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1

Characterisation of Transverse Cracking in a Quasi-Isotropic GFRP Laminate under Flexural Loading  

Microsoft Academic Search

Transverse cracking behaviour in a quasi-isotropic glass\\/epoxy (GFRP) laminate loaded in flexure is studied experimentally and theoretically. A theory developed for cross-ply laminates is applied to a [0°\\/90°\\/-45°\\/45°]S quasi-isotropic laminate. An equivalent laminate is introduced to derive the Young's modulus of a cracked transverse ply on the basis of a shear lag analysis. The model predicts the flexural stiffness, the

Keiji Ogi; P. A. Smith

2002-01-01

2

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

SciTech Connect

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

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

1996-02-01

3

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

NASA Technical Reports Server (NTRS)

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

Raines, J. K.

1975-01-01

4

Delamination Monitoring of Quasi-Isotropic CFRP Laminate Using Electric Potential Change Method  

Microsoft Academic Search

Real-time detection of delamination in carbon fiber reinforce plastic (CFRP) laminates has been requiring to maintain the structural reliability of aircraft. In this paper, electric potential change method (EPCM) was applied to monitor delaminations in quasi-isotropic CFRP laminate. As the coefficient of thermal expansion and mold shrinkage factor of carbon fiber and epoxy matrix is different, residual stress is developed

Masahito Ueda; Akira Todoroki

2008-01-01

5

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

6

Flexural stiffnesses of and dimensional stability in circular quasi-isotropic laminate mirrors  

NASA Astrophysics Data System (ADS)

Composite fiber reinforced plastics are being given favorable consideration for emerging applications in large aperture telescopes, such as the Hubble telescope or communication dishes. Many lightweight mirror fabrication concepts are currently being pursued. Presently, the technology is limited because it has an incomplete understanding of the mechanics associated with quasi-isotropic laminates for diffraction-limited displacement constraints, and lack of understanding for effects of resin buffer layers on composite mirrors for high surface smoothness. In this dissertation document, radial stiffness associated with stacking sequence effects in quasi-isotropic laminates (pi/n, where n=3, 4, and 6) and dimensional stability in the composite laminates are investigated numerically. The numerical results show that directional dependency of flexural stiffness in the laminates, which is strongly associated with stacking sequences, is a significant factor causing unfavorable sinusoidal surface waviness. The maximum radial flexural stiffness variation is found as +/-12.85% in pi/3 laminate while a minimum of +/-5.63% is found in pi/4 laminate. Mechanics of maximum asymmetry by +/-2º misorientation based on ideal pi/n laminate lay-ups are evaluated and the results are compared with ideal lay-up sequence cases. The calculated extensional and flexural stiffness values from the maximum asymmetric cases are within less than 0.05%. As such, the radial flexural stiffness variations in quasi-isotropic laminates are shown to be more problematic than asymmetry caused by common manufacturing variance. The types of surface deformations in quasi-isotropic laminates associated with directional dependency of flexural stiffness are evaluated using finite element analyses. Also, fiber print-through in replicated composite mirrors and the effects of the resin buffer layer present in the mirrors for mitigation of the fiber print-through are investigated and discussed. Numerical results reveal that there will be an unfavorable sinusoidal surface deformation in each ideal p/n laminate and the shapes are strongly associated with principal fiber directions due to stacking sequence effects. The surface deformations in quasi-isotropic laminates are shown to be typical and such surface deformations are inevitable when composite mirrors are fabricated from discrete layers of anisotropic carbon fiber reinforced plastics. Moreover, the use of additional resin layers appears to more adversely influence the composite mirror substrates. The validation of predicted surface deformations and dimensional distortions are achieved by comparing experimental results on a 8-inch-diameter composite mirror sample fabricated at the University of Kansas Dept. of Aerospace Engineering (KUAE) and Bennett Optical Research (BOR). A study of quasi-homogeneous materials such as short fiber products as alternative composite materials is investigated. Furthermore, the relation between resin property effects and corresponding resin thickness effects is evaluated and discussed. The analyses provide information on alternative types of materials that primarily affect optical performance and thus are most important for precision optics. Based on the results, locally varying radial surface deformations in quasi-isotropic laminates fabricated from continuous fiber reinforced plastics distort optical performance. These surface deformations might be eliminated by utilizing short fiber materials and a soft resin system with a very low coefficient of thermal expansion compared to conventional resins.

Kim, Kyung-Pyo

7

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

NASA Technical Reports Server (NTRS)

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

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

1992-01-01

8

Delamination Monitoring of Quasi-Isotropic CFRP Laminate Using Electric Potential Change Method  

NASA Astrophysics Data System (ADS)

Real-time detection of delamination in carbon fiber reinforce plastic (CFRP) laminates has been requiring to maintain the structural reliability of aircraft. In this paper, electric potential change method (EPCM) was applied to monitor delaminations in quasi-isotropic CFRP laminate. As the coefficient of thermal expansion and mold shrinkage factor of carbon fiber and epoxy matrix is different, residual stress is developed in the laminate during the fabrication process of curing. The local strain variation due to delaminations was measured by EPCM utilizing the piezoresistivity of the laminate itself. Finite element simulation was performed to investigate the applicability of the method.

Ueda, Masahito; Todoroki, Akira

9

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

NASA Technical Reports Server (NTRS)

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

Sullivan, T. L.

1977-01-01

10

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

NASA Technical Reports Server (NTRS)

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

Wichorek, G. R.

1982-01-01

11

Analyses of quasi-isotropic composite plates under quasi-static point loads simulating low-velocity impact phenomena  

NASA Technical Reports Server (NTRS)

In thin composite laminates, the first level of visible damage occurs in the back face and is called back face spalling. A plate-membrane coupling model, and a finite element model to analyze the large deformation behavior of eight-ply quasi-isotropic circular composite plates under impact type point loads are developed. The back face spalling phenomenon in thin composite plates is explained by using the plate-membrane coupling model and the finite element model in conjunction with the fracture mechanics principles. The experimental results verifying these models are presented. Several conclusions concerning the deformation behavior are reached and discussed in detail.

Kelkar, A. D.

1984-01-01

12

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

NASA Technical Reports Server (NTRS)

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

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

1979-01-01

13

Quantitative evaluation of transverse cracks in carbon fiber reinforced plastic quasi-isotropic laminates with embedded small-diameter fiber Bragg grating sensors  

NASA Astrophysics Data System (ADS)

The authors have applied newly developed small-diameter fiber Bragg grating (FBG) sensors, whose cladding is 40 µm in diameter, for the detection of transverse cracks in carbon fiber reinforced plastic (CFRP) laminates. In previous research, the small-diameter FBG sensors were embedded in CFRP cross-ply laminates. When transverse cracks occurred, reflection spectra from the FBG sensors broadened with an increase in the crack density. Thus, the authors showed that small-diameter FBG sensors had the potential to detect the occurrence of cracks. In the present research, this technique is applied to the detection of the transverse crack evolution in CFRP quasi-isotropic laminates, whose laminate configuration is more suitable for practical use. Through the experiment and the theoretical calculation, it was found that the small-diameter FBG sensor could also detect transverse cracks in quasi-isotropic laminates quantitatively.

Mizutani, Tadahito; Okabe, Yoji; Takeda, Nobuo

2003-12-01

14

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

NASA Technical Reports Server (NTRS)

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

Illg, W.

1986-01-01

15

Effects of moisture, residual thermal curing stresses, and mechanical load on the damage development in quasi-isotropic laminates  

NASA Technical Reports Server (NTRS)

This investigation demonstrates how moisture absorbed in (0/+ or - 45/90)s and (0/90/+ or - 45)s graphite epoxy laminates significantly alters the stress state and chronology of damage development along the laminate edge during static tension and tension-tension cyclic loading. Emphasis is placed on using reasonable approximations for wet and dry elastic properties, including out-of-plane properties (nu sub 23 and G sub 23), since these properties are required by finite element and shear lag models to predict the stress state at the laminate edge. Moisture was observed to alter the dry edge stress state in the 90-deg plies of the (0/+ or - 45/90)s laminate such that delaminations occurred at a lower load and transverse cracks occurred at a higher load. A model was developed which predicted the differences in loads required to initiate damage in the 90-deg plies of the two laminates in the wet and dry conditions. Although moisture can alter the chronology of damage development, the damage state in each laminate observed prior to fracture appeared to be independent of moisture content.

Kriz, R. D.; Stinchcomb, W. W.

1982-01-01

16

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

NASA Technical Reports Server (NTRS)

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

Rose, Cheryl A.; Herakovich, Carl T.

1992-01-01

17

WKBJ Approximation.  

National Technical Information Service (NTIS)

A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution t...

M. El Sawi

1983-01-01

18

Multivariate Approximation.  

National Technical Information Service (NTIS)

Methods for representing multi-dimensional objects, such as functions of several variables and, more generally, (hyper-)surfaces is the main objective. One goal of such representation, whether approximate or exact, is the efficient evaluation of the objec...

C. DE Boor A. Ron

1998-01-01

19

Approximating pi  

NSDL National Science Digital Library

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

British Broadcasting Corporation (BBC)

2003-01-01

20

Prediction of long-term fatigue life of quasi-isotropic CFRP laminates for aircraft use  

Microsoft Academic Search

We have proposed the accelerated testing method to predict the fatigue life of FRP under an arbitrary combination of frequency, temperature, and stress ratio based on the time–temperature superposition principle and discussed experimentally about the validity and applicability of our proposed method. It has been clarified from these studies that our proposed method is applicable to predict the tensile and

Yasushi Miyano; Masayuki Nakada; Kazuyoshi Nishigaki

2006-01-01

21

Stresses in a quasi-isotropic pin loaded connector using photoelasticity  

NASA Technical Reports Server (NTRS)

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

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

1983-01-01

22

Interpolation and Approximation Theory.  

ERIC Educational Resources Information Center

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

Kaijser, Sten

1991-01-01

23

Polynomial Approximation: The Weierstrass Approximation Theorem.  

National Technical Information Service (NTIS)

In this paper we will look at three proofs of the Weierstrass Approximation Theorem. The first proof is in much the same form in which Weierstrass originally proved his theorem. The next is due to Lebesgue. It is by far the easiest proof to follow, with o...

S. J. Nichols

1982-01-01

24

Multivariate Padé approximants revisited  

Microsoft Academic Search

Several definitions of multivariate Padé approximants have been introduced during the last decade. We will here consider all types of definitions based on the choice that the coefficients in numerator and denominator of the multivariate Padé approximant are defined by means of a linear system of equations. In this case a determinant representation for the multivariate Padé approximant exists. We

Annie Cuyt

1986-01-01

25

Quasicrystals and crystalline approximants  

Microsoft Academic Search

Over the past seven years, many examples of periodic crystals closely related to quasicrystalline alloys have been discovered. These crystals have been termed approximants, since the arrangements of atoms within their unit cells closely approximate the local atomic structures in quasicrystals. This colloquium focuses on these approximant structures, their description, and their relationship to quasicrystals.

A. I. Goldman; R. F. Kelton

1993-01-01

26

Approximate Posterior Distributions  

Microsoft Academic Search

This paper proposes the use of approximate posterior distributions resulting from operational prior distributions chosen with regard to the realized likelihood function. L.J. Savage's “precise measurement” is generalized for approximation in terms of an arbitrary operational prior density, including mixed-type prior distributions with positive probabilities on singular subsets. A new approximation is also given relating such distributions to absolutely continuous

James M. Dickey

1976-01-01

27

Approximation of Laws  

NASA Astrophysics Data System (ADS)

Approximation of laws is an important theme in the philosophy of science. If we can make sense of the idea that two scientific laws are "close" to each other, then we can also analyze such methodological notions as approximate explanation of laws, approximate reduction of theories, approximate empirical success of theories, and approximate truth of laws. Proposals for measuring the distance between quantitative scientific laws were given in Niiniluoto (1982, 1987). In this paper, these definitions are reconsidered as a response to the interesting critical remarks by Liu (1999).

Niiniluoto, Ilkka

2014-03-01

28

Approximations of satellite stability  

NASA Technical Reports Server (NTRS)

Modifications and corrections are presented to relations obtained in an investigation conducted by Szebehely (1978), who has discussed the problem of Hill's (1878) stability of satellites in the restricted problem of three bodies. Attention is given to an approximation of the Jacobian constant for the satellite, the critical value of the Jacobian constant, and approximate solutions.

Markellos, V. V.; Szebehely, V.

1981-01-01

29

Approximation Error Maps.  

National Technical Information Service (NTIS)

In order to analyze the accuracy of a fixed, finite-dimensional approximation space which is not uniform over its domain Omega, we define approximation error map, a description of how the error is distributed over Omega-not for a single test function but ...

A. Gomide J. Stolfi

2001-01-01

30

Approximate spatial reasoning  

NASA Technical Reports Server (NTRS)

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

Dutta, Soumitra

1988-01-01

31

Approximation of Hopf bifurcation  

Microsoft Academic Search

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

C. Bernardi; M. Curie

1982-01-01

32

Geometric Approximation via Coresets  

Microsoft Academic Search

The paradigm of coresets has recently emerged as a powerful tool for eciently approximating various extent measures of a point set P. Using this paradigm, one quickly computes a small subset Q of P, called a coreset, that approximates the original set P and and then solves the problem on Q using a relatively inecient algorithm. The solution for Q

PANKAJ K. AGARWAL; SARIEL HAR-PELED; KASTURI R. VARADARAJAN

33

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

34

Fourier Series Approximation  

NSDL National Science Digital Library

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

2012-08-14

35

Selection Sample Size Approximations.  

National Technical Information Service (NTIS)

Two conservative sample size approximations are given for the Bechhofer formulation of the problem of selecting the population with the largest mean, when the populations have a common known variance. A table of numerical comparisons of these approximatio...

J. S. Ramberg

1972-01-01

36

Approximate spatial reasoning  

NASA Technical Reports Server (NTRS)

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 alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.

Dutta, Soumitra

1988-01-01

37

Dynamical Cluster Approximation  

NASA Astrophysics Data System (ADS)

The dynamical cluster approximation (DCA) is a method which systematically incorporates nonlocal corrections to the dynamical mean-field approximation. Here we present a pedagogical discussion of the DCA by describing it as a ?-derivable coarse-graining approximation in k-space, which maps an infinite lattice problem onto a periodic finite-sized cluster embedded in a self-consistently determined effective medium. We demonstrate the method by applying it to the two-dimensional Hubbard model. From this application, we show evidences of the presence of a quantum critical point (QCP) at a finite doping underneath the superconducting dome. The QCP is associated with the second-order terminus of a line of first order phase separation transitions. This critical point is driven to zero temperature by varying the band parameters, generating the QCP. The effect of the proximity of the QCP to the superconducting dome is also discussed.

Fotso, H.; Yang, S.; Chen, K.; Pathak, S.; Moreno, J.; Jarrell, M.; Mikelsons, K.; Khatami, E.; Galanakis, D.

38

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

39

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

40

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

41

Interpolation by Pade Approximants.  

National Technical Information Service (NTIS)

The interpolation problem for error affected complex functions in order to best extrapolate them in the cutcomplex plane is studied. The methods used for interpolation are the diagonal and near-diagonal Pade approximants (PA) of the second type (PA2) and ...

N. Bogdanova F. Nichitiu

1983-01-01

42

About Accuracy and Approximation  

NSDL National Science Digital Library

Students learn about the concepts of accuracy and approximation as they pertain to robotics, gain insight into experimental accuracy, and learn how and when to estimate values that they measure. Students also explore sources of error stemming from the robot setup and rounding numbers.

Applying Mechatronics to Promote Science (AMPS) GK-12 Program,

43

Approximating the Selection Process.  

National Technical Information Service (NTIS)

The article describes research performed by the author on his own time in response to a problem posed by animal geneticists. The problem is that of approximating the consequences of the types of artificial selection to which domestic animals are subjected...

D. A. Harville

1969-01-01

44

Optimizing the Zeldovich approximation  

NASA Technical Reports Server (NTRS)

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

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

1994-01-01

45

Variational truncated Wigner approximation  

NASA Astrophysics Data System (ADS)

In this paper we reconsider the notion of an optimal effective Hamiltonian for the semiclassical propagation of the Wigner distribution in phase space. An explicit expression for the optimal effective Hamiltonian is obtained in the short-time limit by minimizing the Hilbert-Schmidt distance between the semiclassical approximation and the real state of the system. The method is illustrated for the quartic oscillator.

Sels, Dries; Brosens, Fons

2014-04-01

46

Variational truncated Wigner approximation.  

PubMed

In this paper we reconsider the notion of an optimal effective Hamiltonian for the semiclassical propagation of the Wigner distribution in phase space. An explicit expression for the optimal effective Hamiltonian is obtained in the short-time limit by minimizing the Hilbert-Schmidt distance between the semiclassical approximation and the real state of the system. The method is illustrated for the quartic oscillator. PMID:24827193

Sels, Dries; Brosens, Fons

2014-04-01

47

Fuzzy approximately cubic mappings  

Microsoft Academic Search

We establish some stability results concerning the cubic functional equationf(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)in fuzzy normed spaces. We discuss the fuzzy continuity of the cubic mappings and show that the existence of a solution for any approximately cubic mapping guarantees the completeness of the fuzzy normed space.

Alireza Kamel Mirmostafaee; Mohammad Sal Moslehian

2008-01-01

48

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

49

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

50

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

51

Self-similar factor approximants.  

PubMed

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Padé approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Padé approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties. PMID:12636750

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

2003-02-01

52

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

53

Multifocus lemniscates: Approximation of curves  

NASA Astrophysics Data System (ADS)

A focal method for the continuous approximation of smooth closed plane curves is proposed. Multifocus lemniscates are used as the approximating functions. The curve to be approximated is represented by a finite set of foci inside the curve; the number and the location of the foci provide the degrees of freedom for the focal approximation. An algorithmic solution of this problem in various modifications is constructed. Proximity criteria for curves are proposed. A comparative analysis of the approximative capabilities of the focal method with the capabilities of the classical harmonic approximation method is performed.

Rakcheeva, T. A.

2010-11-01

54

On uniform approximation of elliptic functions by Pade approximants  

SciTech Connect

Diagonal Pade approximants of elliptic functions are studied. It is known that the absence of uniform convergence of such approximants is related to them having spurious poles that do not correspond to any singularities of the function being approximated. A sequence of piecewise rational functions is proposed, which is constructed from two neighbouring Pade approximants and approximates an elliptic function locally uniformly in the Stahl domain. The proof of the convergence of this sequence is based on deriving strong asymptotic formulae for the remainder function and Pade polynomials and on the analysis of the behaviour of a spurious pole. Bibliography: 23 titles.

Khristoforov, Denis V [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2009-06-30

55

On uniform approximation of elliptic functions by Padé approximants  

NASA Astrophysics Data System (ADS)

Diagonal Padé approximants of elliptic functions are studied. It is known that the absence of uniform convergence of such approximants is related to them having spurious poles that do not correspond to any singularities of the function being approximated. A sequence of piecewise rational functions is proposed, which is constructed from two neighbouring Padé approximants and approximates an elliptic function locally uniformly in the Stahl domain. The proof of the convergence of this sequence is based on deriving strong asymptotic formulae for the remainder function and Padé polynomials and on the analysis of the behaviour of a spurious pole. Bibliography: 23 titles.

Khristoforov, Denis V.

2009-06-01

56

Approximation for Bayesian Ability Estimation.  

National Technical Information Service (NTIS)

An approximation is proposed for the posterior mean and standard deviation of the ability parameter in an item response model. The procedure assumes that approximations to the posterior mean and covariance matrix of item parameters are available. It is ba...

R. K. Tsutakawa M. J. Soltys

1987-01-01

57

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

58

Combining global and local approximations  

Microsoft Academic Search

A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method

Raphael T. Haftka

1991-01-01

59

Taylor Approximations and Definite Integrals  

ERIC Educational Resources Information Center

We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)

Gordon, Sheldon P.

2007-01-01

60

Fuzzy systems are universal approximators  

Microsoft Academic Search

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

Li-Xin Wang

1992-01-01

61

Beta approximations for bridge sampling  

Microsoft Academic Search

We consider the problem of simulating X conditional on the value of X +Y , when X and Y are independent positive random variables. We propose approximate methods for sampling (X|X+Y) by approximating the fraction (X\\/z|X+ Y = z) with a beta random variable. We discuss applications to Levy processes and infinitely divisible distributions, and we report numerical tests for

Paul Glasserman; Kyoung-kuk Kim

2008-01-01

62

Parameterized Complexity and Approximation Algorithms  

Microsoft Academic Search

Approximation algorithms and parameterized complexity are usually considered to be two separate ways of dealing with hard algorithmic problems. In this paper, our aim is to investigate how these two fields can be combined to achieve better algorithms than what any of the two theories could offer. We discuss the different ways parameterized complexity can be extended to approximation algorithms,

Dániel Marx

2008-01-01

63

Secure Multiparty Computation of Approximations  

Microsoft Academic Search

Approximation algorithms can sometimes provide efficient solutions when no efficient exact computation is known. In particular, approximations are often useful in a distributed setting where the inputs are held by different parties and are extremely large. Furthermore, for some applications, the parties want to cooperate to compute a function of their inputs without revealing more information than necessary. If ˆ

Joan Feigenbaum; Yuval Ishai; Tal Malkin; Kobbi Nissim; Martin J. Strauss; Rebecca N. Wright

2001-01-01

64

Multivariate Frobenius-Pade approximants  

NASA Astrophysics Data System (ADS)

The aim of this paper is to construct rational approximants for multivariate functions given by their expansion in an orthogonal polynomial system. This will be done by generalizing the concept of multivariate Pade approximation. After defining the multivariate Frobenius-Pade approximants, we will be interested in the two following problems: the first one is to develop recursive algorithms for the computation of the value of a sequence of approximants at a given point. The second one is to compute the coefficients of the numerator and denominator of the approximants by solving a linear system. For some particular cases we will obtain a displacement rank structure for the matrix of the system we have to solve. The case of a Tchebyshev expansion is considered in more detail.

Matos, Ana C.

2007-05-01

65

Multivariate sigmoidal neural network approximation.  

PubMed

Here we study the multivariate quantitative constructive approximation of real and complex valued continuous multivariate functions on a box or RN, N?N, by the multivariate quasi-interpolation sigmoidal neural network operators. The "right" operators for our goal are fully and precisely described. This approximation is derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order partial derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the logarithmic sigmoidal function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer. PMID:21310590

Anastassiou, George A

2011-05-01

66

Constructive Approximations of Markov Operators  

Microsoft Academic Search

We construct piecewise linear Markov finite approximations of Markov operators defined on L1([0, 1]N) and we study various properties, such as consistency, stability, and convergence, for the purpose of numerical analysis of Markov operators.

Jiu Ding; Aihui Zhou

2001-01-01

67

Approximate Inference and Scientific Method.  

National Technical Information Service (NTIS)

A new identification criterion, motivated by notions of successively improving approximations in the philosophy of science, is defined. It is shown that the class of recursive functions is identifiable under this criterion. This result is extended to perm...

M. Fulk S. Jain

1989-01-01

68

Approximate Complexity and Functional Representation.  

National Technical Information Service (NTIS)

Results are obtained dealing with the exact and the approximate representation of a function F as a superposition, in designated formats, of functions of fewer variables. Two main cases are considered. In the classical nomographic case one seeks criteria ...

R. C. Buck

1976-01-01

69

Mathematical algorithms for approximate reasoning  

NASA Technical Reports Server (NTRS)

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

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

1988-01-01

70

Towards Approximate SQL - Infobright's Approach  

Microsoft Academic Search

\\u000a We discuss various ideas how to implement execution of approximate SQL statements within Infobright database engine. We first\\u000a outline the engine’s architecture, which is designed entirely to work with standard SQL. We then discuss several possible\\u000a extensions towards approximate querying and point out at some analogies with the principles of the theory of rough sets. Finally,\\u000a we present the results

Dominik Slezak; Marcin Kowalski

2010-01-01

71

Exponential approximations in optimal design  

NASA Technical Reports Server (NTRS)

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

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

1990-01-01

72

Wavelet Sparse Approximate Inverse Preconditioners  

NASA Technical Reports Server (NTRS)

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

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

1996-01-01

73

Approximate entropy of network parameters  

NASA Astrophysics Data System (ADS)

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.

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

2012-04-01

74

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

2012-04-01

75

Sequential approximate optimization using variable fidelity response surface approximations  

Microsoft Academic Search

The dimensionality and complexity of typi- cal multidisciplinary systems hinders the use of formal optimization techniques in application to this class of problems. The use of approximations to represent the system design metrics and constraints has become vi- tal for achieving good performance in many multidis- ciplinary design optimization (MDO) algorithms. This paper reports recent research efforts on the use

J. F. Rodr ´ iguez; V. M. Perez; D. Padmanabhan; J. E. Renaud

2000-01-01

76

Analytical approximations and Padé approximants for Volterra's population model  

Microsoft Academic Search

In this paper, an analytic approximation for Volterra's model for population growth of a species in a closed system is presented. The nonlinear integro-differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation. The series solution method and the decomposition method are implemented independently to the model and

Abdul-majid Wazwaz

1999-01-01

77

Approximating spatially exclusive invasion processes  

NASA Astrophysics Data System (ADS)

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

Ross, Joshua V.; Binder, Benjamin J.

2014-05-01

78

Approximation of the geoid height  

NASA Astrophysics Data System (ADS)

A modification of Molodensky's method for mean square geoid height approximation is derived on the basis of the simple layer potential instead of Stokes' formula. The compactness of the formulas derived makes it possible to readily take into account harmonics of any degree in the far-zone component expansion, as well as to conduct a qualitative analysis of the dependence of harmonic coefficient behavior on the harmonic degree and the near zone radius. Numerical experiments show that the method developed is the most effective for approximating the far-zone influence beyond a spherical cap with a radius of 5 deg.

Pishchukhina, K. V.

1991-06-01

79

Alternative implementation of Pade approximants  

SciTech Connect

In this paper we devise an alternative approach to the use of Pade approximants in the resummation of the perturbative (either divergent or convergent) series. Our procedure relies on the introduction of a nonphysical parameter and on the constraint that the physical observable be linear in this parameter. The relation between the unphysical parameter and the physical perturbative parameter is expressed in terms of a Pade approximant, whose form can be fully determined. We have applied this strategy to a number of examples and we have compared the results to those obtained following the standard Pade approach, observing that in many cases our approach is superior.

Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico)

2007-10-01

80

The Zel'dovich approximation  

NASA Astrophysics Data System (ADS)

This year marks the 100th anniversary of the birth of Yakov Zel'dovich. Amongst his many legacies is the Zel'dovich approximation for the growth of large-scale structure, which remains one of the most successful and insightful analytic models of structure formation. We use the Zel'dovich approximation to compute the two-point function of the matter and biased tracers, and compare to the results of N-body simulations and other Lagrangian perturbation theories. We show that Lagrangian perturbation theories converge well and that the Zel'dovich approximation provides a good fit to the N-body results except for the quadrupole moment of the halo correlation function. We extend the calculation of halo bias to third order and also consider non-local biasing schemes, none of which remove the discrepancy. We argue that a part of the discrepancy owes to an incorrect prediction of inter-halo velocity correlations. We use the Zel'dovich approximation to compute the ingredients of the Gaussian streaming model and show that this hybrid method provides a good fit to clustering of haloes in redshift space down to scales of tens of Mpc.

White, Martin

2014-04-01

81

Approximate quantum and acoustic cloaking  

Microsoft Academic Search

At any energy E > 0, we construct a sequence of bounded potentials $V^E_{n}, n\\\\in\\\\N$, supported in an annular region $B_{out}\\\\setminus B_{inn}$ in three-space, which act as approximate cloaks for solutions of Schr\\\\\\

Allan Greenleaf; Yaroslav Kurylev; Matti Lassas; Gunther Uhlmann

2008-01-01

82

Optimization, Approximation, and Complexity Classes  

Microsoft Academic Search

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

Christos H. Papadimitriou; Mihalis Yannakakis

1991-01-01

83

Bandelet Image Approximation and Compression  

Microsoft Academic Search

Finding ecien t geometric representations of images is a central issue to improve image compression and noise removal algorithms. We introduce bandelet orthogonal bases and frames that are adapted to the geometric regularity of an image. Images are approximated by nding a best bandelet basis or frame that produces a sparse representation. For functions that are uniformly regular outside a

E. Le Pennec; S. Mallat

2005-01-01

84

Measuring the approximate number system  

Microsoft Academic Search

Recent theories in numerical cognition propose the existence of an approximate number system (ANS) that supports the representation and processing of quantity information without symbols. It has been claimed that this system is present in infants, children, and adults, that it supports learning of symbolic mathematics, and that correctly harnessing the system during tuition will lead to educational benefits. Various

Camilla Gilmore; Nina Attridge; Matthew Inglis

2011-01-01

85

Diffeomorphic Approximation of Sobolev Homeomorphisms  

NASA Astrophysics Data System (ADS)

Every homeomorphism {h : mathbb X to mathbb Y} between planar open sets that belongs to the Sobolev class {fancyscript{W}^{1,p} (mathbb X, mathbb Y), 1 < p < infty}, can be approximated in the Sobolev norm by {fancyscript{C}^infty}-smooth diffeomorphisms.

Iwaniec, Tadeusz; Kovalev, Leonid V.; Onninen, Jani

2011-09-01

86

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

87

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

88

Pad? approximations and diophantine geometry  

PubMed Central

Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves.

Chudnovsky, D. V.; Chudnovsky, G. V.

1985-01-01

89

Error Bounds for Interpolative Approximations.  

ERIC Educational Resources Information Center

Elementary error estimation in the approximation of functions by polynomials as a computational assignment, error-bounding functions and error bounds, and the choice of interpolation points are discussed. Precalculus and computer instruction are used on some of the calculations. (KR)

Gal-Ezer, J.; Zwas, G.

1990-01-01

90

PIECEWISE APPROXIMATION AND NEURAL NETWORKS  

Microsoft Academic Search

The paper deals with the recently proposed autotracking piecewise cubic approxima- tion (APCA) based on the discrete projective transformation, and neural networks (NN). The suggested new approach facilitates the analysis of data with complex dependence and relatively small errors. We introduce a new representation of polynomials that can pro- vide dierent local approximation models. We demonstrate how APCA can be

Martina Revayova; Csaba T

91

Approximations to Certain Feynman Integrals.  

National Technical Information Service (NTIS)

The paper investigates certain approximations to the limiting Feynman integrals of functionals of the form F(x) = Phi(the integral from a to b of theta (t, x(t))dt) sigma (x(b)) which can be given in terms of finite fold integrals, and obtains estimates o...

R. H. Cameron

1966-01-01

92

Quantitative evaluation of transverse cracks in carbon fiber reinforced plastic quasi-isotropic laminates with embedded small-diameter fiber Bragg grating sensors  

Microsoft Academic Search

The authors have applied newly developed small-diameter fiber Bragg grating (FBG) sensors, whose cladding is 40 µm in diameter, for the detection of transverse cracks in carbon fiber reinforced plastic (CFRP) laminates. In previous research, the small-diameter FBG sensors were embedded in CFRP cross-ply laminates. When transverse cracks occurred, reflection spectra from the FBG sensors broadened with an increase in

Tadahito Mizutani; Yoji Okabe; Nobuo Takeda

2003-01-01

93

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

94

Approximating extent measures of points  

Microsoft Academic Search

We present a general technique for approximating various descriptors of the extent of a set P of n points in Rd when the dimension d is an arbitrary fixed constant. For a given extent measure ? and a parameter ϵ > 0, it computes in time O(n + 1\\/ϵO(1)) a subset Q ? P of size 1\\/ϵO(1), with the property

Pankaj K. Agarwal; Sariel Har-Peled; Kasturi R. Varadarajan

2004-01-01

95

Approximate reasoning using terminological models  

NASA Technical Reports Server (NTRS)

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

Yen, John; Vaidya, Nitin

1992-01-01

96

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

97

Generalized Gradient Approximation Made Simple  

SciTech Connect

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

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

1996-10-01

98

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

99

Approximate simulation of quantum channels  

SciTech Connect

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

Beny, Cedric [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrass e 2, 30167 Hannover (Germany); Oreshkov, Ognyan [QuIC, Ecole Polytechnique, CP 165, Universite Libre de Bruxelles, B-1050 Brussels (Belgium)

2011-08-15

100

Wavelet Approximation in Data Assimilation  

NASA Technical Reports Server (NTRS)

Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.

Tangborn, Andrew; Atlas, Robert (Technical Monitor)

2002-01-01

101

Least Squares Approximations to Lognormal Sum Distributions  

Microsoft Academic Search

In this paper, the least squares (LS) approximation approach is applied to solve the approximation problem of a sum of lognormal random variables (RVs). The LS linear approximation is based on the widely accepted assumption that the sum of lognormal RVs can be approximated by a lognormal RV. We further derive the solution for the LS quadratic (LSQ) approximation, and

Lian Zhao; Jiu Ding

2007-01-01

102

Approximately clean quantum probability measures  

NASA Astrophysics Data System (ADS)

A quantum probability measure-or quantum measurement-is said to be clean if it cannot be irreversibly connected to any other quantum probability measure via a quantum channel. The notion of a clean quantum measure was introduced by Buscemi et al. [``Clean positive operator valued measures,'' J. Math. Phys. 46(8), 082109 (2005)] for finite-dimensional Hilbert space, and was studied subsequently by Kahn [``Clean positive operator-valued measures for qubits and similar cases,'' J. Phys. A 40(18), 4817-4832 (2007)] and Pellonpää [``Complete characterization of extreme quantum observables in finite dimensions,'' J. Phys. A 44(8), 085304 (2011)]. The present paper provides new descriptions of clean quantum probability measures in the case of finite-dimensional Hilbert space. For Hilbert spaces of infinite dimension, we introduce the notion of ``approximately clean quantum probability measures'' and characterise this property for measures whose range determines a finite-dimensional operator system.

Farenick, Douglas; Floricel, Remus; Plosker, Sarah

2013-05-01

103

Indexing the approximate number system.  

PubMed

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

Inglis, Matthew; Gilmore, Camilla

2014-01-01

104

Statistics for approximate gene clusters  

PubMed Central

Background Genes occurring co-localized in multiple genomes can be strong indicators for either functional constraints on the genome organization or remnant ancestral gene order. The computational detection of these patterns, which are usually referred to as gene clusters, has become increasingly sensitive over the past decade. The most powerful approaches allow for various types of imperfect cluster conservation: Cluster locations may be internally rearranged. The individual cluster locations may contain only a subset of the cluster genes and may be disrupted by uninvolved genes. Moreover cluster locations may not at all occur in some or even most of the studied genomes. The detection of such low quality clusters increases the risk of mistaking faint patterns that occur merely by chance for genuine findings. Therefore, it is crucial to estimate the significance of computational gene cluster predictions and discriminate between true conservation and coincidental clustering. Results In this paper, we present an efficient and accurate approach to estimate the significance of gene cluster predictions under the approximate common intervals model. Given a single gene cluster prediction, we calculate the probability to observe it with the same or a higher degree of conservation under the null hypothesis of random gene order, and add a correction factor to account for multiple testing. Our approach considers all parameters that define the quality of gene cluster conservation: the number of genomes in which the cluster occurs, the number of involved genes, the degree of conservation in the different genomes, as well as the frequency of the clustered genes within each genome. We apply our approach to evaluate gene cluster predictions in a large set of well annotated genomes.

2013-01-01

105

Forward-Scattering Approximation for Disordered Systems.  

National Technical Information Service (NTIS)

Changes in the Fermi surface with disorder can be defined for only two cases: (a) when ordinary perturbation theory is applicable and (b) when the forward-scattering approximation is applicable. In the forward-scattering approximation (FSA) the perturbati...

E. A. Stern

1972-01-01

106

Approximation of Pearson Type IV Tail Probabilities.  

National Technical Information Service (NTIS)

Simple approximating functions for tail probabilities of the Pearson Type IV distribution are obtained by using the B sub n transformations and by truncating the continued fraction expansion. The behavior of these approximations is then investigated for v...

W. A. Woodward

1975-01-01

107

Diagonal Pade Approximations for Initial Value Problems.  

National Technical Information Service (NTIS)

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...

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

1987-01-01

108

Finite Difference Generalized Pade Approximant Propagation Methods.  

National Technical Information Service (NTIS)

We present a simple series of high-order finite difference and finite element propagation procedures based on approximating the exponential of two noncommuting operators as a product of single-operator Pade approximants. We have previously generated a cla...

D. Yevick M. Glasner B. Hermansson

1992-01-01

109

Approximation algorithms for the traveling salesman problem  

Microsoft Academic Search

.   We first prove that the minimum and maximum traveling salesman problems, their metric versions as well as some versions defined\\u000a on parameterized triangle inequalities (called sharpened and relaxed metric traveling salesman) are all equi-approximable\\u000a under an approximation measure, called differential-approximation ratio, that measures how the value of an approximate solution\\u000a is placed in the interval between the worst- and

Jérôme Monnot; Vangelis Th. Paschos; Sophie Toulouse

2003-01-01

110

Energy conservation - A test for scattering approximations  

NASA Technical Reports Server (NTRS)

The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.

Acquista, C.; Holland, A. C.

1980-01-01

111

A4: Analytic Approximation and Perturbation Methods  

NASA Astrophysics Data System (ADS)

The oral presentations of the Workshop A4 on Analytic Approximation and Perturbation Methods are summarised. Topics covered include post-Newtonian approximations, radiation reaction in general relativity, post-Minkowskian approximations, rotational perturbations, black hole perturbations and quasi-normal modes, Efroimsky formalism, background independent gravitational waves and cosmological perturbations.

Iyer, Bala R.

2005-11-01

112

Efficient Approximation for Triangulation of Minimum Treewidth  

Microsoft Academic Search

We present four novel approximation algorithms for finding triangulation of minimum treewidth. Two of the algorithms improve on the running times of algorithms by Robertson and Seymour, and Becker and Geiger that approximate the op- timum by factors of4 and323 , respectively. A third algorithm is faster than those but gives an approximation factor of412 . The last algorithm is

Eyal Amir

2001-01-01

113

Strong approximation for the supermarket model  

Microsoft Academic Search

We prove three strong approximation theorems for the “supermarket” or “join the shortest queue” model—a law of large numbers, a jump process approximation and a central limit theorem. The estimates are carried through rather explicitly, and rely in part on couplings. This allows us to approximate each of the infinitely many components of the process in its own scale and

Malwina J. Luczak; James Norris

2005-01-01

114

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.

115

Continuous Subdifferential Approximations and Their Applications  

Microsoft Academic Search

In this paper, we study continuous approximations to the Clarke subdifferential and the Demyanov– Rubinov quasidifferential. Different methods have been proposed and discussed for the construction of the continuous approximations. Numerical methods for minimization of the locally Lipschitzian functions which are based on the continuous approximations are described and their convergence is studied. To test the proposed methods, numerical experiments

A. M. Bagirov

2003-01-01

116

A unified approach to the Darwin approximation  

SciTech Connect

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

Krause, Todd B.; Apte, A.; Morrison, P. J. [Institute for Fusion Studies and Physics Department, University of Texas at Austin, Austin, Texas 78712 (United States); Centre for Applied Mathematics, Tata Institute of Fundamental Research, Bangalore (India); Physics Department and Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712 (United States)

2007-10-15

117

Connection of Pade Approximants with Stationary Variational Principles and the Convergence of Certain Pade Approximants.  

National Technical Information Service (NTIS)

The aim of the paper is to describe the connection between Pade approximants and approximations derived from stationary variational principles. The author discusses some possible implications about the convergence of Pade approximants and concludes by pro...

J. Nuttall

1970-01-01

118

Output time response approximation. [of nonlinear systems  

NASA Technical Reports Server (NTRS)

The approximation of the output response of a nonlinear system by the output response of a linear system to a desired order irrespective of the admissible input applied should prove useful for purposes of control generation and simulation. Given a nonlinear system, an integer k, and an open subset of state space, sufficient conditions are stated that such a linear approximation exists to order k for every point in the set. In addition, a method for finding the approximating linear systems is presented.

Hunt, L. R.; Su, R.

1986-01-01

119

Diffusion approximation of neuronal models revisited.  

PubMed

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

Cupera, Jakub

2014-02-01

120

Bent approximations to synchrotron radiation optics  

SciTech Connect

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

Heald, S.

1981-01-01

121

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

122

Piecewise linear approximation for hereditary control problems  

NASA Technical Reports Server (NTRS)

This paper presents finite-dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems, when a quadratic cost integral must be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in the case where the cost integral ranges over a finite time interval, as well as in the case where it ranges over an infinite time interval. The arguments in the last case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense.

Propst, Georg

1990-01-01

123

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

124

Study of Trotter-like approximations  

SciTech Connect

Many quantum Monte Carlo techniques require a Trotter-like approximation before they can be implemented. In an effort to understand better the performance of these techniques, we explore the errors when Trotter-like approximations are used for calculating free energies and operator expectation values.

Fye, R.M.

1986-06-01

125

Diagonal Pade approximations for initial value problems  

Microsoft Academic Search

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.

Michael F. Reusch; Lee Ratzan; Neil Pomphrey

1988-01-01

126

Impulse-approximation Dirac optical potential  

SciTech Connect

The impulse approximation to the Dirac optical potential for proton-nucleus elastic scattering is deduced from elementary considerations and found to be in remarkably good agreement with phenomenological parameters. The large difference between the real parts of scalar and vector optical potentials is explained by the impulse approximation.

McNeil, J.A.; Shepard, J.R.; Wallace, S.J.

1983-05-09

127

Impulse-Approximation Dirac Optical Potential  

NASA Astrophysics Data System (ADS)

The impulse approximation to the Dirac optical potential for proton-nucleus elastic scattering is deduced from elementary considerations and found to be in remarkably good agreement with phenomenological parameters. The large difference between the real parts of scalar and vector optical potentials is explained by the impulse approximation.

McNeil, J. A.; Shepard, J. R.; Wallace, S. J.

1983-05-01

128

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

129

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

130

Approximate equation of state of condensed substances  

Microsoft Academic Search

The functions entering into the equation of state of Mie-Gruneisen solids are constructed approximately. In [1] an approximate equation of state was proposed for solids whose adiabatic curves obey a linear relationship between the velocity of the shock wave D and the mass velocity U; the slope of the shock adiabatic curve was equal to 1.5. In the present work,

G. A. Bogachev

1975-01-01

131

Strong approximation for the supermarket model  

Microsoft Academic Search

We prove three strong approximation theorems for the `supermarket' or `join the shortest queue' model -- a law of large numbers, a jump process approximation and a central limit theorem. The estimates are carried through rather explicitly. This allows us to estimate each of the infinitely many components of the process in its own scale and to exhibit a cut-off

Malwina J. Luczak; James Norris

2004-01-01

132

Quirks of Stirling's Approximation  

ERIC Educational Resources Information Center

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

Macrae, Roderick M.; Allgeier, Benjamin M.

2013-01-01

133

Approximate Nearest Neighbor Searching in Multimedia Databases  

Microsoft Academic Search

In this paper, we develop a general framework for approximate nearest neighbor queries. We firstcategorize the current approaches for nearest neighbor query processing based on either their abilityto reduce the data set that needs to be examined, or their ability to reduce the representation ofeach data object. We first propose modifications to well-known techniques to support the progressiveprocessing of approximate

Hakan Ferhatosmanoglu; Ertem Tuncel; Divyakant Agrawal; Amr El Abbadi

2001-01-01

134

QUASI-LOCAL-DENSITY APPROXIMATION FOR A  

Microsoft Academic Search

We discuss a possible form for a theory akin to local density functional the- ory, but able to produce van der Waals energies in a natural fashion. The usual Local Density Approximation (LDA) for the exchange and correlation energy Exc of an inhomogeneous electronic system can be derived by making a quasilocal approximation for the interacting density-density response func- tion

VAN DER WAALS; John F. Dobson

135

Relaxation approximation of the Euler equations  

Microsoft Academic Search

The aim of this paper is to show how solutions to the one-dimensional compressible Euler equations can be approximated by solutions to an enlarged hyperbolic system with a strong relaxation term. The enlarged hyperbolic system is linearly degenerate and is therefore suitable to build an efficient approximate Riemann solver. From a theoretical point of view, the convergence of solutions to

Christophe Chalons; Jean-François Coulombel

2008-01-01

136

Approximation of the Quadratic Set Covering problem  

Microsoft Academic Search

We study in this article the polynomial approximation properties of the Quadratic Set Covering problem. This problem, which arises in many applications, is a natural generalization of the usual Set Covering problem. We show that this problem is very hard to approximate in the general case, and even in classical subcases (when the size of each set or when the

Bruno Escoffier; Peter L. Hammer

2007-01-01

137

Convergence of sequences of Pade approximants  

SciTech Connect

Criteria are specified for the selection of a convergent subsequence of Pade approximants out of a given sequence. Conditions which may be implemented computationally are given for establishing spherical equicontinuity of a sequence of Pade approximants, and these conditions suffice to prove spherical convergence.

Baker, G.A. Jr.; Graves-Morris, P.R.

1982-06-01

138

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.

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

1988-09-01

139

Approximate Bézier curves by cubic LN curves  

Microsoft Academic Search

In order to derive the offset curves by using cubic Bézier curves with a linear field of normal vectors (the so-called LN Bézier curves) more efficiently, three methods for approximating degree n Bézier curves by cubic LN Bézier curves are considered, which includes two traditional methods and one new method based on Hausdorff distance. The approximation based on shifting control

Wei-Xian Huang; Cong-Jian Jin; Guo-Jin Wang

2011-01-01

140

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

141

Polynomial approximation of Morison wave loading  

SciTech Connect

For offshore structures with slender elements, the modeling of random wave loads by the Morison equation yields an equation of motion which has no analytical solution for response moments except in a few limiting cases. If polynomial approximations of the Morison drag loads are introduced, some procedures are available to obtain the stationary moments of the approximate response. If the response process is fitted by non-Gaussian models such as proposed by Winterstein (1988), the first four statistical moments of the response are necessary. The paper investigates how many terms should be included in the polynomial approximation of the Morison drag loading to accurately estimate the first four response moments. It is shown that a cubic approximation of the drag loading is necessary to accurately predict the response variance for any excitation. For the fit of the first four response moments, at least a fifth-order approximation appears necessary.

Bouyssy, V.; Rackwitz, R. [Technische Univ. Muenchen (Germany). Inst. fuer Tragwerksbau

1997-02-01

142

An improved proximity force approximation for electrostatics  

NASA Astrophysics Data System (ADS)

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

Fosco, César D.; Lombardo, Fernando C.; Mazzitelli, Francisco D.

2012-08-01

143

Relativistic stellar pulsations in the Cowling approximation  

NASA Astrophysics Data System (ADS)

Much that is known about the general pulsational properties of non-rotating Newtonian stars is traceable to the fact that in the Cowling approximation, the stellar pulsation equations can be cast in a nearly Sturm-Liouville form. In this paper, the relativistic Cowling approximation (an approximation scheme first introduced by McDermott, Van Horn and Scholl and analogous to the Newtonian Cowling approximation) is investigated, and it is shown that in this approximation the equations for non-radial relativistic stellar pulsations are also of nearly Sturm-Liouville character. The consequences of this are discussed as a series of theorems regarding the eigenfrequencies and eigenfunctions of g-, f- and p-modes in relativistic stars.

Finn, Lee Samuel

1988-05-01

144

Piecewise linear approximation for hereditary control problems  

NASA Technical Reports Server (NTRS)

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

Propst, Georg

1987-01-01

145

Approximate master equations for atom optics  

SciTech Connect

In the field of atom optics, the basis of many experiments is a two-level atom coupled to a light field. The evolution of this system is governed by a master equation. The irreversible components of this master equation describe the spontaneous emission of photons from the atom. For many applications, it is necessary to minimize the effect of this irreversible evolution. This can be achieved by having a far detuned light field. The drawback of this regime is that making the detuning very large makes the time step required to solve the master equation very small, much smaller than the time scale of any significant evolution. This makes the problem very numerically intensive. For this reason, approximations are used to simulate the master equation, which are more numerically tractable to solve. This paper analyzes four approximations: The standard adiabatic approximation, a more sophisticated adiabatic approximation (not used before), a secular approximation, and a fully quantum dressed-state approximation. The advantages and disadvantages of each are investigated with respect to accuracy, complexity, and the resources required to simulate. In a parameter regime of particular experimental interest, only the sophisticated adiabatic and dressed-state approximations agree well with the exact evolution.

Atkins, D.J.; Wiseman, H.M.; Warszawski, P. [Centre For Quantum Dynamics, School of Science, Griffith University, Nathan, Queensland 4111 (Australia)

2003-02-01

146

Approximations to the plasma refractive index  

NASA Astrophysics Data System (ADS)

For fifty years the quasi-longitudinal and quasi-transverse approximations to the refractive index formula for an ionized plasma have been used. Recent investigations have sought to generalize the traditional treatment in various ways. In the author's opinion, something further remains to be explained, and in the present paper various algebraic identities are examined between distinct forms of the refractive index, whereby a radical can sometimes be switched between numerator and denominator. Approximations to this radical are kept distinct algebraically from any subsequent expansions that may be made in the refractive index formula. The properties of this radical and its various approximations are examined in detail, both algebraically and numerically.

Heading, J.

1984-12-01

147

Alternative approximation concepts for space frame synthesis  

NASA Technical Reports Server (NTRS)

A method for space frame synthesis based on the application of a full gamut of approximation concepts is presented. It is found that with the thoughtful selection of design space, objective function approximation, constraint approximation and mathematical programming problem formulation options it is possible to obtain near minimum mass designs for a significant class of space frame structural systems while requiring fewer than 10 structural analyses. Example problems are presented which demonstrate the effectiveness of the method for frame structures subjected to multiple static loading conditions with limits on structural stiffness and strength.

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

1985-01-01

148

Number-operator approximation for pairing  

NASA Astrophysics Data System (ADS)

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. NUCLEAR STRUCTURE Number conservation and Pauli principle in number-operator approximation for pairing.

Vincent, C. M.

1983-01-01

149

Self-similar continued root approximants  

NASA Astrophysics Data System (ADS)

A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Padé approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.

Gluzman, S.; Yukalov, V. I.

2012-12-01

150

Approximate controllability of nonlinear fractional dynamical systems  

NASA Astrophysics Data System (ADS)

In this paper, we consider the controllability problems for a class of nonlinear fractional differential equations of order 1approximate controllability of nonlinear fractional dynamical systems by assuming the associated linear system is approximately controllable. Further, the result is extended to study the approximate controllability result for the nonlocal fractional control system with infinite delay. Also, as a remark, the conditions for the exact controllability results are obtained. The results are established by using solution operator theory, fractional calculations and fixed point techniques. Finally, an example is provided to illustrate the obtained theory.

Sakthivel, R.; Ganesh, R.; Ren, Yong; Anthoni, S. M.

2013-12-01

151

Quantum Mechanical Approximations in Quantum Field Theory.  

National Technical Information Service (NTIS)

Some cooperative, coherent effects in quantum field theory, such as spontaneous symmetry violation, bound states, and entrapment of various excitations, can be exposed only by approximation procedures which do not rely on analyticity or regularity in the ...

R. Jackiw

1975-01-01

152

Pade Approximants and Linear Integral Equations.  

National Technical Information Service (NTIS)

Pade approximants are used to extend the scope of Neumann Series solution of linear integral equations. The general properties of classes of linear integral equations are discussed and these properties are used to establish two theorems on Pade approximan...

J. S. R. Chisholm

1970-01-01

153

On Padé approximants to virial series.  

PubMed

Padé approximants have long been used to predict virial series coefficients and to provide equations of state for low and high density materials. However, some justified criticism has appeared about this procedure. Although we agree to impose several restrictions on the use of Padé approximants, we indicate that the Padé approximant is still an excellent way to predict the first unknown virial series coefficients. As an example, we report a calculation of the B11=128.6 and B12=155 virial coefficients of the three dimensional hard sphere model that are in excellent agreement with the two most recent estimates. We also consider that the commonly used method to choose among Padé approximants is not completely reliable for this specific application and suggest an alternative new method. PMID:18681662

Guerrero, André O; Bassi, Adalberto B M S

2008-07-28

154

Instantaneous approximation for the dynamical Casimir effect  

NASA Astrophysics Data System (ADS)

The one-dimensional model for the dynamical Casimir effect, i.e. the effect of creation of photons in a nonstationary cavity, is studied in the framework of the instantaneous approximation. Different exact and approximate expressions for the energy distribution of created photons are derived. A region of applicability of the instantaneous approximation is established. In particular, it is shown that the instantaneous approximation predicts no more than the low-energy part of the energy distribution. Recent proposals for experimental realization of a cavity with fast variation of parameters are reviewed, and a new proposal based on fast creation of an additional mirror in the interior of the cavity by instant injection of dense electron plasma in thin semiconductor film is presented.

Fedotov, Alexander; Narozhny, Nikolay; Lozovik, Yurii

2005-03-01

155

Linear Approximation SAR Azimuth Processing Study  

NASA Technical Reports Server (NTRS)

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

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

1979-01-01

156

Computational Aspects of Pseudospectral Laguerre Approximations.  

National Technical Information Service (NTIS)

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

D. Funaro

1989-01-01

157

Computational aspects of pseudospectral Laguerre approximations  

NASA Technical Reports Server (NTRS)

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

Funaro, Daniele

1989-01-01

158

Linear approximation SAR azimuth processing study  

NASA Technical Reports Server (NTRS)

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

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

1979-01-01

159

Local Exchange Approximation and the Virial Theorem.  

National Technical Information Service (NTIS)

Whereas the determinantal wave functions constructed from the solutions of the Hartree-Fock equations satisfy the virial theorem, those constructed from self-consistent-field schemes with a local exchange approximation do not necessarily. A scaling proced...

M. Berrondo O. Goscinski

1969-01-01

160

Pade Approximants for Linear Boltzmann Equation.  

National Technical Information Service (NTIS)

The iteration and iteration-perturbation techniques are used to find the relation between the linear functional and Pade' approximants. Application is made for linear Boltzmann equation, and it is found that the iteration-perturbation method is equivalent...

S. A. El Walik E. Abbas

1976-01-01

161

Approximation and Data Fitting Methods: Part 1, Introduction to Numerical Approximation Methods.  

National Technical Information Service (NTIS)

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 an...

F. N. Fritsch

1986-01-01

162

Disjoint Cycles: Integrality Gap, Hardness, and Approximation  

Microsoft Academic Search

\\u000a In the edge-disjoint cycle packing problem we are given a graph G and we have to find a largest set of edge-disjoint cycles in G. The problem of packing vertex-disjoint cycles in G is defined similarly. The best approximation algorithms for edge-disjoint cycle packing are due to Krivelevich et al. [16],\\u000a where they give an OÖ{log n}O\\\\sqrt{\\\\rm log n}-approximation for

Mohammad R. Salavatipour; Jacques Verstraëte

2005-01-01

163

A systematic sequence of relativistic approximations  

Microsoft Academic Search

An approach to the development of a systematic sequence of relativistic approximations is reviewed. The approach depends on the atomically localized nature of relativistic effects, and is based on the normalized elimination of the small component in the matrix modified Dirac equation. Errors in the approximations are assessed relative to four-component Dirac-Hartree-Fock calculations or other reference points. Projection onto the

Kenneth G. Dyall; Kenneth G

2002-01-01

164

Approximate Solutions Of Equations Of Steady Diffusion  

NASA Technical Reports Server (NTRS)

Rigorous analysis yields reliable criteria for "best-fit" functions. Improved "curve-fitting" method yields approximate solutions to differential equations of steady-state diffusion. Method applies to problems in which rates of diffusion depend linearly or nonlinearly on concentrations of diffusants, approximate solutions analytic or numerical, and boundary conditions of Dirichlet type, of Neumann type, or mixture of both types. Applied to equations for diffusion of charge carriers in semiconductors in which mobilities and lifetimes of charge carriers depend on concentrations.

Edmonds, Larry D.

1992-01-01

165

An analytical approximation of a pendulum trajectory  

NASA Astrophysics Data System (ADS)

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

Salinas-Hernández, E.; Ares de Parga, G.; Domínguez-Hernández, S.; Muñoz-Vega, R.

2014-07-01

166

The closure approximation in the hierarchy equations.  

NASA Technical Reports Server (NTRS)

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

Adomian, G.

1971-01-01

167

Rational approximants as analytic polyatomic potential surfaces  

SciTech Connect

This report investigates one- and two-dimensional rational approximants as a convenient systematic means for analytical representation of numerical data for molecular potential energy surfaces. Discussed in this paper are the linearized least-square equations for determination of Pade approximants and the iterative method for the elimination of zeros as demonstrated for the cases of Li{sub 2} and two-mode HCN.

Stevens, R.E.; Kinsey, J.L.; Johnson, B.R. [Rice Univ., Houston, TX (United States)

1992-09-17

168

Approximate clustering via core-sets  

Microsoft Academic Search

In this paper, we show that for several clustering problems one can extract a small set of points, so that using those core-sets enable us to perform approximate clustering efficiently. The surprising property of those core-sets is that their size is independent of the dimension.Using those, we present a (1+ ?)-approximation algorithms for the k-center clustering and k-median clustering problems

Mihai B?doiu; Sariel Har-Peled; Piotr Indyk

2002-01-01

169

Adaptive Approximation Based Control-Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches-  

Microsoft Academic Search

This book, by two of the key people who have developed rigorous methods in the arena of Intelligent Control, provides a long-awaited overall perspective that unifies nonlinear network approximators and adaptive control techniques. The focus of the book is continuous-time adaptive systems. The text consists of eight chapters. Some of the topics discussed include: approximation theory; approximation structures used in

Frank Lewis; M. M. Polycarpou

2007-01-01

170

Semiclassical initial value approximation for Green's function  

NASA Astrophysics Data System (ADS)

A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincaré surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.

Kay, Kenneth G.

2010-06-01

171

Recent advances in discrete dipole approximation  

NASA Astrophysics Data System (ADS)

I will describe recent advances and results related to Discrete Dipole Approximation. I will concentrate on Discrete Dipole Scattering (DDSCAT) code which has been jointly developed by myself and Bruce T. Draine. Discussion will concentrate on calculation of scattering and absorption by isolated particles (e.g., dust grains, ice crystals), calculations of scattering by periodic structures with applications to studies of scattering and absorption by periodic arrangement of finite cylinders, cubes, etc), very fast near field calculation, ways to display scattering targets and their composition using three dimensional graphical codes. I will discuss possible extensions. References Flatau, P. J. and Draine, B. T., 2012, Fast near field calculations in the discrete dipole approximation for regular rectilinear grids, Optics Express, 20, 1247-1252. Draine B. T. and Flatau P. J., 2008, Discrete-dipole approximation for periodic targets: theory and tests , J. Opt. Soc. Am. A., 25, 2693-2703. Draine BT and Flatau PJ, 2012, User Guide for the Discrete Dipole Approximation Code DDSCAT 7.2, arXiv:1202.3424v3.ear field calculations (Fast near field calculations in the discrete dipole approximation for regular rectilinear grids P. J. Flatau and B. T. Draine, Optics Express, Vol. 20, Issue 2, pp. 1247-1252 (2012))

Flatau, P. J.

2012-12-01

172

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

173

Tunneling probability: an evaluation of different approximations  

NASA Astrophysics Data System (ADS)

Before the recent developments in the quantum-defect theoryootnotetextB. Gao, Phys. Rev. A 78, 012702 (2008). and the related analytic solutions for 1/r^n type of long-range potentials, there were virtually no exact result of tunneling for physically realistic systems, which made the evaluation of different approximations, such as the ubiquitous semiclassical approximation, difficult. By comparing with the exact analytic results of tunneling for -1/r^6 and -1/r^4 types of potentials, we carefully evaluate the validity of the semiclassical and the top-of-barrierootnotetextS. J. Ward and J. H. Macek, Phys. Rev. A 62, 052715 (2000). approximations for tunneling through the angular momentum barrier in atom-atom, ion-atom, and electron-atom interactions.

Li, Ming; Makrides, Constantinos; Gao, Bo

2010-03-01

174

The Cell Cycle Switch Computes Approximate Majority  

PubMed Central

Both computational and biological systems have to make decisions about switching from one state to another. The ‘Approximate Majority’ computational algorithm provides the asymptotically fastest way to reach a common decision by all members of a population between two possible outcomes, where the decision approximately matches the initial relative majority. The network that regulates the mitotic entry of the cell-cycle in eukaryotes also makes a decision before it induces early mitotic processes. Here we show that the switch from inactive to active forms of the mitosis promoting Cyclin Dependent Kinases is driven by a system that is related to both the structure and the dynamics of the Approximate Majority computation. We investigate the behavior of these two switches by deterministic, stochastic and probabilistic methods and show that the steady states and temporal dynamics of the two systems are similar and they are exchangeable as components of oscillatory networks.

Cardelli, Luca; Csikasz-Nagy, Attila

2012-01-01

175

Optical pulse propagation with minimal approximations  

SciTech Connect

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

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

2010-01-15

176

Exponential Approximations Using Fourier Series Partial Sums  

NASA Technical Reports Server (NTRS)

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

Banerjee, Nana S.; Geer, James F.

1997-01-01

177

Approximate solution to the stochastic Kuramoto model  

NASA Astrophysics Data System (ADS)

We study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the time-dependent order parameter, which characterizes the synchronization between the oscillators. The known critical coupling strength is exactly recovered by the Gaussian theory. Extensive numerical experiments further show that the analytical results are very accurate below and sufficiently above the critical value. We obtain the asymptotic order parameter in closed form, which suggests a tighter upper bound for the corresponding scaling. As a last point, we elaborate the Gaussian approximation in complex networks with distributed degrees.

Sonnenschein, Bernard; Schimansky-Geier, Lutz

2013-11-01

178

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

179

Approximation algorithms for planning and control  

NASA Technical Reports Server (NTRS)

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

Boddy, Mark; Dean, Thomas

1989-01-01

180

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

181

2-D Hydrogen Molecule Using AMO Approximation.  

National Technical Information Service (NTIS)

The eigenenergies of the hydrogen molecule are calculated in the Alternate Molecular Orbital (AMO) approximation. Emphasis is given to two-dimensional (2-D) systems. Results are compared for the 2-D and 3-D cases and also with the singlet state of the Var...

E. A. Deandradaesilva I. C. Dacunhalima A. Ferreiradasilva

1985-01-01

182

Approximation Algorithms for Broadcasting and Gossiping  

Microsoft Academic Search

Broadcasting and gossiping are two basic communication patterns which commonly occur when programming parallel and distributed systems. This paper deals with approximation algorithms for solving these problems on arbitrary topologies. We present new strategies to derive efficient broadcasting and gossiping algorithms in any networks in the telephone model. Our objective is to minimize both round complexity and step complexity. Broadcasting

Pierre Fraigniaud; Sandrine Vial

1997-01-01

183

Kravchuk functions for the finite oscillator approximation  

NASA Technical Reports Server (NTRS)

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

Atakishiyev, Natig M.; Wolf, Kurt Bernardo

1995-01-01

184

Dynamic Padé approximants for chemical center waves  

Microsoft Academic Search

A model of reaction and diffusion is shown to exhibit composition center waves. The analysis is based on a Padé approximant scheme carried out in a completely self-consistent way. Evidence is given to show that these patterns may exist over a domain of wave vectors (of the outer plane wave region) that may exceed that of plane waves but may

Shubha Bose; Subir Bose; P. Ortoleva

1980-01-01

185

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

186

Are approximation algorithms for consensus clustering worthwhile?  

Microsoft Academic Search

Consensus clustering has emerged as one of the principal clustering problems in the data mining community. In recent years the theoretical computer science community has generated a number of approximation algorithms for consensus clustering and similar problems. These algorithms run in polynomial time, with performance guaranteed to be at most a certain factor worse than optimal. We investigate the feasibility

Michael Bertolacci; Anthony Wirth

187

3D Similarity Search by Shape Approximation  

Microsoft Academic Search

This paper presents a new method for similarity retrieval of 3D surface seg- ments in spatial database systems as used in molecular biology, medical imaging, or CAD. We propose a similarity criterion and algorithm for 3D surface segments which is based on the approximation of segments by using multi-parametric functions. The method can be adjusted to individual requirements of specific

Hans-peter Kriegel; Thomas Schmidt; Thomas Seidl

1997-01-01

188

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

189

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

190

New Approximation Techniques for Some Ordering Problems.  

National Technical Information Service (NTIS)

We describe O(log n) times optimal approximation algorithms for the NP-hard graph optimization problems of minimum linear arrangement, minimum containing interval graph and minimum storage-time product. This improves on the O(log n log log n) approximatio...

S. Rao A. W. Richa

1997-01-01

191

Approximate Data Stream Joins in Distributed Systems  

Microsoft Academic Search

The emergence of applications producing continuous high-frequency data streams has brought forth a large body of research in the area of distributed stream processing. In presence of high volumes of data, efforts have primarily concentrated on providing approximate aggregate or top-k type results. Scalable solutions for providing answers to window join queries in distributed stream processing sys- tems have received

Vassil Kriakov; Alex Delis; George Kollios

2007-01-01

192

Layered Neural Networks as Universal Approximators  

Microsoft Academic Search

The paper considers Ito's results on the approximation capability of layered neural networks with sigmoid units in two layers. First of all the paper recalls one of Ito's main results. Then the results of Ito regarding Heaviside function as sigmoid functions are extended using a signum function. For Heaviside functions a layered neural network implementation is presented that is also

Ion Ciuca; J. Andrew Ware

1997-01-01

193

Calculating Bessel Functions with Pade Approximants.  

National Technical Information Service (NTIS)

The solution of the two-body Schrodinger equation with a C/r squared potential is a Bessel function. The asymptotic series in 1/r, which is generated from the Schrodinger equation, has a zero radius of convergence. The Pade approximants to the asymptotic ...

J. Nuttall J. E. Golden J. H. McGuire

1973-01-01

194

Multivariate Approximation by Locally Blended Univariate Interpolants  

PubMed Central

A method is given for constructing simple new “finite elements” that seem well-suited to approximating smooth functions in rectangular polygons decomposed into rectangular cells. Some of the key properties of the elements are derived, and analogous three-dimensional “bricks” are constructed.

Birkhoff, Garrett; Cavendish, James C.; Gordon, William J.

1974-01-01

195

Successive Approximation in Parallel Graph Algorithms  

Microsoft Academic Search

The notion of successive approximation is introduced in the context of parallel graph algorithms. The implementation of graph algorithms on Leighton's mesh of trees network model is considered. The implementations that have appeared so far in the literature are relatively straightforward. A common characteristic of these algorithms is that, in each iteration, for each vertex v, at most one edge

Donald S. Fussell; Ramakrishna Thurimella

1989-01-01

196

Using Learning for Approximation in Stochastic Processes  

Microsoft Academic Search

To monitor or control a stochastic dynamic system, we need to reason about its current state. Exact inference for this task requires that we maintain a complete joint probability distribution over the pos- sible states, an impossible requirement for most pro- cesses. Stochastic simulation algorithms provide an alternative solution by approximating the distribu- tion at time via a (relatively small)

Daphne Koller; Raya Fratkina

1998-01-01

197

Supersymmetric electroweak baryogenesis in the WKB approximation  

Microsoft Academic Search

We calculate the baryon asymmetry generated at the electroweak phase transition in the minimal supersymmetric standard model, treating the particles in a WKB approximation in the bubble wall background. A set of diffusion equations for the particle species relevant to baryon generation, including source terms arising from the CP violation associated with the complex phase ? of the ? parameter,

James M. Cline; Michael Joyce; Kimmo Kainulainen

1998-01-01

198

Online Amnesic Approximation of Streaming Time Series  

Microsoft Academic Search

The past decade has seen a wealth of research on time se- ries representations, because the manipulation, storage, and indexing of large volumes of raw time series data is imprac- tical. The vast majority of research has concentrated on rep- resentations that are calculated in batch mode and represent each value with approximately equal fidelity. However, the in- creasing deployment

Themistoklis Palpanas; Michail Vlachos; Eamonn J. Keogh; Dimitrios Gunopulos; Wagner Truppel

2004-01-01

199

Relativistic point interactions: Approximation by smooth potentials  

NASA Astrophysics Data System (ADS)

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

Hughes, Rhonda J.

1997-06-01

200

Incremental neural networks for function approximation  

Microsoft Academic Search

A new strategy for incremental building of multilayer feedforward neural networks is proposed in the context of approximation of functions from Rp to Rq using noisy data. A stopping criterion based on the properties of the noise is also proposed. Experimental results for both artificial and real data are performed and two alternatives of the proposed construction strategy are compared.

R. Chentouf; C. Jutten; M. Maignan; M. Kanevsky

1997-01-01

201

Capacity Approximations for a Deterministic MIMO Channel.  

National Technical Information Service (NTIS)

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

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

2011-01-01

202

Alternative approximation concepts for space frame synthesis  

NASA Technical Reports Server (NTRS)

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

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

1985-01-01

203

Sensing Position With Approximately Constant Contact Force  

NASA Technical Reports Server (NTRS)

Computer-controlled electromechanical system uses number of linear variable-differential transformers (LVDTs) to measure axial positions of selected points on surface of lens, mirror, or other precise optical component with high finish. Pressures applied to pneumatically driven LVDTs adjusted to maintain small, approximately constant contact forces as positions of LVDT tips vary.

Sturdevant, Jay

1996-01-01

204

Progressive Image Coding by Hierarchical Linear Approximation.  

ERIC Educational Resources Information Center

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

Wu, Xiaolin; Fang, Yonggang

1994-01-01

205

Approximate Message Authentication and Biometric Entity Authentication  

Microsoft Academic Search

Approximate Message Authentication Code (AMAC) is a recently introduced cryptographic primitive with several applications in the areas of cryptography and coding theory. Briefly speaking, AMACs represent a way to provide data authentication that is tolerant to ac- ceptable modifications of the original message. Although constructs had been proposed for this primitive, no security analysis or even modeling had been done.

Giovanni Di Crescenzo; R. F. Graveman; Renwei Ge; Gonzalo R. Arce

2005-01-01

206

Optical pulse propagation with minimal approximations  

Microsoft Academic Search

Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations---including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first-order propagation equation using a minimum of approximations and a straightforward ``factorization'' mathematical scheme. The approach generates exact coupled bidirectional equations, after which it is clear

Paul Kinsler

2010-01-01

207

Optical pulse propagation with minimal approximations  

Microsoft Academic Search

Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations -- including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first order propagation equation using a minimum of approximations and a straightforward \\

Paul Kinsler

2008-01-01

208

Optical pulse propagation with minimal approximations  

Microsoft Academic Search

Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations--including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first-order propagation equation using a minimum of approximations and a straightforward 'factorization' mathematical scheme. The approach generates exact coupled bidirectional equations, after which it is clear

Kinsler

2010-01-01

209

UNCERTAINTY QUANTIFICATION USING RESPONSE SURFACE APPROXIMATIONS  

Microsoft Academic Search

This report describes an initial investigation into the error convergence trends in sampling-based uncertainty quantification (UQ) studies performed both with and without response surface approximations. The data provided by this limited study indicate that RS-based UQ methods exhibit error trends that are as good or better (converging faster to zero) when compared to conventional sampling-based UQ methods.

A. A. Giunta; M. S. Eldred; J. P. Castro

210

Consistency of variational approximations in statistical thermodynamics  

Microsoft Academic Search

It is shown that a large class of approximations in statistical thermodynamics that are based on the free-energy variational principle for the density operator yield expressions for the macroscopic quantities of the system that are consistent from both the statistical-mechanical and thermodynamical points of view. This corrects some erroneous statements in the literature.

Petros N. Argyres; T. A. Kaplan; Nilton P. Silva

1974-01-01

211

Quickly Approximating the Distance Between Two Objects  

NASA Technical Reports Server (NTRS)

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

Hammen, David

2009-01-01

212

Can Distributional Approximations Give Exact Answers?  

ERIC Educational Resources Information Center

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

Griffiths, Martin

2013-01-01

213

Exponential approximations to compacted sediment porosity profiles  

Microsoft Academic Search

Sediment compaction and corresponding porosity variations can be modeled by a simple exponential with depth. The porosity solution is derived analytically as a complicated function of pore water pressure, but the underlying form is shown to approximate an exponential except near the surface where the behavior is linear. Even though the analytical simplifications ignore some of the detailed effects of

David B. Bahr; Eric W. H. Hutton; James P. M. Syvitski; Lincoln F. Pratson

2001-01-01

214

Finite Difference Approximation of Free Discontinuity Problems  

Microsoft Academic Search

We approximate functionals depending on the gradient of $u$ and on the behaviour of $u$ near the discontinuity points, by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, $\\\\Gamma$-convergence, and a compactness result which implies, in particular, the convergence of minima and minimizers.

Massimo Gobbino; Maria Giovanna Mora

2000-01-01

215

Improvements of the Discrete Dipole Approximation method  

Microsoft Academic Search

The discrete-dipole approximation (DDA) is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. In this paper we perform systematic study of various non-stationary iterative (conjugate gradient) methods in search for the most efficient one in order to solve the system of equations arising in DDA. We document implementation of these methods in our public domain

Piotr J. Flatau

2000-01-01

216

Approximation by Fully Complex Multilayer Perceptrons  

Microsoft Academic Search

We investigate the approximation ability of a multi layer perceptron (MLP) network when it is extended to the complex domain. The main challenge for processing complex data with neural networks has been the lack of bounded and analytic complex nonlinear activation functions in the complex domain, as stated by Liouville's theorem. To avoid the conflict between the boundedness and the

Taehwan Kim; Tülay Adali

2003-01-01

217

Intermediate Coupling Theory: Pade Approximants for Polarons.  

National Technical Information Service (NTIS)

A general method is presented for obtaining an accurate intermediate-coupling theory from weak- and strong-coupling perturbation theory. The method uses two-point Pade approximants to extrapolate (low-order) expansions about the weak- and the strong-coupl...

P. Sheng J. D. Dow

1971-01-01

218

Stochastic Liouville equation and Pade approximants  

SciTech Connect

The applicability of Pade approximant techniques to solving the stochastic Liouville equation is discussed. The special case of an axially symmetric spin system undergoing isotropic Brownian motion is studied. Two types of expansions are explored which yield efficient algorithms for spectral simulations.

Dammers, A.J.; Levine, Y.K.; Tjon, J.A.

1988-10-01

219

Pade approximations of probability density functions  

Microsoft Academic Search

The analysis of radar detection systems often requires extensive knowledge of the special functions of applied mathematics, and their computation. Yet, the moments of the detection random variable are often easily obtained. We demonstrate here how to employ a limited number of exactly specified moments to approximate the probability density and distribution functions of various random variables. The approach is

Hamidreza Amindavar; J. A. Ritcey

1994-01-01

220

Approximately vanishing of topological cohomology groups  

Microsoft Academic Search

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.

Mohammad Sal Moslehian

2006-01-01

221

Nuclear optical potential in first born approximation  

Microsoft Academic Search

We calculate nuclear scalar and vector optical potentials in the first Born approximation (FBA) using pi, varrho, omega, sigma, eta, and delta 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.

M. J. Iqbal

1985-01-01

222

The optimal XFEM approximation for fracture analysis  

Microsoft Academic Search

The extended finite element method (XFEM) provides an effective tool for analyzing fracture mechanics problems. A XFEM approximation consists of standard finite elements which are used in the major part of the domain and enriched elements in the enriched sub-domain for capturing special solution properties such as discontinuities and singularities. However, two issues in the standard XFEM should specially be

Shouyan Jiang; Zongquan Ying; Chengbin Du

2010-01-01

223

Block Addressing Indices for Approximate Text Retrieval.  

ERIC Educational Resources Information Center

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

Baeza-Yates, Ricardo; Navarro, Gonzalo

2000-01-01

224

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

225

Generalizing the finite element method: Diffuse approximation and diffuse elements  

Microsoft Academic Search

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

B. Nayroles; G. Touzot; P. Villon

1992-01-01

226

Planetary ephemerides approximation for radar astronomy  

NASA Technical Reports Server (NTRS)

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 approaches are considered and it is shown that the Gram polynomials outperform the commonly used technique based on Chebyshev polynomials. These methods are used to analyze the mean square, the phase error, and the frequency tracking error in the presence of the worst case Doppler shift that one may encounter within the solar system. It is shown that in the worst case the phase error is under one degree and the frequency tracking error less than one hertz when the frequency to the PLO is updated every millisecond.

Sadr, R.; Shahshahani, M.

1991-01-01

227

Simple approximants for natural orbitals of harmonium.  

PubMed

Simple approximations to the natural orbitals (NOs) of harmonium with enforced correct short- and long-range asymptotics yield accurate bounds for the NO occupancies. In particular, expressions involving Pade approximants with just one variational parameter are capable of producing the largest NO occupancies with accuracy better than 10(-4). The comparison of two cases with different coupling strengths omega (1.948 51

Cioslowski, Jerzy; Buchowiecki, Marcin

2005-12-15

228

Block multistep methods based on rational approximants  

NASA Astrophysics Data System (ADS)

In this study, the concept of block multistep methods based on rational approximants is introduced for the numerical solution of first order initial value problems. These numerical methods are also called rational block multistep methods. The main reason to consider block multistep methods in rational setting, is to improve the numerical accuracy and absolute stability property of existing block multistep methods that are based on polynomial approximants. For this pilot study, a 2-point explicit rational block multistep method is developed. Local truncation error and stability analysis for this new method are included as well. Numerical experimentations and results using some test problems are presented. Numerical results are satisfying in terms of numerical accuracy. Finally, future issues on the developments of rational block multistep methods are discussed.

Ying, Teh Yuan; Omar, Zurni; Mansor, Kamarun Hizam

2014-06-01

229

Some approximation concepts for structural synthesis  

NASA Technical Reports Server (NTRS)

An efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles. Static stress and displacement constraints under alternative loading conditions are considered. The optimization algorithm is an adaptation of the method of inscribed hyperspheres and high efficiency is achieved by using several approximation concepts including temporary deletion of noncritical constraints, design variable linking, and Taylor series expansions for response variables in terms of design variables. Optimum designs for several planar and space truss examples problems are presented. The results reported support the contention that the innovative use of approximation concepts in structural synthesis can produce significant improvements in efficiency.

Schmit, L. A., Jr.; Farshi, B.

1974-01-01

230

Airy beams beyond the paraxial approximation  

NASA Astrophysics Data System (ADS)

The behavior of the vectorial Airy beams beyond the paraxial approximation is investigated. Indeed, closed-form (even though non exact) expressions for the electric components of the fields generated by the same boundary conditions, which should pertain to the scalar Airy beams, are obtained on the basis of the vectorial Rayleigh-Sommerfeld diffraction integrals under suitable approximations. Such expressions may accompany more complete approaches, like that in Opt. Expr. 17, 22432 (2009), where a fully numerical analysis of the propagation of exponentially smoothed Airy beams has been presented, faithfully reproducing the conditions of their experimental demonstration as reported in Phys. Rev. Lett. 99, 213907 (2007). Comments on other well known approaches to the investigation of the nonparaxial propagation of definite paraxial beams are also given.

Torre, A.

2010-11-01

231

Comparison of quasilinear and WKB approximations  

SciTech Connect

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

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

2006-12-15

232

Smooth polynomial approximation of spiral arcs  

NASA Astrophysics Data System (ADS)

Constructing fair curve segments using parametric polynomials is difficult due to the oscillatory nature of polynomials. Even NURBS curves can exhibit unsatisfactory curvature profiles. Curve segments with monotonic curvature profiles, for example spiral arcs, exist but are intrinsically non-polynomial in nature and thus difficult to integrate into existing CAD systems. A method of constructing an approximation to a generalised Cornu spiral (GCS) arc using non-rational quintic Bézier curves matching end points, end slopes and end curvatures is presented. By defining an objective function based on the relative error between the curvature profiles of the GCS and its Bézier approximation, a curve segment is constructed that has a monotonic curvature profile within a specified tolerance.

Cripps, R. J.; Hussain, M. Z.; Zhu, S.

2010-03-01

233

Small Clique Detection and Approximate Nash Equilibria  

NASA Astrophysics Data System (ADS)

Recently, Hazan and Krauthgamer showed [12] that if, for a fixed small ?, an ?-best ?-approximate Nash equilibrium can be found in polynomial time in two-player games, then it is also possible to find a planted clique in G n, 1/2 of size C logn, where C is a large fixed constant independent of ?. In this paper, we extend their result to show that if an ?-best ?-approximate equilibrium can be efficiently found for arbitrarily small ?> 0, then one can detect the presence of a planted clique of size (2 + ?) logn in G n, 1/2 in polynomial time for arbitrarily small ?> 0. Our result is optimal in the sense that graphs in G n, 1/2 have cliques of size (2 - o(1)) logn with high probability.

Minder, Lorenz; Vilenchik, Dan

234

The optimal XFEM approximation for fracture analysis  

NASA Astrophysics Data System (ADS)

The extended finite element method (XFEM) provides an effective tool for analyzing fracture mechanics problems. A XFEM approximation consists of standard finite elements which are used in the major part of the domain and enriched elements in the enriched sub-domain for capturing special solution properties such as discontinuities and singularities. However, two issues in the standard XFEM should specially be concerned: efficient numerical integration methods and an appropriate construction of the blending elements. In the paper, an optimal XFEM approximation is proposed to overcome the disadvantage mentioned above in the standard XFEM. The modified enrichment functions are presented that can reproduced exactly everywhere in the domain. The corresponding FORTRAN program is developed for fracture analysis. A classic problem of fracture mechanics is used to benchmark the program. The results indicate that the optimal XFEM can alleviate the errors and improve numerical precision.

Jiang, Shouyan; Ying, Zongquan; Du, Chengbin

2010-06-01

235

Conductance quantization in graphene nanoribbons: adiabatic approximation  

NASA Astrophysics Data System (ADS)

A theory of electron states for graphene nanoribbons with a smoothly varying width is developed. It is demonstrated that the standard adiabatic approximation allowing to neglect the mixing of different standing waves is more restrictive for the massless Dirac fermions in graphene than for the conventional electron gas. For the case of zigzag boundary conditions, one can expect a well-pronounced conductance quantization only for highly excited states. This difference is related to the relativistic Zitterbewegung effect in graphene.

Katsnelson, M. I.

2007-06-01

236

Capacitor-Chain Successive-Approximation ADC  

NASA Technical Reports Server (NTRS)

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

Cunningham, Thomas

2003-01-01

237

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

238

Estimate sequence methods: extensions and approximations  

Microsoft Academic Search

The approach of estimate sequence oers an interesting rereading of a number of accelerating schemes proposed by Nesterov (Nes03), (Nes05), and (Nes06). It seems to us that this framework is the most appropriate descriptive framework to develop an analysis of the sensitivity of the schemes to approximations. We develop in this work a simple, self-contained, and unified framework for the

Michel Baes

2009-01-01

239

Approximate Graph Coloring by Semidefinite Programming  

Microsoft Academic Search

We consider the problem of coloring k-colorable graphs with the fewest possible colors. We present a randomized polynomial time algorithm that colors a 3-colorable graph on n vertices with min{O(?1\\/3 log1\\/2 ?log n), O(n1\\/4 log1\\/2 n)} colors whereis the maximum degree of any vertex. Besides giving the best known approximation ratio in terms of n, this marks the first non-trivial

David R. Karger; Rajeev Motwani; Madhu Sudan

1994-01-01

240

Viscosity approximation methods for nonexpansive mappings  

Microsoft Academic Search

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

Hong-Kun Xu

2004-01-01

241

Nonlinear amplitude approximation for bilinear systems  

NASA Astrophysics Data System (ADS)

An efficient method to predict vibration amplitudes at the resonant frequencies of dynamical systems with piecewise-linear nonlinearity is developed. This technique is referred to as bilinear amplitude approximation (BAA). BAA constructs a single vibration cycle at each resonant frequency to approximate the periodic steady-state response of the system. It is postulated that the steady-state response is piece-wise linear and can be approximated by analyzing the response over two time intervals during which the system behaves linearly. Overall the dynamics is nonlinear, but the system is in a distinct linear state during each of the two time intervals. Thus, the approximated vibration cycle is constructed using linear analyses. The equation of motion for analyzing the vibration of each state is projected along the overlapping space spanned by the linear mode shapes active in each of the states. This overlapping space is where the vibratory energy is transferred from one state to the other when the system switches from one state to the other. The overlapping space can be obtained using singular value decomposition. The space where the energy is transferred is used together with transition conditions of displacement and velocity compatibility to construct a single vibration cycle and to compute the amplitude of the dynamics. Since the BAA method does not require numerical integration of nonlinear models, computational costs are very low. In this paper, the BAA method is first applied to a single-degree-of-freedom system. Then, a three-degree-of-freedom system is introduced to demonstrate a more general application of BAA. Finally, the BAA method is applied to a full bladed disk with a crack. Results comparing numerical solutions from full-order nonlinear analysis and results obtained using BAA are presented for all systems.

Jung, Chulwoo; D?Souza, Kiran; Epureanu, Bogdan I.

2014-06-01

242

Approximate Acoustic Cloaking in Inhomogeneous Isotropic Space  

Microsoft Academic Search

In this paper, we consider the approximate acoustic cloaking in inhomogeneous isotropic background space. By employing transformation media, together with the use of a sound-soft layer lining right outside the cloaked region, we show that one can achieve the near-invisibility by the `blow-up-a-small-region' construction. This is based on the scattering estimates corresponding to small sound-soft obstacles located in isotropic space.

Hongyu Liu

2010-01-01

243

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

244

Approximate Factorization in Generalized Hardy Spaces  

Microsoft Academic Search

.  In this paper we establish a connection between the approximate factorization property appearing in the theory of dual algebras\\u000a and the spectral inclusion property for a class of Toeplitz operators on Hilbert spaces of vector valued square integrable\\u000a functions. As an application, it follows that a wide range of dual algebras of subnormal Toeplitz operators on various Hardy\\u000a spaces associated

Bebe Prunaru

2008-01-01

245

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

1995-07-15

246

MLPG approximation to the p Laplace problem  

Microsoft Academic Search

Meshless local Petrov-Galerkin (MLPG) method is discussed for solving 2D, nonlinear, elliptic p-Laplace or p-harmonic equation in this article. The problem is transferred to corresponding local boundary integral equation (LBIE) using\\u000a Divergence theorem. The analyzed domain is divided into small circular sub-domains to which the LBIE is applied. To approximate\\u000a the unknown physical quantities, nodal points spread over the analyzed

Davoud Mirzaei; Mehdi Dehghan

2010-01-01

247

Parameter Biases Introduced by Approximate Gravitational Waveforms  

NASA Astrophysics Data System (ADS)

The production of the most accurate gravitational waveforms from compact binary mergers require Einstein's equations to be solved numerically, a process far too expensive to produce the ˜10^7 waveforms necessary to estimate the parameters of a measured gravitational wave signal. Instead, parameter estimation depends on approximate or phenomenological waveforms to characterize measured signals. As part of the Ninja collaboration, we study the biases introduced by these methods when estimating the parameters of numerically produced waveforms.

Farr, Benjamin; Coughlin, Scott; Le, John; Skeehan, Connor; Kalogera, Vicky

2013-04-01

248

Approximation methods for stochastic petri nets  

NASA Technical Reports Server (NTRS)

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

Jungnitz, Hauke Joerg

1992-01-01

249

Microscopic justification of the equal filling approximation  

SciTech Connect

The equal filling approximation, a procedure widely used in mean-field calculations to treat the dynamics of odd nuclei in a time-reversal invariant way, is justified as the consequence of a variational principle over an average energy functional. The ideas of statistical quantum mechanics are employed in the justification. As an illustration of the method, the ground and lowest-lying states of some octupole deformed radium isotopes are computed.

Perez-Martin, Sara; Robledo, L. M. [Departamento de Fisica Teorica C-XI, Facultad de Ciencias, Universidad Autonoma de Madrid, 28049 Madrid (Spain)

2008-07-15

250

A DCT Approximation for Image Compression  

Microsoft Academic Search

An orthogonal approximation for the 8-point discrete cosine transform (DCT) is introduced. The proposed transforma- tion matrix contains only zeros and ones; multiplications and bit- shift operations are absent. Close spectral behavior relative to the DCT was adopted as design criterion. The proposed algorithm is superior to the signed discrete cosine transform. It could also out- perform state-of-the-art algorithms in

Renato J. Cintra; Fábio M. Bayer

2011-01-01

251

Approximate black holes for numerical relativity  

NASA Astrophysics Data System (ADS)

Spherically symmetric solutions in Brans-Dicke theory of relativity with a zero coupling constant, ?=0, are derived in the Schwarzschild line element. The solutions are obtained from a cubic transition equation with one small parameter. The exterior space-time of one family of solutions is arbitrarily close to the exterior Schwarzschild space-time, while maintaining global regularity. These nontopological solitons are proposed as candidates for approximate black holes in numerical relativity, particularly for the treatment of horizon boundary conditions.

van Putten, Maurice H. P. M.

1996-11-01

252

Rounded Approximate Step Functions For Interpolation  

NASA Technical Reports Server (NTRS)

Rounded approximate step functions of form x(Sup m)/(x(Sup n) + 1) and 1/(x(Sup n) + 1) useful in interpolating between local steep slopes or abrupt changes in tabulated data varying more smoothly elsewhere. Used instead of polynomial curve fits. Interpolation formulas based on these functions implemented quickly and easily on computers. Used in real-time control computations to interpolate between tabulated data governing control responses.

Nunes, Arthur C., Jr.

1993-01-01

253

Finding polynomials of best approximation with weight  

SciTech Connect

A new iterative method for finding the parameters of polynomials of best approximation with weight in C[-1, 1] is presented. It is based on the representation of the error in the trigonometric form in terms of the phase function. The iterative method of finding the corrections to the phase functions that determine the joint motion of the zeros and the e-points of the error is based on inverse analysis, perturbation theory, and asymptotic formulae for extremal polynomials. Bibliography: 24 titles.

Lebedev, V I [Russian Research Centre 'Kurchatov Institute', Moscow (Russian Federation)

2008-02-28

254

A Stochastic Approximation Method for Reachability Computations  

Microsoft Academic Search

We develop a grid-based method for estimating the probability that the trajectories of a given stochastic system will eventually\\u000a enter a certain target set during a – possibly infinite – look-ahead time horizon. The distinguishing feature of the proposed\\u000a methodology is that it rests on the approximation of the solution to stochastic differential equations by using Markov chains.\\u000a From an

Maria Prandini; Jianghai Hu

255

Improvements of the Discrete Dipole Approximation method  

Microsoft Academic Search

The discrete-dipole approximation (DDA) is a flexible technique for computing\\u000ascattering and absorption by targets of arbitrary geometry. In this paper we\\u000aperform systematic study of various non-stationary iterative (conjugate\\u000agradient) methods in search for the most efficient one in order to solve the\\u000asystem of equations arising in DDA. We document implementation of these methods\\u000ain our public domain

Piotr J. Flatau

2000-01-01

256

Using Approximations to Accelerate Engineering Design Optimization  

NASA Technical Reports Server (NTRS)

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

Torczon, Virginia; Trosset, Michael W.

1998-01-01

257

Quasicrystalline decagonal and related crystalline approximant structures  

SciTech Connect

The icosahedral phase is a condensed phase of matter that has a noncrystallographic point group with long range orientational and translational order but lacks strict periodicity. Periodicity is replaced in all dimensions by a mathematically well defined quasiperiodicity. Two and one dimensional quasicrystals also form in the same metallic-alloy systems as does the icosahedral quasicrystal. The decagonal phase is an example of a two-dimensional quasicrystal that occurs with dicrete one dimensional periodicites of approximately 4 [angstrom] x (1, 2, 3, and 4). The different periodicity decagonal phases are studied with an analytical transmission electron microscope (TEM), using high resolution electron microscopy (HREM), convergent beam electron diffraction (CBED), selected area diffraction (SAD), energy-dispersive x-ray spectroscopy (EDXS), and electron energy-loss spectroscopy (EELS). X-ray powder diffraction studies are also presented. Closely related crystalline structures that approximate well the noncrystallographic symmetries of quasicrystals, were also studied. These crystals also exhibit the same discrete periodicities present in the decagonal phases. The striking similarities between the different periodicity decagonal phases, the icosahedral phase, and the crystalline approximant structures suggest that they all contain similar fundamental atomic clusters. Further, the discrete decagonal periodicities observed suggest that the decagonal structures are formed by different stacking sequences of similar atomic clusters. An atomic model that is based on distorted icosahedrally symmetric clusters that are stacked with different interpenentration depths to form the different periodicity decagonal phases is presented.

Daulton, T.L.

1992-01-01

258

Radiance modelling using the P3 approximation  

NASA Astrophysics Data System (ADS)

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

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

1998-12-01

259

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

260

Structural design utilizing updated, approximate sensitivity derivatives  

NASA Technical Reports Server (NTRS)

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

Scotti, Stephen J.

1993-01-01

261

Discrete-dipole approximation for scattering calculations  

SciTech Connect

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 contiguous spheres. It is shown that, for dielectric materials ([vert bar][ital m][vert bar] [approx lt] 2), the DDA permits calculations of scattering and absorption that are accurate to within a few percent.

Draine, B.T. (Princeton University Observatory, Princeton, New Jersey 08544-1001 (United States)); Flatau, P.J. (Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California 92093-0221 (United States))

1994-04-01

262

Shear viscosity in the postquasistatic approximation  

SciTech Connect

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

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

2010-05-15

263

Approximately diagonalizing matrices over C(Y)  

PubMed Central

Let X be a compact metric space which is locally absolutely retract and let ?: C(X) ? C(Y,Mn) be a unital homomorphism, where Y is a compact metric space with dim Y ? 2. It is proved that there exists a sequence of n continuous maps ?i,m: Y ? X (i = 1,2,…,n) and a sequence of sets of mutually orthogonal rank-one projections {p1,m,p2,m,…,pn,m}?C(Y,Mn) such that This is closely related to the Kadison diagonal matrix question. It is also shown that this approximate diagonalization could not hold in general when dim Y?3.

Lin, Huaxin

2012-01-01

264

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

265

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

266

On asymptotic approximations to entire functions  

NASA Astrophysics Data System (ADS)

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

Avanesyan, Gagik T.

2008-07-01

267

Model approximation of cosmic ray spectrum  

NASA Astrophysics Data System (ADS)

An analytical model which generalizes the equations describing the intensity of galactic cosmic rays (CR), including both processes, making it applicable in the inner heliosphere (where energy losses dominate) and outer heliosphere (influenced primarily by convection-diffusion processes) is derived. By a suitable choice of a parameter, the proposed model turns into two approximations: solution close to "force-field" model (describing the energy losses of CR in the inner heliosphere) and "convection-diffusion" equation (giving the reduction of CR intensity in the outer heliosphere). A mathematical relation between parameters in the proposed model and the modulation parameter ? is derived.

Buchvarova, M.; Velinov, P. I. Y.; Buchvarov, I.

2011-03-01

268

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

269

Fast Approximate Analysis Of Modified Antenna Structure  

NASA Technical Reports Server (NTRS)

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

Levy, Roy

1991-01-01

270

Investigating Material Approximations in Spacecraft Radiation Analysis  

NASA Technical Reports Server (NTRS)

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

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

2011-01-01

271

Sparse deterministic approximation of Bayesian inverse problems  

NASA Astrophysics Data System (ADS)

We present a parametric deterministic formulation of Bayesian inverse problems with an input parameter from infinite-dimensional, separable Banach spaces. In this formulation, the forward problems are parametric, deterministic elliptic partial differential equations, and the inverse problem is to determine the unknown, parametric deterministic coefficients from noisy observations comprising linear functionals of the solution. We prove a generalized polynomial chaos representation of the posterior density with respect to the prior measure, given noisy observational data. We analyze the sparsity of the posterior density in terms of the summability of the input data’s coefficient sequence. The first step in this process is to estimate the fluctuations in the prior. We exhibit sufficient conditions on the prior model in order for approximations of the posterior density to converge at a given algebraic rate, in terms of the number N of unknowns appearing in the parametric representation of the prior measure. Similar sparsity and approximation results are also exhibited for the solution and covariance of the elliptic partial differential equation under the posterior. These results then form the basis for efficient uncertainty quantification, in the presence of data with noise.

Schwab, C.; Stuart, A. M.

2012-04-01

272

Perturbed kernel approximation on homogeneous manifolds  

NASA Astrophysics Data System (ADS)

Current methods for interpolation and approximation within a native space rely heavily on the strict positive-definiteness of the underlying kernels. If the domains of approximation are the unit spheres in euclidean spaces, then zonal kernels (kernels that are invariant under the orthogonal group action) are strongly favored. In the implementation of these methods to handle real world problems, however, some or all of the symmetries and positive-definiteness may be lost in digitalization due to small random errors that occur unpredictably during various stages of the execution. Perturbation analysis is therefore needed to address the stability problem encountered. In this paper we study two kinds of perturbations of positive-definite kernels: small random perturbations and perturbations by Dunkl's intertwining operators [C. Dunkl, Y. Xu, Orthogonal polynomials of several variables, Encyclopedia of Mathematics and Its Applications, vol. 81, Cambridge University Press, Cambridge, 2001]. We show that with some reasonable assumptions, a small random perturbation of a strictly positive-definite kernel can still provide vehicles for interpolation and enjoy the same error estimates. We examine the actions of the Dunkl intertwining operators on zonal (strictly) positive-definite kernels on spheres. We show that the resulted kernels are (strictly) positive-definite on spheres of lower dimensions.

Levesley, J.; Sun, X.

2007-02-01

273

Approximate Bayesian computation in population genetics.  

PubMed Central

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 achieved by fitting a local-linear regression of simulated parameter values on simulated summary statistics, and then substituting the observed summary statistics into the regression equation. The method combines many of the advantages of Bayesian statistical inference with the computational efficiency of methods based on summary statistics. A key advantage of the method is that the nuisance parameters are automatically integrated out in the simulation step, so that the large numbers of nuisance parameters that arise in population genetics problems can be handled without difficulty. Simulation results indicate computational and statistical efficiency that compares favorably with those of alternative methods previously proposed in the literature. We also compare the relative efficiency of inferences obtained using methods based on summary statistics with those obtained directly from the data using MCMC.

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

2002-01-01

274

Electronic structure via potential functional approximations  

NASA Astrophysics Data System (ADS)

The universal functional of Hohenberg and Kohn is given as a coupling-constant integral over the density as a functional of the potential [1]. Conditions are derived under which potential-functional approximations are variational. Construction via this method and imposition of these conditions are shown to greatly improve the accuracy of the non-interacting kinetic energy needed for orbital-free Kohn-Sham calculations. This result provides a direct route to a self-consistent, orbital-free theory for the electronic structure of matter within the Kohn-Sham framework. It solely requires an approximation to the non-interacting density as a functional of the potential, which, so far, has been derived for simple systems [2,3]. [4pt] [1] A. Cangi, D. Lee, P. Elliott, K. Burke, E. K. U. Gross, Phys. Rev. Lett. 106, 236404, (2011).[0pt] [2] A. Cangi, D. Lee, P. Elliott, K. Burke, Phys. Rev. B 81, 235128, (2010).[0pt] [3] P. Elliott, D. Lee, A. Cangi, K. Burke, Phys. Rev. Lett. 100, 256406, (2008).

Cangi, Attila; Lee, Donghyung; Elliott, Peter; Burke, Kieron; Gross, E. K. U.

2012-02-01

275

On some applications of diophantine approximations  

PubMed Central

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 + ?” exponent of irrationality: ?? - p/q? > ?q?-2-? for relatively prime rational integers p,q, with q ? q0 (?, ?). 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].

Chudnovsky, G. V.

1984-01-01

276

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

277

Perturbative approach to the adiabatic approximation  

SciTech Connect

A new and intuitive perturbative approach to time-dependent quantum mechanics problems is presented, which is useful in situations where the evolution of the Hamiltonian is slow. The state of a system which starts in an instantaneous eigenstate of the initial Hamiltonian is written as a power series which has a straightforward diagrammatic representation. Each term of the series corresponds to a sequence of ''adiabatic'' evolutions, during which the system remains in an instantaneous eigenstate of the Hamiltonian, punctuated by transitions from one state to another. The first term of this series is the standard adiabatic evolution, the next is the well known first correction to it, and subsequent terms can be written down essentially by inspection. Although the final result is perhaps not terribly surprising, it seems to not be widely known, and the interpretation is new, as far as we know. Application of the method to the adiabatic approximation is given, and some discussion of the validity of this approximation is presented.

MacKenzie, R. [Physique des Particules, Universite de Montreal, C.P. 6128, Succ. Centre-ville, Montreal, QC H3C 3J7 (Canada); Departement IRO, Universite de Montreal, C.P. 6128, Succ. Centre-ville, Montreal, QC H3C 3J7 (Canada); Marcotte, E.; Paquette, H. [Physique des Particules, Universite de Montreal, C.P. 6128, Succ. Centre-ville, Montreal, QC H3C 3J7 (Canada)

2006-04-15

278

Exact and Approximate Sizes of Convex Datacubes  

NASA Astrophysics Data System (ADS)

In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.

Nedjar, Sébastien

279

An Approximation for the Error of the Normal Approximation to a Linear Combination of Independently Distributed Random Variables  

Microsoft Academic Search

A new approximation introduced elsewhere is employed to approximate the error associated with the central limit approximation. In particular, the respective error obtained on approximating a linear combination of n independently distributed random variables (Sn) is examined, and it is shown that the unstandardized error is approximately independent of n. Two examples, for a discrete and for a continuous Sn,

HAIM SHORE

1988-01-01

280

Animal Models and Integrated Nested Laplace Approximations  

PubMed Central

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

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

2013-01-01

281

Approximate Techniques for Representing Nuclear Data Uncertainties  

SciTech Connect

Computational tools are available to utilize sensitivity and uncertainty (S/U) methods for a wide variety of applications in reactor analysis and criticality safety. S/U analysis generally requires knowledge of the underlying uncertainties in evaluated nuclear data, as expressed by covariance matrices; however, only a few nuclides currently have covariance information available in ENDF/B-VII. Recently new covariance evaluations have become available for several important nuclides, but a complete set of uncertainties for all materials needed in nuclear applications is unlikely to be available for several years at least. Therefore if the potential power of S/U techniques is to be realized for near-term projects in advanced reactor design and criticality safety analysis, it is necessary to establish procedures for generating approximate covariance data. This paper discusses an approach to create applications-oriented covariance data by applying integral uncertainties to differential data within the corresponding energy range.

Williams, Mark L [ORNL; Broadhead, Bryan L [ORNL; Dunn, Michael E [ORNL; Rearden, Bradley T [ORNL

2007-01-01

282

Dark energy from approximate U(1 symmetry  

NASA Astrophysics Data System (ADS)

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

Kim, Jihn E.; Nilles, Hans Peter

2014-03-01

283

Heat flow in the postquasistatic approximation  

SciTech Connect

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

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

2010-08-15

284

An approximate CPHD filter for superpositional sensors  

NASA Astrophysics Data System (ADS)

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

Mahler, Ronald; El-Fallah, Adel

2012-05-01

285

The random phase approximation applied to ice  

NASA Astrophysics Data System (ADS)

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

Macher, M.; Klimeš, J.; Franchini, C.; Kresse, G.

2014-02-01

286

The random phase approximation applied to ice.  

PubMed

Standard density functionals without van der Waals interactions yield an unsatisfactory description of ice phases, specifically, high density phases occurring under pressure are too unstable compared to the common low density phase Ih observed at ambient conditions. Although the description is improved by using functionals that include van der Waals interactions, the errors in relative volumes remain sizable. Here we assess the random phase approximation (RPA) for the correlation energy and compare our results to experimental data as well as diffusion Monte Carlo data for ice. The RPA yields a very balanced description for all considered phases, approaching the accuracy of diffusion Monte Carlo in relative energies and volumes. This opens a route towards a concise description of molecular water phases on surfaces and in cavities. PMID:24588180

Macher, M; Klimeš, J; Franchini, C; Kresse, G

2014-02-28

287

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

288

Accelerated convergence for synchronous approximate agreement  

NASA Technical Reports Server (NTRS)

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

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

1988-01-01

289

Optimal approximation algorithms for digital filter design  

NASA Astrophysics Data System (ADS)

Several new algorithms are presented for the optimal approximation and design of various classes of digital filters. An iterative algorithm is developed for the efficient design of unconstrained and constrained infinite impulse response (IIR) digital filters. Both in the unconstrained and constrained cases, the numerator and denominator of the filter transfer function are designed iteratively by recourse to the Remez algorithm and to appropriate design parameters and criteria, at each iteration. This makes it possible for the algorithm to be implemented by means of a short main program which uses (at each iteration) the linear phase FIR filter design algorithm of McClellan et al. as a subroutine. The approach taken also permits the filter to be designed with a desired ripple ratio. Also, the algorithm determines automatically the minimum passband ripple corresponding to the prescribed orders and band edges of the filter. The filter is designed directly without guessing the passband ripple or stopband ripple.

Liang, J. K.

290

Spline Approximation of Thin Shell Dynamics  

NASA Technical Reports Server (NTRS)

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

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

1996-01-01

291

Sivers function in the quasiclassical approximation  

NASA Astrophysics Data System (ADS)

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

Kovchegov, Yuri V.; Sievert, Matthew D.

2014-03-01

292

Magnetic reconnection under anisotropic magnetohydrodynamic approximation  

NASA Astrophysics Data System (ADS)

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

Hirabayashi, K.; Hoshino, M.

2013-11-01

293

Approximate maximum likelihood decoding of block codes  

NASA Technical Reports Server (NTRS)

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

Greenberger, H. J.

1979-01-01

294

The Bloch Approximation in Periodically Perforated Media  

SciTech Connect

We consider a periodically heterogeneous and perforated medium filling an open domain {omega} of R{sup N}. Assuming that the size of the periodicity of the structure and of the holes is O({epsilon}),we study the asymptotic behavior, as {epsilon} {sup {yields}} 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in {omega}{sup {epsilon}}({omega}{sup {epsilon}} being {omega} minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and the first Bloch eigenfunction. We first consider the case where {omega}is R{sup N} and then localize the problem for abounded domain {omega}, considering a homogeneous Dirichlet condition on the boundary of {omega}.

Conca, C. [Departamento de Ingenieria Matematica and CMM, UMI 2807, CNRS-U, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Casilla 170/3 - Correo 3, Santiago (Chile)], E-mail: cconca@dim.uchile.cl; Gomez, D., E-mail: gomezdel@unican.es; Lobo, M. [Departamento de Matematicas, Estadistica y Computacion, Universidad de Cantabria, Av. de los Castros s/n, 39071 Santander (Spain)], E-mail: lobom@unican.es; Perez, E. [Departamento de Matematica Aplicada y Ciencias de la Computacion, Universidad de Cantabria, Av. de los Castros s/n, 39071 Santander (Spain)], E-mail: meperez@unican.es

2005-06-15

295

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

296

The Guarding Problem - Complexity and Approximation  

NASA Astrophysics Data System (ADS)

Let G = (V, E) be the given graph and G R = (V R ,E R ) and G C = (V C ,E C ) be the sub graphs of G such that V R ? V C = ? and V R ? V C = V. G C is referred to as the cops region and G R is called as the robber region. Initially a robber is placed at some vertex of V R and the cops are placed at some vertices of V C . The robber and cops may move from their current vertices to one of their neighbours. While a cop can move only within the cops region, the robber may move to any neighbour. The robber and cops move alternatively. A vertex v ? V C is said to be attacked if the current turn is the robber's turn, the robber is at vertex u where u ? V R , (u,v) ? E and no cop is present at v. The guarding problem is to find the minimum number of cops required to guard the graph G C from the robber's attack. We first prove that the decision version of this problem when G R is an arbitrary undirected graph is PSPACE-hard. We also prove that the complexity of the decision version of the guarding problem when G R is a wheel graph is NP-hard. We then present approximation algorithms if G R is a star graph, a clique and a wheel graph with approximation ratios H(n 1), 2 H(n 1) and left( H(n1) + 3/2 right) respectively, where H(n1) = 1 + 1/2 + ... + 1/n1 and n 1 = ? V R ?.

Reddy, T. V. Thirumala; Krishna, D. Sai; Rangan, C. Pandu

297

Methodology for approximating and implementing fixed-point approximations of cosines for order-16 DCT  

NASA Astrophysics Data System (ADS)

Spatial transformations whose kernels employ sinusoidal functions for the decorrelation of signals remain as fundamental components of image and video coding systems. Practical implementations are designed in fixed precision for which the most challenging task is to approximate these constants with values that are both efficient in terms of complexity and accurate with respect to their mathematical definitions. Scaled architectures, for example, as used in the implementations of the order-8 Discrete Cosine Transform and its corresponding inverse both specified in ISO/IEC 23002-2 (MPEG C Pt. 2), can be utilized to mitigate the complexity of these approximations. That is, the implementation of the transform can be designed such that it is completed in two stages: 1) the main transform matrix in which the sinusoidal constants are roughly approximated, and 2) a separate scaling stage to further refine the approximations. This paper describes a methodology termed the Common Factor Method, for finding fixed-point approximations of such irrational values suitable for use in scaled architectures. The order-16 Discrete Cosine Transform provides a framework in which to demonstrate the methodology, but the methodology itself can be employed to design fixed-point implementations of other linear transformations.

Hinds, Arianne T.

2011-09-01

298

Approximation properties of the poles of diagonal Pade approximants for certain generalizations of Markov functions  

SciTech Connect

A non-linear system of differential equations ('generalized Dubrovin system') is obtained to describe the behaviour of the zeros of polynomials orthogonal on several intervals that lie in lacunae between the intervals. The same system is shown to describe the dynamical behaviour of zeros of this kind for more general orthogonal polynomials: the denominators of the diagonal Pade approximants of meromorphic functions on a real hyperelliptic Riemann surface. On the basis of this approach several refinements of Rakhmanov's results on the convergence of diagonal Pade approximants for rational perturbations of Markov functions are obtained.

Suetin, S P [V.A. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2002-12-31

299

Optimal Approximation Algorithms for Digital Filter Design.  

NASA Astrophysics Data System (ADS)

Several new algorithms are presented for the optimal approximation and design of various classes of digital filters. An iterative algorithm is developed for the efficient design of unconstrained and constrained infinite impulse response (IIR) digital filters. Both in the unconstrained and constrained cases, the numerator and denominator of the filter transfer function are designed iteratively by recourse to the Remez algorithm and to appropriate design parameters and criteria, at each iteration. This makes it possible for the algorithm to be implemented by means of a short main program which uses (at each iteration) the linear phase FIR filter design algorithm of McClellan et al. as a subroutine. The approach taken also permits the filter to be designed with a desired ripple ratio. Also, the algorithm determines automatically the minimum passband ripple corresponding to the prescribed orders and band edges of the filter. The filter is designed directly without guessing the passband ripple or stopband ripple. Another algorithm, based on similar principles, is developed for the design of a nonlinear phase finite impulse response (FIR) filter, whose transfer function optimally approximates a desired magnitude response, there being no constraints imposed on the phase response. A similar algorithm is presented for the design of two new classes of FIR digital filters, one linear phase and the other nonlinear phase. A filter of either class has significantly reduced number of multiplications compared to the one obtained by its conventional counterpart, with respect to a given frequency response. In the case of linear phase, by introducing the new class of digital filters into the design of multistage decimators and interpolators for narrow-band filter implementation, it is found that an efficient narrow-band filter requiring considerably lower multiplication rate than the conventional linear phase FIR design can be obtained. The amount of data storage required by the new class of nonlinear phase FIR filters is significantly less than its linear phase counterpart. Finally, the design of a (finite-impulse-response) FIR digital filter with some of the coefficients constrained to zero is formulated as a linear programming (LP) problem and the LP technique is then used to design this class of constrained FIR digital filters. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI.

Liang, Junn-Kuen

300

Improved Discrete Approximation of Laplacian of Gaussian  

NASA Technical Reports Server (NTRS)

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

Shuler, Robert L., Jr.

2004-01-01

301

Magnetic stability under the magnetostrophic approximation  

NASA Astrophysics Data System (ADS)

We determine the stability of s- and z-dependent basic fields under the magnetostrophic approximation in a cylindrical geometry. The geostrophic flow VG is the dominant nonlinearity in the nonlinear regime. This work assesses the impact of the geostrophic flow at critical linear stability ?= ?c by imposing VG as a differential rotation. Here, the Elsasser number ? is the appropriate nondimensional measure of imposed field strength. Fearn et al. [Fearn, D.R., Lamb, C.J., McLean, D.R., Ogden, R.R., 1997. The influence of differential rotation on magnetic instability and nonlinear magnetic instability in the magnetostrophic limit. Geophys. Astrophys. Fluid Dyn. 86, 173-200] showed that for simple s-dependent basic fields, certain imposed differential rotations could lower ?c. McLean and Fearn [McLean, D.R., Fearn, D.R., 1999. The geostrophic nonlinearity and its effect on magnetic instability. Geophys. Astrophys. Fluid Dyn., In Press.] then showed that the geostrophic flow-induced subcritical behaviour in the most unstable mode for various combinations of basic fields and aspect ratios. Here, both linear and nonlinear results are new; previous analyses only considered radially ( s-)dependent basic fields. We will derive a consistency condition necessary for the existence of solutions before investigating whether subcriticality exists under a dipolar basic field configuration.

McLean, Douglas R.; Fearn, David R.; Hollerbach, Rainer

1999-02-01

302

Approximate von Neumann entropy for directed graphs  

NASA Astrophysics Data System (ADS)

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

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

2014-05-01

303

Approximate Methods for State-Space Models  

PubMed Central

State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace’s method, an asymptotic series expansion, to approximate the state’s conditional mean and variance, together with a Gaussian conditional distribution. This Laplace-Gaussian filter (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data. We find that the LGF can deliver superior results in a small fraction of the computing time.

Perez-Bolde, Lucia Castellanos; Shalizi, Cosma Rohilla; Kass, Robert E.

2011-01-01

304

Magnetic reconnection under anisotropic magnetohydrodynamic approximation  

SciTech Connect

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

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

2013-11-15

305

Configuring Airspace Sectors with Approximate Dynamic Programming  

NASA Technical Reports Server (NTRS)

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

Bloem, Michael; Gupta, Pramod

2010-01-01

306

Grover's quantum search algorithm and Diophantine approximation  

SciTech Connect

In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O({radical}(N)) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using iterations of Grover's basic step only, and no other algorithm. Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m<2{radical}(N)/({radical}(K)-{radical}(M)) obtains. This bound reproduces previous results based on more elaborate algorithms, and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.

Dolev, Shahar; Pitowsky, Itamar; Tamir, Boaz [Edelstein Center, Levi Building, The Hebrew University, Givat Ram, Jerusalem (Israel); Department of Philosophy of Science, Bar-Ilan University, Ramat-Gan (Israel)

2006-02-15

307

Multilayer Perceptrons to Approximate Quaternion Valued Functions.  

PubMed

In this paper a new type of multilayer feedforward neural network is introduced. Such a structure, called hypercomplex multilayer perceptron (HMLP), is developed in quaternion algebra and allows quaternionic input and output signals to be dealt with, requiring a lower number of neurons than the real MLP, thus providing a reduced computational complexity. The structure introduced represents a generalization of the multilayer perceptron in the complex space (CMLP) reported in the literature. The fundamental result reported in the paper is a new density theorem which makes HMLPs universal interpolators of quaternion valued continuous functions. Moreover the proof of the density theorem can be restricted in order to formulate a density theorem in the complex space. Due to the identity between the quaternion and the four-dimensional real space, such a structure is also useful to approximate multidimensional real valued functions with a lower number of real parameters, decreasing the probability of being trapped in local minima during the learning phase. A numerical example is also reported in order to show the efficiency of the proposed structure. Copyright 1997 Elsevier Science Ltd. All Rights Reserved. PMID:12662531

Xibilia, M G.; Muscato, G; Fortuna, L; Arena, P

1997-03-01

308

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

2011-09-01

309

Rainbows: Mie computations and the Airy approximation.  

PubMed

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

Wang, R T; van de Hulst, H C

1991-01-01

310

Geometric video approximation using weighted matching pursuit.  

PubMed

In recent years, works on geometric multidimensional signal representations have established a close relation with signal expansions on redundant dictionaries. For this purpose, matching pursuits (MP) have shown to be an interesting tool. Recently, most important limitations of MP have been underlined, and alternative algorithms like weighted-MP have been proposed. This work explores the use of weighted-MP as a new framework for motion-adaptive geometric video approximations. We study a novel algorithm to decompose video sequences in terms of few, salient video components that jointly represent the geometric and motion content of a scene. Experimental coding results on highly geometric content reflect how the proposed paradigm exploits spatio-temporal video geometry. Two-dimensional weighted-MP improves the representation compared to those based on 2-D MP. Furthermore, the extracted video components represent relevant visual structures with high saliency. In an example application, such components are effectively used as video descriptors for the joint audio-video analysis of multimedia sequences. PMID:19389695

Divorra Escoda, Oscar; Monaci, Gianluca; Figueras I Ventura, Rosa M; Vandergheynst, Pierre; Bierlaire, Michel

2009-08-01

311

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

Microsoft Academic Search

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

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

2005-01-01

312

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

313

Gaussian Variational Approximate Inference for Generalized Linear Mixed Models  

Microsoft Academic Search

Variational approximation methods have become a mainstay of contemporary machine learning methodology, but currently have little presence in statistics. We devise an effective variational approximation strategy for fitting generalized linear mixed models (GLMMs) appropriate for grouped data. It involves Gaussian approximation to the distributions of random effects vectors, conditional on the responses. We show that Gaussian variational approximation is a

J. T. Ormerod; M. P. Wand

2012-01-01

314

Automated Discovery of Numerical Approximation Formulae via Genetic Programming  

Microsoft Academic Search

This paper describes the use of genetic programming to automate the discovery of numerical approximation formulae. The authors present results involving rediscovery of known approximations for Harmonic numbers and discovery of rational polynomial approximations for functions of one or more variables, the latter of which are compared to Padé approximations obtained through a symbolic mathematics package. For functions of a

Matthew J. Streeter; Lee A. Becker

2003-01-01

315

Constructive Heterogeneous Object Modeling Using Signed Approximate Real Distance Functions  

Microsoft Academic Search

We introduce a smooth approximation of the min \\/ max operations, called SARDF (Signed Approximate Real Distance Function), for maintaining an approximate signed distance function in constructive shape modeling. We apply constructive distance-based shape modeling to design objects with heterogeneous material distribution in the constructive hypervolume model framework. The introduced distance approximation helps intuitively model material distributions parameterized by distances

Pierre-Alain Fayolle; Alexander Pasko; Benjamin Schmitt; Nikolay Mirenkov

2006-01-01

316

A Proof Theory for Tractable Approximations of Propositional Reasoning  

Microsoft Academic Search

. This paper proposes an uniform framework for the prooftheory of tractable approximations of propositional reasoning. The keyidea is the introduction of approximate proofs. This makes possible thedevelopment of an approximating sequent calculus for propositional deductionwhere proofs can be sound, complete or multi-directional approximationsof classical logic. We show how this calculus subsumes existingapproaches to approximation such as the BCP \\\\Gamma

Fabio Massacci

1997-01-01

317

A comparison of approximate interval estimators for the Bernoulli parameter  

NASA Technical Reports Server (NTRS)

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

Leemis, Lawrence; Trivedi, Kishor S.

1993-01-01

318

Testing approximations for non-linear gravitational clustering  

NASA Technical Reports Server (NTRS)

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.

1993-01-01

319

Comparison between Beta Wavelets Neural Networks, RBF Neural Networks and Polynomial Approximation for 1D, 2D Functions Approximation  

Microsoft Academic Search

This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn ? R from scattered samples (xi; y = f(xi))

Wajdi Bellil; Chokri Ben Amar; Adel M. Alimi

2005-01-01

320

Approximate nearest neighbors via dictionary learning  

NASA Astrophysics Data System (ADS)

Approximate Nearest Neighbors (ANN) in high dimensional vector spaces is a fundamental, yet challenging problem in many areas of computer science, including computer vision, data mining and robotics. In this work, we investigate this problem from the perspective of compressive sensing, especially the dictionary learning aspect. High dimensional feature vectors are seldom seen to be sparse in the feature domain; examples include, but not limited to Scale Invariant Feature Transform (SIFT) descriptors, Histogram Of Gradients, Shape Contexts, etc. Compressive sensing advocates that if a given vector has a dense support in a feature space, then there should exist an alternative high dimensional subspace where the features are sparse. This idea is leveraged by dictionary learning techniques through learning an overcomplete projection from the feature space so that the vectors are sparse in the new space. The learned dictionary aids in refining the search for the nearest neighbors to a query feature vector into the most likely subspace combination indexed by its non-zero active basis elements. Since the size of the dictionary is generally very large, distinct feature vectors are most likely to have distinct non-zero basis. Utilizing this observation, we propose a novel representation of the feature vectors as tuples of non-zero dictionary indices, which then reduces the ANN search problem into hashing the tuples to an index table; thereby dramatically improving the speed of the search. A drawback of this naive approach is that it is very sensitive to feature perturbations. This can be due to two possibilities: (i) the feature vectors are corrupted by noise, (ii) the true data vectors undergo perturbations themselves. Existing dictionary learning methods address the first possibility. In this work we investigate the second possibility and approach it from a robust optimization perspective. This boils down to the problem of learning a dictionary robust to feature perturbations, viz. paving the way for a novel Robust Dictionary Learning (RDL) framework. In addition to the above model, we also propose a novel LASSO based multi-regularization hashing algorithm which utilizes the consistency properties of the non-zero active basis for increasing values of the regularization weights. Even though our algorithm is generic and has wide coverage in different areas of scientific computing, the experiments in the current work are mainly focused towards improving the speed and accuracy of ANN for SIFT descriptors, which are high-dimensional (128D) and are one of the most widely used interest point detectors in computer vision. Preliminary results from SIFT datasets show that our algorithm is far superior to the state-of-the-art techniques in ANN.

Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos

2011-05-01

321

Differential equation based method for accurate approximations in optimization  

NASA Technical Reports Server (NTRS)

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

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

322

Approximating Action-Value Functions: Addressing Issues of Dynamic Range.  

National Technical Information Service (NTIS)

Function approximation is necessary when applying RL to either Markov decision processes (MDPs) or semi-Markov decision processes (SMDPs) with very large state spaces. An often overlooked issue in approximating Q-functions in either framework arises when ...

M. E. Harmon

1998-01-01

323

Classical Ionic Fluids in the Mean Spherical Approximation.  

National Technical Information Service (NTIS)

The recently obtained analytical solution of the mean spherical approximation (MSA) has been used to calculate thermodynamic and structural properties of aqueous solutions of symmetric as well as of asymmetric electrolytes. The same approximation has been...

R. Triolo A. M. Floriano

1980-01-01

324

Successive Approximation of Solutions of Molodensky'S Basic Integral Equation.  

National Technical Information Service (NTIS)

The report is concerned with the successive approximation of the solutions of linear integral equations by electronic computers. An application is given by the approximation of Molodensky's basic integral equation. By a mathematical model Molodensky's sol...

K. R. Koch

1967-01-01

325

On the Vainshtein Approximation for Electron-Atom Collisions.  

National Technical Information Service (NTIS)

The Vainshtein approximation for electron-atom collisions may be based on either the post or the prior wave function. Both versions involve a supplementary peaking approximation. In using the prior function Vainshtein and his colleagues introduced an arbi...

D. S. F. Crothers

1967-01-01

326

Difference equation state approximations for nonlinear hereditary control problems  

NASA Technical Reports Server (NTRS)

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

Rosen, I. G.

1982-01-01

327

Automatic Approximation for the Verification of Cryptographic Protocols  

Microsoft Academic Search

\\u000a This paper presents an approximation function developed for the verification of cryptographic protocols. The main properties\\u000a of this approximation are that it can be build automatically and its computation is guaranteed to terminate unlike Genet and\\u000a Klay’s algorithm. This approximation has been used for the verification of the Needham-Schroeder, Otway-Rees and Woo Lam protocols.\\u000a To be more precise, the approximation

Frédéric Oehl; Gérard Cécé; Olga Kouchnarenko; David Sinclair

2002-01-01

328

Projected equation methods for approximate solution of large linear systems  

NASA Astrophysics Data System (ADS)

We consider linear systems of equations and solution approximations derived by projection on a low-dimensional subspace. We propose stochastic iterative algorithms, based on simulation, which converge to the approximate solution and are suitable for very large-dimensional problems. The algorithms are extensions of recent approximate dynamic programming methods, known as temporal difference methods, which solve a projected form of Bellman's equation by using simulation-based approximations to this equation, or by using a projected value iteration method.

Bertsekas, Dimitri P.; Yu, Huizhen

2009-05-01

329

Pade approximation for stochastic discrete-event systems  

Microsoft Academic Search

We show that Pade approximation can be effectively used for approximation of performance functions in discrete-event systems. The method is (1) obtaining the MacLaurin coefficients of the performance function and (2) finding a Pade approximant from the MacLaurin coefficients and use it to approximate the function. We use the method with the expected number of renewals in a random interval,

Wei-Bo Gong; S. Nananukul; A. Yan

1995-01-01

330

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

331

A Modal Logic for Multiple-Source Tolerance Approximation Spaces  

NASA Astrophysics Data System (ADS)

Notions of lower and upper approximations are proposed for multiple-source tolerance approximation spaces which consist of a number of tolerance relations over the same domain. A modal logic is proposed for reasoning about the defined notions of approximations. A sound and complete deductive system for the logic is presented. Decidability is also proved.

Khan, Md. Aquil; Ma, Minghui

332

Simple approximate solutions to continuous-time-random-walk transport  

Microsoft Academic Search

This paper presents a procedure for obtaining simple approximate solutions to the continuous-time random walk (CTRW) as it applies to charge transport in amorphous materials. Application of this procedure to a particularly simple trial function leads to an approximate solution that is in excellent agreement with the exact solution for the case in which it is known. The approximate solutions

F. B. McLean; G. A. Ausman

1976-01-01

333

Factorized variational approximations for acoustic multi source localization  

Microsoft Academic Search

Estimation based on received signal strength (RSS) is crucial in sensor networks for sensor localization, target tracking, etc. In this paper, we present a Gaussian approximation of the Chi distribution that is applicable to general RSS source localization problems in sensor networks. Using our Gaussian approximation, we provide a factorized variational Bayes (VB) approximation to the location and power posterior

Volkan Cevher; Aswin C. Sankaranarayanan; Rama Chellappa

2008-01-01

334

The Use of Approximations in a High School Chemistry Course  

ERIC Educational Resources Information Center

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

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

2009-01-01

335

Parametric generalized singular perturbation approximation for model order reduction  

Microsoft Academic Search

A new model reduction technique for the approximation of balanced realization is introduced. The method involves a further generalization of the generalized singular perturbation approximation by adding several parameters that can be tuned according to a specified performance criterion. An a priori bound can be computed guaranteeing the quality of the approximated model in the whole range of parameter variations.

Giovanni Muscato

2000-01-01

336

Self-Consistent Approximations in Many-Body Systems  

Microsoft Academic Search

This paper investigates the criteria for maintenance of the macroscopic conservation laws of number, momentum, and energy by approximate two-particle correlation functions in many-body systems. The methods of generating such approximations are the same as in a previous paper. However, the derivations of the conservation laws given here clarify both why the approximation method works and the connection between the

Gordon Baym

1962-01-01

337

Least Squares Quadratic (LSQ) Approximation to Lognormal Sum Distributions  

Microsoft Academic Search

In this paper, least squares (LS) approximation approach is used to solve the approximation problem of a sum of lognormal random variables. It is shown that least squares quadratic (LSQ) approximation exhibits an excellent match with the simulation results in a wide range of the distributions of the summands. Using the coefficients obtained from the LSQ method, closed-form expressions for

Lian Zhao; Jiu Ding

2006-01-01

338

A Strict Approach to Approximating Lognormal Sum Distributions  

Microsoft Academic Search

In this paper, the least squares (LS) approximation approach is applied to solve the approximation problem of a sum of lognormal random variables (RV). The least squares curve fitting technique is first used to obtain the approximated closed-form pdf of the sum RV. The second time use of the least squares curve fitting technique brings the explicit closed-form expressions of

Lian Zhao; Jiu Ding

2006-01-01

339

Approximation Refinement for Interpolation-Based Model Checking  

Microsoft Academic Search

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

Vijay D’Silva; Mitra Purandare; Daniel Kroening

2008-01-01

340

Accurate Approximations for Posterior Moments and Marginal Densities  

Microsoft Academic Search

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

Luke Tierney; Joseph B. Kadane

1986-01-01

341

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials  

NASA Technical Reports Server (NTRS)

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

Freund, Roland

1989-01-01

342

The MVA Pre-empt resume priority approximation  

Microsoft Academic Search

A Mean Value Analysis (MVA) approximation is presented for computing the average performance measures of closed multiclass queueing networks containing non pre-emptive Head Of Line (HOL) and Pre-empt Resume (PR) priority centers. The approximation has the same storage and computational requirements as MVA thus allowing computationally efficient solutions of large priority queueing networks. The accuracy of the MVA PR approximation

Raymond M. Bryant; Anthony E. Krzesinski; Peter Teunissen

1983-01-01

343

Numerical approximations of the Sommerfeld integral for fast convergence  

Microsoft Academic Search

Several approximation techniques for the Hertz potential of an inf'mitesimal dipole in the presence of a conducting half space are presented. The formal solutions obtained by rigorous mathematical procedures are transformed, with the aid of some approximation, to fast convergent forms. The approximation techniques are different depending on the media where the observer and source are located. All results calculated

W. C. Kuo; K. K. Mei

1978-01-01

344

Reachability Analysis of Nonlinear Systems Using Conservative Approximation  

Microsoft Academic Search

In this paper we present an approach to approximate reacha- bility computation for nonlinear continuous systems. Rather than study- ing a complex nonlinear system ? x = g(x), we study an approximating system ? x = f(x) which is easier to handle. The class of approximating systems we consider in this paper is piecewise linear, obtained by inter- polating g

Eugene Asarin; Thao Dang; Antoine Girard

2003-01-01

345

Two point exponential approximation method for structural optimization  

NASA Technical Reports Server (NTRS)

This paper examines various first order approximation methods commonly used in structural optimization. It considers several attempts at improving the approximation by using previous analytical results and introduces an adaptation of a first order approximation method using an exponent adjusted to better fit the constraints and reduce the overall number of iterations needed to attain the optimum.

Fadel, G. M.; Riley, M. F.; Barthelemy, J. M.

1990-01-01

346

ALGORITHMS FOR SIMULTANEOUS SPARSE APPROXIMATION PART I: GREEDY PURSUIT  

Microsoft Academic Search

A simultaneous sparse approximation problem requests a good approximation of several input signals at once using dierent linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals that participate. These elementary signals typically model coherent structures in the input signals, and they are chosen from

JOEL A. TROPP; ANNA C. GILBERT; MARTIN J. STRAUSS

2004-01-01

347

Model reduction of delay systems using Pade approximants  

Microsoft Academic Search

This paper describes the rational approximation of a certain class of delay systems in the frequency domain using Pad£ approximants of exp(?sT). Three classes of approximants characterized by their relative degrees are considered. Easily computable a priori L? and L L2error bounds are provided.

JAMES LAM

1993-01-01

348

An analogue of Fabry's theorem for generalized Pade approximants  

SciTech Connect

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

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

2009-08-31

349

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

NASA Technical Reports Server (NTRS)

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

Barth, Timothy J.; Larson, Mats G.

2000-01-01

350

Simpler and better approximation algorithms for network design  

Microsoft Academic Search

We give simple and easy-to-analyze randomized approximation algorithms for several well-studied NP-hard network design problems. Our algorithms improve over the previously best known approximation ratios. Our main results are the following.We give a randomized 3.55-approximation algorithm for the connected facility location problem. The algorithm requires three lines to state, one page to analyze, and improves the best-known performance guarantee for

Anupam Gupta; Amit Kumar; Tim Roughgarden

2003-01-01

351

Partially Coherent Scattering in Stellar Chromospheres. IV. Analytic Wing Approximations  

NASA Astrophysics Data System (ADS)

Simple analytic expressions are derived to understand resonance-line wings in stellar chromospheres and similar astrophysical plasmas The results are approximate, but compare well with accurate numerical simulations. The redistribution is modeled using an extension of the partially coherent scattering approximation (PCS) which we term the comoving-frame partially coherent scattering approximation (CPCS). The distinction is made here because Doppler diffusion is included in the coherent/noncoherent decomposition, in a form slightly improved from the earlier papers in this series.

Gayley, K. G.

1993-10-01

352

Quantitative Fourier analysis of approximation techniques. I. Interpolators and projectors  

Microsoft Academic Search

We present a general Fourier-based method that provides an accurate prediction of the approximation error as a function of the sampling step T. Our formalism applies to an extended class of convolution-based signal approximation techniques, which includes interpolation, generalized sampling with prefiltering, and the projectors encountered in wavelet theory. We claim that we can predict the L2-approximation error by integrating

Thierry Blu; Michael Unser

1999-01-01

353

Explanation for Malischewsky's approximate expression for the Rayleigh wave velocity.  

PubMed

An approach for obtaining approximations of the Rayleigh wave velocity created by the principle of least squares is introduced. In view of this approach, Malischewsky's approximation of the Rayleigh wave velocity for Poisson ratios v in the set of [-1, 0.5] proposed quite recently is explained. It is shown that Malischewsky's approximation obtained by trial and error is (almost) identical with the one established by this approach. PMID:16919306

Vinh, Pham Chi; Malischewsky, Peter G

2006-12-01

354

Hardware Implementation Trade-Offs of Polynomial Approximations and Interpolations  

Microsoft Academic Search

This paper examines the hardware implementation trade-offs when evaluating functions via piecewise polynomial approximations and interpolations for precisions of up to 24 bits. In polynomial approximations, polynomials are evaluated using stored coefficients. Polynomial interpolations, however, require the coefficients to be computed on-the-fly by using stored function values. Although it is known that interpolations require less memory than approximations, but at

Dong-u Lee; Ray C. C. Cheung; Wayne Luk; John D. Villasenor

2008-01-01

355

A piecewise linear approximation scheme for hereditary optimal control problems  

NASA Technical Reports Server (NTRS)

An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.

Cliff, E. M.; Burns, J. A.

1977-01-01

356

Efficient approximation of min set cover by moderately exponential algorithms  

Microsoft Academic Search

We study the approximation of min set cover combining ideas and results from polynomial approximation and from exact computation (with non-trivial worst case complexity upper bounds) for NP-hard problems. We design approximation algorithms for min set cover achieving ratios that cannot be achieved in polynomial time (unless problems in NP could be solved by slightly super-polynomial algorithms) with worst-case complexity much

Nicolas Bourgeois; Bruno Escoffier; Vangelis Th. Paschos

2009-01-01

357

The Convergence of Padé Approximants to Functions with Branch Points  

Microsoft Academic Search

Padé approximants are a natural generalization ofTaylor polynomials; however instead of polynomials now rationalfunctions are used for the development of a given function.In this article the convergence in capacity of Padé approximants[m\\/n] withm+n??,m\\/n?1,is investigated. Two types of assumptions are considered: Inthe first case the functionfto be approximated has to haveall its singularities in a compact setE?C of capacityzero (the function

Herbert Stahl

1997-01-01

358

Differential equation based method for accurate approximations in optimization  

NASA Technical Reports Server (NTRS)

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

Pritchard, Jocelyn I.; Adelman, Howard M.

1990-01-01

359

13. BUILDING #5, HOSPITAL, RENDERING OF EAST ELEVATION, APPROXIMATELY 1946 ...  

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

13. BUILDING #5, HOSPITAL, RENDERING OF EAST ELEVATION, APPROXIMATELY 1946 - Sioux Falls Veterans Administration Medical & Regional Office Center, 2501 West Twenty-second, Sioux Falls, Minnehaha County, SD

360

Legendre-tau approximations for functional differential equations  

NASA Technical Reports Server (NTRS)

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

Ito, K.; Teglas, R.

1986-01-01

361

Sensitivity analysis and approximation methods for general eigenvalue problems  

NASA Technical Reports Server (NTRS)

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

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

1986-01-01

362

How to Solve Schroedinger Problems by Approximating the Potential Function  

SciTech Connect

We give a survey over the efforts in the direction of solving the Schroedinger equation by using piecewise approximations of the potential function. Two types of approximating potentials have been considered in the literature, that is piecewise constant and piecewise linear functions. For polynomials of higher degree the approximating problem is not so easy to integrate analytically. This obstacle can be circumvented by using a perturbative approach to construct the solution of the approximating problem, leading to the so-called piecewise perturbation methods (PPM). We discuss the construction of a PPM in its most convenient form for applications and show that different PPM versions (CPM,LPM) are in fact equivalent.

Ledoux, Veerle [Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Krijgslaan 281-S9, B-9000 Gent (Belgium); Van Daele, Marnix [Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Krijgslaan 281-S9, B-9000 Gent (Belgium)

2010-09-30

363

Approximation of Loop Subdivision Surfaces for Fast Rendering.  

PubMed

This paper describes an approach to the approximation of Loop subdivision surfaces for real-time rendering. The approach consists of two phases which separately construct the approximation geometry and the normal field of a subdivision surface. It firstly exploits quartic triangular Bézier patches to approximate the geometry of the subdivision surface by interpolating a grid of sampled points. To remedy the artifact of discontinuity of normal fields between adjacent patches, a continuous normal field is then reconstructed by approximating the tangent vector fields of the subdivision surfaces with quartic triangular Bézier patches. For regular triangles, the approach reproduces the associated subdivision patches, quartic 3-directional box splines. PMID:20513928

Li, Guiqing; Ren, Canjiang; Zhang, Jiahua; Ma, Weiyin

2010-05-26

364

Adiabatic approximation in PT-symmetric quantum mechanics  

NASA Astrophysics Data System (ADS)

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

Guo, ZhiHua; Cao, HuaiXin; Lu, Ling

2014-05-01

365

Approximate implicit solution of a Lane-Emden equation  

NASA Astrophysics Data System (ADS)

In this paper, we obtain an approximate implicit solution admitted by the Lane-Emden equation y? + (2/ x) y' + ey = 0 describing the dimensionless density distribution in an isothermal gas sphere. The new approximate implicit solution has a larger radius of convergence than the power series solution. This is achieved by reducing the Lane-Emden equation to first-order using Lie group analysis and determining a power series solution of the reduced equation. The power series solution of the reduced equation transforms into an approximate implicit solution of the original equation. The approximate implicit solution diverges from the power series solution in the radius of convergence.

Momoniat, E.; Harley, C.

2006-05-01

366

Pointwise approximation by Bézier variant of integrated MKZ operators  

NASA Astrophysics Data System (ADS)

In this paper the pointwise approximation of Bézier variant of integrated MKZ operators for general bounded functions is studied. Two estimate formulas of this type approximation are obtained. The approximation of functions of bounded variation becomes a special case of the main result of this paper. In the case of functions of bounded variation, Theorem B of the paper corrects the mistake of Theorem 1 of the article [V. Gupta, Degree of approximation to functions of bounded variation by Bézier variant of MKZ operators, J. Math. Anal. Appl. 289 (2004) 292-300].

Zeng, Xiao-Ming

2007-12-01

367

New approximations for elastic spheres under an oscillating torsional couple.  

SciTech Connect

The Lubkin solution for two spheres pressed together and then subjected to a monotonically increasing axial couple is examined numerically. The Deresiewicz asymptotic solution is compared to the full solution and its utility is evaluated. Alternative approximations for the Lubkin solution are suggested and compared. One approximation is a Pade rational function which matches the analytic solution over all rotations. The other is an exponential approximation that reproduces the asymptotic values of the analytic solution at infinitesimal and infinite rotations. Finally, finite element solutions for the Lubkin problem are compared with the exact and approximate solutions.

Heinstein, Martin Wilhelm; Segalman, Daniel Joseph; Starr, Michael James

2004-05-01

368

Monotonically improving approximate answers to relational algebra queries  

NASA Technical Reports Server (NTRS)

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

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

1989-01-01

369

Quasiparticle random-phase approximation and {beta}-decay physics: Higher-order approximations in a boson formalism  

SciTech Connect

The quasiparticle random-phase approximation (QRPA) is reviewed and higher-order approximations are discussed with reference to {beta}-decay physics. The approach is fully developed in a boson formalism. Working within a schematic model, we first illustrate a fermion-boson mapping procedure and apply it to construct boson images of the fermion Hamiltonian at different levels of approximation. The quality of these images is tested through a comparison between approximate and exact spectra. Standard QRPA equations are derived in correspondence with the quasi-boson limit of the first-order boson Hamiltonian. The use of higher-order Hamiltonians is seen to improve considerably the stability of the approximate solutions. The mapping procedure is also applied to Fermi {beta} operators: exact and approximate transition amplitudes are discussed together with the Ikeda sum rule. The range of applicabilty of the QRPA formalism is analyzed. {copyright} {ital 1997} {ital The American Physical Society}

Sambataro, M. [Istituto Nazionale di Fisica Nucleare, Sezione di Catania Corso Italia 57, I-95129 Catania (Italy)] [Istituto Nazionale di Fisica Nucleare, Sezione di Catania Corso Italia 57, I-95129 Catania (Italy); Suhonen, J. [Department of Physics, University of Jyvaeskylae, Post Office Box 35, SF-40351 Jyvaeskylae (Finland)] [Department of Physics, University of Jyvaeskylae, Post Office Box 35, SF-40351 Jyvaeskylae (Finland)

1997-08-01

370

Cosmic shear covariance: the log-normal approximation  

NASA Astrophysics Data System (ADS)

Context. Accurate estimates of the errors on the cosmological parameters inferred from cosmic shear surveys require accurate estimates of the covariance of the cosmic shear correlation functions. Aims: We seek approximations to the cosmic shear covariance that are as easy to use as the common approximations based on normal (Gaussian) statistics, but yield more accurate covariance matrices and parameter errors. Methods: We derive expressions for the cosmic shear covariance under the assumption that the underlying convergence field follows log-normal statistics. We also derive a simplified version of this log-normal approximation by only retaining the most important terms beyond normal statistics. We use numerical simulations of weak lensing to study how well the normal, log-normal, and simplified log-normal approximations as well as empirical corrections to the normal approximation proposed in the literature reproduce shear covariances for cosmic shear surveys. We also investigate the resulting confidence regions for cosmological parameters inferred from such surveys. Results: We find that the normal approximation substantially underestimates the cosmic shear covariances and the inferred parameter confidence regions, in particular for surveys with small fields of view and large galaxy densities, but also for very wide surveys. In contrast, the log-normal approximation yields more realistic covariances and confidence regions, but also requires evaluating slightly more complicated expressions. However, the simplified log-normal approximation, although as simple as the normal approximation, yields confidence regions that are almost as accurate as those obtained from the log-normal approximation. The empirical corrections to the normal approximation do not yield more accurate covariances and confidence regions than the (simplified) log-normal approximation. Moreover, they fail to produce positive-semidefinite data covariance matrices in certain cases, rendering them unusable for parameter estimation. Conclusions: The log-normal or simplified log-normal approximation should be used in favour of the normal approximation for parameter estimation and parameter error forecasts. More generally, any approximation to the cosmic shear covariance should ensure a positive-(semi)definite data covariance matrix.

Hilbert, S.; Hartlap, J.; Schneider, P.

2011-12-01

371

Embedding impedance approximations in the analysis of SIS mixers  

NASA Technical Reports Server (NTRS)

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

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

1992-01-01

372

Multiparameter structural optimization using FEM and multipoint explicit approximations  

Microsoft Academic Search

A unified approach to various problems of structural optimization, based on approximation concepts, is presented. The approach is concerned with the development of the iterative technique, which uses in each iteration the information gained at several previous design points (multipoint approximations) in order to better fit constraints and\\/or objective functions and to reduce the total number of FE analyses needed

V. V. Toropov; A. A. Filatov; A. A. Polynkin

1993-01-01

373

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

374

Route planning for irregular measuring area based on polygon approximation  

Microsoft Academic Search

Route planning plays a key role in reverse engineering. Currently, a rectangle is usually taken as the approximation of an irregular measuring area. This would lead to a low efficiency in measuring because unnecessary region is included and blank routes are generated. In this paper, a polygon-based method is presented to more accurately approximate irregular area. An irregular area is

Jun Hu; Ye Li; Yuhan Wang; Jianguo Cai

2003-01-01

375

Finite element approximations of nonlinear eigenvalue problems in quantum physics  

Microsoft Academic Search

In this paper, we study finite element approximations of a class of nonlinear eigenvalue problems arising from quantum physics. We derive both a priori and a posteriori finite element error estimates and obtain optimal convergence rates for both linear and quadratic finite element approximations. In particular, we analyze the convergence and complexity of an adaptive finite element method. In our

Huajie Chen; Lianhua He; Aihui Zhou

2011-01-01

376

Mixed finite element methods and higher-order temporal approximations  

Microsoft Academic Search

The accurate numerical approximation of subsurface flow and transport processes in heterogeneous aquifers remains difficult. A necessary step in this task is the accurate representation of fluid velocity fields. In the recent past, mixed finite element methods have been investigated, since they provide velocity approximations that both conserve mass over individual mesh elements and are continuous across element interfaces. But,

Matthew W. Farthing; Christopher E. Kees; Cass T. Miller

2002-01-01

377

Universal approximation bounds for superpositions of a sigmoidal function  

Microsoft Academic Search

Approximation properties of a class of artificial neural networks are established. It is shown that feedforward networks with one layer of sigmoidal nonlinearities achieve integrated squared error of order O (1\\/n), where n is the number of nodes. The approximated function is assumed to have a bound on the first moment of the magnitude distribution of the Fourier transform. The

Andrew R. Barron

1993-01-01

378

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

379

Approximate solutions to nonlinear fluid networks with periodic inputs  

Microsoft Academic Search

We use Kirchhoff's laws and pipe flow dynamics equations to describe a fluid flow network in the form of a nonlinear differential equation with a periodic right hand side. We apply the averaging method to find an approximate solution of this equation and analyze its stability properties. The approximate solution consists of three parts: a mean flow part due to

Olga I. Koroleva; Miroslav KrstiC

2004-01-01

380

Wavelet-domain approximation and compression of piecewise smooth images  

Microsoft Academic Search

The wavelet transform provides a sparse represen- tation for smooth images, enabling efficient approximation and compression using techniques such as zerotrees. Unfortunately, this sparsity does not extend to piecewise smooth images, where edge discontinuities separating smooth regions persist along smooth contours. This lack of sparsity hampers the efficienc y of wavelet-based approximation and compression. On the class of images containing

Michael B. Wakin; Justin K. Romberg; Hyeokho Choi; Richard G. Baraniuk

2006-01-01

381

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

382

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

ERIC Educational Resources Information Center

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

Oud, Johan H. L.; Folmer, Henk

2011-01-01

383

Approximate solution of singularly perturbed nonlinear pursuit-evasion games  

Microsoft Academic Search

A methodology to obtain an approximate solution of a singularly perturbed nonlinear differential game is presented. The outcome of the game with approximate strategies, defined as extended value, is related to the saddle-point value of the game. In an example of a simple pursuit-evasion game, it is shown that the proposed methodology leads to an easily implementable feedback form solution

N. Farber; J. Shinar

1980-01-01

384

Improvement of Tone's Method with Two-Term Rational Approximation  

Microsoft Academic Search

An improvement of Tone's method, which is a resonance calculation method based on the equivalence theory, is proposed. In order to increase calculation accuracy, the two-term rational approximation is incorporated for the representation of neutron flux. Furthermore, some theoretical aspects of Tone's method, i.e., its inherent approximation and choice of adequate multigroup cross section for collision probability estimation, are also

Akio YAMAMOTO; Tomohiro ENDO; Go CHIBA

2011-01-01

385

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

386

Padé approximants and efficient analytic continuation of a power series  

Microsoft Academic Search

This survey reflects the current state of the theory of Padé approximants, that is, best rational approximations of power series. The main focus is on the so-called inverse problems of this theory, in which one must make deductions about analytic continuation of a given power series on the basis of the known asymptotic behaviour of the poles of some sequence

S P Suetin

2002-01-01

387

A provably efficient computational model for approximate spatiotemporal retrieval  

Microsoft Academic Search

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

Delis Vasilis; Makris Christos; Sioutas Spiros

1999-01-01

388

Approximation in LQG control of a thermoelastic rod  

NASA Technical Reports Server (NTRS)

Control and estimator gains are computed for linear-quadratic-Gaussian (LQG) optimal control of the axial vibrations of a thermoelastic rod. The computations are based on a modal approximation of the partial differential equations representing the rod, and convergence of the approximations to control and estimator gains is the main issue.

Gibson, J. S.; Rosen, I. G.; Tao, G.

1989-01-01

389

Spectral Hermite Approximations for the Actively Mode-Locked Laser  

Microsoft Academic Search

An approximation technique for the governing equations for the mode-locked laser is examined. The technique centers on a transformation of the governing equations in which the resulting equations closely resemble the Hermite equation. The approximation of the system is constructed through a linear combination of Hermite polynomials resulting in a Hermite-spectral method. The rate of decay of the resulting modes

Kelly Black; John B. Geddes

2001-01-01

390

The Validity of Stirling's Approximation: A Physical Chemistry Project  

Microsoft Academic Search

Often in physical chemistry courses, the direct proof of Stirling's approximation is omitted owing to the complexity of the mathematics involved. We present an accessible proof of this result that requires only an understanding of first-year calculus. We also present an undergraduate project dealing with the validity of Stirling's approximation. This assignment asks students to study the validity of the

A. S. Wallner; K. A. Brandt

1999-01-01

391

Approximating pseudopotentials for evolution equations containing a small parameter  

NASA Astrophysics Data System (ADS)

For nonlinear partial differential equations that cannot be integrated by the inverse scattering method, an approach that makes it possible to construct Wahlquist—Estabrook approximating pseudopotentials is proposed. The method is used to find an approximate Lax pair and conservation laws of the Kawahara equation.

Alekseev, A. A.; Kudryashov, N. A.

1992-06-01

392

Reaching Approximate Agreement in the Presence of Faults  

Microsoft Academic Search

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

Danny Dolev; Nancy A. Lynch

1985-01-01

393

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

394

Extending Menzel's Closed-Form Approximation for the Error Function.  

National Technical Information Service (NTIS)

A closed-form approximation for the error function is discussed. The 2nth root of an infinite series in the argument is shown to be a rough approximation to the error function, and linear combinations of such roots provide successively improved fits to th...

I. H. Zimmerman

1975-01-01

395

THE GENERALIZED APPROXIMATION METHOD AND NONLINEAR HEAT TRANSFER EQUATIONS  

Microsoft Academic Search

Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM) are compared with those studied via homotopy perturbation method (HPM). For this problem, the results ob- tained by the GAM are more accurate as

RAHMAT ALI KHAN

2009-01-01

396

On Approximations of First Integrals for Strongly Nonlinear Oscillators  

Microsoft Academic Search

In this paper strongly nonlinear oscillator equations will be studied.It will be shown that the recently developed perturbation method based onintegrating factors can be used to approximate first integrals. Not onlyapproximations of first integrals will be given, butit will also be shown how in a rather efficient way the existence and stability oftime-periodic solutions can be obtained from these approximations.

S. B. Waluya; W. T. van Horssen

2003-01-01

397

A New LLR Approximation for BICM Systems with HARQ  

Microsoft Academic Search

In this letter, a new approximation of log-likelihood ratio (LLR) for soft input channel decoding is proposed. Conventional simplified LLR using log-sum approximation can degrade the performance of bit interleaved coded modulation (BICM) systems employing hybrid automatic repeat request (HARQ) at low SNR. The proposed LLR performs as well as the exact LLR, and at the same time, requires only

Jin Whan Kang; Sang-Hyo Kim; Seokho Yoon; Tae Hee Han; Hyoung Kee Choi

2010-01-01

398

Approximate Throughput Analysis of Cyclic Queueing Networks with Finite Buffers  

Microsoft Academic Search

An approximation method for obtaining the throughput of cyclic queueing networks with blocking as a function of the number of customers in it is presented. The approximation method was developed for two different blocking mechanisms. It was also extended to the case of the central server model with blocking. Validation tests show that the algorithm is fairly accurate.

Raif O. Onvural; Harry G. Perros

1989-01-01

399

Density functional approximation for hard-body liquid crystals  

Microsoft Academic Search

We present a density functional approximation for the free energy of a system of hard bodies with arbitrary shape and orientational distribution. For systems with homogeneous density it reduces to existing treatments, which describe the isotropic liquid and the nematic liquid crystal. The treatment of the inhomogeneous density allows the study of smectic and crystal phases. We applied the approximation

A. M. Somoza; P. Tarazona

1989-01-01

400

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

401

An anisotropic hypernetted chain approximation for the spherical cell model  

NASA Astrophysics Data System (ADS)

The anisotropic hypernetted chain approximation is applied to the spherical cell model. The osmotic pressure obtained with this approximation is different from that of the nonlinear Poisson-Boltzmann equation, and agrees well with the result of Monte Carlo simulations, especially for a system of divalent counterions.

Fushiki, M.

1989-01-01

402

A Comparison Of Approximation Modeling Techniques: Polynomial Versus Interpolating Models  

Microsoft Academic Search

Two methods of creating approximation models arecompared through the calculation of the modelingaccuracy on test problems involving one, five, andten independent variables. Here, the test problemsare representative of the modeling challenges typicallyencountered in realistic engineering optimizationproblems. The first approximation model is aquadratic polynomial created using the method ofleast squares. This type of polynomial model hasseen considerable use in recent engineering...

Anthony A. Giunta; Layne T. Watson

1998-01-01

403

Curve crossing in linear potential grids: The quasidegeneracy approximation  

Microsoft Academic Search

The quasidegeneracy approximation [V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne, and Y. B. Band, J. Phys. B 32, 1845 (1999)] is used here to evaluate transition amplitudes for the problem of curve crossing in linear potential grids involving two sets of parallel potentials. The approximation describes phenomena, such as counterintuitive transitions and saturation (incomplete population transfer), not predictable by

V. A. Yurovsky; A. Ben-Reuven

2001-01-01

404

Inertial Parameters in the Interacting Boson Fermion Approximation.  

National Technical Information Service (NTIS)

The Hartree-Bose-Fermi and the adiabatic approximations are used to derive analytic formulas for the moment of inertia and the decoupling parameter of the interacting boson fermion approximation for deformed systems. These formulas are applied to the SU(3...

J. Dukelsky C. Lima

1986-01-01

405

Markov Chain Approximation for the Analysis of Banyan Networks.  

National Technical Information Service (NTIS)

This paper analyzes the delay suffered by messages in a clocked, packet-switched, square Banyan network with k X k output-buffered switches by approximating the flow processes in the network with Markov chains. We recursively approximate the departure pro...

A. A. Merchant

1990-01-01

406

Local density approximations for the energy of a periodic  

Microsoft Academic Search

We deal with local density approximations for the kinetic and exchange energy term, Ekin( ) and Eex( ), of a periodic Coulomb model. We study asymptotic approximations of the energy when the number of particles goes to infinity and for densities close to the constant averaged density. For the kinetic energy, we recover the usual combination of the von-Weizs¨ acker

Olivier BOKANOWSKI; Norbert J. MAUSERz

407

Simple Approximation of the Value of Callable Convertible Preferred Stock  

Microsoft Academic Search

We develop an analytic approximation of a model of callable convertible preferred stock that allows for deferred callability and cash dividends on the issuing firm's common stock. Predictions of the analytic approximation and the numerical solution are close, hence we show that the benefit of the method (ease of computation) outweighs the cost (negligible computational error). We also show that

Pradipkumar Ramanlal; Steven V. Mann; William T. Moore

1996-01-01

408

Approximating the error probability for the independent rayleigh fading channel  

Microsoft Academic Search

The major contribution of this paper is the computation of an accurate approximation of the symbol error probability of multidimensional signal constellations used for transmission over independent Rayleigh fading channels. Here we attempt to compute the exact error probability and show how some apparently rather gross approximations still lead to an accurate result

J.-C. Belfiore; E. Viterbo

2005-01-01

409

On Krylov Subspace Approximations To The Matrix Exponential Operator  

Microsoft Academic Search

. Krylov subspace methods for approximating the action of matrix exponentials areanalyzed in this paper. We derive error bounds via a functional calculus of Arnoldi and Lanczosmethods that reduces the study of Krylov subspace approximations of functions of matrices to thatof linear systems of equations. As a side result, we obtain error bounds for Galerkin-type Krylovmethods for linear equations, namely

Marlis Hochbruck; Christian Lubich

1996-01-01

410

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

411

Approximately maximizing efficiency and revenue in polyhedral environments  

Microsoft Academic Search

We consider a resource allocation game in polyhedral en- vironments. Polyhedral environments model a wide range of problems, including bandwidth sharing, some models of Adwords auctions and general resource allocation. We ex- tend the fair sharing mechanism for such resource allocation games. We show that our mechanism simultaneously creates approximately ecien t allocations and approximately max- imizes revenue. We also

Thành Nguyen; Éva Tardos

2007-01-01

412

Optimal Controller Synthesis Using Approximating-Graph Dynamic Programming  

Microsoft Academic Search

Dynamic programming is well known as a method of calculating optimal control but is not often used in practice because it is assumed to be computationally expensive. We introduce a new stageless version of dynamic programming that produces numerical approximations to optimal control laws for continuous systems. The method creates an approximating graph that models the possible state transitions in

Michiel van de Panne; Eugene Fiume; Zvonko Vranesic

1993-01-01

413

Approximation of faulted power system trjectories via averaging  

Microsoft Academic Search

The theory of averaging for autonomous systems is used to obtain simple approximate models from the nonlinear swing equation representation for electric power system dynamics. These models can be useful in the study of mid-term dynamics. The linearity of the simplified models makes them ideal for rapid numerical integration. It is shown that the new representation is approximately valid when

E. H. Abed; J. C. Alexander

1987-01-01

414

Approximation of boundary conditions for mimetic finite-difference methods  

Microsoft Academic Search

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

J. M. Hyman; M. Shashkov

1998-01-01

415

Least Fixpoint MBM: Improved Technique for Approximate Reachability  

Microsoft Academic Search

Reachability don't cares (RDCs) can have a dramatic impact on sequential optim ization and CTL model checking. However, since the computation of RDCs is often intractable, approximate reachability don't cares (ARDCs) are often preferable. The challenge in computing approximations of the reachable states is to obtain the best accuracy within given time and memory limits. Cho et al. presented the

In-Ho Moon; James Kukula; Tom Shiple; Fabio Somenzi

1999-01-01

416

A constructive method for multivariate function approximation by multilayer perceptrons  

Microsoft Academic Search

Mathematical theorems establish the existence of feedforward multilayered neural networks, based on neurons with sigmoidal transfer functions, that approximate arbitrarily well any continuous multivariate function. However, these theorems do not provide any hint on how to find the network parameters in practice. It is shown how to construct a perceptron with two hidden layers for multivariate function approximation. Such a

Shlomo Geva; Joaquin Sitte

1992-01-01

417

Differential Approximation of min sat, max sat and Related Problems  

Microsoft Academic Search

We present differential approximation results (both positive and negative) for optimal satisfiability, optimal constraint satisfaction, and some of the most popular restrictive versions of them. As an important corollary, we exhibit an interesting structural difference between the landscapes of approximability classes in standard and differential paradigms.

Bruno Escoffier; Vangelis Th. Paschos

2005-01-01

418

A Padé approximant to the inverse Langevin function  

Microsoft Academic Search

Application of the methodology of Pade approximants to a Taylor expansion of the inverse Langevin function led to an accurate analytical expression. The approximation, retaining a finite extendibility of the Langevin spring, enables a convenient analysis of experimental data and analytical manipulations of material models.

A. Cohen

1991-01-01

419

Analysis of optical waveguide discontinuities using the Pade approximants  

Microsoft Academic Search

We propose a novel method to solve efficiently the dielectric waveguide discontinuity problems. The reflection and transmission fields are expressed in terms of the characteristic matrices and the incident field. Instead of solving eigen systems, the square roots of the matrices are approximated by the Pade approximants. Therefore, the proposed method requires much less computation time and memory. It can

Yih-Peng Chiou; Hung-Chun Chang

1997-01-01

420

AN INVESTIGATION OF THE APPLICABILITY OF THE PADE APPROXIMANT METHOD  

Microsoft Academic Search

By means of analysis and numerical examples, the range of applicability ; of the Pade approximant method is investigated. It is concluded that at least a ; subsequence of the STAN,N! Pada approximants for f(z) converge uniformly to f(z) ; in any closed, connected set on the Riemann sphere containing the origin but not ; containing any of the singular

G. A. Jr. Baker; J. L. Gammel; J. G. Wills

1961-01-01

421

Continuous meshless approximations for nonconvex bodies by diffraction and transparency  

Microsoft Academic Search

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

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

1996-01-01

422

Space-fixed sudden approximation for total differential cross sections  

SciTech Connect

A high-order space-fixed sudden approximation based on the theory of Cross is presented and shown to give improved agreement with exact close coupling results for low-energy He--CO atom-rigid rotor scattering, when compared with the infinite-order-sudden (IOS) approximation. (AIP)

Siska, P.E.

1982-05-15

423

Approximating Catmull-Clark Subdivision Surfaces with Bicubic Patches  

Microsoft Academic Search

We present a simple and computationally efficient algorithm for approximating Catmull-Clark subdivision surfaces using a minimal set of bicubic patches. For each quadrilateral face of the control mesh, we construct a geometry patch and a pair of tangent patches. The geometry patches approximate the shape and silhouette of the Catmull-Clark surface and are smooth everywhere except along patch edges containing

Charles Loop; Scott Schaefer

2007-01-01

424

Recent advances in approximation concepts for optimum structural design  

NASA Technical Reports Server (NTRS)

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

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

1991-01-01

425

An approximation theory for the identification of linear thermoelastic systems  

NASA Technical Reports Server (NTRS)

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

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

1990-01-01

426

Two-point quasifractional approximant in physics. Truncation error  

SciTech Connect

The quasifractional approximation method is developed in a systematic manner. This method uses simultaneously the power series, and at a second point, the asymptotic expansion. The usual form of the approximants is two or more rational fractions, in terms of a suitable variable, combined with auxiliary nonfractional functions. Coincidence in the singularities in the region of interest is pursued. Equal denominators in the rational fractions is required so that the solution of only linear algebraic equations is needed to determine the parameters of the approximant. An upper bound is obtained for the truncation error for a certain class of functions, which contains most of the functions for which this method has been applied so far. It is shown that quasifractional approximants can be derived as a mixed German and Latin polynomial problem in the context of Hermite--Pade approximation theory.

Martin, P. (Deptomento de Fisica, Universidad Simon Bolivar, Apartado 89000, Caracas, Venezuela (VE)); Baker, G.A. Jr. (Theoretical Division, Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545 (USA))

1991-06-01

427

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering  

NASA Technical Reports Server (NTRS)

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

Melott, Adrian L.

1994-01-01

428

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

Microsoft Academic Search

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

J. C. Ravey; P. Mazeron

1983-01-01

429

Cross section angular momentum dependence and the factorisation approximation for electron-atom scattering in the first Born approximation  

Microsoft Academic Search

The factorisation approximation in electron-atom scattering usually consists of eliminating the exchange contribution to the scattering by writing the scattering cross section as the product of the square of a direct scattering target form factor times the Mott cross section for electron-electron scattering. It is shown that a factorisation approximation is only possible for scattering angles less than 30' and

R. A. Bonham

1990-01-01

430

A test of the adhesion approximation for gravitational clustering  

NASA Technical Reports Server (NTRS)

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

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

1993-01-01

431

A test of the adhesion approximation for gravitational clustering  

NASA Technical Reports Server (NTRS)

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

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

1994-01-01

432

Meromorphic approximants to complex Cauchy transforms with polar singularities  

SciTech Connect

We study AAK-type meromorphic approximants to functions of the form F(z)={integral}(d{lambda}(t))/(z-t)+R(z), where R is a rational function and {lambda} is a complex measure with compact regular support included in (-1,1), whose argument has bounded variation on the support. The approximation is understood in the L{sup p}-norm of the unit circle, p{>=}2. We dwell on the fact that the denominators of such approximants satisfy certain non-Hermitian orthogonal relations with varying weights. They resemble the orthogonality relations that arise in the study of multipoint Pade approximants. However, the varying part of the weight implicitly depends on the orthogonal polynomials themselves, which constitutes the main novelty and the main difficulty of the undertaken analysis. We obtain that the counting measures of poles of the approximants converge to the Green equilibrium distribution on the support of {lambda} relative to the unit disc, that the approximants themselves converge in capacity to F, and that the poles of R attract at least as many poles of the approximants as their multiplicity and not much more. Bibliography: 35 titles.

Baratchart, Laurent; Yattselev, Maxim L [Institut National de Recherche en Informatique et en Automatique, Sophia Antipolis - Mediterranee (France)

2009-10-31

433

Some approximations in the linear dynamic equations of thin cylinders  

NASA Technical Reports Server (NTRS)

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

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

1981-01-01

434

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

435

A similarity theory of approximate deconvolution models of turbulence  

NASA Astrophysics Data System (ADS)

We apply the phenomenology of homogeneous, isotropic turbulence to the family of approximate deconvolution models proposed by Stolz and Adams. In particular, we establish that the models themselves have an energy cascade with two asymptotically different inertial ranges. Delineation of these gives insight into the resolution requirements of using approximate deconvolution models. The approximate deconvolution model's energy balance contains both an enhanced energy dissipation and a modification to the model's kinetic energy. The modification of the model's kinetic energy induces a secondary energy cascade which accelerates scale truncation. The enhanced energy dissipation completes the scale truncation by reducing the model's micro-scale from the Kolmogorov micro-scale.

Layton, William; Neda, Monika

2007-09-01

436

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

437

Analytic Approximate Solution for Falkner-Skan Equation  

PubMed Central

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

Marinca, Bogdan

2014-01-01

438

Evaluation of fault-tolerant system performance by approximate techniques  

NASA Technical Reports Server (NTRS)

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

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

1985-01-01

439

Approximation of Optimally Controlled Ordinary and Partial Dierential Equations  

Microsoft Academic Search

Abstract In this thesis, which consists of four papers, approximation of optimal control problems is studied. In Paper I the Symplectic,Pontryagin method for approximation,of optimally controlled ordinary,dieren,tial equations,is presented. The method consists of a Symplec- tic Euler time stepping,scheme,for a Hamiltonian,system,with a regularized,Hamiltonian. Under some,assumptions,it is shown,that the approximate,value function,associated with this scheme,converges to the original value function,with a linear

MATTIAS SANDBERG

2006-01-01

440

Non-perturbative QCD amplitudes in quenched and eikonal approximations  

NASA Astrophysics Data System (ADS)

Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations at least, physical insights are presented that rely on the newly-discovered property of effective locality. The present article also provides a more rigorous mathematical basis for the crude approximations used in the previous derivation of the binding potential of quarks and nucleons. Furthermore, the techniques of Random Matrix calculus along with Meijer G-functions are applied to analyze the generic structure of fermionic amplitudes in QCD.

Fried, H. M.; Grandou, T.; Sheu, Y.-M.

2014-05-01

441

Temporary tooth separation in the treatment of approximal carious lesions.  

PubMed

The tunnel preparation is among the techniques proposed for restoration of approximal carious lesions. The preparations minimizes the sacrifice of sound tooth structure. The diagnostic and management problems associated with the restricted access to the approximal area, however, have limited use of this treatment modality. The difficulty of ascertaining the possible loss of enamel surface integrity is overcome by temporary tooth separation, which permits direct visual and tactile examination of approximal sites. Additionally, the increased access facilitates both preparation of the cavity and placement of the restorative material. PMID:8941842

Bjarnason, S

1996-04-01

442

Analysis of Adiabatic Approximation Using Stable Hamiltonian Method  

NASA Astrophysics Data System (ADS)

In this paper, we deal with the adiabatic approximation of general Hamiltonians by splitting it into two parts, with one part a Hamiltonian that has at least one time-independent eigenstate up to a phase factor. We first develop the method of finding this kind of Hamiltonians. Then the relationship between adiabatic approximation and these Hamiltonians is discussed. Applying this to a general case, we give both a necessary condition and a sufficient condition for adiabatic approximation, followed by a spin-half example to illustrate.

Ding, Yi-Tian

2014-05-01

443

Approximation algorithms for maximum two-dimensional pattern matching  

SciTech Connect

We introduce the following optimization version of the classical pattern matching problem (referred to as the maximum pattern matching problem). Given a two-dimensional rectangular text and a 2- dimensional rectangular pattern find the maximum number of non- overlapping occurrences of the pattern in the text. Unlike the classical 2-dimensional pattern matching problem, the maximum pattern matching problem is NP - complete. We devise polynomial time approximation algorithms and approximation schemes for this problem. We also briefly discuss how the approximation algorithms can be extended to include a number of other variants of the problem.

Arikati, S.R. [Memphis Univ., TN (United States); Dessmark, A.; Lingas, A. [Lund Univ. (Sweden); Marathe, M.

1996-07-01

444

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

445

An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems  

NASA Astrophysics Data System (ADS)

We construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. It makes the connection between the approximate renormalization procedure derived by Escande and Doveil and a systematic expansion of the transformation. In particular, we show that the two main approximations, consisting in keeping only the quadratic terms in the actions and the two main resonances, keep the essential information on the threshold of the breakup of invariant tori.

Chandre, C.; Jauslin, H. R.; Benfatto, G.

1999-01-01

446

Charged lepton spectrum approximation in a three body nucleon decay  

NASA Astrophysics Data System (ADS)

Only phase space is typically used to obtain final-state particle spectra in rare decay searches, which is a crude approximation in the case of three-body processes. We will demonstrate how both dynamics and phase space can be approximately accounted for in processes originating from grand unification models—such as nucleon decays p?e+? ¯? or p??+? ¯?—using the general effective Fermi theory formalism of electroweak muon decay, ??e+? ¯?. This approach allows for a more precise and only weakly model-dependent approximation of final particle spectra for these and similar decays, which may improve rare process searches in current and near-future experiments.

Chen, Mu-Chun; Takhistov, Volodymyr

2014-05-01

447

Usefulness of bound-state approximations in reaction theory  

SciTech Connect

A bound-state approximation when applied to certain operators, such as the many-body resolvent operator for a two-body fragmentation channel, in many-body scattering equations, reduces such equations to equivalent two-body scattering equations which are supposed to provide a good description of the underlying physical process. In this paper we test several variants of bound-state approximations in the soluble three-boson Amado model and find that such approximations lead to weak and unacceptable kernels for the equivalent two-body scattering equations and hence to a poor description of the underlying many-body process.

Adhikari, S.K.

1981-08-01

448

Rational approximations of viscous losses in vocal tract acoustic modeling  

NASA Astrophysics Data System (ADS)

The modeling of viscous losses in acoustic wave transmission through tubes by a boundary layer approximation is valid if the thickness of the boundary layer is small compared to the hydraulic radius. A method was found to describe the viscous losses that extends the frequency range of the model to very low frequencies and very thin tubes. For higher frequencies, this method includes asymptotically the spectral effects of the boundary layer approximation. The method provides a simplification for the rational approximation of the spectral effects of viscous losses.

Wilhelms-Tricarico, Reiner; McGowan, Richard S.

2004-06-01

449

Model reduction by extended quasi-steady-state approximation.  

PubMed

We extend the quasi-steady-state approximation (QSSA) with respect to the class of differential systems as well as with respect to the order of approximation. We illustrate the first extension by an example which cannot be treated in the frame of the classical approach. As an application of the second extension we prove that the trimolecular autocatalator can be approximated by a fast bimolecular reaction system. Finally we describe a class of singularly perturbed systems for which a higher order QSSA can easily be obtained. PMID:10885593

Schneider, K R; Wilhelm, T

2000-05-01

450

Uniform approximation from symbol calculus on a spherical phase space  

NASA Astrophysics Data System (ADS)

We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a result we announced in an earlier paper, namely the uniform approximation of the 6j-symbol in terms of the rotation matrices. The derivation is based on the Stratonovich-Weyl symbol correspondence between matrix operators and functions on a spherical phase space. The resulting approximation depends on a canonical, or area-preserving, map between two pairs of intersecting level sets on the spherical phase space.

Yu, Liang

2011-12-01

451

Uniform Approximation from Symbol Calculus on a Spherical Phase Space  

NASA Astrophysics Data System (ADS)

We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a uniform approximation of the 6j-symbol in terms of the rotation matrices. The derivation is based on the Stratonovich-Weyl symbol correspondence between matrix operators and functions on a spherical phase space. The resulting approximation depends on a canonical, or area preserving, map between two pairs of intersecting level sets on the spherical phase space.

Yu, Liang

2012-02-01

452

Convergence of multipoint Padé approximants of piecewise analytic functions  

NASA Astrophysics Data System (ADS)

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

Buslaev, Viktor I.

2013-02-01

453

Approximate analytic solutions to the isothermal Lane-Emden equation  

NASA Astrophysics Data System (ADS)

We derive accurate analytic approximations to the solution of the isothermal Lane-Emden equation, a basic equation in Astrophysics that describes the Newtonian equilibrium structure of self-gravitating, isothermal fluid spheres. The solutions we obtain, using analytic arguments and rational approximations, have simple forms, and are accurate over a radial extent that is much larger than that covered by conventional series expansions around the origin. Our best approximation has a maximum error on density of 0.04 % at 10 core radii, and is still within 1 % from an accurate numerical solution at a radius three times larger.

Iacono, R.; De Felice, M.

2014-03-01

454

Efficient Approximation for Structural Optimization Under Multiple Constraints  

NASA Technical Reports Server (NTRS)

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

Haftka, Raphael T.

1997-01-01

455

Convergence of multipoint Pade approximants of piecewise analytic functions  

SciTech Connect

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

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

2013-02-28

456

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

457

On Finite-Difference Approximations and Entropy Conditions for Shocks.  

National Technical Information Service (NTIS)

Weak solutions of hyperbolic conservation laws are not uniquely determined by their initial values; an entropy condition is needed to pick out the physically relevant solution. The question arises whether finite-difference approximations converge to this ...

A. Harten J. M. Hyman P. D. Lax B. Keyfitz

1976-01-01

458

A COMPARISON OF POWER APPROXIMATIONS FOR SATTERTHWAITE'S TEST  

PubMed Central

When testing equality of means from two independent normal populations, many statisticians prefer heterogeneity tolerant tests. Moser, Stevens, and Watts described the noncentral density and a numerical integration algorithm for computing power. We present simple and accurate approximations for the power of the Satterthwaite test statistic. Two advantages accrue. First, the approximations substantially reduce the computational burden for tasks such as plotting power curves. Second, the approximations substantially simplify the programming and thereby make power calculations more widely available. Four methods of power approximation are evaluated for test sizes of .001, .01, .05, and .10, sample sizes of 6 and 51, variance ratios of 1 and 10, and noncentrality parameters from 0 to 50 by 1. A method based on a ratio of expected values is recommended due to its accuracy and simplicity.

DiSantostefano, Rachael L.; Muller, Keith E.

2013-01-01

459

Simple Approximate Solutions to Continuous-Time-Random-Walk Transport.  

National Technical Information Service (NTIS)

This paper presents a procdure for obtaining simple approximate solutions to the continuous-time random walk (CTRW) as it applies to charge transport in amorphous materials. Application of this procedure to a particularly simple trial function leads to an...

F. B. McLean G. A. Ausman

1976-01-01

460

Numerical Stability and Convergence of Approximate Methods for Conservation Laws  

NASA Astrophysics Data System (ADS)

We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.

Galkin, V. A.

461

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

462

Numerical solution of the optimized random phase approximation.  

National Technical Information Service (NTIS)

An accurate, efficient and robust numerical method for the solution of the Optimized Random Phase Approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is rigorously proved. The method, hinging on the character...

G. Pastore F. Matthews O. Akinlade Z. Badirkhan

1994-01-01

463

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

464

3. BUILDING 413, INTERIOR, EASTERN STOREROOM, FROM APPROXIMATELY 10 FEET ...  

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

3. BUILDING 413, INTERIOR, EASTERN STOREROOM, FROM APPROXIMATELY 10 FEET EAST OF SOUTHEAST CORNER OF BUILDING, LOOKING NORTH. - Oakland Naval Supply Center, Heavy Materials & Paint-Oil Storehouses, Between Fourth & Sixth streets, between B & D Streets, Oakland, Alameda County, CA

465

The Power Approximation: Inventory Policies Based on Limited Demand Information.  

National Technical Information Service (NTIS)

This investigation examines the problem of managing inventory systems when the probability distributions for demand are incompletely specified. An approximately optimal (s,S) policy rule is derived, requiring knowledge of only the mean and variance of dem...

R. Ehrhardt

1976-01-01

466

Far Field Approximation in the Generalized Geometry Holdup (GGH) Model.  

National Technical Information Service (NTIS)

Quantitative gamma spectrometry measurements of uranium frequently require corrections for attenuation by an equipment or container layer and by the uranium bearing material itself. It is common to correct for attenuation using the far-field approximation...

C. A. Gunn L. G. Chiang R. B. Oberer

2006-01-01

467

Padé approximation for the exponential of a block triangular matrix  

Microsoft Academic Search

In this work, we obtain improved error bounds for Padé approximations to eA when A is block triangular. As a result, improved scaling strategies ensue which avoid some common overscaling difficulties.

Luca Dieci; Alessandra Papini

2000-01-01

468

HERMITE-PADÉ APPROXIMANTS AND SPECTRAL ANALYSIS OF NONSYMMETRIC OPERATORS  

Microsoft Academic Search

A class of operators related to Hermite-Padé approximants is defined. The spectral analysis of these operators is connected with the asymptotic behavior of polynomials defined by systems of orthogonality relations.Bibliography: 39 titles.

V A Kalyagin

1995-01-01

469

Approximate derivative calculated by using continuous wavelet transform.  

PubMed

A novel method of calculating approximate derivative of signals in analytical chemistry by using the continuous wavelet transform (CWT) is proposed. As compared with numerical differentiation, FT method and DWT method, fast calculation, and simple mathematical operation are remarkable advantages of CWT method. The signal-to-noise ratio (SNR) of approximate derivative of signals calculated by CWT method is easily enhanced only through appropriately adjusting the dilation, even in the case of very low SNR. Therefore, CWT method is a powerful tool for performing the approximate derivative calculation of signals in analytical chemistry. Additionally, the approximate second derivative evaluated via CWT method can be used to determine the peak potentials of the overlapping square wave voltammogram (SWV) of Cd(II) and In(III), and the results are very satisfactory. PMID:11911696

Nie, Lei; Wu, Shouguo; Lin, Xiangqin; Zheng, Longzhen; Rui, Lei

2002-01-01

470

Approximate Riemann solvers for the Godunov SPH (GSPH)  

NASA Astrophysics Data System (ADS)

The Godunov Smoothed Particle Hydrodynamics (GSPH) method is coupled with non-iterative, approximate Riemann solvers for solutions to the compressible Euler equations. The use of approximate solvers avoids the expensive solution of the non-linear Riemann problem for every interacting particle pair, as required by GSPH. In addition, we establish an equivalence between the dissipative terms of GSPH and the signal based SPH artificial viscosity, under the restriction of a class of approximate Riemann solvers. This equivalence is used to explain the anomalous “wall heating” experienced by GSPH and we provide some suggestions to overcome it. Numerical tests in one and two dimensions are used to validate the proposed Riemann solvers. A general SPH pairing instability is observed for two-dimensional problems when using unequal mass particles. In general, Ducowicz Roe's and HLLC approximate Riemann solvers are found to be suitable replacements for the iterative Riemann solver in the original GSPH scheme.

Puri, Kunal; Ramachandran, Prabhu

2014-08-01

471

Approximate self-consistent models for tidally truncated star clusters  

NASA Astrophysics Data System (ADS)

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

Heggie, D. C.; Ramamani, N.

1995-01-01

472

Dynamical Cluster Approximation: Cluster Extension of CPA for Disordered System  

NASA Astrophysics Data System (ADS)

The dynamical mean-field approximation (DMFA) or the coherent potential approximation (CPA) provides a convenient and effective method for studying disordered systems; however, non-local short range correlations of the disorder potential are neglected leading to a self-consistent single-site approximation. We combine the recently developed first principles method of Wei Ku and co-workers for the simulation of disordered systems with the dynamical cluster approximation (DCA) to develop a highly efficient means to treat disordered systems. We solve this model system using the DCA, which systematically incorporates short-range nonlocal correlations to the CPA. We apply this method to a number of model systems to illustrate where the DCA or a finite size simulation is more appropriate.

Ekuma, Chinedu; Ku, Wei; Berlijn, Tom; Moreno, Juana; Jarrell, Mark

2012-02-01

473

Contextual classification of multispectral image data: Approximate algorithm  

NASA Technical Reports Server (NTRS)

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

Tilton, J. C. (principal investigator)

1980-01-01

474

View looking to grotto to approximate that seen in HABS ...  

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

View looking to grotto to approximate that seen in HABS No. MD-1109-41 - National Park Seminary, Bounded by Capitol Beltway (I-495), Linden Lane, Woodstove Avenue, & Smith Drive, Silver Spring, Montgomery County, MD

475

Exact and Approximate Dependent Failure Reliability Models for Telecommunications Networks.  

National Technical Information Service (NTIS)

Previous papers by one of the authors have presented both an exact, but computationally slow, method for computing the reliability of telecommunication networks with dependent failures and a much faster approximation to this method. Both methods are based...

D. R. Shier J. D. Spragins

1985-01-01

476

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

477

Approximation of trigonometric functions by trigonometric polynomials with interpolation  

Microsoft Academic Search

The paper studies the approximation order of periodic functions by trigonometric polynomials with interpolation in arbitrary\\u000a set of nodes. A method of construction of Hermite interpolation polynomials is pointed out.

R. M. Trigub

2010-01-01

478

Controlling chaos using nonlinear approximations and delay coordinate embedding  

NASA Astrophysics Data System (ADS)

In a previous paper we showed that a chaos control method proposed by Ott, Grebogi and Yorke can be improved by using nonlinear approximations for chaotic dynamical systems and stable manifolds of targets. Here we consider systems whose governing equations are unknown and apply the chaos control method using the nonlinear approximations. Delay coordinate embedding techniques are used, so that approximate saddle points to be stabilized and nonlinear approximations of the systems and stable manifolds are obtained from time series of single variables. We also take into account the fact that the obtained section maps depend on the current and previous parameters. To demonstrate our approach, we give two numerical examples for the Hénon map and a pendulum with feedforward and feedback control. Some influences of noise are also discussed in these examples.

Yagasaki, Kazuyuki; Uozumi, Tomotsugu

1998-10-01

479

The Herman Kluk approximation: Derivation and semiclassical corrections  

NASA Astrophysics Data System (ADS)

The Herman-Kluk (HK) approximation for the propagator is derived semiclassically for a multidimensional system as an asymptotic solution of the Schrödinger equation. The propagator is obtained in the form of an expansion in ?, in which the lowest-order term is the HK formula. Thus, the result extends the HK approximation to higher orders in ?. Examination of the various terms shows that the expansion is a uniform asymptotic series and establishes the HK formula as a uniform semiclassical approximation. Successive terms in the series should allow one to improve the accuracy of the HK approximation for small ? in a systematic and purely semiclassical manner, analogous to a higher-order WKB treatment of time-independent wave functions.

Kay, Kenneth G.

2006-03-01

480

Non-ideal boson system in the Gaussian approximation  

SciTech Connect

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

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

1997-01-01

481

Approximate penetration factors for nuclear reactions of astrophysical interest  

NASA Technical Reports Server (NTRS)

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

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

1987-01-01

482

Vacancy-rearrangement theory in the first Magnus approximation  

SciTech Connect

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

Becker, R.L.

1984-01-01

483

The local potential approximation in the background field formalism  

NASA Astrophysics Data System (ADS)

Working within the familiar local potential approximation, and concentrating on the example of a single scalar field in three dimensions, we show that the commonly used approximation method of identifying the total and background fields, leads to pathologies in the resulting fixed point structure and the associated spaces of eigenoperators. We then show how a consistent treatment of the background field through the corresponding modified shift Ward identity, can cure these pathologies, restoring universality of physical quantities with respect to the choice of dependence on the background field, even within the local potential approximation. Along the way we point out similarities to what has been previously found in the f( R) approximation in asymptotic safety for gravity.

Bridle, I. Hamzaan; Dietz, Juergen A.; Morris, Tim R.

2014-03-01

484

Comparison of the Pade approximation method to perturbative QCD calculations  

SciTech Connect

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

Samuel, M.A. [Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078 (United States)] [Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078 (United States); [Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305 (United States); Ellis, J. [CERN, Geneva (Switzerland)] [CERN, Geneva (Switzerland); Karliner, M. [School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv (Israel)] [School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv (Israel)

1995-05-29

485

HERMITE-PADÉ Approximation for Nikishin Systems of Analytic Functions  

Microsoft Academic Search

Nikishin type systems of analytic functions are considered. For such systems, convergence of the main diagonal of the associated Hermite-Padé approximants is proved, when interpolation is equally distributed between the functions. If interpolation is \\

Zh Bustamante; G. L. Lagomasino

1994-01-01

486

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

487

Wavelet kernel Support Vector Machines for sparse approximation  

Microsoft Academic Search

Wavelet, a powerful tool for signal processing, can be used to approximate the target function. For enhancing the sparse property\\u000a of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support Vector Machines (SVM), which can converge\\u000a to minimum error with better sparsity. Here, wavelet functions would be firstly used to construct the admitted kernel for\\u000a SVM according

Yubing Tong; Dongkai Yang; Qishan Zhang

2006-01-01

488

Atomic multipole polarizabilities in the extended Coulomb approximation  

Microsoft Academic Search

A new and computationally convenient exact analytic expression for the 2l-pole static polarizabilities of mono and divalent atoms and ions is obtained within the extended Coulomb approximation of Adelman and Szabo. In this approximation the valence electron wavefunction is represented by an asymptotically valid Whittaker function with hydrogenic normalization and the l-symmetry excited orbitals are eigenfunctions of a Coulombic Hamiltonian

Gene Lamm; Attila Szabo

1977-01-01

489

Approximate Numerical Hartree-Fock Method for Molecular Calculations  

Microsoft Academic Search

Calculations are presented which show that the atomic orbitals which result from approximate numerical Hartree—Fock calculations (by the X? method) are as close to the Hartree—Fock limit for atoms as are those calculated using a double-zeta basis. Arguments are given which show that the exchange is treated with sufficient accuracy by the X? method. With the additional ``muffin-tin'' approximation, which

Karlheinz Schwarz; John W. D. Connolly

1971-01-01

490

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

491

An Improved Grid-Based Approximation Algorithm for POMDPs  

Microsoft Academic Search

Although a partially observable Markov decision process (POMDP) provides an appealing model for problems of planning under uncertainty, exact algo- rithms for POMDPs are intractable. This motivates work on approximation algorithms, and grid-based approximation is a widely-used approach. We de- scribe a novel approach to grid-based approxima- tion that uses a variable-resolution regular grid, and show that it outperforms previous

Rong Zhou; Eric A. Hansen

2001-01-01

492

A Complete Approximation Algorithm for Shortest Bounded-Curvature Paths  

Microsoft Academic Search

We address the problem of finding a polynomial-time approximation scheme for shortest bounded-curvature paths in the presence\\u000a of obstacles. Given an arbitrary environment E\\\\mathcal{E} consisting of polygonal obstacles, two feasible configurations, a length ?, and an approximation factor ?, our algorithm either (i) verifies that every feasible bounded-curvature path joining the two configurations is longer than\\u000a ? or (ii) constructs

Jonathan Backer; David Kirkpatrick

2008-01-01

493

Convergence of Padé Approximants for the Bethe-Salpeter Amplitude  

Microsoft Academic Search

We extend some earlier work on the Bethe-Salpeter equation to show that the sequence of [N, N] Padé approximants to deltal converges to the correct result if the scattered particles are of equal mass. The proof includes a demonstration that the symmetrized kernel of the Bethe-Salpeter equation after a coordinatespace Wick rotation is L2. An interesting connection between Padé approximants

J. Nuttall

1967-01-01

494

Approximation Properties of Two-Dimensional Continued Fractions  

Microsoft Academic Search

By using the difference formula for approximations of two-dimensional continued fractions, the method of fundamental inequalities, the Stieltjes–Vitali theorem, and generalizations of divided and inverse differences, we estimate the accuracy of approximations of two-dimensional continued fractions with complex elements by their convergents and obtain estimates for the real and imaginary parts of remainders of two-dimensional continued fractions. We also prove

Kh. I. Kuchmins'ka; S. M. Vozna

2003-01-01

495

Approximation of 2-D separable in denominator filters  

Microsoft Academic Search

After introducing a two-dimensional (2-D) model for the class of causal, recursive, and separable in denominator (CRSD) filters, a technique for approximating a given 2-D filter by a CRSD filter is presented. Also, a technique for 2-D CRSD model reduction is considered. Both the stability and minimality properties of the approximate model are explored. Some examples are also given to

BIJAN LASHGARI; LEONARD M. SILVERMAN; JEAN-FRANCOIS ABRAMATIC

1983-01-01

496

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

497

Robustness of controllers designed using Galerkin type approximations  

NASA Technical Reports Server (NTRS)

One of the difficulties in designing controllers for infinite-dimensional systems arises from attempting to calculate a state for the system. It is shown that Galerkin type approximations can be used to design controllers which will perform as designed when implemented on the original infinite-dimensional system. No assumptions, other than those typically employed in numerical analysis, are made on the approximating scheme.

Morris, K. A.

1990-01-01

498

A New LLR Approximation for BICM Systems with HARQ  

NASA Astrophysics Data System (ADS)

In this letter, a new approximation of log-likelihood ratio (LLR) for soft input channel decoding is proposed. Conventional simplified LLR using log-sum approximation can degrade the performance of bit interleaved coded modulation (BICM) systems employing hybrid automatic repeat request (HARQ) at low SNR. The proposed LLR performs as well as the exact LLR, and at the same time, requires only a small number of elementary operations.

Kang, Jin Whan; Kim, Sang-Hyo; Yoon, Seokho; Han, Tae Hee; Choi, Hyoung Kee

499

Overcoming Limitations of Approximate Query Answering in OLAP  

Microsoft Academic Search

Two important limitations of approximate query answering in OLAP are recognized and investigated. These limitations are: (i) scalability of the techniques, i.e. their reliability on highly-dimensional data cubes; and (ii) need for guarantees on the degree of approximation of the answers. In this paper, we focus on the first limitation, and propose adopting the well-known Karhunen-Loeve transform (KLT) to obtain

Alfredo Cuzzocrea

2005-01-01

500

An Integer Approximation Method for Discrete Sinusoidal Transforms  

Microsoft Academic Search

Approximate methods have been considered as a means to the evaluation of discrete transforms. In this work, we propose and\\u000a analyze a class of integer transforms for the discrete Fourier, Hartley, and cosine transforms (DFT, DHT, and DCT), based\\u000a on simple dyadic rational approximation methods. The introduced method is general, applicable to several blocklengths, whereas\\u000a existing approaches are usually dedicated

R. J. Cintra