Kravtsov, Yu. A. [Space Research Institute, Profsoyuznaya St. 82/34, Moscow 117997 (Russian Federation); Institute of Physics, Maritime University of Szczecin, Waly Chrobrego 1/., 70-500 Szczecin (Poland); Bieg, B. [Institute of Physics, Maritime University of Szczecin, Waly Chrobrego 1/., 70-500 Szczecin (Poland); Bliokh, K. Yu. [Institute of Radio Astronomy, 4 Krasnoznamyonnaya St., Kharkov 61002 (Ukraine); Optical Engineering Laboratory, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000 (Israel); Hirsch, M. [Max Planck Institute for Plasma Physics, Greifswald, Wendelsteinstrasse D-17491 (Germany)
2008-03-19
Three different theoretical approaches are presented: quasi-isotropic approximation (QIA), Stokes vector formalism and complex polarization angle method, which allow describing polarization of electromagnetic waves in weakly anisotropic plasma. QIA stems directly from the Maxwell equations under assumption of weak anisotropy and has a form of coupled differential equations for the transverse components of the electromagnetic wave field. Being applied to high frequency (microwave or IR) electromagnetic waves in magnetized plasma, QIA describes combined action of Faraday and Cotton-Mouton phenomena. QIA takes into account curvature and torsion of the ray, describes normal modes conversion in the inhomogeneous plasma and allows specifying area of applicability of the method.In distinction to QIA, Stokes vector formalism (SVF) deals with quantities, quadratic in a wave field. It is shown (and this is the main result of the paper) that equation for Stokes vector evolution can be derived directly from QIA. This evidences deep unity of two seemingly different approaches. In fact QIA suggests somewhat more information than SVF; in particular, it describes the phases of both transverse components of the electromagnetic field, whereas SVF operates only with the phase difference.At last, the coupled equations of the quasi-isotropic approximation can be reduced to a single equation for complex polarization angle (CPA), which describes both the shape and orientation of the polarization ellipse. In turn, equation for CPA allows obtaining equations for traditional parameters of polarization ellipse, which in fact are equivalent to the equation for Stokes vector evolution. It is pointed out that every method under discussion has its own advantages plasma polarimetry.
Quasi-isotropic approximation in dynamical elasticity and some problems of geotomography
Sharafutdinov, Vladimir
Quasi-isotropic approximation in dynamical elasticity and some problems of geotomography Vladimir approximation have the next features. First, the formula for the amplitude of a compressional wave contains some, the Rytov law for shear waves contains a term that depends linearly on the anisotropic part
Cerveny, Vlastislav
with the eigenvectors of the Christo#11;el matrix which may rotate rapidly about the ray. In \\weakly anisotropic" models anisotropic model. The e#11;ects of the quasi{isotropic approximation of the Christo#11;el matrix, the quasi in the 1-D anisotropic \\oblique twisted crystal" model Petr Bulant & Lud#20;ek Klime#20;s Department
Cerveny, Vlastislav
rapidly about the ray. In \\weakly anisotropic" models, at moderate frequencies, the S{wave polarization in a 1-D anisotropic model. The e#11;ects of the quasi{isotropic approximation of the Christo#11;el in the 1-D anisotropic \\oblique twisted crystal" model Petr Bulant & Lud#20;ek Klime#20;s #3; Department
Uniform domains, John domains and quasi-isotropic domains
NASA Astrophysics Data System (ADS)
Huang, M.; Wang, X.; Ponnusamy, S.; Sahoo, S. K.
2008-07-01
We study for two metrics j and d whether a plane domain for which there exists a constant c>0 with j(z,w)[less-than-or-equals, slant]cd(z,w) for all z,w[set membership, variant]D is a uniform domain. In particular, we study the case when d is the [lambda]-Apollonian metric a'. We also study for a simply connected domain that whether quasi-isotropic domains are John disks and conversely.
Narrow-field radiometry in a quasi-isotropic atmosphere
NASA Technical Reports Server (NTRS)
Holmes, A.; Palmer, J. M.; Tomasko, M. G.
1979-01-01
If a radiometer having a narrow field of view is used to measure the radiance of a source such as a quasi-isotropic atmosphere, a knowledge of the out-of-field responsivity is critical. For example, if a radiometer with a field of view of 5 deg (full-angle) has a relative responsivity of 0.0001 for the out-of-field radiation, the contribution of the out-of-field radiation (assuming an isotropic source subtending 2 steradians) is 10.5% of the total signal. Either the stray light suppression of the radiometer must be extremely high or methods of determining the out-of-field response must be developed. A description of one method of determining the effect of out-of-field response and its application to a planetary atmospheric radiometer is presented.
Quasi-isotropic VHF antenna array design study for the International Ultraviolet Explorer satellite
NASA Technical Reports Server (NTRS)
Raines, J. K.
1975-01-01
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.
NASA Astrophysics Data System (ADS)
Dey, S.; Karmakar, A.
2013-01-01
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.
Durability-Based Design Criteria for a Quasi-Isotropic Carbon-Fiber Automotive Composite
J. M. Corum; R. L. Battiste; M. B. Ruggles-Wrenn
2002-01-01
This report provides recommended durability-based design properties and criteria for a quasi-isotropic carbon-fiber composite for possible automotive structural applications. The composite, which was made by a rapid molding process suitable for high-volume automotive applications, consisted of continuous Thornel T300 fibers (6K tow) in a Baydur 420 IMR urethane matrix. The reinforcement was in the form of four {+-}45{sup o} stitch-bonded
Failure analysis of quasi-isotropic composite laminates with free edges under off-axis loading
Zhou, S.G.
1987-01-01
Composite materials with traction-free edges are known to develop interlaminar stress concentrations near the edge region. Such stresses play a vital role in failure of composite laminates. Experiments showed that a stiffness-quasi-isotropic laminate was not quasi-isotropic in strength. To interpret this phenomenon, an extensive experimental program was carried out on quasi-isotropic laminates. A typical matrix-dominated crack and delamination mode was found near the free edge of the specimen for all the off-axis cases. Such a through-the-thickness-matrix-crack would result in complete loss of load-carrying capability in the small-failure zone and would trigger an unstable failure progression into the interior of the laminate ending in total laminate failure. Classical failure criteria were found inadequate in predicting laminate strength. To predict those failures, a new criterion based on interlaminar free edge stresses and average stress method was introduced. The theoretical results obtained using this new approach were shown to agree very well with experimental results.
NASA Technical Reports Server (NTRS)
Hinkley, J. A.; Obrien, T. K.
1992-01-01
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.
NASA Technical Reports Server (NTRS)
Hinkley, J. A.; O'Brien, T. K.
1991-01-01
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/0 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.
Buckling Behavior of Compression-Loaded Quasi-Isotropic Curved Panels with a Circular Cutout
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Britt, Vicki O.; Nemeth, Michael P.
1999-01-01
Results from a numerical and experimental study of the response of compression-loaded quasi-isotropic curved panels with a centrally located circular cutout are presented. The numerical results were obtained by using a geometrically nonlinear finite element analysis code. The effects of cutout size, panel curvature and initial geo- metric imperfections on the overall response of compression-loaded panels are described. In addition, results are presented from a numerical parametric study that indicate the effects of elastic circumferential edge restraints on the prebuckling and buckling response of a selected panel and these numerical results are compared to experimentally measured results. These restraints are used to identify the effects of circumferential edge restraints that are introduced by the test fixture that was used in the present study. It is shown that circumferential edge restraints can introduce substantial nonlinear prebuckling deformations into shallow compression-loaded curved panels that can results in a significant increase in buckling load.
High-Q/V Monolithic Diamond Microdisks Fabricated with Quasi-isotropic Etching.
Khanaliloo, Behzad; Mitchell, Matthew; Hryciw, Aaron C; Barclay, Paul E
2015-08-12
Optical microcavities enhance light-matter interactions and are essential for many experiments in solid state quantum optics, optomechanics, and nonlinear optics. Single crystal diamond microcavities are particularly sought after for applications involving diamond quantum emitters, such as nitrogen vacancy centers, and for experiments that benefit from diamond's excellent optical and mechanical properties. Light-matter coupling rates in experiments involving microcavities typically scale with Q/V, where Q and V are the microcavity quality-factor and mode-volume, respectively. Here we demonstrate that microdisk whispering gallery mode cavities with high Q/V can be fabricated directly from bulk single crystal diamond. By using a quasi-isotropic oxygen plasma to etch along diamond crystal planes and undercut passivated diamond structures, we create monolithic diamond microdisks. Fiber taper based measurements show that these devices support TE- and TM-like optical modes with Q > 1.1 × 10(5) and V < 11(?/n) (3) at a wavelength of 1.5 ?m. PMID:26134379
NASA Technical Reports Server (NTRS)
Dost, Ernest F.; Ilcewicz, Larry B.; Avery, William B.; Coxon, Brian R.
1991-01-01
Residual strength of an impacted composite laminate is dependent on details of the damage state. Stacking sequence was varied to judge its effect on damage caused by low-velocity impact. This was done for quasi-isotropic layups of a toughened composite material. Experimental observations on changes in the impact damage state and postimpact compressive performance were presented for seven different laminate stacking sequences. The applicability and limitations of analysis compared to experimental results were also discussed. Postimpact compressive behavior was found to be a strong function of the laminate stacking sequence. This relationship was found to depend on thickness, stacking sequence, size, and location of sublaminates that comprise the impact damage state. The postimpact strength for specimens with a relatively symmetric distribution of damage through the laminate thickness was accurately predicted by models that accounted for sublaminate stability and in-plane stress redistribution. An asymmetric distribution of damage in some laminate stacking sequences tended to alter specimen stability. Geometrically nonlinear finite element analysis was used to predict this behavior.
Leckey, Cara A C; Rogge, Matthew D; Raymond Parker, F
2014-01-01
Three-dimensional (3D) elastic wave simulations can be used to investigate and optimize nondestructive evaluation (NDE) and structural health monitoring (SHM) ultrasonic damage detection techniques for aerospace materials. 3D anisotropic elastodynamic finite integration technique (EFIT) has been implemented for ultrasonic waves in carbon fiber reinforced polymer (CFRP) composite laminates. This paper describes 3D EFIT simulations of guided wave propagation in undamaged and damaged anisotropic and quasi-isotropic composite plates. Comparisons are made between simulations of guided waves in undamaged anisotropic composite plates and both experimental laser Doppler vibrometer (LDV) wavefield data and dispersion curves. Time domain and wavenumber domain comparisons are described. Wave interaction with complex geometry delamination damage is then simulated to investigate how simulation tools incorporating realistic damage geometries can aid in the understanding of wave interaction with CFRP damage. In order to move beyond simplistic assumptions of damage geometry, volumetric delamination data acquired via X-ray microfocus computed tomography is directly incorporated into the simulation. Simulated guided wave interaction with the complex geometry delamination is compared to experimental LDV time domain data and 3D wave interaction with the volumetric damage is discussed. PMID:23769180
EVIDENCE FOR QUASI-ISOTROPIC MAGNETIC FIELDS FROM HINODE QUIET-SUN OBSERVATIONS
Asensio Ramos, A.
2009-08-20
Some recent investigations of spectropolarimetric observations of the Zeeman effect in the Fe I lines at 630 nm carried out with the Hinode solar space telescope have concluded that the strength of the magnetic field vector in the internetwork regions of the quiet Sun is in the hG regime and that its inclination is predominantly horizontal. We critically reconsider the analysis of such observations and carry out a complete Bayesian analysis with the aim of extracting as much information as possible from them, including error bars. We apply the recently developed BAYES-ME code that carries out a complete Bayesian inference for Milne-Eddington atmospheres. The sampling of the posterior distribution function is obtained with a Markov Chain Monte Carlo scheme and the marginal distributions are analyzed in detail. The Kullback-Leibler divergence is used to study the extent to which the observations introduce new information in the inference process resulting in sufficiently constrained parameters. Our analysis clearly shows that only upper limits to the magnetic field strength can be inferred, with fields in the kG regime completely discarded. Furthermore, the noise level present in the analyzed Hinode observations induces a substantial loss of information for constraining the azimuth of the magnetic field. Concerning the inclination of the field, we demonstrate that some information is available to constrain it for those pixels with the largest polarimetric signal. The results also point out that the field in pixels with small polarimetric signals can be nicely reproduced in terms of a quasi-isotropic distribution.
Durability-Based Design Criteria for a Quasi-Isotropic Carbon-Fiber Automotive Composite
Corum, J.M.
2002-04-17
This report provides recommended durability-based design properties and criteria for a quasi-isotropic carbon-fiber composite for possible automotive structural applications. The composite, which was made by a rapid molding process suitable for high-volume automotive applications, consisted of continuous Thornel T300 fibers (6K tow) in a Baydur 420 IMR urethane matrix. The reinforcement was in the form of four {+-}45{sup o} stitch-bonded mats in the following layup: [0/90{sup o}/{+-}45{sup o}]{sub S}. This material is the second in a progression of three candidate thermoset composites to be characterized and modeled as part of an Oak Ridge National Laboratory project entitled Durability of Carbon-Fiber Composites. The overall goal of the project, which is sponsored by the U.S. Department of Energy's Office of Advanced Automotive Technologies and is closely coordinated with the industry Automotive Composites Consortium, is to develop durability-driven design data and criteria to assure the long-term integrity of carbon-fiber-based composite systems for large automotive structural components. This document is in two parts. Part I provides the design criteria, and Part 2 provides the underlying experimental data and models. The durability issues addressed include the effects on deformation, strength, and stiffness of cyclic and sustained loads, operating temperature, automotive fluid environments, and low-energy impacts (e.g., tool drops and kickups of roadway debris). Guidance is provided for design analysis, time-dependent allowable stresses, rules for cyclic loadings, and damage tolerance design guidance, including the effects of holes. Chapter 6 provides a brief summary of the design criteria.
NASA Technical Reports Server (NTRS)
Kelkar, A. D.
1984-01-01
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.
NASA Technical Reports Server (NTRS)
Sohi, M. M.; Hahn, H. T.; Williams, J. G.
1986-01-01
Compressive failure mechanisms in quasi-isotropic graphite/epoxy laminates were characterized for both unnotched and notched specimens and also following damage by impact. Two types of fibers (Thornel 300 and 700) and four resin systems (Narmco 5208, American Cyanamid BP907, and Union Carbide 4901/MDA and 4901/mPDA) were studied. For all material combinations, failure of unnotched specimens was initiated by kinking of fibers in the 0-degree plies. A major difference was observed, however, in the mode of failure propagation after the 0-degree ply failure. The strength of quasi-isotropic laminates in general increased with increasing resin tensile modulus. The laminates made with Thornel 700 fibers exhibited slightly lower compressive strengths than did the laminates made with Thornel 300 fibers. The notch sensitivity as measured by the hole strength was lowest for the BP907 resin and highest for the 5208 resin. For the materials studied, however, the type of fiber had no effect on the notch sensitivity.
NASA Technical Reports Server (NTRS)
Illg, W.
1986-01-01
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.
NASA Technical Reports Server (NTRS)
Kriz, R. D.; Stinchcomb, W. W.
1982-01-01
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.
Cerveny, Vlastislav
of the Christo#11;el matrix which may rotate rapidly about the ray. In \\weakly anisotropic" models, at moderate seismograms calculated by the coupling ray theory in a 1-D anisotropic model. The e#11;ects of the quasi in the 1-D anisotropic \\oblique twisted crystal" model Petr Bulant & Lud#20;ek Klime#20;s #3; , Department
NASA Astrophysics Data System (ADS)
Kostopoulos, V.; Vavouliotis, A.; Loutas, T.; Karapappas, P.
2009-03-01
In this study, CNTs were used as modifiers of the epoxy matrix of quasi-isotropic carbon fibre reinforced laminates. The prepared laminates were subjected to tensile loading and tension-tension fatigue and, the changes in the longitudinal resistance were monitored via a digital multimeter. In addition, Acoustic Emission and Acousto-Ultrasonic techniques were used for monitoring the fatigue process of the laminates. The nano-enhanced laminates on the one hand exhibited superior fatigue properties and on the other hand they demonstrated the full-potential of the material to be used as an integrated sensor to monitor the fatigue life.
THE LINEARIZED PROBLEM OF MAGNETO-PHOTOELASTICITY
Sharafutdinov, Vladimir
is based on the quasi-isotropic approximation of geometric optics. The method was first proposed by Kravtsov [5]. In Section 2, we use the same quasi-isotropic approximation for deriving the equa- tions demonstrate that these equations co- incide with the Rytov law for quasi-isotropic gyrotropic media
C. Scovel; D. Hush; I. Steinwart
2007-01-01
We extend the Lagrangian duality theory for convex optimization problems to incorporate approximate solutions. In particular,\\u000a we generalize well-known relationships between minimizers of a convex optimization problem, maximizers of its Lagrangian dual,\\u000a saddle points of the Lagrangian, Kuhn–Tucker vectors, and Kuhn–Tucker conditions to incorporate approximate versions. As an\\u000a application, we show how the theory can be used for convex quadratic
Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Elber, W.
1984-01-01
A geometrically nonlinear finite-element analysis has been developed to calculate the strain energy released by delaminating plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, GI, and shear sliding, GII, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow first before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, GI, for a near-surface delamination can be as high as 0.5GII, and can contribute significantly to the delamination growth.
Elastic properties and fracture strength of quasi-isotropic graphite/epoxy composites
NASA Technical Reports Server (NTRS)
Sullivan, T. L.
1977-01-01
The layups of the studied laminates are (0, + or - 60) sub s, (0, + or - 45, 90) sub s, (0, + or - 30, + or - 60, 90) sub s (0, + or - 22 1/2, + or - 45, + or - 67 1/2, 90) sub s. The properties determined were tensile modulus, Poisson's ratio, bending stiffness, fracture strength and fracture strain. Measured properties and properties predicted using laminate theory were found to be in reasonable agreement. Reasons for data scatter were determined.
Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Elber, W.
1984-01-01
A geometrically nonlinear finite-element analysis was developed to calculate the strain energy released by delamination plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, G sub I, and shear sliding, G sub II, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding (G sub II) was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, G sub I, for a near-surface delamination can be as high as 0.5G sub II and can contribute significantly to the delamination growth.
Wissenschaftliches Approximation
Weinmüller, Ewa B.
' am Digitalcomputer Archimedes und die Berechnung von = 3.14159 . . . Das leidige Integral Das Einleitung: `Alles ist Zahl' am Digitalcomputer Archimedes und die Berechnung von = 3.14159 . . . Das Approximation als Sparmaßnahme Anhang Überblick Einleitung: `Alles ist Zahl' am Digitalcomputer Archimedes und
Neukirch, SÃ©bastien
In this paper, we study the bifurcation of limit cycles in Li' enard systems of the form dx dt = y \\Gamma F. By using a method introduced in a previous paper, we obtain a sequence of algebraic approximations, selfÂexcited vibrations in bridges and airplane wings, etc. In each case, there is a standard
John W. Tukey
1948-01-01
The greatest fractional increase in variance when a weighted mean is calculated with approximate weights is, quite closely, the square of the largest fractional error in an individual weight. The average increase will be about one-half this amount. The use of weights accurate to two significant figures, or even to the nearest number of the form: 10, 11, 12, 12,
Schulz, A S; Shmoys, D B; Williamson, D P
1997-11-25
Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 10(6) separate "yes" or "no" decisions to be made. Although one could, in principle, try all 2(10(6)) possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science. PMID:9370525
Approximate Information Theory
Penny, Will
Approximate Inference Will Penny Information Theory Information Entropy Kullback-Liebler Divergence Approximate Inference Will Penny 31st March 2011 #12;Approximate Inference Will Penny Information Theory Will Penny Information Theory Information Entropy Kullback-Liebler Divergence Gaussians Asymmetry
Fast Approximate Convex Decomposition
Ghosh, Mukulika
2012-10-19
Approximate convex decomposition (ACD) is a technique that partitions an input object into "approximately convex" components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can...
Verre, Ruggero; Antosiewicz, Tomasz J; Svedendahl, Mikael; Lodewijks, Kristof; Shegai, Timur; Käll, Mikael
2014-09-23
Quasicrystals are structures that possess long-range order without being periodic. We investigate the unique characteristics of a photonic quasicrystal that consists of plasmonic Ag nanodisks arranged in a Penrose pattern. The quasicrystal scatters light in a complex but spectacular diffraction pattern that can be directly imaged in the back focal plane of an optical microscope, allowing us to assess the excitation efficiency of the various diffraction modes. Furthermore, surface plasmon polaritons can be launched almost isotropically through near-field grating coupling when the quasicrystal is positioned close to a homogeneous silver surface. We characterize the dispersion relation of the different excited plasmon modes by reflection measurements and simulations. It is demonstrated that the quasicrystal in-coupling efficiency is strongly enhanced compared to a nanoparticle array with the same particle density but only short-range lateral order. We envision that the system can be useful for a number of advanced light harvesting and optoelectronic applications. PMID:25182843
Quasicrystals and crystalline approximants
A. I. Goldman; R. F. Kelton
1993-01-01
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.
Contemporary Mathematics Reconstruction algorithm
Sharafutdinov, Vladimir
in reflected light which is ignored in Rytov, and that this is part of the definition of quasi-isotropic given by Kravtsov and Fuki) Is subject classification ok? of the light on for each ray path is approximated
NASA Astrophysics Data System (ADS)
Niiniluoto, Ilkka
2014-03-01
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).
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
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.
Approximation Theory for Matrices
A. D. Kennedy
2004-02-27
We review the theory of optimal polynomial and rational Chebyshev approximations, and Zolotarev's formula for the sign function over the range (\\epsilon \\leq |z| \\leq1). We explain how rational approximations can be applied to large sparse matrices efficiently by making use of partial fraction expansions and multi-shift Krylov space solvers.
Parameter identifiability under approximation
NASA Technical Reports Server (NTRS)
Kunisch, K.; White, L. W.
1986-01-01
The problem of injectivity of the parameter-to-state map is discussed for Galerkin approximations of a linear parabolic equation. A necessary and sufficient condition is derived and illustrated by means of simple examples. Finally, output least squares identifiability of the Galerkin approximations is discussed.
Variational Bayes Approximation Rice University
Cevher, Volkan
Variational Bayes Approximation Rice University STAT 631 / ELEC 639: Graphical Models Instructor of variational Bayes (VB) approximation. This is the second example of a deterministic scheme in approximating
Characteristics Representative Approximately
Swimming Mode Characteristics Representative Image Hovering · Approximately 45° body angle · Low Institute of Technology, Atlanta, GA, USA. 2. Australian Antarctic Division, Kingston, TAS, Australia. 3. School of Biology, Georgia Institute of Technology, Atlanta, GA, USA. Introduction Euphausiids, or krill
Tsunami Travel Time Approximation
NSDL National Science Digital Library
Eric Grosfils
Eric Grosfils, Pomona College Summary Students are asked to calculate approximate tsunami travel times across the Pacific basin. The assignment builds off of a lab introducing students to Spatial Analyst, and ...
Anomalous diffraction approximation limits
NASA Astrophysics Data System (ADS)
Videen, Gorden; Chýlek, Petr
It has been reported in a recent article [Liu, C., Jonas, P.R., Saunders, C.P.R., 1996. Accuracy of the anomalous diffraction approximation to light scattering by column-like ice crystals. Atmos. Res., 41, pp. 63-69] that the anomalous diffraction approximation (ADA) accuracy does not depend on particle refractive index, but instead is dependent on the particle size parameter. Since this is at odds with previous research, we thought these results warranted further discussion.
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. PMID:25528318
Advisory function of the Tales of the Prophets (Qi?a? al-anbiy??)
Helewa, Sami
2012-06-26
This thesis examines the advisory function of the tales of three prophets (Joseph, David and Solomon) in al-?abar?’s (d. 923/310 AH) History and al-Tha?lab?’s (d. 1025/416) Tales of the Prophets within their religio-political ...
Covariant approximation averaging
NASA Astrophysics Data System (ADS)
Shintani, Eigo; Arthur, Rudy; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2015-06-01
We present a new class of statistical error reduction techniques for Monte Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in Nf=2 +1 lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte Carlo calculations over conventional methods for the same cost.
Covariant approximation averaging
Eigo Shintani; Rudy Arthur; Thomas Blum; Taku Izubuchi; Chulwoo Jung; Christoph Lehner
2015-07-08
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Approximate Degradable Quantum Channels
David Sutter; Volkher B. Scholz; Andreas Winter; Renato Renner
2015-08-31
Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact that the complementary channel can be obtained from the channel by applying a degrading map. In this work we introduce the concept of approximate degradable channels, which satisfy this condition up to some finite $\\varepsilon\\geq 0$. That is, there exists a degrading map which upon composition with the channel is $\\varepsilon$-close in the diamond norm to the complementary channel. We show that for any fixed channel the smallest such $\\varepsilon$ can be efficiently determined via a semidefinite program. Moreover, these approximate degradable channels also approximately inherit all other properties of degradable channels. As an application, we derive improved upper bounds to the quantum and private classical capacity for certain channels of interest in quantum communication.
Approximate Bayesian Computation
NASA Astrophysics Data System (ADS)
Cisewski, Jessi
2015-08-01
Explicitly specifying a likelihood function is becoming increasingly difficult for many problems in astronomy. Astronomers often specify a simpler approximate likelihood - leaving out important aspects of a more realistic model. Approximate Bayesian computation (ABC) provides a framework for performing inference in cases where the likelihood is not available or intractable. I will introduce ABC and explain how it can be a useful tool for astronomers. In particular, I will focus on the eccentricity distribution for a sample of exoplanets with multiple sub-populations.
PARALLEL COST APPROXIMATION ALGORITHMS
Patriksson, Michael
9 PARALLEL COST APPROXIMATION ALGORITHMS FOR DIFFERENTIABLE OPTIMIZATION Michael Patriksson Department of Mathematics, Box 354350 University of Washington, Seattle, Washington 98195Â4350 ABSTRACT, a synchronized parallel algorithm which encompasses the Jacobi method, and a parÂ tially asynchronous parallel
The parabolic approximation method
Fred D. Tappert
This article has dealt with various aspects of parabolic approximation methods in underwater acoustics, mostly for propagation of sinusoidal signals. Extensions of these methods to time-dependent problems are also available: pulse propagation, moving sources and receivers, frequency shifting effects due to rapid temporal variations of oceanic conditions, and so forth. However, an adequate description of these extensions would require another
approximate replication a dissertation
Pratt, Vaughan
approximate replication a dissertation submitted to the department of computer science Alden Remi Olston 2003 All Rights Reserved ii #12; I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor
approximate replication a dissertation
Pratt, Vaughan
approximate replication a dissertation submitted to the department of computer science Alden Remi Olston 2003 All Rights Reserved ii #12;I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor
Approximating Integrals Using Probability
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.; Caudle, Kyle A.
2005-01-01
As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…
Optimizing the Zeldovich approximation
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Pellman, Todd F.; Shandarin, Sergei F.
1994-01-01
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.
Fast Approximate Spectral Clustering
Donghui Yan; Ling Huang; Michael I. Jordan
2009-01-01
Spectral clustering refers to a flexible class of clustering proce- dures that can produce high-quality clusterings on small data sets but which has limited applicability to large-scale problems due to its computational complexity of O(n3), with n the number of data points. We extend the range of spectral clustering by develop- ing a general framework for fast approximate spectral clustering
Chalasani, P.; Saias, I.; Jha, S.
1996-04-08
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.
Anytime Classification by Ontology Approximation
ten Teije, Annette
for classification based on approximate subsumption. We give the formal definitions for approximate subsumption. In both cases, approximate reasoning can be useful, in particular when algorithms are monotonic: whenAnytime Classification by Ontology Approximation S.Schlobach, E.Blaauw, M.El Kebir, A.ten Teije, F
Approximate Bayesian Computation
Sunnåker, Mikael; Corander, Jukka; Foll, Matthieu; Dessimoz, Christophe
2013-01-01
Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology). PMID:23341757
Approximate Bayesian computation.
Sunnåker, Mikael; Busetto, Alberto Giovanni; Numminen, Elina; Corander, Jukka; Foll, Matthieu; Dessimoz, Christophe
2013-01-01
Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology). PMID:23341757
Exploring Machin's Approximation of Exploring Machin's Approximation of
Knaust, Helmut
#12;Exploring Machin's Approximation of Precursors Method of Exhaustion `a la Archimedes Archimedes of Precursors Method of Exhaustion `a la Archimedes Archimedes of Syracuse ( 287212 BC) approximated la Archimedes Archimedes of Syracuse ( 287212 BC) approximated by the Method of Exhaustion: 3
Tsuyoshi Ito; Stacey Jeffery
2015-07-02
Span programs are a model of computation that have been used to design quantum algorithms, mainly in the query model. For any decision problem, there exists a span program that leads to an algorithm with optimal quantum query complexity, but finding such an algorithm is generally challenging. We consider new ways of designing quantum algorithms using span programs. We show how any span program that decides a problem $f$ can also be used to decide "property testing" versions of $f$, or more generally, approximate the span program witness size, a property of the input related to $f$. For example, using our techniques, the span program for OR, which can be used to design an optimal algorithm for the OR function, can also be used to design optimal algorithms for: threshold functions, in which we want to decide if the Hamming weight of a string is above a threshold or far below, given the promise that one of these is true; and approximate counting, in which we want to estimate the Hamming weight of the input. We achieve these results by relaxing the requirement that 1-inputs hit some target exactly in the span program, which could make design of span programs easier. We also give an exposition of span program structure, which increases the understanding of this important model. One implication is alternative algorithms for estimating the witness size when the phase gap of a certain unitary can be lower bounded. We show how to lower bound this phase gap in some cases. As applications, we give the first upper bounds in the adjacency query model on the quantum time complexity of estimating the effective resistance between $s$ and $t$, $R_{s,t}(G)$, of $\\tilde O(\\frac{1}{\\epsilon^{3/2}}n\\sqrt{R_{s,t}(G)})$, and, when $\\mu$ is a lower bound on $\\lambda_2(G)$, by our phase gap lower bound, we can obtain $\\tilde O(\\frac{1}{\\epsilon}n\\sqrt{R_{s,t}(G)/\\mu})$, both using $O(\\log n)$ space.
Generalized Low-Rank Approximations
Srebro, Nathan
2003-01-15
We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving {\\\\em weighted} low rank approximation problems, which, unlike simple ...
DALI: Derivative Approximation for LIkelihoods
NASA Astrophysics Data System (ADS)
Sellentin, Elena
2015-07-01
DALI (Derivative Approximation for LIkelihoods) is a fast approximation of non-Gaussian likelihoods. It extends the Fisher Matrix in a straightforward way and allows for a wider range of posterior shapes. The code is written in C/C++.
Approximation by hinge functions
Faber, V.
1997-05-01
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.
NASA Astrophysics Data System (ADS)
Lubkin, Elihu
2002-04-01
In 1993,(E. & T. Lubkin, Int.J.Theor.Phys. 32), 993 (1993) we gave exact mean trace
Powell, Warren B.
CHAPTER 6 STOCHASTIC APPROXIMATION METHODS Stochastic approximation methods are the foundation otherwise seem completely intractable. This chapter provides a basic introduction to stochastic. By Warren B. Powell Copyright c 2007 John Wiley & Sons, Inc. 179 #12;180 STOCHASTIC APPROXIMATION METHODS
Supporting Text Approximation of the Multinomial. Using Stirling's approximation
Samuelsson, BjÃ¶rn
Supporting Text Approximation of the Multinomial. Using Stirling's approximation n! (n/e)n 2n! . [S12] To calculate B L (^n) limN BN L (^n), we apply Stirling's formula to N!, n0!, and n1!, which that r Stirling's formula
Approximate Bayesian Inference Approximate Bayesian Inference for Survival
Steinsland, Ingelin
Approximate Bayesian Inference Approximate Bayesian Inference for Survival Models Rupali Akerkar1 Inference Introduction Outline Basic idea Survival model Present survival model as a latent Gaussian model Basic idea Survival model Present survival model as a latent Gaussian model Apply INLA Verify results
Approximation Algorithms for Spreading Points
Cabello, Sergio
Approximation Algorithms for Spreading Points Sergio Cabello institute of information and computing for Spreading Points Sergio Cabello Institute of Information and Computing Sciences Universiteit Utrecht
Approximation Algorithms for Spreading Points
Utrecht, Universiteit
Approximation Algorithms for Spreading Points Sergio Cabello institute of information and computing for Spreading Points # Sergio Cabello Institute of Information and Computing Sciences Universiteit Utrecht
Unbiased Approximation in Multicriteria Optimization
Klamroth, Kathrin
to the problem structure and scaling which makes the approximation process unbiased and self-driven. Decision budgeting and location and layout plan- ning. To support the decision making process, approximations of the non- dominated set are an attractive tool since they visualize the alternatives for the decision maker
Unbiased Approximation in Multicriteria Optimization
Klamroth, Kathrin
to the problem structure and scaling which makes the approximation process unbiased and selfdriven. Decision budgeting and location and layout plan ning. To support the decision making process, approximations of the non dominated set are an attractive tool since they visualize the alternatives for the decision maker
Secure Multiparty Computation of Approximations
Wright, Rebecca N.
Secure Multiparty Computation of Approximations (Extended Abstract) Joan Feigenbaum 1? , Yuval. However, secure computation of â?? f may not be as private as secure comÂ putation of f , because the output of secure multiparty approximate computations that retain the privacy of a secure computation of f . We
Secure Multiparty Computation of Approximations
Ishai, Yuval
Secure Multiparty Computation of Approximations Joan Feigenbaum 1# , Yuval Ishai 2,3 , Tal Malkin 3 revealing more information than necessary. Let â?? f be an approximation to f . Secure multiparty computation of â?? f allows the parties to compute â?? f without revealing unnecessary informaÂ tion, but a secure
Approximate Graph Products Marc Hellmutha
Stadler, Peter F.
Approximate Graph Products Marc Hellmutha , Wilfried Imrichb , Werner KlÂ¨ocklb , Peter F. Stadlera87501, USA Abstract The problem of recognizing approximate graph products arises in theoretical biology. This paper presents an algorithm that recognizes a large class of ap- proximate graph products. The main part
Approximate Inference and Scientific Method
Mark A. Fulk; Sanjay Jain
1990-01-01
Abstract A new identication criterion, motivated by notions of successively improving approximations in the philosophy of science, is dened. It is shown that the class of recursive functions is identiable under this criterion. This result is extended to permit somewhat more realistic types of data than usual. This criterion is then modied to consider restrictions on the quality of approximations,
Fuzzy systems are universal approximators
Li-Xin Wang
1992-01-01
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
) Hermite approximation for conic sections
Floater, Michael S.
An O(h 2n ) Hermite approximation for conic sections Michael Floater SINTEF P.O. Box 124, Blindern in the form of a rational quadratic B´ezier curve and any positive odd integer n, a geometric Hermite having an approximation order of O(h2n ). A bound on the Hausdorff error of the Hermite interpolant
Structural optimization with approximate sensitivities
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.
1994-01-01
Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.
Mechanism design with approximate types
Zhu, Zeyuan Allen
2012-01-01
In mechanism design, we replace the strong assumption that each player knows his own payoff type exactly with the more realistic assumption that he knows it only approximately: each player i only knows that his true type ...
Approximate Correspondences in High Dimensions
Grauman, Kristen
2006-06-15
Pyramid intersection is an efficient method for computing an approximate partial matching between two sets of feature vectors. We introduce a novel pyramid embedding based on a hierarchy of non-uniformly shaped bins that ...
Interplay of approximate planning strategies
Huys, Quentin J. M.
Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and ...
Metrical Diophantine approximation for quaternions
NASA Astrophysics Data System (ADS)
Dodson, Maurice; Everitt, Brent
2014-11-01
Analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general `lim sup' sets.
Approximate inference in graphical models
Hennig, Philipp
2011-02-08
aspects of the problem itself. In effect, this entire thesis is a collection of approximations and design tricks. This is not necessarily a deficiency: Entire disciplines in other fields, e.g. condensed matter physics, could arguably be described... as collections of highly developed integration tricks. The 2.3 Approximate Inference Methods 15 hope is that the algorithms presented in the following sections and the remaining chapters of this thesis can convey concepts necessary for applied inference problems...
Approximate entropy of network parameters
NASA Astrophysics Data System (ADS)
West, James; Lacasa, Lucas; Severini, Simone; Teschendorff, Andrew
2012-04-01
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.
Kirchhoff approximation for diffusive waves.
Ripoll, J; Ntziachristos, V; Carminati, R; Nieto-Vesperinas, M
2001-11-01
Quantitative measurements of diffuse media, in spectroscopic or imaging mode, rely on the generation of appropriate forward solutions, independently of the inversion scheme employed. For complex boundaries, the use of numerical methods is generally preferred due to implementation simplicity, but usually results in great computational needs, especially in three dimensions. Analytical expressions are available, but are limited to simple geometries such as a diffusive slab, a sphere or a cylinder. An analytical approximation, the Kirchhoff approximation, also called the tangent-plane method is presented for the case of diffuse light. Using this approximation, analytical solutions of the diffusion equation for arbitrary boundaries and volumes can be derived. Also, computation time is minimized since no matrix inversion is involved. The accuracy of this approximation is evaluated on comparison with results from a rigorous numerical technique calculated for an arbitrary geometry. Performance of the approximation as a function of the optical properties and the size of the medium is examined and it is demonstrated that the computation time of the direct scattering model is reduced at least by two orders of magnitude. PMID:11735978
Relativistic regular approximations revisited: An infinite-order relativistic approximation
Dyall, K.G. [Thermosciences Institute, NASA Ames Research Center, Mail Stop 230-3, Moffett Field, California 94035-1000 (United States)] [Thermosciences Institute, NASA Ames Research Center, Mail Stop 230-3, Moffett Field, California 94035-1000 (United States); van Lenthe, E. [Afdeling Theoretisch Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam (The Netherlands)] [Afdeling Theoretisch Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam (The Netherlands)
1999-07-01
The concept of the regular approximation is presented as the neglect of the energy dependence of the exact Foldy{endash}Wouthuysen transformation of the Dirac Hamiltonian. Expansion of the normalization terms leads immediately to the zeroth-order regular approximation (ZORA) and first-order regular approximation (FORA) Hamiltonians as the zeroth- and first-order terms of the expansion. The expansion may be taken to infinite order by using an un-normalized Foldy{endash}Wouthuysen transformation, which results in the ZORA Hamiltonian and a nonunit metric. This infinite-order regular approximation, IORA, has eigenvalues which differ from the Dirac eigenvalues by order E{sup 3}/c{sup 4} for a hydrogen-like system, which is a considerable improvement over the ZORA eigenvalues, and similar to the nonvariational FORA energies. A further perturbation analysis yields a third-order correction to the IORA energies, TIORA. Results are presented for several systems including the neutral U atom. The IORA eigenvalues for all but the 1s spinor of the neutral system are superior even to the scaled ZORA energies, which are exact for the hydrogenic system. The third-order correction reduces the IORA error for the inner orbitals to a very small fraction of the Dirac eigenvalue. {copyright} {ital 1999 American Institute of Physics.}
Approximating Graphic TSP by Matchings
Mömke, Tobias
2011-01-01
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a decreased cost. For the TSP on graphic metrics (graph-TSP), the approach yields a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted to a class of graphs that contains degree three bounded and claw-free graphs, we show that the integrality gap of the Held-Karp relaxation matches the conjectured ratio 4/3. The framework allows for generalizations in a natural way and also leads to a 1.586-approximation algorithm for the traveling salesman path problem on graphic metrics where the start and end vertices are prespecified.
Lecture 1: Normal approximation Lecture 2: Poisson approximation and other distributions
Lecture 1: Normal approximation Lecture 2: Poisson approximation and other distributions A Short #12;Lecture 1: Normal approximation Lecture 2: Poisson approximation and other distributions Outline Lecture 1: Normal approximation Motivation Distributional distances The Stein equation Local dependence
Assessing approximate broadband omnidirectional antireflection
NASA Astrophysics Data System (ADS)
Barriuso, A. G.; Monzón, J. J.; Sánchez-Soto, L. L.; Felipe, A.
2007-02-01
By introducing the notion of wavelength- and angle-averaged transmittance, we assess in a systematic way the possibility of achieving approximate omnidirectional antireflection in a wide spectral range by using double-layer systems. We also determine the optimum range of thicknesses for which this broadband omnidirectional antireflection occurs.
PSEUDOSPECTRAL APPROXIMATION UNSTEADY STOKES EQUATION
Heinrichs, Wilhelm
Lobatto nodes (no staggered grids!) does not introduce spurious modes. Finally we present effective finite. This means that the solution is approximated by global Chebyshev polynomials (see, e.g., Canuto et al. [6 the properties of this operator. For dis cretization we employ the Chebyshev GaussLobatto nodes. We avoid
Online Learning and Stochastic Approximations
Bottou, LÃ©on
, realÂlife training sets (Le Cun et al., 1989) (MË?uller, Gunzinger and GuggenbË?uhl, 1995). The earlyOnline Learning and Stochastic Approximations Lâ??eon Bottou AT&T Labs--Research Red Bank, NJ07701 Introduction Almost all of the early work on Learning Systems focused on online algoÂ rithms (Hebb, 1949
Online Learning and Stochastic Approximations
Bottou, LÃ©on
, real-life training sets (Le Cun et al., 1989) (MÂ¨uller, Gunzinger and GuggenbÂ¨uhl, 1995). The earlyOnline Learning and Stochastic Approximations LÂ´eon Bottou AT&T LabsÂResearch Red Bank, NJ07701 Introduction Almost all of the early work on Learning Systems focused on online algo- rithms (Hebb, 1949
Normality, Computability and Diophantine Approximation
Becher, Verónica
Normality, Computability and Diophantine Approximation Ver´onica Becher Yann Bugeaud Theodore (Becher, Bugeaud, Slaman 2014) Let a be a real greater than or equal to 2. Then, the real (Becher, Bugeaud, Slaman 2014) Let a be a real greater than or equal to 2. Then, the real
Weak non-Gaussian approximation
Vasil'ev, O.V.; Dawson, K.A. (Theory Group, Department of Chemistry, University College Dublin, Belfield, Dublin 4 (Ireland))
1995-01-01
A superposition of Gaussian functionals is considered as a trial functional for the Bogoliubov inequality. The direct optimization of the Bogoliubov inequality generates a non-Gaussian approximation. This function may be strongly non-Gaussian but the kernel is the same as the usual one, up to a multiplicative constant.
ERROR BOUNDED APPROXIMATE REPARAMETRIZATION OF
Utah, University of
ERROR BOUNDED APPROXIMATE REPARAMETRIZATION OF NON-UNIFORM RATIONAL B-SPLINE CURVES by Mark D SCHOOL SUPERVISORY COMMITTEE APPROVAL of a thesis submitted by Mark D. Bloomenthal This thesis has been to be satisfactory. Chair: Elaine Cohen Frank Stenger Peter Shirley #12;THE UNIVERSITY OF UTAH GRADUATE SCHOOL FINAL
Pythagorean Approximations and Continued Fractions
ERIC Educational Resources Information Center
Peralta, Javier
2008-01-01
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
Chemical Laws, Idealization and Approximation
NASA Astrophysics Data System (ADS)
Tobin, Emma
2013-07-01
This paper examines the notion of laws in chemistry. Vihalemm ( Found Chem 5(1):7-22, 2003) argues that the laws of chemistry are fundamentally the same as the laws of physics they are all ceteris paribus laws which are true "in ideal conditions". In contrast, Scerri (2000) contends that the laws of chemistry are fundamentally different to the laws of physics, because they involve approximations. Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34-50, 2000) agree that the laws of chemistry are operationally different to the laws of physics, but claim that the distinction between exact and approximate laws is too simplistic to taxonomise them. Approximations in chemistry involve diverse kinds of activity and often what counts as a scientific law in chemistry is dictated by the context of its use in scientific practice. This paper addresses the question of what makes chemical laws distinctive independently of the separate question as to how they are related to the laws of physics. From an analysis of some candidate ceteris paribus laws in chemistry, this paper argues that there are two distinct kinds of ceteris paribus laws in chemistry; idealized and approximate chemical laws. Thus, while Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34--50, 2000) are correct to point out that the candidate generalisations in chemistry are diverse and heterogeneous, a distinction between idealizations and approximations can nevertheless be used to successfully taxonomise them.
Envy-Free Makespan Approximation
Cohen, Edith; Fiat, Amos; Kaplan, Haim; Olonetsky, Svetlana
2009-01-01
We study envy-free mechanisms for scheduling tasks on unrelated machines (agents) that approximately minimize the makespan. For indivisible tasks, we put forward an envy-free poly-time mechanism that approximates the minimal makespan to within a factor of $O(\\log m)$, where $m$ is the number of machines. We also show a lower bound of $\\Omega(\\log m / \\log\\log m)$. This improves the recent result of Hartline {\\sl et al.} \\cite{Ahuva:2008} who give an upper bound of $(m+1)/2$, and a lower bound of $2-1/m$. For divisible tasks, we show that there always exists an envy-free poly-time mechanism with optimal makespan.
Hydrogen Beyond the Classic Approximation
Scivetti, I
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Iterative Thresholding for Sparse Approximations
Thomas Blumensath; Mike E. Davies
2008-01-01
Sparse signal expansions represent or approximate a signal using a small number of elements from a large collection of elementary\\u000a waveforms. Finding the optimal sparse expansion is known to be NP hard in general and non-optimal strategies such as Matching\\u000a Pursuit, Orthogonal Matching Pursuit, Basis Pursuit and Basis Pursuit De-noising are often called upon. These methods show\\u000a good performance in
Approximate Counting of Graphical Realizations.
Erd?s, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erd?s and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erd?s and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994
Approximate reasoning using terminological models
NASA Technical Reports Server (NTRS)
Yen, John; Vaidya, Nitin
1992-01-01
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.
Neighbourhood approximation using randomized forests.
Konukoglu, Ender; Glocker, Ben; Zikic, Darko; Criminisi, Antonio
2013-10-01
Leveraging available annotated data is an essential component of many modern methods for medical image analysis. In particular, approaches making use of the "neighbourhood" structure between images for this purpose have shown significant potential. Such techniques achieve high accuracy in analysing an image by propagating information from its immediate "neighbours" within an annotated database. Despite their success in certain applications, wide use of these methods is limited due to the challenging task of determining the neighbours for an out-of-sample image. This task is either computationally expensive due to large database sizes and costly distance evaluations, or infeasible due to distance definitions over semantic information, such as ground truth annotations, which is not available for out-of-sample images. This article introduces Neighbourhood Approximation Forests (NAFs), a supervised learning algorithm providing a general and efficient approach for the task of approximate nearest neighbour retrieval for arbitrary distances. Starting from an image training database and a user-defined distance between images, the algorithm learns to use appearance-based features to cluster images approximating the neighbourhood structured induced by the distance. NAF is able to efficiently infer nearest neighbours of an out-of-sample image, even when the original distance is based on semantic information. We perform experimental evaluation in two different scenarios: (i) age prediction from brain MRI and (ii) patch-based segmentation of unregistered, arbitrary field of view CT images. The results demonstrate the performance, computational benefits, and potential of NAF for different image analysis applications. PMID:23725639
Computer Experiments for Function Approximations
Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C
2007-10-15
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.
Approximate Counting of Graphical Realizations
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erd?s and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erd?s and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994
Networks and the Best Approximation Property
Girosi, Federico
1989-10-01
Networks can be considered as approximation schemes. Multilayer networks of the backpropagation type can approximate arbitrarily well continuous functions (Cybenko, 1989; Funahashi, 1989; Stinchcombe and White, 1989). We ...
Approximately Independent Features of Languages
NASA Astrophysics Data System (ADS)
Holman, Eric W.
To facilitate the testing of models for the evolution of languages, the present paper offers a set of linguistic features that are approximately independent of each other. To find these features, the adjusted Rand index (R?) is used to estimate the degree of pairwise relationship among 130 linguistic features in a large published database. Many of the R? values prove to be near zero, as predicted for independent features, and a subset of 47 features is found with an average R? of -0.0001. These 47 features are recommended for use in statistical tests that require independent units of analysis.
Generalized Gradient Approximation Made Simple
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
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.}
Fermion tunneling beyond semiclassical approximation
Majhi, Bibhas Ranjan [S. N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata-700098 (India)
2009-02-15
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in R. Banerjee and B. R. Majhi, J. High Energy Phys. 06 (2008) 095 for the scalar particle, Hawking radiation as tunneling of the Dirac particle through an event horizon is analyzed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.
Rotating wave approximation and entropy
Andreas Kurcz; Antonio Capolupo; Almut Beige; Emilio Del Giudice; Giuseppe Vitiello
2010-06-03
This paper studies composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. Going beyond the rotating wave approximation, it is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the entropy operator and generates an irreversible time evolution. The vacuum state of the system is shown to evolve into a generalized coherent state exhibiting entanglement of the modes in which the counter-rotating terms are expressed. Possible consequences at observational level in quantum optics experiments are currently under study.
LUBRICATION APPROXIMATION WITH PRESCRIBED NONZERO CONTACT ANGLE
Otto, Felix
LUBRICATION APPROXIMATION WITH PRESCRIBED NONZERO CONTACT ANGLE Felix Otto Department--time existence for a weak solution s(t; x) â?? 0 of the lubrication approximation @ t s + @ x (s @ 3 x s) = 0 in fs will later motivate the way we construct approximate solutions for the lubrication approximation we are going
Approximate simulation of quantum channels
NASA Astrophysics Data System (ADS)
Bény, Cédric; Oreshkov, Ognyan
2011-08-01
Earlier, we proved a duality between two optimizations problems [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.104.120501 104, 120501 (2010)]. The primary one is, given two quantum channels M and N, to find a quantum channel R such that R?N is optimally close to M as measured by the worst-case entanglement fidelity. The dual problem involves the information obtained by the environment through the so-called complementary channels M? and N?, and consists in finding a quantum channel R' such that R'?M? is optimally close to N?. It turns out to be easier to find an approximate solution to the dual problem in certain important situations, notably when M is the identity channel—the problem of quantum error correction—yielding a good near-optimal worst-case entanglement fidelity as well as the corresponding near-optimal correcting channel. Here we provide more detailed proofs of these results. In addition, we generalize the main theorem to the case where there are certain constraints on the implementation of R, namely, on the number of Kraus operators. We also offer a simple algebraic form for the near-optimal correction channel in the case M=id. For approximate error correction, we show that any ?-correctable channel is, up to appending an ancilla, ?-close to an exactly correctable one. We also demonstrate an application of our theorem to the problem of minimax state discrimination.
Finite approximations in fluid mechanics
Hirschel, E.H.
1986-01-01
This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems.
The Monostatic/Bistatic Approximation
NASA Technical Reports Server (NTRS)
Schuh, Michael J.; Woo, Alex C.; Simon, Michael P.
1994-01-01
Many Radar Cross Section (RCS) prediction codes are limited to one monostatic return per run. However, such codes can calculate multiple bistatic returns per incident angle for a relatively small amount of additional computer resources. This note describes a method of using bistatic returns to generate multiple monostatic predictions for each incident angle computed. Typical results are presented and show the accuracy is initially good and then degrades as the separation angle between the incident and viewing angles becomes large. Introduction Since 1990, the monostatic/bistatic approximation has been used to reduce the number of runs required by finite-volume time-domain (FVTD) codes for making RCS versus azimuth plots. This approximation was spawned by the observation of a range test where the transmit and receive antennas were separated by a few degrees to prevent cross talk between the antennas. The measurements from this range are presented as monostatic RCS rather than bistatic: RCS. The procedure of reporting experimental bistatic RCS as the monostatic RCS at the angle bisecting the transmit and receive antennas was extended to FVTD codes and produces excellent results.
Approximate simulation of quantum channels
Beny, Cedric; Oreshkov, Ognyan
2011-08-15
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.
Nonrenormalizability of the classical statistical approximation
NASA Astrophysics Data System (ADS)
Epelbaum, Thomas; Gelis, François; Wu, Bin
2014-09-01
In this paper, we discuss questions related to the renormalizability of the classical statistical approximation, an approximation scheme that has been used recently in several studies of out-of-equilibrium problems in quantum field theory. Although the ultraviolet power counting in this approximation scheme is identical to that of the unapproximated quantum field theory, this approximation is not renormalizable. The leading cause of this nonrenormalizability is the breakdown of Weinberg's theorem in this approximation. We also discuss some practical implications of this negative result for simulations that employ this approximation scheme, and we speculate about a possible modification of the classical statistical approximation in order to systematically subtract the leading residual divergences.
Reconstruction within the Zeldovich approximation
White, Martin
2015-01-01
The Zeldovich approximation, 1st order Lagrangian perturbation theory, provides a good description of the clustering of matter and galaxies on large scales. The acoustic feature in the large-scale correlation function of galaxies imprinted by sound waves in the early Universe has been successfully used as a `standard ruler' to constrain the expansion history of the Universe. The standard ruler can be improved if a process known as density field reconstruction is employed. In this paper we develop the Zeldovich formalism to compute the correlation function of biased tracers in both real- and redshift-space using the simplest reconstruction algorithm with a Gaussian kernel and compare to N-body simulations. The model qualitatively describes the effects of reconstruction on the simulations, though its quantitative success depends upon how redshift-space distortions are handled in the reconstruction algorithm.
Interplay of approximate planning strategies
Huys, Quentin J. M.; Lally, Níall; Faulkner, Paul; Eshel, Neir; Seifritz, Erich; Gershman, Samuel J.; Dayan, Peter; Roiser, Jonathan P.
2015-01-01
Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and hierarchically decompose hard tasks into simpler subtasks. Theoretical and cognitive research has revealed several such strategies; however, little is known about their establishment, interaction, and efficiency. Here, we use model-based behavioral analysis to provide a detailed examination of the performance of human subjects in a moderately deep planning task. We find that subjects exploit the structure of the domain to establish subgoals in a way that achieves a nearly maximal reduction in the cost of computing values of choices, but then combine partial searches with greedy local steps to solve subtasks, and maladaptively prune the decision trees of subtasks in a reflexive manner upon encountering salient losses. Subjects come idiosyncratically to favor particular sequences of actions to achieve subgoals, creating novel complex actions or “options.” PMID:25675480
Analytical approximations for spiral waves
NASA Astrophysics Data System (ADS)
Löber, Jakob; Engel, Harald
2013-12-01
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency ? and core radius R0. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent ?(R+) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R+ with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
Analytical approximations for spiral waves
Löber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald [Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin (Germany)] [Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin (Germany)
2013-12-15
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency ? and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent ?(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
Analytical approximations for spiral waves.
Löber, Jakob; Engel, Harald
2013-12-01
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency ? and core radius R(0). For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent ?(R(+)) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R(+) with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium. PMID:24387574
Producing approximate answers to database queries
NASA Technical Reports Server (NTRS)
Vrbsky, Susan V.; Liu, Jane W. S.
1993-01-01
We have designed and implemented a query processor, called APPROXIMATE, that makes approximate answers available if part of the database is unavailable or if there is not enough time to produce an exact answer. The accuracy of the approximate answers produced improves monotonically with the amount of data retrieved to produce the result. The exact answer is produced if all of the needed data are available and query processing is allowed to continue until completion. The monotone query processing algorithm of APPROXIMATE works within the standard relational algebra framework and can be implemented on a relational database system with little change to the relational architecture. We describe here the approximation semantics of APPROXIMATE that serves as the basis for meaningful approximations of both set-valued and single-valued queries. We show how APPROXIMATE is implemented to make effective use of semantic information, provided by an object-oriented view of the database, and describe the additional overhead required by APPROXIMATE.
Rational Approximation for a Quasilinear Parabolic Equation
P. M. Gauthier; N. Tarkhanov
2007-09-22
Approximation theorems, analogous to known results for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for a nonlinear parabolic equation, Burgers' equation.
Convergence of Simultaneous Perturbation Stochastic Approximation for
Marcus, Steven I.
1 Convergence of Simultaneous Perturbation Stochastic Approximation for Nondifferentiable Perturbation Stochastic Approximation (SPSA) for function minimization. The standard assumption for convergence the differentiability requirement and prove convergence using convex analysis. Keywords Simultaneous Perturbation
Raftery, Adrian
___________________________________________________________________________________________________ Approximate Bayes Factors for Image Segmentation: The Pseudolikelihood Information Criterion (PLIC) Derek C as corresponding to a statistical model for the image, and the resulting models are compared via approximate Bayes factors. The Bayes factors are approximated using BIC (Bayesian Information Criterion), where the required
OBNER BASES AND GENERALIZED PAD APPROXIMATION
Gao, Shuhong
GR Ë? OBNER BASES AND GENERALIZED PAD â?? E APPROXIMATION JEFFREY B. FARR AND SHUHONG GAO Abstract. It is shown how to find general multivariate Padâ??e approximation using GrË?obner basis technique. This method The classical Padâ??e approximation theory for univariate polynomials says that for any polynomials f, g # F
ON BADLY APPROXIMABLE NUMBERS AND CERTAIN GAMES
Kleinbock, Dmitry
ON BADLY APPROXIMABLE NUMBERS AND CERTAIN GAMES BY WOLFGANG M. SCHMIDT 1. Introduction. A number a is called badly approximable if ja --p/q | > c/q2 for some c > 0 and all rationals pjq. It is known that an irrational number a is badly approximable if and only if the partial denominators in its continued fraction
On the Approximation of Complicated Dynamical Behavior
On the Approximation of Complicated Dynamical Behavior Michael Dellnitz and Oliver Junge techniques for the numerical approximation of compli- cated dynamical behavior. In particular, we develop numerical methods which allow to approximate SBR-measures as well as (almost) cyclic behavior of a dynamical
Corrected Pade Approximants for Indeterminate Problem
Simon Gluzman; Vyacheslav I. Yukalov
2015-09-29
A method of self-similarly corrected Pade approximants is suggested making it possible to essentially widen the class of functions treated by these approximants. The method works even in those cases, where the standard Pade approximants are not applicable, resulting in divergent sequences.
Statistics for approximate gene clusters
2013-01-01
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. PMID:24564620
On Gakerkin approximations for the quasigeostrophic equations
Rocha, Cesar B; Grooms, Ian
2015-01-01
We study the representation of approximate solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes. In particular, we show that standard modes are compatible with nonzero buoyancy at the surfaces and can be used to solve the Eady problem. We extend two existing Galerkin approaches (A and B) and develop a new Galerkin approximation (C). Approximation A, due to Flierl (1978), represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith (2009b), represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series, but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the b...
A unified approach to the Darwin approximation
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
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.
Comparison of some approximations for isotropic turbulence.
NASA Technical Reports Server (NTRS)
Herring, J. R.; Kraichnan, R. H.
1972-01-01
Study of several related turbulence approximations with regard to dynamical properties and agreement of numerical predictions with laboratory and computer experiments. The approximations considered include the direct-interaction equations (Kraichnan, 1964), Herring's (1966) self-consistent-field theory, a generalization of Edwards' (1964) theory, the abridged Lagrangian-history, direct-interaction approximation (Kraichnan, 1966), the test-field model (Kraichnan, 1971), and an approximation, not previously described, in which one velocity field passively suffers convection by another. Most of the cited approximations are representable by stochastic model equations for the velocity amplitude. Explicit constructions are given for the stochastic models, in a form that can be approximated on a digital computer. These constructions are used to discuss the physical and mathematical differences between the model dynamics and actual Navier-Stokes dynamics.-
A greedy algorithm for yield surface approximation
NASA Astrophysics Data System (ADS)
Bleyer, Jérémy; de Buhan, Patrick
This Note presents an approximation method for convex yield surfaces in the framework of yield design theory. The proposed algorithm constructs an approximation using a convex hull of ellipsoids such that the approximate criterion can be formulated in terms of second-order conic constraints. The algorithm can treat bounded as well as unbounded yield surfaces. Its efficiency is illustrated on two yield surfaces obtained using up-scaling procedures.
Bent approximations to synchrotron radiation optics
Heald, S.
1981-01-01
Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors.
Adiabatic approximation for weakly open systems
Thunstroem, Patrik; Aaberg, Johan; Sjoeqvist, Erik
2005-08-15
We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is 'physically reasonable' as under wide conditions it leads to a completely positive evolution, if the original master equation can be written on a time-dependent Lindblad form. We demonstrate the approximation for a non-Abelian holonomic implementation of the Hadamard gate, disturbed by a decoherence process. We compare the resulting approximate evolution with numerical simulations of the exact equation.
Near approximations via general ordered topological spaces
M. Abo-Elhamayel
2014-12-27
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The topology induced by binary relations is used to generalize the basic rough set concepts. This paper studies near approximation via general ordered topological approximation spaces which may be viewed as a generalization of the study of near approximation from the topological view. The basic concepts of some increasing (decreasing) near approximations, increasing (decreasing) near boundary regions and increasing (decreasing) near accuracy were introduced and sufficiently illustrated. Moreover, proved results, implications and add examples.
On Approximation Complexity of Metric Dimension Problem
NASA Astrophysics Data System (ADS)
Hauptmann, Mathias; Schmied, Richard; Viehmann, Claus
We study the approximation complexity of the Metric Dimension problem in bounded degree, dense as well as in general graphs. For the general case, we prove that the Metric Dimension problem is not approximable within ( 1 - ? ) ln n for any ? > 0, unless NP subseteq DTIME( n^{log log n} ), and we give an approximation algorithm which matches the lower bound. Even for bounded degree instances it is APX-hard to determine (compute) the exact value of the metric dimension which we prove by constructing an approximation preserving reduction from the bounded degree Vertex Cover problem.
Approximability and Parameterized Complexity of Minmax Values
Miltersen, Peter Bro
Dueholm Hansen, Peter Bro Miltersen, and Troels Bjerre Sørensen Department of Computer Science, UniversityApproximability and Parameterized Complexity of Minmax Values Kristoffer Arnsfelt Hansen , Thomas
Determination of approximate nonlinear self-adjointenss and approximate conservation law
Zhi-Yong Zhang
2013-04-22
Approximate nonlinear self-adjointness is an effective method to construct approximate conservation law of perturbed partial differential equations (PDEs). In this paper, we study the relations between approximate nonlinear self-adjointness of perturbed PDEs and nonlinear self-adjointness of the corresponding unperturbed PDEs, and consequently provide a simple approach to discriminate approximate nonlinear self-adjointness of perturbed PDEs. Moreover, a succinct approximate conservation law formula by virtue of the known conservation law of the unperturbed PDEs is given in an explicit form. As an application, we classify a class of perturbed wave equations to be approximate nonlinear self-adjointness and construct the general approximate conservation laws formulae. The specific examples demonstrate that approximate nonlinear self-adjointness can generate new approximate conservation laws.
Private Approximation of NPhard Functions [Extended Abstract
Krauthgamer, Robert
digital or hard copies of all or part of this work for personal or classroom use is granted without fee to compute some approximation for f(x). This hap- pens either because the exact value for f is hardPrivate Approximation of NPÂhard Functions [Extended Abstract] Shai Halevi #3; Robert Krauthgamer y
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Notion of p-value Parametric Approximations
Nuel, Gregory
Notion of p-value Parametric Approximations Power Significance of an Observation in Post-Genomics G, March 7 - 10, 2011 G. NUEL Significance of an Observation in Post-Genomics #12;Notion of p-value Parametric Approximations Power Outline 1 Notion of p-value Spacer Example Random Sequences Empirical p-values
REMAINDER PAD E APPROXIMANTS FOR THE EXPONENTIAL
Rivoal, Tanguy
REMAINDER PAD â?? E APPROXIMANTS FOR THE EXPONENTIAL FUNCTION MARC PR â?? EVOST AND TANGUY RIVOAL Abstract. Following earlier research of ours, we propose a new method for obtaining the complete Padâ??e table of the exponential function. It is based on an explicit construction of certain Padâ??e approximants
MULTIPLE ZETA VALUES, PAD E APPROXIMATION AND
Rivoal, Tanguy
MULTIPLE ZETA VALUES, PAD â?? E APPROXIMATION AND VASILYEV'S CONJECTURE S. FISCHLER AND T. RIVOAL Abstract. Sorokin gave in 1996 a new proof that # is transcendental. It is based on a simultaneous Pad zeta values equal to powers of #. In this paper we construct a Padâ??e approximation problem of the same
Efficient Real Root Approximation Michael Kerber
Waldmann, Uwe
Efficient Real Root Approximation Michael Kerber IST (Institute of Science and Technology) Austria real roots of a square- free polynomial f. Given isolating intervals, our algorithm refines each of them to a certain width 2-L, that is, each of the roots is approximated to L bits after the binary
Efficient Real Root Approximation Michael Kerber
Waldmann, Uwe
Efficient Real Root Approximation Michael Kerber IST (Institute of Science and Technology) Austria real roots of a square- free polynomial f . Given isolating intervals, our algorithm refines each of them to a width at most 2-L, that is, each of the roots is approximated to L bits after the binary
FIRSTORDER ROUGH LOGIC I: APPROXIMATE REASONING
Lin, Tsau Young
FIRSTORDER ROUGH LOGIC I: APPROXIMATE REASONING VIA ROUGH SETS T.Y. Lin Mathematics and Computer Earlier the authors have shown that rough sets can be characterized by six topological properties for Rough Approximation or simply Rough Logic. The axiom schemas of rough logic turn out to be the same
Greedy Algorithm and m Term Trigonometric Approximation
V. N. Temlyakov
1998-01-01
. We study the following nonlinear method of approximation by trigonometric polynomials in this paper. For a periodic function\\u000a f we take as an approximant a trigonometric polynomial of the form , where is a set of cardinality m containing the indices of the m biggest (in absolute value) Fourier coefficients of function f . We compare the efficiency
Approximation Metrics based on Probabilistic Bisimulations
Abate, Alessandro
HAS 2011 Approximation Metrics based on Probabilistic Bisimulations for General State-Space Markov Mekelweg 2, 2628 CD Delft The Netherlands Abstract This article provides a survey of approximation metrics, namely on domains with infinite cardinality and endowed with proper measurability and metric structures
Quirks of Stirling's Approximation
ERIC Educational Resources Information Center
Macrae, Roderick M.; Allgeier, Benjamin M.
2013-01-01
Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…
ANALYSIS AND FINITE ELEMENT APPROXIMATION OF A
Fairag, Faisal
ANALYSIS AND FINITE ELEMENT APPROXIMATION OF A LADYZHENSKAYA MODEL FOR VISCOUS FLOW existence and uniqueness results for the model. Finite element approximation procedures are presented: Finite element method, Ladyzhenskaya model, streamfunction formulation. 1991 MSC: 65N30, 76M10, 78M10, 76
Learning incoherent dictionaries for sparse approximation using
Plumbley, Mark
2 Learning incoherent dictionaries for sparse approximation using iterative projections dictionaries for sparse approximation whose atoms are both adapted to a training set of signals and mutually incoherent. To meet this objective, we employ a dictionary learning scheme consisting of sparse approx
Computing Functions by Approximating the Input
ERIC Educational Resources Information Center
Goldberg, Mayer
2012-01-01
In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…
Approximate amenability for Banach sequence algebras
Haase, Markus
Approximate amenability for Banach sequence algebras H. G. Dales, R. J. Loy, and Y. Zhang Abstract. We consider when certain Banach sequence algebras A on the set N are approximately amenable. Some. Introduction The concept of amenability for a Banach algebra A, introduced by Johnson in 1972 [7], has proved
Approximate protein structural alignment in polynomial time
Kolodny, Rachel
problems and develop an approximate polynomial-time algorithm to solve them. For a commonly used scoring be approximated efficiently and perhaps in the development of efficient algorithms for the multiple struc- tural simplify the model by comparing the structures using one atom per residue, generally but not necessarily
Semantics by lub's of Approximations fact
Ábrahám, Erika
Semantics by lub's of Approximations fact :: Int -> Int fact = \\x -> if x fact(x-1) * x Regard non-recursively defined approximations fact0 = \\x -> bot fact1 = \\x -> if x else fact0(x - 1) x fact2 = \\x -> if x fact1(x - 1) x . . . Thus: facti+1 = ff facti
A cubic approximation for Kepler's equation
Seppo Mikkola
1987-01-01
We derive a new method to obtain an approximate solution for Kepler's equation. By means of an auxiliary variable it is possible to obtain a starting approximation correct to about three figures. A high order iteration formula then corrects the solution to high precision at once. The method can be used for all orbit types, including hyperbolic. To obtain this
Inversion and approximation of Laplace transforms
NASA Technical Reports Server (NTRS)
Lear, W. M.
1980-01-01
A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.
An approximation for inverse Laplace transforms
NASA Technical Reports Server (NTRS)
Lear, W. M.
1981-01-01
Programmable calculator runs simple finite-series approximation for Laplace transform inversions. Utilizing family of orthonormal functions, approximation is used for wide range of transforms, including those encountered in feedback control problems. Method works well as long as F(t) decays to zero as it approaches infinity and so is appliable to most physical systems.
FUNCTORIAL CW-APPROXIMATION PHILIP S. HIRSCHHORN
Hirschhorn, Philip S.
FUNCTORIAL CW-APPROXIMATION PHILIP S. HIRSCHHORN Contents 1. The main theorems 1 1.3. Relative CW is a relative CW-complex and p is a weak equivalence. To obtain a CW-approximation to a space X, you apply that factorization to the map X. The outline of the proof follows that of the standard construction of a CW
Fast Parallel and Serial Approximate String Matching
Amir, Amihood
7 Fast Parallel and Serial Approximate String Matching Consider the string matching problem, where, a pattern of length m and an integer k, serial and parallel algorithms for nding all occurrences to g. 8. h to h. The correspondence can be illustrated as #12;2 FAST PARALLEL AND SERIAL APPROXIMATE
Evolving Intervening Variables for Response Surface Approximations
Sóbester, András
Evolving Intervening Variables for Response Surface Approximations Andr´as S´obester , Prasanth B. Although initially conceived with the more general aim of automatically producing computer code for com. Introduction RESPONSE surface approximation techniques are widely used in modern engineering design prac- tice
Rough Set Approximations in Formal Concept Analysis
Yao, Yiyu
Rough Set Approximations in Formal Concept Analysis Y.Y. Yao, Yaohua Chen Department of Computer}@cs.uregina.ca Abstract-- An important topic of rough set theory is the approximation of undefinable sets or concepts through definable sets. It involves the construction of a system of definable sets and the definition
Approximation by polynomials on quaternionic compact sets
NASA Astrophysics Data System (ADS)
Gal, S. G.; Sabadini, I.
2015-09-01
In this paper we obtain several extensions to the quaternionic setting of some results concerning the approximation by polynomials of functions continuous on a compact set and holomorphic in its interior. The results include approximation on compact starlike sets and compact axially symmetric sets. The cases of some concrete particular sets are described in details, including quantitative estimates too.
Approximation algorithms for multiple sequence alignment
Kececioglu, John
Approximation algorithms for multiple sequence alignment under a fixed evolutionary tree \\Lambda R, approximation algorithms, multiple sequence alignÂ ment, evolutionary trees. 1 Introduction Multiple sequence], and objectives defined in terms of an evolutionary tree [16, \\Lambda Dedicated to the memory of Eugene Lawler
Polynomial approximation of Morison wave loading
Bouyssy, V.; Rackwitz, R.
1997-02-01
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.
Piecewise linear approximation for hereditary control problems
NASA Technical Reports Server (NTRS)
Propst, Georg
1987-01-01
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.
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
Error Bounds on the SCISSORS Approximation Method
Haque, Imran S.; Pande, Vijay S.
2011-01-01
The SCISSORS method for approximating chemical similarities has shown excellent empirical performance on a number of real-world chemical data sets, but lacks theoretically-proven bounds on its worst-case error performance. This paper first proves reductions showing SCISSORS to be equivalent to two previous kernel methods: kernel principal components analysis and the rank-k Nyström approximation of a Gram matrix. These reductions allow the use of generalization bounds on these techniques to show that the expected error in SCISSORS approximations of molecular similarity kernels is bounded in expected pairwise inner product error, in matrix 2-norm and Frobenius norm for full kernel matrix approximations, and in RMS deviation for approximated matrices. Finally, we show that the actual performance of SCISSORS is significantly better than these worst-case bounds, indicating that chemical space is well-structured for chemical sampling algorithms. PMID:21851122
Lyuu, Yuh-Dauh
) #15; CC(pluck(X [ Y)) introduces a false negative if a positive example makes either CC(X ) or CC(Y) return true but makes CC(pluck(X [ Y)) return false. #15; CC(pluck(X [ Y)) introduces a false positive many false positives and false negatives are introduced by CC(pluck(X [ Y))? c 2001 Yuh-Dauh Lyuu
Ayako Yoshisato; Takahiko Matsubara; Masahiro Morikawa
1997-08-11
Among various analytic approximations for the growth of density fluctuations in the expanding Universe, Zel'dovich approximation and its extensions in Lagrangian scheme are known to be accurate even in mildly non-linear regime. The aim of this paper is to investigate the reason why these Zel'dovich-type approximations work accurately beyond the linear regime from the following two points of view: (1) Dimensionality of the system and (2) the Lagrangian scheme on which the Zel'dovich approximation is grounded. In order to examine the dimensionality, we introduce a model with spheroidal mass distribution. In order to examine the Lagrangian scheme, we introduce the Pad\\'e approximation in Eulerian scheme. We clarify which of these aspects supports the unusual accuracy of the Zel'dovich-type approximations. We also give an implication for more accurate approximation method beyond the Zel'dovich-type approximations.
Alternative approximation concepts for space frame synthesis
NASA Technical Reports Server (NTRS)
Lust, R. V.; Schmit, L. A.
1985-01-01
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.
A NEW APPROXIMATION THEORY WHICH UNIFIES SPHERICAL AND COHEN-MACAULAY APPROXIMATIONS
Takahashi, Ryo
A NEW APPROXIMATION THEORY WHICH UNIFIES SPHERICAL AND COHEN-MACAULAY APPROXIMATIONS RYO TAKAHASHI and Buchweitz [3] intro- duced the notion of Cohen-Macaulay approximation which they used to show that the category of finitely generated modules over a Cohen-Macaulay local ring with the canonical module
Linear source approximation in CASMO5
Ferrer, R.; Rhodes, J. [Studsvik Scandpower, Inc., 504 Shoup Ave., Idaho Falls, ID 83402 (United States); Smith, K. [Dept. of Nuclear Science and Engineering, Massachusetts Inst. of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States)
2012-07-01
A Linear Source (LS) approximation has been implemented in the two-dimensional Method of Characteristics (MOC) transport solver in a prototype version of CASMO5. The LS approximation, which relies on the computation of trajectory-based spatial moments over source regions to obtain the linear source expansion coefficients, improves the solution accuracy relative to the 'flat' or constant source approximation. In addition, the LS formulation is capable of treating arbitrarily-shaped source regions and is compatible with standard Coarse-Mesh Finite Difference (CMFD) acceleration. Numerical tests presented in this paper for the C5G7 MOX benchmark show that, for comparable accuracy with respect to the reference solution, the LS approximation can reduce the run time by a factor of four and the memory requirements by a factor often relative to the FS scheme. (authors)
Stochastic Approximation and Its Application in MCMC
Cheng, Yichen
2013-05-31
Stochastic approximation has been widely used since first proposed by Herbert Robbins and Sutton Monro in 1951. It is an iterative stochastic method that attempts to find the zeros of functions that cannot be computed ...
VECTOR POLYNOMIAL APPROXIMATIONS FOR ROBUST SPEECH RECOGNITION
Stern, Richard
, and Richard M. Stern Department of Electrical and Computer Engineering and School of Computer Science Carnegie of the enviromentally-corrupted speech signal can be well approximated by an appropriately derived polynomial function
A fresh look at the adhesion approximation
Thomas Buchert
1997-11-04
I report on a systematic derivation of the phenomenological ``adhesion approximation'' from gravitational instability together with a brief evaluation of the related status of analytical modeling of large-scale structure.
Approximate probability distributions of the master equation.
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems. PMID:26274137
Approximation Techniques for Stochastic Combinatorial Optimization Problems
at CMU for all good times -- courses, theory lunches, and just the positive vibe in general. The last ve to designing approximation algorithms which provably output good so- lutions. However, a common assumption
Approximate inference in Gaussian graphical models
Malioutov, Dmitry M., 1981-
2008-01-01
The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a ...
Local graph partitions for approximation and testing
Hassidim, Avinatan
We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of bounded-degree graphs with an excluded minor, and in general, for any ...
A Monte-Carlo AIXI Approximation
Silver, David
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. Our approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement ...
Learning Approximate Sequential Patterns for Classification
Syed, Zeeshan
In this paper, we present an automated approach to discover patterns that can distinguish between sequences belonging to different labeled groups. Our method searches for approximately conserved motifs that occur with ...
Polymer state approximations of Schroedinger wave functions
Klaus Fredenhagen; Felix Reszewski
2006-08-25
It is shown how states of a quantum mechanical particle in the Schroedinger representation can be approximated by states in the so-called polymer representation. The result may shed some light on the semiclassical limit of loop quantum gravity.
Approximation concepts for efficient structural synthesis
NASA Technical Reports Server (NTRS)
Schmit, L. A., Jr.; Miura, H.
1976-01-01
It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.
Approximate amenability for Banach sequence algebras
Haase, Markus
Approximate amenability for Banach sequence algebras H. G. Dales, R. J. Loy, and Y. Zhang Abstract. We consider when certain Banach sequence(!). 1. Introduction The concept of amenability for a Banach algebra A, introduced by Johnson in 1972
Linear Approximation SAR Azimuth Processing Study
NASA Technical Reports Server (NTRS)
Lindquist, R. B.; Masnaghetti, R. K.; Belland, E.; Hance, H. V.; Weis, W. G.
1979-01-01
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.
Computational aspects of pseudospectral Laguerre approximations
NASA Technical Reports Server (NTRS)
Funaro, Daniele
1989-01-01
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.
Approximate probability distributions of the master equation
NASA Astrophysics Data System (ADS)
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
Optimization in Geometric Graphs: Complexity and Approximation
Kahruman-Anderoglu, Sera
2011-02-22
and approximate solutions. In addition, we establish complexity-based theoretical justifications for several greedy heuristics. Unit ball graphs, which are defined in the three dimensional Euclidian space, have several application areas such as computational...
Function Classes That Approximate the Bayes Risk
Ingo Steinwart; Don R. Hush; Clint Scovel
2006-01-01
\\u000a Many learning algorithms approximately minimize a risk functional over a predefined function class. In order to establish\\u000a consistency for such algorithms it is therefore necessary to know whether this function class approximates the Bayes risk.\\u000a In this work we present necessary and sufficient conditions for the latter. We then apply these results to reproducing kernel\\u000a Hilbert spaces used in support
The closure approximation in the hierarchy equations.
NASA Technical Reports Server (NTRS)
Adomian, G.
1971-01-01
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.
The Actinide Transition Revisited by Gutzwiller Approximation
NASA Astrophysics Data System (ADS)
Xu, Wenhu; Lanata, Nicola; Yao, Yongxin; Kotliar, Gabriel
2015-03-01
We revisit the problem of the actinide transition using the Gutzwiller approximation (GA) in combination with the local density approximation (LDA). In particular, we compute the equilibrium volumes of the actinide series and reproduce the abrupt change of density found experimentally near plutonium as a function of the atomic number. We discuss how this behavior relates with the electron correlations in the 5 f states, the lattice structure, and the spin-orbit interaction. Our results are in good agreement with the experiments.
Approximate Solutions Of Equations Of Steady Diffusion
NASA Technical Reports Server (NTRS)
Edmonds, Larry D.
1992-01-01
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.
A new approximation procedure for fractals
NASA Astrophysics Data System (ADS)
de Amo, E.; Chitescu, I.; Díaz Carrillo, M.; Secelean, N. A.
2003-02-01
This paper is based upon Hutchinson's theory of generating fractals as fixed points of a finite set of contractions, when considering this finite set of contractions as a contractive set-valued map. We approximate the fractal using some preselected parameters and we obtain formulae describing the "distance" between the "exact fractal" and the "approximate fractal" in terms of the preselected parameters. Some examples and also computation programs are given, showing how our procedure works.
Polynomial approximation of Morison wave loading
Bouyssy, V.; Rackwitz, R.
1995-12-31
For offshore structures with slender elements, the modeling of random wave loads by the Morison equation yields an equation of motion which admits no analytical solution except in few limit cases. This also holds for response moments. If polynomial approximations of the Morison drag loads are introduced, some procedures are available to obtain the stationary moments of the approximate response. These procedures result in large computer codes and time consuming computations if accurate approximations and large structural models are considered. 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. In the paper the authors investigate how many terms should be included in the polynomial approximation of the Morison drag loading to accurately estimate the first four response moments. Analysis is performed in the time domain for a standardized form of the equation of motion. It is shown that a cubic approximation of the drag loading is necessary to accurately predict response variance for any excitation. For the fit of the first four response moments, at least a fifth-order approximation appears necessary. It is concluded that practical fatigue or reliability analyses can require much effort if the influence of nonlinearities in Morison loading needs to be accurately accounted for.
An improved proximity force approximation for electrostatics
Fosco, Cesar D. [Centro Atomico Bariloche, Comision Nacional de Energia Atomica, R8402AGP Bariloche (Argentina) [Centro Atomico Bariloche, Comision Nacional de Energia Atomica, R8402AGP Bariloche (Argentina); Instituto Balseiro, Universidad Nacional de Cuyo, R8402AGP Bariloche (Argentina); Lombardo, Fernando C. [Departamento de Fisica Juan Jose Giambiagi, FCEyN UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina) [Departamento de Fisica Juan Jose Giambiagi, FCEyN UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina); IFIBA (Argentina)] [Argentina; Mazzitelli, Francisco D., E-mail: fdmazzi@cab.cnea.gov.ar [Centro Atomico Bariloche, Comision Nacional de Energia Atomica, R8402AGP Bariloche (Argentina); Departamento de Fisica Juan Jose Giambiagi, FCEyN UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina)
2012-08-15
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called 'proximity force approximation' the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction in atomic force microscopes. - Highlights: Black-Right-Pointing-Pointer The proximity force approximation (PFA) has been widely used in different areas. Black-Right-Pointing-Pointer The PFA can be improved using a derivative expansion in the shape of the surfaces. Black-Right-Pointing-Pointer We use the improved PFA to compute electrostatic forces between conductors. Black-Right-Pointing-Pointer The results can be used as an analytic benchmark for numerical calculations in AFM. Black-Right-Pointing-Pointer Insight is provided for people who use the PFA to compute nuclear and Casimir forces.
Mimetic difference approximations of partial differential equations
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
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.
Improved approximations of displacements for structural optimization
NASA Technical Reports Server (NTRS)
Kirsch, Uri
1990-01-01
In most structural optimization problems the implicit behavior constraints are evaluated for successive modifications in the design. For each trial design, the analysis equations must be solved and the multiple repeated analyses usually involve extensive computational effort. This difficulty motivated several studies on explicit approximations of the structural behavior in terms of the design variables. The latter approach can considerably reduce the amount of computations, but the quality of the approximations might not be sufficient. Many of the approximate behavior models proposed in the past are valid only for relatively small changes in the design variables. The accuracy of the results is often insufficient for large changes in the design. The object of this study is to present efficient and high quality approximations of the structural behavior. It will be shown that the quality of the approximations can greatly be improved by combining scaling of the initial design, using intervening variables, and scaling a set of fictitious loads. Integrating these means, a powerful solution procedure can be introduced. In addition, the errors in satisfying the analysis equations can readily be evaluated. A numerical example illustrates the solution methodology and the effectiveness of the proposed approach.
Estimation of distribution algorithms with Kikuchi approximations.
Santana, Roberto
2005-01-01
The question of finding feasible ways for estimating probability distributions is one of the main challenges for Estimation of Distribution Algorithms (EDAs). To estimate the distribution of the selected solutions, EDAs use factorizations constructed according to graphical models. The class of factorizations that can be obtained from these probability models is highly constrained. Expanding the class of factorizations that could be employed for probability approximation is a necessary step for the conception of more robust EDAs. In this paper we introduce a method for learning a more general class of probability factorizations. The method combines a reformulation of a probability approximation procedure known in statistical physics as the Kikuchi approximation of energy, with a novel approach for finding graph decompositions. We present the Markov Network Estimation of Distribution Algorithm (MN-EDA), an EDA that uses Kikuchi approximations to estimate the distribution, and Gibbs Sampling (GS) to generate new points. A systematic empirical evaluation of MN-EDA is done in comparison with different Bayesian network based EDAs. From our experiments we conclude that the algorithm can outperform other EDAs that use traditional methods of probability approximation in the optimization of functions with strong interactions among their variables. PMID:15901427
Approximation of delays in biochemical systems.
Mocek, W T; Rudnicki, R; Voit, E O
2005-12-01
In the past metabolic pathway analyses have mostly ignored the effects of time delays that may be due to processes that are slower than biochemical reactions, such as transcription, translation, translocation, and transport. We show within the framework of biochemical systems theory (BST) that delay processes can be approximated accurately by augmenting the original variables and non-linear differential equations with auxiliary variables that are defined through a system of linear ordinary differential equations. These equations are naturally embedded in the structure of S-systems and generalized mass action systems within BST and can be interpreted as linear signaling pathways or cascades. We demonstrate the approximation method with the simplest generic modules, namely single delayed steps with and without feedback inhibition. These steps are representative though, because they are easily incorporated into larger systems. We show that the dynamics of the approximated systems reflects that of the original delay systems well, as long as the systems do not operate in very close vicinity of threshold values where the systems lose stability. The accuracy of approximation furthermore depends on the selected number of auxiliary variables. In the most relevant situations where the systems operate at states away from their critical thresholds, even a few auxiliary variables lead to satisfactory approximations. PMID:16181644
Binary Decision Diagrams for Affine Approximation
Henshall, Kevin; Sondergaard, Harald; Whiting, Leigh
2008-01-01
Selman and Kautz's work on ``knowledge compilation'' established how approximation (strengthening and/or weakening) of a propositional knowledge-base can be used to speed up query processing, at the expense of completeness. In this classical approach, querying uses Horn over- and under-approximations of a given knowledge-base, which is represented as a propositional formula in conjunctive normal form (CNF). Along with the class of Horn functions, one could imagine other Boolean function classes that might serve the same purpose, owing to attractive deduction-computational properties similar to those of the Horn functions. Indeed, Zanuttini has suggested that the class of affine Boolean functions could be useful in knowledge compilation and has presented an affine approximation algorithm. Since CNF is awkward for presenting affine functions, Zanuttini considers both a sets-of-models representation and the use of modulo 2 congruence equations. In this paper, we propose an algorithm based on reduced ordered bina...
Approximation of Various Quantum Query Types
Arvid J. Bessen
2004-02-13
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our definition of equivalence is based on the ability to simulate (or approximate) one query type by another. We show that a bit query can always approximate a phase query with just two queries, while there exist problems for which the number of phase queries which are necessary to approximate a bit query must grow exponentially with the precision of the bit query. This result follows from the query complexity bounds for the evaluation problem, for which we establish a strong lower bound for the number of phase queries by exploiting a relation between quantum algorithms and trigonometric polynomials.
Markovian stochastic approximation with expanding projections
Andrieu, Christophe
2011-01-01
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be unstable without additional stabilisation techniques. We study a stochastic approximation procedure with expanding projections similar to Andrad\\'ottir [Oper. Res. 43 (2010) 1037--1048]. We focus on Markovian noise and show the stability and convergence under general conditions. Our framework also incorporates the possibility to use a random step size sequence, which allows us to consider settings with a non-smooth family of Markov kernels. We apply the theory to stochastic approximation expectation maximisation with particle independent Metropolis-Hastings sampling.
Approximate solutions of the hyperbolic Kepler equation
NASA Astrophysics Data System (ADS)
Avendano, Martín; Martín-Molina, Verónica; Ortigas-Galindo, Jorge
2015-08-01
We provide an approximate zero widetilde{S}(g,L) for the hyperbolic Kepler's equation S-g {{arcsinh}}(S)-L=0 for gin (0,1) and Lin [0,? ) . We prove, by using Smale's ? -theory, that Newton's method starting at our approximate zero produces a sequence that converges to the actual solution S(g, L) at quadratic speed, i.e. if S_n is the value obtained after n iterations, then |S_n-S|? 0.5^{2^n-1}|widetilde{S}-S| . The approximate zero widetilde{S}(g,L) is a piecewise-defined function involving several linear expressions and one with cubic and square roots. In bounded regions of (0,1) × [0,? ) that exclude a small neighborhood of g=1, L=0 , we also provide a method to construct simpler starters involving only constants.
Approximation methods in gravitational-radiation theory
NASA Technical Reports Server (NTRS)
Will, C. M.
1986-01-01
The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
The cell cycle switch computes approximate majority.
Cardelli, Luca; Csikász-Nagy, Attila
2012-01-01
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. PMID:22977731
The binary collision approximation: Background and introduction
Robinson, M.T.
1992-08-01
The binary collision approximation (BCA) has long been used in computer simulations of the interactions of energetic atoms with solid targets, as well as being the basis of most analytical theory in this area. While mainly a high-energy approximation, the BCA retains qualitative significance at low energies and, with proper formulation, gives useful quantitative information as well. Moreover, computer simulations based on the BCA can achieve good statistics in many situations where those based on full classical dynamical models require the most advanced computer hardware or are even impracticable. The foundations of the BCA in classical scattering are reviewed, including methods of evaluating the scattering integrals, interaction potentials, and electron excitation effects. The explicit evaluation of time at significant points on particle trajectories is discussed, as are scheduling algorithms for ordering the collisions in a developing cascade. An approximate treatment of nearly simultaneous collisions is outlined and the searching algorithms used in MARLOWE are presented.
The Cell Cycle Switch Computes Approximate Majority
NASA Astrophysics Data System (ADS)
Cardelli, Luca; Csikász-Nagy, Attila
2012-09-01
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.
Testing approximations beyond the proton-neutron quasiparticle random phase approximation
Civitarese, O.; Mariano, A. [Department of Physics. University of La Plata, C. C. 67 1900 La Plata (Argentina); Hirsch, J. G. [Instituto de Ciencias Nucleares, UNAM, A. P. 70-543, 04510 Mexico City, D. F. (Mexico); Reboiro, M. [Department of Physics. University of La Plata, C. C. 67 1900 La Plata (Argentina); Faculty of Engineering, University of Lomas de Zamora, Km 2 (1836) Lavallol (Argentina)
2007-08-15
In this work we analyze the validity of recently proposed extensions of the Quasiparticle Random Phase Approximation (QRPA). Particularly, we focus our attention on the Fully Renormalized QRPA (FRQRPA). We found that the results of this approximation do not differ from the results of the QRPA. This finding is supported by a detailed comparison between both formalisms, their assumptions and approximations, in the context of realistic calculations.
Chudnovsky, D.V.; Chudnovsky, G.V.
1995-12-01
High precision solution of extremal and (complex analytic) approximations problems that can be represented in terms of multiple integrals or integral equations involving hypergeornetric functions are examined. Fast algorithms of computations of (approximate) solutions are presented that are well suited for parallelization. Among problems considered are: WKB and adelic asymptotics of multidimensional hypergeometric Pade approximations to classical functions, and high accuracy computations of high order eigenvalues and eigenstates for 2D and 3D domains of complex geometry.
Multiple scattering and eikonal pole approximation
Mandelzweig, V.B.; Wallace, S.J.
1982-01-01
The eikonal pole approximation to the multiple scattering Watson series is introduced and explored. For noncommuting potentials this approximation naturally defines the ordering to the z coordinates of the scatterers and for commuting potentials leads to Glauber multiple scattering series. It is shown that the cancellations in the Watson expansion which produce the usual form of Glauber theory are between the infinite series of reflection terms and the off-pole contribution of nonreflective ones. This generalizes the earlier result on cancellations for a two-particle target to targets of arbitrary size.
HALOGEN: Approximate synthetic halo catalog generator
NASA Astrophysics Data System (ADS)
Avila Perez, Santiago; Murray, Steven
2015-05-01
HALOGEN generates approximate synthetic halo catalogs. Written in C, it decomposes the problem of generating cosmological tracer distributions (eg. halos) into four steps: generating an approximate density field, generating the required number of tracers from a CDF over mass, placing the tracers on field particles according to a bias scheme dependent on local density, and assigning velocities to the tracers based on velocities of local particles. It also implements a default set of four models for these steps. HALOGEN uses 2LPTic (ascl:1201.005) and CUTE (ascl:1505.016); the software is flexible and can be adapted to varying cosmologies and simulation specifications.
Approximating Catastrophic Risk Through Statistics of Extremes
NASA Astrophysics Data System (ADS)
Mitsiopoulos, James; Haimes, Yacov Y.; Li, Duan
1991-06-01
This paper studies the approximation of the partitioned multiobjective risk method's (PMRM) extreme-event risk function ƒ4. The analytic expression of the approximation for ƒ4 is derived through the use of the statistics of extremes for cases where the underlying distribution is of an extreme-value type I, II, or III, and it thus provides an effective theoretical tool for understanding the behavior of conditional expected values for a large class of distribution functions used in science and engineering. The results are confirmed for example problems of normal, Gumbel, Weibull, Pareto, lognormal, and uniform distributions.
Approximating European Options by Rebate Barrier Options
Song, Qingshuo
2011-01-01
When the underlying stock price is a strict local martingale process under an equivalent local martingale measure, Black-Scholes PDE associated with an European option may have multiple solutions. In this paper, we study an approximation for the smallest hedging price of such an European option. Our results show that a class of rebate barrier options can be used for this approximation, when its rebate and barrier are chosen appropriately. An asymptotic convergence rate is also achieved when the knocked-out barrier moves to infinity under suitable conditions.
Approximate Killing Fields as an Eigenvalue Problem
Christopher Beetle
2008-08-12
Approximate Killing vector fields are expected to help define physically meaningful spins for non-symmetric black holes in general relativity. However, it is not obvious how such fields should be defined geometrically. This paper relates a definition suggested recently by Cook and Whiting to an older proposal by Matzner, which seems to have been overlooked in the recent literature. It also describes how to calculate approximate Killing fields based on these proposals using an efficient scheme that could be of immediate practical use in numerical relativity.
Faddeev Random Phase Approximation for Molecules
Degroote, Matthias; Barbieri, Carlo
2010-01-01
The Faddeev Random Phase Approximation is a Green's function technique that makes use of Faddeev-equations to couple the motion of a single electron to the two-particle--one-hole and two-hole--one-particle excitations. This method goes beyond the frequently used third-order Algebraic Diagrammatic Construction method: all diagrams involving the exchange of phonons in the particle-hole and particle-particle channel are retained, but the phonons are described at the level of the Random Phase Approximation. This paper presents the first results for diatomic molecules at equilibrium geometry. The behavior of the method in the dissociation limit is also investigated.
Approximate average deployments versus defense parameters
Canavan, G.H.
1991-12-01
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.
Approximation and compression with sparse orthonormal transforms.
Sezer, Osman Gokhan; Guleryuz, Onur G; Altunbasak, Yucel
2015-08-01
We propose a new transform design method that targets the generation of compression-optimized transforms for next-generation multimedia applications. The fundamental idea behind transform compression is to exploit regularity within signals such that redundancy is minimized subject to a fidelity cost. Multimedia signals, in particular images and video, are well known to contain a diverse set of localized structures, leading to many different types of regularity and to nonstationary signal statistics. The proposed method designs sparse orthonormal transforms (SOTs) that automatically exploit regularity over different signal structures and provides an adaptation method that determines the best representation over localized regions. Unlike earlier work that is motivated by linear approximation constructs and model-based designs that are limited to specific types of signal regularity, our work uses general nonlinear approximation ideas and a data-driven setup to significantly broaden its reach. We show that our SOT designs provide a safe and principled extension of the Karhunen-Loeve transform (KLT) by reducing to the KLT on Gaussian processes and by automatically exploiting non-Gaussian statistics to significantly improve over the KLT on more general processes. We provide an algebraic optimization framework that generates optimized designs for any desired transform structure (multiresolution, block, lapped, and so on) with significantly better n -term approximation performance. For each structure, we propose a new prototype codec and test over a database of images. Simulation results show consistent increase in compression and approximation performance compared with conventional methods. PMID:25823033
Approximation Algorithms for Capacitated Location Routing #
Nabben, Reinhard
, and besides location routing we also obtain approximation algorithms for multidepot capacitated vehicle for different variants of capacitated location routing, an important general ization of vehicle routing where the cost of opening the depots from which vehicles operate is taken into account. Our results originate
POINCAR PARADOX AND APPROXIMATE SIMILARITIES Giangiacomo Gerla
Gerla, Giangiacomo
by the fuzzy equivalence relations. In this note we argue that the deduction apparatus of fuzzy logic gives is proposed by fuzzy logic in which the paradoxical effect of the transitivity is avoided by assuming@libero.it APPROXIMATE SIMILARITIES AND POINCARÃ? PARADOX Abstract This is an extended abstract of the published paper
The Asymmetric Superfluid Local Density Approximation (ASLDA)
Aurel Bulgac; Michael McNeil Forbes
2008-08-11
Here we describe the form of the Asymmetric Superfluid Local Density Approximation (ASLDA), a Density Functional Theory (DFT) used to model the two-component unitary Fermi gas. We give the rational behind the functional, and describe explicitly how we determine the form of the DFT from the to the available numerical and experimental data.
A Monte Carlo Application to Approximate Pi.
ERIC Educational Resources Information Center
Easterday, Kenneth; Smith, Tommy
1991-01-01
The Monte Carlo procedure of generating random points that lie within the unit square is used to approximate pi, as the ratio of points within the first quadrant of the unit circle to the total number of randomly generated points. A BASIC computer program for this method is included. (JJK)
Kirchhoff approximation for diffusive waves Jorge Ripoll*
Lorenzo, Jorge Ripoll
and Laser, Foundation for Research and Technology-Hellas, P.O. Box 1527, 71110 Heraklion, Crete, Greece propagation in tissue see Ref. 10 for a review , combined with technological advancements in photon sourcesKirchhoff approximation for diffusive waves Jorge Ripoll* Institute for Electronic Structure
Submitted to Statistical Science Models as Approximations --
Buja, Andreas
Submitted to Statistical Science Models as Approximations -- A Conspiracy of Random Regressors that the deepest conse- quences for inference arise from a synergistic effect (a "conspiracy") of nonlinearity-07657. Supported in part by NSF Grant DMS-10-07689. 1 imsart-sts ver. 2014/07/30 file: Buja_et_al_A_Conspiracy-rev1
Approximate stability estimates in inverse transport theory
Bal, Guillaume
of inverse transport has many applications in medical and geo- physical imaging. The forward transport of a domain of interest. Typical applications of inverse transport in medical imaging are optical tomography physical noise models. The resulting approximate stability estimates provide a quantitative description
Real-time creased approximate subdivision surfaces
Denis Kovacs; Jason Mitchell; Shanon Drone; Denis Zorin
2009-01-01
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.
Multiple trapping model: Approximate and exact solutions
NASA Astrophysics Data System (ADS)
Arkhipov, V. I.; Iovu, M. S.; Rudenko, A. I.; Shutov, S. D.
1987-05-01
Approximate methods of analysis of the multiple trapping model for amorphous semiconductors, which is based on the concept of demarcation energy between the two fractions of shallow and deep traps, are comparatively considered. The necessity is shown to take into account the real trap energy distribution function to obtain the results adequate to exact analytical solution of the problem.
Continuity of Semantic Operators and Their Approximation
Hitzler, Pascal
Continuity of Semantic Operators and Their Approximation by Arti#12;cial Neural Networks Pascal with Logic Programs by Arti#12;cial Neural Networks. P. Hitzler, Arti#12;cial Intelligence Institute; #2; #1; Idea #15; Logic Programs and Neural Networks are very di#11;erent paradigms. #15; Neural
Secure Multiparty Computation of Approximations Joan Feigenbaum ?
International Association for Cryptologic Research (IACR)
Secure Multiparty Computation of Approximations Joan Feigenbaum ? Yuval Ishai ?? Tal Malkin to the function f . Secure multiparty computation of f allows the parties to compute f without revealing more than, if computation of f is inefficient or just efficient enough to be practical, then secure computation of f may
Unifled LASSO Estimation via Least Squares Approximation
Hansheng Wang; Chenlei Leng
We propose a method of least squares approximation (LSA) for unifled yet simple LASSO estimation. Our general theoretical framework includes ordinary least squares, generalized linear models, quantile regression, and many others as special cases. Speciflcally, LSA can transfer many difierent types of LASSO objective functions into their asymptotically equivalent least-squares problems. Thereafter, the standard asymptotic theory can be established and
Approximation of virus structure by icosahedral tilings.
Salthouse, D G; Indelicato, G; Cermelli, P; Keef, T; Twarock, R
2015-07-01
Viruses are remarkable examples of order at the nanoscale, exhibiting protein containers that in the vast majority of cases are organized with icosahedral symmetry. Janner used lattice theory to provide blueprints for the organization of material in viruses. An alternative approach is provided here in terms of icosahedral tilings, motivated by the fact that icosahedral symmetry is non-crystallographic in three dimensions. In particular, a numerical procedure is developed to approximate the capsid of icosahedral viruses by icosahedral tiles via projection of high-dimensional tiles based on the cut-and-project scheme for the construction of three-dimensional quasicrystals. The goodness of fit of our approximation is assessed using techniques related to the theory of polygonal approximation of curves. The approach is applied to a number of viral capsids and it is shown that detailed features of the capsid surface can indeed be satisfactorily described by icosahedral tilings. This work complements previous studies in which the geometry of the capsid is described by point sets generated as orbits of extensions of the icosahedral group, as such point sets are by construction related to the vertex sets of icosahedral tilings. The approximations of virus geometry derived here can serve as coarse-grained models of viral capsids as a basis for the study of virus assembly and structural transitions of viral capsids, and also provide a new perspective on the design of protein containers for nanotechnology applications. PMID:26131897
Alternative approximation concepts for space frame synthesis
NASA Technical Reports Server (NTRS)
Lust, R. V.; Schmit, L. A.
1985-01-01
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.
THRIFTY APPROXIMATIONS OF CONVEX BODIES BY POLYTOPES
Barvinok, Alexander
body, polytope, Chebyshev polynomial, John decomposition. This research was partially supported by NSFTHRIFTY APPROXIMATIONS OF CONVEX BODIES BY POLYTOPES Alexander Barvinok July 2012 Abstract. Given a convex body C Rd containing the origin in its interior and a real number > 1 we seek to construct
Approximating Pareto Curves using Semidefinite Relaxations
Henrion, Didier
a numerical scheme such as the modified Polak method [11]: first, one considers a finite discretization (y (k))}, where f1 and f2 are two conflicting polynomial criteria and S Rn is a compact basic semialgebraic set lead to consider different parametric POPs, namely (a) a weighted convex sum approximation, (b
PREDICTIVE SHAPE CODING USING GENERIC POLYGON APPROXIMATION
Evans, Brian L.
PREDICTIVE SHAPE CODING USING GENERIC POLYGON APPROXIMATION Jongil Kim and Brian L. Evans://anchovy.ece.utexas.edu/ ABSTRACT We introduce an efficient predictive binary shape coding method that consists of (1) global motion estimation, (2) local motion estimation, (3) matched segment coding, and (4) residual segment coding. Global
PREDICTIVE SHAPE CODING USING GENERIC POLYGON APPROXIMATION
Evans, Brian L.
PREDICTIVE SHAPE CODING USING GENERIC POLYGON APPROXIMATION Jong-il Kim and Brian L. Evans.ece.utexas.edu ABSTRACT We introduce an e cient predictive binary shape coding method that consists of 1 global motion estimation, 2 local motion estimation, 3 matched segment coding, and 4 residual segment coding. Global
DICTIONARY APPROXIMATION FOR MATCHING PURSUIT VIDEO CODING
Zakhor, Avideh
DICTIONARY APPROXIMATION FOR MATCHING PURSUIT VIDEO CODING Ralph Neff and Avideh Zakhor Department is an important issue for this system, and others have shown alternate dictionaries which lead to either coding. The key to our new method is an algorithm which takes an arbitrary 2D dictionary and generates
Equational Approximations for Tree Automata Completion
Paris-Sud XI, Université de
Equational Approximations for Tree Automata Completion Thomas Genet IRISA/Universit´e de Rennes 1 supported by ANR grant number ANR-06-SETI-14 Email addresses: genet@irisa.fr (Thomas Genet), rusu@irisa.fr (Vlad Rusu). URLs: www.irisa.fr/lande/genet (Thomas Genet), www.irisa.fr/vertecs/Equipe/Rusu (Vlad Rusu
Verifying Statistical Zero Knowledge with Approximate Implementations
International Association for Cryptologic Research (IACR)
approximate simulation relations. This technique separates proof obligations into two categories: those requir- able, and then prove that the existence of a polynomial-time distinguisher for the two protocol systems implies the existence of a distinguisher for the well- known systems, which violates the fundamental
Asynchronous Stochastic Approximation and Q-Learning
John N. Tsitsiklis
1994-01-01
We provide some general results on the convergence of a class of stochastic approximation algorithms and their parallel and asynchronous variants. We then use these results to study the Q-learning algorithm, a rein- forcement learning method for solving Markov decision problems, and establish its convergence under conditions more general than previously available.
Sensing Position With Approximately Constant Contact Force
NASA Technical Reports Server (NTRS)
Sturdevant, Jay
1996-01-01
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.
Matchings, permanents and their random approximations
Friedland, Shmuel
Matchings, permanents and their random approximations Shmuel Friedland Univ. Illinois at Chicago Tutte seminar series, U. Waterloo, Nov 20, 2009 Shmuel Friedland Univ. Illinois at Chicago () Matchings Matchings in graphs Number of k-matchings in bipartite graphs as permanents Lower and upper bounds
Fusion Tracking Algorithm Based on Stochastic Approximation
Liwei Guo; Xueguang Chen; Shiqiang Hu
2006-01-01
A practical fusion algorithm for tracking maneuvering target based on centralized structure of multi-sensor is proposed. This algorithm is implemented with two filters and state fusion, together with the current statistic model and adaptive filtering. Firstly, the fusion weighting coefficients are obtained using the stochastic approximation theory, a suitable method of estimation measurements noise variance is developed based on fuzzy
Approximate counting with a floatingpoint Miklos Csuros
CsÃ¼rÃ¶s, MiklÃ³s
on counting in order to identify repeating sequence patterns. In these applications, billions of counters need a length surpassÂ ing three billion. More than four billion (4 16 ) di#erent words need to be countedApproximate counting with a floatingÂpoint counter Miklâ??os Csï¿½urË?os Department of Computer Science
Tree-structured approximations by expectation propagation
Minka,Tom
approximations have been utilized in the variational method of Ghahramani & Jordan (1997) and the se- quential is to force the convergence of BP, by appealing to a free- energy interpretation (Welling & Teh, 2001; Teh. (2000) describe an extension of BP involving the Kikuchi free-energy. The resulting algorithm resembles
Uniform Approximation by (Quantum) Polynomials Andrew Drucker
de Wolf, Ronald
Uniform Approximation by (Quantum) Polynomials Andrew Drucker MIT Ronald de Wolf CWI August 10 independent coins, each coming up `1' with probability x. Count the Hamming weight |w| of the resulting string w {0, 1}n, and output g(|w|/n). Note that the expected value of |w|/n is exactly x, and with high
ORIGINAL ARTICLE Approximate recovery of coseismic deformation
Wu, Yih-Min
offer a good opportunity to determine coseismic displace- ments from strong-motion recordsORIGINAL ARTICLE Approximate recovery of coseismic deformation from Taiwan strong-motion records January 2007 # Springer Science + Business Media B.V. 2007 Abstract Since 1990, digital strong
Revisiting Twomey's approximation for peak supersaturation
NASA Astrophysics Data System (ADS)
Shipway, B. J.
2014-10-01
Twomey's seminal 1959 paper provided lower and upper bound approximations to the estimation of peak supersaturation within an updraft and thus provides the first closed expression for the number of nucleated cloud droplets. The form of this approximation is simple, but provides a surprisingly good estimate and has subsequently been employed in more sophisticated treatments of nucleation parametrization. In the current paper, we revisit the lower bound approximation of Twomey and make a small adjustment which can be used to obtain a more accurate calculation of peak supersaturation under all potential aerosol loadings and thermodynamic conditions. In order to make full use of this improved approximation, the underlying integro-differential equation for supersaturation evolution and the condition for calculating peak supersaturation are examined. A simple rearrangement of the algebra allows for an expression to be written down which can then be solved with a single lookup table with only one independent variable for an underlying lognormal aerosol population. Multimode aerosol with only N different dispersion characteristics require only N of these one-dimensional lookup tables. No additional information is required in the lookup table to deal with additional chemical, physical or thermodynamic properties. The resulting implementation provides a relatively simple, yet computationally cheap and very accurate physically-based parametrization of droplet nucleation for use in climate and NWP models.
General Constrained Polynomial Optimization: an Approximation Approach
Zhang, Shuzhong
with a (relative) worst-case performance ratio for polynomial optimization over some general set: for instanceGeneral Constrained Polynomial Optimization: an Approximation Approach Simai HE Zhening LI for optimizing a generic multi-variate (inhomogeneous) polynomial function, subject to some fairly general
An approximate classical unimolecular reaction rate theory
NASA Astrophysics Data System (ADS)
Zhao, Meishan; Rice, Stuart A.
1992-05-01
We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.
Mesh Clustering by Approximating Centroidal Voronoi Tessellation
Cheng, Fuhua "Frank"
Mesh Clustering by Approximating Centroidal Voronoi Tessellation Fengtao Fan Depart. of Computer Science Virginia State University slai@vsu.edu ABSTRACT An elegant and efficient mesh clustering algorithm is pre- sented. The faces of a polygonal mesh are divided into dif- ferent clusters for mesh coarsening
Universitat Regensburg Numerical approximation of phase field
Regensburg, UniversitÃ¤t - Naturwissenschaftliche FakultÃ¤t I
Introduction Shape and topology optimization in fluid mechanics is an important mathematical field attracting/2014 #12;Numerical Approximation of phase field based shape and topology optimization for fluids Harald words. Shape optimization, topology optimization, diffuse interfaces, CahnÂ Hilliard, Navier
Indivisible Markets with Good Approximate Equilibrium Prices
Cole, Richard
Indivisible Markets with Good Approximate Equilibrium Prices Richard Cole Computer Science are obtained for smooth Fisher markets that obey a relaxed weak gross substitutes property (WGS). A smooth market is one in which small changes in prices cause only proportionately small changes in demand, which
Approximate Lifted Belief Propagation Parag Singla
Anderson, Richard
Approximate Lifted Belief Propagation Parag Singla Department of Computer Science University}@cs.washington.edu Abstract Lifting can greatly reduce the cost of inference on first- order probabilistic models, but constructing the lifted network can itself be quite costly. In addition, the mini- mal lifted network is often
Approximating the Generalized Minimum Manhattan Network Problem
Kobourov, Stephen G.
Approximating the Generalized Minimum Manhattan Network Problem Aparna Das1 , Krzysztof Fleszar2¨urzburg, Germany Abstract. We consider the generalized minimum Manhattan network problem (GMMN). The input-length rectilinear network that connects every pair in R by a Manhattan path, that is, a path of axis-parallel line
Universitat Regensburg Numerical Approximation of Anisotropic
Regensburg, Universität - Naturwissenschaftliche Fakultät I
Equations John W. Barrett, Harald Garcke and Robert N¨urnberg Preprint Nr. 09/2006 #12;Numerical Approximation of Anisotropic Geometric Evolution Equations John W. Barrett Harald Garcke Robert N order. We refer to the papers Wulff (1901), Herring (1951), Frank (1963), Taylor, Cahn, and Handwerker
Causal Approximate Inversion for Control of
Damaren, Christopher J.
Causal Approximate Inversion for Control of Structurally Flexible Manipulators Using Nonlinear A control scheme for flexible-link manipulators is advanced which is based on the notion of nonlinear inner results from a planar three-link manipulator with two flexible links demonstrate the efficacy
Block Addressing Indices for Approximate Text Retrieval.
ERIC Educational Resources Information Center
Baeza-Yates, Ricardo; Navarro, Gonzalo
2000-01-01
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)
Approximate Killing Vectors on S^2
Gregory B. Cook; Bernard F. Whiting
2007-06-01
We present a new method for computing the best approximation to a Killing vector on closed 2-surfaces that are topologically S^2. When solutions of Killing's equation do not exist, this method is shown to yield results superior to those produced by existing methods. In addition, this method appears to provide a new tool for studying the horizon geometry of distorted black holes.
Octree approximation and compression methods Hanan Samet
Samet, Hanan
Octree approximation and compression methods£ Hanan Samet Computer Science Department Center objects (as well as objects of arbitrary dimen- sionality). The objects are represented by a region octree the use of a forest. This method labels the internal nodes of the octree as GB or GW, depending
Revisiting Twomey's approximation for peak supersaturation
NASA Astrophysics Data System (ADS)
Shipway, B. J.
2015-04-01
Twomey's seminal 1959 paper provided lower and upper bound approximations to the estimation of peak supersaturation within an updraft and thus provides the first closed expression for the number of nucleated cloud droplets. The form of this approximation is simple, but provides a surprisingly good estimate and has subsequently been employed in more sophisticated treatments of nucleation parametrization. In the current paper, we revisit the lower bound approximation of Twomey and make a small adjustment that can be used to obtain a more accurate calculation of peak supersaturation under all potential aerosol loadings and thermodynamic conditions. In order to make full use of this improved approximation, the underlying integro-differential equation for supersaturation evolution and the condition for calculating peak supersaturation are examined. A simple rearrangement of the algebra allows for an expression to be written down that can then be solved with a single lookup table with only one independent variable for an underlying lognormal aerosol population. While multimodal aerosol with N different dispersion characteristics requires 2N+1 inputs to calculate the activation fraction, only N of these one-dimensional lookup tables are needed. No additional information is required in the lookup table to deal with additional chemical, physical or thermodynamic properties. The resulting implementation provides a relatively simple, yet computationally cheap, physically based parametrization of droplet nucleation for use in climate and Numerical Weather Prediction models.
Interpolant-based Transition Relation Approximation
Jhala, Ranjit
. For this reason, software model checkers typically use a weak approximation of the image. This can result on counterexample analysis. 1 Introduction Predicate abstraction [15] is a technique commonly used in software model. This can be done by enumerating the pred- icate states, using a suitable decision procedure to determine
6D SLAM with approximate data association
A. Nuchter; Kai Lingemann; Joachim Hertzberg; Hartmut Surmann
2005-01-01
This paper provides a new solution to the simultaneous localization and mapping (SLAM) problem with six degrees of freedom. A fast variant of the iterative closest points (ICP) algorithm registers 3D scans taken by a mobile robot into a common coordinate system and thus provides relocalization. Hereby, data association is reduced to the problem of searching for closest points. Approximation
Unit Disk Graph Approximation Fabian Kuhn
Unit Disk Graph Approximation Fabian Kuhn Computer Engineering and Networks Laboratory ETH Zurich embedding of a unit disk graph given by its connectivity information is a problem of practical impor- tance disk graph. Particularly, we show that if non-neighboring nodes are not allowed to be closer to each
Truth Revelation in Approximately Ecient Combinatorial Auctions
Lehmann, Daniel
Truth Revelation in Approximately EÆcient Combinatorial Auctions Daniel Lehmann School of Computer). Traditional analysis of these mechanisms - in partic- ular, their truth revelation properties - assumes payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does
The Laplace Approximation Sargur N. Srihari
The Laplace Approximation Sargur N. Srihari University at Buffalo, State University of New York USA #12;Pierre-Simon, marquis de Laplace 1749-1827 Â· ``Newton" of France Â Known for Work in Celestial Mechanics Laplace's equation Laplacian Laplace transform Laplace distribution Laplace's demon Laplace
Approximations to the Distributed Activation Energy Model
Approximations to the Distributed Activation Energy Model for Pyrolysis C.P. Please, 1 M.J. Mc, then resubmitted after minor revisions in September 2002. Abstract The Distributed Activation Energy Model (DAEM), used for the pyrolysis of a range of materials (including coal, biomass, residual oils and kerogen
Approximating Border Length for DNA Microarray Synthesis
Wong, Prudence W.H.
Approximating Border Length for DNA Microarray Synthesis Cindy Y. Li1 Prudence W.H. Wong1 Qin Xin2 Introduction DNA microarrays [9] have become a very important research tool which have proved to benefit areas about the pres- ence or absence of biological target sequences in a sample. A DNA microarray ("chip
Multidimensional stochastic approximation using locally contractive functions
NASA Technical Reports Server (NTRS)
Lawton, W. M.
1975-01-01
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
FRACTAL APPROXIMATION AND COMPRESSION USING PROJECTED IFS
GuÃ©rin, Eric
FRACTAL APPROXIMATION AND COMPRESSION USING PROJECTED IFS Ã?ric GuÃ©rin, Ã?ric Tosan and Atilla, or images) with fractal models is an important center of interest for research. The general inverse problem.The most known of them is the fractal image compression method introduced by Jacquin. Generally speaking
Striking sound extracting based on Approximate Entropy
Zhihua Qiao; Chuan Lin; Zijuan Wang
2010-01-01
The extract accuracy of signal is vital to signal process, directly affects result of all next doing. To sound signal Approximate Entropy was taken as acoustics character to analyze sound signal got by experiment, and judging it's start and stop point accurately, then extracting striking sound from original signal. It is proved by experiment result the aim of extracting striking
Simplifying Mixture Models through Function Approximation
Kwok, James Tin-Yau
as the dis- tance measure between mixture models, we can derive closed-form solutions that are more robustSimplifying Mixture Models through Function Approximation Kai Zhang James T. Kwok Department, Kowloon, Hong Kong {twinsen, jamesk}@cse.ust.hk Abstract Finite mixture model is a powerful tool in many
Rough Set Approximations in Formal Concept Analysis
Yao, Yiyu
Rough Set Approximations in Formal Concept Analysis Yiyu Yao and Yaohua Chen Department of Computer}@cs.uregina.ca Abstract. A basic notion shared by rough set analysis and formal concept anal- ysis is the definability of a set of objects based on a set of properties. The two theories can be compared, combined and applied
On the Approximation of Computing Evolutionary Trees
Boyer, Edmond
115 On the Approximation of Computing Evolutionary Trees Vincent Berry , Sylvain Guillemot, Fran phylogenetics which is con- cerned with evolutionary trees, i.e. trees representing the evolutionary history Montpellier Cedex 5 {vberry,sguillem,nicolas,paul}@lirmm.fr Abstract. Given a set of leaf-labelled trees
Texture descriptor based on local approximations
NASA Astrophysics Data System (ADS)
Sherstobitov, A. I.; Marchuk, V. I.; Timofeev, D. V.; Voronin, V. V.; Egiazarian, K. O.; Agaian, Sos S.
2014-05-01
This paper proposes a novel texture descriptor based indices of degrees of local approximating polynomials. An input image is divided into non-overlapping patches which are reshaped into a one-dimensional source vectors. These vectors are approximated using local polynomial functions of various degrees. For each element of the source vector, these approximations are ranked according to the difference between the original and approximated values. A set of indices of polynomial degrees form a local feature. This procedure is repeated for every pixel. Finally, a proposed texture descriptor is obtained from the frequency histogram of all obtained local features. A nearest neighbor classifier utilizing distance metric is used to evaluate a performance of the introduced descriptor on the following datasets: Brodatz, KTH-TIPS, KTH-TIPS2b, UCLA and Columbia-Utrecht (CUReT) with respect to different methods of texture analysis and classification. A proper parameter setup of the proposed texture descriptor is discussed. The results of this comparison demonstrate that the proposed method is competitive with the recent statistical approaches such as local binary patterns (LBP), local ternary patterns, completed LBP, Weber's local descriptor, and VZ algorithms (VZ-MR8 and VZ-Joint). At the same time, on KTH-TIPS2-b and KTH-TIPS datasets, the proposed method is slightly inferior to some of the state-of-the-art methods.
Kravchuk functions for the finite oscillator approximation
NASA Technical Reports Server (NTRS)
Atakishiyev, Natig M.; Wolf, Kurt Bernardo
1995-01-01
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.
Approximation space for intelligent system design patterns
James F. Peters
2004-01-01
This article introduces an approximation space for graded acceptance of proposed models for intelligent system design relative to design patterns that conform to a design standard. A fundamental problem in system design is that feature values extracted from experimental design models tend not to match exactly patterns associated with standard design models. It is not generally known how to measure
Workshop on Semiclassical Approximation and Vacuum Energy
Kuchment, Peter
Workshop on Semiclassical Approximation and Vacuum Energy Texas A&M University January 1216, 2005 A Brief Survey on Quantum Graphs and Their Applications Peter Kuchment Mathematics Department Texas A is a quantum graph? · Origins of quantum graphs · Some spectral features 2. Sources: V. Kostrykin and R
Counting independent sets using the Bethe approximation
Chertkov, Michael; Chandrasekaran, V; Gamarmik, D; Shah, D; Sin, J
2009-01-01
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.
Thick domain walls in a polynomial approximation
H. Arodz
1995-01-18
Relativistic domain walls are studied in the framework of a polynomial approximation to the field interpolating between different vacua and forming the domain wall. In this approach we can calculate evolution of a core and of a width of the domain wall. In the single, cubic polynomial approximation used in this paper, the core obeys Nambu-Goto equation for a relativistic membrane. The width of the domain wall obeys a nonlinear equation which is solved perturbatively. There are two types of corrections to the constant zeroth order width: the ones oscillating in time, and the corrections directly related to curvature of the core. We find that curving a static domain wall is associated with an increase of its width. As an example, evolution of a toroidal domain wall is investigated.
Approximate Solutions in Planted 3-SAT
NASA Astrophysics Data System (ADS)
Hsu, Benjamin; Laumann, Christopher; Moessner, Roderich; Sondhi, Shivaji
2013-03-01
In many computational settings, there exists many instances where finding a solution requires a computing time that grows exponentially in the number of variables. Concrete examples occur in combinatorial optimization problems and cryptography in computer science or glassy systems in physics. However, while exact solutions are often known to require exponential time, a related and important question is the running time required to find approximate solutions. Treating this problem as a problem in statistical physics at finite temperature, we examine the computational running time in finding approximate solutions in 3-satisfiability for randomly generated 3-SAT instances which are guaranteed to have a solution. Analytic predictions are corroborated by numerical evidence using stochastic local search algorithms. A first order transition is found in the running time of these algorithms.
Semiclassical approximation with zero velocity trajectories
Yair Goldfarb; Ilan Degani; David; J. Tannor
2007-05-15
We present a new semiclassical method that yields an approximation to the quantum mechanical wavefunction at a fixed, predetermined position. In the approach, a hierarchy of ODEs are solved along a trajectory with zero velocity. The new approximation is local, both literally and from a quantum mechanical point of view, in the sense that neighboring trajectories do not communicate with each other. The approach is readily extended to imaginary time propagation and is particularly useful for the calculation of quantities where only local information is required. We present two applications: the calculation of tunneling probabilities and the calculation of low energy eigenvalues. In both applications we obtain excellent agrement with the exact quantum mechanics, with a single trajectory propagation.
Approximation techniques of a selective ARQ protocol
NASA Astrophysics Data System (ADS)
Kim, B. G.
Approximations to the performance of selective automatic repeat request (ARQ) protocol with lengthy acknowledgement delays are presented. The discussion is limited to packet-switched communication systems in a single-hop environment such as found with satellite systems. It is noted that retransmission of errors after ARQ is a common situation. ARQ techniques, e.g., stop-and-wait and continuous, are outlined. A simplified queueing analysis of the selective ARQ protocol shows that exact solutions with long delays are not feasible. Two approximation models are formulated, based on known exact behavior of a system with short delays. The buffer size requirements at both ends of a communication channel are cited as significant factor for accurate analysis, and further examinations of buffer overflow and buffer lock-out probability and avoidance are recommended.
Evolutionary Algorithm in Approximation of Defuzzification Functional
NASA Astrophysics Data System (ADS)
WÈ©grzyn-Wolska, Katarzyna; Borzymek, Piotr; Kosi?ski, Witold
2010-09-01
The space of ordered fuzzy numbers (OFN) forms a normed space on which defuzzification functionals can be defined. They play the main role when dealing with fuzzy controllers and fuzzy inference systems. An approximation formula for a general nonlinear functional is given. If a training set is given which describes an action of the functional on OFN then a dedicated evolutionary algorithm can be presented to determine its form. Genotypes composed of chromosomes are proposed together with the fitness function and genetic operators. Some numerical experiments are also performed in the case when ordered fuzzy numbers are given in terms of step functions. For the comparison an approximation procedure with the use of artificial neural networks is also implemented.
Analysing organic transistors based on interface approximation
Akiyama, Yuto [Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Tokyo 152-8552 (Japan)] [Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Tokyo 152-8552 (Japan); Mori, Takehiko [Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Tokyo 152-8552 (Japan) [Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Tokyo 152-8552 (Japan); ACT-C, JST, Honcho, Kawaguchi, Saitama 332-0012 (Japan)
2014-01-15
Temperature-dependent characteristics of organic transistors are analysed thoroughly using interface approximation. In contrast to amorphous silicon transistors, it is characteristic of organic transistors that the accumulation layer is concentrated on the first monolayer, and it is appropriate to consider interface charge rather than band bending. On the basis of this model, observed characteristics of hexamethylenetetrathiafulvalene (HMTTF) and dibenzotetrathiafulvalene (DBTTF) transistors with various surface treatments are analysed, and the trap distribution is extracted. In turn, starting from a simple exponential distribution, we can reproduce the temperature-dependent transistor characteristics as well as the gate voltage dependence of the activation energy, so we can investigate various aspects of organic transistors self-consistently under the interface approximation. Small deviation from such an ideal transistor operation is discussed assuming the presence of an energetically discrete trap level, which leads to a hump in the transfer characteristics. The contact resistance is estimated by measuring the transfer characteristics up to the linear region.
Flexible least squares for approximately linear systems
NASA Astrophysics Data System (ADS)
Kalaba, Robert; Tesfatsion, Leigh
1990-10-01
A probability-free multicriteria approach is presented to the problem of filtering and smoothing when prior beliefs concerning dynamics and measurements take an approximately linear form. Consideration is given to applications in the social and biological sciences, where obtaining agreement among researchers regarding probability relations for discrepancy terms is difficult. The essence of the proposed flexible-least-squares (FLS) procedure is the cost-efficient frontier, a curve in a two-dimensional cost plane which provides an explicit and systematic way to determine the efficient trade-offs between the separate costs incurred for dynamic and measurement specification errors. The FLS estimates show how the state vector could have evolved over time in a manner minimally incompatible with the prior dynamic and measurement specifications. A FORTRAN program for implementing the FLS filtering and smoothing procedure for approximately linear systems is provided.
Planetary ephemerides approximation for radar astronomy
NASA Technical Reports Server (NTRS)
Sadr, R.; Shahshahani, M.
1991-01-01
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.
Testing the Frozen-Flow Approximation
NASA Astrophysics Data System (ADS)
Melott, A. L.; Lucchin, F.; Matarrese, S.; Moscardini, L.
1994-05-01
We investigate the accuracy of the frozen-flow approximation (FFA), recently proposed by Matarrese et al., for tracing of the non-linear evolution of cosmological density fluctuations under gravitational instability. We compare a number of statistics between results of the FFA and N-body simulations, including those used by Melon, Pellman & Shandarin to test the Zel'dovich approximation. The FFA performs reasonably well in a statistical sense (for example, in reproducing the counts-in-cells distribution) at small scales, but it does poorly in the cross-correlation with N-body simulations, which means that it is generally not moving mass to the right place, especially in models with high small-scale power.
Edinburgh Research Explorer Approximating Markov Processes by Averaging
Millar, Andrew J.
Edinburgh Research Explorer Approximating Markov Processes by Averaging Citation for published version: Chaput, P, Danos, V, Panangaden, P & Plotkin, G 2014, 'Approximating Markov Processes date: 07. Jul. 2015 #12;Approximating Markov Processes by Averaging Philippe Chaput1, , Vincent Danos2
Nonlinear adaptive control using radial basis function approximants
Petersen, Jerry Lee
1993-01-01
The purpose of this research is to present an adaptive control strategy using the radial basis function approximation method. Surface approximation methods using radial basis function approximants will first be discussed. ...
Ioffe Time in Double Logarithmic Approximation
Yuri V. Kovchegov; Mark Strikman
2001-07-25
We analyze the light cone (Ioffe) time structure of the gluon distribution function in the double logarithmic approximation. We show that due to QCD evolution Ioffe equation is modified. The characteristic light cone time of the gluons does not increase as fast with increasing energy (decreasing Bjorken x) as predicted by the parton distributions exhibiting Bjorken scaling due to the increase of the transverse momenta of the gluons in the DGLAP ladder.
SPSS procedures for approximate randomization tests
Andrew F. Hayes
1998-01-01
Randomization tests are valid alternatives to parametric tests like the t test and analysis of variance when the normality\\u000a or random sampling assumptions of these tests are violated. Three SPSS programs are listed and described that will conduct\\u000a approximate randomization tests for testing the null hypotheses that two or more means or distributions are the same or that\\u000a two variables
Approximate Metric for a Rotating Deformed Mass
Francisco Frutos-Alfaro; Paulo Montero-Camacho; Miguel Araya-Arguedas; Javier Bonatti-Gonzalez
2015-09-12
A new Kerr-like metric with quadrupole moment is obtained by means of perturbing the Kerr spacetime. The form of this new metric is simple as the Kerr metric. By comparison with the exterior Hartle-Thorne metric, it is shown that it could be matched to an interior solution. This approximate metric may represent the spacetime of a real astrophysical object with any Kerr rotation parameter a and slightly deformed.
Approximation methods for stochastic petri nets
NASA Technical Reports Server (NTRS)
Jungnitz, Hauke Joerg
1992-01-01
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.
Fast Approximate Wavelet Tracking on Streams
Graham Cormode; Minos N. Garofalakis; Dimitris Sacharidis
2006-01-01
Recent years have seen growing interest in effective algorithms for summarizing and querying massive, high-speed data streams. Randomized sketch synopses provide accurate approximations for general-purpose summaries of the streaming data distribution (e.g., wavelets). The focus of existing work has typi- cally been on minimizing space requirementsof the maintained synopsis — how- ever, to effectively support high-speed data-stream analysis, a crucial
Approximation Algorithms for Model-Based Diagnosis
A. B. Feldman
2010-01-01
Model-based diagnosis is an area of abductive inference that uses a system model, together with observations about system behavior, to isolate sets of faulty components (diagnoses) that explain the observed behavior, according to some minimality criterion. This thesis presents greedy approximation algorithms for three problems closely related to model-based diagnosis: (1) computation of cardinality-minimal diagnoses, (2) computation of max-fault min-cardinality
Linear Value Function Approximation Linear Models
Parr, Ronald
Linear Value Function Approximation and Linear Models Ronald Parr Duke University Joint work] Â· Set of features/basis vectors/basis functions h1(x)...hk(x) Â· Find weight vector w=[w ...w ] s.t.Â· Find weight vector w=[w1...wk] s.t. i k j ijj xxhw =1 )( #12;More Regression Notation K basis functions
Geometry-aware bases for shape approximation.
Sorkine, Olga; Cohen-Or, Daniel; Irony, Dror; Toledo, Sivan
2005-01-01
We introduce a new class of shape approximation techniques for irregular triangular meshes. Our method approximates the geometry of the mesh using a linear combination of a small number of basis vectors. The basis vectors are functions of the mesh connectivity and of the mesh indices of a number of anchor vertices. There is a fundamental difference between the bases generated by our method and those generated by geometry-oblivious methods, such as Laplacian-based spectral methods. In the latter methods, the basis vectors are functions of the connectivity alone. The basis vectors of our method, in contrast, are geometry-aware since they depend on both the connectivity and on a binary tagging of vertices that are "geometrically important" in the given mesh (e.g., extrema). We show that, by defining the basis vectors to be the solutions of certain least-squares problems, the reconstruction problem reduces to solving a single sparse linear least-squares problem. We also show that this problem can be solved quickly using a state-of-the-art sparse-matrix factorization algorithm. We show how to select the anchor vertices to define a compact effective basis from which an approximated shape can be reconstructed. Furthermore, we develop an incremental update of the factorization of the least-squares system. This allows a progressive scheme where an initial approximation is incrementally refined by a stream of anchor points. We show that the incremental update and solving the factored system are fast enough to allow an online refinement of the mesh geometry. PMID:15747640
Approximation by Piecewise Constants on Convex Partitions
Davydov, Oleg
], and hence (2) implies that the PoincarÂ´e inequality f - f Lp() d diam() f Lp(), f W1 p (), (3) holds. It follows from (2) that for any convex partition , En(f, )p Cd,n diamn () |f|W n p (), diam() := max diam(). Obviously, diam() C||-1/d , where C depends only on || and d. Hence, in terms of ||, the approximation
Capacitor-Chain Successive-Approximation ADC
NASA Technical Reports Server (NTRS)
Cunningham, Thomas
2003-01-01
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.
HVAC simulation studies: Solution by successive approximation
J. A. Wright
1993-01-01
Large-scale system simulations are efficient in solving large equation sets. However, where the simulation is restricted to a single component or subsystem; however, it is often more efficient to solve the equation set by a simple iteration. This paper describes the use of a successive approximation algorithm in solving equations for small-scale steady-state HVAC system simulations. The algorithm is shown
Greedy Function Approximation: A Gradient Boosting Machine
Jerome H. Friedman
2000-01-01
Function approximation is viewed from the perspective of numerical optimization infunction space, rather than parameter space. A connection is made between stagewise additiveexpansions and steepest{descent minimization. A general gradient{descent \\\\boosting"paradigm is developed for additive expansions based on any tting criterion. Specic algorithmsare presented for least{squares, least{absolute{deviation, and Huber{M loss functionsfor regression, and multi{class logistic likelihood...
Approximations to the plasma dispersion function
NASA Technical Reports Server (NTRS)
Brinca, A. L.
1972-01-01
Linear wave propagation in hot collisionless plasmas is described by the linearized Vlasov and Maxwell equations. In uniform media, the utilization of spatial and temporal transforms of those equations leads to the consideration of integrals of the Hilbert transform type. Analysis and comparison of two simple approximations are provided based on the utilization of resonance velocity distributions. Application is then made to the Landau and whistler waves, along with a discussion of the results, and commentary on possible improvements.
Sparse greedy matrix approximation for machine learning
Alex J. Smola; B. Scholkopf
2000-01-01
In kernel based methods such as RegularizationNetworks large datasets pose signi-cant problems since the number of basis functionsrequired for an optimal solution equalsthe number of samples. We present a sparsegreedy approximation technique to constructa compressed representation of the designmatrix. Experimental results are given andconnections to Kernel-PCA, Sparse KernelFeature Analysis, and Matching Pursuit arepointed out.1. IntroductionMany recent advances in...
The concept of the approximants of quasicrystals
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
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.
Vainshtein mechanism beyond the quasistatic approximation
NASA Astrophysics Data System (ADS)
Winther, Hans A.; Ferreira, Pedro G.
2015-09-01
Theories of modified gravity, in both the linear and fully nonlinear regimes, are often studied under the assumption that the evolution of the new (often scalar) degree of freedom present in the theory is quasistatic. This approximation significantly simplifies the study of the theory, and one often has good reason to believe that it should hold. Nevertheless it is a crucial assumption that should be explicitly checked whenever possible. In this paper we do so for the Vainshtein mechanism in a cosmological setting. By solving for the full spatial and time evolution of the Dvali-Gabadadze-Porrati and the cubic Galileon models, in an expanding spherical symmetric spacetime, we are able to demonstrate that the Vainshtein solution is a stable attractor and forms no matter what initial conditions we take for the scalar field. Furthermore,the quasistatic approximation is also found to be a very good approximation whenever it exists. For the best-fit cubic Galileon model, however, we find that for deep voids at late times the numerical solution blows up at the same time as the quasistatic solution ceases to exist. We argue that this phenomenon is a true instability of the model.
Using Approximations to Accelerate Engineering Design Optimization
NASA Technical Reports Server (NTRS)
Torczon, Virginia; Trosset, Michael W.
1998-01-01
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.
Strong washout approximation to resonant leptogenesis
Garbrecht, Björn; Gautier, Florian; Klaric, Juraj E-mail: florian.gautier@tum.de
2014-09-01
We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ?=Xsin(2?)/(X{sup 2}+sin{sup 2}?), where X=8??/(|Y{sub 1}|{sup 2}+|Y{sub 2}|{sup 2}), ?=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), ?=arg(Y{sub 2}/Y{sub 1}), and M{sub 1,2}, Y{sub 1,2} are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y{sub 1,2}|{sup 2}>> ?, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.
Approximation abilities of neuro-fuzzy networks
NASA Astrophysics Data System (ADS)
Mrówczy?ska, Maria
2010-01-01
The paper presents the operation of two neuro-fuzzy systems of an adaptive type, intended for solving problems of the approximation of multi-variable functions in the domain of real numbers. Neuro-fuzzy systems being a combination of the methodology of artificial neural networks and fuzzy sets operate on the basis of a set of fuzzy rules "if-then", generated by means of the self-organization of data grouping and the estimation of relations between fuzzy experiment results. The article includes a description of neuro-fuzzy systems by Takaga-Sugeno-Kang (TSK) and Wang-Mendel (WM), and in order to complement the problem in question, a hierarchical structural self-organizing method of teaching a fuzzy network. A multi-layer structure of the systems is a structure analogous to the structure of "classic" neural networks. In its final part the article presents selected areas of application of neuro-fuzzy systems in the field of geodesy and surveying engineering. Numerical examples showing how the systems work concerned: the approximation of functions of several variables to be used as algorithms in the Geographic Information Systems (the approximation of a terrain model), the transformation of coordinates, and the prediction of a time series. The accuracy characteristics of the results obtained have been taken into consideration.
Quasicrystalline decagonal and related crystalline approximant structures
Daulton, T.L.
1992-01-01
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.
Rindler approximation to Kerr black hole
H. A. Camargo; M. Socolovsky
2014-10-23
We show that the Rindler approximation to the time-radial part of the Kerr and Kerr-Newman metrics near their external $h_+$ and internal $h_-$ horizons {\\bf only} holds {\\bf outside} $h_+$ and {\\bf inside} $h_-$, so respectively inside and outside the external and internal ergospheres, regions where, in Boyer-Lindquist coordinates, both $g_{tt}$ and $g_{rr}$ are negative, but preserving the Lorentzian character of the metric, and $r>0$ i.e. outside the region $rsurface gravities $\\kappa_\\pm$ as the corresponding proper accelerations, and therefore the Hawking temperatures $\\tau_\\pm$ at $h_\\pm$.
Relativistic Random Phase Approximation At Finite Temperature
Niu, Y. F.; Paar, N.; Vretenar, D.; Meng, J.
2009-08-26
The fully self-consistent finite temperature relativistic random phase approximation (FTRRPA) has been established in the single-nucleon basis of the temperature dependent Dirac-Hartree model (FTDH) based on effective Lagrangian with density dependent meson-nucleon couplings. Illustrative calculations in the FTRRPA framework show the evolution of multipole responses of {sup 132}Sn with temperature. With increased temperature, in both monopole and dipole strength distributions additional transitions appear in the low energy region due to the new opened particle-particle and hole-hole transition channels.
Approximate Black Holes for Numerical Relativity
Maurice H. P. M. van Putten
1996-07-30
Spherically symmetric solutions in Brans-Dicke theory of relativity with zero coupling constant, $\\omega=0$, 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. These nontopological solitons have some similarity with soliton stars, and are proposed as candidates for {\\em approximate black holes} for the use in numerical relativity, in particular for treatment of horizon boundary conditions.
Variational method for approximating energy levels
NASA Astrophysics Data System (ADS)
Zhou, Yu; Mancini, Jay D.; Meier, Peter F.; Bowen, Samuel P.
1995-04-01
We present here a systematic scheme for improving the variational wave functions and corresponding energy levels for quantum systems. By expanding the wave function around a variational parameter value, a family of independent functions can be systematically generated. The eigenstates are then obtained by diagonalizing the Hamiltonian matrix within the basis and optimized with respect to the variational parameter. As a test, the ground state of the quartic anharmonic oscillator has been investigated, and it is found that this scheme converges more rapidly than the conventional Lanczos method and yields better approximations of the energy levels than other variational methods. The effectiveness of this scheme for larger systems remains to be seen.
[Bond selective chemistry beyond the adiabatic approximation
Butler, L.J.
1993-02-28
The adiabatic Born-Oppenheimer potential energy surface approximation is not valid for reaction of a wide variety of energetic materials and organic fuels; coupling between electronic states of reacting species plays a key role in determining the selectivity of the chemical reactions induced. This research program initially studies this coupling in (1) selective C-Br bond fission in 1,3- bromoiodopropane, (2) C-S:S-H bond fission branching in CH[sub 3]SH, and (3) competition between bond fission channels and H[sub 2] elimination in CH[sub 3]NH[sub 2].
Optimal Markov Approximations and Generalized Embeddings
Detlef Holstein; Holger Kantz
2008-08-11
Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible memory into account and minimal statistical errors by working in embedding spaces of rather small dimension. A key ingredient is an estimate of the statistical error of entropy estimates. The method is illustrated with several examples and the consequences for prediction are evaluated by means of the root mean squard prediction error for point prediction.
Fuzzy systems with defuzzification are universal approximators.
Castro, J L; Delgado, M
1996-01-01
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
Fast Approximate Analysis Of Modified Antenna Structure
NASA Technical Reports Server (NTRS)
Levy, Roy
1991-01-01
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.
Approximations for crossing two nearby spin resonances
NASA Astrophysics Data System (ADS)
Ranjbar, V. H.
2015-01-01
Solutions to the Thomas-Bargmann-Michel-Telegdi spin equation for spin 1 /2 particles have to date been confined to the single-resonance crossing. However, in reality, most cases of interest concern the overlapping of several resonances. While there have been several serious studies of this problem, a good analytical solution or even an approximation has eluded the community. We show that this system can be transformed into a Hill-like equation. In this representation, we show that, while the single-resonance crossing represents the solution to the parabolic cylinder equation, the overlapping case becomes a parametric type of resonance.
Mass insertion approximation without squark degeneracy
NASA Astrophysics Data System (ADS)
Raz, Guy
2002-08-01
We study the applicability of the mass insertion approximation (MIA) for calculations of neutral meson mixing when squark masses are not degenerate and, in particular, in models of alignment. We show that the MIA can give results that are much better than an order of magnitude estimate as long as the masses are not strongly hierarchical. We argue that, in an effective two-squark framework, mq=(m1+m1)/2 is the best choice for the MIA expansion point, rather than, for example, m2q=(m21+m22)/2.
Virial expansion coefficients in the harmonic approximation
J. R. Armstrong; N. T. Zinner; D. V. Fedorov; A. S. Jensen
2012-12-24
The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated to reproduce ground state properties at low temperature and the non-interacting large temperature limit of constant virial coefficients. This resembles the smearing of shell effects in finite systems with increasing temperature. Numerical results are discussed for the second and third virial coefficients as function of dimension, temperature, interaction, and the transition temperature between low and high energy limits.
Retroreflector approximation of a generalized Eaton lens
NASA Astrophysics Data System (ADS)
Kim, Sang-Hoon
2012-05-01
We extended a previous study of the Eaton lens at specific refraction angles to the Eaton lens at any refraction angle. The refractive index of the Eaton lens is complicated and has not analytical form except at a few specific angles. We derived a more accessible form of the refractive index for any refraction angle with some accuracy by retroreflector approximation. The finding of this study will be useful for a rapid estimation of the refractive index, and the the design of various Eaton lenses.
Fast Color Space Transformations Using Minimax Approximations
Celebi, M Emre; Celiker, Fatih; 10.1049/iet-ipr.2008.0172
2010-01-01
Color space transformations are frequently used in image processing, graphics, and visualization applications. In many cases, these transformations are complex nonlinear functions, which prohibits their use in time-critical applications. In this paper, we present a new approach called Minimax Approximations for Color-space Transformations (MACT).We demonstrate MACT on three commonly used color space transformations. Extensive experiments on a large and diverse image set and comparisons with well-known multidimensional lookup table interpolation methods show that MACT achieves an excellent balance among four criteria: ease of implementation, memory usage, accuracy, and computational speed.
Vacuum polarization around stars: Nonlocal approximation
Satz, Alejandro [School of Mathematical Sciences, University of Nottingham, NG7 2RD Nottingham (United Kingdom); Mazzitelli, Francisco D. [Departamento de Fisica Juan Jose Giambiagi, FCEyN UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina); Alvarez, Ezequiel [Departament de Fisica Teorica, IFIC, CSIC, Universitat de Valencia, Dr Moliner 50, E-46100 Burjassot, Valencia Spain (Spain)
2005-03-15
We compute the vacuum polarization associated with quantum massless fields around stars with spherical symmetry. The nonlocal contribution to the vacuum polarization is dominant in the weak field limit and induces quantum corrections to the static exterior metric that depend on the inner structure of the star. It also violates the null energy conditions. We argue that similar results also hold in the low energy limit of quantum gravity. Previous calculations of the vacuum polarization in spherically symmetric spacetimes, based on local approximations, are not adequate for Newtonian stars.
Improved approximations for dynamic displacements using intermediate response quantities
NASA Technical Reports Server (NTRS)
Thomas, Harold L.; Sepulveda, Abdon E.; Schmit, Lucien A.
1990-01-01
An approximation for dynamic displacements, which captures the nonlinearities associated with resonance, is presented. This approximation is constructed using approximate intermediate response quantities. When dynamic displacements are constrained using this high quality approximation, frequency constraints are no longer needed to keep the design away from resonance.
Bethe free energy, Kikuchi approximations and belief propagation
Bethe free energy, Kikuchi approximations and belief propagation algorithms Jonathan S. Yedidia to a stationary point of an approximate free energy, known as the Bethe free energy in statis- tical physics- curate free energy approximations, of which Bethe's approximation is the simplest. Exploiting
Noise suppression based on approximate KLT with wavelet packet expansion
Chung-Hsien Yang; Jhing-Fa Wang
2002-01-01
In this paper, we perform the noise suppression based on approximate Karhunen-Loeve transform (KL T). The discrete cosine transform(DCT) has been a good candidate for approximate KLT when the signal is modeled as an autoregressive process. However, for nonstationary signals, wavelet transform is more capable than DCT while approximating KLT. To calculate approximate KLT, we first represent the signal by
Gaussian Variational Approximate Inference for Generalized Linear Mixed Models
J. T. Ormerod; M. P. Wand
2012-01-01
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
Black-Box Approximation of high dimensional Tensors
Hackbusch, Wolfgang
Black-Box Approximation of high dimensional Tensors Melanie Kluge For the approximation of order d to approximate the matricizations by low rank, and one has to ensure that they are nested. We approach, L. Grasedyck and M. Kluge. Black Box Approximation of Tensors in Hierarchical Tucker Format. www
Function approximation using adaptive and overlapping intervals
Patil, R.B.
1995-05-01
A problem common to many disciplines is to approximate a function given only the values of the function at various points in input variable space. A method is proposed for approximating a function of several to one variable. The model takes the form of weighted averaging of overlapping basis functions defined over intervals. The number of such basis functions and their parameters (widths and centers) are automatically determined using given training data and a learning algorithm. The proposed algorithm can be seen as placing a nonuniform multidimensional grid in the input domain with overlapping cells. The non-uniformity and overlap of the cells is achieved by a learning algorithm to optimize a given objective function. This approach is motivated by the fuzzy modeling approach and a learning algorithms used for clustering and classification in pattern recognition. The basics of why and how the approach works are given. Few examples of nonlinear regression and classification are modeled. The relationship between the proposed technique, radial basis neural networks, kernel regression, probabilistic neural networks, and fuzzy modeling is explained. Finally advantages and disadvantages are discussed.
Approximate discrete dynamics of EMG signal
Sayan Mukherjee; Sanjay Kumar Palit; D. K. Bhattacharya
2014-09-23
Approximation of a continuous dynamics by discrete dynamics in the form of Poincare map is one of the fascinating mathematical tool, which can describe the approximate behaviour of the dynamics of the dynamical system in lesser dimension than the embedding diemnsion. The present article considers a very rare biomedical signal like Electromyography (EMG) signal. It determines suitable time delay and reconstruct the attractor of embedding diemnsion three. By measuring its Lyapunov exponent, the attractor so reconstructed is found to be chaotic. Naturally the Poincare map obtained by corresponding Poincare section is to be chaotic too. This may be verified by calculation of Lyapunov exponent of the map. The main objective of this article is to show that Poincare map exists in this case as a 2D map for a suitable Poincare section only. In fact, the article considers two Poincare sections of the attractor for construction of the Poincare map. It is seen that one such map is chaotic but the other one is not so, both are verified by calculation of Lyapunov exponent of the map.
Approximation of Failure Probability Using Conditional Sampling
NASA Technical Reports Server (NTRS)
Giesy. Daniel P.; Crespo, Luis G.; Kenney, Sean P.
2008-01-01
In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.
Fast approximate hierarchical clustering using similarity heuristics
Kull, Meelis; Vilo, Jaak
2008-01-01
Background Agglomerative hierarchical clustering (AHC) is a common unsupervised data analysis technique used in several biological applications. Standard AHC methods require that all pairwise distances between data objects must be known. With ever-increasing data sizes this quadratic complexity poses problems that cannot be overcome by simply waiting for faster computers. Results We propose an approximate AHC algorithm HappieClust which can output a biologically meaningful clustering of a large dataset more than an order of magnitude faster than full AHC algorithms. The key to the algorithm is to limit the number of calculated pairwise distances to a carefully chosen subset of all possible distances. We choose distances using a similarity heuristic based on a small set of pivot objects. The heuristic efficiently finds pairs of similar objects and these help to mimic the greedy choices of full AHC. Quality of approximate AHC as compared to full AHC is studied with three measures. The first measure evaluates the global quality of the achieved clustering, while the second compares biological relevance using enrichment of biological functions in every subtree of the clusterings. The third measure studies how well the contents of subtrees are conserved between the clusterings. Conclusion The HappieClust algorithm is well suited for large-scale gene expression visualization and analysis both on personal computers as well as public online web applications. The software is available from the URL PMID:18822115
Analytic approximate radiation effects due to Bremsstrahlung
Ben-Zvi I.
2012-02-01
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.
NASA Astrophysics Data System (ADS)
Osborn, T. A.; Molzahn, F. H.
1986-09-01
The mutual consistency and structural interconnection between the Wentzel-Kramers-Brillouin (WKB) and Wigner-Kirkwood (WK) semiclassical approximations is investigated for nonrelativistic N-particle systems, with mutual scalar interactions and coupling to an external time-varying electromagnetic field. The generalized WK expansion of the propagator
NASA Astrophysics Data System (ADS)
Bervillier, C.; Boisseau, B.; Giacomini, H.
2008-02-01
The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).
C. Bervillier; B. Boisseau; H. Giacomini
2007-10-11
The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).
Hunting resonance poles with Rational Approximants
Pere Masjuan
2010-12-13
Based on the mathematically well defined Pad\\'e Theory, a theoretically safe new procedure for the extraction of the pole mass and width of resonances is proposed. In particular, thanks to the Montessus de Ballore's theorem we are able to unfold the Second Riemann sheet of an amplitude to search the position of the resonant pole in the complex plane. The method is systematic and provides a model-independent treatment of the prediction and the corresponding errors of the approximation. This letter partially covers the material presented by the author at the 15th International QCD Conference: QCD 10 (25th anniversary), Montpellier, France, 28 Jun - 3 Jul 2010 and at the Quark Confinement and the Hadron Spectrum IX, 30 August - 3 September 2010, Madrid, Spain.
Gutzwiller approximation for the Emery model
Sarker, S.K.
1989-02-01
Normal-state properties of the two-dimensional model proposed by Emery for copper-oxide superconductors are studied within the Gutzwiller approximation. For larger intrasite repulsion it is found that hybridization produces quasihole bands with a reduced kinetic energy. For hole densities between 1 and 2, the reduction factor q is proportional to (epsilon/sub 0//sup -1/+(u-epsilon/sub 0/)/sup -1/)/sup 2/ where epsilon/sub 0/ = deltaepsilon/t, u = U/t, deltaepsilon is the difference in energy between the copper and the oxygen levels, and t is the hybridization energy. These results differ qualitatively from those for the heavy-fermion case where q is exponentially small, resulting in small Fermi energy (large effective mass). In the present case holes are only moderately heavy so that the Fermi energy is large.
Markovian approximation in foreign exchange markets
NASA Astrophysics Data System (ADS)
Baviera, Roberto; Vergni, Davide; Vulpiani, Angelo
2000-06-01
In this paper, using the exit-time statistic, we study the structure of the price variations for the high-frequency data set of the bid-ask Deutschemark/US dollar exchange rate quotes registered by the inter-bank Reuters network over the period October 1, 1992 to September 30, 1993. Having rejected random-walk models for the returns, we propose a Markovian model which reproduce the available information of the financial series. Besides the usual correlation analysis we have verified the validity of this model by means of other tools all inspired by information theory. These techniques are not only severe tests of the approximation but also evidence of some aspects of the data series which have a clear financial relevance.
Dihedral manifold approximate fibrations over the circle
Hughes, Bruce
2009-01-01
Consider the cyclic group C_2 of order two acting by complex-conjugation on the unit circle S^1. The main result is that a finitely dominated manifold W of dimension > 4 admits a cocompact, free, discontinuous action by the infinite dihedral group D_\\infty if and only if W is the infinite cyclic cover of a free C_2-manifold M such that M admits a C_2-equivariant manifold approximate fibration to S^1. The novelty in this setting is the existence of codimension-one, invariant submanifolds of M and W. Along the way, we develop an equivariant sucking principle for certain orthogonal actions of finite groups on Euclidean space.
Approximating Densities of States with Gaps
NASA Astrophysics Data System (ADS)
Haydock, Roger; Nex, C. M. M.
2011-03-01
Reconstructing a density of states or similar distribution from moments or continued fractions is an important problem in calculating the electronic and vibrational structure of defective or non-crystalline solids. For single bands a quadratic boundary condition introduced previously [Phys. Rev. B 74, 205121 (2006)] produces results which compare favorably with maximum entropy and even give analytic continuations of Green functions to the unphysical sheet. In this paper, the previous boundary condition is generalized to an energy-independent condition for densities with multiple bands separated by gaps. As an example it is applied to a chain of atoms with s, p, and d bands of different widths with different gaps between them. The results are compared with maximum entropy for different levels of approximation. Generalized hypergeometric functions associated with multiple bands satisfy the new boundary condition exactly. Supported by the Richmond F. Snyder Fund.
Generic sequential sampling for metamodel approximations
Turner, C. J.; Campbell, M. I.
2003-01-01
Metamodels approximate complex multivariate data sets from simulations and experiments. These data sets often are not based on an explicitly defined function. The resulting metamodel represents a complex system's behavior for subsequent analysis or optimization. Often an exhaustive data search to obtain the data for the metalnodel is impossible, so an intelligent sampling strategy is necessary. While inultiple approaches have been advocated, the majority of these approaches were developed in support of a particular class of metamodel, known as a Kriging. A more generic, cotninonsense approach to this problem allows sequential sampling techniques to be applied to other types of metamodeis. This research compares recent search techniques for Kriging inetamodels with a generic, inulti-criteria approach combined with a new type of B-spline metamodel. This B-spline metamodel is competitive with prior results obtained with a Kriging metamodel. Furthermore, the results of this research highlight several important features necessary for these techniques to be extended to more complex domains.
Polarized constituent quarks in NLO approximation
NASA Astrophysics Data System (ADS)
Khorramian, Ali N.; Tehrani, S. Atashbar; Mirjalili, A.
2006-02-01
The valon representation provides a basis between hadrons and quarks, in terms of which the bound-state and scattering properties of hadrons can be united and described. We studied polarized valon distributions which have an important role in describing the spin dependence of parton distribution in leading and next-to-leading order approximation. Convolution integral in frame work of valon model as a useful tool, was used in polarized case. To obtain polarized parton distributions in a proton we need to polarized valon distribution in a proton and polarized parton distributions inside the valon. We employed Bernstein polynomial averages to get unknown parameters of polarized valon distributions by fitting to available experimental data.
Heat flow in the postquasistatic approximation
B. Rodríguez-Mueller; C. Peralta; W. Barreto; L. Rosales
2010-08-05
We apply the postquasistatic approximation to study the evolution of spherically symmetric fluid distributions undergoing dissipation in the form of radial heat flow. For a model which corresponds to an incompressible fluid departing from the static equilibrium, it is not possible to go far from the initial state after the emission of a small amount of energy. Initially collapsing distributions of matter are not permitted. Emission of energy can be considered as a mechanism to avoid the collapse. If the distribution collapses initially and emits one hundredth of the initial mass only the outermost layers evolve. For a model which corresponds to a highly compressed Fermi gas, only the outermost shell can evolve with a shorter hydrodynamic time scale.
Approximating Densities of States with Gaps
Roger Haydock; C. M. M. Nex
2010-10-12
Reconstructing a density of states or similar distribution from moments or continued fractions is an important problem in calculating the electronic and vibrational structure of defective or non-crystalline solids. For single bands a quadratic boundary condition introduced previously [Phys. Rev. B 74, 205121 (2006)] produces results which compare favorably with maximum entropy and even give analytic continuations of Green functions to the unphysical sheet. In this paper, the previous boundary condition is generalized to an energy-independent condition for densities with multiple bands separated by gaps. As an example it is applied to a chain of atoms with s, p, and d bands of different widths with different gaps between them. The results are compared with maximum entropy for different levels of approximation. Generalized hypergeometric functions associated with multiple bands satisfy the new boundary condition exactly.
Approximating densities of states with gaps
NASA Astrophysics Data System (ADS)
Haydock, Roger; Nex, C. M. M.
2010-11-01
Reconstructing a density of states or similar distribution from moments or continued fractions is an important problem in calculating the electronic and vibrational structure of defective or noncrystalline solids. For single bands a quadratic boundary condition introduced previously [R. Haydock and C. M. M. Nex, Phys. Rev. B 74, 205121 (2006)10.1103/PhysRevB.74.205121] produces results which compare favorably with maximum entropy and even give analytic continuations of Green’s functions to the unphysical sheet. In this paper, the previous boundary condition is generalized to an energy-independent condition for densities with multiple bands separated by gaps. As an example it is applied to a chain of atoms with s , p , and d bands of different widths with different gaps between them. The results are compared with maximum entropy for different levels of approximation. Generalized hypergeometric functions associated with multiple bands satisfy the new boundary condition exactly.
Hunting resonance poles with Rational Approximants
Masjuan, Pere
2010-01-01
Based on the mathematically well defined Pad\\'e Theory, a theoretically safe new procedure for the extraction of the pole mass and width of resonances is proposed. In particular, thanks to the Montessus de Ballore's theorem we are able to unfold the Second Riemann sheet of an amplitude to search the position of the resonant pole in the complex plane. The method is systematic and provides a model-independent treatment of the prediction and the corresponding errors of the approximation. This letter partially covers the material presented by the author at the 15th International QCD Conference: QCD 10 (25th anniversary), Montpellier, France, 28 Jun - 3 Jul 2010 and at the Quark Confinement and the Hadron Spectrum IX, 30 August - 3 September 2010, Madrid, Spain.
Exact and Approximate Probabilistic Symbolic Execution
NASA Technical Reports Server (NTRS)
Luckow, Kasper; Pasareanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem
2014-01-01
Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.
Approximate truncation robust computed tomography—ATRACT
NASA Astrophysics Data System (ADS)
Dennerlein, Frank; Maier, Andreas
2013-09-01
We present an approximate truncation robust algorithm to compute tomographic images (ATRACT). This algorithm targets at reconstructing volumetric images from cone-beam projections in scenarios where these projections are highly truncated in each dimension. It thus facilitates reconstructions of small subvolumes of interest, without involving prior knowledge about the object. Our method is readily applicable to medical C-arm imaging, where it may contribute to new clinical workflows together with a considerable reduction of x-ray dose. We give a detailed derivation of ATRACT that starts from the conventional Feldkamp filtered-backprojection algorithm and that involves, as one component, a novel original formula for the inversion of the two-dimensional Radon transform. Discretization and numerical implementation are discussed and reconstruction results from both, simulated projections and first clinical data sets are presented.
A realistic formulation of approximate CP
Thomas Dent; Joaquim Silva-Marcos
2002-12-16
CP violation in the SM is naturally implemented as a small imaginary perturbation to real Yukawa couplings. For example, a large CP asymmetry in B_d decays can arise if the imaginary parts of quark mass matrices are of order 10^(-3)m_t,b or smaller. Applying the same principle of ``additive CP violation'' to soft SUSY-breaking terms, the electric dipole moments of the neutron and mercury atom are predicted near current experimental limits; for nonuniversal A-terms, EDM bounds can be satisfied given certain flavour structures. The proposal is conveniently formulated in a democratic basis, with Yukawas and soft terms of the form const. x (1+eps+i zeta) where eps<<1, zeta<~10^(-3), motivated by approximate permutation x CP symmetry.
A realistic formulation of approximate CP
Dent, T; Dent, Thomas; Silva-Marcos, Joaquim
2003-01-01
CP violation in the SM is naturally implemented as a small imaginary perturbation to real Yukawa couplings. For example, a large CP asymmetry in B_d decays can arise if the imaginary parts of quark mass matrices are of order 10^(-3)m_t,b or smaller. Applying the same principle of ``additive CP violation'' to soft SUSY-breaking terms, the electric dipole moments of the neutron and mercury atom are predicted near current experimental limits; for nonuniversal A-terms, EDM bounds can be satisfied given certain flavour structures. The proposal is conveniently formulated in a democratic basis, with Yukawas and soft terms of the form const x (1+eps+i zeta) where eps<<1, zeta<~10^(-3), motivated by approximate permutation x CP symmetry.
Nanostructures: Scattering beyond the Born approximation
NASA Astrophysics Data System (ADS)
Grigoriev, S. V.; Syromyatnikov, A. V.; Chumakov, A. P.; Grigoryeva, N. A.; Napolskii, K. S.; Roslyakov, I. V.; Eliseev, A. A.; Petukhov, A. V.; Eckerlebe, H.
2010-03-01
The neutron scattering on a two-dimensional ordered nanostructure with the third nonperiodic dimension can go beyond the Born approximation. In our model supported by the exact theoretical solution a well-correlated hexagonal porous structure of anodic aluminum oxide films acts as a peculiar two-dimensional grating for the coherent neutron wave. The thickness of the film L (length of pores) plays important role in the transition from the weak to the strong scattering regimes. It is shown that the coherency of the standard small-angle neutron scattering setups suits to the geometry of the studied objects and often affects the intensity of scattering. The proposed theoretical solution can be applied in the small-angle neutron diffraction experiments with flux lines in superconductors, periodic arrays of magnetic or superconducting nanowires, as well as in small-angle diffraction experiments on synchrotron radiation.
Semiclassical approximation to supersymmetric quantum gravity
Kiefer, Claus; Lueck, Tobias; Moniz, Paulo [Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Cologne (Germany); Astronomy Unit, School of Mathematical Sciences, Queen Mary College, University of London, Mile End Road, London E1 4NS (United Kingdom)
2005-08-15
We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schroedinger equation, and quantum gravitational correction terms to this Schroedinger equation. In particular, the following consequences are found: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many-fingered) local time parameter has to be present on super Riem {sigma} (the space of all possible tetrad and gravitino fields) (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early Universe. The physical meaning of these equations and results, in particular, the similarities to and differences from the pure bosonic case, are discussed.
Estimating Mutual Information by Local Gaussian Approximation
Gao, Shuyang; Galstyan, Aram
2015-01-01
Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly dependent variables and have sample complexity that scales exponentially with the true MI. This undesired behavior was attributed to the reliance of those estimators on local uniformity of the underlying (and unknown) probability density function. Here we present a novel semi-parametric estimator of mutual information, where at each sample point, densities are {\\em locally} approximated by a Gaussians distribution. We demonstrate that the estimator is asymptotically unbiased. We also show that the proposed estimator has a superior performance compared to several baselines, and is able to accurately measure relationship strengths over many orders of magnitude.
Magnetic reconnection under anisotropic magnetohydrodynamic approximation
NASA Astrophysics Data System (ADS)
Hirabayashi, K.; Hoshino, M.
2013-11-01
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.
Approximate Stokes Drift Profiles in Deep Water
Breivik, Øyvind; Bidlot, Jean-Raymond
2014-01-01
A deep-water approximation to the Stokes drift velocity profile is explored as an alternative to the monochromatic profile. The alternative profile investigated relies on the same two quantities required for the monochromatic profile, viz the Stokes transport and the surface Stokes drift velocity. Comparisons with parametric spectra and profiles under wave spectra from the ERA-Interim reanalysis and buoy observations reveal much better agreement than the monochromatic profile even for complex sea states. That the profile gives a closer match and a more correct shear has implications for ocean circulation models since the Coriolis-Stokes force depends on the magnitude and direction of the Stokes drift profile and Langmuir turbulence parameterizations depend sensitively on the shear of the profile. The alternative profile comes at no added numerical cost compared to the monochromatic profile.
Robust Generalized Low Rank Approximations of Matrices
Shi, Jiarong; Yang, Wei; Zheng, Xiuyun
2015-01-01
In recent years, the intrinsic low rank structure of some datasets has been extensively exploited to reduce dimensionality, remove noise and complete the missing entries. As a well-known technique for dimensionality reduction and data compression, Generalized Low Rank Approximations of Matrices (GLRAM) claims its superiority on computation time and compression ratio over the SVD. However, GLRAM is very sensitive to sparse large noise or outliers and its robust version does not have been explored or solved yet. To address this problem, this paper proposes a robust method for GLRAM, named Robust GLRAM (RGLRAM). We first formulate RGLRAM as an l1-norm optimization problem which minimizes the l1-norm of the approximation errors. Secondly, we apply the technique of Augmented Lagrange Multipliers (ALM) to solve this l1-norm minimization problem and derive a corresponding iterative scheme. Then the weak convergence of the proposed algorithm is discussed under mild conditions. Next, we investigate a special case of RGLRAM and extend RGLRAM to a general tensor case. Finally, the extensive experiments on synthetic data show that it is possible for RGLRAM to exactly recover both the low rank and the sparse components while it may be difficult for previous state-of-the-art algorithms. We also discuss three issues on RGLRAM: the sensitivity to initialization, the generalization ability and the relationship between the running time and the size/number of matrices. Moreover, the experimental results on images of faces with large corruptions illustrate that RGLRAM obtains the best denoising and compression performance than other methods. PMID:26367116
Robust Generalized Low Rank Approximations of Matrices.
Shi, Jiarong; Yang, Wei; Zheng, Xiuyun
2015-01-01
In recent years, the intrinsic low rank structure of some datasets has been extensively exploited to reduce dimensionality, remove noise and complete the missing entries. As a well-known technique for dimensionality reduction and data compression, Generalized Low Rank Approximations of Matrices (GLRAM) claims its superiority on computation time and compression ratio over the SVD. However, GLRAM is very sensitive to sparse large noise or outliers and its robust version does not have been explored or solved yet. To address this problem, this paper proposes a robust method for GLRAM, named Robust GLRAM (RGLRAM). We first formulate RGLRAM as an l1-norm optimization problem which minimizes the l1-norm of the approximation errors. Secondly, we apply the technique of Augmented Lagrange Multipliers (ALM) to solve this l1-norm minimization problem and derive a corresponding iterative scheme. Then the weak convergence of the proposed algorithm is discussed under mild conditions. Next, we investigate a special case of RGLRAM and extend RGLRAM to a general tensor case. Finally, the extensive experiments on synthetic data show that it is possible for RGLRAM to exactly recover both the low rank and the sparse components while it may be difficult for previous state-of-the-art algorithms. We also discuss three issues on RGLRAM: the sensitivity to initialization, the generalization ability and the relationship between the running time and the size/number of matrices. Moreover, the experimental results on images of faces with large corruptions illustrate that RGLRAM obtains the best denoising and compression performance than other methods. PMID:26367116
Differential equation based method for accurate approximations in optimization
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.
1990-01-01
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.
Initiation and propagation of delamination in a centrally notched composite laminate
Jen, M.H.R.; Kau, Y.S.; Hsu, J.M. )
1993-01-01
A prediction model based on boundary layer theory is proposed to obtain interlaminar stress distributions and singularities at the free edge around the hole in a composite laminate. The Hashin-Rotem failure criterion is used to predict the loading and location at which initiation of delamination occurred. The model has been validated by a series of experiments for static tension and T-T fatigue tests. The test specimens include both the orthotropic and quasi-isotropic laminates. A circular hole was drilled in the center of each specimen. X-ray radiography was used to examine damage mode, location of the onset of delamination and propagation at each loading step. An approximately linear relationship is found between delamination area and stiffness reduction for the centrally notched quasi-isotropic laminates. The residual strength of the laminate first increases as applied cycles increased and then decreases during fatigue tests. Residual stiffness always decreases monotonically with the increase of applied cycles. 19 refs.
Sorin A. Lusceac; Markus Rosenstihl; Michael Vogel; Catalin Gainaru; Ariane Fillmer; Roland Böhmer
2010-04-23
Using a combination of dielectric spectroscopy and solid-state deuteron NMR, the hydration water dynamics of connective tissue proteins is studied at sub-ambient temperatures. In this range, the water dynamics follows an Arrhenius law. A scaling analysis of dielectric losses, 'two-phase' NMR spectra, and spin-lattice relaxation times consistently yield evidence for a Gaussian distribution of energy barriers. With the dielectric data as input, random-walk simulations of a large-angle, quasi-isotropic water reorientation provide an approximate description of stimulated-echo data on hydrated elastin. This secondary process takes place in an essentially rigid energy landscape, but in contrast to typical {\\beta}-relaxations it is quasi-isotropic and delocalized. The delocalization is inferred from previous NMR diffusometry experiments. To emphasize the distinction from conventional {\\beta}-processes, for aqueous systems such a matrix-decoupled relaxation was termed a {\
Approximate stoichiometry for rich hydrocarbon mixtures
Beans, E.W. )
1993-03-01
The stoichiometry of lean mixtures can readily and accurately be determined from the assumption that all the carbon oxidizes to carbon dioxide and all the hydrogen oxidizes to water. This assumption is valid up to an equivalence ratio ([sigma]) of 0.8 and can be used with little error up to [sigma] = 1. The composition of the products of a hydrocarbon burnt in air under the foregoing assumption can be obtained from simple carbon, hydrogen, oxygen and nitrogen balances. Given the composition, one can determine the energy released and/or the adiabatic flame temperature. For rich mixtures, the foregoing assumption, of course, is not valid. Hence, there is no easy way to determine the stoichiometry of the products of a rich mixture. The objective of this note is to present an equation' which will allow one to readily determine the composition of the products of rich hydrocarbon mixtures. The equation is based on equilibrium composition calculations and some assumptions regarding the characteristics of hydrocarbons. The equation gives approximate results. However, the results are sufficiently accurate for many situations. If more accuracy is wanted, one should use an equilibrium combustion program like the one by Gordon and McBride.
The time-dependent Gutzwiller approximation
NASA Astrophysics Data System (ADS)
Fabrizio, Michele
2015-03-01
The time-dependent Gutzwiller Approximation (t-GA) is shown to be capable of tracking the off-equilibrium evolution both of coherent quasiparticles and of incoherent Hubbard bands. The method is used to demonstrate that the sharp dynamical crossover observed by time-dependent DMFT in the quench-dynamics of a half-filled Hubbard model can be identified within the t-GA as a genuine dynamical transition separating two distinct physical phases. This result, strictly variational for lattices of infinite coordination number, is intriguing as it actually questions the occurrence of thermalization. Next, we shall present how t-GA works in a multi-band model for V2O3 that displays a first-order Mott transition. We shall show that a physically accessible excitation pathway is able to collapse the Mott gap down and drive off-equilibrium the insulator into a metastable metal phase. Work supported by the European Union, Seventh Framework Programme, under the project GO FAST, Grant Agreement No. 280555.
An approximate treatment of gravitational collapse
NASA Astrophysics Data System (ADS)
Ascasibar, Yago; Granero-Belinchón, Rafael; Moreno, José Manuel
2013-11-01
This work studies a simplified model of the gravitational instability of an initially homogeneous infinite medium, represented by Td, based on the approximation that the mean fluid velocity is always proportional to the local acceleration. It is shown that, mathematically, this assumption leads to the restricted Patlak-Keller-Segel model considered by Jäger and Luckhaus or, equivalently, the Smoluchowski equation describing the motion of self-gravitating Brownian particles, coupled to the modified Newtonian potential that is appropriate for an infinite mass distribution. We discuss some of the fundamental properties of a non-local generalization of this model where the effective pressure force is given by a fractional Laplacian with 0
Approximate algorithms for partitioning and assignment problems
NASA Technical Reports Server (NTRS)
Iqbal, M. A.
1986-01-01
The problem of optimally assigning the modules of a parallel/pipelined program over the processors of a multiple computer system under certain restrictions on the interconnection structure of the program as well as the multiple computer system was considered. For a variety of such programs it is possible to find linear time if a partition of the program exists in which the load on any processor is within a certain bound. This method, when combined with a binary search over a finite range, provides an approximate solution to the partitioning problem. The specific problems considered were: a chain structured parallel program over a chain-like computer system, multiple chain-like programs over a host-satellite system, and a tree structured parallel program over a host-satellite system. For a problem with m modules and n processors, the complexity of the algorithm is no worse than O(mnlog(W sub T/epsilon)), where W sub T is the cost of assigning all modules to one processor and epsilon the desired accuracy.
Grover's quantum search algorithm and Diophantine approximation
Dolev, Shahar; Pitowsky, Itamar; Tamir, Boaz
2006-02-15
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.
Configuring Airspace Sectors with Approximate Dynamic Programming
NASA Technical Reports Server (NTRS)
Bloem, Michael; Gupta, Pramod
2010-01-01
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.
Approximate theory for radial filtration/consolidation
Tiller, F.M.; Kirby, J.M.; Nguyen, H.L.
1996-10-01
Approximate solutions are developed for filtration and subsequent consolidation of compactible cakes on a cylindrical filter element. Darcy`s flow equation is coupled with equations for equilibrium stress under the conditions of plane strain and axial symmetry for radial flow inwards. The solutions are based on power function forms involving the relationships of the solidosity {epsilon}{sub s} (volume fraction of solids) and the permeability K to the solids effective stress p{sub s}. The solutions allow determination of the various parameters in the power functions and the ratio k{sub 0} of the lateral to radial effective stress (earth stress ratio). Measurements were made of liquid and effective pressures, flow rates, and cake thickness versus time. Experimental data are presented for a series of tests in a radial filtration cell with a central filter element. Slurries prepared from two materials (Microwate, which is mainly SrSO{sub 4}, and kaolin) were used in the experiments. Transient deposition of filter cakes was followed by static (i.e., no flow) conditions in the cake. The no-flow condition was accomplished by introducing bentonite which produced a nearly impermeable layer with negligible flow. Measurement of the pressure at the cake surface and the transmitted pressure on the central element permitted calculation of k{sub 0}.
Extended Thin Sheet Approximation, new iterative approach
NASA Astrophysics Data System (ADS)
Medvedev, S.; Podladchikov, Yu.
2003-04-01
Geodynamic problems are often characterized by localized zones of active deformation. The majority of the modelled lithospheric domain remains low-deformed. That uneven distribution of active deformation results in inefficient use of direct numerical methods, which spend most of the calculating time on the background, low deformed, areas. That hurts especially 3D calculations. There is a need in a simple and reliable approach to iterative process of numerical calculations of evolution of large geodynamic structures. The approaches that are recently in use (thin viscous sheets, elastic plates) suffer from low accuracy and/or inability to satisfy boundary conditions. We developed an Extended Thin Sheet Approximation (ETSA) to overcome these problems while keeping simplicity of numerical treatment of semi-analytical methods. The main target of this work is to present simple logics behind the ETSA and to illustrate its advantages. The new approach presents ETSA as an iterative process. Started with a very rough guess for stresses and velocities profiles, several stages of analytical iterations lead to solutions that describe accurately dynamics of the rheologically layered lithosphere. Examples illustrate simplicity of building analytical and numerical models based on the ETSA.
A simple, approximate model of parachute inflation
Macha, J.M.
1992-11-01
A simple, approximate model of parachute inflation is described. The model is based on the traditional, practical treatment of the fluid resistance of rigid bodies in nonsteady flow, with appropriate extensions to accommodate the change in canopy inflated shape. Correlations for the steady drag and steady radial force as functions of the inflated radius are required as input to the dynamic model. In a novel approach, the radial force is expressed in terms of easily obtainable drag and reefing fine tension measurements. A series of wind tunnel experiments provides the needed correlations. Coefficients associated with the added mass of fluid are evaluated by calibrating the model against an extensive and reliable set of flight data. A parameter is introduced which appears to universally govern the strong dependence of the axial added mass coefficient on motion history. Through comparisons with flight data, the model is shown to realistically predict inflation forces for ribbon and ringslot canopies over a wide range of sizes and deployment conditions.
A simple, approximate model of parachute inflation
Macha, J.M.
1992-01-01
A simple, approximate model of parachute inflation is described. The model is based on the traditional, practical treatment of the fluid resistance of rigid bodies in nonsteady flow, with appropriate extensions to accommodate the change in canopy inflated shape. Correlations for the steady drag and steady radial force as functions of the inflated radius are required as input to the dynamic model. In a novel approach, the radial force is expressed in terms of easily obtainable drag and reefing fine tension measurements. A series of wind tunnel experiments provides the needed correlations. Coefficients associated with the added mass of fluid are evaluated by calibrating the model against an extensive and reliable set of flight data. A parameter is introduced which appears to universally govern the strong dependence of the axial added mass coefficient on motion history. Through comparisons with flight data, the model is shown to realistically predict inflation forces for ribbon and ringslot canopies over a wide range of sizes and deployment conditions.
Magnetic reconnection under anisotropic magnetohydrodynamic approximation
Hirabayashi, K.; Hoshino, M.
2013-11-15
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.
Adaptive approximation of higher order posterior statistics
Lee, Wonjung
2014-02-01
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively.
Approximate forms of daytime ionospheric conductance
NASA Astrophysics Data System (ADS)
Ieda, A.; Oyama, S.; Vanhamäki, H.; Fujii, R.; Nakamizo, A.; Amm, O.; Hori, T.; Takeda, M.; Ueno, G.; Yoshikawa, A.; Redmon, R. J.; Denig, W. F.; Kamide, Y.; Nishitani, N.
2014-12-01
The solar zenith angle (SZA) dependence of the conductance is studied and a simple theoretical form for the Hall-to-Pedersen conductance ratio is developed, using the peak plasma production height. The European Incoherent Scatter (EISCAT) radar observations at Tromsø (67 MLAT) on 30 March 2012 were used to calculate the conductance. The daytime electric conductance is associated with plasma created by solar extreme ultraviolet radiation incident on the neutral atmosphere of the Earth. However, it has been uncertain whether previous conductance models are consistent with the ideal Chapman theory for such plasma productions. We found that the SZA dependence of the conductance is consistent with the Chapman theory after simple modifications. The Pedersen conductance can be understood by approximating the plasma density height profile as being flat in the topside E region and by taking into account the upward gradient of atmospheric temperature. An additional consideration is necessary for the Hall conductance, which decreases with increasing SZA more rapidly than the Pedersen conductance. This rapid decrease is presumably caused by a thinning of the Hall conductivity layer from noon toward nighttime. We expressed this thinning in terms of the peak production height in the Chapman theory.
Structural physical approximations and entanglement witnesses
Bang-Hai Wang; Dong-Yang Long
2013-07-21
The structural physical approximation (SPA) to a positive map is considered to be one of the most important method to detect entanglement in the real physical world. We first show that an arbitrary entanglement witness (EW) $W$ can be constructed from a separable density matrix $\\sigma$ in the form of $W=\\sigma-c_{\\sigma} I$, where $c_{\\sigma}$ is a non-negative number and $I$ is the identity matrix. Following the general form of EWs from separable states, we show a sufficient condition and a sufficient and necessary condition in low dimensions of that SPAs to positive maps do not define entanglement-breaking channels. We show that either the SPA of an EW or the SPA of the partial transposition of the EW in low dimensions is an entanglement-breaking channel. We give sufficient conditions of violating the SPA conjecture [\\emph{Phys. Rev. A}{\\bf 78,} 062105 (2008)]. Our results indicate that the SPA conjecture is independent of whether or not positive maps are optimal.
Coulomb glass in the random phase approximation
NASA Astrophysics Data System (ADS)
Basylko, S. A.; Onischouk, V. A.; Rosengren, A.
2002-01-01
A three-dimensional model of the electrons localized on randomly distributed donor sites of density n and with the acceptor charge uniformly smeared on these sites, -Ke on each, is considered in the random phase approximation (RPA). For the case K=1/2 the free energy, the density of the one-site energies (DOSE) ?, and the pair OSE correlators are found. In the high-temperature region (e2n1/3/T)<1 (T is the temperature) RPA energies and DOSE are in a good agreement with the corresponding data of Monte Carlo simulations. Thermodynamics of the model in this region is similar to the one of an electrolyte in the regime of Debye screening. In the vicinity of the Fermi level ?=0 the OSE correlations, depending on sgn(?1.?2) and with very slow decoupling law, have been found. The main result is that even in the temperature range where the energy of a Coulomb glass is determined by Debye screening effects, the correlations of the long-range nature between the OSE still exist.
Precision variational approximations in statistical data assimilation
NASA Astrophysics Data System (ADS)
Ye, J.; Kadakia, N.; Rozdeba, P. J.; Abarbanel, H. D. I.; Quinn, J. C.
2014-10-01
Data assimilation transfers information from observations of a complex system to physically-based system models with state variables x(t). Typically, the observations are noisy, the model has errors, and the initial state of the model is uncertain, so the data assimilation is statistical. One can thus ask questions about expected values of functions ?G(X)? on the path X = {x(t0), ..., x(tm)} of the model as it moves through an observation window where measurements are made at times {t0, ..., tm}. The probability distribution on the path P(X) = exp[-A0(X)] determines these expected values. Variational methods seeking extrema of the "action" A0(X), widely known as 4DVar (Talagrand and Courtier, 1987; Evensen, 2009),, are widespread for estimating ?G(X) ? in many fields of science. In a path integral formulation of statistical data assimilation, we consider variational approximations in a standard realization of the action where measurement and model errors are Gaussian. We (a) discuss an annealing method for locating the path X0 giving a consistent global minimum of the action A0(X0), (b) consider the explicit role of the number of measurements at each measurement time in determining A0(X0), and (c) identify a parameter regime for the scale of model errors which allows X0 to give a precise estimate of ?G(X0)? with computable, small higher order corrections.
Rainbows: Mie computations and the Airy approximation.
Wang, R T; van de Hulst, H C
1991-01-01
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
An asymptotic homogenized neutron diffusion approximation. II. Numerical comparisons
Trahan, T. J.; Larsen, E. W. [Dept. of Nuclear Engineering and Radiological Sciences, Univ. of Michigan, 2355 Bonisteel Blvd., Ann Arbor, MI 48109 (United States)
2012-07-01
In a companion paper, a monoenergetic, homogenized, anisotropic diffusion equation is derived asymptotically for large, 3-D, multiplying systems with a periodic lattice structure [1]. In the present paper, this approximation is briefly compared to several other well known diffusion approximations. Although the derivation is different, the asymptotic diffusion approximation matches that proposed by Deniz and Gelbard, and is closely related to those proposed by Benoist. The focus of this paper, however, is a numerical comparison of the various methods for simple reactor analysis problems in 1-D. The comparisons show that the asymptotic diffusion approximation provides a more accurate estimate of the eigenvalue than the Benoist diffusion approximations. However, the Benoist diffusion approximations and the asymptotic diffusion approximation provide very similar estimates of the neutron flux. The asymptotic method and the Benoist methods both outperform the standard homogenized diffusion approximation, with flux weighted cross sections. (authors)
Policy Gradient vs. Value Function Approximation: A Reinforcement Learning Shootout
McGovern, Amy
review by the International Con- ference on Machine Learning (ICML). Do not distribute. Figure 1Policy Gradient vs. Value Function Approximation: A Reinforcement Learning Shootout Technical Approximation: A Reinforcement Learning Shootout Reinforcement Learning, Sarsa(), Policy Gradient, Agent
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1982-01-01
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.
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1984-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589
Faster streaming algorithms for low-rank matrix approximations
Galvin, Timothy Matthew
2014-01-01
Low-rank matrix approximations are used in a significant number of applications. We present new algorithms for generating such approximations in a streaming fashion that expand upon recently discovered matrix sketching ...
approximation of scalar waves in the space—frequency domain
tigate numerical (?nite element) methods for approximating the solution of this ... a ?nite element approximation of a family of Helmholz—like elliptic problems, with ... equation leads to a better regularity result than for the general case. In Sec
Approximations for the rotational excitation of molecules by atoms
Chu, Shih-I; Dalgarno, A.
1975-01-01
The applicability of the effective close?coupling approximation of Rabitz and the centrifugal decoupling approximation of McGuire and Kouri is examined for a system which models the rotational excitation of molecular nitrogen in collisions...
Approximate similarity relations for general control Markov processes
Van den Hof, Paul
Approximate similarity relations for general control Markov processes: characterisation via lifting Abstract. In this work we propose new approximate similarity relations for general control Markov processes output spaces. We show that the new probabilistic similarity relations, inspired by Segala's notion
Orthogonal Polynomial Approximation in Higher Dimensions: Applications in Astrodynamics
Bani Younes, Ahmad H.
2013-08-05
the approximations are differentiated or integrated. Two sets of applications are considered that are challenges in astrodynamics. The first application addresses local approximation of high degree and order geopotential models, replacing the global spherical...
APPROXIMATION IN THE CONE OF POSITIVE HARMONIC FUNCTIONS
Sjödin, Tomas
1 APPROXIMATION IN THE CONE OF POSITIVE HARMONIC FUNCTIONS TOMAS SJ¨ODIN Abstract. In the course and phrases. positive harmonic function, approximation, Martin boundary. 1 #12;2 TOMAS SJ ¨ODIN in the closure
Particle versus Gaussian Approximations: What is the difference?
Crisan, Dan
. . . . . . . ...... Particle versus Gaussian Approximations: What is the difference? Dan Crisan Assimilation Oberwolfach 2-8 December, 2012 Dan Crisan (Imperial College London) Particle versus Gaussian/continuous time What constitutes an approximation ? Quantized information = particles From Gaussian to particle
Piecewise Constant Policy Approximations to Hamilton-Jacobi-Bellman Equations
Forsyth, Peter A.
Piecewise Constant Policy Approximations to Hamilton-Jacobi-Bellman Equations C. Reisinger and P for Hamilton-Jacobi- Bellman (HJB) equations is that different linear approximation schemes, and indeed
Three fast computational approximation methods in hypersonic aerothermodynamics
Riabov, Vladimir V.
Three fast computational approximation methods in hypersonic aerothermodynamics V.V. Riabov* Rivier analyzed to study nonequilibrium hypersonic viscous flows near blunt bodies. These approximations allow; Nonequilibrium hypersonic flows 1. Introduction Numerous methods [1,2] that require significant computational
Non-Parametric Approximate Dynamic Programming via the Kernel Method
Bhat, Nikhil
This paper presents a novel non-parametric approximate dynamic programming (ADP) algorithm that enjoys graceful approximation and sample complexity guarantees. In particular, we establish both theoretically and computationally ...
Approximating Probability Density Functions with Mixtures of Truncated Exponentials
Cobb, Barry R.; Shenoy, Prakash P.; Rumi, Rafael
2004-07-01
Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for approximating probability density functions (PDF’s). This paper presents MTE potentials that approximate standard PDF’s and applications of these potentials...
Pawlak Algebra and Approximate Structure on Fuzzy Lattice
Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai
2014-01-01
The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties. PMID:25152922
Signal detection using approximate Karhunen-Loève expansions
Juan Carlos Ruiz-molina; Jesús Navarro-moreno; Antonia Oya
2001-01-01
A new approach to the signal detection problem in continuous time is presented on the basis of approximate Karhunen-Loeve (K-L) expansions. This methodology gives approximate solutions to the problem of detecting either deterministic or Gaussian signals in Gaussian noise. Furthermore, for this last problem an approximate estimator-correlator representation is provided which approaches the optimum detection statistic
Constructing analytic approximate solutions to the Lane-Emden equation
NASA Astrophysics Data System (ADS)
Iacono, R.; De Felice, M.
2015-09-01
We derive analytic approximations to the solutions of the Lane-Emden equation, a basic equation in Astrophysics that describes the Newtonian equilibrium structure of a self-gravitating polytropic fluid sphere. After recalling some basic results, we focus on the construction of rational approximations, discussing the limitations of previous attempts, and providing new accurate approximate solutions.
Accurate Approximations for Posterior Moments and Marginal Densities
Luke Tierney; Joseph B. Kadane
1986-01-01
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
Gaussian Variational Approximate Inference for Generalized Linear Mixed Models
Sydney, University of
generalized linear mixed models (GLMM) appro- priate for grouped data. It involves Gaussian approximationGaussian Variational Approximate Inference for Generalized Linear Mixed Models BY J.T. ORMEROD approximation in this context. Key Words: Best prediction; Longitudinal data analysis; Likelihood
Post-Selection Inference for Models that are Approximations
Buja, Andreas
Post-Selection Inference for Models that are Approximations (Work in Progress) Andreas Buja joint by later studies. Andreas Buja (Wharton, UPenn) Post-Selection Inference for Models that are Approximations" Andreas Buja (Wharton, UPenn) Post-Selection Inference for Models that are Approximations (Work
A constructive neural network algorithm for function approximation
Tim Draelos; Don Hush
1996-01-01
A study of the approximation capabilities of single hidden layer neural networks leads to a strong motivation for investigating constructive learning techniques as a means of realizing established error bounds. Learning characteristics employed by constructive algorithms provide ideas for development of new algorithms applicable to the function approximation problem. A novel constructive algorithm, the iterative incremental function approximation (IIFA) algorithm
An Equivalence Between Sparse Approximation and Support Vector Machines 1
Poggio, Tomaso
An Equivalence Between Sparse Approximation and Support Vector Machines 1 Federico Girosi Center approximation techniques: the Support Vector Machines (SVM), proposed by V. Vapnik (1995), and a sparse ap an approximation technique based on the principle of sparsity and the Support Vector Machines (SVM) technique
BADLY APPROXIMABLE VECTORS ON FRACTALS DMITRY KLEINBOCK AND BARAK WEISS
Weiss, Barak
BADLY APPROXIMABLE VECTORS ON FRACTALS DMITRY KLEINBOCK AND BARAK WEISS Revised version, July 2004 of badly approximable vec- tors has the same Hausdorff dimension as C. The sets are described in terms. 1. Introduction We say that x Rn is badly approximable if there is c > 0 such that for any p Zn
Accepted Manuscript A rounding algorithm for approximating minimum Manhattan
Chepoi, Victor
Accepted Manuscript A rounding algorithm for approximating minimum Manhattan networks Victor Chepoi algorithm for approximating minimum Manhattan networks, Theoretical Computer Science (2007), doi:10.1016/j MANUSCRIPT A rounding algorithm for approximating minimum Manhattan networks1 Victor Chepoi, Karim Nouioua
Improved first order approximation method for structural optimization
NASA Technical Reports Server (NTRS)
Fadel, Georges M.; Riley, Michael F.; Barthelemy, Jean-Francois M.
1990-01-01
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.
Two point exponential approximation method for structural optimization
NASA Technical Reports Server (NTRS)
Fadel, G. M.; Riley, M. F.; Barthelemy, J. M.
1990-01-01
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.
Approximating Q-values with Basis Function Representations Philip Sabes
Sabes, Philip
Approximating Q-values with Basis Function Representations Philip Sabes Department of Brain@psyche.mit.edu The consequences of approximating Q-Values with function approximators are investigated. Two criteria of optimality. Q-Learning requires the storage of a Q- Value for every state-action pair, a daunting
Cophylogeny Reconstruction via an Approximate Bayesian Computation
Baudet, C.; Donati, B.; Sinaimeri, B.; Crescenzi, P.; Gautier, C.; Matias, C.; Sagot, M.-F.
2015-01-01
Despite an increasingly vast literature on cophylogenetic reconstructions for studying host–parasite associations, understanding the common evolutionary history of such systems remains a problem that is far from being solved. Most algorithms for host–parasite reconciliation use an event-based model, where the events include in general (a subset of) cospeciation, duplication, loss, and host switch. All known parsimonious event-based methods then assign a cost to each type of event in order to find a reconstruction of minimum cost. The main problem with this approach is that the cost of the events strongly influences the reconciliation obtained. Some earlier approaches attempt to avoid this problem by finding a Pareto set of solutions and hence by considering event costs under some minimization constraints. To deal with this problem, we developed an algorithm, called Coala, for estimating the frequency of the events based on an approximate Bayesian computation approach. The benefits of this method are 2-fold: (i) it provides more confidence in the set of costs to be used in a reconciliation, and (ii) it allows estimation of the frequency of the events in cases where the data set consists of trees with a large number of taxa. We evaluate our method on simulated and on biological data sets. We show that in both cases, for the same pair of host and parasite trees, different sets of frequencies for the events lead to equally probable solutions. Moreover, often these solutions differ greatly in terms of the number of inferred events. It appears crucial to take this into account before attempting any further biological interpretation of such reconciliations. More generally, we also show that the set of frequencies can vary widely depending on the input host and parasite trees. Indiscriminately applying a standard vector of costs may thus not be a good strategy. PMID:25540454
Cophylogeny reconstruction via an approximate Bayesian computation.
Baudet, C; Donati, B; Sinaimeri, B; Crescenzi, P; Gautier, C; Matias, C; Sagot, M-F
2015-05-01
Despite an increasingly vast literature on cophylogenetic reconstructions for studying host-parasite associations, understanding the common evolutionary history of such systems remains a problem that is far from being solved. Most algorithms for host-parasite reconciliation use an event-based model, where the events include in general (a subset of) cospeciation, duplication, loss, and host switch. All known parsimonious event-based methods then assign a cost to each type of event in order to find a reconstruction of minimum cost. The main problem with this approach is that the cost of the events strongly influences the reconciliation obtained. Some earlier approaches attempt to avoid this problem by finding a Pareto set of solutions and hence by considering event costs under some minimization constraints. To deal with this problem, we developed an algorithm, called Coala, for estimating the frequency of the events based on an approximate Bayesian computation approach. The benefits of this method are 2-fold: (i) it provides more confidence in the set of costs to be used in a reconciliation, and (ii) it allows estimation of the frequency of the events in cases where the data set consists of trees with a large number of taxa. We evaluate our method on simulated and on biological data sets. We show that in both cases, for the same pair of host and parasite trees, different sets of frequencies for the events lead to equally probable solutions. Moreover, often these solutions differ greatly in terms of the number of inferred events. It appears crucial to take this into account before attempting any further biological interpretation of such reconciliations. More generally, we also show that the set of frequencies can vary widely depending on the input host and parasite trees. Indiscriminately applying a standard vector of costs may thus not be a good strategy. PMID:25540454
Finite element approximation of field dislocation mechanics
NASA Astrophysics Data System (ADS)
Roy, Anish; Acharya, Amit
2005-01-01
A tool for studying links between continuum plasticity and dislocation theory within a field framework is presented. A finite element implementation of the geometrically linear version of a recently proposed theory of field dislocation mechanics (J. Mech. Phys. Solids 49 (2001) 761; Proc. Roy. Soc. 459 (2003) 1343; J. Mech. Phys. Solids 52 (2004) 301) represents the main idea behind the tool. The constitutive ingredients of the theory under consideration are simply elasticity and a specification of dislocation velocity and nucleation. The set of equations to be approximated are non-standard in the context of solid mechanics applications. It comprises the standard second-order equilibrium equations, a first-order div-curl system for the elastic incompatibility, and a first-order, wave-propagative system for the evolution of dislocation density. The latter two sets of equations require special treatment as the standard Galerkin method is not adequate, and are solved utilizing a least-squares finite element strategy. The implementation is validated against analytical results of the classical elastic theory of dislocations and analytical results of the theory itself. Elastic stress fields of dislocation distributions in generally anisotropic media of finite extent, deviation from elastic response, yield-drop, and back-stress are shown to be natural consequences of the model. The development of inhomogeneity, from homogeneous initial conditions and boundary conditions corresponding to homogeneous deformation in conventional plasticity, is also demonstrated. To our knowledge, this work represents the first computational implementation of a theory of dislocation mechanics where no analytical results, singular solutions in particular, are required to formulate the implementation. In particular, a part of the work is the first finite element implementation of Kröner's linear elastic theory of continuously distributed dislocations in its full generality.
Visual nesting impacts approximate number system estimation.
Chesney, Dana L; Gelman, Rochel
2012-08-01
The approximate number system (ANS) allows people to quickly but inaccurately enumerate large sets without counting. One popular account of the ANS is known as the accumulator model. This model posits that the ANS acts analogously to a graduated cylinder to which one "cup" is added for each item in the set, with set numerosity read from the "height" of the cylinder. Under this model, one would predict that if all the to-be-enumerated items were not collected into the accumulator, either the sets would be underestimated, or the misses would need to be corrected by a subsequent process, leading to longer reaction times. In this experiment, we tested whether such miss effects occur. Fifty participants judged numerosities of briefly presented sets of circles. In some conditions, circles were arranged such that some were inside others. This circle nesting was expected to increase the miss rate, since previous research had indicated that items in nested configurations cannot be preattentively individuated in parallel. Logically, items in a set that cannot be simultaneously individuated cannot be simultaneously added to an accumulator. Participants' response times were longer and their estimations were lower for sets whose configurations yielded greater levels of nesting. The level of nesting in a display influenced estimation independently of the total number of items present. This indicates that miss effects, predicted by the accumulator model, are indeed seen in ANS estimation. We speculate that ANS biases might, in turn, influence cognition and behavior, perhaps by influencing which kinds of sets are spontaneously counted. PMID:22810562
Collisionless magnetic reconnection under anisotropic MHD approximation
NASA Astrophysics Data System (ADS)
Hirabayashi, Kota; Hoshino, Masahiro
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless magneto-hydro-dynamic (MHD) simulations based on the double adiabatic approximation, which is an important step to bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observation. According to our results, a pair of slow shocks does form in the reconnection layer. The resultant shock waves, however, are quite weak compared with those in an isotropic MHD from the point of view of the plasma compression and the amount of the magnetic energy released across the shock. Once the slow shock forms, the downstream plasma are heated in highly anisotropic manner and a firehose-sense (P_{||}>P_{?}) pressure anisotropy arises. The maximum anisotropy is limited by the marginal firehose criterion, 1-(P_{||}-P_{?})/B(2) =0. In spite of the weakness of the shocks, the resultant reconnection rate is kept at the same level compared with that in the corresponding ordinary MHD simulations. It is also revealed that the sequential order of propagation of the slow shock and the rotational discontinuity, which appears when the guide field component exists, changes depending on the magnitude of the guide field. Especially, when no guide field exists, the rotational discontinuity degenerates with the contact discontinuity remaining at the position of the initial current sheet, while with the slow shock in the isotropic MHD. Our result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere.
NASA Astrophysics Data System (ADS)
Lanzerotti, L. J.; Maclennan, C. G.; Gold, R. E.; Armstrong, T. P.; Roelof, E. C.; Krimigis, S. M.; Simnett, G. M.; Sarris, E. T.; Anderson, K. A.; Pick, M.
1995-02-01
We report measurements of the oxygen component (0.5 - 22 MeV/nucl) of the interplanetary cosmic ray flux as a function of heliolatitude. The measurements reported here were made with the Wart telescope of the Heliosphere Instrument for Spectra, Composition, and Anisotropy at Low Energies (HI-SCALE) low energy particle instrument on the Ulysses spacecraft as the spacecraft climbed from approximately 24 deg to approximately 64 deg south solar heliolatitude during 1993 and early 1994. As a function of heliolatitude, the O abundance at 2-2.8 MeV/nucl drops sharply at latitudes above the heliospheric current sheet. The oxygen spectrum obtained above the current sheet has a broad peak centered at an energy of approximately 2.5 MeV/nucl that is the anomalous O component at these latitudes. There is little evidence for a latitude dependence in the anomalous O fluxes as measured above the current sheet. Within the heliospheric current sheet, the O measurements are composed of both solar and anomalous origin particles.
Systematic corrections to the Born-Oppenheimer approximation
NASA Astrophysics Data System (ADS)
Wilder, J. A.; Gerogian, T.; Findley, G. L.
1987-06-01
A method for providing systematic diabatic corrections to the Born-Oppenheimer approximation is presented. We begin with an adiabatic expansion of the exact vibronic wavefunctions and, via the molecular Hamiltonian, develop expressions for the diabatic terms in the Schrödinger equation. We then derive recursion relations which allow one to introduce the diabatic interactions to any desired degree of approximation. As an example, the first approximation (beyond the Born-Oppenheimer approximation) is discussed explicitly. In passing, we assess some of the common misconceptions associated with the Born-Oppenheimer approximation.
Approximate nearest neighbors via dictionary learning
NASA Astrophysics Data System (ADS)
Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos
2011-06-01
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.
An analogue of Fabry's theorem for generalized Padé approximants
NASA Astrophysics Data System (ADS)
Buslaev, Viktor I.
2009-08-01
The current theory of Padé approximation emphasises results of an inverse character, when conclusions about the properties of the approximated function are drawn from information about the behaviour of the approximants. In this paper Gonchar's conjecture is proved; it states that analogues of Fabry's classical `ratio' theorem hold for rows of the table of Padé approximants for orthogonal expansions, multipoint Padé approximants and Padé-Faber approximants. These are the most natural generalizations of the construction of classical Padé approximants. For these Gonchar's conjecture has already been proved by Suetin. The proof presented here is based, on the one hand, on Suetin's result and, on the other hand, on an extension of Poincaré's theorem on recurrence relations with coefficients constant in the limit, which is obtained in the paper. Bibliography: 19 titles.
Complex angular momentum approximation to hard-core scattering
NASA Technical Reports Server (NTRS)
Nussenzveig, H. M.; Wiscombe, W. J.
1991-01-01
The complex angular momentum (CAM) approximation for nonrelativistic quantum scattering by a hard sphere - a union of the recently developed CAM uniform approximation with a semiclassical WKB-like approximation valid at large angles - is shown to be remarkably accurate over the complete range of scattering angles and down to size parameters (circumference to de Broglie wavelength ratios) of order unity. The best approximations previously derivable (Fock-type) cannot reach large scattering angles where semiclassical approximations are useful; even at angles where Fock-type approximations are valid, they are typically two or more orders of magnitude less accurate than CAM. The crucial new feature responsible for the high accuracy of the CAM approximation is the treatment of large-angle diffraction associated with (1) tunneling near the edge of the scatterer, and (2) anomalous reflection.
A novel for prediction and approximation of functions (self approximation method)
M. Abolghasemi; F Didehvar; E Safayieh; N. Hashemi
2009-07-27
Throughout this article the major idea and conclusion is about comparing this method with some very famous methods like fourier series and wavelet, to show that the power of this approximation method is as much as to predicate many natural and finance methods, something which we can not say the same for wavelets and Fourier series, since this method consider the function itself to make the base functions, and it is more natural rather than wavelets method and fourier series, which they consider some prior functions as basis.
NASA Astrophysics Data System (ADS)
Peng, Degao; Yang, Yang; Zhang, Peng; Yang, Weitao
2014-12-01
In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N4). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as < hat{S}2rangle are also developed and tested.
A lattice-theoretic approach to multigranulation approximation space.
He, Xiaoli; She, Yanhong
2014-01-01
In this paper, we mainly investigate the equivalence between multigranulation approximation space and single-granulation approximation space from the lattice-theoretic viewpoint. It is proved that multigranulation approximation space is equivalent to single-granulation approximation space if and only if the pair of multigranulation rough approximation operators [Formula in text] forms an order-preserving Galois connection, if and only if the collection of lower (resp., upper) definable sets forms an (resp., union) intersection structure, if and only if the collection of multigranulation upper (lower) definable sets forms a distributive lattice when n = 2, and if and only if [Formula in text]. The obtained results help us gain more insights into the mathematical structure of multigranulation approximation spaces. PMID:25243226
The gravimetric boundary value problem in spheroidal approximation
NASA Astrophysics Data System (ADS)
Panou, Georgios
2015-04-01
In this presentation the linear gravimetric boundary value problem is discussed in spheroidal approximation. The input to the problem is gravity disturbances, using the known Earth's topography as boundary and corresponds to an oblique derivative problem. From the physical viewpoint, it has many advantages and can serve as the basis in establishing a world vertical datum. Adopting the spheroidal approximation in this boundary value problem, an integral equation results which can be solved analytically using successive approximations. However, the mathematical model becomes simpler and can be solved more easily by applying certain permissible approximations: neglecting the Earth's topography, a spheroidal normal derivative (Neumann) problem is obtained. Under the spherical approximation, the result is a normal derivative problem plus suitable corrections. In this case, neglecting the Earth's topography, the solution corresponds to the well-known spherical Hotine integral. Finally, the relative errors in the above approximations and derivations are quantitatively estimated.
Multijet final states: exact results and the leading pole approximation
Ellis, R.K.; Owens, J.F.
1984-09-01
Exact results for the process gg ..-->.. ggg are compared with those obtained using the leading pole approximation. Regions of phase space where the approximation breaks down are discussed. A specific example relevant for background estimates to W boson production is presented. It is concluded that in this instance the leading pole approximation may underestimate the standard QCD background by more than a factor of two in certain kinematic regions of physical interest.
Structural approximations to positive maps and entanglement-breaking channels
NASA Astrophysics Data System (ADS)
Korbicz, J. K.; Almeida, M. L.; Bae, J.; Lewenstein, M.; Acín, A.
2008-12-01
Structural approximations to positive, but not completely positive maps are approximate physical realizations of these nonphysical maps. They find applications in the design of direct entanglement-detection methods. We show that many of these approximations, in the relevant case of optimal positive maps, define an entanglement breaking channel and, consequently, can be implemented via a measurement and state-preparation protocol. We also show how our findings can be useful for the design of better and simpler direct entanglement detection methods.
Online and Offline Approximation Algorithms for Vector Covering Problems
Epstein, Leah
OnÂline and OffÂline Approximation Algorithms for Vector Covering Problems Noga Alon \\Lambda Yossi interested in its onÂline and offÂline approximability. For the onÂline version, we construct approximation a statement of Csirik and Frenk (1990) in [5] where it is claimed that for d â?? 2, no onÂline algorithm can
Continued fraction approximation for the nuclear matter response function
Margueron, J.; Giai, Nguyen Van; Schuck, P.; Navarro, J.
2008-06-15
A continued fraction approximation is used to calculate the Random Phase Approximation (RPA) response function of nuclear matter. The convergence of the approximation is assessed by comparing it with the numerically exact response function obtained with a typical effective finite-range interaction used in nuclear physics. It is shown that just the first order term of the expansion can give reliable results at densities up to the saturation density value.
Approximation Algorithms for the Largest Common Subtree Problem
Motwani, Rajeev
trees, it is possible to achieve an approximation ratio of O(n(log log n)= log 2 n). For unbounded degree trees, we give an algorithm with approximation ratio O(n(log log n) 2 = log 2 n) when the trees are unlabeled. An approximation ratio of O(n(log log n) 2 = log 2 n) is also achieved for the case of labeled
Sensitivity analysis and approximation methods for general eigenvalue problems
NASA Technical Reports Server (NTRS)
Murthy, D. V.; Haftka, R. T.
1986-01-01
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.
Differential equation based method for accurate approximations in optimization
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.
1990-01-01
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.
Properties of the Boltzmann equation in the classical approximation
NASA Astrophysics Data System (ADS)
Epelbaum, Thomas; Gelis, François; Tanji, Naoto; Wu, Bin
2014-12-01
We study the Boltzmann equation with elastic pointlike scalar interactions in two different versions of the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the nonrenormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one also has access to the nonapproximated result for comparison.
Monotonically improving approximate answers to relational algebra queries
NASA Technical Reports Server (NTRS)
Smith, Kenneth P.; Liu, J. W. S.
1989-01-01
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.
13. BUILDING #5, HOSPITAL, RENDERING OF EAST ELEVATION, APPROXIMATELY 1946 ...
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
Diffusion approximation of stochastic master equations with jumps
Pellegrini, C.; Petruccione, F. [School of Physics, National Institute for Theoretical Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa)
2009-12-15
In the presence of quantum measurements with direct photon detection, the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, diffusion models can be obtained from these equations as an approximation. A condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using techniques for Markov processes, which are based on the convergence of Markov generators and martingale problems. This result is illustrated by rigorously obtaining the diffusion approximation for homodyne and heterodyne detection.
Finding Approximate Competitive Equilibria: Efficient and Fair Course Allocation
Finding Approximate Competitive Equilibria: Efficient and Fair Course Allocation Abraham Othman Competitive Equilibria: Efficient and Fair Course Allocation, Abraham Othman, Eric Budish, and Tuomas Sandholm
Multilayer perceptrons: approximation order and necessary number of hidden units.
Trenn, Stephan
2008-05-01
This paper considers the approximation of sufficiently smooth multivariable functions with a multilayer perceptron (MLP). For a given approximation order, explicit formulas for the necessary number of hidden units and its distributions to the hidden layers of the MLP are derived. These formulas depend only on the number of input variables and on the desired approximation order. The concept of approximation order encompasses Kolmogorov-Gabor polynomials or discrete Volterra series, which are widely used in static and dynamic models of nonlinear systems. The results are obtained by considering structural properties of the Taylor polynomials of the function in question and of the MLP function. PMID:18467212
Approximation functions for airblast environments from buried charges
Reichenbach, H.; Behrens, K.; Kuhl, A.L.
1993-11-01
In EMI report E 1/93, ``Airblast Environments from Buried HE-Charges,`` fit functions were used for the compact description of blastwave parameters. The coefficients of these functions were approximated by means of second order polynomials versus DOB. In most cases, the agreement with the measured data was satisfactory; to reduce remaining noticeable deviations, an approximation by polygons (i.e., piecewise-linear approximation) was used instead of polynomials. The present report describes the results of the polygon approximation and compares them to previous data. We conclude that the polygon representation leads to a better agreement with the measured data.
How to Solve Schroedinger Problems by Approximating the Potential Function
Ledoux, Veerle; Van Daele, Marnix
2010-09-30
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.
Approximating the physical inner product of Loop Quantum Cosmology
Benjamin Bahr; Thomas Thiemann
2006-07-19
In this article, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: Firstly, we compute it analytically via a trick, secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We will find that the approximation is able to recover the analytic solution of the problem, which solidifies hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity.
Legendre-tau approximations for functional differential equations
NASA Technical Reports Server (NTRS)
Ito, K.; Teglas, R.
1986-01-01
The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.
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
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}
On Exponential Approximation to the Hockey Stick Ken Jackson
Toronto, University of
On Exponential Approximation to the Hockey Stick Function Ian Iscoe Ken Jackson Alex Kreinin§ Xiaofang Ma¶ January 24, 2007 Abstract The hockey stick function is a basic function in pricing and risk management of many financial derivatives. This paper considers approximating the hockey stick function
An Exponential Approximation to the Hockey Stick Function
Toronto, University of
An Exponential Approximation to the Hockey Stick Function Ian Iscoe Ken Jackson Alex Kreinin§ Xiaofang Ma¶ March 19, 2010 Abstract The hockey stick (HS) function plays an important role in pricing and Monz´on is used to determine the parameters of the exponential approximation to the hockey stick
APPROXIMATE ROOTS OF A VALUATION AND THE PIERCEBIRKHOFF CONJECTURE
APPROXIMATE ROOTS OF A VALUATION AND THE PIERCEBIRKHOFF CONJECTURE F. Lucas D´epartement de Math. Abstract In this paper, we construct an object, called a system of approximate roots of a valuation, centered in a regular local ring, which describes the fine structure of the valuation (namely, its
The Role of Intuitive Approximation Skills for School Math Abilities
ERIC Educational Resources Information Center
Libertus, Melissa E.
2015-01-01
Research has shown that educated children and adults have access to two ways of representing numerical information: an approximate number system (ANS) that is present from birth and allows for quick approximations of numbers of objects encountered in one's environment, and an exact number system (ENS) that is acquired through experience and…
Anisotropic common ray approximation of the coupling ray theory
Cerveny, Vlastislav
rays calculated in the anisotropic model. The errors due to the anisotropic common ray approximation of equal S{wave eigenvalues of the Christo#11;el matrix. In \\weakly anisotropic" models, at moderateAnisotropic common ray approximation of the coupling ray theory Petr Bulant & Lud#20;ek Klime#20;s
Approximate Majorization and Fair Online Load Balancing Ashish Goel
Goel, Ashish
: Approximate Fairness in Scheduling. 1 Introduction Fair Resource Allocation The problems of online allocationApproximate Majorization and Fair Online Load Balancing Ashish Goel Adam Meyerson Serge Plotkin § Abstract This paper relates the notion of fairness in online routing and load balancing to vector
Approximation Algorithms for Disjoint Paths Problems Jon Michael Kleinberg
Kleinberg, Jon
a number of related algorithms by this approach, including a routing algorithm for the mesh that is optimalApproximation Algorithms for Disjoint Paths Problems by Jon Michael Kleinberg S.M., Electrical Students #12; 2 #12; Approximation Algorithms for Disjoint Paths Problems by Jon Michael Kleinberg
The orthogonal approximation of an oblique structure in factor analysis
Bert F. Green
1952-01-01
A procedure is derived for obtaining an orthogonal transformation which most nearly transforms one given matrix into another given matrix, according to some least-squares criterion of fit. From this procedure, three analytic methods are derived for obtaining an orthogonal factor matrix which closely approximates a given oblique factor matrix. The case is considered of approximating a specified subset of oblique
Nonlinear and dynamic structural analysis using combined approximations
Uri Kirsch; Michael Bogomolni
2007-01-01
It is shown how the combined approximations (CA) approach, developed originally for linear reanalysis, can improve the solution efficiency of nonlinear and dynamic analysis problems. In such problems the analysis equations are modified repeatedly during the solution process. The CA approach is based on the integration of several concepts and methods. The advantage is that efficient local approximations and accurate
Approximate reasoning for real-time probabilistic processes Vineet Gupta
Cortes, Corinna
Approximate reasoning for real-time probabilistic processes Vineet Gupta Google Inc. vineet on approximate reasoning in the presence of numerical information - such as probabili- ties and time- soning principles for reasoning about distances. We demonstrate that our approach is insensitive to po
An Approximate Method for Performance Evaluation of Asynchronous Pipeline Rings
Lei Wang; Zhi-ying Wang; Kui Dai
2006-01-01
Performance evaluation of asynchronous circuits is one of the most difficult parts in asynchronous circuit research. This Paper presents an approximate method by queuing network modeling for performance evaluation of asynchronous pipeline rings. The asynchronous pipeline rings are modeled by closed queuing networks with transfer blocking. An efficient approximation method is used to analyze the performance metrics, such as response
Reply to Steele & Ferrer: Modeling Oscillation, Approximately or Exactly?
ERIC Educational Resources Information Center
Oud, Johan H. L.; Folmer, Henk
2011-01-01
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…
Six Simple Schemata for Approximating Bayesian Belief Networks
Overill, Richard E.
Six Simple Schemata for Approximating Bayesian Belief Networks Richard E Overill and Jantje A M.overill | jantje.a.silomon}@ kcl.ac.uk Abstract. Two families comprising six simple schemata, which reproduce probabilities was studied in detail in [3]. We have developed six simple schemata for approximating
Approximation in Mechanism Design By JASON D. HARTLINE
Hartline, Jason D.
and there are environments, see, e.g., Vincent and Manelli (2007), where any un- dominated mechanism is optimal for some set conclusion I will make is that reserve-price-based auctions and posted pricings are approximately optimal- scribe how mechanisms based on reserve prices are often sufficient to approximate ones parame- terized
Post-Selection Inference for Models that are Approximations
Buja, Andreas
Post-Selection Inference for Models that are Approximations Andreas Buja joint work with the Po/11/13 #12;Larger Problem: Non-Reproducible Empirical Findings Andreas Buja (Wharton, UPenn) Post Are False" Andreas Buja (Wharton, UPenn) Post-Selection Inference for Models that are Approximations 2013
NIST Special Publication 800-168 Approximate Matching
NIST Special Publication 800-168 Approximate Matching: Definition and Terminology Frank.SP.800-168 #12;#12;NIST Special Publication 800-168 Approximate Matching: Definition and Terminology Vassil Roussev University of New Orleans New Orleans, LA http://dx.doi.org/10.6028/NIST.SP.800-168 May
Approximating Description Logic Classification for Semantic Web Reasoning
Groot, Perry
Approximating Description Logic Classification for Semantic Web Reasoning Perry Groot1, Heiner Web is that they are all based on formal logic. This makes it possible to formally reason about;Approximating Description Logic Classification for Semantic Web Reasoning 319 Research in the past few years has
Approximating k-node connected subgraphs via critical Guy Kortsarz
Nutov, Zeev
Approximating k-node connected subgraphs via critical graphs Guy Kortsarz Rutgers University;nding a k-node connected spanning subgraph (directed or undirected) of minimum cost. The best known approximation guarantees for this problem were O(minfk; n p n k g) for both di- rected and undirected graphs
Approximation of functions over redundant dictionaries using coherence
Anna C. Gilbert; S. Muthukrishnan; Martin J. Strauss
2003-01-01
One of the central problems of modern mathematical approximation theory is to approximate functions, or signals, concisely, with elements from a large candidate set called a dictionary. Formally, we are given a signal A ? RN and a dictionary D = {?i}i?I of unit vectors that span RN. A representation R of B terms for input A ? RN is
Matching Pursuit Video Coding Part I: Dictionary Approximation
Zakhor, Avideh
1 Matching Pursuit Video Coding Part I: Dictionary Approximation Ralph Neff and Avideh Zakhor. The key to the method is an algorithm which takes an arbitrary 2D dictionary and generates approximations of the dictionary which have fast 2stage implementations according to the method of Redmill, et.al. [1] By varying
Distributed Approximation of Minimum Routing Cost Trees Alexandra Hochuli
to the optimal solution. Every network contains a tree whose total cost of communication between all pairsDistributed Approximation of Minimum Routing Cost Trees Alexandra Hochuli ETH Zurich hochulia We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message
ROUGH SET APPROXIMATIONS: A CONCEPT ANALYSIS POINT OF VIEW
Yao, Yiyu
ROUGH SET APPROXIMATIONS: A CONCEPT ANALYSIS POINT OF VIEW Yiyu Yao University of Regina, Regina and content of data, definable concepts, lower and upper ap- proximations, rough set approximations Contents 1. Conclusion Bibliography Biographical Sketches Summary Rough set theory was proposed by Pawlak for analyzing
APPROXIMATING THE RANDOM WALK USING THE CENTRAL LIMIT THEOREM
May, J. Peter
, if one considers only even steps then the simple random walk is aperiodic, so the results of this paperAPPROXIMATING THE RANDOM WALK USING THE CENTRAL LIMIT THEOREM MITCH HILL Abstract. This paper will define the random walk on an integer lattice and will approximate the probability that the random walk
A new approximation for the dynamics of topographic Rossby waves
Ashkenazy, Yossi "Yosef"
A new approximation for the dynamics of topographic Rossby waves By YOSEF ASHKENAZY1 *, NATHAN theory of non-harmonic topographic Rossby waves over a slowly varying bottom depth of arbitrary, 1-D explicit approximate expressions for the phase speed and non-harmonic cross-slope structure of waves
On Approximating Arbitrary Metrics by Tree Metrics Yair Bartal
Bartal, Yair
On Approximating Arbitrary Metrics by Tree Metrics Yair Bartal #3; Abstract This paper is concerned with probabilistic approxima- tion of metric spaces. In previous work we introduced the method of eÆcient approximation of metrics by more simple families of metrics in a probabilistic fash- ion. In particular we study
Improved Approximation Algorithms for Directed Steiner Forest Moran Feldman
Kortsarz, Guy
Improved Approximation Algorithms for Directed Steiner Forest Moran Feldman Guy Kortsarz Zeev Nutov Abstract We consider the k-Directed Steiner Forest (k-DSF) problem: Given a directed graph G = (V, E the Directed Steiner Forest (DSF) problem. The best known approximation ratios for these problems are: ~O(k2
SPARSE APPROXIMATION USING LEAST SQUARES SUPPORT VECTOR MACHINES
SPARSE APPROXIMATION USING LEAST SQUARES SUPPORT VECTOR MACHINES J.A.K. Suykens, L. Lukas, J (Heverlee), Belgium Email: johan.suykens@esat.kuleuven.ac.be ABSTRACT In least squares support vector. Function estimation, support vector machines, ridge regression, sparse approximation, prun ing, radial
Feature selection for best mean square approximation of class densities
NASA Technical Reports Server (NTRS)
Peters, C.
1978-01-01
A criterion for linear feature selection is proposed which is based on mean square apporximation of class density functions. It is shown that for the widest possible class of approximants, the criterion reduces to Devijver's Bayesian distance. For linear approximants the criterion is equivalent to well known generalized Fisher criteria.
GRECS: Graph Encryption for Approximate Shortest Distance Queries
International Association for Cryptologic Research (IACR)
GRECS: Graph Encryption for Approximate Shortest Distance Queries Xianrui Meng1 , Seny Kamara2 Research 3 Department of Computer Science, Ben-Gurion University Abstract We propose graph encryption schemes that efficiently support approximate shortest distance queries on large-scale encrypted graphs
BADLY APPROXIMABLE SYSTEMS OF AFFINE FORMS Dmitry Kleinbock
Kleinbock, Dmitry
BADLY APPROXIMABLE SYSTEMS OF AFFINE FORMS Dmitry Kleinbock Rutgers University To appear in J on the Hausdorff dimension of the set of badly approximable systems of linear forms. The proof is based on ideas dimension at any point of X). A system of m linear forms in n variables given by A Mm,n(R) is called badly
Generalization of Ramanujan Method of Approximating root of an equation
Muthumalai, Ramesh Kumar
2011-01-01
We generalize Ramanujan method of approximating the smallest root of an equation which is found in Ramanujan Note books, Part-I. We provide simple analytical proof to study convergence of this method. Moreover, we study iterative approach of this method on approximating a root with arbitrary order of convergence.
The blind leading the blind: Mutual refinement of approximate theories
NASA Technical Reports Server (NTRS)
Kedar, Smadar T.; Bresina, John L.; Dent, C. Lisa
1991-01-01
The mutual refinement theory, a method for refining world models in a reactive system, is described. The method detects failures, explains their causes, and repairs the approximate models which cause the failures. The approach focuses on using one approximate model to refine another.
Practical Experiments with Regular Approximation of Context-Free Languages
implemented a large number of meth- ods, and where necessary, refined them with an analysis of the grammar. We. The nature of this processing differs for the respective approximation meth- ods. For other parts several meth- ods to approximate the language generated by a grammar if the sufficient condition mentioned
Motivation and Outline Hatree-Fock Theory and KLI Approximation
Holzwarth, Natalie
Motivation and Outline Hatree-Fock Theory and KLI Approximation Frozen core orbital approximation March 24, 2011 Xiao Xu, N. A. W. Holzwarth PAW + HF & KLI #12;Motivation and Outline Hatree-Fock Theory of HF and KLI Conclusion Outline 1 Motivation of this work: Why? orbital dependent functionals + PAW 2
Atomic Structure Schrdinger equation has approximate solutions for multi-
Zakarian, Armen
Atomic Structure Schrödinger equation has approximate solutions for multi- electron atoms, which indicate that all atoms are like hydrogen Atomic Structure Schrödinger equation has approximate solutions 3s 3p 3d Energy hydrogen multi-electron #12;Atomic Structure · orbitals are populated by electrons
Empirical Risk Approximation: An Induction Principle for Unsupervised Learning
Clausen, Michael
Empirical Risk Approximation: An Induction Principle for Unsupervised Learning Joachim M. Buhmann, Germany email: jb@cs.unibonn.de WWW: http://wwwdbv.cs.unibonn.de April 3, 1998 Abstract Unsupervised process. This paper proposes Empirical Risk Approximation as a new induction principle for unsupervised
Moment and SDP relaxation techniques for smooth approximations of nonlinear
Henrion, Didier
numerical results are reported. 1 Introduction Problems involving nonlinear differential equations arise, an approximation for the solution of the differential equation is obtained in closed form by maximum entropyMoment and SDP relaxation techniques for smooth approximations of nonlinear differential equations
Note on the ring approximation in nuclear matter
E. Bauer
2008-05-01
The response function to an external prove is evaluated using the ring approximation in nuclear matter. Contrary to what it is usually assumed, it is shown that the summation of the ring series and the solution of the Dyson's equation are two different approaches. The numerical results exhibit a perceptible difference between both approximations.
Dynamic Enthalpy, Conservative Temperature, and the Seawater Boussinesq Approximation
Young, William R.
Dynamic Enthalpy, Conservative Temperature, and the Seawater Boussinesq Approximation WILLIAM R of the kinetic energy plus the Boussinesq dynamic enthalpy hz , which is the integral of the buoyancy approximation, the full specific enthalpy h is the sum of four terms: McDougall's potential en- thalpy, minus
On the Convergence Rate of Vanishing Viscosity Approximations
On the Convergence Rate of Vanishing Viscosity Approximations Alberto Bressan (#3;) and Tong Yang that the corresponding solutions u " of (1.2) exist for all t #21; 0, have uniformly small total variation and converge(t) L 1 , thus providing a convergence rate for these vanishing viscosity approximations. We use
Exponential Product Approximation to Integral Kernel of Schrodinger Semigroup
to the heat kernel generated by the Dirichlet Laplacian through the product formula. 1. Introduction the approximation to the heat kernel generated by the Dirichlet Laplacian through the product formula. We beginExponential Product Approximation to Integral Kernel of SchrË?odinger Semigroup and to Heat Kernel
Cosmic shear covariance: the log-normal approximation
S. Hilbert; J. Hartlap; P. Schneider
2011-01-01
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.
Perturbation approximation for orbits in axially symmetric funnels
NASA Astrophysics Data System (ADS)
Nauenberg, Michael
2014-11-01
A perturbation method that can be traced back to Isaac Newton is applied to obtain approximate analytic solutions for objects sliding in axially symmetric funnels in near circular orbits. Some experimental observations are presented for balls rolling in inverted cones with different opening angles, and in a funnel with a hyperbolic surface that approximately simulates the gravitational force.
Cost versus Precision for Approximate Typing for Levin Fritz
Utrecht, Universiteit
Cost versus Precision for Approximate Typing for Python Levin Fritz Jurriaan Hage Technical Report for Python Jurriaan Hage Universiteit Utrecht levinfritz@gmail.com J.Hage@uu.nl Abstract In this paper we describe a variation of monotone frame- works that enables us to perform approximate typing of Python
Approximating scattered data with discontinuities * Erlend Arge and Michael Floater
Floater, Michael S.
by the The Royal Norwegian Council for Scientific and Industrial Research 1 #12;intersect any fault. The steps Abstract. A method is presented for approximating scattered data by a function defined on a regular two domain known as faults. The method has three phases: regularisation, local approximation
Continued Fraction Approximations of the Riemann Zeta Function
Morrow, James A.
Continued Fraction Approximations of the Riemann Zeta Function MATH 336 Shawn Apodaca #12;1 Introduction Continued fractions serve as a useful tool for approximation and as a field of their own. Here we will concern ourselves with results from Cvijovic and Klinowski from Continued-Fraction Expansions
Approximate Killing Vectors for Computing Spin in Black-Hole
Cook, Greg
Approximate Killing Vectors for Computing Spin in Black-Hole Initial Data and Evolutions Gregory B-local definition: e.g. Brown & York[2] or Ashtekar & Krishnan[1] S = - 1 8 BH Kiji sj hd2 x i = i CK : Killing vector of ~hij conformal Killing vector of hij i AKV : Approximate Killing vector of hij Â Greg Cook
Approximate Killing Vectors and Black-Hole Diagnostics
Cook, Greg
Approximate Killing Vectors and Black-Hole Diagnostics Gregory B. Cook Wake Forest University[2] or Ashtekar & Krishnan[1] S = - 1 8 BH Kiji sj hd2 x i = i CK : Killing vector of ~hij conformal Killing vector of hij i AKV : Approximate Killing vector of hij Â Greg Cook Â (WFU Physics) 1 #12
Approximate Belief Updating in Max-2-Connected Bayes Networks is
Beimel, Amos
Approximate Belief Updating in Max-2-Connected Bayes Networks is NP-Hard Erez Karpas Faculty}@cs.bgu.ac.il Abstract A max-2-connected Bayes network is one where there are at most 2 distinct di- rected paths between to approximate. Key words: Bayes network, Complexity, Max-k-connected 1 Introduction Bayes networks are a compact
Approximate Belief Updating in Max2Connected Bayes Networks is
Beimel, Amos
Approximate Belief Updating in Max2Connected Bayes Networks is NPHard Erez Karpas Faculty}@cs.bgu.ac.il Abstract A max2connected Bayes network is one where there are at most 2 distinct di rected paths between to approximate. Key words: Bayes network, Complexity, Maxkconnected 1 Introduction Bayes networks are a compact
Modeling and Synthesis of Quality-Energy Optimal Approximate Adders
Gerstlauer, Andreas
, in accumulation, a reduced-variance error. We demonstrate synthesized approximate adders with energy up to 60Modeling and Synthesis of Quality-Energy Optimal Approximate Adders Jin Miao, Ku He, Andreas Gerstlauer, and Michael Orshansky Department of Electrical & Computer Engineering, The University of Texas
On the Approximations of Multiple target filtering P. Del Moral
Del Moral , Pierre
On the Approximations of Multiple target filtering equations P. Del Moral Centre INRIA de Bordeaux (2010). To appear in Stochastic Analysis and Applications (2011). P. Del Moral (INRIA) INRIA Bordeaux Approximation models P. Del Moral (INRIA) INRIA Bordeaux-Sud Ouest 2 / 25 #12;Some notation : E measurable space
On the Approximations of Multiple target filtering P. Del Moral
Del Moral , Pierre
On the Approximations of Multiple target filtering equations P. Del Moral Centre INRIA Bordeaux (2010). To appear in Stochastic Analysis and Applications (2011). Del Moral (INRIA) INRIA Centre models 7 Approximation models Del Moral (INRIA) INRIA Centre Bordeaux-Sud Ouest, France 2 / 25 #12;Some
Distributional Importance Sampling for Approximate Weighted Model Counting
Bacchus, Fahiem
Distributional Importance Sampling for Approximate Weighted Model Counting Jessica Davies|fbacchus]@cs.toronto.edu Abstract. We present a sampling method to approximate the weighted model count of Boolean satisfiability problems. Our method is based on distributional importance sampling, where a subset of the variables