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.
Design and Measurements of a quasi-isotropic UWB micro-strip antenna
Paris-Sud XI, Université de
Design and Measurements of a quasi-isotropic UWB micro-strip antenna Antoine Diet, Nicolas Ribière.diet@lss.supelec.fr Abstract This paper summarizes the design and measurements of a quasi-isotropic printed UWB antenna with a simple micro-strip design and a standard technology. The design of this antenna is based
A quasi-isotropic reflecting boundary condition for the TIBERE heterogeneous leakage model
Petrovic, I.; Marleau, G. [Ecole Polytechnique de Montreal, Quebec, Montreal (Canada). Institut de Genie Nucleaire; Benoist, P.
1996-02-01
The influence of assembly or cell heterogeneity on neutron leakage has been consistently taken into account in the TIBERE simplified heterogeneous B{sub 1} model. The assumption adopted within the TIBERE model that neutrons are specularly reflected on the boundary introduces two problems. Calculations with this model may become rather time consuming and even unnecessarily long in the case of a Canada deuterium uranium reactor cell, and the peripheral or total coolant voiding of a pressurized water reactor assembly leads to infinite leakage coefficients. These problems have been overcome by the development of another simplified heterogeneous B{sub 1} leakage model, TIBERE-2, which has quasi-isotropic reflecting boundary conditions. The TIBERE-2 model uses similar approximations as the TIBERE model and yields an iterative scheme to simultaneously compute multigroup scalar fluxes and directional currents in a heterogeneous geometry. These values enable the evaluation of directional space-dependent leakage coefficients. This new model requires the classical and directional escape and transmission probabilities in addition to the classical and directional first-flight collision probabilities calculated for an open assembly. The TIBERE-2 model has been introduced for general two-dimensional geometry into the DRAGON multigroup transport code. The numerical results obtained by DRAGON show that the TIBERE-2 model represents leakages much better than the homogeneous B{sub 1} leakage model. Moreover, the TIBERE-2 model yields results that are extremely close to those obtained by the TIBERE model with considerably shorter computing times.
Construction of a polarization insensitive lens from a quasi-isotropic metamaterial slab
Hailu Luo; Zhongzhou Ren; Weixing Shu; Fei Li
2007-01-01
We propose to employ the quasi-isotropic metamaterial (QIMM) slab to construct a polarization insensitive lens, in which both E - and H -polarized waves exhibit the same refocusing effect. For shallow incident angles, the QIMM slab will provide some degree of refocusing in the same manner as an isotropic negative index material. The refocusing effect allows us to introduce the
NASA Astrophysics Data System (ADS)
Liu, Xing-Xiang; Alù, Andrea
2011-06-01
In this work, we discuss the homogenization of a metamaterial geometry composed of periodic arrays of densely packed subwavelength magnetodielectric spheres, in order to study whether a local quasi-isotropic homogenization model may accurately describe its wave interaction in its negative-index or zero-index operation. We analyze and compare the electromagnetic response of these arrays with their retrieved metamaterial model, for frequency regimes in which positive or negative values of effective index of refraction are expected. We pay special attention to the effects of array truncation and complex forms of excitation, showing that it is possible to realize quasi-isotropic negative-index or zero-index metamaterials with negligible spatial dispersion effects in certain frequency bands. We then apply these concepts to specific configurations of interest for metamaterial devices, showing that, despite their finite size and complex operation, their response is consistent with the one associated with their homogenized local description.
Xing-Xiang Liu; Andrea Alù
2011-01-01
In this work, we discuss the homogenization of a metamaterial geometry composed of periodic arrays of densely packed subwavelength magnetodielectric spheres, in order to study whether a local quasi-isotropic homogenization model may accurately describe its wave interaction in its negative-index or zero-index operation. We analyze and compare the electromagnetic response of these arrays with their retrieved metamaterial model, for frequency
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.
The effects of stress ratio and load sequence on damage accumulation in quasi-isotropic laminates
Bartley-Cho, J.D.; Lee, S.; Hahn, H.T. [Univ. of California, Los Angeles, CA (United States). Mechanical and Aerospace Dept.
1995-12-31
The effects of load sequence and stress ratio on damage development were studied for a quasi-isotropic laminates under high cycle fatigue conditions. Ply crack density was used as the main damage parameter. AS4/3501-6 quasi-isotropic laminates of [0/{+-}45/90]{sub S3} lay-up were fatigued in tension-tension to 10{sup 6} cycles. Constant amplitude tests at a stress ratio, R=0.1, and frequency of 10 Hz were performed to gain baseline crack density data. Additional constant amplitude tests at 60% of ultimate tensile strength and at R=0.4, 0.6, and 0.8 were performed. Two-stress-level two block tests were performed in high/low and low/high sequences at 40%/30% and 40%/20% of ultimate tensile strength. The R variation tests showed that, for outer plies, damage mode changed from ply cracking to delamination as R decreased. The two block spectrum tests revealed that low/high fatigue resulted in a higher crack density than for high/low fatigue. A cumulative damage method was developed based on crack density data and the assumption that damage state reached is independent of load history. The method predicted unconservatively, either giving values between or above the observed crack densities.
Buckling of a sublaminate in a quasi-isotropic composite laminate
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Whitcomb, J. D.
1984-01-01
The buckling of an elliptic delamination embedded near the surface of a thick quasi-isotropic laminate was predicted. The thickness of the delaminated ply group (the sublaminate) was assumed to be small compared to the total laminate thickness. Finite-element and Rayleigh-Ritz methods were used for the analyses. The Rayleigh-Ritz method was found to be simple, inexpensive, and accurate, except for highly anisotropic delaminated regions. Effects of delamination shape and orientation, material anisotropy, and layup on buckling strains were examined. Results show that: (1) the stress state around the delaminated region is biaxial, which may lead to buckling when the laminate is loaded in tension; (2) buckling strains for multi-directional fiber sublaminates generally are bounded by those for the 0 deg and 90 deg unidirectional sublaminates; and (3) the direction of elongation of the sublaminate that has the lowest buckling strain correlates with the delamination growth direction.
Construction of a polarization insensitive lens from a quasi-isotropic metamaterial slab.
Luo, Hailu; Ren, Zhongzhou; Shu, Weixing; Li, Fei
2007-02-01
We propose to employ the quasi-isotropic metamaterial (QIMM) slab to construct a polarization insensitive lens, in which both E- and H-polarized waves exhibit the same refocusing effect. For shallow incident angles, the QIMM slab will provide some degree of refocusing in the same manner as an isotropic negative index material. The refocusing effect allows us to introduce the ideas of paraxial beam focusing and phase compensation by the QIMM slab. On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through a QIMM slab is presented. Because of the negative phase velocity in the QIMM slab, the inverse Gouy phase shift and the negative Rayleigh length of paraxial Gaussian beam are proposed. We find that the phase difference caused by the Gouy phase shift in vacuum can be compensated by that caused by the inverse Gouy phase shift in the QIMM slab. If certain matching conditions are satisfied, the intensity and phase distributions at object plane can be completely reconstructed at image plane. Our simulation results show that the superlensing effect with subwavelength image resolution could be achieved in the form of a QIMM slab. PMID:17358430
Experimental data on single-bolt joints in quasi isotropic graphite/polyimide laminates
NASA Technical Reports Server (NTRS)
Wichorek, G. R.
1982-01-01
Sixteen ply, quasi-isotropic laminates of Celanese Celion 6000/PMR-15 and Celion 6000/LARC-160 with a fiber orientation of (0/45/90/-45) sub 2S were evaluated. Tensile and open hole specimens were tested at room temperature to establish laminate tensile strength and net tensile strength at an unloaded bolt hole. Double lap joint specimens with a single 4.83-mm (0.19 in.) diameter bolt torqued to 1.7 N-m (15 lbf-in.) were tested in tension at temperatures of 116 K (-250F), 297 K (75F), and 589 K (600F). The joint ratios of w/d (specimen width to hole diameter) and e/d (edge distance to hole diameter) were varied from 4 to 6 and from 2 to 4, respectively. The effect of joint geometry and temperature on failure mode and joint stresses are shown. Joint stresses calculated at maximum load for each joint geometry and test temperature are reported. Joint strength in net tension, bearing, and shear out at 116 K (-250F), 297 K (75F), and 589 K (600F) are given for the Celion 6000/PMR-15 and Celion 6000/LARC-160 laminates.
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
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.
1992-01-01
This study investigated the behavior of the SCS6\\/Ti-15-3 metal matrix composite with a quasi-isotropic layup when tested under static and fatigue conditions. Specimens were subjected to in-phase and out-of-phase thermo-mechanical and isothermal fatigue loading. In-phase and isothermal loading produced a fiber dominated failure while the out-of-phase loading produced a matrix dominated failure. Also, fiber domination in all three profiles was
Atsushi Hosoi; Hiroyuki Kawada; Hiromichi Yoshino
2006-01-01
In this study the fatigue characteristics of quasi-isotropic carbon fiber reinforced plastics laminates subjected to variable amplitude cyclic two-stage loading were investigated. The cumulative damage was evaluated by considering residual strength as a parameter since the Linear Cumulative Damage rule, i.e., the Palmgren–Miner rule, did not show good agreement. Further, the internal microscopic damage was observed with an optical microscope.
EVIDENCE FOR QUASI-ISOTROPIC MAGNETIC FIELDS FROM HINODE QUIET-SUN OBSERVATIONS
Asensio Ramos, A. [Instituto de AstrofIsica de Canarias, 38205, La Laguna, Tenerife (Spain)], E-mail: aasensio@iac.es
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.
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.
Jonathan Bartley-Cho; Seung Gyu Lim; H. Thomas Hahn; Peter Shyprykevich
1997-01-01
A study has been made of ply cracking in quasi-isotropic AS4\\/3501-6 laminates under tension–tension (T–T) and tension–compression (T–C) constant-amplitude (CA) fatigue loading and two-block loading. The CA fatigue and two-block fatigue tests were performed on unnotched laminates having two different lay-ups: [0\\/±45\\/90]S3 and [0\\/±45\\/90]S4. The thinner lay-up was tested in T–T fatigue, and the thicker lay-up in T–C fatigue to
NASA Technical Reports Server (NTRS)
Hyer, M. W.; Hagaman, J. A.
1979-01-01
The results of a series of tests of graphite-polyimide honeycomb sandwich panels are presented. The panels were 1.22 m long, 0.508 m wide, and approximately 13.3 m thick. The face sheets were a T-300/PMR-15 fabric in a quasi-isotropic layup and were 0.279 mm thick. The core was Hexcel HRH 327-3/16 - 4.0 glass reinforced polyimide honeycomb, 12.7 mm thick. Three panels were used in the test: one was cut into smaller pieces for testing as beam, compression, and shear specimens; a second panel was used for plate bending tests; the third panel was used for in-plane stability tests. Presented are the experimental results of four point bending tests, short block compression tests, core transverse shear modulus, three point bending tests, vibration tests, plate bending tests, and panel stability tests. The results of the first three tests are used to predict the results of some of the other tests. The predictions and experimental results are compared, and the agreement is quite good.
Cambridge, University of
been different. We believe, however, that the tabulated figures are fairly accurate. The values- tion to the cubic axes. The mean value J of the three properties of a quasi-isotropic polycrystal[100Jand lnll] represent the values for cube edges and the body diagonals. There is close agreement between
Hart, K.A.
1992-12-01
This study investigated the behavior of the SCS6/Ti-15-3 metal matrix composite with a quasi-isotropic layup when tested under static and fatigue conditions. Specimens were subjected to in-phase and out-of-phase thermo-mechanical and isothermal fatigue loading. In-phase and isothermal loading produced a fiber dominated failure while the out-of-phase loading produced a matrix dominated failure. Also, fiber domination in all three profiles was present at higher maximum applied loads and al three profiles demonstrated matrix domination at lower maximum applied loads. Thus, failure is both profile dependent and load equipment. Additional analyses, using laminated plate theory, Halpin-Tsai equations, METCAN, and the Linear Life Fraction Model (LLFM), showed: the as-received specimens contained plies where a portion of the fibers are debonded from the matrix; during fatigue cycling, the 90 deg. plies and a percentage of the 45 deg. plies failed immediately with greater damage becoming evident with additional cycles; and, the LLFM suggests that there may be a non-linear combination of fiber and matrix domination for in-phase and isothermal cycling.
G. A. O. Davies; D. Hitchings; J. Wang
2000-01-01
This paper describes a procedure for the prediction of the threshold impact energy for the onset of delamination in fibre-reinforced quasi-isotropic laminates under low-velocity impact. It is primarily based upon two models. One is the energy-balance model which equates the kinetic energy of the impactor with the static deformation energy of the laminate. The geometrical non-linearity of the deformation of
Iyengar, N.; Guerdal, Z. [Virginia Polytechnic Institute and State Univ., Blacksburg, VA (United States)
1994-12-31
A combined experimental and numerical study of the compression response and the failure characteristics of various quasi-isotropic coupons with a hole obtained from a [{+-}45/90/0]{sub s}, stacking sequence quasi-isotropic laminate was carried out. Specimens with various quasi-isotropic stacking sequences of [{+-}45+{phi}/90+{phi}/{phi}]{sub s}, were acquired by cutting the coupons at various angles 0 from the quasi-isotropic laminate. Analysis of the coupons based on 2-D and 3-D finite element models were performed to evaluate the stresses around the hole. Two different compressive failure, prediction techniques based on distinctly different failure modes, namely fiber kinking and delamination, have been evaluated. The validity of these techniques was measured against experimental data of quasiisotropic coupons tested. The failure of the laminated coupons with a hole has been shown to be sensitive to the stacking sequence. It is also shown that a 2-D finite element model does not provide the required stacking sequence sensitivity. Thus, a 3-D analysis of the stress state in the vicinity of the hole is necessary. The study shows that no one mode of failure is responsible for limiting the strength for all laminate off-axis orientations, but rather the failure mode changes with change in stacking sequence. The analysis also substantiates the experimental data presented, that the peak strength of the laminate is achieved for a stacking sequence of [32.5/{minus}57.5/77.5/{minus}12.5] which corresponds to an off-axis angle of {phi} = {minus}12.5 with respect to the loading direction.
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.
Manifestation of the cotton-mouton effect in the ionosphere plasma
NASA Astrophysics Data System (ADS)
Kravtsov, Yu. A.; Naida, O. N.
Polarization methods used to sound ionospheric plasma are based on the Faraday and Cotton-Mouton effects. While the Faraday effect (rotation of the polarization plane) covers almost the entire ray path, the Cotton-Mouton effect gives rise to local transformation of circularly polarized waves near a point of orthogonality of the ray and the Earth's magnetic field. Comparison of the input and output polarization of probing electromagnetic waves, emitted by a satellite and received by ground stations, can provide valuable information about local plasma parameters near the orthogonality point. This paper presents a theory of interaction of circular waves near this point based on the quasi-isotropic approximation (QIA) of geometrical optics and describes algorithms that can be used to retrieve local plasma parameters from polarization measurements. Experimental configurations to observe the Cotton-Mouton effect with linearly and arbitrarily polarized receivers are discussed.
An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program
NASA Technical Reports Server (NTRS)
Rose, Cheryl A.; Herakovich, Carl T.
1992-01-01
An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.
NSDL National Science Digital Library
British Broadcasting Corporation (BBC)
2003-01-01
This web page features mathematical information about Archimedes' successful approach to finding an approximation to pi and an interactive manipulative that replicates the approach. The user can approximate pi as a number between the lengths of the perimeters of two polygons, one inscribed inside a circle and one circumscribed around the circle. The number of sides for the polygons may be increased to 96 with the value for pi always being between the two approximations. Similarities and differences between Archimedes' approach and the manipulative's approach are noted. The page is part of a NOVA web site that describes the discovery of the Archimedes palimpsest and examines the mathematical and philosophical meanings of infinity. Copyright 2005 Eisenhower National Clearinghouse
Flexural Stiffnesses of and Dimensional Stability in Circular Quasi-isotropic Laminate Mirrors
Kim, Kyungpyo
2009-01-01
................................................ 21 Figure 5: Fabricated flat composite mirror substrates. a) 8-inch diameter 12 layer thin composite laminate mirror blank with chopped mat carbon and Kevlar, b) 8-inch diameter 8 layer thin composite mirrors with carbon and Kevlar cloth with 2...
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
Auzinger, Winfried
' am Digitalcomputer Archimedes und die Berechnung von = 3.14159 . . . Das leidige Integral Das Einleitung: `Alles ist Zahl' am Digitalcomputer Archimedes und die Berechnung von = 3.14159 . . . Das Approximation als SparmaÃ?nahme Anhang Ã?berblick Einleitung: `Alles ist Zahl' am Digitalcomputer Archimedes und
Interpolation and Approximation Theory.
ERIC Educational Resources Information Center
Kaijser, Sten
1991-01-01
Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH)
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...
Rey Juan Carlos, Universidad
laser I. Leyva,* E. Allaria, and R. Meucci Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6 of a single-mode CO2 laser during the switch-on transient of the laser intensity. We find a strong competition.3437, 260.5430, 270.2500, 270.3430. Laser dynamics is commonly studied in light of the fact
Naus, Dan J [ORNL; Corum, James [ORNL; Klett, Lynn B [ORNL; Davenport, Mike [ORNL; Battiste, Rick [ORNL; Simpson, Jr., William A [ORNL
2006-04-01
This report provides recommended durability-based design properties and criteria for a quais-isotropic carbon-fiber thermoplastic composite for possible automotive structural applications. The composite consisted of a PolyPhenylene Sulfide (PPS) thermoplastic matrix (Fortron's PPS - Ticona 0214B1 powder) reinforced with 16 plies of carbon-fiber unidirectional tape, [0?/90?/+45?/-45?]2S. The carbon fiber was Hexcel AS-4C and was present in a fiber volume of 53% (60%, by weight). The overall goal of the project, which is sponsored by the U.S. Department of Energy's Office of Freedom Car and Vehicle Technologies and is closely coordinated with the Advanced Composites Consortium, is to develop durability-driven design data and criteria to assure the long-term integrity of carbon-fiber-based composite systems for automotive structural applications. This document is in two parts. Part 1 provides design data and correlations, while Part 2 provides the underlying experimental data and models. The durability issues addressed include the effects of short-time, cyclic, and sustained loadings; temperature; fluid environments; and low-energy impacts (e.g., tool drops and kickups of roadway debris) on deformation, strength, and stiffness. Guidance for design analysis, time-independent and time-dependent allowable stresses, rules for cyclic loadings, and damage-tolerance design guidance are provided.
APPROXIMATE DYNAMIC PROGRAMMING
Mahadevan, Sridhar
LEARNING AND APPROXIMATE DYNAMIC PROGRAMMING Scaling Up to the Real World #12;#12;LEARNING AND APPROXIMATE DYNAMIC PROGRAMMING Scaling Up to the Real World Edited by Jennie Si, Andy Barto, Warren Powell
Approximating distributions from moments
R. F. Pawula
1987-01-01
A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous
Approximate solution in gasdynamics
NASA Technical Reports Server (NTRS)
Sirovich, L.; Chong, T. H.
1980-01-01
One-dimensional unsteady gasdynamics is considered. An approximation based mainly on the interaction of simple and entropy waves is adopted. A discussion supporting this approximation, based in part on shock expansion theory, is given. By the use of certain transformations the approximation leads to solution in terms of quadratures. Excellent agreement with exact numerical results is obtained over a wide range of cases.
Approximate Maximum Principle for Discrete Approximations of ...
2012-03-20
we have the following relationships: either d(uN (??(N)) .... Therefore, in what follows, we prove Theorem 3.1 in the case q = 0, breaking down the proof .... combination of type (4.10) can be approximated up to a small quantity of order o(
APPROXIMATE DYNAMIC PROGRAMMING
Ferrari, Silvia
LEARNING AND APPROXIMATE DYNAMIC PROGRAMMING Scaling Up to the Real World #12;#12;LEARNING AND APPROXIMATE DYNAMIC PROGRAMMING Scaling Up to the Real World Edited by Jennie Si, Andy Barto, Warren Powell-reference adaptive critic designs. Various ADP designs such as Heuristic Dynamic Programming (HDP), Dual HDP (DHP
Approximation of Hopf bifurcation
C. Bernardi; M. Curie
1982-01-01
Summary We make several assumptions on a nonlinear evolution problem, ensuring the existence of a Hopf bifurcation. Under a fairly general approximation condition, we define a discrete problem which retains the bifurcation property and we prove an error estimate between the branches of exact and approximate periodic solutions.
NASA Astrophysics Data System (ADS)
Barry, D. A.; Parlange, J.-Y.; Li, L.; Jeng, D.-S.; Crapper, M.
2005-10-01
The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 × 10 -5%. This error is orders of magnitude lower than any existing analytical approximations.
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 ...
Approximate Decentralized Bayesian Inference
Campbell, Trevor David
This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each ...
Calculator Function Approximation.
ERIC Educational Resources Information Center
Schelin, Charles W.
1983-01-01
The general algorithm used in most hand calculators to approximate elementary functions is discussed. Comments on tabular function values and on computer function evaluation are given first; then the CORDIC (Coordinate Rotation Digital Computer) scheme is described. (MNS)
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
Approximate Degradable Quantum Channels
David Sutter; Volkher B. Scholz; Renato Renner
2014-12-02
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 $\\varepsilon\\geq0$. 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.
Extended Abstract Approximating Visibility
Franklin, W. Randolph
for Figure 4 June 1, 2000, 21:3 #12;Franklin Approximating Visibility 7 Figure 6: Lake Champlain W Cell 2.2 Lake Champlain West The second test case was the Â£Â¥Â¤Â§Â¦Â¨Â£TÂ©UÂ£Â¥Â¤Â§Â¦AÂ£ Lake Champlain West level-1 DEM from
Hypergeometric approximations to polylogarithms
Zudilin, Wadim
values and, in particular, of zeta values. Part 1 is joint work with Khodabakhsh and Tatiana Hessami and Tatiana Hessami 1 A talk at the conference "Diophantine approximation and transcendental numbers" (CIRM values of the di- and trilogarithm The irrationality result proved jointly with Khodabakhsh and Tatiana
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…
Multicriteria approximation through decomposition
Burch, C. [Carnegie Mellon Univ., Pittsburgh, PA (United States). School of Computer Science; Krumke, S. [Univ. of Wuerzburg (Germany). Dept. of Computer Science; Marathe, M. [Los Alamos National Lab., NM (United States); Phillips, C. [Sandia National Labs., Albuquerque, NM (United States). Applied Mathematics Dept.; Sundberg, E. [Rutgers Univ., NJ (United States). Dept. of Computer Science
1998-06-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of their technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. Their method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) the authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing; (2) they also show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
Multicriteria approximation through decomposition
Burch, C. [Carnegie Mellon Univ., Pittsburgh, PA (United States). School of Computer Sciences]|[Sandia National Labs., Albuquerque, NM (United States); Krumke, S. [Univ. of Wuerzburg (Germany). Dept. of Computer Science; Marathe, M. [Los Alamos National Lab., NM (United States); Phillips, C. [Sandia National Labs., Albuquerque, NM (United States). Applied Mathematics Dept.; Sundberg, E. [Rutgers Univ., NJ (United States). Dept. of Computer Science]|[Sandia National Labs., Albuquerque, NM (United States)
1997-12-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
NASA Astrophysics Data System (ADS)
Huang, Siendong
2009-11-01
The nonlocality of quantum states on a bipartite system \\mathcal {A+B} is tested by comparing probabilistic outcomes of two local observables of different subsystems. For a fixed observable A of the subsystem \\mathcal {A,} its optimal approximate double A' of the other system \\mathcal {B} is defined such that the probabilistic outcomes of A' are almost similar to those of the fixed observable A. The case of ?-finite standard von Neumann algebras is considered and the optimal approximate double A' of an observable A is explicitly determined. The connection between optimal approximate doubles and quantum correlations is explained. Inspired by quantum states with perfect correlation, like Einstein-Podolsky-Rosen states and Bohm states, the nonlocality power of an observable A for general quantum states is defined as the similarity that the outcomes of A look like the properties of the subsystem \\mathcal {B} corresponding to A'. As an application of optimal approximate doubles, maximal Bell correlation of a pure entangled state on \\mathcal {B}(\\mathbb {C}^{2})\\otimes \\mathcal {B}(\\mathbb {C}^{2}) is found explicitly.
Saddlepoint Approximations in Statistics
H. E. Daniels
1954-01-01
It is often required to approximate to the distribution of some statistic whose exact distribution cannot be conveniently obtained. When the first few moments are known, a common procedure is to fit a law of the Pearson or Edgeworth type having the same moments as far as they are given. Both these methods are often satisfactory in practice, but have
Uncorrelated scattering approximation revisited
A. M. Moro; J. A. Caballero; J. Gomez-Camacho
2004-05-24
The formalism to describe the scattering of a weakly bound projectile nucleus by a heavy target is investigated, using the Uncorrelated Scattering Approximation. The main assumption involved is to neglect the correlation between the fragments of the projectile in the region where the interaction with the target is important. It is shown that the angular momentum of each fragment with respect to the target is conserved. Moreover, when suitable approximations are assumed, the kinetic energy of each fragment is also shown to be conserved. The S-matrix for the scattering of the composite system can be written as a combination of terms, each one being proportional to the product of the S-matrices of the fragments.
Accelerated Stochastic Approximation
Harry Kesten
1958-01-01
Using a stochastic approximation procedure $\\\\{X_n\\\\}, n = 1, 2, \\\\cdots$, for a value $\\\\theta$, it seems likely that frequent fluctuations in the sign of $(X_n - \\\\theta) - (X_{n - 1} - \\\\theta) = X_n - X_{n - 1}$ indicate that $|X_n - \\\\theta|$ is small, whereas few fluctuations in the sign of $X_n - X_{n - 1}$ indicate
Approximation of Time-Dependent Viscoelastic Fluid Flow: SUPG Approximation
Vincent J. Ervin; William W. Miles
2003-01-01
In this article we consider the numerical approximation to the time dependent vis- coelasticity equations with an Oldroyd B constitutive equation. The approximation is stabilized by using a SUPG approximation for the constitutive equation. We analyse both the semi-discrete and fully discrete numerical approximations. For both discretizations we prove the existence of, and derive a priori error estimates for, the
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
The distinguishable cluster approximation
Kats, Daniel
2013-01-01
A new method that accurately describes strongly correlated states and captures dynamical correlation is presented. It is derived as a modification of coupled-cluster theory with single and double excitations (CCSD) through consideration of particle distinguishability between dissociated fragments, whilst retaining the key desirable properties of particle-hole symmetry, size extensivity, invariance to rotations within the occupied and virtual spaces, and exactness for two-electron subsystems. The resulting method called the distinguishable cluster approximation, smoothly dissociates difficult cases such as the nitrogen molecule, with the modest N^6 computational cost of CCSD. Even for molecules near their equilibrium geometries, the new model outperforms CCSD. It also accurately describes the massively correlated states encountered when dissociating hydrogen lattices, a proxy for the metal-insulator transition, and the fully dissociated system is treated exactly.
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 ( 287Â212 BC) approximated la Archimedes Archimedes of Syracuse ( 287Â212 BC) approximated by the Method of Exhaustion: 3
Approximation of Time-Dependent, Viscoelastic Fluid Flow: SUPG Approximation
Ervin, Vincent J.
equations with an Oldroyd B constitutive equation. The approximation is stabilized by using a SUPG the modeling equations, giving the NavierStokes equations. In viscoelasticity, assuming an Oldroyd B typeApproximation of Time-Dependent, Viscoelastic Fluid Flow: SUPG Approximation Vincent J. Ervin
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
Transient approximations in queueing networks
Andrewartha, John Michael
1989-01-01
Jackson network. The approximations were tested on networks ranging in size from 4 to 61 nodes, with various initial conditions and loading. Both stationary and nonstationary systems were tested. The closure approximations performed well for the Jackson... approximation simulations. The closure simulation and Monte Carlo simulations were compared for networks of up to 32 nodes, containing up to 80 queues. The network simulations were also tested with various parameters. The results of the closure approximation...
INTRODUCTION TO APPROXIMATE DYNAMIC PROGRAMMING
Powell, Warren B.
CHAPTER 4 INTRODUCTION TO APPROXIMATE DYNAMIC PROGRAMMING In chapter 3, we saw that we could solve cannot solve Bellman's equation exactly. Approximate dynamic programming offers a powerful set the expectation. Alternatively, consider Approximate Dynamic Programming. By Warren B. Powell Copyright c 2010
Noncommutative lattices as finite approximations
A. P. Balachandran; G. Bimonte; E. Ercolessi; G. Landi; F. Lizzi; G. Sparano; P. Teotonio-Sobrinho
1996-01-01
Lattice discretizations of continuous manifolds are common tools used in a variety of physical contexts. Conventional discrete approximations, however, cannot capture all aspects of the original manifold, notably its topology. In this paper we discuss an approximation scheme due to Sorkin (1991) which correctly reproduces important topological aspects of continuum physics. The approximating topological spaces are partially ordered sets (posets),
Approximate equivalence and approximate synchronization of metric transition systems
A. Agung Julius; George J. Pappas
2006-01-01
In this paper, we consider metric transition systems which are transition systems equipped with metrics for observation and synchronization labels. The existence of metrics leads to the introduction of two new concepts, (i) (epsi, delta)-approximate (bi)simulation of transition systems and (ii) approximate synchronization of transition systems. We show that the notion of (epsi, delta)-approximate (bi)simulation can be thought of as
Communicative Approximations as Rough Sets
Mohua Banerjee; Abhinav Pathak; Gopal Krishna; Amitabha Mukerjee
2010-01-01
\\u000a Communicative approximations, as used in language, are equivalence relations that partition a continuum, as opposed to observational\\u000a approximations on the continuum. While the latter can be addressed using tolerance interval approximations on interval algebra,\\u000a new constructs are necessary for considering the former, including the notion of a “rough interval”, which is the indiscernibility\\u000a region for an event described in language,
Compression of ephemerides. [Chebyshev approximation
NASA Technical Reports Server (NTRS)
Deprit, A.; Poplarchek, W.; Deprit-Bartholome, A.
1975-01-01
An algorithm is proposed for generating sequences of Chebyshev series which are the best approximations of an astronomical ephemeris in the sense of Chebyshev over large intervals of time. The criterion for a polynomial approximation of a function to be the best polynomial approximation of the function is that the error function present certain rippling characteristics as described by Remez (1957). General features of the program in PL/1 are described.
Multivariate stochastic approximation using a simultaneous perturbation gradient approximation
James C. Spall
1992-01-01
The problem of finding a root of the multivariate gradient equation that arises in function minimization is considered. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm for the general Kiefer-Wolfowitz type is appropriate for estimating the root. The paper presents an SA algorithm that is based on a simultaneous perturbation gradient approximation instead of
NASA Technical Reports Server (NTRS)
Harris, C. E.; Morris, D. H.
1985-01-01
Notched and unnotched geometries at 16, 32, and 64-ply thicknesses of a 90/45/0-45 (ns) laminate and a 45/0/-45/90 (ns) laminate were tested in compression-compression fatigue. The fatigue life and the initiation, type, and progression of damage were determined. Interlaminar stresses generated at straight, free edges of axially loaded laminates were used to interpret the test results. The fatigue lives of the notched specimens did not appear to be a strong function of laminate stacking sequence or specimen thickness. The stress concentration at the hole dominated over the interlaminar stresses at the straight free edge. The unnotched specimens of the 90/45/0/-45 (ns) laminate with tensile interlaminar normal stresses delaminated more readily than did the 45/0/-45/90 (ns) laminate with compressive interlaminar normal stress. The life of the 16-ply unnotched specimens was lower than the 32and 64-ply specimens. Delaminations were located at the interface where the maximum shear stress occurred regardless of the sense or magnitude of the interlaminar normal stress. An antibuckling fixture was effective in preventing out-of-plane motion without overconstraining the specimen.
Approximate dynamic programming for management
Powell, Warren B.
Approximate dynamic programming for management of high-value spare parts Hugo Simao and Warren is solved using approximate dynamic programming (ADP), but this requires developing new methods dynamic programming 147 Received January 2008 Revised June 2008 Accepted July 2008 Journal
APPROXIMATE DISASSEMBLY USING DYNAMIC PROGRAMMING
Stamp, Mark
APPROXIMATE DISASSEMBLY USING DYNAMIC PROGRAMMING A Research Project Presented to The Faculty DISASSEMBLY USING DYNAMIC PROGRAMMING by Abhishek Shah APPROVED FOR THE DEPARTMENT OF COMPUTER SCIENCE Dr of Graduate Studies and Research Date #12;i Abstract APPROXIMATE DISASSEMBLY USING DYNAMIC PROGRAMMING
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.
Medial spheres for shape approximation.
Stolpner, Svetlana; Kry, Paul; Siddiqi, Kaleem
2012-06-01
We study the problem of approximating a 3D solid with a union of overlapping spheres. In comparison with a state-of-the-art approach, our method offers more than an order of magnitude speedup and achieves a tighter approximation in terms of volume difference with the original solid while using fewer spheres. The spheres generated by our method are internal and tangent to the solid's boundary, which permits an exact error analysis, fast updates under local feature size preserving deformation, and conservative dilation. We show that our dilated spheres offer superior time and error performance in approximate separation distance tests than the state-of-the-art method for sphere set approximation for the class of (?,?)-fat solids. We envision that our sphere-based approximation will also prove useful for a range of other applications, including shape matching and shape segmentation. PMID:22516653
Approximate Genealogies Under Genetic Hitchhiking
Pfaffelhuber, P.; Haubold, B.; Wakolbinger, A.
2006-01-01
The rapid fixation of an advantageous allele leads to a reduction in linked neutral variation around the target of selection. The genealogy at a neutral locus in such a selective sweep can be simulated by first generating a random path of the advantageous allele's frequency and then a structured coalescent in this background. Usually the frequency path is approximated by a logistic growth curve. We discuss an alternative method that approximates the genealogy by a random binary splitting tree, a so-called Yule tree that does not require first constructing a frequency path. Compared to the coalescent in a logistic background, this method gives a slightly better approximation for identity by descent during the selective phase and a much better approximation for the number of lineages that stem from the founder of the selective sweep. In applications such as the approximation of the distribution of Tajima's D, the two approximation methods perform equally well. For relevant parameter ranges, the Yule approximation is faster. PMID:17182733
Powell, Warren B.
distribution. This is especially important in dynamic programming because we use these methods to estimate general class of functional approximations for dynamic programming. The basic problem can be stated as one observation of the value of the state which helps us improve the estimate. Approximate Dynamic Programming
PIECEWISE QUADRATIC APPROXIMATIONS IN CONVEX ...
2010-12-11
For instance, the recent [31] uses a different model ...... Fortunately, increasing ? and/or ? is a reaction to the fact that the ? obtained by ..... Piecewise quadratic approximations in convex numerical optimization. 25 name n function. 1 CB2. 2.
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 ...
Deconstructing Approximate Offsets Eric Berberich
. The result- ing shape is bounded by straight-line segments and circular arcs. However, a customary practice us to the question what is the original polygon whose approximate offset we have at hand. Of course
Greedy approximation in convex optimization
2012-06-02
Jun 2, 2012 ... linear combinations of elements from a given system (dictionary) is ... a certain functional determined by information from the previous steps of ... (choosing coefficients of the linear combination) the m-term approximant.
Mathematical algorithms for approximate reasoning
NASA Technical Reports Server (NTRS)
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away from the conclusion. These algorithms allow one to reason accurately with uncertain data. The above environment can replicate state-f-the-art expert system environments which provides a continuity between the current expert systems which cannot be validated or verified and future expert systems which should be both validated and verified
Resilient Approximation of Kernel Classifiers
Thorsten Suttorp; Christian Igel
2007-01-01
Trained support vector machines (SVMs) have a slow run-time classification speed if the classification problem is noisy and\\u000a the sample data set is large. Approximating the SVM by a more sparse function has been proposed to solve to this problem.\\u000a In this study, different variants of approximation algorithms are empirically compared. It is shown that gradient descent\\u000a using the improved
Wavelet Sparse Approximate Inverse Preconditioners
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Tang, W.-P.; Wan, W. L.
1996-01-01
There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.
Heat pipe transient response approximation.
Reid, R. S. (Robert Stowers)
2001-01-01
A simple and concise routine that approximates the response of an alkali metal heat pipe to changes in evaporator heat transfer rate is described. This analytically based routine is compared with data from a cylindrical heat pipe with a crescent-annular wick that undergoes gradual (quasi-steady) transitions through the viscous and condenser boundary heat transfer limits. The sonic heat transfer limit can also be incorporated into this routine for heat pipes with more closely coupled condensers. The advantages and obvious limitations of this approach are discussed. For reference, a source code listing for the approximation appears at the end of this paper.
Approximating spatially exclusive invasion processes
NASA Astrophysics Data System (ADS)
Ross, Joshua V.; Binder, Benjamin J.
2014-05-01
A number of biological processes, such as invasive plant species and cell migration, are composed of two key mechanisms: motility and reproduction. Due to the spatially exclusive interacting behavior of these processes a cellular automata (CA) model is specified to simulate a one-dimensional invasion process. Three (independence, Poisson, and 2D-Markov chain) approximations are considered that attempt to capture the average behavior of the CA. We show that our 2D-Markov chain approximation accurately predicts the state of the CA for a wide range of motility and reproduction rates.
Quasiclassical Born-Oppenheimer approximations
Oleg Zaitsev; R. Narevich; R. E. Prange
2000-09-29
We discuss several problems in quasiclassical physics for which approximate solutions were recently obtained by a new method, and which can also be solved by novel versions of the Born-Oppenheimer approximation. These cases include the so-called bouncing ball modes, low angular momentum states in perturbed circular billiards, resonant states in perturbed rectangular billiards, and whispering gallery modes. Some rare, special eigenstates, concentrated close to the edge or along a diagonal of a nearly rectangular billiard are found. This kind of state has apparently previously escaped notice.
Approximation Algorithms for Combinatorial Problems
David S. Johnson
1974-01-01
Simple, polynomial-time, heuristic algorithms for finding approximate solutions to various polynomial complete optimization problems are analyzed with respect to their worst case behavior, measured by the ratio of the worst solution value that can be chosen by the algorithm to the optimal value. For certain problems, such as a simple form of the knapsack problem and an optimization problem based
Approximation Algorithms for Combinatorial Problems
David S. Johnson
1973-01-01
Simple, polynomial-time, heuristic algorithms for finding approximate solutions to various polynomial complete optimization problems are analyzed with respect to their worst case behavior, measured by the ratio of the worst solution value that can be chosen by the algorithm to the optimal value. For certain problems, such as a simple form of the knapsack problem and an optimization problem based
Normal Approximation to Poisson Distribution
NSDL National Science Digital Library
Dinov, Ivo
This applet, created by Ivo Dinov of the University of California, Los Angeles, demonstrates the normal approximation to the Poisson distribution. Users can set the rate, lambda, and the number of trials, n, and observe how the shape of the distribution changes. The Poisson distribution is shown in blue, and the Normal distribution is shown in red.
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…
Polynomial Approximation Gordon K. Smyth
Smyth, Gordon K.
is put in statistics. The first is to model a nonlinear relationship between a response variable relationships. Approximation of more complicated functions by polyno mials is a basic building block are given by Abramowitz and Stegun [1]. Many statistical texts mention polynomial regression. Kleinbaum [3
Polynomial Approximation Gordon K. Smyth
Smyth, Gordon K.
polynomial approxima- tion is put in statistics. The first is to model a nonlinear relationship between to represent very general nonlinear relationships. Approximation of more complicated functions by poly- nomials formulae to functions used by statisticians are given by Abramowitz & Stegun [1]. Many statistical texts
Approximate Privacy: Foundations and Quantification
Feigenbaum, Joan; Schapira, Michael
2009-01-01
Increasing use of computers and networks in business, government, recreation, and almost all aspects of daily life has led to a proliferation of online sensitive data about individuals and organizations. Consequently, concern about the privacy of these data has become a top priority, particularly those data that are created and used in electronic commerce. There have been many formulations of privacy and, unfortunately, many negative results about the feasibility of maintaining privacy of sensitive data in realistic networked environments. We formulate communication-complexity-based definitions, both worst-case and average-case, of a problem's privacy-approximation ratio. We use our definitions to investigate the extent to which approximate privacy is achievable in two standard problems: the second-price Vickrey auction and the millionaires problem of Yao. For both the second-price Vickrey auction and the millionaires problem, we show that not only is perfect privacy impossible or infeasibly costly to achieve...
Generalized Gradient Approximation Made Simple
John P. Perdew; Kieron Burke; Matthias Ernzerhof
1996-01-01
Generalized gradient approximations (GGA's) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91
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.
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
Approximate Dynamic Programming -II: Warren B. Powell
Powell, Warren B.
Approximate Dynamic Programming - II: Algorithms Warren B. Powell December 8, 2009 #12;Abstract Approximate dynamic programming is a powerful class of algorithmic strategies for solving stochastic Approximate dynamic programming represents a powerful modeling and algorithmic strategy that can address
Strong shock implosion, approximate solution
NASA Astrophysics Data System (ADS)
Fujimoto, Y.; Mishkin, E. A.; Alejaldre, C.
1983-01-01
The self-similar, center-bound motion of a strong spherical, or cylindrical, shock wave moving through an ideal gas with a constant, ?= cp/ cv, is considered and a linearized, approximate solution is derived. An X, Y phase plane of the self-similar solution is defined and the representative curved of the system behind the shock front is replaced by a straight line connecting the mappings of the shock front with that of its tail. The reduced pressure P(?), density R(?) and velocity U1(?) are found in closed, quite accurate, form. Comparison with numerically obtained results, for ?= {5}/{3} and ?= {7}/{5}, is shown.
Approximating the minimum equivalent digraph
Samir Khuller; Balaji Raghavachari; Neal E. Young
1994-01-01
Abstract. The minimum equivalent graph (MEG) problem is as follows: given a directed graph, find a smallest subset,of the,edges,that,maintains,all,teachability,relations,between,nodes.,This problem,is NP-hard; this paper,gives an approximation,algorithm achieving a performance,guarantee of about 1.64 in polynomial time. The algorithm achieves,a performance,guarantee,of,1.75 in the,time,required,for,transitive,closure. The heart of the MEG problem,is the minimum,strongly,connected,spanning subgraph,(SCSS) problem--the MEG problem restricted to strongly connected digraphs. For the minimum
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.}
Approximating Metal-Insulator Transitions
C. Danieli; K. Rayanov; B. Pavlov; G. Martin; S. Flach
2014-05-06
We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate metal-insulator transitions (MIT) at the finite iteration steps. We also report evidence on mobility edges which are at variance to the celebrated Aubry-Andre model. The dynamics near the MIT shows a critical slowing down of the ballistic group velocity in the metallic phase similar to the divergence of the localization length in the insulating phase.
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
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
2015-03-10
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
Linear approximations of nonlinear systems
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Su, R.
1983-01-01
The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.
Indexing the approximate number system.
Inglis, Matthew; Gilmore, Camilla
2014-01-01
Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects. PMID:24361686
IONIS: Approximate atomic photoionization intensities
NASA Astrophysics Data System (ADS)
Heinäsmäki, Sami
2012-02-01
A program to compute relative atomic photoionization cross sections is presented. The code applies the output of the multiconfiguration Dirac-Fock method for atoms in the single active electron scheme, by computing the overlap of the bound electron states in the initial and final states. The contribution from the single-particle ionization matrix elements is assumed to be the same for each final state. This method gives rather accurate relative ionization probabilities provided the single-electron ionization matrix elements do not depend strongly on energy in the region considered. The method is especially suited for open shell atoms where electronic correlation in the ionic states is large. Program summaryProgram title: IONIS Catalogue identifier: AEKK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1149 No. of bytes in distributed program, including test data, etc.: 12 877 Distribution format: tar.gz Programming language: Fortran 95 Computer: Workstations Operating system: GNU/Linux, Unix Classification: 2.2, 2.5 Nature of problem: Photoionization intensities for atoms. Solution method: The code applies the output of the multiconfiguration Dirac-Fock codes Grasp92 [1] or Grasp2K [2], to compute approximate photoionization intensities. The intensity is computed within the one-electron transition approximation and by assuming that the sum of the single-particle ionization probabilities is the same for all final ionic states. Restrictions: The program gives nonzero intensities for those transitions where only one electron is removed from the initial configuration(s). Shake-type many-electron transitions are not computed. The ionized shell must be closed in the initial state. Running time: Few seconds for a large problem with a few thousand configurations.
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.
Approximating Stellar Orbits: Improving on Epicycle Theory
Walter Dehnen
1999-06-04
Already slightly eccentric orbits, such as those occupied by many old stars in the Galactic disk, are not well approximated by Lindblad's epicycle theory. Here, alternative approximations for flat orbits in axisymmetric stellar systems are derived and compared to results from numeric integrations. All of these approximations are more accurate than Lindblad's classical theory. I also present approximate, but canonical, maps from ordinary phase-space coordinates to a set of action-angle variables. Unfortunately, the most accurate orbit approximation leads to non-analytical R(t). However, from this approximation simple and yet very accurate estimates can be derived for the peri- and apo-centers, frequencies, and actions integrals of galactic orbits, even for high eccentricities. Moreover, further approximating this approximation allows for an analytical R(t) and still an accurate approximation to galactic orbits, even with high eccentricities.
Energy-Efficient Approximate Computation in Topaz
Achour, Sara
2014-08-19
We present Topaz, a new task-based language for computations that execute on approximate computing platforms that may occasionally produce arbitrarily inaccurate results. The Topaz implementation maps approximate tasks ...
Reactant stationary approximation in enzyme kinetics.
Hanson, Sonya M; Schnell, Santiago
2008-09-18
In the application of the quasi-steady-state approximation, it is generally assumed that there is an initial transient during which the substrate concentration remains approximately constant while the complex concentration builds up. In this paper, we address the assumption that the substrate concentration does not change significantly during this initial transient and name it the reactant stationary approximation. For the single enzyme, single substrate reaction, the reactant stationary approximation is generally considered a sufficient condition to apply the quasi-steady-state approximation. Studying the dynamic behavior of this reaction with endogenous substrate, we show that the quasi-steady-state approximation and reactant stationary approximation are two separate approximations. We discuss the consequence of this result for the determination of reaction parameters in enzyme catalyzed reactions. PMID:18714952
Finitely approximable groups and actions Christian Rosendal,
St Andrews, University of
Finitely approximable groups and actions Christian Rosendal, University of Illinois at Chicago LMS Northern Regional Meeting and Workshop on Homogeneous Structures Christian Rosendal, University of Illinois: Â· When can a countable group be finitely approximated? Christian Rosendal, University of Illinois
Finding Approximate Analytic Solutions to Differential Equations
Fernandez, Thomas
Finding Approximate Analytic Solutions to Differential Equations Using Genetic Programming Glenn of general differential equations. The approach generates a mathematical expression that is an approximate Analytic Solutions to Differential Equations Using Genetic Programming Executive Summary Differential
Bulk and surface acoustic waves in double negative metamaterial
Ivan Lisenkov; Roman Popov; Sergey Nikitov
2009-01-01
Propagating of the acoustic wave in quasi-isotropic metamaterial is considered. The composite is consisted of an isotropic background material and embedded resonators in it. The frequency of the wave is taken that the wavelength is much longer that size of inclusions and distance between them. Dispersion of effective stiffness and density is calculated by coherent potential approximation. Zones where parameters
The Velocity of Compressional Waves in Rocks to 10 Kilobars, Part 2
Francis Birch
1961-01-01
The measurements of the velocity of compressional waves up to 10 kilobars for some 250 specimens of rock, reported in part 1, are discussed with respect to the effects of porosity, alteration, anisotropy, and composition. The relations of isotropic elasticity are shown to be approximately valid for a number of examples. Reasonable agreement with theoretical values for quasi-isotropic aggregates is
APPROXIMATION METHODS IN CLASSICAL STATISTICAL MECHANICS
J. Percus
1962-01-01
The pair distribution function for a classical fluid in thermal ; equilibrium is found to be more closely approximated by the Percus and Yevick ; (Phys. Rev., 110: 1(1958)) approximation than by the Bogoliubov-Born-Green-; Kirkwood-Yvon (B.B.G.K.Y.) approximation or the hypernettedchain approximation. ; It is noted that the reason for this finding lies in the fact that the Percus and ;
APPROXIMATE DYNAMIC PROGRAMMING--II: ALGORITHMS
Powell, Warren B.
APPROXIMATE DYNAMIC PROGRAMMING--II: ALGORITHMS WARREN B. POWELL Department of Operations Research. Lacking stan- dard notation, we let Wt be the family 1 #12;2 APPROXIMATE DYNAMIC PROGRAMMING and Financial Engineering, Princeton University, Princeton, New Jersey INTRODUCTION Approximate dynamic
Approximate Dynamic Programming in Rail Operations
Powell, Warren B.
Approximate Dynamic Programming in Rail Operations June, 2007 Tristan VI Phuket Island, Thailand based on the principles of "approximate dynamic programming" (the "optimizing-simulator" back then library » Advances in approximate dynamic programming » Used to develop ADP-based optimization model
Analytical approximations for iterated bootstrap confidence intervals
Thomas J. DiCiccio; Michael A. Martin; G. Alastair Young
1992-01-01
Standard algorithms for the construction of iterated bootstrap confidence intervals are computationally very demanding, requiring nested levels of bootstrap resampling. We propose an alternative approach to constructing double bootstrap confidence intervals that involves replacing the inner level of resampling by an analytical approximation. This approximation is based on saddlepoint methods and a tail probability approximation of DiCiccio and Martin (1991).
On approximation of functions by exponential sums
Gregory Beylkin; Lucas Monzón
2005-01-01
We introduce a new approach, and associated algorithms, for the efficient approximation of functions and sequences by short linear combinations of exponential functions with complex-valued exponents and coefficients. These approximations are obtained for a finite but arbitrary accuracy and typically have significantly fewer terms than Fourier representations. We present several examples of these approximations and discuss applications to fast algorithms.
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
The GW Approximation Lucia Reining, Fabien Bruneval
Botti, Silvana
The GW Approximation Lucia Reining, Fabien Bruneval Laboratoire des Solides IrradiÂ´es Ecole Approximation Lucia Reining #12;Reminder GW-approx. GW: practice Easier? More complicated? More results results 7 References The GW Approximation Lucia Reining #12;Reminder GW-approx. GW: practice Easier? More
DISTRIBUTED VERIFICATION AND HARDNESS OF DISTRIBUTED APPROXIMATION
DISTRIBUTED VERIFICATION AND HARDNESS OF DISTRIBUTED APPROXIMATION ATISH DAS SARMA, STEPHAN HOLZER on the hardness of distributed approximation for many classical optimization problems including minimum spanning the previous hardness of approximation bound of Elkin [STOC 2004] as well as the lower bound for (exact) MST
On the hardness of approximating minimization problems
Carsten Lund; Mihalis Yannakakis
1993-01-01
We prove results indicating that it is hard to compute efficiently good approximate solutions to the Graph Coloring, Set Covering and other related minimization problems. Specifi- cally, there is an E > 0 such that Graph Coloring cannot be approximated with ratio n' unless P = NP. Set Covering cannot be approximated with ratio c log n for any c
How Accurate Is the Steady State Approximation
NSDL National Science Digital Library
The steady-state approximation is commonly used in enzyme catalysis kinetics calculations, but how much error does the approximation introduce? This Java applet allows you to visually determine the accuracy of the steady-state and pre-equilibrium approximations.
Direct Observation of Born-Oppenheimer Approximation
Cronin, Steve
Direct Observation of Born-Oppenheimer Approximation Breakdown in Carbon Nanotubes Adam W of the theoretically predicted breakdown of the Born-Oppenheimer approximation in individual single-walled carbon nanotubes. The Born-Oppenheimer (BO) or adiabatic approximation is widely used to simplify the very complex
Mathematical Analysis of Born{Oppenheimer Approximations
Hagedorn, George A.
Mathematical Analysis of Born{Oppenheimer Approximations George A. Hagedorn and Alain Joye concerning Born{Oppenheimer approximations in molecular quantum mechanics. Introduction The goal of this paper is to review rigorous mathematical results concerning Born{Oppenheimer approximations. We make
Frankenstein's Glue: Transition functions for approximate solutions
Yunes, N
2006-01-01
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate solutions together. In particular, we propose certain sufficient conditions on these functions and proof that these conditions guarantee that the joined solution still satisfies the Einstein equations to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the...
Adiabatic approximation in the second quantized formulation
Fujikawa, Kazuo [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan)
2008-02-15
Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and unambiguous criterion of the adiabatic approximation. This is illustrated for the model of Marzlin and Sanders [Phys. Rev. Lett. 93, 160408 (2004)] and a model related to the geometric phase which can be exactly diagonalized in the present sense.
? Conservative approximation for probabilistically constrained convex programs
Yuichi Takano; Jun-ya Gotoh
2010-01-01
In this paper, we address an approximate solution of a probabilistically constrained convex program (PCCP), where a convex\\u000a objective function is minimized over solutions satisfying, with a given probability, convex constraints that are parameterized\\u000a by random variables. In order to approach to a solution, we set forth a conservative approximation problem by introducing\\u000a a parameter ? which indicates an approximate
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.
Born-Oppenheimer approximation in open systems
X. L. Huang; X. X. Yi
2009-09-16
We generalize the standard Born-Oppenheimer approximation to the case of open quantum systems. We define the zeroth order Born-Oppenheimer approximation of an open quantum system as the regime in which its effective Hamiltonian can be diagonalized with fixed slowly changing variables. We then establish validity and invalidity conditions for this approximation for two kinds of dissipations--the spin relaxation and the dissipation of center-of-mass motion. As an example, the Born-Oppenheimer approximation of a two-level open system is analyzed.
Compound Poisson approximation in total variation
A. D. Barbour; Sergey Utev
1999-01-01
Poisson approximation in total variation can be successfully established in a wide variety of contexts, involving sums of weakly dependent random variables which usually take the value 0, and occasionally the value 1. If the random variables can take other positive integer values, or if there is stronger dependence between them, compound Poisson approximation may be more suitable. Stein's method,
APPROXIMATE DYNAMIC PROGRAMMING FOR OPTIMIZING OIL
Van Roy, Ben
CHAPTER 25 APPROXIMATE DYNAMIC PROGRAMMING FOR OPTIMIZING OIL PRODUCTION Zheng Wen, Louis J case. Components D R A F T February 17, 2012, 1:35pm D R A F T #12;2 APPROXIMATE DYNAMIC PROGRAMMING, the globally optimal control (global optimum) can be computed via dynamic programming (DP) [3]. However, most
Approximate Ambient Occlusion For Trees Kyle Hegeman
Paris-Sud XI, Université de
Approximate Ambient Occlusion For Trees Kyle Hegeman Stony Brook University Simon Premoze Michael- proximation to integrated visibility over a hemisphere (ambient oc- clusion) that allows interactive rendering approximation to full global illumination which has be- come quite popular is ambient occlusion [Christensen
Approximate Evolution Strategy using Stochastic Ranking
Thomas Philip Runarsson
2006-01-01
The paper describes the approximation of an evolution strategy using stochastic ranking for nonlinear programming. The aim of the approximation is to reduce the number of function evaluations needed during search. This is achieved using two surrogate models, one for the objective function and another for a penalty function based on the constraint violations. The proposed method uses a sequential
Approximate chattering arc for practical maneuvers
Jeng-Shing Chern; Zuu-Chang Hong
1992-01-01
A approximate estimate of a chattering arc is derived from a theoretically precise chattering arc which can be applied to the maneuvering of a shuttle-type vehicle. The equations of motion are examined to study constant altitude flight and give the state variables for consideration of bank or lift control in a theoretical chattering arc. The approximate chattering arc is then
Approximate Bayesian Computation in Population Genetics
Mark A. Beaumont; Wenyang Zhang; David J. Balding
2002-01-01
We propose a new method for approximate Bayesian statistical inference on the basis of summary statistics. The method is suited to complex problems that arise in population genetics, extending ideas developed in this setting by earlier authors. Properties of the posterior distribution of a parameter, such as its mean or density curve, are approximated without explicit likelihood calculations. This is
Covariance sequence approximation for parametric spectrum modeling
A. Beex; L. Scharf
1981-01-01
Parametric methods of spectrum analysis are founded on finite-dimensional models for covariance sequences. Rational spectrum approximants for continuous spectra are based on autoregressive (AR), moving average (MA), or autoregressive moving average (ARMA) models for covariance sequences. Line spectrum approximants to discrete spectra are based on cosinusoidal models for covariance sequences. In this paper we make the point that a wide
Neural Approximations and the Algebra of Gradients
NASA Astrophysics Data System (ADS)
Pacut, A.
2003-12-01
We characterize neural networks as approximators of functions and dynamic systems. Neural approximations, leading to nonlinear minimization in highly dimensional spaces, require effective gradient calculation typically realized by gradient backpropagation. We discuss the use of gradient backpropagation for static and for dynamic systems. We also show the essential difference between the common chain rule and backpropagation, which is rarely acknowledged.
Diagonal Pade approximations for initial value problems
Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.
1987-06-01
Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab.
On Syntactic versus Computational Views of Approximability
Sanjeev Khanna; Rajeev Motwani; Madhu Sudan; Umesh V. Vazirani
1994-01-01
We attempt to reconcile the two distinct views of approximation classes: syntactic and computational. Syntactic classes such as MAX SNP permit structural results and have natural complete problems, while computational classes such as APX allow us to work with classes of prob- lems whose approximability is well understood. Our results provide a syntactic characterization of computational classes and give a
On approximating planar metrics by tree metrics
Goran Konjevod; R. Ravi; F. Sibel Salman
2001-01-01
We connect the results of Bartal [4] on probabilistic approximation of metric spaces by tree metrics, and Klein, Plotkin and Rao [11] on decompositions of graphs without small Ks,s minors (such as planar graphs) to show that metrics induced by such graphs can be probabilistically approximated by tree metrics with an O(log d) distortion, where d is the diameter of
Blood Management Using Approximate Linear Programming
Shenoy, Prashant
Blood Management Using Approximate Linear Programming Marek Petrik and Shlomo Zilberstein January 13th, 2009 Marek Petrik and Shlomo Zilberstein () Blood Management Using Approximate Linear ProgrammingJanuary 13th, 2009 1 / 36 #12;Blood Inventory Management Problem Regional blood banks: Aggregate
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…
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…
Efficient Real Root Approximation Michael Kerber
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
Efficient Real Root Approximation Michael Kerber
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
Approximate mode filtering Kathleen E. Wage
Wage, Kathleen
Approximate mode filtering Kathleen E. Wage November 2004 Proceedings of the 38th Asilomar component of this work in other works must be obtained from the IEEE. #12;Approximate mode filtering email: kwage@gmu.edu Abstract-- Normal modes, the eigenfunctions of the ocean waveguide, are useful
February 13, 2012 Diophantine approximation and
Waldschmidt, Michel
;Diophantus of Alexandria (250 ±50) #12;Rational approximation The rational numbers are dense in the real : starting from the rational numbers, compute the maximal number of digits of x with the minimum;Rational approximation The rational numbers are dense in the real numbers : For any x in R and any > 0
Escape Dynamics: A Continuous Time Approximation
Dmitri Kolyuzhnov; Anna Bogomolova
2004-01-01
In this paper we provide an explicit characterization of the escape dynamics for the Phellps problem of government controlling inflation with adaptive learning of the approximate Phillips curve, alternative to the one considered by Cho, Williams and Sargent (2002) (CWS in sequel). Our approach is based on approximating the discrete-time stochastic recursive algorithm, which describes dynamics with learning in this
SPECTRAL VISCOSITY APPROXIMATIONS TO HAMILTONJACOBI SOLUTIONS
Tadmor, Eitan
SPECTRAL VISCOSITY APPROXIMATIONS TO HAMILTONÂJACOBI SOLUTIONS OLGA LEPSKY SIAM J. NUMER. ANAL. c. The spectral viscosity approximate solution of convex HamiltonÂJacobi equations with periodic boundary bounded, formally spectral accurate, and converge to the unique viscosity solution. The L1-convergence
Linear-size approximate voronoi diagrams
Sunil Arya; Theocharis Malamatos
2002-01-01
Given a set S of n points in IRd, a (t, ?)-approximate Voronoi diagram (AVD) is a partition of space into constant complexity cells, where each cell c is associated with t representative points of S, such that for any point in c, one of the associated representatives approximates the nearest neighbor to within a factor of (1 + ?).
Thick domain walls in a polynomial approximation
H. Arodz
1995-01-01
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 the 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 the Nambu-Goto equation for
Rational Approximation on the Complex Plane
Geest, Harm G. van der
Rational Approximation on the Complex Plane A Thesis submitted for the degree of Master of Science-valued functions defined on subsets of the complex plane is studied. Let f(z) be a function defined on a subset X of the complex plane C. By rational approximation of f(z) we mean to find a sequence of rational functions fn
Stable Phase Field Approximations of Anisotropic Solidification
Barrett, John W; Nürnberg, Robert
2012-01-01
We introduce unconditionally stable finite element approximations for a phase field model for solidification, which take highly anisotropic surface energy and kinetic effects into account. We hence approximate Stefan problems with anisotropic Gibbs--Thomson law with kinetic undercooling, and quasi-static variants thereof. The phase field model is given by {align*} \\vartheta\\,w_t + \\lambda\\,\\varrho(\\varphi)\\,\\varphi_t & = \
Approximate Shortest Path Queries Using Voronoi Duals
NASA Astrophysics Data System (ADS)
Honiden, Shinichi; Houle, Michael E.; Sommer, Christian; Wolff, Martin
We propose an approximation method to answer point-to-point shortest path queries in undirected edge-weighted graphs, based on random sampling and Voronoi duals. We compute a simplification of the graph by selecting nodes independently at random with probability p. Edges are generated as the Voronoi dual of the original graph, using the selected nodes as Voronoi sites. This overlay graph allows for fast computation of approximate shortest paths for general, undirected graphs. The time-quality tradeoff decision can be made at query time. We provide bounds on the approximation ratio of the path lengths as well as experimental results. The theoretical worst-case approximation ratio is bounded by a logarithmic factor. Experiments show that our approximation method based on Voronoi duals has extremely fast preprocessing time and efficiently computes reasonably short paths.
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.
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.
Frankenstein's glue: transition functions for approximate solutions
NASA Astrophysics Data System (ADS)
Yunes, Nicolás
2007-09-01
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate analytic solutions together. In particular, we propose certain sufficient conditions on these functions and prove that these conditions guarantee that the joined solution still satisfies the Einstein equations analytically to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the proposed conditions, then the joined solution does not contain any violations to the Einstein equations larger than those already inherent in the approximations. We further show that if these functions violate the proposed conditions, then the matter content of the spacetime is modified by the introduction of a matter shell, whose stress energy tensor depends on derivatives of these functions.
Frankenstein's Glue: Transition functions for approximate solutions
Nicolas Yunes
2007-08-17
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate solutions together. In particular, we propose certain sufficient conditions on these functions and proof that these conditions guarantee that the joined solution still satisfies the Einstein equations to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the proposed conditions, the joined solution does not contain any violations to the Einstein equations larger than those already inherent in the approximations. We further show that if these functions violate the proposed conditions, then the matter content of the spacetime is modified by the introduction of a matter-shell, whose stress-energy tensor depends on derivatives of these functions.
Approximate knowledge compilation: The first order case
Val, A. del [Universidad Autonoma de Madrid (Spain)
1996-12-31
Knowledge compilation procedures make a knowledge base more explicit so as make inference with respect to the compiled knowledge base tractable or at least more efficient. Most work to date in this area has been restricted to the propositional case, despite the importance of first order theories for expressing knowledge concisely. Focusing on (LUB) approximate compilation, our contribution is twofold: (1) We present a new ground algorithm for approximate compilation which can produce exponential savings with respect to the previously known algorithm. (2) We show that both ground algorithms can be lifted to the first order case preserving their correctness for approximate compilation.
Self-similar continued root approximants
NASA Astrophysics Data System (ADS)
Gluzman, S.; Yukalov, V. I.
2012-12-01
A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Padé approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.
Approximating Light Rays in the Schwarzschild Field
NASA Astrophysics Data System (ADS)
Semerák, O.
2015-02-01
A short formula is suggested that approximates photon trajectories in the Schwarzschild field better than other simple prescriptions from the literature. We compare it with various "low-order competitors," namely, with those following from exact formulas for small M, with one of the results based on pseudo-Newtonian potentials, with a suitably adjusted hyperbola, and with the effective and often employed approximation by Beloborodov. Our main concern is the shape of the photon trajectories at finite radii, yet asymptotic behavior is also discussed, important for lensing. An example is attached indicating that the newly suggested approximation is usable—and very accurate—for practically solving the ray-deflection exercise.
Stable Function Approximation in Dynamic Programming
Geoffrey J. Gordon
1995-01-01
The success of reinforcement learning in practical problems depends on the ability to combine function approximation with temporal difference methods such as value iteration. Experiments in this area have produced mixed results
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.
Casimir forces beyond the proximity approximation
Bimonte, G.
The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research ...
Approximate Confidence Intervals for Effect Sizes.
ERIC Educational Resources Information Center
Algina, James; Keselman, H. J.
2003-01-01
Investigated the approximate confidence intervals for effect sizes developed by K. Bird (2002) and proposed a more accurate method developed through simulation studies. The average coverage probability for the new method was 0.959. (SLD)
ON SPECTRAL APPROXIMATIONS IN ELLIPTICAL GEOMETRIES ...
2008-07-11
Jul 10, 2008 ... We have the following fundamental approximation result. ...... An exponential convergence rate of order O(e?cN ) is clearly observed. ... Without loss of generality, we consider only the homogeneous boundary conditions.
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.
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.
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 ...
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 ...
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 ...
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.
Polyhedral Approximation of Ellipsoidal Uncertainty Sets via ...
Andreas Bärmann, Christoph Thurner, Andreas Heidt, Sebastian Pokutta, Alexander Martin
2014-11-11
instances as well as (robustified versions of) the MIPLIB and the SNDlib. .... m constraints and over a gradient approximation having to add a potentially large number .... with two variables and m linear inequalities, it is necessary to double the ...
Bandwidth Minimization: An Approximation Algorithm for Caterpillars
James Haralambides; Fillia Makedon; Burkhard Monien
1991-01-01
The Bandwidth Minimization Problem (BMP) is the problem, given a graphG and an integerk, to map the vertices ofG to distinct positive integers, so that no edge ofG has its endpoints mapped to integers that differ by more thank. There is no known approximation algorithm for this problem, even for the case of trees. We present an approximation algorithm for
On the approximation of invariant measures
Fern Y. Hunt; Walter M. Miller
1992-01-01
Given a discrete dynamical system defined by the map t:X ?X, the density of the absolutely continuous (a.c.) invariant measure (if it exists) is the fixed point of the Frobenius-Perron operator defined on L1(X). Ulam proposed a numerical method for approximating such densities based on the computation of a fixed point of a matrix approximation of the operator. T. Y.
A Ballistic Monte Carlo Approximation of {\\pi}
Dumoulin, Vincent
2014-01-01
We compute a Monte Carlo approximation of {\\pi} using importance sampling with shots coming out of a Mossberg 500 pump-action shotgun as the proposal distribution. An approximated value of 3.136 is obtained, corresponding to a 0.17% error on the exact value of {\\pi}. To our knowledge, this represents the first attempt at estimating {\\pi} using such method, thus opening up new perspectives towards computing mathematical constants using everyday tools.
Rational approximants as analytic polyatomic potential surfaces
Stevens, R.E.; Kinsey, J.L.; Johnson, B.R. [Rice Univ., Houston, TX (United States)
1992-09-17
This report investigates one- and two-dimensional rational approximants as a convenient systematic means for analytical representation of numerical data for molecular potential energy surfaces. Discussed in this paper are the linearized least-square equations for determination of Pade approximants and the iterative method for the elimination of zeros as demonstrated for the cases of Li{sub 2} and two-mode HCN.
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.
Sensitivity approximation for robust stability and tracking
McLean, Chris Steven
1984-01-01
Sensitivity Approximation For Robust Stability and Tracking A Thesis by Chris Steven Mcl ean Submitted to the Graduate College of Texas AgcM University in partial fulfillment of the requirement for the degree of MASTER OF SCIENCE May 1984... Major Subject: Electrical Engineering Sensitivity Approximation For Robust Stability and Tracking A Thesis by Chris Steven McLean Approved as to style and content by: alph K. Cavin, III (Chairman of Committee) Shankar P. Bhattacharyya (Member...
Escape Dynamics : A Continuous Time Approximation
Dmitri Kolyuzhnov; Anna Bogomolova
2005-01-01
We use a continuous-time approximation approach to analyze dynamics of a model where government adaptively learns the Phillips curve while running monetary policy (Phellps problem). This approach is based on approximating the discrete-time dynamics with learning by a limiting continuous-time diffusion and subsequent characterization of the escape dynamics (recurrent excursions from the neighborhood of equilibrium) for this limit process. We
Generalizing the finite element method: Diffuse approximation and diffuse elements
B. Nayroles; G. Touzot; P. Villon
1992-01-01
This paper describes the new “diffuse approximation” method, which may be presented as a generalization of the widely used “finite element approximation” method. It removes some of the limitations of the finite element approximation related to the regularity of approximated functions, and to mesh generation requirements. The diffuse approximation method may be used for generating smooth approximations of functions known
Parallel SVD updating using approximate rotations
NASA Astrophysics Data System (ADS)
Goetze, Juergen; Rieder, Peter; Nossek, J. A.
1995-06-01
In this paper a parallel implementation of the SVD-updating algorithm using approximate rotations is presented. In its original form the SVD-updating algorithm had numerical problems if no reorthogonalization steps were applied. Representing the orthogonalmatrix V (right singular vectors) using its parameterization in terms of the rotation angles of n(n - 1)/2 plane rotations these reorthogonalization steps can be avoided during the SVD-updating algorithm. This results in a SVD-updating algorithm where all computations (matrix vector multiplication, QRD-updating, Kogbetliantz's algorithm) are entirely based on the evaluation and application of orthogonal plane rotations. Therefore, in this form the SVD-updating algorithm is amenable to an implementation using CORDIC-based approximate rotations. Using CORDIC-based approximate rotations the n(n - 1)/2 rotations representing V (as well as all other rotations) are only computed to a certain approximation accuracy (in the basis arctan 2i). All necessary computations required during the SVD-updating algorithm (exclusively rotations) are executed with the same accuracy, i.e., only r << w (w: wordlength) elementary orthonormal (mu) rotations are used per plane rotation. Simulations show the efficiency of the implementation using CORDIC-based approximate rotations.
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.
On Born approximation in black hole scattering
D. Batic; N. G. Kelkar; M. Nowakowski
2011-12-15
A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordstr\\"{o}m and Reissner-Nordstr\\"{o}m-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.
On Born approximation in black hole scattering
Batic, D; Nowakowski, M; 10.1140/epjc/s10052-011-1831-y
2011-01-01
A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordstr\\"{o}m and Reissner-Nordstr\\"{o}m-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.
Site superposition approximations for molecular liquids
NASA Astrophysics Data System (ADS)
Quirke, N.; Tildesley, D. J.
Various forms of the site superposition approximation (SSA) have been tested for fluids of homonuclear diatomic molecules. These approximations allow the first and second Legendre moments of the total pair distribution, function &(G)tilde;(r???1??2? to be calculated from the site-site distribution functions, g??(r??), which describe the fluids. These two Legendre moments, g100(r??) and g200(r??), together with the site-site distribution function (?g000(r??)) can be used to calculate many of the structural and thermodynamic properties of a simple ISM fluid. The most accurate SSA for calculating the gl00(r??) includes correlations along only two of the intermolecular distance which define the geometry of a molecular pair. This leads us to suggest a new family of simpler approximations, one of which is exact at low density and which accurately reproduces the pressure and mean squared torque of the fluids.
Eight-moment approximation solar wind models
NASA Technical Reports Server (NTRS)
Olsen, Espen Lyngdal; Leer, Egil
1995-01-01
Heat conduction from the corona is important in the solar wind energy budget. Until now all hydrodynamic solar wind models have been using the collisionally dominated gas approximation for the heat conductive flux. Observations of the solar wind show particle distribution functions which deviate significantly from a Maxwellian, and it is clear that the solar wind plasma is far from collisionally dominated. We have developed a numerical model for the solar wind which solves the full equation for the heat conductive flux together with the conservation equations for mass, momentum, and energy. The equations are obtained by taking moments of the Boltzmann equation, using an 8-moment approximation for the distribution function. For low-density solar winds the 8-moment approximation models give results which differ significantly from the results obtained in models assuming the gas to be collisionally dominated. The two models give more or less the same results in high density solar winds.
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.
Discontinuous Galerkin Methods with Trefftz Approximation
Kretzschmar, Fritz; Tsukerman, Igor; Weiland, Thomas
2013-01-01
We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space-time Trefftz-type basis functions that satisfy the underlying partial differential equations and the respective interface boundary conditions exactly in an element-wise fashion. The basis functions can be of arbitrary high order, and we demonstrate spectral convergence in the $\\Lebesgue_2$-norm. In this context, spectral convergence is obtained with respect to the approximation error in the entire space-time domain of interest, i.e. in space and time simultaneously. Formulating the approximation in terms of a space-time Trefftz basis makes high order time integration an inherent property of the method and clearly sets it apart from methods, that employ a high order approximation in space only.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Selfconsistent approximations, symmetries and choice of representation
Stefan Leupold
2006-10-26
In thermal field theory selfconsistent (Phi-derivable) approximations are used to improve (resum) propagators at the level of two-particle irreducible diagrams. At the same time vertices are treated at the bare level. Therefore such approximations typically violate the Ward identities connected to internal symmetries. Examples are presented how such violations can be tamed by a proper choice of representation for the fields which describe the system under consideration. These examples cover the issue of massless Goldstone bosons in the linear sigma model and the Nambu--Jona-Lasinio model and the problem of current conservation in theories with massive vector mesons.
A numerical approximation to distribution function
Tuttle, Keith Allan
1977-01-01
EXTRAPOLATION 21 28 REFERENCES 37 VITA 3B CHAPTER I INTRODUCTION and let Q c jR be the uni. t cube n n We investigate the following problem. Let x = (x , . . . , x ) I jR I' ''n Q = ((x , . . . , x ) ~ 0 & x & 1 for k = 1, 2, . . . , n). Given a real... to a distribution function for f(x , . . . , x ). An approximation is 1 n constructed that uses the gradient of the function f and an approx- imation is constructed when the gradient of f is not known. An analysis of the error in both approximations...
Approximate Solutions of Perturbed Nonlinear Schrödinger Equations
NASA Astrophysics Data System (ADS)
Cheng, Xue-Ping; Ye, Li-Jun; Lin, Ji
2007-08-01
By applying Lou's direct perturbation method to perturbed nonlinear Schrödinger equation and the critical nonlinear Schrödinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schrödinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations.
On Syntactic versus Computational Views of Approximability
Sanjeev Khanna; Rajeev Motwani; Madhu Sudan; Umesh V. Vazirani
1998-01-01
.
Characterizing inflationary perturbations: The uniform approximation
Habib, Salman [T-8, Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Heinen, Andreas [Institut fuer Physik, Universitaet Dortmund, D - 44221 Dortmund (Germany); Heitmann, Katrin [ISR-1, ISR-Division, MS D436, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Jungman, Gerard [T-6, Theoretical Division, MS B227, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Molina-Paris, Carmen [Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT (United Kingdom)
2004-10-15
The spectrum of primordial fluctuations from inflation can be obtained using a mathematically controlled, and systematically extendable, uniform approximation. Closed-form expressions for power spectra and spectral indices may be found without making explicit slow-roll assumptions. Here we provide details of our previous calculations, extend the results beyond leading-order in the approximation, and derive general error bounds for power spectra and spectral indices. Already at next-to-leading-order, the errors in calculating the power spectrum are less than a percent. This meets the accuracy requirement for interpreting next-generation cosmic microwave background observations.
Bronchopulmonary segments approximation using anatomical atlas
NASA Astrophysics Data System (ADS)
Busayarat, Sata; Zrimec, Tatjana
2007-03-01
Bronchopulmonary segments are valuable as they give more accurate localization than lung lobes. Traditionally, determining the segments requires segmentation and identification of segmental bronchi, which, in turn, require volumetric imaging data. In this paper, we present a method for approximating the bronchopulmonary segments for sparse data by effectively using an anatomical atlas. The atlas is constructed from a volumetric data and contains accurate information about bronchopulmonary segments. A new ray-tracing based image registration is used for transferring the information from the atlas to a query image. Results show that the method is able to approximate the segments on sparse HRCT data with slice gap up to 25 millimeters.
Very fast approximate reconstruction of MR images.
Angelidis, P A
1998-11-01
The ultra fast Fourier transform (UFFT) provides the means for a very fast computation of a magnetic resonance (MR) image, because it is implemented using only additions and no multiplications at all. It achieves this by approximating the complex exponential functions involved in the Fourier transform (FT) sum with computationally simpler periodic functions. This approximation introduces erroneous spectrum peaks of small magnitude. We examine the performance of this transform in some typical MRI signals. The results show that this transform can very quickly provide an MR image. It is proposed to be used as a replacement of the classically used FFT whenever a fast general overview of an image is required. PMID:9822852
ANALOG QUANTUM NEURON FOR FUNCTIONS APPROXIMATION
A. EZHOV; A. KHROMOV; G. BERMAN
2001-05-01
We describe a system able to perform universal stochastic approximations of continuous multivariable functions in both neuron-like and quantum manner. The implementation of this model in the form of multi-barrier multiple-silt system has been earlier proposed. For the simplified waveguide variant of this model it is proved, that the system can approximate any continuous function of many variables. This theorem is also applied to the 2-input quantum neural model analogical to the schemes developed for quantum control.
Supersymmetric electroweak baryogenesis in the WKB approximation
James M. Cline; Michael Joyce; Kimmo Kainulainen
1998-01-01
We calculate the baryon asymmetry generated at the electroweak phase transition in the minimal supersymmetric standard model, treating the particles in a WKB approximation in the bubble wall background. A set of diffusion equations for the particle species relevant to baryon generation, including source terms arising from the CP violation associated with the complex phase ? of the ? parameter,
Matching Based Augmentations for Approximating Connectivity
Narasayya, Vivek
;Warmup: FGM Algorithm for Asymmetric TSP Â· Problem: Given an complete bidirected graph with asymmetric Â· Not clear how to approximate in two iterations #12;FGM Algorithm Â· [Frieze, Galbiati, Maffioli '82 #12;FGM Algorithm Example #12;FGM Algorithm Example #12;FGM Algorithm Example #12;FGM Algorithm
Matching Based Augmentations for Approximating Connectivity Problems
R. Ravi
2006-01-01
We describe a very simple idea for designing approximation algorithms for connectivity problems: For a spanning tree problem, the idea is to start with the empty set of edges, and add matching paths between pairs of components in the current graph that have desirable properties in terms of the objective function of the spanning tree prob- lem being solved. Such
Analytic approximation of matrix functions in Lp
Laurent Baratchart; F. L. Nazarov; V. V. Peller
2009-01-01
We consider the problem of approximation of matrix functions of class Lp on the unit circle by matrix functions ana- lytic in the unit disk in the norm of Lp, 2 p < 1. For an m n matrix function in Lp, we consider the Hankel operator H : Hq(Cn) ! H2 (C m), 1=p + 1=q = 1=2. It
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.
A nonuniform bound for translated Poisson approximation
Barbour, Andrew
of total variation distance. In order to have good approximation in this sense, it is necessary for L error, with respect to the stronger, total variation distance, is of essentially the same order (Barbour to total variation distance. The translated Poisson distribution is chosen to have the same mean as W
Quickly Approximating the Distance Between Two Objects
NASA Technical Reports Server (NTRS)
Hammen, David
2009-01-01
A method of quickly approximating the distance between two objects (one smaller, regarded as a point; the other larger and complexly shaped) has been devised for use in computationally simulating motions of the objects for the purpose of planning the motions to prevent collisions.
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 2ÂD dictionary and generates
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.
Mathematical Analysis of BornOppenheimer Approximations
Joye, Alain
results con- cerning the standard timeÂdependent BornÂOppenheimer approximation in Section 2. We describe extensions to accommodate avoided crossings with small gaps. 1. A Historical Introduction In 1927, just one function. Their expansion for the energy was particularly beautiful. The zeroth order term
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.
Can Distributional Approximations Give Exact Answers?
ERIC Educational Resources Information Center
Griffiths, Martin
2013-01-01
Some mathematical activities and investigations for the classroom or the lecture theatre can appear rather contrived. This cannot, however, be levelled at the idea given here, since it is based on a perfectly sensible question concerning distributional approximations that was posed by an undergraduate student. Out of this simple question, and…
Approximation Algorithms for Flexible Job Shop Problems
Solis-Oba, Roberto
shop scheduling problem called the flexible job shop problem [1], which models a wide variety of probApproximation Algorithms for Flexible Job Shop Problems Klaus Jansen 1 , Monaldo Mastrolilli 2 of Western Ontario, Canada solis@brown.csd.uwo.ca x Abstract. The Flexible Job Shop Problem
Approximating Spanning Tree with Weighted Inner Nodes
a minimum spanning tree with both edge weights and inner node (non-leaf node) weights. This problem is NP is the maximum degree of the graph. Keywords: Minimum spanning tree, approximation algorithm, NP-hard 1 Introduction 1.1 Problem Statement Minimum spanning trees have been widely studied and many efficient
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.
sample approximations of multiobjective stochastic optimization ...
2014-11-22
Approximate optimal solutions are defined as weakly Pareto efficient ones ... stochastic programming problem already contains a vector criterion f(x, g(x, ?)), .... and its ?-optimal subset Y ?(?) and we have to determine what set could be con- ... the set of linear ?w, Eg(x, ?)?, w ? W, or nonlinear U(Eg(x, ?)), U ? U scalar.
Approximate Frequency Counts over Data Streams
Gurmeet Singh Manku; Rajeev Motwani
2002-01-01
We present algorithms for computing frequency counts exceeding a user-specified threshold over data streams. Our algorithms are simple and have provably small memory footprints. Although the output is approximate, the error is guaranteed not to exceed a user-specified parameter. Our algo- rithms can easily be deployed for streams of single- ton items like those found in IP network monitor- ing.
Normal Approximation for Hierarchical Structures Larry Goldstein
Goldstein, Larry
Normal Approximation for Hierarchical Structures Larry variables {Xn}n 0 by Xn+1 = F (Xn,1, * *. .,.Xn,k), where Xn,iare i.i.d. as Xn. Such sequences arise on the rate of convergence to the normal are d* *erived for the hierarchical sequence generated
Constraint Satisfaction: The Approximability of Minimization Problems
Sanjeev Khanna; Madhu Sudan; Luca Trevisan
1997-01-01
This paper continues the work initiated by Creignou (5) and Khanna, Sudan and Williamson (15) who classify maximization problems derived from Boolean constraint satisfaction. Here we study the approximability ofmin- imization problems derived thence. A problem in this framework is characterized by a collection of \\
Learning Linear Threshold Approximations Using Perceptrons
Bylander, Tom
Learning Linear Threshold Approximations Using Perceptrons Tom Bylander Division of Mathematics perceptrons. The central result is as follows. Suppose there exists a vector ~ w \\Lambda of n weights of j ~ w \\Lambda \\Delta ~xj is oe. Then, with probability 1 \\Gamma ffi, the perceptron achieves
An Adaptive Linear Approximation Algorithm for Copositive ...
2008-09-18
Department of Mathematics, Technische Universität Darmstadt, Schloßgartenstr. 7, ... We present new polyhedral inner and outer approximations of the copositive ..... ear form xT Ay on the diagonal of the compact set ?S × ?S, followed by a continuity ...... is Example 5.3 from [4] and arises in a model in population genetics.
Symmetric tensor approximation hierarchies for the completely ...
2012-11-09
Nov 9, 2012 ... Mathematics Subject Classification: 90C05, 90C22, 90C25, 90C27 ... In the literature, several inner-approximation hierarchies exist for the ...... J. Löfberg, Yalmip: A toolbox for modeling and optimization in matalb, Pro- ... ear programs under objective uncertainty: A completely positive representation,.
K-41 optimised approximate deconvolution models
William Layton; Iuliana Stanculescu
2007-01-01
If the Navier-Stokes equations are averaged with a local, spacial convo- lution type lter, = g , the resulting system is not closed due to the ltered nonlinear term uu. An approximate deconvolution operator D is a bounded linear operator which satises
Chebychev optimized approximate deconvolution models of turbulence
William J. Layton; Iuliana Stanculescu
2009-01-01
If the Navier-Stokes equations are averaged with a local, spacial convolution type filter, = g , the resulting system is not closed due to the filtered nonlinear term uu. An approximate deconvolution operator D is a bounded linear operator which satisfies u = D(u) + O( ),
Semantic Types and Approximation for Featherweight Java
van Bakel, Steffen
of Computing, Imperial College London, 180 Queen's Gate, London SW7 2BZ, UK rnr07@doc.ic.ac.uk svb an approximation result, which leads to a sufficient condition for the characterisation of head be seen as a notion of `flow analysis' in that assignable types express how expressions can interact
Distributed Verification and Hardness of Distributed Approximation
Distributed Verification and Hardness of Distributed Approximation Atish Das Sarma Google Foundation (BSF). Permission to make digital or hard copies of all or part of this work for personal on the hardness of distributed approxi- mation for many classical optimization problems including minimum spanning
Approximation Algorithms for NP-Hard Problems
1997-01-01
Approximation algorithms have developed in response to the impossibility of solving a great variety of important optimization problems. Too frequently, when attempting to get a solution for a problem, one is confronted with the fact that the problem is NP-hard. This, in the words of Garey and Johnson, means \\
Approximate Range Searching Department of Computer Science
Mount, David
Approximate Range Searching Sunil Arya Department of Computer Science The Hong Kong University and Inst. for Advanced Computer Studies University of Maryland College Park, MD 20742 Abstract The range is assumed, the problem cannot be solved in polylogarithmic time, except for the case of orthogonal ranges
Approximate Range Searching Department of Computer Science
Arya, Sunil
Approximate Range Searching Sunil Arya Department of Computer Science The Hong Kong University and Institute for Advanced Computer Studies University of Maryland College Park, MD 20742 Abstract The range is assumed, the problem cannot be solved in polylogarithmic time, except for the case of orthogonal ranges
An orthonormalization procedure for multivariable function approximation
NASA Technical Reports Server (NTRS)
Ingram, H. L.
1966-01-01
Where a function of several variables is given numerically in tabular form, an orthonormalization technique allows an approximation of the numerical data to be determined in a convenient functional form. In this technique, the speed and accuracy of coefficient computation are much improved.
Approximating Dependency Graphs Using Tree Automata Techniques
Aart Middeldorp
2001-01-01
The dependency pair method of Arts and Giesl is the most powerful technique for proving termination of term rewrite systems au- tomatically. We show that the method can be improved by using tree automata techniques to obtain better approximations of the dependency graph. This graph determines the ordering constraints that need to be solved in order to conclude termination. We
Auxiliary basis sets to approximate Coulomb potentials
Karin Eichkorn; Oliver Treutler; Holger Öhm; Marco Häser; Reinhart Ahlrichs; Marco Ser
1995-01-01
We demonstrate accuracy and computational efficiency resulting from an approximate treatment of Coulomb operators which is based on the expansion of molecular electron densities in atom-centered auxiliary basis sets. This is of special importance in density functional methods which separate the treatment of Coulomb and exchange-correlation terms. Auxiliary basis sets are optimized as much as possible for isolated atoms and
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.
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
Thick domain walls in a polynomial approximation
H. Arodz
Relativistic domain walls are studied in the framework of a polynomial ap- proximation 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
Double unresolved approximations to multiparton scattering amplitudes
NASA Astrophysics Data System (ADS)
Campbell, J. M.; Glover, E. W. N.
1998-08-01
We present approximations to tree-level multiparton scattering amplitudes which are appropriate when two partons are unresolved. These approximations are required for the analytic isolation of infrared singularities of n + 2 parton scattering processes contributing to the next-to-next-to-leading order corrections to n jet cross sections. In each case the colour ordered matrix elements factorise and yield a function containing the singular factors multiplying the n-parton amplitudes. When the unresolved particles are colour unconnected, the approximations are simple products of the familiar eikonal and Altarelli-Parisi splitting functions used to describe single unresolved emission. However, when the unresolved particles are colour connected the factorisation is more complicated and we introduce new and general functions to describe the triple collinear and soft/collinear limits in addition to the known double soft gluon limits of Berends and Giele. As expected the triple collinear splitting functions obey an N = 1 SUSY identify. To illustrate the use of these double unresolved approximations, we have examined the singular limits of the tree-level matrix elements for e+e- ? 5 partons when only three partons are resolved. When integrated over the unresolved regions of phase space, these expressions will be of use in evaluating the O(? s3) corrections to the three-jet rate in electron-positron annihilation.
Approximating geometric crossover in semantic space
Krzysztof Krawiec; Pawel Lichocki
2009-01-01
We propose a crossover operator that works with genetic programming trees and is approximately geometric crossover in the semantic space. By defining semantic as program's evaluation profile with respect to a set of fitness cases and constraining to a specific class of metric-based fitness functions, we cause the fitness landscape in the semantic space to have perfect fitness-distance correlation. The
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
Approximate dynamic programming of continuous annealing process
Yingwei Zhang; Chao Guo; Xue Chen; Yongdong Teng
2009-01-01
Approximate dynamic programming method is a combination of neural networks, reinforcement learning, as well as the idea of dynamic programming. It is an online control method which bases on actual data rather than a precise mathematical model of the system. This method is suitable for the optimal control of nonlinear systems, and can avoid the problem of dimension disaster. It
Universitat Regensburg Stable phase field approximations
Regensburg, UniversitÃ¤t - Naturwissenschaftliche FakultÃ¤t I
unconditionally stable finite element approximations for a phase field model for solidification, which take highly parabolic partial differential equations. Since phase field models describe very unstable solidification model for anisotropic solidification in the literature. As the phase field model and its quasi
On the Landau approximation in plasma physics
R. ALEXANDRE; C. VILLANI
2004-01-01
This paper studies the approximation of the Boltzmann equation by the Landau equation in a regime when grazing collisions prevail. While all previous results in the subject were limited to the spatially homogeneous case, here we manage to cover the general, space-dependent situation, assuming only basic physical estimates of finite mass, energy, entropy and entropy production. The proofs are based
ON THE LANDAU APPROXIMATION IN PLASMA PHYSICS
Villani, CÃ©dric
ON THE LANDAU APPROXIMATION IN PLASMA PHYSICS R. ALEXANDRE AND C. VILLANI Abstract. This paper of his important works in plasma physics, established the kinetic equation which is now called after him interacting through binary collisions. Since then, this equation has been widely in use in plasma physics, see
Semiparametric Efficiency of GMM under Approximate Constraints
Rochet, Paul
2010-01-01
Generalized empirical likelihood and generalized method of moments are well spread methods of resolution of inverse problems in econometrics. Each method defines a specific semiparametric model for which it is possible to calculate efficiency bounds. By this approach, we provide a new proof of Chamberlain's result on optimal GMM. We also discuss conditions under which GMM estimators remain efficient with approximate moment constraints.
Counting independent sets using the Bethe approximation
Chertkov, Michael [Los Alamos National Laboratory; Chandrasekaran, V [MIT; Gamarmik, D [MIT; Shah, D [MIT; Sin, J [MIT
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.
Zhou, Y. (Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794 (USA)); Stell, G. (Department of Chemistry, State University of New York at Stony Brook, Stony Brook, NY (USA) Department of Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, NY (USA))
1990-05-01
A formally exact nonlocal density-functional expansion procedure for direct correlation functions developed earlier by Stell for a homogeneous system, and extended by Blum and Stell, Sullivan and Stell, and ourselves to various inhomogeneous systems, is used here to derive nonlocal integral-equation approximations. Two of the simplest of these approximations (zeroth order), which we shall characterize here as the hydrostatic Percus--Yevick (HPY) approximation and the hydrostatic hypernetted-chain (HHNC) approximation, respectively, are shown to be capable of accounting for wetting transitions on the basis of general theoretical considerations. Before turning to such transitions, we investigate in this first paper of a series the case of homogeneous hard-sphere fluids and hard spheres near a hard wall as well as the case of hard spheres inside a slit pore. Numerical results show that the HHNC approximation is better than the HNC approximation for both the homogeneous and inhomogeneous systems considered here while the HPY approximation appears to overcorrect the PY approximation.
Approximating Mathematical Semantic Web Services Using Approximation Formulas and Numerical Methods
Paris-Sud XI, UniversitÃ© de
Approximating Mathematical Semantic Web Services Using Approximation Formulas and Numerical Methods.andreica@cs.pub.ro) Abstract: Mathematical semantic web services are very useful in practice, but only a small number of a mathematical semantic web service, from its semantic description, using existing mathematical semantic web
Second derivatives for approximate spin projection methods
NASA Astrophysics Data System (ADS)
Thompson, Lee M.; Hratchian, Hrant P.
2015-02-01
The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical second derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.
Bisimulation-based Approximate Lifted Inference
Sen, Prithviraj; Getoor, Lise
2012-01-01
There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the first-order model is given as input to the system. Here, we describe lifted inference algorithms that determine symmetries and automatically lift the probabilistic model to speedup inference. In particular, we describe approximate lifted inference techniques that allow the user to trade off inference accuracy for computational efficiency by using a handful of tunable parameters, while keeping the error bounded. Our algorithms are closely related to the graph-theoretic concept of bisimulation. We report experiments on both synthetic and real data to show that in the presence of symmetries, run-times for inference can be improved significantly, with approximate lifted inference providing orders of magnitude speedup over ground inference.
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.
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.
Thick domain walls in a polynomial approximation
Arodz, H
1995-01-01
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.
Thick domain walls in a polynomial approximation
NASA Astrophysics Data System (ADS)
Arod?, H.
1995-07-01
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 the 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 the 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 the curvatuve of the core. We find that curving a static domain wall is associated with an increase of its width. As an example, the evolution of a toroidal domain wall is investigated.
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.
Dynamic diffusion as approximation of quantum behavior
Yuri Ozhigov
2010-11-08
The approximation of quantum unitary dynamics of a particle by a swarm of point wise classical samples of this particle is proposed. Quantum mechanism of speedup rests on the creation and annihilation of absolutely rigid bons, which join samples in dot wise symplexes so that the density of swarm approximate the quantum probability. This mechanism does not require differentiation of a density that is adventage of this method over Bohm's quantum hydrodynamics: our method is applicable to many particles in entangled states. In multi particle case the limitation of total number of samples gives the natural model of decoherence, e.g. the divergency from the exact solution of Shredinger equation. Intensity of creation - annihilation of bonds between samples substantially depends on the grain of spatial resolution, which makes impossible to pass to the limits as in a classical substance; this is the price for the scalability of a model to many particles.
Private Medical Record Linkage with Approximate Matching
Durham, Elizabeth; Xue, Yuan; Kantarcioglu, Murat; Malin, Bradley
2010-01-01
Federal regulations require patient data to be shared for reuse in a de-identified manner. However, disparate providers often share data on overlapping populations, such that a patient’s record may be duplicated or fragmented in the de-identified repository. To perform unbiased statistical analysis in a de-identified setting, it is crucial to integrate records that correspond to the same patient. Private record linkage techniques have been developed, but most methods are based on encryption and preclude the ability to determine similarity, decreasing the accuracy of record linkage. The goal of this research is to integrate a private string comparison method that uses Bloom filters to provide an approximate match, with a medical record linkage algorithm. We evaluate the approach with 100,000 patients’ identifiers and demographics from the Vanderbilt University Medical Center. We demonstrate that the private approximation method achieves sensitivity that is, on average, 3% higher than previous methods. PMID:21346965
Approximation Algorithms for a Triangle Enclosure Problem
Given a set S of n points in the plane, we want to find a triangle, with vertices in S, such that the number of points of S enclosed by it is maximum. A solution can be found by considering all () n 3 triples of points in S. We show that, by considering only triangles with at least 1, 2, or 3 vertices on the convex hull of S, we obtain various approximation algorithms that run in o(n3) time. 1
Kerstan's method for compound Poisson approximation
Bero Roos
2003-01-01
We consider the approximation of the distribution of the\\u000asum of independent but not necessarily identically distributed random\\u000avariables by a compound Poisson distribution and also by a finite\\u000asigned measure of higher accuracy. Using Kerstan's method, some new\\u000abounds for the total variation distance are presented. Recently,\\u000aseveral authors had difficulties applying Stein's method to\\u000athe problem given. For
On Surface Approximation Using Developable Surfaces
H.-Y. Chen; I.-K. Lee; Stefan Leopoldseder; Helmut Pottmann; Thomas Randrup; Johannes Wallner
1999-01-01
We introduce a method for approximating a given surface by a developablesurface. It will be either a G1surface consisting of pieces of cones or cylindersof revolution or a GrNURBS developable surface. Our algorithm will also dealproperly with the problems of reverse engineering and produce robust approximationof given scattered data. The presented technique can be applied incomputer aided manufacturing, e.g. in
Asymptotic approximation of hyperbolic weakly nonlinear systems
A. Krylovas; R. Ciegis
2002-09-30
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems. We consider the resonance conditions for some classes of solutions. The averaged system can be solved numerically in the resonance case. The shallow water problem is considered as an example of the resonance system. Results of numerical experiments are presented.
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.
Approximation by superpositions of a sigmoidal function
G. Cybenko
1989-01-01
In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of\\u000a affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results\\u000a settle an open question about representability in the class of single hidden
Approximate Graph Coloring by Semidefinite Programming
David R. Karger; Rajeev Motwani; Madhu Sudan
1994-01-01
We consider the problem of coloring k-colorable graphs with the fewest possible colors. We present a randomized polynomial time algorithm that colors a 3-colorable graph on n vertices with min{O(?1\\/3 log1\\/2 ?log n), O(n1\\/4 log1\\/2 n)} colors whereis the maximum degree of any vertex. Besides giving the best known approximation ratio in terms of n, this marks the first non-trivial
Tractability of approximating multivariate linear functionals
Erich Novak; Henryk Wo?niakowski
2010-01-01
We review selected tractability results for approximating linear tensor product functionals defined over reproducing kernel\\u000a Hilbert spaces. This review is based on Volume II of our book Tractability of Multivariate Problems. In particular, we show that all nontrivial linear tensor product functionals defined over a standard tensor product unweighted\\u000a Sobolev space suffer the curse of dimensionality and therefore they are
Architecture of Approximate Deconvolution Models of Turbulence
A. Labovschii; W. Layton; C. Manica; M. Neda; L. Rebholz; I. Stanculescu; C. Trenchea
This report presents the mathematical foundation of approximate deconvolution LES models together with the model phenomenology\\u000a downstream of the theory. This mathematical foundation now begins to be complete for the incompressible Navier–Stokes equations.\\u000a It is built upon averaging, deconvolving and addressing closure so as to obtain the physically correct energy and helicity\\u000a balances in the LES model. We show how
Approximate active fault detection and control
NASA Astrophysics Data System (ADS)
Škach, Jan; Pun?ochá?, Ivo; Šimandl, Miroslav
2014-12-01
This paper deals with approximate active fault detection and control for nonlinear discrete-time stochastic systems over an infinite time horizon. Multiple model framework is used to represent fault-free and finitely many faulty models. An imperfect state information problem is reformulated using a hyper-state and dynamic programming is applied to solve the problem numerically. The proposed active fault detector and controller is illustrated in a numerical example of an air handling unit.
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.
Universal Gaussian approximations under random censorship
Sándor Csörg?
1996-01-01
Universal Gaussian approximations are established for empirical cumulative hazard and product-limit processes under random censorship. They hold uniformly up to some large order statistics in the sample, with the\\u000aapproximation rates depending on the order of these statistics, and require no assumptions on the censoring mechanism. Weak convergence results and laws of the iterated logarithm follow on the whole line
Approximating Maximum Diameter-Bounded Subgraphs
Yuichi Asahiro; Eiji Miyano; Kazuaki Samizo
2010-01-01
\\u000a The paper studies the maximum diameter-bounded subgraph problem (MaxDBS for short) which is defined as follows: Given an n-vertex graph G and a fixed integer d???1, the goal is to find its largest subgraph of the diameter d. If d?=?1, the problem is identical to the maximum clique problem and thus it is NP{\\\\cal NP}-hard to approximate MaxDBS to within
Approximating Effect Of Spherical Radiation Pattern
NASA Technical Reports Server (NTRS)
Sickles, Louis, II
1994-01-01
Time-division multiple-access TDMA multichannels radio communication system implements scheme of temporal and spatial multiplexing of signals to approximate effect of spherical antenna radiation pattern. Signal to be transmitted sped up by factor of n and transmitted in n replicas via n antennas. During reception, incoming signal processed by use of maximum-signal-selection or diversity-reception demodulated-signal-combining technique.
Microscopic justification of the equal filling approximation
Perez-Martin, Sara; Robledo, L. M. [Departamento de Fisica Teorica C-XI, Facultad de Ciencias, Universidad Autonoma de Madrid, 28049 Madrid (Spain)
2008-07-15
The equal filling approximation, a procedure widely used in mean-field calculations to treat the dynamics of odd nuclei in a time-reversal invariant way, is justified as the consequence of a variational principle over an average energy functional. The ideas of statistical quantum mechanics are employed in the justification. As an illustration of the method, the ground and lowest-lying states of some octupole deformed radium isotopes are computed.
Gaussian Approximation Potentials: a brief tutorial introduction
Bartók, Albert P
2015-01-01
We present a swift walk-through of our recent work that uses machine learning to fit interatomic potentials based on quantum mechanical data. We describe our Gaussian Approximation Potentials (GAP) framework, discussing a variety of descriptors, how to train the model on total energies and derivatives and the simultaneous use of multiple models. We also show a small example using QUIP, the software sandbox implementation of GAP that is available for non-commercial use.
Onsager principle as a tool for approximation
NASA Astrophysics Data System (ADS)
Doi, Masao
2015-02-01
Onsager principle is the variational principle proposed by Onsager in his celebrated paper on the reciprocal relation. The principle has been shown to be useful in deriving many evolution equations in soft matter physics. Here the principle is shown to be useful in solving such equations approximately. Two examples are discussed: the diffusion dynamics and gel dynamics. Both examples show that the present method is novel and gives new results which capture the essential dynamics in the system.
Viscosity approximation methods for nonexpansive mappings
Hong-Kun Xu
2004-01-01
Viscosity approximation methods for nonexpansive mappings are studied. Consider a nonexpansive self-mapping T of a closed convex subset C of a Banach space X. Suppose that the set Fix(T) of fixed points of T is nonempty. For a contraction f on C and t?(0,1), let xt?C be the unique fixed point of the contraction x?tf(x)+(1?t)Tx. Consider also the iteration process
Piecewise linear approximations in nonconvex nonsmooth optimization
M. Gaudioso; E. Gorgone; M. F. Monaco
2009-01-01
We present a bundle type method for minimizing nonconvex nondifferentiable functions of several variables. The algorithm is\\u000a based on the construction of both a lower and an upper polyhedral approximation of the objective function. In particular,\\u000a at each iteration, a search direction is computed by solving a quadratic program aiming at maximizing the difference between\\u000a the lower and the upper
Approximation in the finite element method
Gilbert Strang
1972-01-01
Summary The rate of convergence of the finite element method depends on the order to which the solutionu can be approximated by the trial space of piecewise polynomials. We attempt to unify the many published estimates, by proving that if the trial space is complete through polynomials of degreek-1, then it contains a functionvh such that |u-vh|s?chk-s|u|k. The derivatives of
Computing Machine-Efficient Polynomial Approximations
Muller, Jean-Michel
Lyon Cedex 07 France; email: Nicolas.Brisebarre@ens-lyon.fr; J.-M. Muller, LIP/ArÂ´enaire (CNRS-ENS LyonComputing Machine-Efficient Polynomial Approximations NICOLAS BRISEBARRE UniversitÂ´e J. Monnet, St- Â´Etienne and LIP-E.N.S. Lyon JEAN-MICHEL MULLER CNRS, LIP-ENS Lyon and ARNAUD TISSERAND INRIA, LIP-ENS Lyon
Extensions of Kesten's Adaptive Stochastic Approximation Method
H. J. Kushner; T. Gavin
1973-01-01
Kesten proposed a method for adjusting the coefficients of a scalar stochastic approximation process, and proved w.p. 1 convergence. A family of multidimensional processes for function minimization are treated here. Each method consists of a sequence of truncated one-dimensional procedures of the Kesten type. The methods seem to offer a number of advantages over the usual Kiefer-Wolfowitz procedures, and are
Approximate multiphase flow modeling by characteristic methods
NASA Astrophysics Data System (ADS)
Weaver, J. W.
1991-05-01
The flow of petroleum hydrocarbons, organic solvents and other liquids that are immiscible with water presents the nation with some of the most difficult subsurface remediation problems. One aspect of contaminant transport associated releases of such liquids is the transport as a water-immiscible liquid phase. Approximate models of immiscible flow are presented for two- and three-phase flow. The approximations are constructed by representing the flow by hyperbolic equations which have method of characteristics solutions. This approximation has the additional benefit of being based on the fundamental wave behavior of the flow, which is revealed by the solutions of the models. An important result is that for three-phase flow, two flow regimes exist. The first is characterized by the displacement of one of the liquids into a bank which moves ahead of the other liquid. The second is characterized by almost complete bypassing of a liquid by the other. The occurrence of the flow regimes is dependent on the organic liquid properties, soil type and the initial amounts of the fluids present.
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.
VISCOSITY AND RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
Tzavaras, Athanasios E.
VISCOSITY AND RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS deal with the approximation of conservation * *laws via viscosity or relaxation. The following topics are covered: The general structure of viscosity and relaxation approximations is discu
Interfaces Free Boundaries (2003), 483--529 Rigorous lubrication approximation
Otto, Felix
2003-01-01
Interfaces Free Boundaries (2003), 483--529 Rigorous lubrication approximation LORENZO GIACOMELLI form 2003] rigorously carry lubrication approximation liquid which spreads driven surface tension evolution. show in particular contactÂangle condition is preserved in the lubrication approximation
Heuer, Norbert
Galerkin (SUPG) approximation for the constitutive equation. In this paper we analyze a Crank discretization with a SUPG discretization of the constitutive equation and showed that, in IR #19; d , the method
Quantum entropic security and approximate quantum encryption
Simon Pierre Desrosiers; Frédéric Dupuis
2010-04-15
We present full generalisations of entropic security and entropic indistinguishability to the quantum world where no assumption but a limit on the knowledge of the adversary is made. This limit is quantified using the quantum conditional min-entropy as introduced by Renato Renner. A proof of the equivalence between the two security definitions is presented. We also provide proofs of security for two different cyphers in this model and a proof for a lower bound on the key length required by any such cypher. These cyphers generalise existing schemes for approximate quantum encryption to the entropic security model.
Approximate risk assessment prioritizes remedial decisions
Bergmann, E.P. (Southwest Research Inst., San Antonio, Texas (United States))
1993-08-01
Approximate risk assessment (ARA) is a management tool that prioritizes cost/benefit options for risk reduction decisions. Management needs a method that quantifies how much control is satisfactory for each level of risk reduction. Two risk matrices develop a scheme that estimates the necessary control a unit should implement with its present probability and severity of consequences/disaster. A second risk assessment matrix attaches a dollar value to each failure possibility at various severities. Now HPI operators can see the cost and benefit for each control step contemplated and justify returns based on removing the likelihood of the disaster.
Direct Interaction Approximation of Magnetohydrodynamic Turbulence
Mahendra K. Verma; Jayant K. Bhattacharjee
1995-09-05
In this paper we apply Kraichnan's direct interaction approximation, which is a one loop perturbation expansion, to magnetohydrodynamic turbulence. By substituting the energy spectra both from kolmogorov-like MHD turbulence phenomenology and a generalization of Dobrowolny et al.'s model we obtain Kolmogorov's and Kraichnan's constant for MHD turbulence. We find that the constants depend of the Alfv\\'en ratio and normalized cross helicity; the dependence has been studied here. We also demonstrate the inverse cascade of magnetic energy for Kolmogorov-like models. Our results are in general agreement with the earlier simulation results except for large normalized cross helicity.
On the Implementation of Polygonal Approximation Algorithms
Utrecht, Universiteit
)} , ( ) 1 , ( { min 2 m n ) , 1 ( ) , ( 1 Â n i 1 Â m n i m i D n m n D D(i,j) Âe Â Â Âe Âe Â Â Âe N epsi M,m then ApproxError n,m :=dist SplitPoints n,m :=i if ApproxError N,m Â£ epsi then M_out:=m break // Save,m Â£ epsi then M_out:=m break // Save the polygonal approximation; put the points in the correct order
Approximate Bogomol'nyi-Prasad-Sommerfield states.
Hiller, J R; Pinsky, S S; Trittmann, U
2002-10-28
We consider dimensionally reduced three-dimensional supersymmetric Yang-Mills-Chern-Simons theory. Although the N=1 supersymmetry of this theory does not allow local massive Bogomol'nyi-Prasad-Sommerfield (BPS) states, we find approximate BPS states which have nonzero masses that are almost independent of the Yang-Mills coupling constant and which are a reflection of the massless BPS states of the underlying N=1 super-Yang-Mills theory. The masses of these states at large Yang-Mills coupling are exactly at the n-particle continuum thresholds. This leads to a relation between their masses at zero and large Yang-Mills coupling. PMID:12398590
[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].
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.
Structural design utilizing updated, approximate sensitivity derivatives
NASA Technical Reports Server (NTRS)
Scotti, Stephen J.
1993-01-01
A method to improve the computational efficiency of structural optimization algorithms is investigated. In this method, the calculations of 'exact' sensitivity derivatives of constraint functions are performed only at selected iterations during the optimization process. The sensitivity derivatives utilized within other iterations are approximate derivatives which are calculated using an inexpensive derivative update formula. Optimization results are presented for an analytic optimization problem (i.e., one having simple polynomial expressions for the objective and constraint functions) and for two structural optimization problems. The structural optimization results indicate that up to a factor of three improvement in computation time is possible when using the updated sensitivity derivatives.
The Background Field Approximation in (quantum) cosmology
R. Parentani
1998-03-12
We analyze the Hamilton-Jacobi action of gravity and matter in the limit where gravity is treated at the background field approximation. The motivation is to clarify when and how the solutions of the Wheeler-DeWitt equation lead to the Schr\\"odinger equation in a given background. To this end, we determine when and how the total action, solution of the constraint equations of General Relativity, leads to the HJ action for matter in a given background. This is achieved by comparing two neighboring solutions differing slightly in their matter energy content. To first order in the change of the 3-geometries, the change of the gravitational action equals the integral of the matter energy evaluated in the background geometry. Higher order terms are governed by the ``susceptibility'' of the geometry. These classical properties also apply to quantum cosmology since the conditions which legitimize the use of WKB gravitational waves are concomitant with those governing the validity of the background field approximation.
The validity of the Background Field Approximation
R. Parentani
1997-10-10
In the absence of a tractable theory of quantum gravity, quantum matter field effects have been so far computed by treating gravity at the Background Field Approximation. The principle aim of this paper is to investigate the validity of this approximation which is not specific to gravity. To this end, for reasons of simplicity and clarity, we shall compare the descriptions of thermal processes induced by constant acceleration (i.e. the Unruh effect) in four dynamical frameworks. In this problem, the position of the ``heavy'' accelerated system plays the role of gravity. In the first framework, the trajectory is treated at the BFA: it is given from the outset and unaffected by radiative processes. In the second one, recoil effects induced by these emission processes are taken into account by describing the system's position by WKB wave functions. In the third one, the accelerated system is described by second quantized fields and in the fourth one, gravity is turned on. It is most interesting to see when and why transitions amplitudes evaluated in different frameworks but describing the same process do agree. It is indeed this comparison that determines the validity of the BFA. It is also interesting to notice that the abandonment of the BFA delivers new physical insights concerning the processes. For instance, in the fourth framework, the ``recoils'' of gravity show that the acceleration horizon area acts as an entropy in delivering heat to accelerated systems.
Revisiting approximate dynamic programming and its convergence.
Heydari, Ali
2014-12-01
Value iteration-based approximate/adaptive dynamic programming (ADP) as an approximate solution to infinite-horizon optimal control problems with deterministic dynamics and continuous state and action spaces is investigated. The learning iterations are decomposed into an outer loop and an inner loop. A relatively simple proof for the convergence of the outer-loop iterations to the optimal solution is provided using a novel idea with some new features. It presents an analogy between the value function during the iterations and the value function of a fixed-final-time optimal control problem. The inner loop is utilized to avoid the need for solving a set of nonlinear equations or a nonlinear optimization problem numerically, at each iteration of ADP for the policy update. Sufficient conditions for the uniqueness of the solution to the policy update equation and for the convergence of the inner-loop iterations to the solution are obtained. Afterwards, the results are formed as a learning algorithm for training a neurocontroller or creating a look-up table to be used for optimal control of nonlinear systems with different initial conditions. Finally, some of the features of the investigated method are numerically analyzed. PMID:24846687
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.
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.
Spectrally Invariant Approximation within Atmospheric Radiative Transfer
NASA Technical Reports Server (NTRS)
Marshak, A.; Knyazikhin, Y.; Chiu, J. C.; Wiscombe, W. J.
2011-01-01
Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These spectrally invariant relationships are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.
Sparse deterministic approximation of Bayesian inverse problems
NASA Astrophysics Data System (ADS)
Schwab, C.; Stuart, A. M.
2012-04-01
We present a parametric deterministic formulation of Bayesian inverse problems with an input parameter from infinite-dimensional, separable Banach spaces. In this formulation, the forward problems are parametric, deterministic elliptic partial differential equations, and the inverse problem is to determine the unknown, parametric deterministic coefficients from noisy observations comprising linear functionals of the solution. We prove a generalized polynomial chaos representation of the posterior density with respect to the prior measure, given noisy observational data. We analyze the sparsity of the posterior density in terms of the summability of the input data’s coefficient sequence. The first step in this process is to estimate the fluctuations in the prior. We exhibit sufficient conditions on the prior model in order for approximations of the posterior density to converge at a given algebraic rate, in terms of the number N of unknowns appearing in the parametric representation of the prior measure. Similar sparsity and approximation results are also exhibited for the solution and covariance of the elliptic partial differential equation under the posterior. These results then form the basis for efficient uncertainty quantification, in the presence of data with noise.
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.
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.
A comparison of approximate interval estimators for the Bernoulli parameter
NASA Technical Reports Server (NTRS)
Leemis, Lawrence; Trivedi, Kishor S.
1993-01-01
The goal of this paper is to compare the accuracy of two approximate confidence interval estimators for the Bernoulli parameter p. The approximate confidence intervals are based on the normal and Poisson approximations to the binomial distribution. Charts are given to indicate which approximation is appropriate for certain sample sizes and point estimators.
On the mathematical treatment of the Born-Oppenheimer approximation.
Paris-Sud XI, UniversitÃ© de
On the mathematical treatment of the Born-Oppenheimer approximation. Thierry Jecko AGM, UMR 8088 du the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation of the approximation in Chemistry. We contribute in this way to the discussion on the Born-Oppenheimer approximation
Testing approximations for non-linear gravitational clustering
NASA Technical Reports Server (NTRS)
Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.
1993-01-01
The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.
Decidable Approximations on Generalized and Parameterized Discrete Timed Automata
Zhe Dang; Oscar H. Ibarra; Richard A. Kemmerer
2001-01-01
We consider generalized discrete timed automata with general linear relations over clocks and parameterized constants as clock constraints and with parameterized durations. We look at three approximation techniques (i.e., the -reset-bounded approximation, the -bounded approximation, and the - crossing-bounded approximation), and derive automata-theoretic characteriza- tions of the binary reachability under these approximations. The characteriza- tions allow us to show that
Animal Models and Integrated Nested Laplace Approximations
Holand, Anna Marie; Steinsland, Ingelin; Martino, Sara; Jensen, Henrik
2013-01-01
Animal models are generalized linear mixed models used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast, nonsampling-based Bayesian inference for hierarchical Gaussian Markov models. In this article, we demonstrate that the INLA methodology can be used for many versions of Bayesian animal models. We analyze animal models for both synthetic case studies and house sparrow (Passer domesticus) population case studies with Gaussian, binomial, and Poisson likelihoods using INLA. Inference results are compared with results using Markov Chain Monte Carlo methods. For model choice we use difference in deviance information criteria (DIC). We suggest and show how to evaluate differences in DIC by comparing them with sampling results from simulation studies. We also introduce an R package, AnimalINLA, for easy and fast inference for Bayesian Animal models using INLA. PMID:23708299
Approximate Bayesian inference for complex ecosystems
2014-01-01
Mathematical models have been central to ecology for nearly a century. Simple models of population dynamics have allowed us to understand fundamental aspects underlying the dynamics and stability of ecological systems. What has remained a challenge, however, is to meaningfully interpret experimental or observational data in light of mathematical models. Here, we review recent developments, notably in the growing field of approximate Bayesian computation (ABC), that allow us to calibrate mathematical models against available data. Estimating the population demographic parameters from data remains a formidable statistical challenge. Here, we attempt to give a flavor and overview of ABC and its applications in population biology and ecology and eschew a detailed technical discussion in favor of a general discussion of the advantages and potential pitfalls this framework offers to population biologists. PMID:25152812
Approximately diagonalizing matrices over C(Y).
Lin, Huaxin
2012-02-21
Let X be a compact metric space which is locally absolutely retract and let ?: C(X) ? C(Y,M(n)) be a unital homomorphism, where Y is a compact metric space with dim Y ? 2. It is proved that there exists a sequence of n continuous maps ?(i,m): Y ? X (i = 1,2,…,n) and a sequence of sets of mutually orthogonal rank-one projections {p(1,m),p(2,m),…,p(n,m)} C(Y,M(n)) such that [see formula]. This is closely related to the Kadison diagonal matrix question. It is also shown that this approximate diagonalization could not hold in general when dim Y ? 3. PMID:22323593
Fast Approximate Quadratic Programming for Graph Matching
Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624
Optimal approximation algorithms for digital filter design
NASA Astrophysics Data System (ADS)
Liang, J. K.
Several new algorithms are presented for the optimal approximation and design of various classes of digital filters. An iterative algorithm is developed for the efficient design of unconstrained and constrained infinite impulse response (IIR) digital filters. Both in the unconstrained and constrained cases, the numerator and denominator of the filter transfer function are designed iteratively by recourse to the Remez algorithm and to appropriate design parameters and criteria, at each iteration. This makes it possible for the algorithm to be implemented by means of a short main program which uses (at each iteration) the linear phase FIR filter design algorithm of McClellan et al. as a subroutine. The approach taken also permits the filter to be designed with a desired ripple ratio. Also, the algorithm determines automatically the minimum passband ripple corresponding to the prescribed orders and band edges of the filter. The filter is designed directly without guessing the passband ripple or stopband ripple.
Accelerated convergence for synchronous approximate agreement
NASA Technical Reports Server (NTRS)
Kearns, J. P.; Park, S. K.; Sjogren, J. A.
1988-01-01
The protocol for synchronous approximate agreement presented by Dolev et. al. exhibits the undesirable property that a faulty processor, by the dissemination of a value arbitrarily far removed from the values held by good processors, may delay the termination of the protocol by an arbitrary amount of time. Such behavior is clearly undesirable in a fault tolerant dynamic system subject to hard real-time constraints. A mechanism is presented by which editing data suspected of being from Byzantine-failed processors can lead to quicker, predictable, convergence to an agreement value. Under specific assumptions about the nature of values transmitted by failed processors relative to those transmitted by good processors, a Monte Carlo simulation is presented whose qualitative results illustrate the trade-off between accelerated convergence and the accuracy of the value agreed upon.
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.
Animal models and integrated nested Laplace approximations.
Holand, Anna Marie; Steinsland, Ingelin; Martino, Sara; Jensen, Henrik
2013-08-01
Animal models are generalized linear mixed models used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast, nonsampling-based Bayesian inference for hierarchical Gaussian Markov models. In this article, we demonstrate that the INLA methodology can be used for many versions of Bayesian animal models. We analyze animal models for both synthetic case studies and house sparrow (Passer domesticus) population case studies with Gaussian, binomial, and Poisson likelihoods using INLA. Inference results are compared with results using Markov Chain Monte Carlo methods. For model choice we use difference in deviance information criteria (DIC). We suggest and show how to evaluate differences in DIC by comparing them with sampling results from simulation studies. We also introduce an R package, AnimalINLA, for easy and fast inference for Bayesian Animal models using INLA. PMID:23708299
Approximate Bayesian inference for complex ecosystems.
Stumpf, Michael P H
2014-01-01
Mathematical models have been central to ecology for nearly a century. Simple models of population dynamics have allowed us to understand fundamental aspects underlying the dynamics and stability of ecological systems. What has remained a challenge, however, is to meaningfully interpret experimental or observational data in light of mathematical models. Here, we review recent developments, notably in the growing field of approximate Bayesian computation (ABC), that allow us to calibrate mathematical models against available data. Estimating the population demographic parameters from data remains a formidable statistical challenge. Here, we attempt to give a flavor and overview of ABC and its applications in population biology and ecology and eschew a detailed technical discussion in favor of a general discussion of the advantages and potential pitfalls this framework offers to population biologists. PMID:25152812
Nonlocal Gravity: The General Linear Approximation
B. Mashhoon
2014-12-09
The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field equations is derived. The linear approximation of nonlocal gravity (NLG) is thoroughly examined and the solutions of the corresponding field equations are discussed. It is shown that nonlocality, with a characteristic length scale of order 1 kpc, simulates dark matter in the linear regime while preserving causality. Light deflection in linearized nonlocal gravity is studied in connection with gravitational lensing; in particular, the propagation of light in the weak gravitational field of a uniformly moving source is investigated. The astrophysical implications of the results are briefly mentioned.
Approximate Particle Spectra in the Pyramid Scheme
Tom Banks; T. J. Torres
2012-07-21
We construct a minimal model within the general class of Pyramid Schemes, which is consistent with both supersymmetry breaking and electroweak symmetry breaking. In order to do computations, we make unjustified approximations to the low energy K\\"ahler potential. The phenomenological viability of the resultant mass spectrum is then examined and compared with current collider limits. We show that, for certain regimes of parameters, the Pyramid Scheme can accommodate the current collider mass constraints on physics beyond the standard model with a tree-level light Higgs mass near 125 GeV. However, in this regime the model exhibits a little hierarchy problem, and one must permit fine-tunings that are generically 5%.
Approximate Acoustic Cloaking in Inhomogeneous Isotropic Space
Hongyu Liu
2012-04-30
In this paper, we consider the approximate acoustic cloaking in inhomogeneous isotropic background space. By employing transformation media, together with the use of a sound-soft layer lining right outside the cloaked region, we show that one can achieve the near-invisibility by the `blow-up-a-small-region' construction. This is based on novel scattering estimates corresponding to small sound-soft obstacles located in isotropic space. One of the major novelties of our scattering estimates is that one cannot make use of the scaling argument in the setting of current study due to the simultaneous presence of asymptotically small obstacle components and regularly sized obstacle components, and one has to decouple the nonlinear scattering interaction between the small obstacle components and, the regular obstacle components together with the background medium.
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.
Compact approximate solution to the Kondo problem
NASA Astrophysics Data System (ADS)
Bergmann, Gerd; Zhang, Liye
2007-08-01
A compact approximate ground state of the Kondo problem is introduced. It consists of four Slater states. The spin up and down states of the localized d impurity are paired with two localized s -electron states of opposite spin. All the remaining s -electron states are rearranged, forming two new optimal orthonormal bases. Through a rotation in Hilbert space, the two localized states (and the rest of the bases) are optimized by minimizing the energy expectation value. The ground-state energy E00 and the singlet-triplet excitation energy ?Est are calculated numerically. Although the two energies can differ by a factor of 1000, they are obtained simultaneously. The singlet-triplet excitation energy ?Est is proportional to exp[-1/2J?] and quite close to the Kondo temperature kBTK . The cases for antiferromagnetic (J>0) and ferromagnetic (J<0) couplings are investigated.
Approximate Particle Spectra in the Pyramid Scheme
Banks, Tom
2012-01-01
We construct a minimal model within the general class of Pyramid Schemes, which is consistent with both supersymmetry breaking and electroweak symmetry breaking. In order to do computations, we make unjustified approximations to the low energy K\\"ahler potential. The phenomenological viability of the resultant mass spectrum is then examined and compared with current collider limits. We show that, for certain regimes of parameters, the Pyramid Scheme can accommodate the current collider mass constraints on physics beyond the standard model with a tree-level light Higgs mass near 125 GeV. However, in this regime the model exhibits a little hierarchy problem, and one must permit fine-tunings that are generically 5%.
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.
Improved approximations for control augmented structural synthesis
NASA Technical Reports Server (NTRS)
Thomas, H. L.; Schmit, L. A.
1990-01-01
A methodology for control-augmented structural synthesis is presented for structure-control systems which can be modeled as an assemblage of beam, truss, and nonstructural mass elements augmented by a noncollocated direct output feedback control system. Truss areas, beam cross sectional dimensions, nonstructural masses and rotary inertias, and controller position and velocity gains are treated simultaneously as design variables. The structural mass and a control-system performance index can be minimized simultaneously, with design constraints placed on static stresses and displacements, dynamic harmonic displacements and forces, structural frequencies, and closed-loop eigenvalues and damping ratios. Intermediate design-variable and response-quantity concepts are used to generate new approximations for displacements and actuator forces under harmonic dynamic loads and for system complex eigenvalues. This improves the overall efficiency of the procedure by reducing the number of complete analyses required for convergence. Numerical results which illustrate the effectiveness of the method are given.
Generic sequential sampling for metamodel approximations
Turner, C. J. (Cameron J.); Campbell, M. I. (Matthew 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.
Spline Approximation of Thin Shell Dynamics
NASA Technical Reports Server (NTRS)
delRosario, R. C. H.; Smith, R. C.
1996-01-01
A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material nonhomogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method.
AABC: approximate approximate Bayesian computation for inference in population-genetic models.
Buzbas, Erkan O; Rosenberg, Noah A
2015-02-01
Approximate Bayesian computation (ABC) methods perform inference on model-specific parameters of mechanistically motivated parametric models when evaluating likelihoods is difficult. Central to the success of ABC methods, which have been used frequently in biology, is computationally inexpensive simulation of data sets from the parametric model of interest. However, when simulating data sets from a model is so computationally expensive that the posterior distribution of parameters cannot be adequately sampled by ABC, inference is not straightforward. We present "approximate approximate Bayesian computation" (AABC), a class of computationally fast inference methods that extends ABC to models in which simulating data is expensive. In AABC, we first simulate a number of data sets small enough to be computationally feasible to simulate from the parametric model. Conditional on these data sets, we use a statistical model that approximates the correct parametric model and enables efficient simulation of a large number of data sets. We show that under mild assumptions, the posterior distribution obtained by AABC converges to the posterior distribution obtained by ABC, as the number of data sets simulated from the parametric model and the sample size of the observed data set increase. We demonstrate the performance of AABC on a population-genetic model of natural selection, as well as on a model of the admixture history of hybrid populations. This latter example illustrates how, in population genetics, AABC is of particular utility in scenarios that rely on conceptually straightforward but potentially slow forward-in-time simulations. PMID:25261426
Roberto Hornero; Mateo Aboy; Daniel Abásolo; James McNames; Brahm Goldstein
2005-01-01
We studied changes in intracranial pressure (ICP) complexity, estimated by the approximate entropy (ApEn) of the ICP signal, as subjects progressed from a state of normal ICP (25 mmHg for ? 5 min). We hypothesized that the measures of intracranial pressure (ICP) complexity and irregularity would decrease during acute elevations in ICP. To test this hypothesis we studied ICP spikes
Ervin, Vincent J.
to the time dependent viscoelas- ticity equations with an Oldroyd B constitutive equation in IR ´d , ´d = 2, 3Approximation of Time-Dependent, Viscoelastic Fluid Flow: CrankNicolson, Finite Element are important in the ability to predict flow instabilities in non-Newtonian fluid mechanics. The underlying
Optimal Approximation Algorithms for Digital Filter Design.
NASA Astrophysics Data System (ADS)
Liang, Junn-Kuen
Several new algorithms are presented for the optimal approximation and design of various classes of digital filters. An iterative algorithm is developed for the efficient design of unconstrained and constrained infinite impulse response (IIR) digital filters. Both in the unconstrained and constrained cases, the numerator and denominator of the filter transfer function are designed iteratively by recourse to the Remez algorithm and to appropriate design parameters and criteria, at each iteration. This makes it possible for the algorithm to be implemented by means of a short main program which uses (at each iteration) the linear phase FIR filter design algorithm of McClellan et al. as a subroutine. The approach taken also permits the filter to be designed with a desired ripple ratio. Also, the algorithm determines automatically the minimum passband ripple corresponding to the prescribed orders and band edges of the filter. The filter is designed directly without guessing the passband ripple or stopband ripple. Another algorithm, based on similar principles, is developed for the design of a nonlinear phase finite impulse response (FIR) filter, whose transfer function optimally approximates a desired magnitude response, there being no constraints imposed on the phase response. A similar algorithm is presented for the design of two new classes of FIR digital filters, one linear phase and the other nonlinear phase. A filter of either class has significantly reduced number of multiplications compared to the one obtained by its conventional counterpart, with respect to a given frequency response. In the case of linear phase, by introducing the new class of digital filters into the design of multistage decimators and interpolators for narrow-band filter implementation, it is found that an efficient narrow-band filter requiring considerably lower multiplication rate than the conventional linear phase FIR design can be obtained. The amount of data storage required by the new class of nonlinear phase FIR filters is significantly less than its linear phase counterpart. Finally, the design of a (finite-impulse-response) FIR digital filter with some of the coefficients constrained to zero is formulated as a linear programming (LP) problem and the LP technique is then used to design this class of constrained FIR digital filters. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI.
Nonaxisymmetric stability in the shearing sheet approximation
Axel Brandenburg; Boris Dintrans
2006-01-19
Aims: To quantify the transient growth of nonaxisymmetric perturbations in unstratified magnetized and stratified non-magnetized rotating linear shear flows in the shearing sheet approximation of accretion disc flows. Method: The Rayleigh quotient in modal approaches for the linearized equations (with time-dependent wavenumber) and the amplitudes from direct shearing sheet simulations using a finite difference code are compared. Results: Both approaches agree in their predicted growth behavior. The magneto-rotational instability for axisymmetric and non-axisymmetric perturbations is shown to have the same dependence of the (instantaneous) growth rate on the wavenumber along the magnetic field, but in the nonaxisymmetric case the growth is only transient. However, a meaningful dependence of the Rayleigh quotient on the radial wavenumber is obtained. While in the magnetized case the total amplification factor can be several orders of magnitude, it is only of order ten or less in the nonmagnetic case. Stratification is shown to have a stabilizing effect. In the present case of shearing-periodic boundaries the (local) strato-rotational instability seems to be absent.
Approximate von Neumann entropy for directed graphs
NASA Astrophysics Data System (ADS)
Ye, Cheng; Wilson, Richard C.; Comin, César H.; Costa, Luciano da F.; Hancock, Edwin R.
2014-05-01
In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks.
Approximate von Neumann entropy for directed graphs.
Ye, Cheng; Wilson, Richard C; Comin, César H; Costa, Luciano da F; Hancock, Edwin R
2014-05-01
In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks. PMID:25353841
Network histograms and universality of blockmodel approximation
Olhede, Sofia C.; Wolfe, Patrick J.
2014-01-01
In this paper we introduce the network histogram, a statistical summary of network interactions to be used as a tool for exploratory data analysis. A network histogram is obtained by fitting a stochastic blockmodel to a single observation of a network dataset. Blocks of edges play the role of histogram bins and community sizes that of histogram bandwidths or bin sizes. Just as standard histograms allow for varying bandwidths, different blockmodel estimates can all be considered valid representations of an underlying probability model, subject to bandwidth constraints. Here we provide methods for automatic bandwidth selection, by which the network histogram approximates the generating mechanism that gives rise to exchangeable random graphs. This makes the blockmodel a universal network representation for unlabeled graphs. With this insight, we discuss the interpretation of network communities in light of the fact that many different community assignments can all give an equally valid representation of such a network. To demonstrate the fidelity-versus-interpretability tradeoff inherent in considering different numbers and sizes of communities, we analyze two publicly available networks—political weblogs and student friendships—and discuss how to interpret the network histogram when additional information related to node and edge labeling is present. PMID:25275010
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.
Adaptive approximation of higher order posterior statistics
Lee, Wonjung, E-mail: leew@maths.ox.ac.uk
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.
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 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.
Magnetic reconnection under anisotropic magnetohydrodynamic approximation
Hirabayashi, K.; Hoshino, M. [Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo (Japan)] [Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo (Japan)
2013-11-15
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.
Approximate Methods for State-Space Models
Pérez-Bolde, Lucia Castellanos; Shalizi, Cosma Rohilla; Kass, Robert E.
2011-01-01
State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace’s method, an asymptotic series expansion, to approximate the state’s conditional mean and variance, together with a Gaussian conditional distribution. This Laplace-Gaussian filter (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data. We find that the LGF can deliver superior results in a small fraction of the computing time. PMID:21753862
APPROXIMATE DYNAMIC PROGRAMMING METHODS FOR COOPERATIVE UAV SEARCH
Fernandez, Emmanuel
APPROXIMATE DYNAMIC PROGRAMMING METHODS FOR COOPERATIVE UAV SEARCH Matthew Flint Emmanuel the decentralized dynamic programming path planning decision processes of multiple cooperating autonomous aerial previous work is that a functional approximation is used for the dynamic programming (DP) cost
NONLINEAR PROGRAMMING IN APPROXIMATE DYNAMIC PROGRAMMING: BANG-BANG SOLUTIONS,
Paris-Sud XI, Université de
NONLINEAR PROGRAMMING IN APPROXIMATE DYNAMIC PROGRAMMING: BANG-BANG SOLUTIONS, STOCK stochastic dynamic programming tasks in continuous action-spaces are tackled through discretization. We here avoid discretization; then, approximate dynamic programming (ADP) involves (i) many learning tasks
Approximation Algorithms and Heuristics for a Heterogeneous Traveling Salesman Problem
Rangarajan, Rahul
2011-08-08
minimum spanning tree algorithm. We use 3 different approaches to solve the sequencing problem; namely, the 2 approximation algorithm, Christofide's algorithm and the Lin - Kernighan Heuristic (LKH). The approximation algorithms were implemented in MATLAB...
L^p Bernstein Inequalities and Radial Basis Function Approximation
Ward, John P.
2012-10-19
In approximation theory, three classical types of results are direct theorems, Bernstein inequalities, and inverse theorems. In this paper, we include results about radial basis function (RBF) approximation from all three classes. Bernstein...
Design and analysis of an approximation algorithm for Stackelberg ...
2003-03-17
Mar 17, 2003 ... Keywords: network pricing, approximation algorithms, Stackelberg ... for a network design problem with user-optimized flows by Marcotte [13], who proved ..... approximation algorithms, the reader is referred to [6] and [18].
Moment and SDP relaxation techniques for smooth approximations of nonlinear
Henrion, Didier
and nonlinear ordinary differential equations (ODE) and partial differential equations (PDE) and preliminaryMoment and SDP relaxation techniques for smooth approximations of nonlinear differential equations approximations for solutions of nonlinear differential equations. Given a system of nonlinear differential
VISCOSITY AND RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
Tzavaras, Athanasios E.
VISCOSITY AND RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS Athanasios E. Tzavaras Abstract. These lecture notes deal with the approximation of conservation laws via viscosity or relaxation. The following topics are covered: The general structure of viscosity and relaxation
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)
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
Bond selective chemistry beyond the adiabatic approximation
Butler, L.J. [Univ. of Chicago, IL (United States)
1993-12-01
One of the most important challenges in chemistry is to develop predictive ability for the branching between energetically allowed chemical reaction pathways. Such predictive capability, coupled with a fundamental understanding of the important molecular interactions, is essential to the development and utilization of new fuels and the design of efficient combustion processes. Existing transition state and exact quantum theories successfully predict the branching between available product channels for systems in which each reaction coordinate can be adequately described by different paths along a single adiabatic potential energy surface. In particular, unimolecular dissociation following thermal, infrared multiphoton, or overtone excitation in the ground state yields a branching between energetically allowed product channels which can be successfully predicted by the application of statistical theories, i.e. the weakest bond breaks. (The predictions are particularly good for competing reactions in which when there is no saddle point along the reaction coordinates, as in simple bond fission reactions.) The predicted lack of bond selectivity results from the assumption of rapid internal vibrational energy redistribution and the implicit use of a single adiabatic Born-Oppenheimer potential energy surface for the reaction. However, the adiabatic approximation is not valid for the reaction of a wide variety of energetic materials and organic fuels; coupling between the electronic states of the reacting species play a a key role in determining the selectivity of the chemical reactions induced. The work described below investigated the central role played by coupling between electronic states in polyatomic molecules in determining the selective branching between energetically allowed fragmentation pathways in two key systems.
Quantum ground states: Manipulation and approximation
NASA Astrophysics Data System (ADS)
Siu, Ming-Ho Stewart
The low energy spectrum of quantum many-body systems is often a subject of great interest to physicists. This thesis covers two subject areas, both involving the study of low energy eigenstates of quasi-local spin-1/2 Hamiltonians. Part I of the thesis is on numerical methods for condensed matter models. Among the many methods used by physicists to study low energy spectra, contractor renormalization (CORE) is a regularly used but poorly understood method. First, I show that its performance on finite Ising chains is comparable to the popular density matrix renormalization (DMRG) method, and that it bears slight theoretical resemblance to entanglement renormalization, a variant of DMRG. Moving on to two dimensions, I perform a series of numerical tests with the Heisenberg antiferromagnet to see the effect of different blocking schemes. I also propose a bootstrap method for approximating long-range terms in CORE. The tests show that on one hand, CORE is capable of revealing very interesting physical pictures. This includes renormalization group flows that reveal a phase transition in a two-dimensional frustrated antiferromagnet. On the other hand, the results also show that the accuracy of the method can be very sensitive to truncation schemes, blocking geometries and long-range terms, so there are important ambiguities and potential sources of error that researchers must pay attention to in using CORE. Part II of this thesis turns to some questions raised by two quantum computing paradigms: the adiabatic (linear interpolation) model and the holonomic model. First, I show that even though the two models appear very different, a well-known algorithm can be interpreted in terms of both. Secondly, I discuss in a general setting how the issue of locality affects the design of adiabatic algorithms. Finally, I propose a new type of adiabatic algorithm, called adiabatic rotation, which traces out arcs in the parameter space of Hamiltonians and has uses in implementing specific unitary transformations, generating known interesting states and solving search problems.
A new approximation method for stress constraints in structural synthesis
NASA Technical Reports Server (NTRS)
Vanderplaats, Garret N.; Salajegheh, Eysa
1987-01-01
A new approximation method for dealing with stress constraints in structural synthesis is presented. The finite element nodal forces are approximated and these are used to create an explicit, but often nonlinear, approximation to the original problem. The principal motivation is to create the best approximation possible, in order to reduce the number of detailed finite element analyses needed to reach the optimum. Examples are offered and compared with published results, to demonstrate the efficiency and reliability of the proposed method.
PWL approximation of nonlinear dynamical systems, part I: structural stability
NASA Astrophysics Data System (ADS)
Storace, M.; DeFeo, O.
2005-01-01
This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes the approximation method and applies it to some particularly significant dynamical systems (topological normal forms). The structural stability of the PWL approximations of such systems is investigated through a bifurcation analysis (via continuation methods).
Approximations of Weyl fractional-order integrals with insurance applications
Chengxiu Ling; Zuoxiang Peng
2015-02-03
In this paper, we investigate the approximations of generalized Weyl fractional-order integrals in extreme value theory framework. We present three applications of our asymptotic results concerning the higher-order tail approximations of deflated risks as well as approximations of Haezendonck-Goovaerts and expectile risk measures. Illustration of the obtained results is done by various examples and some numerical analysis.
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
SUBTRACTING A BEST RANK-1 APPROXIMATION MAY INCREASE TENSOR RANK
Paris-Sud XI, Université de
SUBTRACTING A BEST RANK-1 APPROXIMATION MAY INCREASE TENSOR RANK Alwin Stegeman Heymans Institute, fax: +33 4 92 94 28 98, pcomon@unice.fr ABSTRACT Is has been shown that a best rank-R approximation be solved by consecutively computing and substracting best rank-1 approximations. The reason
Rational Quadratic Approximation to Real Plane Algebraic Curves
Xiao-shan Gao; Ming Li
2004-01-01
An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of f our steps: topol- ogy determination, curve segmentation, segment approximation and curve tracing. Due to the detailed geometric analysis, high accuracy of approximation may be achieved with a small number of quadratic segments. The final
Downward Sets and Their Best Simultaneous Approximation Properties with Applications
H. Mohebi
2005-01-01
We develop a theory of best simultaneous approximations for closed downward sets in a conditionally complete lattice Banach space X with a strong unit. We study best simultaneous approximation in X by elements of downward and normal sets, and give necessary and sufficient conditions for any element of best simultaneous approximation by a closed subset of X. We prove that
A family of MMA approximations for structural optimization
M. Bruyneel; P. Duysinx; C. Fleury
2002-01-01
This paper proposes a new first-order approximation scheme used for solving structural optimization problems. It is based on approximations of the MMA family (MMA and GCMMA), but it utilizes the gradients and\\/or the function values at two successive design points to improve the quality of the approximation. In addition, this scheme can consider simultaneously monotonous and nonmonotonous structural behaviour. According
Approximations and Consistency of Bayes Factors as Model Dimension Grows
Berger, Jim
Approximations and Consistency of Bayes Factors as Model Dimension Grows James O. Berger Duke. Note, however, that BIC was developed as an asymptotic approximation to Bayes factors between models in which BIC is not an adequate approxima- tion. We develop some new approximations to Bayes factors
A Fast Distributed Approximation Algorithm for Minimum Spanning Trees
Khan, Maleq
A Fast Distributed Approximation Algorithm for Minimum Spanning Trees Maleq Khan and Gopal}@cs.purdue.edu Abstract. We give a distributed algorithm that constructs a O(log n)- approximate minimum spanning tree: Distributed Approximation Algorithm, Minimum Spanning Tree. 1 Introduction 1.1 Background and Previous Work
A SIMILARITY THEORY OF APPROXIMATE DECONVOLUTION MODELS OF TURBULENCE
MONIKA NEDAz
We apply the phenomenology of homogeneous, isotropic turbulence to the family of approximate deconvolution models proposed by Stolz and Adams. In particular, we establish that the models themselves have an energy cascade with two asymptotically dierent inertial ranges. Delineation of these gives insight into the resolution requirements of using approximate deconvolution models. The approximate deconvolution model's energy balance contains both
On Set Partitions, Words, Approximate Counting and Digital Search Trees
Fuchs, Michael
On Set Partitions, Words, Approximate Counting and Digital Search Trees (joint with Chung-Kuei Lee, Taiwan Changsha, June 28, 2013 Michael Fuchs (NCTU) Words, Approximate Counting, DSTs Changsha, China 1} with three blocks. Michael Fuchs (NCTU) Words, Approximate Counting, DSTs Changsha, China 2 / 32 #12;Set
Deterministic approximation of marginal probabilities in Bayes nets
Eugene Santos Jr.; Solomon Eyal Shimony
1998-01-01
Computation of marginal probabilities in Bayes nets is central to numerous reasoning and automaticdecision-making systems. This paper presents a deterministic approximation scheme forthis hard problem, that supplies provably correct bounds, by aggregating probability mass inIndependence-Based (IB) assignments.Keywords: Probabilistic Reasoning, Bayesian Belief Networks, Decision-Making Systems, ApproximateBelief Updating, Approximating Marginal Probabilities, Any-time Algorithms....
Numerical approximations of the Sommerfeld integral for fast convergence
W. C. Kuo; K. K. Mei
1978-01-01
Several approximation techniques for the Hertz potential of an inf'mitesimal dipole in the presence of a conducting half space are presented. The formal solutions obtained by rigorous mathematical procedures are transformed, with the aid of some approximation, to fast convergent forms. The approximation techniques are different depending on the media where the observer and source are located. All results calculated
Minimax principle and lower bounds in H2 -rational approximation
Paris-Sud XI, Université de
. Classification numbers (AMS): 31B05, 35J25, 42B35, 46E20, 47B35. 1. Introduction Rational approximationMinimax principle and lower bounds in H2 -rational approximation Laurent Baratcharta,1, Sylvain University of Macao Abstract We derive some lower bounds in rational approximation of given degree
Viscosity and Relaxation Approximation for Hyperbolic Systems of Conservation Laws
Tzavaras, Athanasios E.
Viscosity and Relaxation Approximation for Hyperbolic Systems of Conservation Laws Athanasios E with the approximation of conservation laws via viscosity or relaxation. The following topics are covered: The general structure of viscosity and relaxation approximations is discussed, as suggested by the second law
On the mathematical treatment of the Born-Oppenheimer approximation.
On the mathematical treatment of the Born-Oppenheimer approximation. Thierry Jecko AGM, UMR 8088 du the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation in this way to the discussion on the Born-Oppenheimer approximation initiated in [SW]. The paper neither
On the mathematical treatment of the Born-Oppenheimer approximation.
Paris-Sud XI, UniversitÃ© de
On the mathematical treatment of the Born-Oppenheimer approximation. Thierry Jecko AGM, UMR 8088 du the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation in this way to the discussion on the Born-Oppenheimer approximation initiated in [SW1]. The paper neither
Approximate RBF Kernel SVM and Its Applications in Pedestrian Classification
Paris-Sud XI, Université de
Approximate RBF Kernel SVM and Its Applications in Pedestrian Classification Hui Cao, Takashi Naito. This paper presents an efficient approximation to the non- linear SVM with Radial Basis Function (RBF) kernel. By employing second-order polynomial approximation to RBF kernel, the derived ap- proximate RBF-kernel SVM
Approximating the Bandwidth for Asteroidal Triple-Free Graphs
Ton Kloks; Dieter Kratsch; Haiko Müller
1995-01-01
We show that there is an algorithm to approximate the bandwidth of an AT-free graph with worst case performance ratio 2. Alternatively, at the cost of the approximation factor, we can also obtain an log algorithm to approximate the bandwidth of an AT-free graph within a factor 4 and an algorithm with a factor 6. For the special cases of
Discontinuous Galerkin method based on non-polynomial approximation spaces
Ling Yuan; Chi-Wang Shu
2006-01-01
In this paper, we develop discontinuous Galerkin (DG) methods based on non-polynomial approximation spaces for numerically solving time dependent hyperbolic and parabolic and steady state hyperbolic and elliptic partial differential equations (PDEs). The algorithm is based on approximation spaces consisting of non-polynomial elementary functions such as exponential functions, trigonometric functions, etc., with the objective of obtaining better approximations for specific
Smoluchowski-Kramers approximation in the case of variable friction
Mark Freidlin; Wenqing Hu
2012-03-03
We consider the small mass asymptotics (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The limit of the solution in the classical sense does not exist in this case. We study a modification of the Smoluchowski-Kramers approximation. Some applications of the Smoluchowski-Kramers approximation to problems with fast oscillating or discontinuous coefficients are considered.
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.
Approximations by gravitational fields due to restricted unit point masses
Shull, Carolyn Sue Flowers
1973-01-01
approximations by Chui (1, 3, 4j and D. J. Newman $12$. Some open problems will be discussed including a conjecture by Chui f2]. I ht th ' th ~Pdl f~hA 1 Mth i I ~gociet is used as a pattern for format, CHAPTER I UNIFORM APPROXIMATION ON COMPACT SETS Let C...-approximations of h(z) when one of the components of D is bounded by a nonanalytic curve. 21 ~CTER 11 AREA APPROXIMATIONS In this chapter we will discuss the results obtained in L 1 approximation by Chui [1, 3, 4] and D. J. Newman [12] and some open problems...
Mappings and accuracy for Chebyshev pseudo-spectral approximations
NASA Technical Reports Server (NTRS)
Bayliss, Alvin; Turkel, Eli
1990-01-01
The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed.
NASA Astrophysics Data System (ADS)
Lim, Hyang-Tag; Kim, Yong-Su; Ra, Young-Sik; Bae, Joonwoo; Kim, Yoon-Ho
2012-10-01
Although important for detecting entanglement, the transpose operation cannot be directly realized in laboratory because it is a nonphysical operation. It is, however, possible to find an approximate transpose operation using the method known as the structural physical approximation (SPA); recently, SPA-based implementations of the transpose and partial transpose have been demonstrated for a single-qubit [Phys. Rev. A1050-2947PLRAAN10.1103/PhysRevA.83.020301 83, 020301(R) (2011)] and an entangled two-qubit system [Phys. Rev. Lett.0031-9007PRLTAO10.1103/PhysRevLett.107.160401 107, 160401 (2011)]. In this work, we expand SPA-transpose to a three-dimensional quantum system: a qutrit. The photonic qutrit state is encoded in the polarization, and path degrees of freedom of a single-photon and the SPA-transpose operation, which is based on measurement and preparation of quantum states, is implemented with linear optics. Our work paves the way toward entanglement detection for higher-dimensional quantum systems.
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
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 (?i=1nRi¯,?i=1nRi_) forms an order-preserving Galois connection, if and only if the collection of lower (resp., upper) definable sets forms an (resp., union) intersection structure, if and only if the collection of multigranulation upper (lower) definable sets forms a distributive lattice when n = 2, and if and only if ?X?U,???i=1nRi_(X)=?i=1nRi_(X). The obtained results help us gain more insights into the mathematical structure of multigranulation approximation spaces. PMID:25243226
The selection of approximating functions for tabulated numerical data
NASA Technical Reports Server (NTRS)
Ingram, H. L.; Hooker, W. R.
1972-01-01
A computer program was developed that selects, from a list of candidate functions, the approximating functions and associated coefficients which result in the best curve fit of a given set of numerical data. The advantages of the approach used here are: (1) Multivariable approximations can be performed. (2) Flexibility with respect to the type of approximations used is available. (3) The program is designed to choose the best terms to be used in the approximation from an arbitrary list of possible terms so that little knowledge of the proper approximating form is required. (4) Recursion relations are used in determining the coefficients of the approximating functions, which reduces the computer execution time of the program.
Discontinuous Galerkin method based on non-polynomial approximation spaces
Yuan Ling [Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912 (United States)]. E-mail: lyuan@dam.brown.edu; Shu Chiwang [Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912 (United States)]. E-mail: shu@dam.brown.edu
2006-10-10
In this paper, we develop discontinuous Galerkin (DG) methods based on non-polynomial approximation spaces for numerically solving time dependent hyperbolic and parabolic and steady state hyperbolic and elliptic partial differential equations (PDEs). The algorithm is based on approximation spaces consisting of non-polynomial elementary functions such as exponential functions, trigonometric functions, etc., with the objective of obtaining better approximations for specific types of PDEs and initial and boundary conditions. It is shown that L {sup 2} stability and error estimates can be obtained when the approximation space is suitably selected. It is also shown with numerical examples that a careful selection of the approximation space to fit individual PDE and initial and boundary conditions often provides more accurate results than the DG methods based on the polynomial approximation spaces of the same order of accuracy.
Yukawa model on a lattice in the quenched approximation
NASA Astrophysics Data System (ADS)
de Soto, Feliciano; Anglès d'Auriac, Jean-Christian
2012-04-01
The Yukawa model in the quenched approximation is expressed as a disordered statistical mechanics model on a four-dimensional Euclidean lattice. We study this model, giving particular attention to the singularities of the Dirac operator in the phase diagram. A careful analysis of a particular limiting case shows that finite volume effects can be huge and questions the quenched approximation. This is confirmed by numerical simulation performed in this limiting case and without the quenched approximation.
PWL approximation of nonlinear dynamical systems, part II: identification issues
NASA Astrophysics Data System (ADS)
DeFeo, O.; Storace, M.
2005-01-01
This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes a black-box identification method based on state space reconstruction and PWL approximation, and applies it to some particularly significant dynamical systems (two topological normal forms and the Colpitts oscillator).
Approximate equivalence and synchronization of metric transition systems
A. Agung Julius; Alessandro D’Innocenzo; Maria Domenica Di Benedetto; George J. Pappas
2009-01-01
In this paper, we consider metric transition systems which are transition systems equipped with metrics for observation and synchronization labels. The existence of metrics leads to the introduction of two new concepts, (i) (?,?)-approximate (bi)simulation of transition systems and (ii) approximate synchronization of transition systems.We show that the notion of (?,?)-approximate (bi)simulation can be thought of as a generalization or
Nonlinear weighted best simultaneous approximation in Banach spaces
Xianfa Luo; Chong Li; Genaro Lopez
2008-01-01
The present paper is concerned with the problem of weighted best simultaneous approximations in Banach spaces. The weighted best simultaneous approximations to sequences from S- and BS-suns in the Banach space are characterized in view of the Kolmogorov conditions. Applications are provided for weighted best simultaneous approximations from RS-sets and strict RS-sets. Our results obtained in the present paper extend
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.
Approximation of Loop Subdivision Surfaces for Fast Rendering.
Li, Guiqing; Ren, Canjiang; Zhang, Jiahua; Ma, Weiyin
2010-05-26
This paper describes an approach to the approximation of Loop subdivision surfaces for real-time rendering. The approach consists of two phases which separately construct the approximation geometry and the normal field of a subdivision surface. It firstly exploits quartic triangular Bézier patches to approximate the geometry of the subdivision surface by interpolating a grid of sampled points. To remedy the artifact of discontinuity of normal fields between adjacent patches, a continuous normal field is then reconstructed by approximating the tangent vector fields of the subdivision surfaces with quartic triangular Bézier patches. For regular triangles, the approach reproduces the associated subdivision patches, quartic 3-directional box splines. PMID:20513928
Bethe free-energy approximations for disordered quantum systems.
Biazzo, I; Ramezanpour, A
2014-06-01
Given a locally consistent set of reduced density matrices, we construct approximate density matrices which are globally consistent with the local density matrices we started from when the trial density matrix has a tree structure. We employ the cavity method of statistical physics to find the optimal density matrix representation by slowly decreasing the temperature in an annealing algorithm, or by minimizing an approximate Bethe free energy depending on the reduced density matrices and some cavity messages originated from the Bethe approximation of the entropy. We obtain the classical Bethe expression for the entropy within a naive (mean-field) approximation of the cavity messages, which is expected to work well at high temperatures. In the next order of the approximation, we obtain another expression for the Bethe entropy depending only on the diagonal elements of the reduced density matrices. In principle, we can improve the entropy approximation by considering more accurate cavity messages in the Bethe approximation of the entropy. We compare the annealing algorithm and the naive approximation of the Bethe entropy with exact and approximate numerical simulations for small and large samples of the random transverse Ising model on random regular graphs. PMID:25019754
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.
Nonlocal integral-equation approximations. II. Lennard-Jones fluids
Zhou, Y. (Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794 (USA)); Stell, G. (Departments of Chemistry, State University of New York at Stony Brook, Stony Brook, NY (USA) Department of Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, NY (USA))
1990-05-01
The zeroth order (hydrostatic) nonlocal integral-equation approximation is applied here to Lennard-Jones (LJ) fluids. Systems of homogeneous LJ fluids are investigated, as well as LJ fluids near a hard wall, a model CO{sub 2} wall, and inside two model CO{sub 2} walls. The hydrostatic hypernetted chain (HHNC) approximation is shown to be better than both the Percus--Yevick and the hypernetted chain approximations when compared with computer simulations. The phenomena of solid wetting by liquid, solid wetting by gas, and capillary condensation are predicted by the HHNC approximation.
Orthogonal polynomial approximation in higher dimensions: Applications in astrodynamics
NASA Astrophysics Data System (ADS)
Bani Younes, Ahmad Hani Abd Alqader
We propose novel methods to utilize orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical differential equation solvers to perform high precision, long-term orbit propagation. These methods have immediate application to efficient propagation of catalogs of Resident Space Objects (RSOs) and improved accounting for the uncertainty in the ephemeris of these objects. More fundamentally, the methodology promises to be of broad utility in solving initial and two point boundary value problems from a wide class of mathematical representations of problems arising in engineering, optimal control, physical sciences and applied mathematics. We unify and extend classical results from function approximation theory and consider their utility in astrodynamics. Least square approximation, using the classical Chebyshev polynomials as basis functions, is reviewed for discrete samples of the to-be-approximated function. We extend the orthogonal approximation ideas to n-dimensions in a novel way, through the use of array algebra and Kronecker operations. Approximation of test functions illustrates the resulting algorithms and provides insight into the errors of approximation, as well as the associated errors arising when the approximations are differentiated or integrated. Two sets of applications are considered that are challenges in astrodynamics. The first application addresses local approximation of high degree and order geopotential models, replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. A method is introduced which adapts the approximation degree radially, compatible with the truth that the highest degree approximations (to ensure maximum acceleration error < 10-9 ms-2, globally) are required near the Earths surface, whereas lower degree approximations are required as radius increases. We show that a four order of magnitude speedup is feasible, with both speed and storage efficiency op- timized using radial adaptation. The second class of problems addressed includes orbit propagation and solution of associated boundary value problems. The successive Chebyshev-Picard path approximation method is shown well-suited to solving these problems with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. Used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss.
Approximation of Real Numbers by Rationals: Some Metric Theorems
Pavel Kargaev; Anatoly Zhigljavsky
1996-01-01
Letxbe a real number in [0, 1], Fnbe the Farey sequence of ordernand?n(x) be the distance betweenxand Fn. The first result concerns the average rate of approximation:[formula]The second result states that any badly approximable number is better approximable by rationals than all numbers in average. Namely, we show that ifx?[0, 1] is a badly approximable number thenc1?n2?n(x)?c2for all integersn?1 and some constantsc1>0,c2>0.
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.
Approximation functions for airblast environments from buried charges
Reichenbach, H.; Behrens, K. [Fraunhofer-Institut fuer Kurzzeitdynamik - Ernst-Mach-Institut (EMI), Freiburg im Breisgau (Germany); Kuhl, A.L. [Lawrence Livermore National Lab., El Segundo, CA (United States)
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.
NASA Astrophysics Data System (ADS)
Olsen, Thomas; Thygesen, Kristian S.
2012-08-01
The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation of the ALDA kernel for wave vectors q>2kF, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can be straightforwardly applied to other adiabatic local kernels.
Embedding impedance approximations in the analysis of SIS mixers
NASA Technical Reports Server (NTRS)
Kerr, A. R.; Pan, S.-K.; Withington, S.
1992-01-01
Future millimeter-wave radio astronomy instruments will use arrays of many SIS receivers, either as focal plane arrays on individual radio telescopes, or as individual receivers on the many antennas of radio interferometers. Such applications will require broadband integrated mixers without mechanical tuners. To produce such mixers, it will be necessary to improve present mixer design techniques, most of which use the three-frequency approximation to Tucker's quantum mixer theory. This paper examines the adequacy of three approximations to Tucker's theory: (1) the usual three-frequency approximation which assumes a sinusoidal LO voltage at the junction, and a short-circuit at all frequencies above the upper sideband; (2) a five-frequency approximation which allows two LO voltage harmonics and five small-signal sidebands; and (3) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R(sub N)C for the SIS junctions used. For large omega R(sub N)C, all three approximations approach the eight-harmonic solution. For omega R(sub N)C values in the range 0.5 to 10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, and should be suitable for much design work. For the realistic SIS mixers considered here, the five-frequency approximation gives results very close to those of the eight-harmonic solution. Use of these approximations, where appropriate, considerably reduces the computational effort needed to analyze an SIS mixer, and allows the design and optimization of mixers using a personal computer.
Atomic Structure Schrdinger equation has approximate solutions for multi-
Zakarian, Armen
Atomic Structure SchrÃ¶dinger equation has approximate solutions for multi- electron atoms, which indicate that all atoms are like hydrogen Atomic Structure SchrÃ¶dinger equation has approximate solutions 3s 3p 3d Energy hydrogen multi-electron #12;Atomic Structure Â· orbitals are populated by electrons
Bounds for Approximation in Total Variation Distance by Quantum Circuits
E. Knill
1995-01-01
It was recently shown that for reasonable notions of approximation of states and functions by quantum circuits, almost all states and functions are exponentially hard to approximate [Knill 1995]. The bounds obtained are asymptotically tight except for the one based on total variation distance (TVD). TVD is the most relevant metric for the performance of a quantum circuit. In this
Improvements in the Poisson approximation of mixed Poisson distributions
Bero Roos
2003-01-01
We consider the approximation of mixed Poisson distributions by Poisson laws and also by related finite signed measures of higher order. Upper bounds and asymptotic relations are given for several distances. Even in the case of the Poisson approximation with respect to the total variation distance, our bounds have better order than those given in the literature. In particular, our
2007 Warren B. Powell Slide 1 Approximate Dynamic Programming for
Powell, Warren B.
© 2007 Warren B. Powell Slide 1 Approximate Dynamic Programming for High-Dimensional Problems 2007 IEEE Symposium on Approximate Dynamic Programming and Reinforcement Learning April, 2007 Warren Powell reliable aircraft? #12;© 2007 Warren B. Powell Slide 15 Outline The languages of dynamic programming
Nonlinear approximation theory on compact groups K.-L. Kueh
Rockmore, Dan
x September 7, 2000 Abstract In this paper we extend to the setting of band-limited functions at the heart of linear approximation theory and can be stated simply. Theorem 1.1 (Jackson's Theorem, see [11 41A29, Secondary: 43-04, 43A77; Keywords: Approximation, positive func- tions, band-limited functions
Floating-point L2 -approximations to functions
California at Davis, University of
Floating-point L2 -approximations to functions Nicolas Brisebarre UniversitÂ´e de Saint by a polynomial with floating-point coefficients; we are looking for the best approximation in the L2 sense pro- jections. However, truncating the coefficients to floating-point numbers, which is needed for fur
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 2ÂD dictionary and generates approximations of the dictionary which have fast 2Âstage implementations according to the method of Redmill, et.al. [1] By varying
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
An Investigation of Practical Approximate Nearest Neighbor Algorithms
Ting Liu; Andrew W. Moore; Alexander G. Gray; Ke Yang
2004-01-01
This paper concerns approximate nearest neighbor searching algorithms, which have become increasingly important, especially in high dimen- sional perception areas such as computer vision, with dozens of publica- tions in recent years. Much of this enthusiasm is due to a successful new approximate nearest neighbor approach called Locality Sensitive Hash- ing (LSH). In this paper we ask the question: can
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…
The approximation of one matrix by another of lower rank
Carl Eckart; Gale Young
1936-01-01
The mathematical problem of approximating one matrix by another of lower rank is closely related to the fundamental postulate of factor-theory. When formulated as a least-squares problem, the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another. The solution of the problem is simplified by first expressing the matrices
Continuous meshless approximations for nonconvex bodies by diffraction and transparency
D. Organ; M. Fleming; T. Terry; T. Belytschko
1996-01-01
Continuous meshless approximations are developed for domains with non-convex boundaries, with emphasis on cracks. Two techniques are developed in the context of the element-free Galerkin method: a transparency method wherein smooth approximations are generated by making boundaries partially transparent, and a diffraction method, where the domain of influence wraps around a concave boundary. They are compared to the original method
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.
Born-Oppenheimer approximation for a harmonic molecule
Francisco M. Fernandez
2008-10-13
We apply the Born-Oppenheimer approximation to a harmonic diatomic molecule with one electron. We compare the exact and approximate results not only for the internal degrees of freedom but also for the motion of the center of mass. We address the problem of identical nuclei and discuss other applications of the model and its limitations.
On Approximation Preserving Reductions: Complete Problems and Robust Measures
Orponen, Pekka
in the approximability properties of NP-complete optimization problems. We define a notion of polynomial time reduction, the traveling salesperson problem, and the zero-one integer programming problem are in a strong sense-complete, and thus probably not solvable in poly- nomial time, approximate solution methods for them are of great
A Polynomial Time Approximation Scheme for k-Consensus Clustering
Chudnovsky, Maria
A Polynomial Time Approximation Scheme for k-Consensus Clustering Date Tuesday, January 26 Time 3 pm Location 303 Mudd Abstract: We introduce a polynomial time approximation scheme for the metric Correlation Clustering problem, when the number of clusters returned is bounded (by k). Consensus Clustering
Approximate Top-k Queries in Sensor Networks (Extended Abstract)
Patt-Shamir, Boaz
Approximate Top-k Queries in Sensor Networks (Extended Abstract) Boaz Patt-Shamir and Allon Shafrir to elections where nodes are ballot boxes and items are candidates). A top-k query in such a system asks which approximates the top-k items. The algorithm is motivated by sensor networks in that it fo- cuses on reducing
Haze of surface random systems: An approximate analytic approach
Ingve Simonsen; Åge Larsen; Erik Andreassen; Espen Ommundsen; Katrin Nord-Varhaug
2009-01-01
Approximate analytic expressions for haze (and gloss) of Gaussian randomly rough surfaces for various types of correlation functions are derived within phase-perturbation theory. The approximations depend on the angle of incidence, polarization of the incident light, the surface roughness, sigma , and the average of the power spectrum taken over a small angular interval about the specular direction. In particular
Value Function Approximation with Diffusion Wavelets and Laplacian Eigenfunctions
Sridhar Mahadevan; Mauro Maggioni
2005-01-01
We investigate the problem of automatically constructing efficient rep- resentations or basis functions for approximating value fu nctions based on analyzing the structure and topology of the state space. I n particu- lar, two novel approaches to value function approximation are explored based on automatically constructing basis functions on state spaces that can be represented as graphs or manifolds: one
A greedy approximation algorithm for the group Steiner problem
Chekuri, Chandra
i j) 1+'' \\Delta log m) approximation in polynomial time. As pointed out in [14], approximation on trees is slightly worse than the ratio of O(log(max i jg i j) \\Delta log m) provided by the LP based denote the number of groups by m, the number of terminals j [ m i=1 g i j by n, and the size
Single-frequency approximation of the coupling ray theory
Cerveny, Vlastislav
Single-frequency approximation of the coupling ray theory Ludek Klimes & Petr Bulant DepartmentÂrayÂtheory Green tensor is frequency dependent, and is usually calculated for many frequencies. This frequency this frequency dependence. In the vicinity of a given prevailing frequency, we approximate the frequencyÂ domain
A unified approach to approximating resource allocation and scheduling
Amotz Bar-Noy; Reuven Bar-Yehuda; Ari Freund; Baruch Schieber
2000-01-01
We present a general framework for solving resource allocation and scheduling problems. Given a resource of fixed size, we present algorithms that approximate the maximum throughput or the minimum loss by a constant factor. Our approximation factors apply to many problems, among which are: (i) real-time scheduling of jobs on parallel machines, (ii) bandwidth allocation for sessions between two endpoints,
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
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
A 3-approximation for the minimum tree spanning k vertices
Garg, N. [Max-Planck-Institut fuer Informatik, Saabruecken (Germany)
1996-12-31
In this paper we give a 3-approximation algorithm for the problem of finding a minimum tree spanning any k-vertices in a graph. Our algorithm extends to a 3-approximation algorithm for the minimum tour that visits any k-vertices.
Neural networks for functional approximation and system identification
Mhaskar, Hrushikesh Narhar
is a static neural network, L has a simple representation in terms of bounded linear functionalsNeural networks for functional approximation and system identification H. N. Mhaskar Department translation networks to uniformly approximate a class of nonlinear, continuous functionals defined on Lp ([-1
Confidently Cutting a Cake into Approximately Fair Jeff Edmonds1
Edmonds, Jeff
Confidently Cutting a Cake into Approximately Fair Pieces Jeff Edmonds1 , Kirk Pruhs2 protocol for the classic cake cutting problem that guarantees approximate proportional fairness, and with high probability uses a linear number of cuts. 1 Introduction The classic cake cutting problems
SPECTRAL APPROXIMATION OF A NONLINEAR ELASTIC LIMITING STRAIN MODEL
Jensen, Max
the linearized strain. In particular, within the realm of implicit constitutive theory, it is possible to haveSPECTRAL APPROXIMATION OF A NONLINEAR ELASTIC LIMITING STRAIN MODEL ENDRE S¨ULI Abstract. We construct a numerical algorithm for the approximate solution of a nonlinear elastic limiting strain model
A provably efficient computational model for approximate spatiotemporal retrieval
Delis Vasilis; Makris Christos; Sioutas Spiros
1999-01-01
The paper is concerned with the effective and efficient processing of spatiotemporal selection queries under varying degrees of approximation. Such queries may employ operators like overlaps, north, during, etc., and their result is a set of entities standing approximately in some spatiotemporal relation with respect to a query object X. The contribution of our work is twofold: i) First we
A New and Simpler Approximation for ANOVA under Variance Heterogeneity.
ERIC Educational Resources Information Center
Alexander, Ralph A.; Govern, Diane M.
1994-01-01
A new approximation is proposed for testing the equality of "k" independent means in the face of heterogeneity of variance. Monte Carlo simulations show that the new procedure has nearly nominal Type I error rates and Type II error rates that are close to those produced by James's second-order approximation. (SLD)
Multilayer perceptrons: Approximation order and necessary number of hidden units
Trenn, Stephan
1 Multilayer perceptrons: Approximation order and necessary number of hidden units Stephan Trenn--multilayer perceptron, approximation, necessary number of hidden units I. INTRODUCTION The original motivation the biological background and historical remarks are given. In this paper only the multilayer perceptron (MLP
On the Accuracy of Uniform Polyhedral Approximations of the ...
2009-07-18
Jul 18, 2009 ... hedral approximations with the inner polyhedral approximations ... tive orthant in Rn. Equipping Sn with the usual trace inner product ...... ear, semidefinite and copositive programming. ... Mathematical Programming, 120(2):479–495, 2009. ... YALMIP: A toolbox for modeling and optimization in MATLAB.
Manifold Representations for Value-Function Approximation in Reinforcement Learning
Smart, William
representations and methods for using these representations for value function approximation. We provide empiricalManifold Representations for Value-Function Approximation in Reinforcement Learning Robert Glaubius. Louis, MO 63130 United States {rlg1,wds}@cse.wustl.edu 1 Introduction Reinforcement learning (RL) has
Stochastic population dynamics: The Poisson approximation Hernan G. Solari*
Natiello, Mario
of the projection from the space of events into the space of populations that determine the state of the systemStochastic population dynamics: The Poisson approximation HernaÂ´n G. Solari* Departamento de Fi an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters
SPLINE APPROXIMATION OF THIN SHELL DYNAMICS --NUMERICAL EXAMPLES 1
of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Modal Solution -- SimplyÂSupported Boundary Conditions, Constant CoefÂ ficients, No Damping 9 4 Approximation Method 13 4.1 Axial Basis.5 Approximation of Natural Frequencies and Modes . . . . . . . . . . . . . . . . 22 5 Examples 23 5.1 Modal
Reaching Approximate Agreement in the Presence of Faults
Danny Dolev; Nancy A. Lynch
1985-01-01
This paper considers a variant on the Byzantine Generals problem, in which processes start with arbitrary real values rather than Boolean values or values from some bounded range, and in which approximate, rather than exact, agreement is the desired goal. Algorithms are presented to reach approximate agreement in asynchronous, as well as synchronous systems. The asynchronous agreement algorithm is an
Reaching Approximate Agreement in the Presence of Faults
Danny Dolev; Nancy A. Lynch; Shlomit S. Pinter; Eugene W. Stark; William E. Weihl
1983-01-01
This paper considers a variant of the Byzantine Generals problem, in which processes start with arbitrary real values rather than Boolean values or values from some bounded range, and in which approximate, rather than exact, agreement is the desired goal. Algorithms are presented to reach approximate agreement in asynchronous, as well as synchronous systems. The asynchronous agreement algorithm is an
On approximate phasor models in dissipative bilinear systems
Gilead Tadmor
2002-01-01
Dynamic phasors models capture transients in (main) harmonic coefficients of periodically dominated systems, and their utility in state approximations is supported by machine and power systems case studies. The author explores analytical plausibility arguments, and inherent restrictions of such approximations in dissipative systems with quadratically nonlinear lossless components.
Sensitivity, Approximation and Uncertainty in Power System Dynamic Simulation
1 Sensitivity, Approximation and Uncertainty in Power System Dynamic Simulation Ian A. Hiskens sensitivities can be used to generate accurate first-order approximations of trajecto- ries that arise from perturbed parameter sets. The computational cost of obtaining the sensitivities and perturbed trajectories
Least square approximation of a nonlinear ordinary differential equation
T. Benouaz; O. Arino
1996-01-01
The aim of this paper is to present an optimal approximation method for a nonlinear ordinary differential equation based on the minimization in the least square sense. The approximation is order two or higher in the vicinity of the origin. We provide a few examples.
Improved Approximation Algorithms for the Capacitated Multicast Routing Problem
Zhipeng Cai; Guohui Lin; Guoliang Xue
2005-01-01
For the Capacitated Multicast Routing Problem, we con- sidered two models which are the Multicast k-Path Routing and the Multicast k-Tree Routing. We presented two improved approximation algorithms for them, which have worst case performance ratios of 3 and (2 + ) ( is the best approximation ratio for the Steiner Tree problem, and is about 1.55), respectively, thus improving
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.
The Flamingo Software Package on Approximate String Queries
Li, Chen
The Flamingo Software Package on Approximate String Queries Chen Li Department of Computer Science an overview of recent results on this problem, and describe the development history of the Flamingo pack- age Cleaning, Flamingo Package, Approximate String Search This research is partially supported by the US NSF
New Approximations of Dioeerential Entropy for Independent Component
Hyvärinen, Aapo
computationally more expensive. The approximation has applications, for example, in independent component analysis in which entropy is minimal, for constant variance. Unfortunately, the estimation of entropy is quite diNew Approximations of Dioeerential Entropy for Independent Component Analysis and Projection
Fast approximate calculation of multiply scattered lidar returns
Hogan, Robin
Fast approximate calculation of multiply scattered lidar returns Robin J. Hogan An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view
Tree approximation with anisotropic decompositions June 19, 2011
Grohs, Philipp
anisotropic transforms like the shearlet or curvelet transform have received a considerable amount of interest which is very simple Â it is defined by hard thresholding of the transform coefficients in a curvelet-term approximation. In this paper we study tree-approximation properties of such transforms where the N
Approximate Queueing Network Analysis of Patient Treatment Times
Knottenbelt, William J.
to a model of a large hospital's Accident and Emer- gency department for which we obtain the mean and stan Theory, Analytical Models and Approximation Methods ABSTRACT We develop an approximate generating-threatening incidents within 8 minutes [15]. In such contexts, it is important to develop effective performance models
The Born-Oppenheimer Approximation C. David Sherrill
Sherrill, David
The Born-Oppenheimer Approximation C. David Sherrill School of Chemistry and Biochemistry Georgia as a product of nuclear and elec- tronic terms, (r, R) = (r)(R). We thus introduce the Born-Oppenheimer that the total wavefunction is given as (r; R)(R). The Born-Oppenheimer approximation rests on the fact
On Approximating the Translational Velocity of Vortex Rings
Mohseni, Kamran
into the reservoir spirals up on itself rolling into a vor- tex ring. Jet flows created from cylinderOn Approximating the Translational Velocity of Vortex Rings Michael Krieg Department of Mechanical whereby the translational velocity of a vor- tex ring can be approximated from the total circulation
The Approximate Average Rate of Interest Cognitive Approach
F. Briquet
2000-01-01
This research work treats formalization of the knowledge of decision makers of SME. It aims at identifying their diagram of reasoning when they make financial decisions. When they prepare the investment plan, these decision makers make an approximation of the distribution of interests and repayments in the annual instalment of loan. These approximations are similar of one decision maker to
Numerical approximations of the 10-moment Gaussian closure
Christophe Berthon
2006-01-01
We propose a numerical scheme to approximate the weak solu- tions of the 10-moment Gaussian closure. The moment Gaussian closure for gas dynamics is governed by a conservative hyperbolic system supplemented by entropy inequalities whose solutions satisfy positiveness of density and ten- sorial pressure. We consider a Suliciu type relaxation numerical scheme to approximate the solutions. These methods are proved
SOME APPROXIMATION PROPERTIES OF BANACH SPACES AND BANACH LATTICES
Johnson, William B.
approximation property = BAP (resp. the uniform approximation property = UAP ) of a pair [Banach. UAP ), then the quotient X=Y has the BAP (resp. UAP ). If Q : X ! Z is a sur- jection, X is a L1-space and Z is a Lp-space (1 p 1) then kerQ has the UAP . A complemented subspace
FUZZY AND TILE CODING FUNCTION APPROXIMATION IN AGENT COEVOLUTION
Tokarchuk, Laurissa
a synopsis of the two implemented function approximation algorithms, Fuzzy Sarsa and gradient-descent SarsaFUZZY AND TILE CODING FUNCTION APPROXIMATION IN AGENT COEVOLUTION ABSTRACT Reinforcement learning in many small-scale domains. The true potential of this technique cannot be fully realised until it can
Approximate solution of nonlinear differential equations with convolution product nonlinearities
Ji-Huan He
1998-01-01
In this paper, a new iteration method is proposed to solve nonlinear problems. Special attention is paid to nonlinear differential equations with convolution product nonlinearities. The results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems. Furthermore, the first order of approximations are more accurate than perturbation solutions at
Recent advances in approximation concepts for optimum structural design
NASA Technical Reports Server (NTRS)
Barthelemy, Jean-Francois M.; Haftka, Raphael T.
1991-01-01
The basic approximation concepts used in structural optimization are reviewed. Some of the most recent developments in that area since the introduction of the concept in the mid-seventies are discussed. The paper distinguishes between local, medium-range, and global approximations; it covers functions approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It also appears that some new methodologies are emerging which could greatly benefit from the introduction of new computer architecture.
Rytov approximation for x-ray phase imaging.
Sung, Yongjin; Barbastathis, George
2013-02-11
In this study, we check the accuracy of the first-order Rytov approximation with a homogeneous sphere as a candidate for application in x-ray phase imaging of large objects e.g., luggage at the airport, or a human patient. Specifically, we propose a validity condition for the Rytov approximation in terms of a parameter V that depends on the complex refractive index of the sphere and the Fresnel number, for Fresnel numbers larger than 1000. In comparison with the exact Mie solution, we provide the accuracy of the Rytov approximation in predicting the intensity and phase profiles after the sphere. For large objects, where the Mie solution becomes numerically impractical, we use the principle of similarity to predict the accuracy of the Rytov approximation without explicit calculation of the Mie solution. Finally, we provide the maximum radius of the sphere for which the first order Rytov approximation remains valid within 1% accuracy. PMID:23481723
An approximation theory for the identification of linear thermoelastic systems
NASA Technical Reports Server (NTRS)
Rosen, I. G.; Su, Chien-Hua Frank
1990-01-01
An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.
Approximate number word knowledge before the cardinal principle.
Gunderson, Elizabeth A; Spaepen, Elizabet; Levine, Susan C
2015-02-01
Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge. PMID:25462030
Non-perturbative QCD amplitudes in quenched and eikonal approximations
NASA Astrophysics Data System (ADS)
Fried, H. M.; Grandou, T.; Sheu, Y.-M.
2014-05-01
Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations at least, physical insights are presented that rely on the newly-discovered property of effective locality. The present article also provides a more rigorous mathematical basis for the crude approximations used in the previous derivation of the binding potential of quarks and nucleons. Furthermore, the techniques of Random Matrix calculus along with Meijer G-functions are applied to analyze the generic structure of fermionic amplitudes in QCD.
Post-Newtonian approximation of the Vlasov-Nordström system
Sebastian Bauer
2004-10-23
We study the Nordstr\\"om-Vlasov system which describes the dynamics of a self-gravitating ensemble of collisionless particles in the framework of the Nordstr\\"om scalar theory of gravitation. If the speed of light $c$ is considered as a parameter, it is known that in the Newtonian limit $c\\to\\infty$ the Vlasov-Poisson system is obtained. In this paper we determine a higher approximation and establish a pointwise error estimate of order $O(c^{-4})$. Such an approximation is usually called a 1.5 post-Newtonian approximation.
Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers
NASA Technical Reports Server (NTRS)
Wong, Yau Shu; Jiang, Hong
1987-01-01
Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method used in conjunction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used.
The Space Complexity of Approximating the Frequency Moments
Noga Alon; Yossi Matias; Mario Szegedy
1999-01-01
The frequency moments of a sequence containingmielements of typei, 1?i?n, are the numbersFk=?ni=1mki. We consider the space complexity of randomized algorithms that approximate the numbersFk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the numbersF0,F1, andF2can be approximated in logarithmic space, whereas the approximation ofFkfork?6 requiresn?(1)space. Applications to
Baby Skyrme model, near-BPS approximations, and supersymmetric extensions
NASA Astrophysics Data System (ADS)
Bolognesi, S.; Zakrzewski, W.
2015-02-01
We study the baby Skyrme model as a theory that interpolates between two distinct BPS systems. For this, a near-BPS approximation can be used when there is a small deviation from each of the two BPS limits. We provide analytical explanation and numerical support for the validity of this approximation. We then study the set of all possible supersymmetric extensions of the baby Skyrme model with N =1 and the particular ones with extended N =2 supersymmetries and relate this to the above mentioned almost-BPS approximation.
A Topological Approach to Soft Covering Approximation Space
Naime Tozlu; Saziye Yuksel; Tugba Han Simsekler
2015-03-25
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this paper, we study soft covering based rough sets from the topological view. We present under which conditions soft covering lower approximation operation become interior operator and the soft covering upper approximation become closure operator. Also some new methods for generating topologies are obtained. Finally, we study the relationship between concepts of topology and soft covering lower and soft covering upper approximations.
Approximation algorithms for maximum two-dimensional pattern matching
Arikati, S.R. [Memphis Univ., TN (United States); Dessmark, A.; Lingas, A. [Lund Univ. (Sweden); Marathe, M.
1996-07-01
We introduce the following optimization version of the classical pattern matching problem (referred to as the maximum pattern matching problem). Given a two-dimensional rectangular text and a 2- dimensional rectangular pattern find the maximum number of non- overlapping occurrences of the pattern in the text. Unlike the classical 2-dimensional pattern matching problem, the maximum pattern matching problem is NP - complete. We devise polynomial time approximation algorithms and approximation schemes for this problem. We also briefly discuss how the approximation algorithms can be extended to include a number of other variants of the problem.
Linear approximation in the nonsymmetric Jordan-Thiry theory
M. W. Kalinowski; R. B. Mann
1986-01-01
Summary This paper is devoted to a linear approximation of the nonsymmetric Jordan-Thiry theory. We deal basically with the Langrangian\\u000a for the scalar field ? connected to the «gravitational constant». We compute this Lagrangian up to the second order of approximation\\u000a inh\\u000a \\u000a ??\\u000a =g\\u000a \\u000a ??\\u000a -?\\u000a \\u000a ??\\u000a . We prove that, in the zeroth and first orders of approximation in the
Communication: Improved pair approximations in local coupled-cluster methods
NASA Astrophysics Data System (ADS)
Schwilk, Max; Usvyat, Denis; Werner, Hans-Joachim
2015-03-01
In local coupled cluster treatments the electron pairs can be classified according to the magnitude of their energy contributions or distances into strong, close, weak, and distant pairs. Different approximations are introduced for the latter three classes. In this communication, an improved simplified treatment of close and weak pairs is proposed, which is based on long-range cancellations of individually slowly decaying contributions in the amplitude equations. Benchmark calculations for correlation, reaction, and activation energies demonstrate that these approximations work extremely well, while pair approximations based on local second-order Møller-Plesset theory can lead to errors that are 1-2 orders of magnitude larger.
Communication: Improved pair approximations in local coupled-cluster methods.
Schwilk, Max; Usvyat, Denis; Werner, Hans-Joachim
2015-03-28
In local coupled cluster treatments the electron pairs can be classified according to the magnitude of their energy contributions or distances into strong, close, weak, and distant pairs. Different approximations are introduced for the latter three classes. In this communication, an improved simplified treatment of close and weak pairs is proposed, which is based on long-range cancellations of individually slowly decaying contributions in the amplitude equations. Benchmark calculations for correlation, reaction, and activation energies demonstrate that these approximations work extremely well, while pair approximations based on local second-order Møller-Plesset theory can lead to errors that are 1-2 orders of magnitude larger. PMID:25833558
Analytic approximate solution for Falkner-Skan equation.
Marinca, Vasile; Ene, Remus-Daniel; Marinca, Bogdan
2014-01-01
This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration. PMID:24883417
Analytic approximations to the modon dispersion relation. [in oceanography
NASA Technical Reports Server (NTRS)
Boyd, J. P.
1981-01-01
Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.
NASA Astrophysics Data System (ADS)
van Berkel, M.; Hogeweij, G. M. D.; Tamura, N.; Zwart, H. J.; Inagaki, S.; de Baar, M. R.; Ida, K.
2014-11-01
In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (?), convectivity (V), and damping (?) in a cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based upon the heat equation in a semi-infinite cylindrical domain. The approximations are based upon continued fractions, asymptotic expansions, and multiple harmonics. The relative error for the different derived approximations is presented for different values of frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can yield good approximations over a wide parameter space for different cases, such as no convection and damping, only damping, and both convection and damping. This paper is the second part (Part II) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part III, cylindrical approximations are treated for heat waves traveling towards the center of the plasma.
Approximate Dynamic Programming in Knowledge Discovery for Rapid Peter Frazier
Keinan, Alon
Approximate Dynamic Programming in Knowledge Discovery for Rapid Response Peter Frazier Princeton as a dynamic programming problem with, unfortunately, a huge state space. Several specific heuristics now to benefit future decisions. We address this using dynamic programming. Specifically, the state
Randomized accuracy-aware program transformations for efficient approximate computations
Misailovic, Sasa
Despite the fact that approximate computations have come to dominate many areas of computer science, the field of program transformations has focused almost exclusively on traditional semantics-preserving transformations ...
PLASMA Approximate Dynamic Programming finally cracks the locomotive optimization problem
Powell, Warren B.
PLASMA Â Approximate Dynamic Programming finally cracks the locomotive optimization problem programming to optimize the flows of locomotives over their networks. The problem was always to be handled if a model is going to accurately capture locomotive productivity. In addition
Proving acceptability properties of relaxed nondeterministic approximate programs
Carbin, Michael James
Approximate program transformations such as skipping tasks [29, 30], loop perforation [21, 22, 35], reduction sampling [38], multiple selectable implementations [3, 4, 16, 38], dynamic knobs [16], synchronization elimination ...
Construction of nonlinear filter algorithms using the saddlepoint approximation
Amayo, Esosa O
2006-01-01
In this thesis we propose the use of the saddlepoint method to construct nonlinear filtering algorithms. To our knowledge, while the saddlepoint approximation has been used very successfully in the statistics literature ...
Bayesian approximation error approach in full-wave ultrasound tomography.
Koponen, Janne; Huttunen, Tomi; Tarvainen, Tanja; Kaipio, Jari P
2014-10-01
In ultrasound tomography, the spatial distribution of the speed of sound in a region of interest is reconstructed based on transient measurements made around the object. The computation of the forward problem (the full-wave solution) within the object is a computationally intensive task and can often be prohibitive for practical purposes. The purpose of this paper is to investigate the feasibility of using approximate forward solvers and the partial recovery from the related errors by employing the Bayesian approximation error approach. In addition to discretization error, we also investigate whether the approach can be used to reduce the reconstruction errors that are due to the adoption of approximate absorbing boundary models. We carry out two numerical studies in which the objective is to reduce the computational times to around 3% of the time that would be required by a numerically accurate forward solver. The results show that the Bayesian approximation error approach improves the reconstructions. PMID:25265173
15. Looking north from east bank of ditch, approximately halfway ...
15. Looking north from east bank of ditch, approximately halfway between cement pipe to north and burned irrigation pump station to south - Natomas Ditch System, Blue Ravine Segment, Juncture of Blue Ravine & Green Valley Roads, Folsom, Sacramento County, CA
Tractability through approximation : a study of two discrete optimization problems
Farahat, Amr, 1973-
2004-01-01
(cont.) algorithm, at one extreme, and complete enumeration, at the other extreme. We derive worst-case approximation guarantees on the solution produced by such an algorithm for matroids. We then define a continuous ...
Approximate penetration factors for nuclear reactions of astrophysical interest
NASA Technical Reports Server (NTRS)
Humblet, J.; Fowler, W. A.; Zimmerman, B. A.
1987-01-01
The ranges of validity of approximations of P(l), the penetration factor which appears in the parameterization of nuclear-reaction cross sections at low energies and is employed in the extrapolation of laboratory data to even lower energies of astrophysical interest, are investigated analytically. Consideration is given to the WKB approximation, P(l) at the energy of the total barrier, approximations derived from the asymptotic expansion of G(l) for large eta, approximations for small values of the parameter x, applications of P(l) to nuclear reactions, and the dependence of P(l) on channel radius. Numerical results are presented in tables and graphs, and parameter ranges where the danger of serious errors is high are identified.
Finding approximately rank-one submatrices with the nuclear norm ...
2010-11-08
the largest rank-one approximation of A (up to the scaling factor ?A?. ?1. ). ..... some weaker statements about the relationship between ? and sparsity are possible. ..... Breaking the equation Y + Z = A into blocks and scaling by 1/?A?? ?.
Envelope Computation in the Plane by Approximate Implicitization
JÃ¼ttler, Bert
Envelope Computation in the Plane by Approximate Implicitization Tino Schulz Johannes Kepler University of Linz, Austria tino.schulz@jku.at Bert JÂ¨uttler Johannes Kepler University of Linz, Austria bert
Approximate Self-Consistent Models for Tidally Truncated Star Clusters
D. C. Heggie; N. Ramamani
1993-03-19
This paper generalises King's models for tidally truncated star clusters by including approximately the non-spherical symmetry of the tidal field and the resulting non-spherical distortion of the cluster.
The local potential approximation in the background field formalism
I. Hamzaan Bridle; Juergen A. Dietz; Tim R. Morris
2014-03-20
Working within the familiar local potential approximation, and concentrating on the example of a single scalar field in three dimensions, we show that the commonly used approximation method of identifying the total and background fields, leads to pathologies in the resulting fixed point structure and the associated spaces of eigenoperators. We then show how a consistent treatment of the background field through the corresponding modified shift Ward identity, can cure these pathologies, restoring universality of physical quantities with respect to the choice of dependence on the background field, even within the local potential approximation. Along the way we point out similarities to what has been previously found in the f(R) approximation in asymptotic safety for gravity.
7. BUILDING 324, REAR YARD AREA, FROM APPROXIMATELY 25 FEET ...
7. BUILDING 324, REAR YARD AREA, FROM APPROXIMATELY 25 FEET NORTHWEST OF NORTHWEST CORNER OF NORTH WING, LOOKING WEST. - Oakland Naval Supply Center, Commanding Officers Residences, Between E & F Streets, West of Fourth Street, Oakland, Alameda County, CA
5. BUILDING 324, EAST SIDE, FROM APPROXIMATELY 20 FEET EAST ...
5. BUILDING 324, EAST SIDE, FROM APPROXIMATELY 20 FEET EAST OF BUILDING 324, LOOKING WEST. - Oakland Naval Supply Center, Commanding Officers Residences, Between E & F Streets, West of Fourth Street, Oakland, Alameda County, CA
6. BUILDING 324, WESTERN PORTION OF NORTH SIDE, FROM APPROXIMATELY ...
6. BUILDING 324, WESTERN PORTION OF NORTH SIDE, FROM APPROXIMATELY 15 FEET NORTHWEST OF MAIN STRUCTURE, LOOKING SOUTH. - Oakland Naval Supply Center, Commanding Officers Residences, Between E & F Streets, West of Fourth Street, Oakland, Alameda County, CA
3. BUILDING 324, NORTH SIDE (OBSCURED), FROM APPROXIMATELY 40 FEET ...
3. BUILDING 324, NORTH SIDE (OBSCURED), FROM APPROXIMATELY 40 FEET NORTH OF BUILDING, LOOKING SOUTH. - Oakland Naval Supply Center, Commanding Officers Residences, Between E & F Streets, West of Fourth Street, Oakland, Alameda County, CA
6. NORTH SIDE, FROM APPROXIMATELY 25 FEET SOUTHEAST OF SOUTHWEST ...
6. NORTH SIDE, FROM APPROXIMATELY 25 FEET SOUTHEAST OF SOUTHWEST CORNER OF BUILDING 320, LOOKING SOUTH. - Oakland Naval Supply Center, Administration Building-Dental Annex-Dispensary, Between E & F Streets, East of Third Street, Oakland, Alameda County, CA
Perspective view looking from the northwest from approximately the same ...
Perspective view looking from the northwest from approximately the same vantage point as in MD-1109-19 - National Park Seminary, Colonial House, 2745 Dewitt Circle, Silver Spring, Montgomery County, MD
Some approximations to the flapping stability of helicopter rotors
NASA Technical Reports Server (NTRS)
Biggers, J. C.
1974-01-01
The flapping equation for a helicopter in forward flight has coefficients which are periodic in time, and this effect complicates the calculation of stability. This paper presents a constant coefficient approximation which will allow the use of all the well known methods for analyzing constant coefficient equations. The flapping equation is first transformed into the nonrotating coordinate frame, where some of the periodic coefficients are transformed into constant terms. The constant coefficient approximation is then made by using time averaged coefficients in the nonrotating frame. Stability calculations based on the approximation are compared to results from a theory which correctly includes all of the periodicity. The comparison indicates that the approximation is reasonably accurate at advance ratios up to 0.5.
Some approximations to the flapping stability of helicopter rotors
NASA Technical Reports Server (NTRS)
Biggers, J. C.
1974-01-01
The flapping equation for a helicopter in forward flight are reported which have coefficients that are periodic in time, and this effect complicates the calculation of stability. A constant coefficient approximation which will allow the use of all the well known methods for analyzing constant coefficient equations are presented. The flapping equation is first transformed into the nonrotating coordinate frame, where some of the periodic coefficients are transformed into constant terms. The constant coefficient approximation is then made by using time averaged coefficients in the nonrotating frame. Stability calculations based on the approximation are compared to results from a theory which correctly includes all of the periodicity. The comparison indicates that the approximation is reasonably accurate at advance ratios up to 0.5.
Real-time creased approximate subdivision surfaces with displacements.
Kovacs, Denis; Mitchell, Jason; Drone, Shanon; Zorin, Denis
2010-01-01
We present an extension of Loop and Schaefer's approximation of Catmull-Clark surfaces (ACC) for surfaces with creases and corners. We discuss the integration of ACC into Valve's Source game engine and analyze performance of our implementation. PMID:20616390
Approximate dynamic programming with applications in multi-agent systems
Valenti, Mario J. (Mario James), 1976-
2007-01-01
This thesis presents the development and implementation of approximate dynamic programming methods used to manage multi-agent systems. The purpose of this thesis is to develop an architectural framework and theoretical ...
Contextual classification of multispectral image data: Approximate algorithm
NASA Technical Reports Server (NTRS)
Tilton, J. C. (principal investigator)
1980-01-01
An approximation to a classification algorithm incorporating spatial context information in a general, statistical manner is presented which is computationally less intensive. Classifications that are nearly as accurate are produced.
11. INTERIOR, LOADING DOOR DETAIL, NORTHWEST STORAGE AREA, FROM APPROXIMATELY ...
11. INTERIOR, LOADING DOOR DETAIL, NORTHWEST STORAGE AREA, FROM APPROXIMATELY 20 FEET SOUTH OF LOADING DOOR, LOOKING NORTH. - Oakland Naval Supply Center, Pier Transit Shed, South of D Street between First & Second Streets, Oakland, Alameda County, CA
Controlling chaos using nonlinear approximations and delay coordinate embedding
NASA Astrophysics Data System (ADS)
Yagasaki, Kazuyuki; Uozumi, Tomotsugu
1998-10-01
In a previous paper we showed that a chaos control method proposed by Ott, Grebogi and Yorke can be improved by using nonlinear approximations for chaotic dynamical systems and stable manifolds of targets. Here we consider systems whose governing equations are unknown and apply the chaos control method using the nonlinear approximations. Delay coordinate embedding techniques are used, so that approximate saddle points to be stabilized and nonlinear approximations of the systems and stable manifolds are obtained from time series of single variables. We also take into account the fact that the obtained section maps depend on the current and previous parameters. To demonstrate our approach, we give two numerical examples for the Hénon map and a pendulum with feedforward and feedback control. Some influences of noise are also discussed in these examples.
Provably Good Approximation Algorithms for Optimal Kinodynamic Planning: Robots with
Richardson, David
Provably Good Approximation Algorithms for Optimal Kinodynamic Planning: Robots with Decoupled-7501 Patrick Xavier Sandia National Laboratories, Albuquerque NM 87185-0951 Keywords: robot motion planning, kinodynamics, polyhedral obstacles Abstract: We consider the following problem: given a robot system, nd
Numerical Test of Born-Oppenheimer Approximation in Chaotic Systems
Jeong-Bo Shim; Mahir S. Hussein; Martina Hentschel
2009-08-04
We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators, we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space.
On the mathematical treatment of the Born-Oppenheimer approximation
Thierry Jecko
2014-04-24
Motivated by a paper by B.T. Sutcliffe and R.G. Woolley, we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigourous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by B.T. Sutcliffe and R.G. Woolley. The paper neither contains mathematical statements nor proofs. Instead we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.
An Approximate Truthfulness Motivated Spectrum Auction for Dynamic Spectrum Access
Zhou, Yuanyuan
An Approximate Truthfulness Motivated Spectrum Auction for Dynamic Spectrum Access Qinhui Wang, China Institute of Computer Science, University of Goettingen, Germany Abstract--Secondary Spectrum Auction (SSA) has been pro- posed as an effective approach to design spectrum sharing mechanism
ON LEAST SQUARES EUCLIDEAN DISTANCE MATRIX APPROXIMATION AND COMPLETION
in biological or engineering applications, including molecular structure analysis, protein folding problem, remote exploration and sensing, antenna array processing, and utility allocation problem. Key words. distance geometry, least squares approximation, matrix completion, molecular structure, protein folding
Improved Approximation Bounds for Planar Point Pattern Matching
Mount, David
. This is a well studied problem in computational geometry. Goodrich, Mitchell, and Orletsky [GMO94] presented, and Orletsky [GMO94]. They presented a very simple approximation algorithm for a number of pattern matching
Tighter Approximated MILP Formulations for Unit Commitment Problems
Antonio Frangioni; Claudio Gentile; Fabrizio Lacalandra
2009-01-01
The short-term unit commitment (UC) problem in hydrothermal power generation is a large-scale, mixed-integer nonlinear program, which is difficult to solve efficiently, especially for large-scale instances. It is possible to approximate the nonlinear objective function of the problem by means of piecewise-linear functions, so that UC can be approximated by an mixed-integer linear program (MILP); applying the available efficient general-purpose
A Dual Variable Approximation Based Heuristic for Dynamic Congestion Pricing
Dung-Ying Lin; Avinash Unnikrishnan; S. Travis Waller
2011-01-01
This work presents a heuristic combining dual variable approximation techniques and the method of successive average to determine\\u000a the time-varying tolls in a general transportation network. The dual approximation techniques exploit the linear programming\\u000a structure of the underlying assignment problem which uses the cell transmission model to propagate the traffic dynamics. Both\\u000a the first best and second best time-varying tolls
Approximation Methods in Multidisciplinary Analysis and Optimization: A Panel Discussion
Timothy W. Simpson; Andrew J. Booker; Dipankar Ghosh; Anthony A. Giunta; Patrick N. Koch; Ren-Jye Yang
2002-01-01
This paper summarizes the discussion at the Approximation Methods Panel that was held at the 9th AIAA\\/ISSMO Symposium on Multidisciplinary Analysis & Optimization in Atlanta, GA on September 2-4, 2002. The objective in the panel was to discuss the current state-of-the-art of approximation methods and identify future research directions important to the community. The panel consisted of five representatives from
Approximation methods in multidisciplinary analysis and optimization: a panel discussion
T. W. Simpson; A. J. Booker; D. Ghosh; A. A. Giunta; P. N. Koch; R.-J. Yang
2004-01-01
This paper summarizes the discussion at the Approximation Methods Panel that was held at the 9 th AIAA\\/ISSMO Symposium on Multidisciplinary Analysis & Optimization in Atlanta, GA on September 2–4, 2002. The objective of the panel was to discuss the current state-of-the-art of approximation methods and identify future research directions important to the community. The panel consisted of five representatives