating variationally the ground state wave function by projecting out multi-occupation configurations that are energetically costly. The projection can be carried out analytically in the Gutzwiller approximation that offers an approximate way of calculating expectation values in the Gutzwiller projected wave function. This approach has proven to be very successful in strongly correlated systems such as the high temperature cuprate superconductors, the sodium cobaltates, and the heavy fermion compounds. In recent years, it has become increasingly evident that strongly correlated systems have a strong propensity towards forming inhomogeneous electronic states with spatially periodic superstrutural modulations. A good example is the commonly observed stripes and checkerboard states in high- Tc superconductors under a variety of conditions where superconductivity is weakened. There exists currently a real challenge and demand for new theoretical ideas and approaches that treats strongly correlated inhomogeneous electronic states, which is the subject matter of this thesis. This thesis contains four parts. In the first part of the thesis, the Gutzwiller approach is formulated in the grand canonical ensemble where, for the first time, a spatially (and spin) unrestricted Gutzwiller approximation (SUGA) is developed for studying inhomogeneous (both ordered and disordered) quantum electronic states in strongly correlated electron systems. The second part of the thesis applies the SUGA to the t-J model for doped Mott insulators which led to the discovery of checkerboard-like inhomogeneous electronic states competing with d-wave superconductivity, consistent with experimental observations made on several families of high-Tc superconductors. In the third part of the thesis, new concepts and techniques are developed to study the Mott transition in inhomogeneous electronic superstructures. The latter is termed "SuperMottness" which is shown to be a general framework that unifies the two paradigms in the physics of strong electronic correlation: Mott transition and Wigner crystallization. A cluster Gutzwiller approximation (CGA) approach is developed that treats the local ( U) and extended Coulomb interactions (V) on equal footing. It is shown with explicit calculations that the Mott-Wigner metal-insulator transition can take place far away from half-filling. The mechanism by which a superlattice potential enhances the correlation effects and the tendency towards local moment formation is investigated and the results reveal a deeper connection among the strongly correlated inhomogeneous electronic states, the Wigner-Mott physics, and the multiorbital Mott physics that can all be united under the notion of SuperMottness. It is proposed that doping into a superMott insulator can lead to coexistence of local moment and itinerant carriers. The last part of the thesis studies the possible Kondo effect that couples the local moment and the itinerant carriers. In connection to the sodium rich phases of the cobaltates, a new Kondo lattice model is proposed where the itinerant carriers form a Stoner ferromagnet. The competition between the Kondo screening and the Stoner ferromagnetism is investigated when the conduction band is both at and away from half-filling.

Li, Chunhua

281

Approximate theory for radiation from mesh reflectors  

NASA Astrophysics Data System (ADS)

Reconfigurable shaped reflector antennas have potential applications in satellite communications and satellite broadcasting. When a metallic mesh is employed pillowing occurs between the points at which the reflector is constrained. This paper describes an approximate theory to explain this behavior, and results are obtained which are in good agreement with exact analysis. The effect of pillowing is found to produce a periodic phase modulation across the antenna aperture. This is superimposed on the primary phase variation which controls the beam shape. For a given pillowing amplitude, it produces a gain loss which is independent of the shape of the antenna pattern, provided that the angular position of the first grating lobe of the periodic array is much larger than the intrinsic beamwidth of the antenna. For a regular distribution of points of attachment, the shape of an isotropically elastic mesh surface depends only on the ratio of the area of the attachment region to that of the unit cell.

Poulton, G. T.; Zhou, H.; Clarricoats, P. J. B.

1988-11-01

282

Tumor Growth Rate Approximation-Assisted Estimation  

PubMed Central

From tumor to tumor, there is a great variation in the proportion of cancer cells growing and making daughter cells that ultimately metastasize. The differential growth within a single tumor, however, has not been studied extensively and this may be helpful in predicting the aggressiveness of a particular cancer type. The estimation problem of tumor growth rates from several populations is studied. The baseline growth rate estimator is based on a family of interacting particle system models which generalize the linear birth process as models of tumor growth. These interacting models incorporate the spatial structure of the tumor in such a way that growth slows down in a crowded system. Approximation-assisted estimation strategy is proposed when initial values of rates are known from the previous study. Some alternative estimators are suggested and the relative dominance picture of the proposed estimator to the benchmark estimator is investigated. An over-riding theme of this article is that the suggested estimation method extends its traditional counterpart to non-normal populations and to more realistic cases.

An, Lihua; Ahmed, S. Ejaz; Ali, Adnan

2007-01-01

283

Heisenberg approximation in passive scalar turbulence.  

PubMed

We use Heisenberg's approximation to derive analytic expressions for eddy viscosity and eddy diffusivity from the transfer integrals of energy and mean-square scalar arising from the Navier-Stokes and passive scalar dynamics. In the same scheme, we evaluate the flux integrals for the transports of energy and mean-square scalar. These procedures allow for the evaluation of relevant amplitude ratios, from which we calculate the universal numbers, namely, Batchelor constant B, Kolmogorov constant C, and turbulent Prandtl number ?, under two different schemes (with and without ? expansion). Our results are comparable with existing theoretical, numerical, and experimental values. As a byproduct, we obtain a relation between C, B, and ?, namely, B=? C. To compare our results with the experimental values, we calculate Batchelor constant in one dimension (B'). Within the same framework, we also see that with increasing values of space dimension d, the Prandtl number ? increases and approaches unity, while the Kolmogorov constant C and Batchelor constant B approach very close to each other. For large space dimensions, we find the asymptotic B=B(0)d(1/3), and evaluate B(0). PMID:22060500

Dutta, Kishore; Nandy, Malay K

2011-09-21

284

Structural physical approximations and entanglement witnesses  

NASA Astrophysics Data System (ADS)

The structural physical approximation (SPA) to a positive map is considered to be one of the most important methods to detect entanglement in the real physical world. We first show that an arbitrary entanglement witness (EW) W can be constructed from a separable density matrix ? in the form of W=?-c?I, where c? is a non-negative number and I is the identity matrix. Following the general form of EWs from separable states, we show a sufficient condition and a sufficient and necessary condition in low dimensions of that SPAs to positive maps do not define entanglement-breaking channels. We show that either the SPA of an EW or the SPA of the partial transposition of the EW in low dimensions is an entanglement-breaking channel. We give sufficient conditions of violating the SPA conjecture [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.78.062105 78, 062105 (2008)]. Our results indicate that the SPA conjecture is independent of whether or not positive maps are optimal.

Wang, Bang-Hai; Long, Dong-Yang

2013-06-01

285

Approximate theory for radial filtration/consolidation  

SciTech Connect

Approximate solutions are developed for filtration and subsequent consolidation of compactible cakes on a cylindrical filter element. Darcy`s flow equation is coupled with equations for equilibrium stress under the conditions of plane strain and axial symmetry for radial flow inwards. The solutions are based on power function forms involving the relationships of the solidosity {epsilon}{sub s} (volume fraction of solids) and the permeability K to the solids effective stress p{sub s}. The solutions allow determination of the various parameters in the power functions and the ratio k{sub 0} of the lateral to radial effective stress (earth stress ratio). Measurements were made of liquid and effective pressures, flow rates, and cake thickness versus time. Experimental data are presented for a series of tests in a radial filtration cell with a central filter element. Slurries prepared from two materials (Microwate, which is mainly SrSO{sub 4}, and kaolin) were used in the experiments. Transient deposition of filter cakes was followed by static (i.e., no flow) conditions in the cake. The no-flow condition was accomplished by introducing bentonite which produced a nearly impermeable layer with negligible flow. Measurement of the pressure at the cake surface and the transmitted pressure on the central element permitted calculation of k{sub 0}.

Tiller, F.M. [Univ. of Houston, TX (United States); Kirby, J.M. [Commonwealth Scientific and Industrial Research Organization, Canberra (Australia). Soils Div.; Nguyen, H.L. [Veteran`s Hospital, Los Angeles, CA (United States)

1996-10-01

286

An approximate treatment of gravitational collapse  

NASA Astrophysics Data System (ADS)

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

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

2013-11-01

287

Bilayer graphene spectral function in the random phase approximation and self-consistent GW approximation  

NASA Astrophysics Data System (ADS)

We calculate the single-particle spectral function for doped bilayer graphene in the low energy limit, described by two parabolic bands with zero band gap and long range Coulomb interaction. Calculations are done using thermal Green's functions in both the random phase approximation (RPA) and the fully self-consistent GW approximation. Consistent with previous studies RPA yields a spectral function which, apart from the Landau quasiparticle peaks, shows additional coherent features interpreted as plasmarons, i.e., composite electron-plasmon excitations. In the GW approximation the plasmaron becomes incoherent and peaks are replaced by much broader features. The deviation of the quasiparticle weight and mass renormalization from their noninteracting values is small which indicates that bilayer graphene is a weakly interacting system. The electron energy loss function, Im[??q?1(?)] shows a sharp plasmon mode in RPA which in the GW approximation becomes less coherent and thus consistent with the weaker plasmaron features in the corresponding single-particle spectral function.

Sabashvili, Andro; Östlund, Stellan; Granath, Mats

2013-08-01

288

Using Fuzzy Clustering Technique for Function Approximation to Approximate ECG Signals  

Microsoft Academic Search

Abstract. Radial Basis Function Neural Networks (RBFNN) has been applied successfully to solve function approximation problems. In the design of an RBFNN, it is required a flrst initialization step for the centers of the RBFs. Clustering algorithms have been used to initialize the centers, but these algorithms were not designed for this task but rather for classiflcation problems. The initialization

Alberto Guillén; Ignacio Rojas; Eduardo Ros; Luis Javier Herrera

2005-01-01

289

Physically motivated approximations in some inverse scattering problems  

Microsoft Academic Search

Consideration is given to a number of physically motivated approximations in inverse scattering problems. In contrast to rigorous approaches, the approximations allow more physical insight. The approximations are considered for both perfectly conducting bodies and dielectric bodies. The results show that the approximate methods: (1) simplify the interpretations of results; (2) provide simple relations between the measured field and the

J. C. Bolomey; D. Lesselier; C. Pichot; W. Tabbara

1982-01-01

290

Comparison of various approximation theories for randomly rough surface scattering  

Microsoft Academic Search

Comparisons of several approximation solutions to rough surface scattering are conducted for randomly topographies with an analytical description of the scaled wavenumber ka and the scaled rms height h\\/a (where k is the wavenumber, h is the surface rms height, and a is the surface correlation length). These approximations include the Kirchhoff approximation, Taylor expansion-based perturbation theory, Rytov phase approximation,

ShanZheng Hu; Li-Yun Fu; ZhenXing Yao

2009-01-01

291

Nearness approximation space based on axiomatic fuzzy sets  

Microsoft Academic Search

The approximation space model was originally proposed by Pawlak (1982) [19]. It was Or?owska who first observed that approximation spaces serves as a formal counterpart of perception, or observation [16, §2, p. 8], in which approximations provide a means of approximating one set of objects with another set of objects using the indiscernibility relation. Topology has been used to enrich

Lidong Wang; Xiaodong Liu; Wangren Qiu

292

Coronal Loops: Evolving Beyond the Isothermal Approximation  

NASA Astrophysics Data System (ADS)

Are coronal loops isothermal? A controversy over this question has arisen recently because different investigators using different techniques have obtained very different answers. Analysis of SOHO-EIT and TRACE data using narrowband filter ratios to obtain temperature maps has produced several key publications that suggest that coronal loops may be isothermal. We have constructed a multi-thermal distribution for several pixels along a relatively isolated coronal loop on the southwest limb of the solar disk using spectral line data from SOHO-CDS taken on 1998 Apr 20. These distributions are clearly inconsistent with isothermal plasma along either the line of sight or the length of the loop, and suggested rather that the temperature increases from the footpoints to the loop top. We speculated originally that these differences could be attributed to pixel size -- CDS pixels are larger, and more `contaminating' material would be expected along the line of sight. To test this idea, we used CDS iron line ratios from our data set to mimic the isothermal results from the narrowband filter instruments. These ratios indicated that the temperature gradient along the loop was flat, despite the fact that a more complete analysis of the same data showed this result to be false! The CDS pixel size was not the cause of the discrepancy; rather, the problem lies with the isothermal approximation used in EIT and TRACE analysis. These results should serve as a strong warning to anyone using this simplistic method to obtain temperature. This warning is echoed on the EIT web page: ``Danger! Enter at your own risk!'' In other words, values for temperature may be found, but they may have nothing to do with physical reality. Solar physics research at the University of Memphis is supported by NASA grant NAG5-9783. This research was funded in part by the NASA/TRACE MODA grant for Montana State University.

Schmelz, J. T.; Cirtain, J. W.; Allen, J. D.

2002-05-01

293

Approximate Method for Modelling Laser Light Scattering from Biological Cells.  

National Technical Information Service (NTIS)

A new technique for approximating the scattering of laser light by biological cells is reported. This technique is based on a three-dimensional scalar wave equation approximation of the full Maxwell's field equations for the electromagnetic field. This sc...

Y. Shao E. Yee

2004-01-01

294

Pad6 Approximants for the q-Elementary Functions  

Microsoft Academic Search

We give a simple construction of the Padb approximants to q analogues of exp and log. The construction is based on the functional relations they satisfy. The Pad6 approximants for the ordinary exp and log are then limiting cases.

Peter B. Borwein

1988-01-01

295

An asymptotic homogenized neutron diffusion approximation. II. Numerical comparisons  

SciTech Connect

In a companion paper, a monoenergetic, homogenized, anisotropic diffusion equation is derived asymptotically for large, 3-D, multiplying systems with a periodic lattice structure [1]. In the present paper, this approximation is briefly compared to several other well known diffusion approximations. Although the derivation is different, the asymptotic diffusion approximation matches that proposed by Deniz and Gelbard, and is closely related to those proposed by Benoist. The focus of this paper, however, is a numerical comparison of the various methods for simple reactor analysis problems in 1-D. The comparisons show that the asymptotic diffusion approximation provides a more accurate estimate of the eigenvalue than the Benoist diffusion approximations. However, the Benoist diffusion approximations and the asymptotic diffusion approximation provide very similar estimates of the neutron flux. The asymptotic method and the Benoist methods both outperform the standard homogenized diffusion approximation, with flux weighted cross sections. (authors)

Trahan, T. J.; Larsen, E. W. [Dept. of Nuclear Engineering and Radiological Sciences, Univ. of Michigan, 2355 Bonisteel Blvd., Ann Arbor, MI 48109 (United States)

2012-07-01

296

Approximation Dispersion Equations for Thin Walled Liquid Filled Tubes.  

National Technical Information Service (NTIS)

The dispersion equation for an initially stressed thin walled viscoelastic tube filled with a linear elastic fluid is derived. The validity of the long wavelength approximation of an inviscid liquid in a viscoelastic tube is discussed. An approximate disp...

G. D. C. Kuiken

1983-01-01

297

Test of the Adhesion Approximation for Gravitational Clustering.  

National Technical Information Service (NTIS)

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, bet...

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

1993-01-01

298

Approximation Techniques in the Solution of Queueing Problems.  

National Technical Information Service (NTIS)

In the study of complex queueing systems analysis techniques aimed at providing exact solutions become ineffective. Approximation techniques provide an attractive alternative in such cases. This paper gives and overview of different types of approximation...

U. N. Bhat M. J. Fischer M. Shalaby

1976-01-01

299

System, Apparatus and Method for Forensic Facial Approximation.  

National Technical Information Service (NTIS)

A system, method and apparatus for performing a facial approximation is described. The system includes an acquisition subsystem and a facial approximation algorithm. The method includes the steps of acquiring models of known skulls and a model of a questi...

K. W. P. Miller M. A. Taister P. H. Tu R. E. B. Brown T. P. Kelliher W. D. Turner

2004-01-01

300

Hierarchized Block Wise Image Approximation by Greedy Pursuit Strategies  

NASA Astrophysics Data System (ADS)

An approach for effective implementation of greedy selection methodologies, to approximate an image partitioned into blocks, is proposed. The method is specially designed for approximating partitions on a transformed image. It evolves by selecting, at each iteration step, i) the elements for approximating each of the blocks partitioning the image and ii) the hierarchized sequence in which the blocks are approximated to reach the required global condition on sparsity.

Rebollo-Neira, Laura; Maciol, Ryszard; Bibi, Shabnam

2013-12-01

301

Unique solvability of restrictive Padé and restrictive Taylor's approximations  

Microsoft Academic Search

From 1995 to 2002 the author and others succeeded to apply a new approach for approximation which called restrictive Padé approximation and restrictive Taylor approximation. Almost the work is summarized in the nine papers [J. Faculty Educat. (1995) 63; Int. J. Comput. Math. 66 (1998) 343; Int. J. Comput. Math. 72 (1999) 271; Int. J. Comput. Math. 77 (2000) 251;

Hassan N. A. Ismail

2004-01-01

302

Approximating the Bandwidth for Asteroidal Triple-Free Graphs  

Microsoft Academic Search

We show that there is an algorithm to approximate the bandwidth of an AT-free graph with worst case performance ratio 2. Alternatively, at the cost of the approximation factor, we can also obtain an log algorithm to approximate the bandwidth of an AT-free graph within a factor 4 and an algorithm with a factor 6. For the special cases of

Ton Kloks; Dieter Kratsch; Haiko Müller

1995-01-01

303

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

304

Focusing Bistaitc Images use RDA based on Hyperbolic Approximating  

Microsoft Academic Search

This paper, shows a hyperbolic approximating approach for bistatic range histories where both transmitter and receiver work on the squint mode. The approximate approach avoids the linear and quadratic errors, and can also counteract some high order errors. Based on the approximation, a RD algorithm for 'translational invariant' bistatic SAR has been deduced. Finally, simulating results are presented and compared,

Xiaolan Qiu; Donghui Hu; Chibiao Ding

2006-01-01

305

Policy Gradient Methods for Reinforcement Learning with Function Approximation  

Microsoft Academic Search

Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and deter- mining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly represented by its own function approximator, indepen- dent of the value function, and is updated according to

Richard S. Sutton; David A. Mcallester; Satinder P. Singh; Yishay Mansour

1999-01-01

306

Selection of approximation models for electromagnetic device optimization  

Microsoft Academic Search

Approximation models are frequently used in design optimization in order to reduce computational cost. Many new forms of approximation model have appeared recently, but it is difficult to know which one to choose for the problem at hand. This paper investigates a model selection strategy that estimates the accuracy of all the different approximation models under consideration, so that the

Linda Wang; David A. Lowther

2006-01-01

307

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

308

Wong-Zakai approximations for stochastic differential equations  

Microsoft Academic Search

The aim of this paper is to give a wide introduction to approximation concepts in the theory of stochastic differential equations. The paper is principally concerned with Zong-Zakai approximations. Our aim is to fill a gap in the literature caused by the complete lack of monographs on such approximation methods for stochastic differential equations; this will be the objective of

Krystyna Twardowska

1996-01-01

309

On the interval approximation of a fuzzy number  

Microsoft Academic Search

The notion of an approximation interval of a fuzzy number is introduced. It is the interval which fulfills two conditions. In the first, its width is equal to the width of a fuzzy number being approximated. In the second, the Hamming distance between this interval and the approximated number is minimal. The introduced notion is compared with the notion of

Stefan Chanas

2001-01-01

310

Relational Interpretations of Neigborhood Operators and Rough Set Approximation Operators  

Microsoft Academic Search

This paper presents a framework for the formulation, interpretation, and comparison of neighborhood systems and rough set approximations using the more familiar notion of binary relations. A special class of neigh- borhood systems, called 1-neighborhood systems, is introduced. Three extensions of Pawlak approximation operators are analyzed. Properties of neighborhood and approximation operators are studied, and their con- nections are examined.

Y. Y. Yao

1998-01-01

311

LINEAR APPROXIMATION OF RANDOM PROCESSES AND SAMPLING DESIGN PROBLEMS  

Microsoft Academic Search

Linear approximation of random processes is considered as a three-layers problem: for a single process; for a fixed method, an optimization of a sample points design; for a class of random processes, the best approximation order. The close relationship between the smoothness properties of a function and the best rate of its linear approximation is one of the basic ideas

O. V. SELEZNJEV

1999-01-01

312

An upper bound for the adiabatic approximation error  

NASA Astrophysics Data System (ADS)

In this paper, we derive an upper bound for the adiabatic approximation error, which is the distance between the exact solution to a Schrödinger equation and the adiabatic approximation solution. As an application, we obtain an upper bound for 1 minus the fidelity of the exact solution and the adiabatic approximation solution to a Schrödinger equation.

Wang, WenHua; Guo, ZhiHua; Cao, HuaiXin

2013-09-01

313

Rational Approximations of Riemann--Liouville and Weyl Fractional Integrals  

Microsoft Academic Search

We obtain exact rational approximation orders for functions expressible as Riemann--Liouville and Weyl fractional integrals. New results and the strengthening and generalization of theorems due to Popov, Petrusheva, Pekarskii, Rusak, and the author, which are well known in the theory of rational approximation of differentiable functions, are obtained as consequences of theorems due to Pekarskii related to rational approximation of

A. P. Starovoitov

2005-01-01

314

Experimental realization of an approximate transpose operation for qutrit systems using a structural physical approximation  

NASA Astrophysics Data System (ADS)

Although important for detecting entanglement, the transpose operation cannot be directly realized in laboratory because it is a nonphysical operation. It is, however, possible to find an approximate transpose operation using the method known as the structural physical approximation (SPA); recently, SPA-based implementations of the transpose and partial transpose have been demonstrated for a single-qubit [Phys. Rev. A1050-2947PLRAAN10.1103/PhysRevA.83.020301 83, 020301(R) (2011)] and an entangled two-qubit system [Phys. Rev. Lett.0031-9007PRLTAO10.1103/PhysRevLett.107.160401 107, 160401 (2011)]. In this work, we expand SPA-transpose to a three-dimensional quantum system: a qutrit. The photonic qutrit state is encoded in the polarization, and path degrees of freedom of a single-photon and the SPA-transpose operation, which is based on measurement and preparation of quantum states, is implemented with linear optics. Our work paves the way toward entanglement detection for higher-dimensional quantum systems.

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

2012-10-01

315

Toward a consistent random phase approximation based on the relativistic Hartree approximation  

SciTech Connect

We examine the random phase approximation (RPA) based on a relativistic Hartree approximation description for nuclear ground states. This model includes contributions from the negative energy sea at the one-loop level. We emphasize consistency between the treatment of the ground state and the RPA. This consistency is important in the description of low-lying collective levels but less important for the longitudinal ({ital e},{ital e}{prime}) quasielastic response. We also study the effect of imposing a three-momentum cutoff on negative energy sea contributions. A cutoff of twice the nucleon mass improves agreement with observed spin-orbit splittings in nuclei compared to the standard infinite cutoff results, an effect traceable to the fact that imposing the cutoff reduces {ital m}{sup *}/{ital m}. Consistency is much more important than the cutoff in the description of low-lying collective levels. The cutoff model also provides excellent agreement with quasielastic ({ital e},{ital e}{prime}) data.

Price, C.E.; Rost, E.; Shepard, J.R. (Department of Physics, University of Colorado, Boulder, Colorado 80309 (United States)); McNeil, J.A. (Department of Physics, Colorado School of Mines, Golden, Colorado 80401 (United States))

1992-03-01

316

One-way and one-return approximations (de wolf approximation) for fast elastic wave modeling in complex media  

Microsoft Academic Search

The De Wolf approximation has been introduced to overcome the limitation of the Born and Rytov approximations in long range forwardpropagation and backscat- tering calculations. The De Wolf approximation is a multiple-forescattering-single- backscattering (MFSB) approximation, which can be implemented by using an iter- ative marching algorithm with a single backscattering calculation for each march- ing step (a thin-slab). Therefore, it

Ru-Shan Wu; Xiao-Bi Xie; Xian-Yun Wu

2007-01-01

317

An analogue of Fabry's theorem for generalized Padé approximants  

NASA Astrophysics Data System (ADS)

The current theory of Padé 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 Padé approximants for orthogonal expansions, multipoint Padé approximants and Padé-Faber approximants. These are the most natural generalizations of the construction of classical Padé 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 Poincaré's theorem on recurrence relations with coefficients constant in the limit, which is obtained in the paper. Bibliography: 19 titles.

Buslaev, Viktor I.

2009-08-01

318

Discontinuous Galerkin method based on non-polynomial approximation spaces  

SciTech Connect

In this paper, we develop discontinuous Galerkin (DG) methods based on non-polynomial approximation spaces for numerically solving time dependent hyperbolic and parabolic and steady state hyperbolic and elliptic partial differential equations (PDEs). The algorithm is based on approximation spaces consisting of non-polynomial elementary functions such as exponential functions, trigonometric functions, etc., with the objective of obtaining better approximations for specific types of PDEs and initial and boundary conditions. It is shown that L {sup 2} stability and error estimates can be obtained when the approximation space is suitably selected. It is also shown with numerical examples that a careful selection of the approximation space to fit individual PDE and initial and boundary conditions often provides more accurate results than the DG methods based on the polynomial approximation spaces of the same order of accuracy.

Yuan Ling [Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912 (United States)]. E-mail: lyuan@dam.brown.edu; Shu Chiwang [Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912 (United States)]. E-mail: shu@dam.brown.edu

2006-10-10

319

Hybrid adaptive methods for approximating a nonconvex multidimensional Pareto frontier  

NASA Astrophysics Data System (ADS)

New hybrid methods for approximating the Pareto frontier of the feasible set of criteria vectors in nonlinear multicriteria optimization problems with nonconvex Pareto frontiers are considered. Since the approximation of the Pareto frontier is an ill-posed problem, the methods are based on approximating the Edgeworth-Pareto hull (EPH), i.e., the maximum set having the same Pareto frontier as the original feasible set of criteria vectors. The EPH approximation also makes it possible to visualize the Pareto frontier and to estimate the quality of the approximation. In the methods proposed, the statistical estimation of the quality of the current EPH approximation is combined with its improvement based on a combination of random search, local optimization, adaptive compression of the search region, and genetic algorithms.

Berezkin, V. E.; Kamenev, G. K.; Lotov, A. V.

2006-11-01

320

Settle time performance comparisons of stable approximate model inversion techniques  

Microsoft Academic Search

We compare the achievable settle time for small rest-to-rest maneuvers using two stable approximate model inversion output tracking methods: the zero phase error tracking controller (ZPETC) and noncausal series approximation. The plant dynamics of interest are known, discrete-time, single-input single-output (SISO), linear time-invariant (LTI), and nonminimum phase (NMP), with a single left-half-plane zero outside the unit circle. The approximate inversion

Brian P. Rigney; Lucy Y. Pao; Dale A. Lawrence

2006-01-01

321

An approximate thermal analysis of Stirling engine regenerators  

Microsoft Academic Search

This paper approximates the transport phenomena in a Stirling engine regenerator to aid its practical design. The mass flow\\u000a rates are simplified by a square-wave function and the pressure variations, by a saw-tooth function with a phase difference.\\u000a Approximate analytical solutions obtained in this study agree well with the available numerical solutions. Using the approximate\\u000a solutions of the transport phenomena

S. H. Park; Y.-S. Lee

1993-01-01

322

Approximations for the Period of a Simple Pendulum  

NASA Astrophysics Data System (ADS)

In a recent paper1 L. Edward Millet proposed a justification of an approximation for the period of a simple pendulum suggested earlier by Kidd and Fogg,2 and made the argument that the expression should be included in textbooks. This paper presents two other approximations that are more accurate. At this point it would seem that a decision as to which approximation, if any, should be included in textbooks or lab manuals is premature.

Hite, Gerald E.

2005-05-01

323

Approximations based on the adiabatic treatment of rotation for resonances  

SciTech Connect

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

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

1997-12-01

324

Approximation dispersion equations for thin walled liquid filled tubes  

NASA Astrophysics Data System (ADS)

The dispersion equation for an initially stressed thin walled viscoelastic tube filled with a linear elastic fluid is derived. The validity of the long wavelength approximation of an inviscid liquid in a viscoelastic tube is discussed. An approximate dispersion equation applicable in the higher frequency range is derived. Calculations confirm that long wavelength approximation is excellent for the analysis of blood flow through arteries. Even for large arteries, e.g., the human aorta, this means that the first 10 to 15 harmonics of a Fourier analysis of the pressure pulse can be analyzed. The inviscid approximation can be used to determine the phase velocity if the wavelength and viscosity are small.

Kuiken, G. D. C.

1983-06-01

325

Methods to approximate reliabilities in single-step genomic evaluation.  

PubMed

Reliability of predictions from single-step genomic BLUP (ssGBLUP) can be calculated by matrix inversion, but that is not feasible for large data sets. Two methods of approximating reliability were developed based on the decomposition of a function of reliability into contributions from records, pedigrees, and genotypes. Those contributions can be expressed in record or daughter equivalents. The first approximation method involved inversion of a matrix that contains inverses of the genomic relationship matrix and the pedigree relationship matrix for genotyped animals. The second approximation method involved only the diagonal elements of those inverses. The 2 approximation methods were tested with a simulated data set. The correlations between ssGBLUP and approximated contributions from genomic information were 0.92 for the first approximation method and 0.56 for the second approximation method; contributions were inflated by 62 and 258%, respectively. The respective correlations for reliabilities were 0.98 and 0.72. After empirical correction for inflation, those correlations increased to 0.99 and 0.89. Approximations of reliabilities of predictions by ssGBLUP are accurate and computationally feasible for populations with up to 100,000 genotyped animals. A critical part of the approximations is quality control of information from single nucleotide polymorphisms and proper scaling of the genomic relationship matrix. PMID:23127903

Misztal, I; Tsuruta, S; Aguilar, I; Legarra, A; VanRaden, P M; Lawlor, T J

2012-11-03

326

A nonlinear approximation for vortex sheet evolution and singularity formation  

NASA Astrophysics Data System (ADS)

The evolution of a vortex sheet in two-dimensional, incompressible, inviscid flow is governed by the integro-differential equation of Birkhoff-Rott. We derive a simple approximation for vortex sheet evolution, consisting of a system of four first-order differential equations. This approximate system has the advantage of involving only local operators. The errors in the approximation are shown to be relatively small even if the sheet has infinite curvature at a point. For the approximate equations, exact similarity solutions exhibiting singularity formation are constructed. Research supported by the National Science Foundation and the Alfred P. Sloan Foundation.

Caflisch, Russel E.; Semmes, Stephen

1990-03-01

327

Differential polarization imaging. IV. Images in higher Born approximations.  

PubMed Central

The theory of differential polarization imaging developed previously within the framework of the first Born approximation is extended to higher Born approximations, taking into account interactions among the polarizable groups in the object. Several properties of differential polarization images, originally described using first Born approximation are modified when higher Born approximations are used. In particular, (a) when the polarizable groups are spherically symmetric, the off-diagonal Mueller elements Mij (i not equal to j) in bright field do not vanish in higher Born approximations, as they do in the first Born approximation case. (b) In higher Born approximations, the dark field Mi4 and M4i (i = 1, 2, 3) images do not vanish as in the first Born approximation, due to the anisotropy induced by the interactions among the groups. (c) When the polarizability tensor of each group is symmetric and real, the bright field M14 and M41 images always vanish in the first Born approximation. In higher Born approximations, these terms do not vanish if the groups bear a chiral relationship to each other. Quantitative criteria for the validity of the first Born approximation in differential polarization imaging are explicitly derived for three different types of media: (a) linearly anisotropic, (b) circularly anisotropic, and (c) linearly and circularly anisotropic (medium displaying linear birefringence and circular birefringence). These criteria define the limits of thickness and the degree of anisotropy of optically thin media. Finally, the possibility to perform optical sectioning in differential polarization imaging in the presence and absence of group interactions is discussed.

Kim, M; Bustamante, C

1991-01-01

328

Improved reliability approximation for genomic evaluations in the United States  

Technology Transfer Automated Retrieval System (TEKTRAN)

For genomic evaluations, the time required to calculate the inverse of the coefficient matrix for the mixed-model equations increases cubically as the number of genotyped animals increases, and an approximation became necessary for estimating US evaluation reliabilities. The original approximation m...

329

The effect of time delay on Approximate & Sample Entropy calculations  

Microsoft Academic Search

Approximate and Sample Entropy are two widely used techniques to measure system complexity or regularity based on chosen parameters such as pattern length, m, and tolerance, r. In this paper, we investigate how different values of the time delay parameter, tau can be used in conjunction with standard values of m and r in the computation of Approximate and Sample

Farhad Kaffashi; Ryan Foglyano; Christopher G. Wilson; Kenneth A. Loparo

2008-01-01

330

The effect of time delay on Approximate & Sample Entropy calculations  

Microsoft Academic Search

Approximate and Sample Entropy are two widely used techniques to measure system complexity or regularity based on chosen parameters such as pattern length, m, and tolerance, r. In this paper, we investigate how different values of the time delay parameter, ? can be used in conjunction with standard values of m and r in the computation of Approximate and Sample

Farhad Kaffashi; Ryan Foglyano; Christopher G. Wilson; Kenneth A. Loparo

2008-01-01

331

Finding the Best Quadratic Approximation of a Function  

ERIC Educational Resources Information Center

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

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

332

Fast Approximation Algorithms for Fractional Packing and Covering Problems  

Microsoft Academic Search

Fast algorithms that find approximate solutions for a general class of problems, which are called fractional packing and covering problems, are presented. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed greatly outperform the general methods in many applications, and are extensions of a method previously applied to find approximate

Serge A. Plotkin; David B. Shmoyst; Éva Tardos

1991-01-01

333

Approximating a Sum of Random Variables with a Lognormal  

Microsoft Academic Search

A simple, novel, and general method is presented in this paper for approximating the sum of in- dependent or arbitrarily correlated lognormal random variables (RV) by a single lognormal RV. The method is also shown to be applicable for approximating the sum of lognormal-Rice and Suzuki RVs by a single lognormal RV. A sum consisting of a mixture of the

Neelesh B. Mehta; Jingxian Wu; Andreas F. Molisch; Jin Zhang

2007-01-01

334

Error Estimates for the Approximation of the Effective Hamiltonian  

SciTech Connect

We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting.

Camilli, Fabio [Univ. dell'Aquila, Dip. di Matematica Pura e Applicata (Italy)], E-mail: camilli@ing.univaq.it; Capuzzo Dolcetta, Italo [Univ. di Roma 'La Sapienza', Dip. di Matematica (Italy)], E-mail: capuzzo@mat.uniroma1.it; Gomes, Diogo A. [Instituto Superior Tecnico, Departamento de Matematica (Portugal)], E-mail: dgomes@math.ist.utl.pt

2008-02-15

335

Haze of surface random systems: An approximate analytic approach  

Microsoft Academic Search

Approximate analytic expressions for haze (and gloss) of Gaussian randomly rough surfaces for various types of correlation functions are derived within phase-perturbation theory. The approximations depend on the angle of incidence, polarization of the incident light, the surface roughness, sigma , and the average of the power spectrum taken over a small angular interval about the specular direction. In particular

Ingve Simonsen; Åge Larsen; Erik Andreassen; Espen Ommundsen; Katrin Nord-Varhaug

2009-01-01

336

Restrictive padé approximation and parabolic partial differential equations  

Microsoft Academic Search

In this paper, we use the restrictive Pade approximation to approximate the exponential matrix exp(rA). The advantage is that it has the exact value at certain r. We define a new accurate, fast implicit method for the finite difference solution of a parabolic partial differential equations. The stability region is discussed, the obtained results are compared with the exact solution

Hassan N. A. Ismail; Elsayed M. E. Elbarbary

1998-01-01

337

The Density of Alternation Points in Rational Approximation  

Microsoft Academic Search

We investigate the behavior of the equioscillation (alternation) points for the error in best uniform rational approximation on (-1, 1). In the context of the Walsh table (in which the best rational approximant with numerator degree < m , denominator degree < n, is displayed in the nth row and the mth column), we show that these points are dense

P. B. Borwein; A. Kroo; R. Grothmann; E. B. Saff

1989-01-01

338

Space-time tradeoffs for approximate spherical range counting  

Microsoft Academic Search

We present space-time tradeoffs for approximate spherical range counting queries. Given a set S of n data points in Rd along with a positive approximation factor ?, the goal is to preprocess the points so that, given any Euclidean ball B, we can return the number of points of any subset of S that contains all the points within a

Sunil Arya; Theocharis Malamatos; David M. Mount

2005-01-01

339

Approximating MultiDimensional Aggregate Range Queries over Real Attributes  

Microsoft Academic Search

Finding approximate answers to multi-dimensional range queries over real valued attributes has significantapplications in data exploration and database query optimization. In this paper we consider thefollowing problem: given a table of d attributes whose domain is the real numbers, and a query thatspecifies a range in each dimension, find a good approximation of the number of records in the table

Dimitrios Gunopulos; George Kollios; Vassilis J. Tsotras; Carlotta Domeniconi

2000-01-01

340

COARSE GRID APPROXIMATION GOVERNED BY LOCAL FOURIER ANALYSIS  

Microsoft Academic Search

Solving discrete boundary value problems with the help of an appro- priate multigrid method (1, 4, 5, 6) necessitates the construction of a sequence of coarse grids with corresponding coarse grid approximations for the given flne grid discretization. Popular choices in this context are the Galerkin coarse grid approximation (GCA) and the use of the same discretization on the coarser

R. Wienands

2006-01-01

341

Smooth approximation and rendering of large scattered data sets  

Microsoft Academic Search

We present an efficient method to automatically compute a smooth approximation of large functional scattered data sets given over arbitrarily shaped planar domains. Our approach is based on the construction of a C1-continuous bivariate cubic spline and our method offers optimal approximation order. Both local variation and nonuniform distribution of the data are taken into account by using local polynomial

Jörg Haber; Frank Zeilfelder; Oleg Davydov; Hans-Peter Seidel

2001-01-01

342

Eikonal Approximation in Elastic-Wave-Scattering Theory.  

National Technical Information Service (NTIS)

The Eikonal approximation to the elastic wave equation is studied. This approximation, which uses a time-domain picture to include variations in the local velocity of sound, is appropriate in two different cases: (i) weak scattering at all frequencies; an...

J. H. Rose B. DeFacio

1981-01-01

343

ADMiRA: atomic decomposition for minimum rank approximation  

Microsoft Academic Search

In this paper, we address compressed sensing of a low-rank matrix posing the inverse problem as an approximation problem with a specified target rank of the solution. A simple search over the target rank then provides the minimum rank solution satisfying a prescribed data approximation bound. We propose an atomic decomposition providing an analogy between parsimonious representations of a sparse

Kiryung Lee; Yoram Bresler

2010-01-01

344

A Discrepancy Principle For Tikhonov Regularization With Approximately Specified Data  

Microsoft Academic Search

Many discrepancy principles are known for choosing the parameter ff in the regularized operator equation (TT + ffI)xffiff = Tyffi,ky \\\\Gamma yffik ffi, in order to approximate the minimal norm least-squaressolution of the operator equation Tx = y. In this paper we consider aclass of discrepancy principles for choosing the regularization parameterwhen TT and Tyffiare approximated by A n and

M. Thamban Nair; Eberhard Schock

345

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

346

On global-local artificial neural networks for function approximation  

Microsoft Academic Search

We present a hybrid radial basis function (RBF) sigmoid neural network with a three-step training algorithm that utilizes both global search and gradient descent training. The algorithm used is intended to identify global features of an input-output relationship before adding local detail to the approximating function. It aims to achieve efficient function approximation through the separate identification of aspects of

David Wedge; David Ingram; David Mclean; Clive G. Mingham; Zuhair Bandar

2006-01-01

347

A resistive sheet approximation for mesh reflector antennas  

Microsoft Academic Search

A simplified method of estimating the equivalent surface resistance of a reflecting mesh is presented. The equivalent resistance is obtained from the approximate mesh reflection coefficients, which are based on averaged boundary conditions. This resistance approximation allows an integral equation solution for the mesh reflector that is a simple extension of that for the perfectly conducting reflector. Paraboloid radiation patterns

David C. Jenn; A. Prata Jr.; Willard V. T. Rusch; M. R. Barclay

1989-01-01

348

Sparse Wiener Chaos approximations of Zakai equation for nonlinear filtering  

Microsoft Academic Search

Sparse Wiener chaos approximations of Zakai equation is considered. The objective is to optimize an approach to nonlinear filtering based on the Cameron-Martin version of Wiener chaos expansion (WCE). The error of the approximation is obtained. The main feature of Wiener chaos expansion is that it allows one to separate the computations involving the observations from those dealing only with

Jian Xu; Jianxun Li

2009-01-01

349

Approximate dynamic programming using model-free Bellman Residual Elimination  

Microsoft Academic Search

This paper presents an modification to the method of Bellman Residual Elimination (BRE) for approximate dynamic programming. While prior work on BRE has focused on learning an approximate policy for an underlying Markov Decision Process (MDP) when the state transition model of the MDP is known, this work proposes a model-free variant of BRE that does not require knowledge of

Brett Bethke

2010-01-01

350

5 Approximate Nearest Neighbor Regression in Very High Dimensions  

Microsoft Academic Search

Fast and approximate nearest-neighbor search methods have recently be- come popular for scaling nonparameteric regression to more complex and high-dimensional applications. As an alternative to fast nearest neighbor search, training data can also be incorporated online into appropriate suffi- cient statistics and adaptive data structures, such that approximate nearest- neighbor predictions can be accelerated by orders of magnitude by means

Sethu Vijayakumar; Aaron D'Souza; Stefan Schaal

351

An approximate deconvolution procedure for large-eddy simulation  

Microsoft Academic Search

An alternative approach to large-eddy simulation based on approximate deconvolution (ADM) is developed. The main ingredient is an approximation of the nonfiltered field by truncated series expansion of the inverse filter operator. A posteriori tests for decaying compressible isotropic turbulence show excellent agreement with direct numerical simulation. The computational overhead of ADM is similar to that of a scale-similarity model

S. Stolz; N. A. Adams

1999-01-01

352

On the berger approximation: A critical re-examination  

Microsoft Academic Search

Since the first paper by Berger some two decades ago, the simplification known as the Berger approximation has been invoked by the authors of several score papers in spite of the fact that no rational mechanical basis for the approximation could be found. Many recent papers have raised doubts on its applicability. In this paper, using certain well known results

G. Prathap

1979-01-01

353

The nearest approximation of a fuzzy quantity in parametric form  

Microsoft Academic Search

Abstract Applications of fuzzy logic and fuzzy mathematics are increasing widely all around the world. Thus working with fuzzy numbers are very important. In many applications of fuzzy mathematics we need (or it is better) to work with the same fuzzy numbers. In this work we approximate parametric fuzzy numbers with polynomial parametric fuzzy numbers. Keywords: Approximation, Trapezoidal fuzzy number,

Saeid Abbasbandy; Majid Amirfakhrian

2006-01-01

354

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

1986-01-01

355

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

356

Slowly varying amplitude approximation appraised by transfer-matrix approach  

Microsoft Academic Search

The slowly varying amplitude approximation that is widely adopted in nonlinear optics is appraised by the transfer-matrix method. Rigorous solution for second harmonic generation in nonlinear optical superlattices shows that this approximation is invalid when the reflection of the second harmonic (SH) wave from the crystal interface cannot be neglected. When the modulation period of the superlattice is comparable to

Zhi-Yuan Li; Ben-Yuan Gu; Guo-Zhen Yang

1999-01-01

357

Multinomial Approximations for Identification of Nonlinear Dynamic System's Parameters  

NASA Astrophysics Data System (ADS)

In the paper a new method (a MPA-algorithm) for a numerical solution of explicit and implicit problems of multinomial approximation is offered. Consideration is focused on a parameter estimation of nonlinear dynamic system by means of approximating a vector of an estimation by a vector power series which members there are products of degrees of results of digital observations with noise.

Boguslavsky, I. A.

2009-09-01

358

Approximation of functions over redundant dictionaries using coherence  

Microsoft Academic Search

One of the central problems of modern mathematical approximation theory is to approximate functions, or signals, concisely, with elements from a large candidate set called a dictionary. Formally, we are given a signal A ? RN and a dictionary D = {?i}i?I of unit vectors that span RN. A representation R of B terms for input A ? RN is

Anna C. Gilbert; S. Muthukrishnan; Martin J. Strauss

2003-01-01

359

''Optimal'' approximation to elastic projectile-nucleus scattering  

Microsoft Academic Search

An approximation which minimizes binding and recoil corrections is derived for projectile nucleus elastic scattering. We generalize previous work on single scattering and consider now multiple scattering amplitudes in this approximation. These are expressed in terms of amplitudes for elastic scattering off on-shell target nucleons and form factors. The first nonvanishing correction terms are estimated.

S. Gurvitz

1979-01-01

360

On approximate phasor models in dissipative bilinear systems  

Microsoft Academic Search

Dynamic phasors models capture transients in (main) harmonic coefficients of periodically dominated systems, and their utility in state approximations is supported by machine and power systems case studies. The author explores analytical plausibility arguments, and inherent restrictions of such approximations in dissipative systems with quadratically nonlinear lossless components.

Gilead Tadmor

2002-01-01

361

Back to the subseismic approximation for core undertones  

Microsoft Academic Search

The problem of the long-period gravity modes of the Earth outer fluid core is investigated using either the subseismic or the anelastic approximation These two approximations aim at filtering out the uninteresting short-period seismic or acoustic oscillations while taking into account the density variations across the core However, they differ on the form of the equation of mass conservation since

Boris Dintrans

2001-01-01

362

Landau-Zener approximations for resonant neutrino oscillations  

SciTech Connect

A simple method for calculating the effects of resonant neutrino oscillations using Landau-Zener approximations is presented. For any given set of oscillation parameters, the method is to use the Landau-Zener approximation which works best in that region.

Whisnant, K.

1988-07-15

363

Spline approximation of random processes and design problems  

Microsoft Academic Search

We consider the spline approximation of a continuous (continuously differentiable) random process with finite second moments based on n observations of the process (and its derivatives). The performance of the approximation is measured by mean errors (e.g., integrated or maximal quadratic mean errors). For Hermite interpolation splines, an optimal rule sets n observation locations (i.e., a design, a mesh). While,

Oleg Seleznjev

2000-01-01

364

Smooth approximation and rendering of large scattered data sets  

Microsoft Academic Search

Presents an efficient method to automatically compute a smooth approximation of large functional scattered data sets given over arbitrarily shaped planar domains. Our approach is based on the construction of a C 1-continuous bivariate cubic spline and our method offers optimal approximation order. Both local variation and nonuniform distribution of the data are taken into account by using local polynomial

J. Haber; F. Zeilfelder; O. Davydov; H.-P. Seidel

2001-01-01

365

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

366

Rytov approximation for x-ray phase imaging.  

PubMed

In this study, we check the accuracy of the first-order Rytov approximation with a homogeneous sphere as a candidate for application in x-ray phase imaging of large objects e.g., luggage at the airport, or a human patient. Specifically, we propose a validity condition for the Rytov approximation in terms of a parameter V that depends on the complex refractive index of the sphere and the Fresnel number, for Fresnel numbers larger than 1000. In comparison with the exact Mie solution, we provide the accuracy of the Rytov approximation in predicting the intensity and phase profiles after the sphere. For large objects, where the Mie solution becomes numerically impractical, we use the principle of similarity to predict the accuracy of the Rytov approximation without explicit calculation of the Mie solution. Finally, we provide the maximum radius of the sphere for which the first order Rytov approximation remains valid within 1% accuracy. PMID:23481723

Sung, Yongjin; Barbastathis, George

2013-02-11

367

Parquet approximation for the 4x4 Hubbard cluster.  

PubMed

We present a numerical solution of the parquet approximation, a conserving diagrammatic approach which is self-consistent at both the single-particle and the two-particle levels. The fully irreducible vertex is approximated by the bare interaction thus producing the simplest approximation that one can perform with the set of equations involved in the formalism. The method is applied to the Hubbard model on a half-filled 4x4 cluster. Results are compared to those obtained from determinant quantum Monte Carlo (DQMC), FLuctuation EXchange (FLEX), and self-consistent second-order approximation methods. This comparison shows a satisfactory agreement with DQMC and a significant improvement over the FLEX or the self-consistent second-order approximation. PMID:19905481

Yang, S X; Fotso, H; Liu, J; Maier, T A; Tomko, K; D'Azevedo, E F; Scalettar, R T; Pruschke, T; Jarrell, M

2009-10-21

368

TSK fuzzy function approximators: design and accuracy analysis.  

PubMed

Fuzzy systems are excellent approximators of known functions or for the dynamic response of a physical system. We propose a new approach to approximate any known function by a Takagi-Sugeno-Kang fuzzy system with a guaranteed upper bound on the approximation error. The new approach is also used to approximately represent the behavior of a dynamic system from its input-output pairs using experimental data with known error bounds. We provide sufficient conditions for this class of fuzzy systems to be universal approximators with specified error bounds. The new conditions require a smaller number of membership functions than all previously published conditions. We illustrate the new results and compare them to published error bounds through numerical examples. PMID:22155964

Sonbol, Assem H; Fadali, M Sami; Jafarzadeh, Saeed

2011-12-02

369

Synthetic seismograms in heterogeneous media by one-return approximation  

NASA Astrophysics Data System (ADS)

When reverberations between heterogeneities or resonance scattering can be neglected but accumulated effects of forward scattering are strong, the Born approximation is not valid but the De Wolf approximation can be applied in such cases. In this paper, renormalized MFSB (multiple-forescattering single-backscattering) equations and the dual-domain expression for scalar, acoustic and elastic waves are derived by a unified approach. Two versions of the one-return method (using MFSB approximation) are given: One is the wide-angle dual-domain formulation (thin-slab approximation); the other is the screen approximation. In the screen approximation, which involves a small-angle approximation for the wave-medium interaction, it can be seen clearly that the forward scattered, or transmitted waves are mainly controlled by velocity perturbations; while the backscattered or reflected waves, by impedance perturbations. The validity of the method and the wide-angle capability of the dual-domain implementation are demonstrated by numerical examples. Reflection coefficients of a plane interface derived from numerical simulations by the wide-angle method match the theoretical curves well up to critical angles. For the reflections of a low-velocity slab, the agreement between theory and synthetics only starts to deteriorate for angles greater than 70°. The accuracy of the wide-angle version of the method could be further improved by optimizing the wave-number filtering for the forward propagation and shrinking the step length along the propagation direction.

Wu, Ru-Shan

1996-03-01

370

A test of the adhesion approximation for gravitational clustering  

NASA Astrophysics Data System (ADS)

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.

371

A test of the adhesion approximation for gravitational clustering  

NASA Astrophysics Data System (ADS)

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.

1994-06-01

372

Pair approximations of takeover dynamics in regular population structures.  

PubMed

In complex adaptive systems, the topological properties of the interaction network are strong governing influences on the rate of flow of information throughout the system. For example, in epidemiological models, the structure of the underlying contact network has a pronounced impact on the rate of spread of infectious disease throughout a population. Similarly, in evolutionary systems, the topology of potential mating interactions (i.e., population structure) affects the rate of flow of genetic information and therefore affects selective pressure. One commonly employed method for quantifying selective pressure in evolutionary algorithms is through the analysis of the dynamics with which a single favorable mutation spreads throughout the population (a.k.a. takeover time analysis). While models of takeover dynamics have been previously derived for several specific regular population structures, these models lack generality. In contrast, so-called pair approximations have been touted as a general technique for rapidly approximating the flow of information in spatially structured populations with a constant (or nearly constant) degree of nodal connectivities, such as in epidemiological and ecological studies. In this work, we reformulate takeover time analysis in terms of the well-known Susceptible-Infectious-Susceptible model of disease spread and adapt the pair approximation for takeover dynamics. Our results show that the pair approximation, as originally formulated, is insufficient for approximating pre-equilibrium dynamics, since it does not properly account for the interaction between the size and shape of the local neighborhood and the population size. After parameterizing the pair approximation to account for these influences, we demonstrate that the resulting pair approximation can serve as a general and rapid approximator for takeover dynamics on a variety of spatially-explicit regular interaction topologies with varying population sizes and varying uptake and reversion probabilities. Strengths, limitations, and potential applications of the pair approximation to evolutionary computation are discussed. PMID:19413488

Payne, Joshua L; Eppstein, Margaret J

2009-01-01

373

The Space Complexity of Approximating the Frequency Moments  

Microsoft Academic Search

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

Noga Alon; Yossi Matias; Mario Szegedy

1999-01-01

374

Approximate Controllability of Fractional Neutral Stochastic System with Infinite Delay  

NASA Astrophysics Data System (ADS)

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

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

2012-12-01

375

A modified anomalous diffraction approximation for intermediate size soft particles  

NASA Astrophysics Data System (ADS)

A correction to the anomalous diffraction approximation (ADA) has been obtained in such a way that while it gives a significant improvement over the ADA, it also preserves the simplicity and hence the ease of calculations achieved in the ADA. The domain over which this correction has been defined is x(m2-1)2/4<1, where m is the relative refractive index of the scatterer and x is its size parameter. Numerical comparisons of the modified approximation with the exact results and other approximations are presented for homogeneous spheres and infinitely long cylinders for various values of refractive index and size parameters.

Sharma, S. K.

1993-07-01

376

Quadrupole collective inertia in nuclear fission: Cranking approximation  

NASA Astrophysics Data System (ADS)

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

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

2011-11-01

377

Error Approximation and Minimum Phone Error Acoustic Model Estimation  

Microsoft Academic Search

Minimum phone error (MPE) acoustic parameter estimation involves calculation\\u000a\\u0009of edit distances (errors) between correct and incorrect hypotheses.\\u000a\\u0009In the context of large-vocabulary continuous-speech recognition,\\u000a\\u0009this error calculation becomes prohibitively expensive and so errors\\u000a\\u0009are approximated. This paper introduces a novel error approximation\\u000a\\u0009technique. Analysis shows that this approximation yields a higher\\u000a\\u0009correlation to the Levenshtein error metric than a

Matthew Gibson; Thomas Hain

2010-01-01

378

Validity of the adiabatic approximation in quantum mechanics  

SciTech Connect

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the 'standard criterion' for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic theorem and the adiabatic approximation, two quite different, although closely related, ideas.

MacKenzie, R.; Morin-Duchesne, A.; Paquette, H.; Pinel, J. [Groupe de physique des particules, Universite de Montreal, Case Postale 6128, Succursale Centre-ville, Montreal, Quebec, H3C 3J7 (Canada)

2007-10-15

379

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

380

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

381

Parameter Identification of Linear Approximation Models through Particle Filters  

NASA Astrophysics Data System (ADS)

This paper considers system identification for linearly approximated models. Linear approximation models are useful for identification, but their accuracy may not be estimated by the conventional linear identification methods. This paper proposes a method to evaluate not only the system parameters but also the influence of the linear approximation errors in identification. The method is based on particle filters, which are known for its applicability to a wide class of nonlinear systems. Numerical examples are given to demonstrate the effectiveness of the proposed method in detail. Furthermore, experimental validation is performed for a simple pendulum system.

Masuda, Tetsuya; Sugie, Toshiharu

382

Finite temperature lattice properties of graphene beyond the quasiharmonic approximation.  

PubMed

The thermal and mechanical stability of graphene is important for many potential applications in nanotechnology. We calculate the temperature dependence of the lattice parameter, elastic properties, and heat capacity by means of atomistic Monte Carlo simulations that allow us to go beyond the quasiharmonic approximation. We predict an unusual, nonmonotonic, behavior of the lattice parameter with a minimum at T approximately 900 K and of the shear modulus with a maximum at the same temperature. The Poisson ratio in graphene is found to be small approximately 0.1 in a broad temperature interval. PMID:19257461

Zakharchenko, K V; Katsnelson, M I; Fasolino, A

2009-01-29

383

Approximation Algorithms for the Minimum Convex Partition Problem  

Microsoft Academic Search

We present two algorithms that compute constant factor approximations of a minimum convex partition of a set P of n points in the plane. The first algorithm is very simple and computes a 3-approximation in O(n logn) time. The second algorithm improves the approximation factor to \\u000a\\u000a\\u000a\\u000a\\u000a\\u000a\\\\frac3011 \\\\frac{30}{11} but it is more complex and a straight forward implementation will run

Christian Knauer; Andreas Spillner

2006-01-01

384

Exact and approximate expressions for the period of anharmonic oscillators  

Microsoft Academic Search

In this paper, we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulae for the period of anharmonic oscillators and other problems of interest in classical mechanics.

Paolo Amore; Francisco M. Fernández

2005-01-01

385

Close-limit approximation to neutron star collisions.  

NASA Astrophysics Data System (ADS)

The authors develop a close-limit approximation to the head-on collision of two neutron stars similar to that used to treat the merger of black hole binaries. This approximation can serve as a useful benchmark test for future fully non-linear studies. For neutron star binaries, the close-limit approximation involves assuming that the merged object can be approximated as a perturbed, stable neutron star during the ring-down phase of the coalescence. The authoras introduce a prescription for the construction of initial data sets, discuss the physical plausibility of the various assumptions involved, and briefly investigate the character of the gravitational radiation produced during the merger. The numerical results show that several of the merged object's fluid pulsation modes are excited to a significant level.

Gabrielle, D.; Andersson, N.; Kokkotas, K. D.; Laguna, P.; Pullin, J. A.; Ruoff, J.

1999-11-01

386

6. NORTH SIDE, FROM APPROXIMATELY 25 FEET SOUTHEAST OF SOUTHWEST ...  

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

6. NORTH SIDE, FROM APPROXIMATELY 25 FEET SOUTHEAST OF SOUTHWEST CORNER OF BUILDING 320, LOOKING SOUTH. - Oakland Naval Supply Center, Administration Building-Dental Annex-Dispensary, Between E & F Streets, East of Third Street, Oakland, Alameda County, CA

387

Validity of the Rytov Approximation in Optical Propagation Calculations.  

National Technical Information Service (NTIS)

The applicability of the Rytov approximation to the calculation of the characteristics of optical propagation in a weakly inhomogenous random medium is investigated. The condition that the mean square value of the second term in the associated perturbatio...

W. P. Brown

1966-01-01

388

Renormalization group interpretation of the Born and Rytov approximations.  

PubMed

In this paper the method of renormalization group (RG) [Phys. Rev. E54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. PMID:18830328

Kirkinis, Eleftherios

2008-10-01

389

Successive approximations of solutions to stochastic functional differential equations  

Microsoft Academic Search

In the present paper, by means of the successive approximations method, the local or global existence and uniqueness theorems for a stochastic functional differential equation of the Ito type are proved.

Jan Turo

1995-01-01

390

Parabolic Approximation Method for Fast Magnetosonic Wave Propagation in Tokamaks.  

National Technical Information Service (NTIS)

Fast magnetosonic wave propagation in a cylindrical tokamak model is studied using a parabolic approximation method in which poloidal variations of the wave field are considered weak in comparison to the radial variations. Diffraction effects, which are i...

C. K. Phillips F. W. Perkins D. Q. Hwang

1985-01-01

391

Approximate Decoupling and Asymptotic Tracking for MIMO Systems.  

National Technical Information Service (NTIS)

This paper presents an algorithm for approximate input-output decoupling of nonlinear MIMO systems that are either numerically ill-posed or exhibit nearly singular behavior in the application of decoupling algorithms. Although the systems considered are r...

D.N. Godbole S. S. Sastry

1995-01-01

392

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

393

Overview of the Relationship Between Approximation Theory and Filtration.  

National Technical Information Service (NTIS)

This paper gives an overview of the similarities and differences between the requirements and techniques used in mathematical approximation theory and filtration in surface metrology. Although the two fields tend to use the same or similar mathematical ob...

L. A. Blunt P. J. Scott X. Q. Jiang

2001-01-01

394

Approximate trajectories for projectile motion with air resistance  

Microsoft Academic Search

To remarkable accuracy and under a wide variety of conditions, the trajectories of projectiles under various laws of resistance may be approximated by cubic curves. This allows for the relatively simple calculation of many details of the flight.

Michael A. B. Deakin; G. J. Troup

1998-01-01

395

Interpolation function for approximating knee joint behavior in human gait  

NASA Astrophysics Data System (ADS)

Starting from the importance of analyzing the kinematic data of the lower limb in gait movement, especially the angular variation of the knee joint, the paper propose an approximation function that can be used for processing the correlation among a multitude of knee cycles. The approximation of the raw knee data was done by Lagrange polynomial interpolation on a signal acquired using Zebris Gait Analysis System. The signal used in approximation belongs to a typical subject extracted from a lot of ten investigated subjects, but the function domain of definition belongs to the entire group. The study of the knee joint kinematics plays an important role in understanding the kinematics of the gait, this articulation having the largest range of motion in whole joints, in gait. The study does not propose to find an approximation function for the adduction-abduction movement of the knee, this being considered a residual movement comparing to the flexion-extension.

Toth-Ta?c?u, Mirela; Pater, Flavius; Stoia, Dan Ioan

2013-10-01

396

Approximate Calculation of Electrostatic Field under AC Overhead Transmission Lines.  

National Technical Information Service (NTIS)

Simple approximate equations were proposed to estimate accurately the maximum electrostatic field value at 1m above the ground level under AC vertical double circuit transmission lines of low-reactance phase arrangement or one circuit energized on double ...

Y. Amano

1988-01-01

397

Vesicle computers: Approximating a Voronoi diagram using Voronoi automata  

NASA Astrophysics Data System (ADS)

Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata --- finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one excited neighbour; the cell precipitates if a ratio of excited cells in its neighbourhood to its number of neighbours exceed certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate in result of the interaction. Configuration of precipitate represents edges of approximated Voronoi diagram. We discover relation between quality of Voronoi diagram approximation and precipitation threshold, and demonstrate feasibility of our model in approximation Voronoi diagram of arbitrary-shaped objects and a skeleton of a planar shape.

Adamatzky, Andrew; de Lacy Costello, Ben; Holley, Julian; Gorecki, Jerzy; Bull, Larry

2011-07-01

398

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

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

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

399

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

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

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

400

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

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

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

401

A Comparison and Evaluation of Approximate Continuous Review Inventory Models.  

National Technical Information Service (NTIS)

Several approximate continuous review, trigger point-reorder quantity models, differing in degree of complexity, are compared and evaluated under varying conditions. Their performances are compared to those of an exact model, under the assumption of Poiss...

D. Gross J. F. Ince

1972-01-01

402

Slowly varying envelope approximation in a laser with optical feedback  

NASA Astrophysics Data System (ADS)

We examine the application of the slowly varying envelope approximation (SVEA) to the study of the laser with optical feedback, comparing the monochromatic modes obtained using a SVEA approximation with those emerging from a full treatment of the Maxwell-Bloch equations in a coupled cavity formulation of the laser with optical feedback [A. A. Duarte and H. G. Solari Phys. Rev. A 58, 614 (1998)]. While the SVEA approximation in the body of laser produces reliable results, the same approximation applied to the boundary conditions completely distorts the metamorphosis of the spectrum present in the original model, yet far from the transition region the SVEA gives acceptable results. The failure of the SVEA at the metamorphosis is related to the high sensitivity of the dispersion relations k(w) with respect to frequency changes.

Duarte, Alejandro A.; Solari, Hernán G.

2001-09-01

403

B-term approximation using tree-structured Haar transforms  

NASA Astrophysics Data System (ADS)

We present a heuristic solution for B-term approximation using Tree-Structured Haar (TSH) transforms. Our solution consists of two main stages: best basis selection and greedy approximation. In addition, when approximating the same signal with different B constraint or error metric, our solution also provides the flexibility of having less overall running time at expense of more storage space. We adopted lattice structure to index basis vectors, so that one index value can fully specify a basis vector. Based on the concept of fast computation of TSH transform by butterfly network, we also developed an algorithm for directly deriving butterfly parameters and incorporated it into our solution. Results show that, when the error metric is normalized l1-norm and normalized l2-norm, our solution has comparable (sometimes better) approximation quality with prior data synopsis algorithms.

Ho, Hsin-Han; Egiazarian, Karen O.; Mitra, Sanjit K.

2009-02-01

404

Bounds for the adiabatic approximation with applications to quantum computation  

SciTech Connect

We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.

Jansen, Sabine; Ruskai, Mary-Beth; Seiler, Ruedi [Institut fuer Mathematik, TU Berlin, MA 7-2, Strasse des 17, Juni 136, D-10623 Berlin (Germany); Department of Mathematics, Tufts University, Medford, Massachusetts 02155 (United States); Institut fuer Mathematik, TU Berlin, MA 7-2, Strasse des 17, Juni 136, D-10623 Berlin (Germany)

2007-10-15

405

Perspective view of the Indian Mission looking from approximately the ...  

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

Perspective view of the Indian Mission looking from approximately the same vantage point as that seen in MD-1109-N-12 - National Park Seminary, Indian Mission, 2790 Linden Lane, Silver Spring, Montgomery County, MD

406

Approximation of nonlinear boundary integral equations for the combined method.  

National Technical Information Service (NTIS)

The nonlinear boundary integral equations that arise in research of nonlinear magnetostatic problems are investigated in combined formulation on an unbounded domain. Approximations of the derived operator equations are studied based on the Galerkin method...

M. Gregus B. N. Khoromsky G. E. Mazurkevich E. P. Zhidkov

1989-01-01

407

Non-ideal boson system in the Gaussian approximation  

SciTech Connect

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

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

1997-01-01

408

1. Rockwork approximately 6 of a mile upstream from Keystone ...  

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

1. Rockwork approximately 6 of a mile upstream from Keystone Bridge. View looking south from a distance of 50 feet. - Denver & Rio Grande Rockwork, East of South Platte, Waterton, Jefferson County, CO

409

Existence and Uniqueness in Approximation by Integral Polynomials.  

National Technical Information Service (NTIS)

In the paper the author studies the existence and uniqueness questions for uniform approximation over compact sets by polynomials whose coefficients are, in some sense, integers. These polynomials are the integral polynomials of the title. The author also...

L. B. O. Ferguson

1974-01-01

410

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

411

Some Approximation Properties in Orlicz-Sobolev Spaces.  

National Technical Information Service (NTIS)

We prove that weak derivatives in general Orlicz spaces are globally strong derivatives with respect to the modular convergence. Other approximation theorems involving the modular convergence are presented, which improve known density results of interest ...

J. P. Gossez

1980-01-01

412

13. ARROYO SECO PARKWAY SEEN FROM DEBS PARK (APPROXIMATELY 34° ...  

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

13. ARROYO SECO PARKWAY SEEN FROM DEBS PARK (APPROXIMATELY 34° 7' BY 118° 11' ON USGS LOS ANGELES QUADRANGLE). AVENUE 60 BRIDGE AT CENTER. LOOKING 240° WSW. - Arroyo Seco Parkway, Los Angeles to Pasadena, Los Angeles, Los Angeles County, CA

413

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

414

Implicit Lower-Upper\\/Approximate-Factorization Schemes for Incompressible Flows  

Microsoft Academic Search

A lower-upper\\/approximate-factorization (LU\\/AF) scheme is developed for the incompressible Euler or Navier–Stokes equations. The LU\\/AF scheme contains an iteration parameter that can be adjusted to improve iterative convergence rate. The LU\\/AF scheme is to be used in conjunction with linearized implicit approximations and artificial compressibility to compute steady solutions, and within sub-iterations to compute unsteady solutions. Formulations based on time

W. Roger Briley; Shyam S. Neerarambam; David L. Whitfield

1996-01-01

415

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

416

Inverse-scattering theory within the Rytov approximation.  

PubMed

A method for determining the internal structure of a localized scattering potential from field measurements performed outside the scattering volume is developed by using the Rytov approximation. The theory is compared with the inverse-scattering method within the Born and eikonal approximations and found to reduce to these methods in the weak-scattering (Born) and very-short-wavelength (eikonal) limits. PMID:19701437

Devaney, A J

1981-08-01

417

Using the Inhomogeneous Simultaneous Approximation Problem for Cryptographic Design  

Microsoft Academic Search

\\u000a We introduce the Inhomogeneous Simultaneous Approximation Problem (ISAP), an old problem from the field of analytic number\\u000a theory. Although the Simultaneous Approximation Problem (SAP) is already known in cryptography, it has mainly been considered\\u000a in its homogeneous instantiation for attacking schemes. We take a look at the hardness and applicability of ISAP, i.e., the inhomogeneous variant, for designing schemes.\\u000a \\u000a \\u000a More

Frederik Armknecht; Carsten Elsner; Martin Schmidt

418

Weak approximation and non-abelian fundamental groups  

Microsoft Academic Search

. We introduce a new obstruction to weak approximation related tonon-abelian coverings of a proper and smooth variety X defined over a numberfield k. It provides some counter-examples to weak approximation which are notaccounted for by the Manin obstruction, for example bielliptic surfaces.0. IntroductionLet X be a smooth and proper algebraic variety over a number field k and\\\\Omegak be the

D. Harari

1998-01-01

419

Approximation methods in multidisciplinary analysis and optimization: a panel discussion  

Microsoft Academic Search

This paper summarizes the discussion at the Approximation Methods Panel that was held at the 9 th AIAA\\/ISSMO Symposium on Multidisciplinary Analysis & Optimization in Atlanta, GA on September 2–4, 2002. The objective of the panel was to discuss the current state-of-the-art of approximation methods and identify future research directions important to the community. The panel consisted of five representatives

T. W. Simpson; A. J. Booker; D. Ghosh; A. A. Giunta; P. N. Koch; R.-J. Yang

2004-01-01

420

On the Complexity of Approximating a Nash Equilibrium  

Microsoft Academic Search

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 constant inapproximability result for the problem, since the appearance of the original results on the complexity of the Nash equilibrium [8, 5, 7]. Moreover, it provides an apparent---assuming that

Constantinos Daskalakis

2011-01-01

421

Weighted curvature approximation: numerical tests for 2D dielectric surfaces  

Microsoft Academic Search

The weighted curvature approximation (WCA) was recently introduced by Elfouhaily et al [7] as a unifying scattering theory that reproduces formally both the tangent-plane and the small-perturbation model in the appropriate limits, and is structurally identical to the former approximation with some different slope-dependent kernel. Due to the simplicity of its formulation, the WCA is interesting from a numerical point

Charles-Antoine Guérin; Gabriel Soriano; Tanos Elfouhaily

2004-01-01

422

The linear noise approximation for molecular fluctuations within cells  

NASA Astrophysics Data System (ADS)

We study the applicability of Van Kampen's linear noise approximation to the calculation of fluctuations in cells due to small number of molecules for simple genetic systems not previously considered. These systems include dimer formation and feedback. We explain why the linear noise approximation can be surprisingly effective, but also illustrate how it fails in a simple example when a protein probability distribution is not purely Gaussian.

Hayot, F.; Jayaprakash, C.

2004-12-01

423

Approximate policy iteration: a survey and some new methods  

Microsoft Academic Search

We consider the classical policy iteration method of dynamic programming (DP), where approximations and simulation are used\\u000a to deal with the curse of dimensionality. We survey a number of issues: convergence and rate of convergence of approximate\\u000a policy evaluation methods, singularity and susceptibility to simulation noise of policy evaluation, exploration issues, constrained\\u000a and enhanced policy iteration, policy oscillation and chattering,

Dimitri P. Bertsekas

2011-01-01

424

Construction of rational approximations by means of REDUCE  

Microsoft Academic Search

1. In recent years the rational approximations have been widely used to solve physical and computational problems \\/1,2\\/. When a real function f(x) is repeatedly calculated on a ? × ? b, it is reasonable to replace it by a polynomial or rational approximation on [a,b]. For example, if f(x) is a composite combination of elementary and special functions any

A. P. Kryukov; Y. Rodionov; G. L. Litvinov

1986-01-01

425

RBFs approximation method for time fractional partial differential equations  

NASA Astrophysics Data System (ADS)

In this paper, radial basis functions (RBFs) approximation method is implemented for time fractional advection–diffusion equation on a bounded domain. In this method the first order time derivative is replaced by the Caputo fractional derivative of order ? ? (0, 1], and spatial derivatives are approximated by the derivative of interpolation in the Kansa method. Stability and convergence of the method is discussed. Several numerical examples are include to demonstrate effectiveness and accuracy of the method.

Uddin, Marjan; Haq, Sirajul

2011-11-01

426

Tiling of canonical cells: large Pa3 approximants  

Microsoft Academic Search

We report the discovery of 5\\/3, 8\\/5 and 13\\/8 periodic approximants to the quasi-periodic tiling of canonical cells with Pa3 (P213) space symmetry. Although the method–Monte Carlo optimization of the density–cannot produce quasi-periodic tiling of canonical cells, the approximants are large enough to demonstrate remarkable properties of the network, appearing as an alternative to the 3D Penrose-tiling-based models of quasi-crystals.

M. Mihalkovic; P. Mrafko

1993-01-01

427

Second harmonic scattering from small particles using Discrete Dipole Approximation.  

PubMed

We extend a simple dipole approximation model to predict nonlinear scattering from small particles. This numerical method is known as Discrete Dipole Approximation (DDA) and has been extensively used to model linear scattering by small particles of various shapes and sizes. We show here that DDA can be used to efficiently model second harmonic scattering by small particles. Our results are compared with experimental data and other computational methods. PMID:20941058

Balla, Naveen K; So, Peter T C; Sheppard, Colin J R

2010-10-11

428

Rough Temporal Vague Sets in Pawlak Approximation Space  

Microsoft Academic Search

\\u000a The combination of temporal vague set theory and rough set theory is developed in this paper. The lower and upper approximation\\u000a operators of a temporal vague set are constructed, which is partitioned by an indiscernibility relation in Pawlak approximation\\u000a space, and the concept of rough temporal vague sets is proposed as a generalization of rough vague sets. Further properties\\u000a associated

Yonghong Shen

2010-01-01

429

Approximation of stochastic processes by TS fuzzy systems  

Microsoft Academic Search

Fuzzy systems can provide us with universal approximation models of deterministic input–output relationships, but in the stochastic environment few achievements related to the subject have so far achieved. In the paper a novel stochastic Takagi–Sugeno (T–S) fuzzy system is introduced to represent approximately existing randomness in many real-world systems. By recapitulating the general architecture of the stochastic T–S fuzzy rule-based

Puyin Liu; Hongxing Li

2005-01-01

430

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

431

Off-Policy Temporal Difference Learning with Function Approximation  

Microsoft Academic Search

We introduce the first algorithm for off-policy temporal-difference learning that is stable with linear function approximation. Off-policy learn- ing is of interest because it forms the basis for popular reinforcement learning methods such as Q-learning, which has been known to diverge with linear function approximation, and because it is critical to the practical utility of multi-scale, multi-goal, learning frameworks such

Doina Precup; Richard S. Sutton; Sanjoy Dasgupta

2001-01-01

432

Approximation algorithms for homogeneous polynomial optimization with quadratic constraints  

Microsoft Academic Search

In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimiza- tion models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are non- convex in general, the problems under consideration are all NP-hard. In this paper

Simai He; Zhening Li; Shuzhong Zhang

2010-01-01

433

On Approximation Behavior of the Greedy Triangulation for Convex Polygons  

Microsoft Academic Search

We prove that the greedy triangulation heuristic for minimum weight triangulation of convex polygons yields solutions within\\u000a a constant factor from the optimum. For interesting classes of convex polygons, we derive small upper bounds on the constant\\u000a approximation factor. Our results contrast with Kirkpatrick's ?(n) bound on the approximation factor of the Delaunay triangulation heuristic for minimum weight triangulation of

Christos Levcopoulos; Andrzej Lingas

1987-01-01

434

Rough mereology: A new paradigm for approximate reasoning  

Microsoft Academic Search

We are concerned with formal models of reasoning under uncertainty. Many approachesto this problem are known in the literature e.g. Dempster-Shafer theory,bayesian-based reasoning, belief networks, fuzzy logics etc. We propose rough mereologyas a foundation for approximate reasoning about complex objects. Our notionof a complex object includes approximate proofs understood as schemes constructedto support our assertions about the world on the

Lech Polkowski; Andrzej Skowron

1996-01-01

435

Algebraic model of optical intelligence systems: geometrical optics approximation  

NASA Astrophysics Data System (ADS)

We consider algebraic foundations of geometrical optics approximation. The consideration is aimed at optical implementation of computational intelligence models. Theory of triangular norms and measure means are used to formulate the description. The process of negative photo-registration is considered as the implementation of the negation, which generates the algebra. Three approximations of negative recording media transmittance are considered: linear, involutive, and non-involutive one. Optically realizable orders and relations of fuzzy numbers, fuzzy sets and images are considered.

Zakirov, Ravil Z.; Pavlov, Alexander V.

2001-11-01

436

Approximations to Self-Consistent Field Molecular Wavefunctions  

Microsoft Academic Search

Unparameterized and parameterized versions are outlined of a new method for approximating self-consistent field wavefunctions from first principles at the minimum basis set level for complex molecules containing hydrogen and first-row atoms. The Hartree-Fock self-consistent field equations for closed-shell molecules are solved, retaining all one-electron integrals, and approximating the two-electron Coulomb integrals, hybrid integrals, and exchange integrals of the form

Thomas A. Halgren; William N. Lipscomb

1972-01-01

437

Approximating the largest eigenvalue of network adjacency matrices  

NASA Astrophysics Data System (ADS)

The largest eigenvalue of the adjacency matrix of a network plays an important role in several network processes (e.g., synchronization of oscillators, percolation on directed networks, and linear stability of equilibria of network coupled systems). In this paper we develop approximations to the largest eigenvalue of adjacency matrices and discuss the relationships between these approximations. Numerical experiments on simulated networks are used to test our results.

Restrepo, Juan G.; Ott, Edward; Hunt, Brian R.

2007-11-01

438

Using the thermal Gaussian approximation approximation for theBoltzmann Operator in Semiclassical Initial Value Time CorrelationFunctions  

SciTech Connect

The thermal Gaussian approximation (TGA) recently developed by Mandelshtam et al has been demonstrated to be a practical way for approximating the Boltzmann operator exp(-{beta}H) for multidimensional systems. In this paper the TGA is combined with semiclassical (SC) initial value representations (IVRs) for thermal time correlation functions. Specifically, it is used with the linearized SC-IVR (LSC-IVR, equivalent to the classical Wigner model), and the 'forward-backward semiclassical dynamics' (FBSD) approximation developed by Makri et al. Use of the TGA with both of these approximate SC-IVRs allows the oscillatory part of the IVR to be integrated out explicitly, providing an extremely simple result that is readily applicable to large molecular systems. Calculation of the force-force autocorrelation for a strongly anharmonic oscillator demonstrates its accuracy, and of the velocity autocorrelation function (and thus the diffusion coefficient) of liquid neon demonstrates its applicability.

Liu, Jian; Miller, William H.

2006-09-06

439

Finite volume approximation of two phase-fluid flows based on an approximate Roe-Type Riemann solver  

SciTech Connect

We introduce an approximate Roe type Riemann solver for the numerical simulation of two-phase fluid flows composed of liquid droplets suspended in gas. We compute a Roe linearization of some well-conditioned approximate Rankine-Hugoniot relations in nonconservation form. The computed solutions are found to be in good agreement with the exact solution in one dimension slab geometry. We extend this solver to two-dimensional geometries using a fininte volume formulation. 24 refs., 15 figs., 2 tabs.

Sainsaulieu, L. [C.E.R.M.I.C.S., E.N.P.C., Noisy-le-Grand (France)]|[Centre de Mathematiques Appliquees, Palaiseau (France)

1995-10-01

440

A new closure approximation for shallow-water wave propagation  

NASA Astrophysics Data System (ADS)

The prediction of wind-generated ocean waves has seen much progress over the last few decades, which - in turn - has contributed to major improvements in coastal circulation and transport models. However, in the nearshore, where accurate wave information is often important, shallow-water nonlinearity can cause significant deviations from Gaussian statistics, which is presently not (or very crudely) represented in stochastic wave models. The statistical description of weakly dispersive, nonlinear waves requires a closure of the hierarchy of wave statistical moments, a problem in many ways similar to the closure problem in turbulence. Although the wave problem is potentially simpler on account of the relatively weak nonlinearity, there appears no first-principle solution available. As a consequence, various more or less ad hoc approximations have been introduced in the past. Although these approaches have had variable success, very little is understood about the characteristics of the various closure approximations, their implied relaxation length scales, and the role of dissipation (wave breaking) on the nonlinear dynamics. In this study we derive a new closure approximation, following the ideas underlying the direct-interaction approximation in turbulence. Through comparison against Monte Carlo simulations, laboratory observations, and field observations, we will assess the potential of the new approximation. We will show how this new model is related to earlier approaches (including a quasi-normal closure, a Markov model, and an empirical relaxation approximation), and present a detailed comparison between the nonlinear dynamics predicted by the various approximations. This research is funded by the National Oceanographic Partnership Program and the Office of Naval Research.

Janssen, T. T.; Herbers, T. H.

2010-12-01

441

Anthropometric approximation of body weight in unresponsive stroke patients  

PubMed Central

Background and purpose Thrombolysis of acute ischaemic stroke is based strictly on body weight to ensure efficacy and to prevent bleeding complications. Many candidate stroke patients are unable to communicate their body weight, and there is often neither the means nor the time to weigh the patient. Instead, weight is estimated visually by the attending physician, but this is known to be inaccurate. Methods Based on a large general population sample of nearly 7000 subjects, we constructed approximation formulae for estimating body weight from simple anthropometric measurements (body height, and waist and hip circumference). These formulae were validated in a sample of 178 consecutive inpatients admitted to our stroke unit, and their accuracy was compared with the best visual estimation of two experienced physicians. Results The simplest formula gave the most accurate approximation (mean absolute difference 3.1 (2.6)?kg), which was considerably better than the best visual estimation (physician 1: 6.5 (5.2)?kg; physician 2: 7.4 (5.7)?kg). It reduced the proportion of weight approximations mismatched by >10% from 31.5% and 40.4% (physicians 1 and 2, respectively) to 6.2% (anthropometric approximation). Only the patient's own estimation was more accurate (mean absolute difference 2.7 (2.4)?kg). Conclusions By using an approximation formula based on simple anthropometric measurements (body height, and waist and hip circumference), it is possible to obtain a quick and accurate approximation of body weight. In situations where the exact weight of unresponsive patients cannot be ascertained quickly, we recommend using this approximation method rather than visual estimation.

Lorenz, M W; Graf, M; Henke, C; Hermans, M; Ziemann, U; Sitzer, M; Foerch, C

2007-01-01

442

An efficient symplectic approximation for fringe-field maps  

NASA Astrophysics Data System (ADS)

The fringe fields of particle optical elements have a strong effect on optical properties. In particular higher order aberrations are often dominated by fringe-field effects. So far their transfer maps can only be calculated accurately using numerical integrators, which is rather time consuming. Any alternative or approximate calculation scheme should be symplectic because of the importance of the symplectic symmetry for long term behavior. We introduce a method to approximate fringe-field maps of magnetic elements in a symplectic fashion which works extremely quickly and accurately. It is based on differential algebra (DA) techniques and was implemented in COSY INFINITY. The approximation exploits the advantages of Lie transformations, generating functions, scaling of the map with field strength and aperture, and the dependence of transfer maps on the ratio of magnetic rigidity to magnetic field strength. The results are compared to numerical integration and to the approximation via fringe-field integrals. The quality of the approximation will be illustrated on some examples including linear design, high order effects, and long term tracking.

Hoffstätter, G. H.; Berz, M.

1993-12-01

443

Crashworthiness design optimization using successive response surface approximations  

NASA Astrophysics Data System (ADS)

Finite Element (FE) method is among the most powerful tools for crash analysis and simulation. Crashworthiness design of structural members requires repetitive and iterative application of FE simulation. This paper presents a crashworthiness design optimization methodology based on efficient and effective integration of optimization methods, FE simulations, and approximation methods. Optimization methods, although effective in general in solving structural design problems, loose their power in crashworthiness design. Objective and constraint functions in crashworthiness optimization problems are often non-smooth and highly non-linear in terms of design variables and follow from a computationally costly (FE) simulation. In this paper, a sequential approximate optimization method is utilized to deal with both the high computational cost and the non-smooth character. Crashworthiness optimization problem is divided into a series of simpler sub-problems, which are generated using approximations of objective and constraint functions. Approximations are constructed by using statistical model building technique, Response Surface Methodology (RSM) and a Genetic algorithm. The approximate optimization method is applied to solve crashworthiness design problems. These include a cylinder, a simplified vehicle and New Jersey concrete barrier optimization. The results demonstrate that the method is efficient and effective in solving crashworthiness design optimization problems.

Kurtaran, H.; Eskandarian, A.; Marzougui, D.; Bedewi, N. E.

444

APPROXIMATION ALGORITHMS FOR CLUSTERING TO MINIMIZE THE SUM OF DIAMETERS  

SciTech Connect

We consider the problem of partitioning the nodes of a complete edge weighted graph into {kappa} clusters so as to minimize the sum of the diameters of the clusters. Since the problem is NP-complete, our focus is on the development of good approximation algorithms. When edge weights satisfy the triangle inequality, we present the first approximation algorithm for the problem. The approximation algorithm yields a solution that has no more than 10k clusters such the total diameter of these clusters is within a factor O(log (n/{kappa})) of the optimal value fork clusters, where n is the number of nodes in the complete graph. For any fixed {kappa}, we present an approximation algorithm that produces {kappa} clusters whose total diameter is at most twice the optimal value. When the distances are not required to satisfy the triangle inequality, we show that, unless P = NP, for any {rho} {ge} 1, there is no polynomial time approximation algorithm that can provide a performance guarantee of {rho} even when the number of clusters is fixed at 3. Other results obtained include a polynomial time algorithm for the problem when the underlying graph is a tree with edge weights.

Kopp, S.; Mortveit, H.S.; Reidys, S.M.

2000-02-01

445

?-connectedness, finite approximations, shape theory and coarse graining in hyperspaces  

NASA Astrophysics Data System (ADS)

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

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

2008-12-01

446

An optimized semiclassical approximation for vibrational response functions  

NASA Astrophysics Data System (ADS)

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.

Gerace, Mallory; Loring, Roger F.

2013-03-01

447

Note on the semiclassical approximation in quantum gravity  

SciTech Connect

We reexamine the semiclassical approximation to quantum gravity in the canonical formulation, focusing on the definition of a quasiclassical state for the gravitational field. It is shown that a state with classical correlations must be a superposition of states of the form {ital e}{sup {ital i}}{sup {ital S}}. In terms of a reduced phase space formalism, this type of state can be expresesd as a coherent superposition of eigenstates of operators that commute with the constraints and so correspond to constants of the motion. Contact is made with the usual semiclassical approximation by showing that a superposition of this kind can be approximated by a WKB state with an appropriately localized prefactor. A qualitative analysis is given of the effects of geometry fluctuations, and the possibility of a breakdown of the semiclassical approximation due to interference between neighboring classical trajectories is discussed. It is shown that a breakdown in the semiclassical approximation can be a coordinate-dependent phenomenon, as has beeen argued to be the case close to a black hole horizon. {copyright} {ital 1996 The American Physical Society.}

Lifschytz, G.; Mathur, S.D. [Center for Theoretical Physics, Laboratory for Nuclear Science, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Ortiz, M. [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155 (United States)

1996-01-01

448

Efficient algorithm for approximating one-dimensional ground states  

NASA Astrophysics Data System (ADS)

The density-matrix renormalization-group method is very effective at finding ground states of one-dimensional (1D) quantum systems in practice, but it is a heuristic method, and there is no known proof for when it works. In this article we describe an efficient classical algorithm which provably finds a good approximation of the ground state of 1D systems under well-defined conditions. More precisely, our algorithm finds a matrix product state of bond dimension D whose energy approximates the minimal energy such states can achieve. The running time is exponential in D, and so the algorithm can be considered tractable even for D, which is logarithmic in the size of the chain. The result also implies trivially that the ground state of any local commuting Hamiltonian in 1D can be approximated efficiently; we improve this to an exact algorithm.

Aharonov, Dorit; Arad, Itai; Irani, Sandy

2010-07-01

449

Assessment of approximations in nonequilibrium Green's function theory  

NASA Astrophysics Data System (ADS)

A nonequilibrium Green’s function (NEGF) method for stationary carrier dynamics in open semiconductor nanodevices is presented that includes all relevant incoherent scattering mechanisms. A consistent lead model is developed that ensures all observables to reflect intrinsic device properties. By restricting the charge self-consistent calculations to vertical transport through heterostructures, the Green’s functions and self-energies can be determined very accurately. This allows us to assess many commonly used approximations, such as ballistic leads, decoupling of Dyson’s and Keldysh’s equations, truncated or momentum-averaged self-energies, and local self-energies in the NEGF formalism in detail, and to study limiting cases such as diffusive transport in resistors. The comparison of exact and approximated NEGF calculations illustrates the physical implications and validity of common approximations and suggests numerically efficient simplifications.

Kubis, T.; Vogl, P.

2011-05-01

450

Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems  

SciTech Connect

We recently introduced the dynamical cluster approximation (DCA), a technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean-field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite-size periodic cluster. The dynamical mean-field approximation (exact result) is obtained by taking the cluster to a single site (the thermodynamic limit). Here, we provide details of our method, explicitly show that it is causal, systematic, {phi} derivable, and that it becomes conserving as the cluster size increases. We demonstrate the DCA by applying it to a quantum Monte Carlo and exact enumeration study of the two-dimensional Falicov-Kimball model. The resulting spectral functions preserve causality, and the spectra and the charge-density-wave transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases. (c) 2000 The American Physical Society.

Hettler, M. H. [Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221 (United States); Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States); Mukherjee, M. [Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221 (United States); Jarrell, M. [Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221 (United States); Krishnamurthy, H. R. [Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221 (United States); Department of Physics, Indian Institute of Science, Bangalore 560012, (India)

2000-05-15

451

Validity of anomalous diffraction approximation in m- ? domain  

NASA Astrophysics Data System (ADS)

In a recent paper, Liu et al. [Liu, C., Jonas, P.R., Saunders, C.P.R., 1996. Accuracy of the anomalous diffraction approximation to the light scattering by column-like ice crystals. Atmos. Res. 41, 63-69] reported that the anomalous diffraction approximation (ADA) accuracy is not sensitive to van de Hulst's condition | m-1|?1, but is dependent on the size parameter ?. Videen and Chýlek [Videen, G., Chýlek, P., 1998. Anomalous diffraction approximation limits. Atmos. Res., this issue] pointed out that this result is at odds with previous research, and their results indicated that the accuracy of ADA is much dependent on the condition of | m-1|?1. Some calculated results are presented here to provide further discussion of the ADA validity in the calculation of particle extinction and absorption efficiencies.

Liu, Chun-Lei

452

Models to Approximate the Motions of Protein Loops  

PubMed Central

We approximate the loop motions of various proteins by using a coarse-grained model and the theory of rubberlike elasticity of polymer chains. The loops are considered as chains where only the first and the last residues thereof are tethered by their connections to the main structure; while within the loop, the loop residues are connected only to their sequence neighbors. We applied these approximate models to five proteins. Our approximation shows that the loop motions can usually be computed locally which shows these motions are robust and not random. But most interestingly, the new method presented here can be used to compute the likely motions of loops that are missing in the structures.

Skliros, Aris; Jernigan, Robert L.; Kloczkowski, Andrzej

2010-01-01

453

Third-Born-approximation effects in electron capture  

SciTech Connect

We have calculated corrections to the strong-potential Born approximation using the distorted-wave Born formalism of Taulbjerg and Briggs. In the sense of a plane-wave Born expansion, all terms of the third Born approximation, and all ''single switching'' fourth Born terms are included, but a peaking approximation is needed to reduce the calculation to tractable form. We believe this to be the first calculation to be so complete in the Born sense. Effects of the higher terms are most visible in the valley between the Thomas peak and the forward peak. The Thomas peak is visible in the correction term even though it includes no second Born contributions. We suggest that this may be interpreted as a third Born effect with two ''hard'' collisions followed by a ''soft'' collision.

Hsin, S.H.; Lieber, M.

1987-06-01

454

An approximate inertial manifold for computing Burgers' equation  

NASA Astrophysics Data System (ADS)

We present a numerical scheme for the approximation of nonlinear evolution equations over large time intervals. Our algorithm is motivated from the dynamical systems point of view. In particular, we adapt the methodology of approximate inertial manifolds to a finite difference scheme. This leads to a differential treatment in which the higher (i.e. unresolved) modes are expressed in terms of the lower modes. As a particular example we derive an approximate inertial manifold for Burgers' equation and develop a numerical algorithm suitable for computing. We perform a parameter study in which we compare the accuracy of a standard scheme with our modified scheme. For all values of the parameters (which are the coefficient of viscosity and the cell size), we obtain a decrease in the numerical error by at least a factor of 2.0 with the modified scheme. The decrease in error is substantially greater over large regions of the parameters space.

Margolin, L. G.; Jones, D. A.

1992-11-01

455

Efficient algorithm for approximating one-dimensional ground states  

SciTech Connect

The density-matrix renormalization-group method is very effective at finding ground states of one-dimensional (1D) quantum systems in practice, but it is a heuristic method, and there is no known proof for when it works. In this article we describe an efficient classical algorithm which provably finds a good approximation of the ground state of 1D systems under well-defined conditions. More precisely, our algorithm finds a matrix product state of bond dimension D whose energy approximates the minimal energy such states can achieve. The running time is exponential in D, and so the algorithm can be considered tractable even for D, which is logarithmic in the size of the chain. The result also implies trivially that the ground state of any local commuting Hamiltonian in 1D can be approximated efficiently; we improve this to an exact algorithm.

Aharonov, Dorit; Arad, Itai; Irani, Sandy [School of Computer Science and Engineering, Hebrew University, Jerusalem (Israel); School of Computer Science, Tel-Aviv University, Tel-Aviv (Israel); Computer Science Department, University of California, Irvine, California (United States)

2010-07-15

456

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

457

An approximate method for residual stress calculation infunctionally graded materials  

SciTech Connect

Thermal residual stresses in functionally graded materials(FGMs) arise primarily from nonlinear spatial variations in the thermalexpansion coefficient, but can be significantly adjusted by variations inmodulus. Thermoelastic analysis of FGMs is complicated by such modulusgradients. A class of problems for which thermal stress solutions formaterials with constant modulus can be used as a basis for approximationsfor FGMs is discussed. The size of the error in this approximation due togradients in elastic modulus is investigated. Analytical and finiteelement solutions for the thermal stresses in various FGM geometries arecompared to results from this approximate method. In a geometry ofpractical interest, a right cylinder graded along the z-axis, the errorfor a Ni-Al2O3 FGM was found to be within 15 percent for all gradientsconsidered. The form of the approximation makes it easier to identifydesirable types of spatial nonlinearity in expansion coefficient andvariations in modulus: this would allow the manipulation of the locationof compressive stresses.

Becker, T.L.

1999-06-02

458

Approximation results for neural network operators activated by sigmoidal functions.  

PubMed

In this paper, we study pointwise and uniform convergence, as well as the order of approximation, for a family of linear positive neural network operators activated by certain sigmoidal functions. Only the case of functions of one variable is considered, but it can be expected that our results can be generalized to handle multivariate functions as well. Our approach allows us to extend previously existing results. The order of approximation is studied for functions belonging to suitable Lipschitz classes and using a moment-type approach. The special cases of neural network operators activated by logistic, hyperbolic tangent, and ramp sigmoidal functions are considered. In particular, we show that for C(1)-functions, the order of approximation for our operators with logistic and hyperbolic tangent functions here obtained is higher with respect to that established in some previous papers. The case of quasi-interpolation operators constructed with sigmoidal functions is also considered. PMID:23587719

Costarelli, Danilo; Spigler, Renato

2013-03-27

459

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

460

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

461

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

462

Composite field approximations for ion traps with apertures on electrodes  

NASA Astrophysics Data System (ADS)

This paper presents two approximate analytical expressions for nonlinear electric fields in the principal direction in axially symmetric (3D) and two dimensional (2D) ion trap mass analysers with apertures (holes in case of 3D traps and slits in case of 2D traps) on the electrodes. Considered together (3D and 2D), we present composite approximations for the principal unidirectional nonlinear electric fields in these ion traps. The composite electric field E has the formE=Enoaperture+Eaperture,where Enoaperture is the field within an imagined trap which is identical to the practical trap except that the apertures are missing and Eaperture is the field contribution due to apertures on the two trap electrodes. The field along the principal axis of the trap can in this way be well approximated for any aperture that is not too large. To derive Eaperture, classical results of electrostatics have been extended to electrodes with finite thickness and different aperture shapes. Enoaperture is a modified truncated multipole expansion for the imagined trap with no aperture. The first several terms in the multipole expansion are in principle exact (though numerically determined using the BEM), while the last term is chosen to match the field at the electrode. This expansion, once computed, works with any aperture in the practical trap. The composite field approximation for axially symmetric (3D) traps is checked for three geometries: the Paul trap, the cylindrical ion trap (CIT) and an arbitrary other trap. The approximation for 2D traps is verified using two geometries: the linear ion trap (LIT) and the rectilinear ion trap (RIT). In each case, for two aperture sizes (10% and 50% of the trap dimension), highly satisfactory fits are obtained. These composite approximations may be used in more detailed nonlinear ion dynamics studies than have been hitherto attempted.

Chattopadhyay, Madhurima; Verma, Neeraj Kumar; Mohanty, Atanu K.

2009-05-01

463

Theory of periodically specified problems: Complexity and approximability  

SciTech Connect

We study the complexity and the efficient approximability of graph and satisfiability problems when specified using various kinds of periodic specifications studied. The general results obtained include the following: (1) We characterize the complexities of several basic generalized CNF satisfiability problems SAT(S) [Sc78], when instances are specified using various kinds of 1- and 2-dimensional periodic specifications. We outline how this characterization can be used to prove a number of new hardness results for the complexity classes DSPACE(n), NSPACE(n), DEXPTIME, NEXPTIME, EXPSPACE etc. These results can be used to prove in a unified way the hardness of a number of combinatorial problems when instances are specified succinctly using various succient specifications considered in the literature. As one corollary, we show that a number of basic NP-hard problems because EXPSPACE-hard when inputs are represented using 1-dimensional infinite periodic wide specifications. This answers a long standing open question posed by Orlin. (2) We outline a simple yet a general technique to devise approximation algorithms with provable worst case performance guarantees for a number of combinatorial problems specified periodically. Our efficient approximation algorithms and schemes are based on extensions of the ideas and represent the first non-trivial characterization of a class of problems having an {epsilon}-approximation (or PTAS) for periodically specified NEXPTIME-hard problems. Two of properties of our results are: (i) For the first time, efficient approximation algorithms and schemes have been developed for natural NEXPTIME-complete problems. (ii) Our results are the first polynomial time approximation algorithms with good performance guarantees for hard problems specified using various kinds of periodic specifications considered in this paper.

Marathe, M.V. [Los Alamos National Lab., NM (United States); Hunt, H.B. III; Stearns, R.E.; Rosenkrantz, D.J. [Univ. at Albany - SUNY, NY (United States). Dept. of Computer Science

1997-12-05

464

Anharmonic Oscillator and Double-Well Potential: Approximating Eigenfunctions  

Microsoft Academic Search

A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical\\u000a anharmonic oscillator and the double-well potential given by V=m\\u000a 2\\u000a x\\u000a 2+g\\u000a x\\u000a 4 at arbitrary g ? 0 for m\\u000a 2>0 and m\\u000a 2<0, respectively, is presented. It is shown that if this approximation is taken as unperturbed problem it leads to

Alexander Turbiner

2005-01-01

465

Approximation of a general singular vertex coupling in quantum graphs  

SciTech Connect

The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a {delta} potential and a vector potential coupled to the 'loose' edges by a {delta} coupling. It is shown that if the lengths of the connecting edges shrink to zero and the potentials are properly scaled, the limit can yield any prescribed singular vertex coupling, and moreover, that such an approximation converges in the norm-resolvent sense.

Cheon, Taksu [Laboratory of Physics, Kochi University of Technology, Tosa Yamada, Kochi 782-8502 (Japan)], E-mail: taksu.cheon@kochi-tech.ac.jp; Exner, Pavel [Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Brehova 7, 11519 Prague (Czech Republic); Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Rez near Prague (Czech Republic)], E-mail: exner@ujf.cas.cz; Turek, Ondrej [Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Brehova 7, 11519 Prague (Czech Republic); Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Trojanova 13, 12000 Prague (Czech Republic)], E-mail: turekond@fjfi.cvut.cz

2010-03-15

466

The strong potential approximation with non-orthogonality terms  

SciTech Connect

Non-orthogonality contributions are included in the Strong Potential Approximation (SPA) for electron capture. These non-orthoganality contributions occur because the off-energy-shell Coulomb wave functions, representing the intermediate states of the collision, are not orthogonal to the intial bound state wave functions. As a result of this non-orthogonality an extra term arises in the matrix element between initial and intermediate states. This term may be written as an addition to the interaction potential which is treated in first order perturbation theory in the SPA method. It is shown here that this nonorthogonality contribution is zero in the SPA when peaking approximations are applied.

McGuire, J.H.

1983-04-01

467

Pade? approximants and their application to scattering from fluid media.  

PubMed

In this work, a numerical method for modeling the scattered acoustic pressure from fluid occlusions is described. The method is based on the asymptotic series expansion of the pressure expressed in terms of sound speed contrast between the host medium and entrained fluid occlusions. Pade? approximants are used to extend the applicability of the result for larger values of sound speed contrast. For scattering from a circular cylinder, an improvement in convergence between the exact and numerical solutions is demonstrated. In the case of scattering from an inhomogeneous medium, a numerical solution with reduced order of Pade? approximants is presented. PMID:21110538

Denis, Max; Tsui, Jing; Thompson, Charles; Chandra, Kavitha

2010-11-01

468

Strong-field approximation for harmonic generation in diatomic molecules  

SciTech Connect

The generation of high-order harmonics in diatomic molecules is investigated within the framework of the strong-field approximation. We show that the conventional saddle-point approximation is not suitable for large internuclear distances. An adapted saddle-point method that takes into account the molecular structure is presented. We analyze the predictions for the harmonic-generation spectra in both the velocity and length gauges. At large internuclear separations, we compare the resulting cutoffs with the predictions of the three-step semiclassical mechanism. Good agreement is obtained only by using the adapted saddle-point method combined with the velocity gauge.0.

Chirila, C. C.; Lein, M. [Max-Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117 Heidelberg (Germany)

2006-02-15

469

Lateral Casimir Force beyond the Proximity-Force Approximation  

SciTech Connect

We argue that the appropriate variable to study a nontrivial geometry dependence of the Casimir force is the lateral component of the Casimir force, which we evaluate between two corrugated metallic plates outside the validity of the proximity-force approximation. The metallic plates are described by the plasma model, with arbitrary values for the plasma wavelength, the plate separation, and the corrugation period, the corrugation amplitude remaining the smallest length scale. Our analysis shows that in realistic experimental situations the proximity-force approximation overestimates the force by up to 30%.

Rodrigues, Robson B.; Neto, Paulo A. Maia [Instituto de Fisica, UFRJ, CP 68528, Rio de Janeiro, RJ, 21941-972 (Brazil); Lambrecht, Astrid; Reynaud, Serge [Laboratoire Kastler Brossel, CNRS, ENS, Universite Pierre et Marie Curie case 74, Campus Jussieu, F-75252 Paris Cedex 05 (France)

2006-03-17

470

Choice of Summary Statistic Weights in Approximate Bayesian Computation  

PubMed Central

In this paper, we develop a Genetic Algorithm that can address the fundamental problem of how one should weight the summary statistics included in an approximate Bayesian computation analysis built around an accept/reject algorithm, and how one might choose the tolerance for that analysis. We then demonstrate that using weighted statistics, and a well-chosen tolerance, in such an approximate Bayesian computation approach can result in improved performance, when compared to unweighted analyses, using one example drawn purely from statistics and two drawn from the estimation of population genetics parameters.

Jung, Hsuan; Marjoram, Paul

2011-01-01

471

Approximating planetary magnetic fields by simplified models using linear regression  

NASA Astrophysics Data System (ADS)

In this paper we attempt to approach the problem of building a non-calculation-intensive model of a planetary magnetic field by fitting the IGRF results with custom parameter values of a simplified multi-variable model, as opposed to the traditional method of solving this problem analytically. We discuss this approach and the results that it produces on the example of approximating the Earth's magnetic field with a shifted dipole's magnetic field. We also discuss the possibilities of using our software to brute-force through an automatically generated set of candidate models in order to find an approximation that satisfies a precondition on either performance or accuracy.

Parunakian, David; Alexeev, Igor

2013-04-01

472

A resistive sheet approximation for mesh reflector antennas  

NASA Astrophysics Data System (ADS)

A simplified method of estimating the equivalent surface resistance of a reflecting mesh is presented. The equivalent resistance is obtained from the approximate mesh reflection coefficients, which are based on averaged boundary conditions. This resistance approximation allows an integral equation solution for the mesh reflector that is a simple extension of that for the perfectly conducting reflector. Paraboloid radiation patterns using physical optics in conjunction with the reflection coefficients are compared to an E-field integral equation solution for a resistive surface. The agreement is excellent for low to moderate resistance values, even in the sidelobe regions.

Jenn, David C.; Prata, A., Jr.; Rusch, Willard V. T.; Barclay, M. R.

1989-11-01

473

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.

Løvsletten, O.; Rypdal, M.

2012-04-01

474

On the Purcell effect beyond the dipole approximation  

NASA Astrophysics Data System (ADS)

We investigate spontaneous emission from excitons in quantum dots beyond the dipole approximation and show how the symmetry of the exciton wavefunction plays a crucial role. We show explicitly that for spherically symmetric excitons, the Purcell effect is independent of the exciton size and is governed by the local density of optical states at the center of the exciton only, which is identical to the result derived with the dipole approximation. This surprising result is a spontaneous emission counterpart to the shell theorem of classical mechanics and electrostatics and provides new insights to the physics of mesoscopic emitters as well as great simplifications in practical calculations.

Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter; Stobbe, Søren

2012-09-01

475

High accuracy Hermite approximation for space curves in Rd  

NASA Astrophysics Data System (ADS)

In this article, it is shown that a space curve in can be approximated by a piecewise polynomial curve of degree m with order (m+1)+[left floor](m+1)/(2d-1)[right floor] rather than m+1. Moreover, we show that the optimal order (m+1)+[left floor](m-1)/(d-1)[right floor] is possible for a particular set of curves of nonzero measure. Analogous results were shown to be true for Taylor polynomial interpolation in [A. Rababah, High order approximation method for curves, Comput. Aided Geom. Design 12 (1995) 89-102].

Rababah, Abedallah

2007-01-01

476

Lagrangians for plasmas in the drift-fluid approximation  

NASA Astrophysics Data System (ADS)

For drift waves and related instabilities, conservation laws can play a crucial role. In an ideal theory these conservation laws are guaranteed when a Lagrangian can be found from which the equations for the various quantities result by Hamilton's principle. Such a Lagrangian for plasmas in the drift-fluid approximation was obtained by a heuristic method in a recent paper by Pfirsch and Correa-Restrepo. In the present paper the same Lagrangian is derived from the exact multifluid Lagrangian via an iterative approximation procedure which resembles the standard method usually applied to the equations of motion. That method, however, does not guarantee that all the conservation laws hold.

Pfirsch, Dieter; Correa-Restrepo, Darío

1997-04-01

477

Essential rate for approximation by spherical neural networks.  

PubMed

We consider the optimal rate of approximation by single hidden feed-forward neural networks on the unit sphere. It is proved that there exists a neural network with n neurons, and an analytic, strictly increasing, sigmoidal activation function such that the deviation of a Sobolev class W²(2r)(S(d)) from the class of neural networks ?(n)(?), behaves asymptotically as n(-2r/d-1). Namely, we prove that the essential rate of approximation by spherical neural networks is n(-2r/d-1). PMID:21621976

Lin, Shaobo; Cao, Feilong; Xu, Zongben

2011-05-11

478

The line-driven instability in Sobolev approximation  

NASA Astrophysics Data System (ADS)

Line-driven winds, e.g., of OB stars, are subject to a strong hydrodynamic instability. As a corollary to the comprehensive linear stability analysis performed by Owocki & Rybicki (1984), we present here a simplified derivation of the growth rates from applying a second order Sobolev approximation. This is applicable for perturbation wavelengths larger than the Sobolev length, and covers the physically most interesting regime of perturbations which can develop into strong reverse shocks, and heat the gas to X-ray temperatures. Since the usual WKB approximation is not applied, we furthermore find the existence of a limiting wavelength beyond which perturbances do not grow, but instead decay.

Feldmeier, A.

1998-04-01

479

Toward making the mean spherical approximation of primitive model electrolytes analytic: An analytic approximation of the MSA screening parameter  

NASA Astrophysics Data System (ADS)

The mean spherical approximation (MSA) for the primitive model of electrolytes provides reasonable estimates of thermodynamic quantities such as the excess chemical potential and screening length. It is especially widely used because of its explicit formulas so that numerically solving equations is minimized. As originally formulated, the MSA screening parameter ? (akin to the reciprocal of the Debye screening length) does not have an explicit analytic formula; an equation for ? must be solved numerically. Here, an analytic approximation for ? is presented whose relative error is generally <~10-5. If more accuracy is desired, one step of an iterative procedure (which also produces an explicit formula for ?) is shown to give relative errors within machine precision in many cases. Even when ion diameter ratios are ~10 and ion valences are ~10, the relative error for the analytic approximation is still <~10-3 and for the single iterative substitution it is <~10-9.

Gillespie, Dirk

2011-01-01

480

Nonapplicability of the viscous approximation method in homogeneous cosmological models  

NASA Astrophysics Data System (ADS)

By considering two conceptually important instances it is shown that the viscous approximation method (Misner, 1967; de Groot et al., 1980) cannot be used to estimate the effects of nonequilibrium processes in homogeneous cosmological models. Despite the widespread acceptance of this method, it is argued that not even qualitative estimates can be obtained by its use.

Ostrowski, M.

1984-10-01

481

The space complexity of approximating the frequency moments  

Microsoft Academic Search

The frequency moments of a sequence containing mi elements of type i, for 1 i n, are the numbers Fk = Pn i=1m k i . We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the

Noga Alon; Yossi Matias; Mario Szegedy

1996-01-01

482

Energy spectrum of anyons in the Hartree-Fock approximation  

NASA Astrophysics Data System (ADS)

We analyse the Hartree-Fock Hamiltonian of anyons. Following the method shown by Hanna, Laughlin and Fetter we find the value of the energy gap and the ground-state energy for any statistics parameter ?=1-1/n. The result is discussed in comparison with predictions of the mean field approximation.

Sitko, Piotr

1992-05-01

483

Stochastic approximation to optimize the performance of human operators  

Microsoft Academic Search

Motivated by optimizing the performance of human operators of Unmanned Aircraft Systems (UAS), we consider the use of stochastic approximation algorithms in this paper. With the increasing levels of automation available for both military and civilian unmanned vehicle systems, the human operators are expected to contribute as high-level planners and decision makers more than as remote-control pilots. Humans and, to

Chaohui Gong; Anouck Girard; Weilin Wang

2010-01-01

484

BINOMIAL APPROXIMATIONS OF SHORTFALL RISK FOR GAME OPTIONS  

Microsoft Academic Search

We show that the shortfall risk of binomial approximations of game (Israeli) options converges to the shortfall risk in the corre- sponding Black-Scholes market considering Lipschitz continuous path dependent payoffs for both discrete and continuous time cases. This results are new also for usual American style options. The paper con- tinues and extends the study of (6) where estimates for

Yan Dolinsky; Yuri Kifer

2007-01-01

485

Improved Approximation Algorithms for Metric Facility Location Problems  

Microsoft Academic Search

Abstract: In this paper we present a 1:52-approximation algorithm for the uncapacitated metric facilitylocation problem. This algorithm uses the idea of cost scaling, a greedy algorithm of Jain,Mahdian, and Saberi, and a greedy augmentation procedure of Charikar, Guha, and Khuller.

Mohammad Mahdian; Yinyu Ye; Jiawei Zhang

2002-01-01

486

Analysis of the diffusive approximation of the Shallow Water equations  

Microsoft Academic Search

In this paper we study the properties of a doubly nonlinear diffusion equation arising in shallow water flow models. Existence, uniqueness, some regularity results and conditions for positivity of classical solutions are presented for the zero Dirichlet initial\\/boundary value problem. The Faedo Galerkin method is used to approximate the solution and the passing to the limit is done by means

Ricardo J. Alonso; Mauricio Santillana; Clint Dawson

487

Enforcing passivity for admittance matrices approximated by rational functions  

Microsoft Academic Search

A linear power system component can be included in a transient simulation as a terminal equivalent by approximating its admittance matrix Y by rational functions in the frequency domain. Physical behavior of the resulting model entails that it should absorb active power for any set of applied voltages, at any frequency. This requires the real part of Y to be

Bjørn Gustavsen; Adam Semlyen

2001-01-01

488

A general approximation technique for constrained forest problems  

Microsoft Academic Search

We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles or paths satisfying certain requirements. In particular, many basic combinatorial optimization problems fit in this framework, including the shortest path, minimum spanning tree, minimum-weight perfect matching, traveling salesman

Michel X. Goemans; David P. Williamson

1992-01-01

489

Improved Approximations for Multilevel Models with Binary Responses  

Microsoft Academic Search

SUMMARY This paper discusses the use of improved approximations for the estimation of generalized linear multilevel models where the response is a proportion. Simulation studies by Rodriguez and Goldman have shown that in extreme situations large biases can occur, most notably when the response is binary, the number of level 1 units per level 2 unit is small and the

HARVEY GOLDSTEIN; JON RASBASH

1996-01-01

490

An analytical solution for approximating simple structure in factor analysis  

Microsoft Academic Search

It is proposed that a satisfactory criterion for an approximation to simple structure is the minimization of the sums of cross-products (across factors) ofsquares of factor loadings. This criterion is completely analytical and yields a unique solution; it requires no plotting, nor any decisions as to the clustering of variables into subgroups. The equations involved appear to be capable only

John B. Carroll

1953-01-01

491

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

492

An efficient symplectic approximation for fringe-field maps  

Microsoft Academic Search

The fringe fields of particle optical elements have a strong effect on optical properties. In particular higher order aberrations are often dominated by fringe-field effects. So far their transfer maps can only be calculated accurately using numerical integrators, which is rather time consuming. Any alternative or approximate calculation scheme should be symplectic because of the importance of the symplectic symmetry

G. H. Hoffstätter; M. Berz

1993-01-01

493

Sample-Efficient Evolutionary Function Approximation for Reinforcement Learning  

Microsoft Academic Search

Reinforcement learning problems are commonly tackled with temporal difference methods, which attempt to estimate the agent's optimal value function. In most real-world problems, learning this value function requires a function approxima- tor, which maps state-action pairs to values via a concise, parameterized function. In practice, the success of func- tion approximators depends on the ability of the human de- signer

Shimon Whiteson; Peter Stone

2006-01-01

494

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 performed…

Kasper, Hirschel; Golden, John

2008-01-01

495

Matchsimile: A Flexible Approximate Matching Tool for Searching Proper Names.  

ERIC Educational Resources Information Center

|Presents the architecture and algorithms behind Matchsimile, an approximate string matching lookup tool designed for extracting person and company names from large texts. Highlights include name formation rules, defining the search problem, system architecture, recognizing pattern words, recognizing whole patterns, and performance. (Author/MES)|

Navarro, Gonzalo; Baeza-Yates, Ricardo; Arcoverde, Joao Marcelo Azevedo

2003-01-01

496

New approximate optimization method for distribution system planning  

Microsoft Academic Search

An algorithm to obtain an approximate optimal solution to the problem of large-scale radial distribution system planning is proposed. The distribution planning problem is formulated as a MIP (mixed integer programming) problem. The set of constraints is reduced to a set of continuous variable linear equations by using the fact that the basis of the simplex tableau consists of the

K. Aoki; K. Nara; T. Satoh; M. Kitagawa; K. Yamanaka

1990-01-01

497

Prediction: Design of experiments based on approximating covariance kernels  

SciTech Connect

Using Mercer`s expansion to approximate the covariance kernel of an observed random function the authors transform the prediction problem to the regression problem with random parameters. The latter one is considered in the framework of convex design theory. First they formulate results in terms of the regression model with random parameters, then present the same results in terms of the original problem.

Fedorov, V.

1998-11-01

498

Design Optimization of Multibody Systems by Sequential Approximation  

Microsoft Academic Search

Design optimization of multibody systems is usually established by a direct coupling of multibody system analysis and mathematical programming algorithms. However, a direct coupling is hindered by the transient and computationally complex behavior of many multibody systems. In structural optimization often approximation concepts are used instead to interface numerical analysis and optimization. This paper shows that such an approach is

L. F. P. Etman; D. H. van Campen; A. J. G. Schoofs

1998-01-01

499

Design optimization of multibody systems by sequential approximation  

Microsoft Academic Search

Design optimization of multibody systems is usually established by a direct coupling of multibody system analysis and mathematical programming algorithms. However, a direct coupling is hindered by the transient and computationally complex behavior of many multibody systems. In structural optimization often approximation concepts are used instead to interface numerical analy- sis and optimization. This paper shows that such an approach

L. F. P. ETMAN; D. H. VAN CAMPEN; A. J. G. SCHOOFS

1998-01-01

500

A Note on Approximate Minimum Volume Enclosing Ellipsoid of Ellipsoids  

Microsoft Academic Search

We study the problem of computing the minimum volume enclosing ellipsoid (MVEE) containing a given set of ellipsoids S = {E1, E2, hellip, En} sube Ropfd. We show how to efficiently compute a small set X sube S of size at most a = |X| = O(d2\\/epsi ) whose minimum volume ellipsoid is an (1 + epsi)-approximation to the minimum

Sachin Jambawalikar; Piyush Kumar

2008-01-01