Quasi-isotropic VHF antenna array design study for the International Ultraviolet Explorer satellite
NASA Technical Reports Server (NTRS)
Raines, J. K.
1975-01-01
Results of a study to design a quasi-isotropic VHF antenna array for the IUE satellite are presented. A free space configuration was obtained that has no nulls deeper than -6.4 dbi in each of two orthogonal polarizations. A computer program named SOAP that analyzes the electromagnetic interaction between antennas and complicated conducting bodies, such as satellites was developed.
NASA Astrophysics Data System (ADS)
Dey, S.; Karmakar, A.
2013-01-01
In this paper, a finite element method is employed to investigate the free vibration characteristics of single and multiple delaminated graphite-epoxy quasi-isotropic composite conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The formulation is based on Mindlin's theory considering eight-noded isoparametric plate bending element. The multipoint constraint algorithm is employed to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The QR iteration algorithm is utilized for solution of standard eigen value problem. Finite element codes are developed to obtain the natural frequencies of single and multiple delaminated quasi-isotropic composite conical shells. The mode shapes for a typical laminate configuration are also depicted. Numerical results obtained are the first known values which could serve as reference solutions for the future investigators.
Flexural stiffnesses of and dimensional stability in circular quasi-isotropic laminate mirrors
NASA Astrophysics Data System (ADS)
Kim, Kyung-Pyo
Composite fiber reinforced plastics are being given favorable consideration for emerging applications in large aperture telescopes, such as the Hubble telescope or communication dishes. Many lightweight mirror fabrication concepts are currently being pursued. Presently, the technology is limited because it has an incomplete understanding of the mechanics associated with quasi-isotropic laminates for diffraction-limited displacement constraints, and lack of understanding for effects of resin buffer layers on composite mirrors for high surface smoothness. In this dissertation document, radial stiffness associated with stacking sequence effects in quasi-isotropic laminates (pi/n, where n=3, 4, and 6) and dimensional stability in the composite laminates are investigated numerically. The numerical results show that directional dependency of flexural stiffness in the laminates, which is strongly associated with stacking sequences, is a significant factor causing unfavorable sinusoidal surface waviness. The maximum radial flexural stiffness variation is found as +/-12.85% in pi/3 laminate while a minimum of +/-5.63% is found in pi/4 laminate. Mechanics of maximum asymmetry by +/-2º misorientation based on ideal pi/n laminate lay-ups are evaluated and the results are compared with ideal lay-up sequence cases. The calculated extensional and flexural stiffness values from the maximum asymmetric cases are within less than 0.05%. As such, the radial flexural stiffness variations in quasi-isotropic laminates are shown to be more problematic than asymmetry caused by common manufacturing variance. The types of surface deformations in quasi-isotropic laminates associated with directional dependency of flexural stiffness are evaluated using finite element analyses. Also, fiber print-through in replicated composite mirrors and the effects of the resin buffer layer present in the mirrors for mitigation of the fiber print-through are investigated and discussed. Numerical results reveal that there will be an unfavorable sinusoidal surface deformation in each ideal p/n laminate and the shapes are strongly associated with principal fiber directions due to stacking sequence effects. The surface deformations in quasi-isotropic laminates are shown to be typical and such surface deformations are inevitable when composite mirrors are fabricated from discrete layers of anisotropic carbon fiber reinforced plastics. Moreover, the use of additional resin layers appears to more adversely influence the composite mirror substrates. The validation of predicted surface deformations and dimensional distortions are achieved by comparing experimental results on a 8-inch-diameter composite mirror sample fabricated at the University of Kansas Dept. of Aerospace Engineering (KUAE) and Bennett Optical Research (BOR). A study of quasi-homogeneous materials such as short fiber products as alternative composite materials is investigated. Furthermore, the relation between resin property effects and corresponding resin thickness effects is evaluated and discussed. The analyses provide information on alternative types of materials that primarily affect optical performance and thus are most important for precision optics. Based on the results, locally varying radial surface deformations in quasi-isotropic laminates fabricated from continuous fiber reinforced plastics distort optical performance. These surface deformations might be eliminated by utilizing short fiber materials and a soft resin system with a very low coefficient of thermal expansion compared to conventional resins.
Buckling of a sublaminate in a quasi-isotropic composite laminate
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Whitcomb, J. D.
1985-01-01
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.
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.
Elastic properties and fracture strength of quasi-isotropic graphite/epoxy composites
NASA Technical Reports Server (NTRS)
Sullivan, T. L.
1977-01-01
A research program is described which was devised to determine experimentally the elastic properties in tension and bending of quasi-isotropic laminates made from high-modulus graphite fiber and epoxy. Four laminate configurations were investigated, and determinations were made of the tensile modulus, Poisson's ratio, bending stiffness, fracture strength, and fracture strain. The measured properties are compared with those predicted by laminate theory, reasons for scatter in the experimental data are discussed, and the effect of fiber misalignment on predicted elastic tensile properties is examined. The results strongly suggest that fiber misalignment in combination with variation in fiber volume content is responsible for the scatter in both elastic constants and fracture strength.
Thermo-oxidative degradation assessment in quasi-isotropic carbon fiber/epoxy composites
NASA Astrophysics Data System (ADS)
Daily, Connor; Barnard, Dan J.; Jones, Roger W.; McClelland, John F.; Bowler, Nicola
2015-03-01
Components made from polymer matrix composites (PMCs) are finding increasing use in armored vehicles for the purpose of weight savings and fuel efficiency. Often times, these PMC components are installed next to engines, or in other high-temperature environments within the vehicle. The present work investigates the change in surface chemistry and its correlation with changes in the interlaminar shear strength (ILSS) due to accelerated thermo-oxidative aging of a quasi-isotropic carbon fiber reinforced epoxy laminate. Samples are aged isothermally at various temperatures whose selection is guided by degradation steps revealed by thermo-gravimetric analysis. Fourier transform infrared (FTIR) photoacoustic spectroscopy is utilized to identify the chemical changes due to aging, and compression-test results reveal a non-linear decrease in ILSS with increasing aging temperature. A correlation between the FTIR and ILSS data sets suggests that nondestructive FTIR techniques may be used for assessing ILSS of PMCs.
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
High-Q/V Monolithic Diamond Microdisks Fabricated with Quasi-isotropic Etching.
Khanaliloo, Behzad; Mitchell, Matthew; Hryciw, Aaron C; Barclay, Paul E
2015-08-12
Optical microcavities enhance light-matter interactions and are essential for many experiments in solid state quantum optics, optomechanics, and nonlinear optics. Single crystal diamond microcavities are particularly sought after for applications involving diamond quantum emitters, such as nitrogen vacancy centers, and for experiments that benefit from diamond's excellent optical and mechanical properties. Light-matter coupling rates in experiments involving microcavities typically scale with Q/V, where Q and V are the microcavity quality-factor and mode-volume, respectively. Here we demonstrate that microdisk whispering gallery mode cavities with high Q/V can be fabricated directly from bulk single crystal diamond. By using a quasi-isotropic oxygen plasma to etch along diamond crystal planes and undercut passivated diamond structures, we create monolithic diamond microdisks. Fiber taper based measurements show that these devices support TE- and TM-like optical modes with Q > 1.1 × 10(5) and V < 11(?/n) (3) at a wavelength of 1.5 ?m. PMID:26134379
NASA Astrophysics Data System (ADS)
Zeng, Chunmei; Yu, Xia; Guo, Peiji
2014-08-01
A regularization stiffness coefficient method was verified further to optimize lay-up sequences of quasi-isotropic laminates for carbon fiber reinforced polymer (CFRP) composite mirrors. Firstly, the deformation due to gravity of 1G and temperature difference of 20-100°C and the modal were analyzed by finite element method (FEM). Secondly, the influence of angle error of ply stacking on quasi-isotropic of bending stiffness was evaluated. Finally, an active support system of 49 actuators in circular arrangement is designed for a 500mm CFRP mirror, and its goal is to deform the spherical CFRP mirror to a parabolic. Therefore, the response functions of the actuators were gotten, and the surface form errors and stresses were calculated and analyzed. The results show that the CFRP mirrors designed by the method have a better symmetrical bending deformation under gravity and thermal load and a higher fundamental frequency, and the larger n the better symmetry (for ?/n quasi-isotropic laminates); the method reduces the sensitivity to misalignment of ply orientation for symmetric bending, and the mirror's maximum von Mises stress and maximum shear stress are less compared to those laminates not optimized in lay-up sequence.
Durability-Based Design Criteria for a Quasi-Isotropic Carbon-Fiber Automotive Composite
Corum, J.M.
2002-04-17
This report provides recommended durability-based design properties and criteria for a quasi-isotropic carbon-fiber composite for possible automotive structural applications. The composite, which was made by a rapid molding process suitable for high-volume automotive applications, consisted of continuous Thornel T300 fibers (6K tow) in a Baydur 420 IMR urethane matrix. The reinforcement was in the form of four {+-}45{sup o} stitch-bonded mats in the following layup: [0/90{sup o}/{+-}45{sup o}]{sub S}. This material is the second in a progression of three candidate thermoset composites to be characterized and modeled as part of an Oak Ridge National Laboratory project entitled Durability of Carbon-Fiber Composites. The overall goal of the project, which is sponsored by the U.S. Department of Energy's Office of Advanced Automotive Technologies and is closely coordinated with the industry Automotive Composites Consortium, is to develop durability-driven design data and criteria to assure the long-term integrity of carbon-fiber-based composite systems for large automotive structural components. This document is in two parts. Part I provides the design criteria, and Part 2 provides the underlying experimental data and models. The durability issues addressed include the effects on deformation, strength, and stiffness of cyclic and sustained loads, operating temperature, automotive fluid environments, and low-energy impacts (e.g., tool drops and kickups of roadway debris). Guidance is provided for design analysis, time-dependent allowable stresses, rules for cyclic loadings, and damage tolerance design guidance, including the effects of holes. Chapter 6 provides a brief summary of the design criteria.
NASA Technical Reports Server (NTRS)
Kelkar, A. D.
1984-01-01
In thin composite laminates, the first level of visible damage occurs in the back face and is called back face spalling. A plate-membrane coupling model, and a finite element model to analyze the large deformation behavior of eight-ply quasi-isotropic circular composite plates under impact type point loads are developed. The back face spalling phenomenon in thin composite plates is explained by using the plate-membrane coupling model and the finite element model in conjunction with the fracture mechanics principles. The experimental results verifying these models are presented. Several conclusions concerning the deformation behavior are reached and discussed in detail.
NASA Technical Reports Server (NTRS)
Sohi, M. M.; Hahn, H. T.; Williams, J. G.
1986-01-01
Compressive failure mechanisms in quasi-isotropic graphite/epoxy laminates were characterized for both unnotched and notched specimens and also following damage by impact. Two types of fibers (Thornel 300 and 700) and four resin systems (Narmco 5208, American Cyanamid BP907, and Union Carbide 4901/MDA and 4901/mPDA) were studied. For all material combinations, failure of unnotched specimens was initiated by kinking of fibers in the 0-degree plies. A major difference was observed, however, in the mode of failure propagation after the 0-degree ply failure. The strength of quasi-isotropic laminates in general increased with increasing resin tensile modulus. The laminates made with Thornel 700 fibers exhibited slightly lower compressive strengths than did the laminates made with Thornel 300 fibers. The notch sensitivity as measured by the hole strength was lowest for the BP907 resin and highest for the 5208 resin. For the materials studied, however, the type of fiber had no effect on the notch sensitivity.
NASA Technical Reports Server (NTRS)
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.
NASA Technical Reports Server (NTRS)
Illg, W.
1986-01-01
A partial-bonding interlaminar toughening concept was evaluated for resistance to impact and for behavior of a loaded hole. Perforated Mylar sheets were interleaved between all 24 plies of a graphite/epoxy quasi-isotropic lay-up. Specimens were impacted by aluminum spheres while under tensile or compressive loads. Impact-failure thresholds and residual strengths were obtained. Loaded-hole specimens were tested in three configurations that were critical in bearing, shear, or tension. Partial bonding reduced the tensile and compressive strengths of undamaged specimens by about one-third. For impact, partial bonding did not change the threshold for impact failure under tensile preload. However, under compressive preload, partial bonding caused serious degradation of impact resistance. Partial bonding reduced the maximum load-carrying capacity of all three types of loaded-hole specimens. Overall, partial bonding degraded both impact resistance and bearing strength of holes.
NASA Astrophysics Data System (ADS)
Kostopoulos, V.; Vavouliotis, A.; Loutas, T.; Karapappas, P.
2009-03-01
In this study, CNTs were used as modifiers of the epoxy matrix of quasi-isotropic carbon fibre reinforced laminates. The prepared laminates were subjected to tensile loading and tension-tension fatigue and, the changes in the longitudinal resistance were monitored via a digital multimeter. In addition, Acoustic Emission and Acousto-Ultrasonic techniques were used for monitoring the fatigue process of the laminates. The nano-enhanced laminates on the one hand exhibited superior fatigue properties and on the other hand they demonstrated the full-potential of the material to be used as an integrated sensor to monitor the fatigue life.
Evolution of complex amplitudes ratio in weakly anisotropic plasma
NASA Astrophysics Data System (ADS)
Kravtsov, Yury A.; Bieg, Bohdan
2010-10-01
The equation for evolution of the complex amplitudes ratio (CAR) ? = Ey/Ex in weakly anisotropic inhomogeneous media is derived on the basis of quasi-isotropic approximation (QIA) of the geometrical optics method. This equation is convenient for the description of electromagnetic wave polarization in magnetized plasma of thermonuclear reactors like the ITER. The equation for the CAR is in agreement with other approaches, analyzing polarization evolution in weakly anisotropic media, in particular, with the equation for complex polarization angle and, via QIA equations, with the Segre equation for Stokes vector evolution. Simple analytical solutions for the CAR, which relates to normal mode propagation in homogeneous and weakly inhomogeneous plasma, are obtained. Besides, the equation for the CAR is solved numerically to describe the phenomenon of normal wave conversion in magnetized plasma in the vicinity of the orthogonality point between the ray and the static magnetic field. In distinction to the line-averaged measurements in traditional plasma polarimetry, the phenomenon of normal wave conversion opens the way for measuring the local plasma parameters near the orthogonality point.
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.
Gautam, Natarajan
the traffic exhibits selfsimilarity . We propose and test an approximation method for ecommerce servers an appropriate design of the ecommerce server to reduce the number of requests in the system, (2) we obtain and suggestions for future work are discussed. 1 Selfsimilarity in telecommunication network traffic 1
Flexural Stiffnesses of and Dimensional Stability in Circular Quasi-isotropic Laminate Mirrors
Kim, Kyungpyo
2009-01-01
. [Ref. 7] ............................................... 3 Figure 2: LEFT, Newtonian CFRP 40cm parabolic primary mirror with aluminum + SiO overcoating, RIGHT, A CFRP Cassegrain 40 cm primary mirror with central hole. [Ref. 7... the 203 reference flat mirror in its mounting ......................... 111 Figure 49: Step 4-Mount the collimator (fl=75mm) on Optino (yellow above). Then screw on the plastic tube onto the collimator. Insert the other end of the tube...
Minimum variance guided wave imaging in a quasi-isotropic composite plate
NASA Astrophysics Data System (ADS)
Hall, James S.; McKeon, Peter; Satyanarayan, L.; Michaels, Jennifer E.; Declercq, Nico F.; Berthelot, Yves H.
2011-02-01
Ultrasonic guided waves are capable of rapidly interrogating large, plate-like structures for both nondestructive evaluation and structural health monitoring (SHM) applications. Distributed sparse arrays of inexpensive piezoelectric transducers offer a cost-effective way to automate the interrogation process. However, the sparse nature of the array limits the amount of information available for performing damage detection and localization. Minimum variance techniques have been incorporated into guided wave imaging to reduce the magnitude of imaging artifacts and improve the imaging performance for sparse array SHM applications. The ability of these techniques to improve imaging performance is related to the accuracy of a priori model assumptions, such as scattering characteristics and dispersion. This paper reports the application of minimum variance imaging under slightly inaccurate model assumptions, such as are expected in realistic environments. Specifically, the imaging algorithm assumes an isotropic, non-dispersive, single mode propagating environment with a scattering field independent of incident angle and frequency. In actuality, the composite material considered here is not only slightly anisotropic and dispersive but also supports multiple propagating modes, and additionally, the scattering field is dependent on the incident angle, scattered angle, and frequency. An isotropic propagation velocity is estimated via calibration prior to imaging to implement the non-dispersive model assumption. Imaging performance is presented under these inaccurate assumptions to demonstrate the robustness of minimum variance imaging to common sources of imaging artifacts.
Approximate Information Theory
Penny, Will
Approximate Inference Will Penny Information Theory Information Entropy Kullback-Liebler Divergence Approximate Inference Will Penny 31st March 2011 #12;Approximate Inference Will Penny Information Theory Will Penny Information Theory Information Entropy Kullback-Liebler Divergence Gaussians Asymmetry
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...
Adaptive Smolyak Pseudospectral Approximations
Marzouk, Youssef M.
Polynomial approximations of computationally intensive models are central to uncertainty quantification. This paper describes an adaptive method for nonintrusive pseudospectral approximation, based on Smolyak's algorithm ...
Naus, Dan J; Corum, James; Klett, Lynn B; Davenport, Mike; Battiste, Rick; Simpson, Jr., William A
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.
Verre, Ruggero; Antosiewicz, Tomasz J; Svedendahl, Mikael; Lodewijks, Kristof; Shegai, Timur; Käll, Mikael
2014-09-23
Quasicrystals are structures that possess long-range order without being periodic. We investigate the unique characteristics of a photonic quasicrystal that consists of plasmonic Ag nanodisks arranged in a Penrose pattern. The quasicrystal scatters light in a complex but spectacular diffraction pattern that can be directly imaged in the back focal plane of an optical microscope, allowing us to assess the excitation efficiency of the various diffraction modes. Furthermore, surface plasmon polaritons can be launched almost isotropically through near-field grating coupling when the quasicrystal is positioned close to a homogeneous silver surface. We characterize the dispersion relation of the different excited plasmon modes by reflection measurements and simulations. It is demonstrated that the quasicrystal in-coupling efficiency is strongly enhanced compared to a nanoparticle array with the same particle density but only short-range lateral order. We envision that the system can be useful for a number of advanced light harvesting and optoelectronic applications. PMID:25182843
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. PMID:25528318
Advisory function of the Tales of the Prophets (Qi?a? al-anbiy??)
Helewa, Sami
2012-06-26
This thesis examines the advisory function of the tales of three prophets (Joseph, David and Solomon) in al-?abar?’s (d. 923/310 AH) History and al-Tha?lab?’s (d. 1025/416) Tales of the Prophets within their religio-political ...
Approximate programmable quantum processors
Hillery, Mark; Ziman, Mario; Buzek, Vladimir
2006-02-15
A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor to approximate a set of unitary operators to a specified level of precision. We measure how well an operation is performed by the process fidelity between the desired operation and the operation produced by the processor. We show how to find the program for a given processor that produces the best approximation of a particular unitary operation. We also place bounds on the dimension of the program space that is necessary to approximate a set of unitary operators to a specified level of precision.
Approximate Bayesian Computation
NASA Astrophysics Data System (ADS)
Cisewski, Jessi
2015-08-01
Explicitly specifying a likelihood function is becoming increasingly difficult for many problems in astronomy. Astronomers often specify a simpler approximate likelihood - leaving out important aspects of a more realistic model. Approximate Bayesian computation (ABC) provides a framework for performing inference in cases where the likelihood is not available or intractable. I will introduce ABC and explain how it can be a useful tool for astronomers. In particular, I will focus on the eccentricity distribution for a sample of exoplanets with multiple sub-populations.
Multicriteria approximation through decomposition
Burch, C.; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E.
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. |; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E. |
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.
Optimizing the Zeldovich approximation
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Pellman, Todd F.; Shandarin, Sergei F.
1994-01-01
We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment of phases in the nonlinear regime. We also report on the accuracy of particle positions and velocities produced by TZA.
NASA Astrophysics Data System (ADS)
Sukumar, N.
2005-11-01
In this paper, the construction of scattered data approximants is studied using the principle of maximum entropy. For under-determined and ill-posed problems, Jaynes's principle of maximum information-theoretic entropy is a means for least-biased statistical inference when insufficient information is available. Consider a set of distinct nodes {xi}i=1n in Rd, and a point p with coordinate x that is located within the convex hull of the set {xi}. The convex approximation of a function u(x) is written as: uh(x) = ?i=1n ?i(x)ui, where {?i}i=1n ? 0 are known as shape functions, and uh must reproduce affine functions (d = 2): ?i=1n ?i = 1, ?i=1n ?ixi = x, ?i=1n ?iyi = y. We view the shape functions as a discrete probability distribution, and the linear constraints as the expectation of a linear function. For n > 3, the problem is under-determined. To obtain a unique solution, we compute ?i by maximizing the uncertainty H(?) = - ?i=1n ?i log ?i, subject to the above three constraints. In this approach, only the nodal coordinates are used, and neither the nodal connectivity nor any user-defined parameters are required to determine ?i—the defining characteristics of a mesh-free Galerkin approximant. Numerical results for {?i}i=1n are obtained using a convex minimization algorithm, and shape function plots are presented for different nodal configurations.
Topics in Metric Approximation
NASA Astrophysics Data System (ADS)
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Countably QC-Approximating Posets
Mao, Xuxin; Xu, Luoshan
2014-01-01
As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice ?c(L)op of all ?-Scott-closed subsets of L is weakly generalized countably approximating. PMID:25165730
Chalasani, P.; Saias, I.; Jha, S.
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Tsuyoshi Ito; Stacey Jeffery
2015-07-02
Span programs are a model of computation that have been used to design quantum algorithms, mainly in the query model. For any decision problem, there exists a span program that leads to an algorithm with optimal quantum query complexity, but finding such an algorithm is generally challenging. We consider new ways of designing quantum algorithms using span programs. We show how any span program that decides a problem $f$ can also be used to decide "property testing" versions of $f$, or more generally, approximate the span program witness size, a property of the input related to $f$. For example, using our techniques, the span program for OR, which can be used to design an optimal algorithm for the OR function, can also be used to design optimal algorithms for: threshold functions, in which we want to decide if the Hamming weight of a string is above a threshold or far below, given the promise that one of these is true; and approximate counting, in which we want to estimate the Hamming weight of the input. We achieve these results by relaxing the requirement that 1-inputs hit some target exactly in the span program, which could make design of span programs easier. We also give an exposition of span program structure, which increases the understanding of this important model. One implication is alternative algorithms for estimating the witness size when the phase gap of a certain unitary can be lower bounded. We show how to lower bound this phase gap in some cases. As applications, we give the first upper bounds in the adjacency query model on the quantum time complexity of estimating the effective resistance between $s$ and $t$, $R_{s,t}(G)$, of $\\tilde O(\\frac{1}{\\epsilon^{3/2}}n\\sqrt{R_{s,t}(G)})$, and, when $\\mu$ is a lower bound on $\\lambda_2(G)$, by our phase gap lower bound, we can obtain $\\tilde O(\\frac{1}{\\epsilon}n\\sqrt{R_{s,t}(G)/\\mu})$, both using $O(\\log n)$ space.
Approximate nonlinear self-adjointness and approximate conservation laws
Zhi-Yong Zhang
2013-04-03
In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed by means of the method. As an application, a class of perturbed nonlinear wave equations is considered to illustrate the effectiveness.
Approximation Bayesian Computation
Marjoram, Paul
2014-01-01
Approximation Bayesian computation [ABC] is an analysis approach that has arisen in response to the recent trend to collect data that is of a magnitude far higher than has been historically the case. This has led to many existing methods become intractable because of difficulties in calculating the likelihood function. ABC circumvents this issue by replacing calculation of the likelihood with a simulation step in which it is estimated in one way or another. In this review we give an overview of the ABC approach, giving examples of some of the more popular specific forms of ABC. We then discuss some of the areas of most active research and application in the field, specifically, choice of low-dimensional summaries of complex datasets and metrics for measuring similarity between observed and simulated data. Next, we consider the question of how to do model selection in an ABC context. Finally, we discuss an area of growing prominence in the ABC world, use of ABC methods in genetic pathway inference. PMID:25606346
Uniform asymptotic approximations of integrals
Khwaja, Sarah Farid
2014-07-01
In this thesis uniform asymptotic approximations of integrals are discussed. In order to derive these approximations, two well-known methods are used i.e., the saddle point method and the Bleistein method. To start with ...
Taylor Approximations and Definite Integrals
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2007-01-01
We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)
Approximating the Minimum Weight Triangulation
Eppstein, David
Approximating the Minimum Weight Triangulation David Eppstein Department of Information be approximated within a constant factor by a triangulation algorithm based on quadtrees. In O(n log n) time we can compute a triangulation with O(n) new points, and no ob- tuse triangles, that approximates
Cosmological applications of Padé approximant
Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan E-mail: 764644314@qq.com
2014-01-01
As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
NASA Technical Reports Server (NTRS)
Harris, C. E.; Morris, D. H.
1983-01-01
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 32- and 64-ply specimens. Delaminations were located at the interface where the maximum shear stress occurred regardless of the sense or magnitude of the interlaminar normal stress. An antibuckling fixture was effective in preventing out-of-plane motion without overconstraining the specimen.
Interplay of approximate planning strategies
Huys, Quentin J. M.
Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and ...
Dual approximations in optimal control
NASA Technical Reports Server (NTRS)
Hager, W. W.; Ianculescu, G. D.
1984-01-01
A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.
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
Approximate quantum and acoustic cloaking
Allan Greenleaf; Yaroslav Kurylev; Matti Lassas; Gunther Uhlmann
2008-12-09
At any energy E > 0, we construct a sequence of bounded potentials $V^E_{n}, n\\in\\N$, supported in an annular region $B_{out}\\setminus B_{inn}$ in three-space, which act as approximate cloaks for solutions of Schr\\"odinger's equation: For any potential $V_0\\in L^\\infty(B_{inn})$ such that E is not a Neumann eigenvalue of $-\\Delta+V_0$ in $B_{inn}$, the scattering amplitudes $a_{V_0+V_n^E}(E,\\theta,\\omega)\\to 0$ as $n\\to\\infty$. The $V^E_{n}$ thus not only form a family of approximately transparent potentials, but also function as approximate invisibility cloaks in quantum mechanics. On the other hand, for $E$ close to interior eigenvalues, resonances develop and there exist {\\it almost trapped states} concentrated in $B_{inn}$. We derive the $V_n^E$ from singular, anisotropic transformation optics-based cloaks by a de-anisotropization procedure, which we call \\emph{isotropic transformation optics}. This technique uses truncation, inverse homogenization and spectral theory to produce nonsingular, isotropic approximate cloaks. As an intermediate step, we also obtain approximate cloaking for a general class of equations including the acoustic equation.
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.
Relativistic regular approximations revisited: An infinite-order relativistic approximation
Dyall, K.G.; van Lenthe, E.
1999-07-01
The concept of the regular approximation is presented as the neglect of the energy dependence of the exact Foldy{endash}Wouthuysen transformation of the Dirac Hamiltonian. Expansion of the normalization terms leads immediately to the zeroth-order regular approximation (ZORA) and first-order regular approximation (FORA) Hamiltonians as the zeroth- and first-order terms of the expansion. The expansion may be taken to infinite order by using an un-normalized Foldy{endash}Wouthuysen transformation, which results in the ZORA Hamiltonian and a nonunit metric. This infinite-order regular approximation, IORA, has eigenvalues which differ from the Dirac eigenvalues by order E{sup 3}/c{sup 4} for a hydrogen-like system, which is a considerable improvement over the ZORA eigenvalues, and similar to the nonvariational FORA energies. A further perturbation analysis yields a third-order correction to the IORA energies, TIORA. Results are presented for several systems including the neutral U atom. The IORA eigenvalues for all but the 1s spinor of the neutral system are superior even to the scaled ZORA energies, which are exact for the hydrogenic system. The third-order correction reduces the IORA error for the inner orbitals to a very small fraction of the Dirac eigenvalue. {copyright} {ital 1999 American Institute of Physics.}
Heat pipe transient response approximation
NASA Astrophysics Data System (ADS)
Reid, Robert S.
2002-01-01
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. .
Quantitative approximation schemes for glasses
Matthieu Mangeat; Francesco Zamponi
2015-10-13
By means of a systematic expansion in $1/d$ around the infinite-dimensional solution, we obtain an approximation scheme to compute properties of glasses in low dimensions. The resulting equations take as input the thermodynamic and structural properties of the equilibrium liquid, and from this they allow one to compute properties of the glass. They are therefore similar in spirit to the Mode-Coupling approximation scheme. Our scheme becomes exact, by construction, in $d\\to\\infty$ and it can be improved systematically by adding more terms in the $1/d$ expansion.
Alternative implementation of Pade approximants
Amore, Paolo
2007-10-01
In this paper we devise an alternative approach to the use of Pade approximants in the resummation of the perturbative (either divergent or convergent) series. Our procedure relies on the introduction of a nonphysical parameter and on the constraint that the physical observable be linear in this parameter. The relation between the unphysical parameter and the physical perturbative parameter is expressed in terms of a Pade approximant, whose form can be fully determined. We have applied this strategy to a number of examples and we have compared the results to those obtained following the standard Pade approach, observing that in many cases our approach is superior.
APPROXIMATE CONSTRUCTIONS IN FINITE FIELDS
Shparlinski, Igor
Polynomial Interpolation [16, 22, 47]: AP3 -- AP7 ffl Testing Permutation Polynomials [29, 30]: AP1 We finishAPPROXIMATE CONSTRUCTIONS IN FINITE FIELDS Igor Shparlinski School of MPCE, Macquarie University. Given a finite field F q , find a primitive root of F q . Unfortunately, no deterministic polynomial
Isotropic Transformation Optics Approximate Cloaking
Maryland at College Park, University of
Isotropic Transformation Optics and Approximate Cloaking Allan Greenleaf joint with Yaroslav Kurylev Matti Lassas Gunther Uhlmann CLK08 @ CSCAMM September 24, 2008 #12;Challenges of cloaking and other transformation optics (TO) designs: #12;Challenges of cloaking and other transformation optics (TO
NASA Astrophysics Data System (ADS)
White, Martin
2014-04-01
This year marks the 100th anniversary of the birth of Yakov Zel'dovich. Amongst his many legacies is the Zel'dovich approximation for the growth of large-scale structure, which remains one of the most successful and insightful analytic models of structure formation. We use the Zel'dovich approximation to compute the two-point function of the matter and biased tracers, and compare to the results of N-body simulations and other Lagrangian perturbation theories. We show that Lagrangian perturbation theories converge well and that the Zel'dovich approximation provides a good fit to the N-body results except for the quadrupole moment of the halo correlation function. We extend the calculation of halo bias to third order and also consider non-local biasing schemes, none of which remove the discrepancy. We argue that a part of the discrepancy owes to an incorrect prediction of inter-halo velocity correlations. We use the Zel'dovich approximation to compute the ingredients of the Gaussian streaming model and show that this hybrid method provides a good fit to clustering of haloes in redshift space down to scales of tens of Mpc.
Padé approximations and diophantine geometry
Chudnovsky, D. V.; Chudnovsky, G. V.
1985-01-01
Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves. PMID:16593552
Pythagorean Approximations and Continued Fractions
ERIC Educational Resources Information Center
Peralta, Javier
2008-01-01
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
Chemical Laws, Idealization and Approximation
NASA Astrophysics Data System (ADS)
Tobin, Emma
2013-07-01
This paper examines the notion of laws in chemistry. Vihalemm ( Found Chem 5(1):7-22, 2003) argues that the laws of chemistry are fundamentally the same as the laws of physics they are all ceteris paribus laws which are true "in ideal conditions". In contrast, Scerri (2000) contends that the laws of chemistry are fundamentally different to the laws of physics, because they involve approximations. Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34-50, 2000) agree that the laws of chemistry are operationally different to the laws of physics, but claim that the distinction between exact and approximate laws is too simplistic to taxonomise them. Approximations in chemistry involve diverse kinds of activity and often what counts as a scientific law in chemistry is dictated by the context of its use in scientific practice. This paper addresses the question of what makes chemical laws distinctive independently of the separate question as to how they are related to the laws of physics. From an analysis of some candidate ceteris paribus laws in chemistry, this paper argues that there are two distinct kinds of ceteris paribus laws in chemistry; idealized and approximate chemical laws. Thus, while Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34--50, 2000) are correct to point out that the candidate generalisations in chemistry are diverse and heterogeneous, a distinction between idealizations and approximations can nevertheless be used to successfully taxonomise them.
Testing the frozen flow approximation
NASA Technical Reports Server (NTRS)
Lucchin, Francesco; Matarrese, Sabino; Melott, Adrian L.; Moscardini, Lauro
1993-01-01
We investigate the accuracy of the frozen-flow approximation (FFA), recently proposed by Matarrese, et al. (1992), for following the nonlinear evolution of cosmological density fluctuations under gravitational instability. We compare a number of statistics between results of the FFA and n-body simulations, including those used by Melott, Pellman & Shandarin (1993) to test the Zel'dovich approximation. The FFA performs reasonably well in a statistical sense, e.g. in reproducing the counts-in-cell distribution, at small scales, but it does poorly in the crosscorrelation with n-body which means it is generally not moving mass to the right place, especially in models with high small-scale power.
Potential of the approximation method
Amano, K.; Maruoka, A.
1996-12-31
Developing some techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph with m vertices: For 5 {le} s {le} m/4, a monotone circuit computing CLIQUE(m, s) contains at least (1/2)1.8{sup min}({radical}s-1/2,m/(4s)) gates: If a non-monotone circuit computes CLIQUE using a {open_quotes}small{close_quotes} amount of negation, then the circuit contains an exponential number of gates. The former is proved very simply using so called bottleneck counting argument within the framework of approximation, whereas the latter is verified introducing a notion of restricting negation and generalizing the sunflower contraction.
Living Expenses5 (includes approximately
Maroncelli, Mark
Law : J.D. $21,300 Dickinson Law : LL.M. $17,700 Penn State Law: Penn State Law: J.D. & S.J.D. $21,300 Penn State Law: LL.M. $17,700 Legal English and Common Law Practice (Summer) With Fall LL.M enrollmentLiving Expenses5 (includes approximately $1,600 for books and supplies ) Dickinson Law4 : Dickinson
Approximate reasoning using terminological models
NASA Technical Reports Server (NTRS)
Yen, John; Vaidya, Nitin
1992-01-01
Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.
Computer Experiments for Function Approximations
Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C
2007-10-15
This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.
Approximate Counting of Graphical Realizations.
Erd?s, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erd?s and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erd?s and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994
Approximate Counting of Graphical Realizations
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erd?s and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erd?s and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994
Approximately Independent Features of Languages
NASA Astrophysics Data System (ADS)
Holman, Eric W.
To facilitate the testing of models for the evolution of languages, the present paper offers a set of linguistic features that are approximately independent of each other. To find these features, the adjusted Rand index (R?) is used to estimate the degree of pairwise relationship among 130 linguistic features in a large published database. Many of the R? values prove to be near zero, as predicted for independent features, and a subset of 47 features is found with an average R? of -0.0001. These 47 features are recommended for use in statistical tests that require independent units of analysis.
Approximate Deconvolution Reduced Order Modeling
Xie, Xuping; Wang, Zhu; Iliescu, Traian
2015-01-01
This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution(AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient(10^{-3})
Approximating metal-insulator transitions
NASA Astrophysics Data System (ADS)
Danieli, Carlo; Rayanov, Kristian; Pavlov, Boris; Martin, Gaven; Flach, Sergej
2015-12-01
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-André 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.
Generalized Gradient Approximation Made Simple
Perdew, J.P.; Burke, K.; Ernzerhof, M.
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.}
Explaining Variational Approximations J. T. ORMEROD and M. P. WAND
Wand, Matt
approximations is a body of deterministic tech- niques for making approximate inference for parameters in complex0877055. approximate inference, as well as Laplace approximation meth- ods. Variational approximations
Wavelet Approximation in Data Assimilation
NASA Technical Reports Server (NTRS)
Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
Dislocation Defects and Diophantine Approximation
Jared C. Bronski; Zoi Rapti
2009-04-16
In this paper we consider a Schrodinger eigenvalue problem with a potential consisting of a periodic part together with a compactly supported defect potential. Such problems arise as models in condensed matter to describe color in crystals as well as in engineering to describe optical photonic structures. We are interested in studying the existence of point eigenvalues in gaps in the essential spectrum, and in particular in counting the number of such eigenvalues. We use a homotopy argument in the width of the potential to count the eigenvalues as they are created. As a consequence of this we prove the following significant generalization of Zheludev's theorem: the number of point eigenvalues in a gap in the essential spectrum is exactly one for sufficiently large gap number unless a certain Diophantine approximation problem has solutions, in which case there exists a subsequence of gaps containing 0,1 or 2 eigenvalues. We state some conditions under which the solvability of the Diophantine approximation problem can be established.
Reconstruction within the Zeldovich approximation
NASA Astrophysics Data System (ADS)
White, Martin
2015-07-01
The Zeldovich approximation, first-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.
Reconstruction within the Zeldovich approximation
White, Martin
2015-01-01
The Zeldovich approximation, 1st order Lagrangian perturbation theory, provides a good description of the clustering of matter and galaxies on large scales. The acoustic feature in the large-scale correlation function of galaxies imprinted by sound waves in the early Universe has been successfully used as a `standard ruler' to constrain the expansion history of the Universe. The standard ruler can be improved if a process known as density field reconstruction is employed. In this paper we develop the Zeldovich formalism to compute the correlation function of biased tracers in both real- and redshift-space using the simplest reconstruction algorithm with a Gaussian kernel and compare to N-body simulations. The model qualitatively describes the effects of reconstruction on the simulations, though its quantitative success depends upon how redshift-space distortions are handled in the reconstruction algorithm.
Interplay of approximate planning strategies
Huys, Quentin J. M.; Lally, Níall; Faulkner, Paul; Eshel, Neir; Seifritz, Erich; Gershman, Samuel J.; Dayan, Peter; Roiser, Jonathan P.
2015-01-01
Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and hierarchically decompose hard tasks into simpler subtasks. Theoretical and cognitive research has revealed several such strategies; however, little is known about their establishment, interaction, and efficiency. Here, we use model-based behavioral analysis to provide a detailed examination of the performance of human subjects in a moderately deep planning task. We find that subjects exploit the structure of the domain to establish subgoals in a way that achieves a nearly maximal reduction in the cost of computing values of choices, but then combine partial searches with greedy local steps to solve subtasks, and maladaptively prune the decision trees of subtasks in a reflexive manner upon encountering salient losses. Subjects come idiosyncratically to favor particular sequences of actions to achieve subgoals, creating novel complex actions or “options.” PMID:25675480
Analytical approximations for spiral waves
Löber, Jakob Engel, Harald
2013-12-15
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency ? and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent ?(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
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.
Decision analysis with approximate probabilities
NASA Technical Reports Server (NTRS)
Whalen, Thomas
1992-01-01
This paper concerns decisions under uncertainty in which the probabilities of the states of nature are only approximately known. Decision problems involving three states of nature are studied. This is due to the fact that some key issues do not arise in two-state problems, while probability spaces with more than three states of nature are essentially impossible to graph. The primary focus is on two levels of probabilistic information. In one level, the three probabilities are separately rounded to the nearest tenth. This can lead to sets of rounded probabilities which add up to 0.9, 1.0, or 1.1. In the other level, probabilities are rounded to the nearest tenth in such a way that the rounded probabilities are forced to sum to 1.0. For comparison, six additional levels of probabilistic information, previously analyzed, were also included in the present analysis. A simulation experiment compared four criteria for decisionmaking using linearly constrained probabilities (Maximin, Midpoint, Standard Laplace, and Extended Laplace) under the eight different levels of information about probability. The Extended Laplace criterion, which uses a second order maximum entropy principle, performed best overall.
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 ...
SOME APPROXIMATE METHODS FOR COMPUTING ELECTROMAGNETIC FIELDS
Torresani, Bruno
SOME APPROXIMATE METHODS FOR COMPUTING ELECTROMAGNETIC FIELDS SCATTERED BY COMPLEX OBJECTS P discuss several approximate methods for computing electromagnetic scattering by objects of complex shape. Dependingon the relative size of the scatterer compared to the incident wavelength, different techniques have
Energy conservation - A test for scattering approximations
NASA Technical Reports Server (NTRS)
Acquista, C.; Holland, A. C.
1980-01-01
The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.
Comparison of two Pareto frontier approximations
NASA Astrophysics Data System (ADS)
Berezkin, V. E.; Lotov, A. V.
2014-09-01
A method for comparing two approximations to the multidimensional Pareto frontier in nonconvex nonlinear multicriteria optimization problems, namely, the inclusion functions method is described. A feature of the method is that Pareto frontier approximations are compared by computing and comparing inclusion functions that show which fraction of points of one Pareto frontier approximation is contained in the neighborhood of the Edgeworth-Pareto hull approximation for the other Pareto frontier.
The Observer Algorithm for Visibility Approximation
Doherty, Patrick
different directions, and uses that data to get an approximate visibility measure in all other directionsThe Observer Algorithm for Visibility Approximation Per-Magnus OLSSON a and Patrick DOHERTY present a novel algorithm for visibility approximation that is sub- stantially faster than ray casting
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
Applications of sparse approximation in communications
Tropp, Joel
. For MIMO wire- less communication channels, we construct simultaneous sparse approximation problems address m-term approximation of functional spaces [2], [3], and electrical engineers use sparse represen on the codebook; we use the notions in sparse approximation to enhance the base codebook and to build
Matrix product approximations to conformal field theories
Robert Koenig; Volkher B. Scholz
2015-09-24
We establish rigorous error bounds for approximating correlation functions of conformal field theories (CFTs) by certain finite-dimensional tensor networks. For chiral CFTs, the approximation takes the form of a matrix product state. For full CFTs consisting of a chiral and an anti-chiral part, the approximation is given by a finitely correlated state. We show that the bond dimension scales polynomially in the inverse of the approximation error and sub-exponentially in the ultraviolett cutoff. We illustrate our findings using Wess-Zumino-Witten models, and show that there is a one-to-one correspondence between group-covariant MPS and our approximation.
More on approximations of Poisson probabilities
Kao, C
1980-05-01
Calculation of Poisson probabilities frequently involves calculating high factorials, which becomes tedious and time-consuming with regular calculators. The usual way to overcome this difficulty has been to find approximations by making use of the table of the standard normal distribution. A new transformation proposed by Kao in 1978 appears to perform better for this purpose than traditional transformations. In the present paper several approximation methods are stated and compared numerically, including an approximation method that utilizes a modified version of Kao's transformation. An approximation based on a power transformation was found to outperform those based on the square-root type transformations as proposed in literature. The traditional Wilson-Hilferty approximation and Makabe-Morimura approximation are extremely poor compared with this approximation. 4 tables. (RWR)
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...
Approximate joint measurements of qubit observables
Paul Busch; Teiko Heinosaari
2008-04-03
Joint measurements of qubit observables have recently been studied in conjunction with quantum information processing tasks such as cloning. Considerations of such joint measurements have until now been restricted to a certain class of observables that can be characterized by a form of covariance. Here we investigate conditions for the joint measurability of arbitrary pairs of qubit observables. For pairs of noncommuting sharp qubit observables, a notion of approximate joint measurement is introduced. Optimal approximate joint measurements are shown to lie in the class of covariant joint measurements. The marginal observables found to be optimal approximators are generally not among the coarse-grainings of the observables to be approximated. This yields scope for the improvement of existing joint measurement schemes. Both the quality of the approximations and the intrinsic unsharpness of the approximators are shown to be subject to Heisenberg-type uncertainty relations.
Approximate Analysis of Semiconductor Laser Arrays
NASA Technical Reports Server (NTRS)
Marshall, William K.; Katz, Joseph
1987-01-01
Simplified equation yields useful information on gains and output patterns. Theoretical method based on approximate waveguide equation enables prediction of lateral modes of gain-guided planar array of parallel semiconductor lasers. Equation for entire array solved directly using piecewise approximation of index of refraction by simple functions without customary approximation based on coupled waveguid modes of individual lasers. Improved results yield better understanding of laser-array modes and help in development of well-behaved high-power semiconductor laser arrays.
A greedy algorithm for yield surface approximation
NASA Astrophysics Data System (ADS)
Bleyer, Jérémy; de Buhan, Patrick
This Note presents an approximation method for convex yield surfaces in the framework of yield design theory. The proposed algorithm constructs an approximation using a convex hull of ellipsoids such that the approximate criterion can be formulated in terms of second-order conic constraints. The algorithm can treat bounded as well as unbounded yield surfaces. Its efficiency is illustrated on two yield surfaces obtained using up-scaling procedures.
APPLICATIONS OF APPROXIMATION SCHEMES TO EVOLUTION EQUATIONS
Louisiana State University
APPLICATIONS OF APPROXIMATION SCHEMES TO EVOLUTION EQUATIONS ADRIANDUMAANDCONSTANTINP. NICULESCU-Petryshynapprox- imationscheme. Partially supportedbyCNCSISGrant 303/1999. 1 #12; 2 ADRIANDUMAANDCONSTANTINP. NICULESCU has
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.
Diffusion approximation of neuronal models revisited.
Cupera, Jakub
2014-02-01
Leaky integrate-and-fire neuronal models with reversal potentials have a number of different diffusion approximations, each depending on the form of the amplitudes of the postsynaptic potentials. Probability distributions of the first-passage times of the membrane potential in the original model and its diffusion approximations are numerically compared in order to find which of the approximations is the most suitable one. The properties of the random amplitudes of postsynaptic potentials are discussed. It is shown on a simple example that the quality of the approximation depends directly on them. PMID:24245676
Approximate maximum parsimony and ancestral maximum likelihood.
Alon, Noga; Chor, Benny; Pardi, Fabio; Rapoport, Anat
2010-01-01
We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP. PMID:20150680
Efficient Approximation Algorithms for Sparse Polynomials
Behnke, Sven
Efficient Approximation Algorithms for Sparse Polynomials over Finite Fields Marek Karpinski 1 Igor of sparse polyÂ nomials and give a fully polynomial time (ffl; ffi) approximation algorithm for the number of nonÂzeros of multivariate sparse polynomials over a finite field of q elements and degree less than q
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 & = \
On Low Treewidth Approximations of Conjunctive Queries
Libkin, Leonid
On Low Treewidth Approximations of Conjunctive Queries Pablo BarcelÂ´o1 , Leonid Libkin2 against very large databases. We have recently initiated a study of approximations of conjunctive queries understanding of their com- plexity. We know which classes of conjunctive queries are easy to evaluate
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…
Notion of p-value Parametric Approximations
Nuel, Gregory
Power of a test ROC and AUC Example with GWAS G. NUEL Significance of an Observation in Post with GWAS G. NUEL Significance of an Observation in Post-Genomics #12;Notion of p-value Parametric Approximations Gumbel Approximations 3 Power Power of a test ROC and AUC Example with GWAS G. NUEL Significance
Mathematical Analysis of Born{Oppenheimer Approximations
Hagedorn, George A.
, just one year after the publication of the Schrodinger equation, Max Born and J. Robert OppenheimerMathematical Analysis of Born{Oppenheimer Approximations George A. Hagedorn and Alain Joye concerning Born{Oppenheimer approximations in molecular quantum mechanics. Introduction The goal
Vanishing Viscosity Approximation to Hyperbolic Conservation Laws
Vanishing Viscosity Approximation to Hyperbolic Conservation Laws Wen Shen and Zhengfu Xu Abstract We study high order convergence of vanishing viscosity approximation to scalar hyperbolic the solution is smooth, the viscous solution admits an expansion in powers of the viscosity parameter
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.
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Efficient Real Root Approximation Michael Kerber
Waldmann, Uwe
Efficient Real Root Approximation Michael Kerber IST (Institute of Science and Technology) Austria real roots of a square- free polynomial f. Given isolating intervals, our algorithm refines each of them to a certain width 2-L, that is, each of the roots is approximated to L bits after the binary
Efficient Real Root Approximation Michael Kerber
Waldmann, Uwe
Efficient Real Root Approximation Michael Kerber IST (Institute of Science and Technology) Austria real roots of a square- free polynomial f . Given isolating intervals, our algorithm refines each of them to a width at most 2-L, that is, each of the roots is approximated to L bits after the binary
Anisotropic Triangulation Methods in Adaptive Image Approximation
Demaret, Laurent
Anisotropic Triangulation Methods in Adaptive Image Approximation L. Demaret1 and A. Iske2 1 triangulations are utilized in recent methods for sparse rep- resentation and adaptive approximation of image- angulations, are discussed. The discussion includes generic triangulations obtained by simulated annealing
Scattering model approximations for neutron thermalization problems
Ritenour, R.L.; Rydin, R.A.; Mulder, R.U. )
1990-12-01
In this paper a variety of scattering model approximations are devised and evaluated. One such scattering model, designated the balanced single collision thermalization (BSCT) approximation, has proven to be very effective. It assumes that neutrons attain a thermalized distribution with only a single collision within the moderating material, independent of incident energy. This approximation leads to separability of the incident and outscattering energies and to significant simplification of the neutron scattering kernel for thermalization problems. The BSCT approximation is particularly useful in thermalization problems involving cold neutron sources, for which it yields flux predictions to within a few percent of exact solutions of theoretical problems. The BSCT approximation also predicts cold neutron fractions to within 10% of measured values for a cold neutron thermalization experiment done at Argonne National Laboratory.
Polynomial approximation of Morison wave loading
Bouyssy, V.; Rackwitz, R.
1997-02-01
For offshore structures with slender elements, the modeling of random wave loads by the Morison equation yields an equation of motion which has no analytical solution for response moments except in a few limiting cases. If polynomial approximations of the Morison drag loads are introduced, some procedures are available to obtain the stationary moments of the approximate response. If the response process is fitted by non-Gaussian models such as proposed by Winterstein (1988), the first four statistical moments of the response are necessary. The paper investigates how many terms should be included in the polynomial approximation of the Morison drag loading to accurately estimate the first four response moments. It is shown that a cubic approximation of the drag loading is necessary to accurately predict the response variance for any excitation. For the fit of the first four response moments, at least a fifth-order approximation appears necessary.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Ito, K.
1985-01-01
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A characteristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
NASA Technical Reports Server (NTRS)
Ito, K.
1984-01-01
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
Approximate knowledge compilation: The first order case
Val, A. del
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.
Approximating light rays in the Schwarzschild field
Oldrich Semerak
2015-02-12
A short formula is suggested which 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 behaviour 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.
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.
Uniformly valid approximation for channel flow
NASA Astrophysics Data System (ADS)
Mauss, Jacques; Dechaume, Antoine; Cousteix, Jean
2006-01-01
The flow at high Reynolds number in a two-dimensional channel whose walls are slightly deformed is considered. This Note addresses the problem of constructing a uniformly valid approximation leading to a better understanding of two-dimensional steady laminar incompressible separated flow. It is proposed to use a new asymptotic approach: the Successive Complementary Expansions Method (SCEM). The starting point is an assumed form of the approximation. The matching principle is a by-product of the method not at all necessary to construct the uniformly valid approximation. To cite this article: J. Mauss et al., C. R. Mecanique 334 (2006).
Energy-efficient approximate computation in Topaz
Achour, Sara
2015-01-01
The increasing prominence of energy consumption as a first-order concern in contemporary computing systems has motivated the design of energy-efficient approximate computing platforms. These computing platforms feature ...
Approximate probability distributions of the master equation.
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems. PMID:26274137
Approximate probability distributions of the master equation
NASA Astrophysics Data System (ADS)
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
Geodesic Gaussian kernels for value function approximation
Sugiyama, Masashi; Hachiya, Hirotaka; Towell, Christopher; Vijayakumar, Sethu
2008-01-01
The least-squares policy iteration approach works efficiently in value function approximation, given appropriate basis functions. Because of its smoothness, the Gaussian kernel is a popular and useful choice as a basis ...
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.
Uniform approximation by interpolating Blaschke products
Mortini, Raymond
Uniform approximation by interpolating Blaschke products Raymond Mortini UniversitÂ´e Paul Verlaine - Metz Oberwolfach, February 15, 2008 R. Mortini Interpolating Blaschke products #12;Blaschke products Blaschke sequence = (an) DN : R. Mortini Interpolating Blaschke products #12;Blaschke products Blaschke
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 ...
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.
A Monte-Carlo AIXI Approximation
Silver, David
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. Our approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement ...
Optimization in Geometric Graphs: Complexity and Approximation
Kahruman-Anderoglu, Sera
2011-02-22
We consider several related problems arising in geometric graphs. In particular, we investigate the computational complexity and approximability properties of several optimization problems in unit ball graphs and develop algorithms to find exact...
Signal approximation using the bilinear transform
Venkataraman, Archana, Ph. D. Massachusetts Institute of Technology
2007-01-01
This thesis explores the approximation properties of a unique basis expansion. The expansion implements a nonlinear frequency warping between a continuous-time signal and its discrete-time representation according to the ...
Linear source approximation in CASMO5
Ferrer, R.; Rhodes, J.; Smith, K.
2012-07-01
A Linear Source (LS) approximation has been implemented in the two-dimensional Method of Characteristics (MOC) transport solver in a prototype version of CASMO5. The LS approximation, which relies on the computation of trajectory-based spatial moments over source regions to obtain the linear source expansion coefficients, improves the solution accuracy relative to the 'flat' or constant source approximation. In addition, the LS formulation is capable of treating arbitrarily-shaped source regions and is compatible with standard Coarse-Mesh Finite Difference (CMFD) acceleration. Numerical tests presented in this paper for the C5G7 MOX benchmark show that, for comparable accuracy with respect to the reference solution, the LS approximation can reduce the run time by a factor of four and the memory requirements by a factor often relative to the FS scheme. (authors)
Stochastic Approximation to Understand Simple Simulation Models
NASA Astrophysics Data System (ADS)
Izquierdo, Segismundo S.; Izquierdo, Luis R.
2013-04-01
This paper illustrates how a deterministic approximation of a stochastic process can be usefully applied to analyse the dynamics of many simple simulation models. To demonstrate the type of results that can be obtained using this approximation, we present two illustrative examples which are meant to serve as methodological references for researchers exploring this area. Finally, we prove some convergence results for simulations of a family of evolutionary games, namely, intra-population imitation models in n-player games with arbitrary payoffs.
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.
Polynomial approximation of functions in Sobolev spaces
NASA Technical Reports Server (NTRS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Polynomial approximation of functions in Sobolev spaces
Dupont, T.; Scott, R.
1980-04-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Polynomial approximation of Morison wave loading
Bouyssy, V.; Rackwitz, R.
1995-12-31
For offshore structures with slender elements, the modeling of random wave loads by the Morison equation yields an equation of motion which admits no analytical solution except in few limit cases. This also holds for response moments. If polynomial approximations of the Morison drag loads are introduced, some procedures are available to obtain the stationary moments of the approximate response. These procedures result in large computer codes and time consuming computations if accurate approximations and large structural models are considered. If the response process is fitted by non-Gaussian models such as proposed by Winterstein (1988), the first four statistical moments of the response are necessary. In the paper the authors investigate how many terms should be included in the polynomial approximation of the Morison drag loading to accurately estimate the first four response moments. Analysis is performed in the time domain for a standardized form of the equation of motion. It is shown that a cubic approximation of the drag loading is necessary to accurately predict response variance for any excitation. For the fit of the first four response moments, at least a fifth-order approximation appears necessary. It is concluded that practical fatigue or reliability analyses can require much effort if the influence of nonlinearities in Morison loading needs to be accurately accounted for.
An improved proximity force approximation for electrostatics
Fosco, Cesar D.; Instituto Balseiro, Universidad Nacional de Cuyo, R8402AGP Bariloche ; Lombardo, Fernando C.; IFIBA ; Mazzitelli, Francisco D.
2012-08-15
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called 'proximity force approximation' the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction in atomic force microscopes. - Highlights: Black-Right-Pointing-Pointer The proximity force approximation (PFA) has been widely used in different areas. Black-Right-Pointing-Pointer The PFA can be improved using a derivative expansion in the shape of the surfaces. Black-Right-Pointing-Pointer We use the improved PFA to compute electrostatic forces between conductors. Black-Right-Pointing-Pointer The results can be used as an analytic benchmark for numerical calculations in AFM. Black-Right-Pointing-Pointer Insight is provided for people who use the PFA to compute nuclear and Casimir forces.
Mimetic difference approximations of partial differential equations
Hyman, J.M.; Shashkov, M.; Staley, M.; Kerr, S.; Steinberg, S.; Castillo, J.
1997-08-01
Goal was to construct local high-order difference approximations of differential operators on nonuniform grids that mimic the symmetry properties of the continuum differential operators. Partial differential equations solved with these mimetic difference approximations automatically satisfy discrete versions of conservation laws and analogies to Stoke`s theorem that are true in the continuum and therefore more likely to produce physically faithful results. These symmetries are easily preserved by local discrete high-order approximations on uniform grids, but are difficult to retain in high-order approximations on nonuniform grids. We also desire local approximations and use only function values at nearby points in the computational grid; these methods are especially efficient on computers with distributed memory. We have derived new mimetic fourth-order local finite-difference discretizations of the divergence, gradient, and Laplacian on nonuniform grids. The discrete divergence is the negative of the adjoint of the discrete gradient, and, consequently, the Laplacian is a symmetric negative operator. The new methods derived are local, accurate, reliable, and efficient difference methods that mimic symmetry, conservation, stability, the duality relations and the identities between the gradient, curl, and divergence operators on nonuniform grids. These methods are especially powerful on coarse nonuniform grids and in calculations where the mesh moves to track interfaces or shocks.
Approximate solutions of the hyperbolic Kepler equation
NASA Astrophysics Data System (ADS)
Avendano, Martín; Martín-Molina, Verónica; Ortigas-Galindo, Jorge
2015-12-01
We provide an approximate zero widetilde{S}(g,L) for the hyperbolic Kepler's equation S-g {{arcsinh}}(S)-L=0 for gin (0,1) and Lin [0,? ). We prove, by using Smale's ? -theory, that Newton's method starting at our approximate zero produces a sequence that converges to the actual solution S( g, L) at quadratic speed, i.e. if S_n is the value obtained after n iterations, then |S_n-S|? 0.5^{2^n-1}|widetilde{S}-S|. The approximate zero widetilde{S}(g,L) is a piecewise-defined function involving several linear expressions and one with cubic and square roots. In bounded regions of (0,1) × [0,? ) that exclude a small neighborhood of g=1, L=0, we also provide a method to construct simpler starters involving only constants.
Approximation methods in gravitational-radiation theory
NASA Technical Reports Server (NTRS)
Will, C. M.
1986-01-01
The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
Reconfiguring smart structures using approximate heteroclinic connections
NASA Astrophysics Data System (ADS)
Zhang, Jiaying; McInnes, Colin R.
2015-10-01
A new method is investigated to reconfigure smart structures using the technique of polynomial series to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to first approximate the heteroclinic connection between two equal-energy, unstable equilibrium points, and then develop an inverse method to control the dynamics of the system to track the reference polynomial trajectory. It is found that high-order polynomials can provide a good approximation to heteroclinic connections and provide an efficient means of generating such trajectories. The method is used first in a simple smart structure model to illustrate the method and is then extended to a more complex model where the numerical generation of true heteroclinic connections is difficult. It is envisaged that being computationally efficient, the method could form the basis for real-time reconfiguration of smart structures using heteroclinic connections between equal-energy, unstable configurations.
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.
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.
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.
Extending the Eikonal Approximation to Low Energy
Pierre Capel; Tokuro Fukui; Kazuyuki Ogata
2014-11-21
E-CDCC and DEA, two eikonal-based reaction models are compared to CDCC at low energy (e.g. 20AMeV) to study their behaviour in the regime at which the eikonal approximation is supposed to fail. We confirm that these models lack the Coulomb deflection of the projectile by the target. We show that a hybrid model, built on the CDCC framework at low angular momenta and the eikonal approximation at larger angular momenta gives a perfect agreement with CDCC. An empirical shift in impact parameter can also be used reliably to simulate this missing Coulomb deflection.
Approximating Likelihood Ratios with Calibrated Discriminative Classifiers
Cranmer, Kyle
2015-01-01
In particle physics likelihood ratio tests are established tools for statistical inference. These tests are complicated by the fact that computer simulators are used as a generative model for the data, but they do not provide a way to evaluate the likelihood function. We demonstrate how discriminative classifiers can be used to approximate the likelihood function when a generative model for the data is available for training and calibration. This offers an approach to parametric inference when simulators are used that is complementary to approximate Bayesian computation.
Characterizing Inflationary Perturbations: The Uniform Approximation
Salman Habib; Andreas Heinen; Katrin Heitmann; Gerard Jungman; Carmen Molina-Paris
2004-06-04
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 per cent. This meets the accuracy requirement for interpreting next-generation CMB observations.
Characterizing Inflationary Perturbations: The Uniform Approximation
Habib, S; Heitmann, K; Jungman, G; Molina-Paris, C; Habib, Salman; Heinen, Andreas; Heitmann, Katrin; Jungman, Gerard; Molina-Paris, Carmen
2004-01-01
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 per cent. This meets the accuracy requirement for interpreting next-generation CMB observations.
Characterizing inflationary perturbations: The uniform approximation
Habib, Salman; Heinen, Andreas; Heitmann, Katrin; Jungman, Gerard; Molina-Paris, Carmen
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.
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.
On the approximation of protein threading
Akutsu, Tatsuya; Miyano, Satoru
1997-12-01
In this paper, we study the protein threading problem, which was proposed for finding a folded 3D protein structure from an amino acid sequence. Since this problem was already proved to be NP-hard by Lathrop, we study polynomial time approximation algorithms. First we show that the protein threading problem is MAX SNP-hard. Next we show that the protein threading problem can be approximated within a factor 4 for a special case in which a graph representing interaction between residues (amino acids) is planar. This case corresponds to a {beta}-sheet substructure, which appears in most protein structures. 14 refs., 9 figs.
Congruence Approximations for Entrophy Endowed Hyperbolic Systems
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Saini, Subhash (Technical Monitor)
1998-01-01
Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.
Approximate Killing Fields as an Eigenvalue Problem
Christopher Beetle
2008-08-12
Approximate Killing vector fields are expected to help define physically meaningful spins for non-symmetric black holes in general relativity. However, it is not obvious how such fields should be defined geometrically. This paper relates a definition suggested recently by Cook and Whiting to an older proposal by Matzner, which seems to have been overlooked in the recent literature. It also describes how to calculate approximate Killing fields based on these proposals using an efficient scheme that could be of immediate practical use in numerical relativity.
Approximate convective heating equations for hypersonic flows
NASA Technical Reports Server (NTRS)
Zoby, E. V.; Moss, J. N.; Sutton, K.
1979-01-01
Laminar and turbulent heating-rate equations appropriate for engineering predictions of the convective heating rates about blunt reentry spacecraft at hypersonic conditions are developed. The approximate methods are applicable to both nonreacting and reacting gas mixtures for either constant or variable-entropy edge conditions. A procedure which accounts for variable-entropy effects and is not based on mass balancing is presented. Results of the approximate heating methods are in good agreement with existing experimental results as well as boundary-layer and viscous-shock-layer solutions.
Revisiting Twomey's approximation for peak supersaturation
NASA Astrophysics Data System (ADS)
Shipway, B. J.
2015-04-01
Twomey's seminal 1959 paper provided lower and upper bound approximations to the estimation of peak supersaturation within an updraft and thus provides the first closed expression for the number of nucleated cloud droplets. The form of this approximation is simple, but provides a surprisingly good estimate and has subsequently been employed in more sophisticated treatments of nucleation parametrization. In the current paper, we revisit the lower bound approximation of Twomey and make a small adjustment that can be used to obtain a more accurate calculation of peak supersaturation under all potential aerosol loadings and thermodynamic conditions. In order to make full use of this improved approximation, the underlying integro-differential equation for supersaturation evolution and the condition for calculating peak supersaturation are examined. A simple rearrangement of the algebra allows for an expression to be written down that can then be solved with a single lookup table with only one independent variable for an underlying lognormal aerosol population. While multimodal aerosol with N different dispersion characteristics requires 2N+1 inputs to calculate the activation fraction, only N of these one-dimensional lookup tables are needed. No additional information is required in the lookup table to deal with additional chemical, physical or thermodynamic properties. The resulting implementation provides a relatively simple, yet computationally cheap, physically based parametrization of droplet nucleation for use in climate and Numerical Weather Prediction models.
THE PARABOLIC WAVE APPROXIMATION AND TIME REVERSAL
Papanicolaou, George C.
focuses approximately on the source because of timereversibility of the wave equation. The refocusing applications in medicine, underwater sound, wireless communications etc., and has been studied experimentally applications. One application is kidney stone destruction, when the signal reflected from a kidney stone
THE PARABOLIC WAVE APPROXIMATION AND TIME REVERSAL
Papanicolaou, George C.
- focuses approximately on the source because of time-reversibility of the wave equation. The refocusing applications in medicine, underwater sound, wireless communications etc., and has been studied experimentally applications. One application is kidney stone destruction, when the signal reflected from a kidney stone
THE PARABOLIC WAVE APPROXIMATION AND TIME REVERSAL
Solna, Knut
-reversibility of the wave equation. The refocusing is approximate since the array of transducers (also called a time of the time-reversed signal has many applications in medicine, underwater sound, wireless communications etc description of various possible applications. One application is kidney stone destruction, when the signal re
Fostering Formal Commutativity Knowledge with Approximate Arithmetic
Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A.; Gaschler, Robert
2015-01-01
How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school. PMID:26560311
Approximation algorithms for facility location problems
Utrecht, Universiteit
Approximation algorithms for facility location problems David B. Shmoys Eva Tardosy Karen Aardalz, The Netherlands. Research partially supported by NSF grant CCR-9307391, and by ESPRIT Long Term Research Project No. 20244 Project ALCOM-IT: Algorithms and Complexity in Informa- tion Technology. 1 #12;be assigned
Approximate Kinetic Analysis of Intense Evaporation
NASA Astrophysics Data System (ADS)
Zudin, Yu. B.
2015-07-01
An approximate kinetic analysis of the process of intense evaporation has been carried out. The analytical solutions obtained for temperatures, pressures, and mass velocities of vapor agree well with the available numerical and analytical solutions. The evaporation limiting mass velocity has been calculated.
Approximations to the Distributed Activation Energy Model
Approximations to the Distributed Activation Energy Model for Pyrolysis C.P. Please, 1 M.J. Mc, then resubmitted after minor revisions in September 2002. Abstract The Distributed Activation Energy Model (DAEM effective method for estimating kinetic parameters and the distribution of activation energies. Comparison
Numerical approximation of SDE with explosions.
Groisman, Pablo
Numerical approximation of SDE with explosions. Joint work with JuÂ´an DÂ´avila, U. de Chile Juli of the largest crack. The explosion time corresponds to the time of ultimate damage or fatigue failure in the material. #12;The Feller Test for Explosions provides a precise criteria to de- termine, in terms of b
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.
Progressive Image Coding by Hierarchical Linear Approximation.
ERIC Educational Resources Information Center
Wu, Xiaolin; Fang, Yonggang
1994-01-01
Proposes a scheme of hierarchical piecewise linear approximation as an adaptive image pyramid. A progressive image coder comes naturally from the proposed image pyramid. The new pyramid is semantically more powerful than regular tessellation but syntactically simpler than free segmentation. This compromise between adaptability and complexity…
Blind Channel Equalization and -Approximation Algorithms
Ye, Yinyu
Blind Channel Equalization and #15;-Approximation Algorithms #3; Qingyu Li 1 , Er-Wei Bai 1 University of Iowa Iowa City, IA 52242 Abstract In this paper, we show that a blind equalizer can be obtained without using any sta- tistical information on the input by formulating the blind channel equalization
Kravchuk functions for the finite oscillator approximation
NASA Technical Reports Server (NTRS)
Atakishiyev, Natig M.; Wolf, Kurt Bernardo
1995-01-01
Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.
Stochastic Approximation and Its Application in MCMC
Cheng, Yichen
2013-05-31
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1 In ll Asymptotics of ~ n . . . . . . . . . . . . . . . . . . . . . . 14 2.3.2 Stochastic Approximation Asymptotics of ^(t)n . . . . . . . . . 19 2.4 Simulation Examples... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.2 Model for NMR Spectrum . . . . . . . . . . . . . . . . . . . . . . . . 39 4.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.3.1 Dimension Invariant Move (M = M(t)) . . . . . . . . . . . . . 44 4.3.2 Birth...
Approximation algorithms for facility location problems
Utrecht, Universiteit
a facility (such as a warehouse), where the cost of build ing at location i is f i ; furthermore (such as warehouses) to serve a given set of n client locations (such as stores); we are also givenApproximation algorithms for facility location problems David B. Shmoys \\Lambda ' Eva Tardos y
Simplifying Mixture Models through Function Approximation
Kwok, James Tin-Yau
Simplifying Mixture Models through Function Approximation Kai Zhang James T. Kwok Department, Kowloon, Hong Kong {twinsen, jamesk}@cse.ust.hk Abstract Finite mixture model is a powerful tool in many. The basic idea is to group the original mixture components into compact clusters, and then minimize an upper
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
The Centroid of Points with Approximate Weights
Eppstein, David
modeling of oil spills [8]. Oil floating on water can be represented by a twodimensional point set; weights represent the varying thickness of the oil #12; layer, which is known only approximately. The total volume of the spill, how ever, may be known more accurately, hence the explicit bounds
Submitted to Statistical Science Models as Approximations --
Buja, Andreas
Submitted to Statistical Science Models as Approximations -- A Conspiracy of Random Regressors has the characteristic "sandwich" form, (X X)-1 forming the "bread" and X DX the "meat". Although residuals r2 i , each r2 i is not a good estimate, but the averaging implicit in the "meat" provides
Submitted to Statistical Science Models as Approximations --
Buja, Andreas
Submitted to Statistical Science Models as Approximations -- A Conspiracy of Random Regressors DX the "meat". Although this sandwich formula does not look actionable for standard error estimation, but the averaging implicit in the "meat" provides an asymptotically valid estimate: (2) ^Vsand[ ^ ] := (X X)-1 (X
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…
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
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.
Diophantine approximation for negatively curved manifolds
Paulin, Frederic
Diophantine approximation problems and hyperbolic geometry (see [Dan, For1, For2, HV, HS, Pat, Ser3, Schmi neighborhood of the cusp. In general, it 1 AMS codes: 53 C 22, 11 J 06, 30 F 40, 11 J 70. Keywords: Diophantine
FRACTAL APPROXIMATION AND COMPRESSION USING PROJECTED IFS
GuÃ©rin, Eric
FRACTAL APPROXIMATION AND COMPRESSION USING PROJECTED IFS Ã?ric GuÃ©rin, Ã?ric Tosan and Atilla, or images) with fractal models is an important center of interest for research. The general inverse problem.The most known of them is the fractal image compression method introduced by Jacquin. Generally speaking
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
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
Pixel Approximation Errors in Common Watershed Algorithms
Hamprecht, Fred A.
Pixel Approximation Errors in Common Watershed Algorithms Hans Meine1 , Peer Stelldinger1 for Image Processing, University of Heidelberg, Germany Abstract. The exact, subpixel watershed algorithm delivers very accu- rate watershed boundaries based on a spline interpolation, but is slow and only works
UNIFORM SEMICLASSICAL APPROXIMATION IN QUANTUM STATISTICAL MECHANICS.
De Carvalho, C.A.A.; Cavalcanit, R.M.; Fraga, E.S.; Joras, S.E.
2000-10-23
We present a simple method to deal with caustics in the semiclassical approximation to the partition function of a one-dimensional quantum system. The procedure, which makes use of complex trajectories, is applied to the quartic double-well potential.
Block Addressing Indices for Approximate Text Retrieval.
ERIC Educational Resources Information Center
Baeza-Yates, Ricardo; Navarro, Gonzalo
2000-01-01
Discusses indexing in large text databases, approximate text searching, and space-time tradeoffs for indexed text searching. Studies the space overhead and retrieval times as functions of the text block size, concludes that an index can be sublinear in space overhead and query time, and applies the analysis to the Web. (Author/LRW)
PREDICTIVE SHAPE CODING USING GENERIC POLYGON APPROXIMATION
Evans, Brian L.
PREDICTIVE SHAPE CODING USING GENERIC POLYGON APPROXIMATION Jong-il Kim and Brian L. Evans.ece.utexas.edu ABSTRACT We introduce an e cient predictive binary shape coding method that consists of 1 global motion estimation, 2 local motion estimation, 3 matched segment coding, and 4 residual segment coding. Global
PREDICTIVE SHAPE CODING USING GENERIC POLYGON APPROXIMATION
Evans, Brian L.
PREDICTIVE SHAPE CODING USING GENERIC POLYGON APPROXIMATION Jongil Kim and Brian L. Evans://anchovy.ece.utexas.edu/ ABSTRACT We introduce an efficient predictive binary shape coding method that consists of (1) global motion estimation, (2) local motion estimation, (3) matched segment coding, and (4) residual segment coding. Global
Counting independent sets using the Bethe approximation
Chertkov, Michael; Chandrasekaran, V; Gamarmik, D; Shah, D; Sin, J
2009-01-01
The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques.
Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin
2016-01-01
What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. PMID:26587963
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.
Approximate gauge symemtry of composite vector bosons
Suzuki, Mahiko
2010-06-01
It can be shown in a solvable field theory model that the couplings of the composite vector mesons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in more an intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.
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.
Stochastic algorithm for approximating soft morphological operators
NASA Astrophysics Data System (ADS)
Zmuda, Michael A.
2001-12-01
A technique that approximates the output of the soft morphological operators is described. The soft operators can be viewed as a voting process across neighborhoods defined by the structuring element. Instead of processing all votes across a neighborhood, this approximation technique randomly samples elements in the neighborhood and uses these values as inputs to a two-state finite state machine, where the state of the machine corresponds to the output at a given pixel. When properly designed, the machines sample a small fraction of the neighborhood, obtain output that is 91 to 100% accurate at each pixel, and is one to two orders of magnitude faster than conventional algorithms. Experiments on binary textures and digits confirm the theoretical results.
Sketching and Streaming Entropy via Approximation Theory
Harvey, Nicholas J A; Onak, Krzysztof
2008-01-01
We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain suboptimal space bounds in the general model, and near-optimal bounds in the insertion-only model without sketching. Our high-level approach is simple: we give algorithms to estimate Renyi and Tsallis entropy, and use them to extrapolate an estimate of Shannon entropy. The accuracy of our estimates is proven using approximation theory arguments and extremal properties of Chebyshev polynomials, a technique which may be useful for other problems. Our work also yields the best-known and near-optimal additive approximations for entropy, and hence also for conditional entropy and mutual information.
An Approximate Model of the Spacetime Foam
NASA Astrophysics Data System (ADS)
Dzhunushaliev, V.; Ahluwalia, D. V.
An approximate model of the spacetime foam is offered in which a quantum handle (wormhole) is a 5D wormhole-like solution. Neglecting the linear sizes of the wormhole throat we can introduce a spinor field for an approximate and effective description of the foam. The definition of the spinor field can be made by a dynamic and nondynamic ways. In the first case some field equations are used and the second case leads to superspace. It is shown that the spacetime with the foam is similar to a dielectric with dipoles and supergravity theories with a nonminimal interaction between spinor and electromagnetic fields can be considered as an effective model for the spacetime foam.
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.
Block multistep methods based on rational approximants
NASA Astrophysics Data System (ADS)
Ying, Teh Yuan; Omar, Zurni; Mansor, Kamarun Hizam
2014-06-01
In this study, the concept of block multistep methods based on rational approximants is introduced for the numerical solution of first order initial value problems. These numerical methods are also called rational block multistep methods. The main reason to consider block multistep methods in rational setting, is to improve the numerical accuracy and absolute stability property of existing block multistep methods that are based on polynomial approximants. For this pilot study, a 2-point explicit rational block multistep method is developed. Local truncation error and stability analysis for this new method are included as well. Numerical experimentations and results using some test problems are presented. Numerical results are satisfying in terms of numerical accuracy. Finally, future issues on the developments of rational block multistep methods are discussed.
Analysing organic transistors based on interface approximation
Akiyama, Yuto; Mori, Takehiko; ACT-C, JST, Honcho, Kawaguchi, Saitama 332-0012
2014-01-15
Temperature-dependent characteristics of organic transistors are analysed thoroughly using interface approximation. In contrast to amorphous silicon transistors, it is characteristic of organic transistors that the accumulation layer is concentrated on the first monolayer, and it is appropriate to consider interface charge rather than band bending. On the basis of this model, observed characteristics of hexamethylenetetrathiafulvalene (HMTTF) and dibenzotetrathiafulvalene (DBTTF) transistors with various surface treatments are analysed, and the trap distribution is extracted. In turn, starting from a simple exponential distribution, we can reproduce the temperature-dependent transistor characteristics as well as the gate voltage dependence of the activation energy, so we can investigate various aspects of organic transistors self-consistently under the interface approximation. Small deviation from such an ideal transistor operation is discussed assuming the presence of an energetically discrete trap level, which leads to a hump in the transfer characteristics. The contact resistance is estimated by measuring the transfer characteristics up to the linear region.
Mean-field approximation minimizes relative entropy
Bilbro, G.L. ); Snyder, W.E. ); Mann, R.C. )
1991-02-01
The authors derive the mean-field approximation from the information-theoretic principle of minimum relative entropy instead of by minimizing Peierls's inequality for the Weiss free energy of statistical physics theory. They show that information theory leads to the statistical mechanics procedure. As an example, they consider a problem in binary image restoration. They find that mean-field annealing compares favorably with the stochastic approach.
Microscopic justification of the equal filling approximation
Perez-Martin, Sara; Robledo, L. M.
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.
Stochastic approximation boosting for incomplete data problems.
Sexton, Joseph; Laake, Petter
2009-12-01
Boosting is a powerful approach to fitting regression models. This article describes a boosting algorithm for likelihood-based estimation with incomplete data. The algorithm combines boosting with a variant of stochastic approximation that uses Markov chain Monte Carlo to deal with the missing data. Applications to fitting generalized linear and additive models with missing covariates are given. The method is applied to the Pima Indians Diabetes Data where over half of the cases contain missing values. PMID:19432768
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 methods for stochastic petri nets
NASA Technical Reports Server (NTRS)
Jungnitz, Hauke Joerg
1992-01-01
Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists.
FAST APPROXIMATION OF CONVEX HULL Ladislav Kavan
Plotkin, Joshua B.
algorithms are described in [2, 1]. However, in certain applications we do not need an exact convex hull, i-spaces, and moreover it is an outer convex hull, i.e. CH(A) ACHk(A) If |A| = N, then the algorithm ACHk(A) runs in OFAST APPROXIMATION OF CONVEX HULL Ladislav Kavan FEE CTU in Prague Karlovo nam. 13 Prague 2, Czech
An approximation formula for the Katugampola integral
Ricardo Almeida; Nuno R. O. Bastos
2015-11-24
The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on first-order derivatives, and thus we convert the fractional problem into a standard one. With some examples we show the accuracy of the method, and then we present the utility of the method by solving a fractional integral equation.
Local approximation and its applications in statistics.
Schmerling, S; Peil, J
1989-01-01
For the discrete and for the continuous case, the problem of evaluating the derivatives of a function f(x) in a given interval of x is solved by local approximation method. Examples of application of the resulting numerical procedures are quoted relating the estimation of smooth function and its derivative for measured values (of a growth process), internal regression, trend elimination of time series, Bernstein polynomial, and kernel estimation of a density function. PMID:2759411
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.
Approximate quantum cloaking and almost trapped states
A. Greenleaf; Y. Kurylev; M. Lassas; G. Uhlmann
2008-08-19
We describe families of potentials which act as approximate cloaks for matter waves, i.e., for solutions of the time-independent Schr\\"odinger equation at energy $E$, with applications to the design of ion traps. These are derived from perfect cloaks for the conductivity and Helmholtz equations, by a procedure we refer to as isotropic transformation optics. If $W$ is a potential which is surrounded by a sequence $\\{V_n^E\\}_{n=1}^\\infty$ of approximate cloaks, then for generic $E$, asymptotically in $n$ (i) $W$ is both undetectable and unaltered by matter waves originating externally to the cloak; and (ii) the combined potential $W+V_n^E$ does not perturb waves outside the cloak. On the other hand, for $E$ near a discrete set of energies, cloaking {\\it per se} fails and the approximate cloaks support wave functions concentrated, or {\\it almost trapped}, inside the cloaked region and negligible outside. Applications include ion traps, almost invisible to matter waves or customizable to support almost trapped states of arbitrary multiplicity. Possible uses include simulation of abstract quantum systems, magnetically tunable quantum beam switches, and illusions of singular magnetic fields.
Blind sensor calibration using approximate message passing
NASA Astrophysics Data System (ADS)
Schülke, Christophe; Caltagirone, Francesco; Zdeborová, Lenka
2015-11-01
The ubiquity of approximately sparse data has led a variety of com- munities to great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them on real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal ac- quisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measures. Cal-AMP shares the scalability of approximate message passing, allowing to treat big sized instances of these problems, and ex- perimentally exhibits a phase transition between domains of success and failure.
Variational chemical data assimilation with approximate adjoints
NASA Astrophysics Data System (ADS)
Singh, Kumaresh; Sandu, Adrian
2012-03-01
Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. In the four-dimensional variational (4D-Var) framework, data assimilation is formulated as an optimization problem, which is solved using gradient-based optimization methods. The 4D-Var gradient is obtained by forcing the adjoint model with observation increments. The construction of the adjoint model requires considerable development effort. Moreover, the computation time associated with the adjoint model is significant (typically, a multiple of the time needed to run the forward model). In this paper we investigate the use of approximate gradients in variational data assimilation. The approximate gradients need to be sufficiently accurate to ensure that the numerical optimization algorithm makes progress toward the maximum likelihood solution. The approximate gradients are obtained through simplified adjoint models; this decreases the adjoint development effort, and reduces the CPU time and the storage requirements associated with the computation of the 4D-Var gradient. The resulting approach, named quasi-4D-Var (Q4D-Var), is illustrated on a global chemical data assimilation problem using satellite observations and the GEOS-Chem chemical transport model.
Strong washout approximation to resonant leptogenesis
Garbrecht, Björn; Gautier, Florian; Klaric, Juraj E-mail: florian.gautier@tum.de
2014-09-01
We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ?=Xsin(2?)/(X{sup 2}+sin{sup 2}?), where X=8??/(|Y{sub 1}|{sup 2}+|Y{sub 2}|{sup 2}), ?=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), ?=arg(Y{sub 2}/Y{sub 1}), and M{sub 1,2}, Y{sub 1,2} are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y{sub 1,2}|{sup 2}>> ?, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.
Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons Learned
Pratt, Vaughan
Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons Learned TIM ROUGHGARDEN Stanford University This survey describes the approximately optimal mechanism design paradigm and uses, Theory Additional Key Words and Phrases: Mechanism design, auctions, approximation 1. INTRODUCTION 1
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
Verified integrity properties for safe approximate program transformations
Kim, Deokhwan
Approximate computations (for example, video, audio, and image processing, machine learning, and many scientific computations) have the freedom to generate a range of acceptable results. Approximate program transformations ...
Corrections beyond the proximity force approximation
NASA Astrophysics Data System (ADS)
Teo, L. P.; Bordag, M.; Nikolaev, V.
2011-12-01
We recalculate the first analytic correction beyond proximity force approximation for a sphere in front of a plane for a scalar field and for the electromagnetic field. We use the method of Bordag and Nikolaev [J. Phys. AJPHAC50305-4470 41, 164002 (2008)10.1088/1751-8113/41/16/164002]. We confirm their result for Dirichlet boundary conditions whereas we find a different one for Robin, Neumann and conductor boundary conditions. The difference can be traced back to a sign error. As a result, the corrections depend on the Robin parameter. Agreement is found with a very recent method of derivative expansion.
Casimir forces beyond the proximity approximation
Bimonte, G; Jaffe, R L; Kardar, M
2011-01-01
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 on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Pad\\'e extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere-plate Casimir force at all separations.
Modeling error in Approximate Deconvolution Models
Adrian Dunca; Roger Lewandowski
2012-10-09
We investigate the assymptotic behaviour of the modeling error in approximate deconvolution model in the 3D periodic case, when the order $N$ of deconvolution goes to $\\infty$. We consider successively the generalised Helmholz filters of order $p$ and the Gaussian filter. For Helmholz filters, we estimate the rate of convergence to zero thanks to energy budgets, Gronwall's Lemma and sharp inequalities about Fouriers coefficients of the residual stress. We next show why the same analysis does not allow to conclude convergence to zero of the error modeling in the case of Gaussian filter, leaving open issues.
Uniform semiclassical approximations for umbilic bifurcation catastrophes
J. Main; G. Wunner
1998-04-03
Gutzwiller's trace formula for the semiclassical density of states diverges at the bifurcation points of periodic orbits and has to be replaced with uniform semiclassical approximations. We present a method to derive these expressions from the standard representations of the elementary catastrophes and to directly relate the uniform solutions to classical periodic orbit parameters, thereby circumventing the numerical application of normal form theory. The technique allows an easy handling of ungeneric bifurcations with corank 2 such as the umbilic catastrophes and is demonstrated on a hyperbolic umbilic in the diamagnetic Kepler problem.
Shear viscosity in the postquasistatic approximation
Peralta, C.; Rosales, L.; Rodriguez-Mueller, B.; Barreto, W.
2010-05-15
We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of anisotropic nonadiabatic radiating and dissipative distributions in general relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in noncomoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the nonadiabatic and adiabatic limit. In both cases, the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity.
Generalized linear response approximation in discrete methods
NASA Astrophysics Data System (ADS)
Orozco, M.; Luque, F. J.
1997-02-01
A generalization of the linear response approximation for the representation of solvent effects is presented. This method allows a simple, fast procedure for calculating the electrostatic component of the free energy of solvation. This strategy has the advantage that polarization contributions are implicity incorporated in the evaluation of the electrostatic free energy of solvation. The procedure, which is designed to be used in conjunction with classical discrete methods (Monte Carlo or molecular dynamics), is a promising alternative to more expensive techniques based on statistical mechanical algorithms, like free energy perturbation or thermodynamic integration.
Gaussian Approximation Potentials: a brief tutorial introduction
Bartók, Albert P.; Csányi, Gábor
2015-04-27
, van der Waals interactions etc. This is an uncontrolled approximation, since there is nothing about the Schro¨dinger equation that tells us a priori that its solutions can be written in this form: the level of accuracy and its applicability in any... not be done over all atoms in the configuration. Similarly, the covariance of two derivative quantities may be written as ? ?EN ??k ?EM ??l ? = ?2?ENEM? ??k??l = ?2w ? i?N ? j?M ?d>i ??k (?diC(di,dj)? > dj) ?dj ??l , (16) 6 where the elements of the Jacobian...
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.
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.
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.
Investigating Material Approximations in Spacecraft Radiation Analysis
NASA Technical Reports Server (NTRS)
Walker, Steven A.; Slaba, Tony C.; Clowdsley, Martha S.; Blattnig, Steve R.
2011-01-01
During the design process, the configuration of space vehicles and habitats changes frequently and the merits of design changes must be evaluated. Methods for rapidly assessing astronaut exposure are therefore required. Typically, approximations are made to simplify the geometry and speed up the evaluation of each design. In this work, the error associated with two common approximations used to simplify space radiation vehicle analyses, scaling into equivalent materials and material reordering, are investigated. Over thirty materials commonly found in spacesuits, vehicles, and human bodies are considered. Each material is placed in a material group (aluminum, polyethylene, or tissue), and the error associated with scaling and reordering was quantified for each material. Of the scaling methods investigated, range scaling is shown to be the superior method, especially for shields less than 30 g/cm2 exposed to a solar particle event. More complicated, realistic slabs are examined to quantify the separate and combined effects of using equivalent materials and reordering. The error associated with material reordering is shown to be at least comparable to, if not greater than, the error associated with range scaling. In general, scaling and reordering errors were found to grow with the difference between the average nuclear charge of the actual material and average nuclear charge of the equivalent material. Based on this result, a different set of equivalent materials (titanium, aluminum, and tissue) are substituted for the commonly used aluminum, polyethylene, and tissue. The realistic cases are scaled and reordered using the new equivalent materials, and the reduced error is shown.
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.
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.
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.
Bethe free energy, Kikuchi approximations and belief propagation
Bethe free energy, Kikuchi approximations and belief propagation algorithms Jonathan S. Yedidia to a stationary point of an approximate free energy, known as the Bethe free energy in statis- tical physics- curate free energy approximations, of which Bethe's approximation is the simplest. Exploiting
Comparison of slope approximations used in rough surface scattering.
Welton, P J
2015-02-01
Two widely used surface slope approximations are compared to an initially exact method that treats the slopes via a differential operator acting on the characteristic function. The differential operator treatment ceases to be exact when the integrand in the scattering integrals is approximated using a Gaussian directivity approximation and Fresnel phase approximation. Analysis is restricted to the Kirchhoff approximation (single scattering). One of the simpler slope approximations agrees with the more comprehensive differential operator approximation for all backscattering geometries, as well as for specular scattering geometries down to grazing angles comparable to the source beamwidth. PMID:25698054
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.
The Bloch Approximation in Periodically Perforated Media
Conca, C. Gomez, D. Lobo, M. Perez, E.
2005-06-15
We consider a periodically heterogeneous and perforated medium filling an open domain {omega} of R{sup N}. Assuming that the size of the periodicity of the structure and of the holes is O({epsilon}),we study the asymptotic behavior, as {epsilon} {sup {yields}} 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in {omega}{sup {epsilon}}({omega}{sup {epsilon}} being {omega} minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and the first Bloch eigenfunction. We first consider the case where {omega}is R{sup N} and then localize the problem for abounded domain {omega}, considering a homogeneous Dirichlet condition on the boundary of {omega}.
Anisotropic local likelihood approximations: theory, algorithms, applications
NASA Astrophysics Data System (ADS)
Katkovnik, Vladimir; Foi, Alessandro; Egiazarian, Karen O.; Astola, Jaakko T.
2005-03-01
We consider a signal restoration from observations corrupted by random noise. The local maximum likelihood technique allows to deal with quite general statistical models of signal dependent observations, relaxes the standard parametric modelling of the standard maximum likelihood, and results in flexible nonparametric regression estimation of the signal. We deal with the anisotropy of the signal using multi-window directional sectorial local polynomial approximation. The data-driven sizes of the sectorial windows, obtained by the intersection of confidence interval (ICI) algorithm, allow to form starshaped adaptive neighborhoods used for the pointwise estimation. The developed approach is quite general and is applicable for multivariable data. A fast adaptive algorithm implementation is proposed. It is applied for photon-limited imaging with the Poisson distribution of data. Simulation experiments and comparison with some of the best results in the field demonstrate an advanced performance of the developed algorithms.
Exact and Approximate Probabilistic Symbolic Execution
NASA Technical Reports Server (NTRS)
Luckow, Kasper; Pasareanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem
2014-01-01
Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.
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
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.
Approximate maximum likelihood decoding of block codes
NASA Technical Reports Server (NTRS)
Greenberger, H. J.
1979-01-01
Approximate maximum likelihood decoding algorithms, based upon selecting a small set of candidate code words with the aid of the estimated probability of error of each received symbol, can give performance close to optimum with a reasonable amount of computation. By combining the best features of various algorithms and taking care to perform each step as efficiently as possible, a decoding scheme was developed which can decode codes which have better performance than those presently in use and yet not require an unreasonable amount of computation. The discussion of the details and tradeoffs of presently known efficient optimum and near optimum decoding algorithms leads, naturally, to the one which embodies the best features of all of them.
An approximate CPHD filter for superpositional sensors
NASA Astrophysics Data System (ADS)
Mahler, Ronald; El-Fallah, Adel
2012-06-01
Most multitarget tracking algorithms, such as JPDA, MHT, and the PHD and CPHD filters, presume the following measurement model: (a) targets are point targets, (b) every target generates at most a single measurement, and (c) any measurement is generated by at most a single target. However, the most familiar sensors, such as surveillance and imaging radars, violate assumption (c). This is because they are actually superpositional-that is, any measurement is a sum of signals generated by all of the targets in the scene. At this conference in 2009, the first author derived exact formulas for PHD and CPHD filters that presume general superpositional measurement models. Unfortunately, these formulas are computationally intractable. In this paper, we modify and generalize a Gaussian approximation technique due to Thouin, Nannuru, and Coates to derive a computationally tractable superpositional-CPHD filter. Implementation requires sequential Monte Carlo (particle filter) techniques.
Approximate spacetime symmetries and conservation laws
Abraham I Harte
2008-08-29
A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincare and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these objects are discussed for both geodesics and extended matter distributions. One example is a generalized Komar integral that may be taken to define the linear and angular momenta of a spacetime volume as seen by a particular observer. This is evaluated explicitly for a gravitational plane wave spacetime.
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.
Heat flow in the postquasistatic approximation
Rodriguez-Mueller, B.; Peralta, C.; Barreto, W.; Rosales, L.
2010-08-15
We apply the postquasistatic approximation to study the evolution of spherically symmetric fluid distributions undergoing dissipation in the form of radial heat flow. For a model that corresponds to an incompressible fluid departing from the static equilibrium, it is not possible to go far from the initial state after the emission of a small amount of energy. Initially collapsing distributions of matter are not permitted. Emission of energy can be considered as a mechanism to avoid the collapse. If the distribution collapses initially and emits one hundredth of the initial mass only the outermost layers evolve. For a model that corresponds to a highly compressed Fermi gas, only the outermost shell can evolve with a shorter hydrodynamic time scale.
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
Dihedral manifold approximate fibrations over the circle
Hughes, Bruce
2009-01-01
Consider the cyclic group C_2 of order two acting by complex-conjugation on the unit circle S^1. The main result is that a finitely dominated manifold W of dimension > 4 admits a cocompact, free, discontinuous action by the infinite dihedral group D_\\infty if and only if W is the infinite cyclic cover of a free C_2-manifold M such that M admits a C_2-equivariant manifold approximate fibration to S^1. The novelty in this setting is the existence of codimension-one, invariant submanifolds of M and W. Along the way, we develop an equivariant sucking principle for certain orthogonal actions of finite groups on Euclidean space.
Estimating Mutual Information by Local Gaussian Approximation
Gao, Shuyang; Galstyan, Aram
2015-01-01
Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly dependent variables and have sample complexity that scales exponentially with the true MI. This undesired behavior was attributed to the reliance of those estimators on local uniformity of the underlying (and unknown) probability density function. Here we present a novel semi-parametric estimator of mutual information, where at each sample point, densities are {\\em locally} approximated by a Gaussians distribution. We demonstrate that the estimator is asymptotically unbiased. We also show that the proposed estimator has a superior performance compared to several baselines, and is able to accurately measure relationship strengths over many orders of magnitude.
An approximate Riemann solver for hypervelocity flows
NASA Technical Reports Server (NTRS)
Jacobs, Peter A.
1991-01-01
We describe an approximate Riemann solver for the computation of hypervelocity flows in which there are strong shocks and viscous interactions. The scheme has three stages, the first of which computes the intermediate states assuming isentropic waves. A second stage, based on the strong shock relations, may then be invoked if the pressure jump across either wave is large. The third stage interpolates the interface state from the two initial states and the intermediate states. The solver is used as part of a finite-volume code and is demonstrated on two test cases. The first is a high Mach number flow over a sphere while the second is a flow over a slender cone with an adiabatic boundary layer. In both cases the solver performs well.
Approximate Riemann solver for hypervelocity flows
NASA Technical Reports Server (NTRS)
Jacobs, P. A.
1992-01-01
We describe an approximate Riemann solver for the computation of hypervelocity flows in which there are strong shocks and viscous interactions. The scheme has three stages, the first of which computes the intermediate states assuming isentropic waves. A second stage, based on the strong shock relations, may then be invoked if the pressure jump across either wave is large. The third stage interpolates the interface state from the two initial states and the intermediate states. The solver is used as part of a finite-volume code and is demonstrated on two test cases. The first is a high Mach number flow over a sphere while the second is a flow over a flow over a slender cone with an adiabatic boundary layer. In both cases the solver performs well.
Robust Generalized Low Rank Approximations of Matrices
Shi, Jiarong; Yang, Wei; Zheng, Xiuyun
2015-01-01
In recent years, the intrinsic low rank structure of some datasets has been extensively exploited to reduce dimensionality, remove noise and complete the missing entries. As a well-known technique for dimensionality reduction and data compression, Generalized Low Rank Approximations of Matrices (GLRAM) claims its superiority on computation time and compression ratio over the SVD. However, GLRAM is very sensitive to sparse large noise or outliers and its robust version does not have been explored or solved yet. To address this problem, this paper proposes a robust method for GLRAM, named Robust GLRAM (RGLRAM). We first formulate RGLRAM as an l1-norm optimization problem which minimizes the l1-norm of the approximation errors. Secondly, we apply the technique of Augmented Lagrange Multipliers (ALM) to solve this l1-norm minimization problem and derive a corresponding iterative scheme. Then the weak convergence of the proposed algorithm is discussed under mild conditions. Next, we investigate a special case of RGLRAM and extend RGLRAM to a general tensor case. Finally, the extensive experiments on synthetic data show that it is possible for RGLRAM to exactly recover both the low rank and the sparse components while it may be difficult for previous state-of-the-art algorithms. We also discuss three issues on RGLRAM: the sensitivity to initialization, the generalization ability and the relationship between the running time and the size/number of matrices. Moreover, the experimental results on images of faces with large corruptions illustrate that RGLRAM obtains the best denoising and compression performance than other methods. PMID:26367116
Investigating material approximations in spacecraft radiation analysis
NASA Astrophysics Data System (ADS)
Walker, Steven A.; Slaba, Tony C.; Clowdsley, Martha S.; Blattnig, Steve R.
2011-07-01
During the design process, the configuration of space vehicles and habitats changes frequently and the merits of design changes must be evaluated. Methods for rapidly assessing astronaut exposure are therefore required. Typically, approximations are made to simplify the geometry and speed-up the evaluation of each design. In this work, the error associated with two common approximations used to simplify space radiation vehicle analyses, scaling into equivalent materials and material reordering, are investigated. Over thirty materials commonly found in spacesuits, vehicles, and human bodies are considered. Each material is placed in a material group (aluminum, polyethylene, or tissue), and the error associated with scaling and reordering was quantified for each material. Of the scaling methods investigated, range scaling is shown to be the superior method, especially for shields less than 30 g/cm 2 exposed to a solar particle event. More complicated, realistic slabs are examined to quantify the separate and combined effects of using equivalent materials and reordering. The error associated with material reordering is shown to be at least comparable to, if not greater than, the error associated with range scaling. In general, scaling and reordering errors were found to grow with the difference between the average nuclear charge of the actual material and average nuclear charge of the equivalent material. Based on this result, a different set of equivalent materials (titanium, aluminum, and tissue) are substituted for the commonly used aluminum, polyethylene, and tissue. The realistic cases are scaled and reordered using the new equivalent materials, and the reduced error is shown.
Approximation Preserving Reductions among Item Pricing Problems
NASA Astrophysics Data System (ADS)
Hamane, Ryoso; Itoh, Toshiya; Tomita, Kouhei
When a store sells items to customers, the store wishes to determine the prices of the items to maximize its profit. Intuitively, if the store sells the items with low (resp. high) prices, the customers buy more (resp. less) items, which provides less profit to the store. So it would be hard for the store to decide the prices of items. Assume that the store has a set V of n items and there is a set E of m customers who wish to buy those items, and also assume that each item i ? V has the production cost di and each customer ej ? E has the valuation vj on the bundle ej ? V of items. When the store sells an item i ? V at the price ri, the profit for the item i is pi = ri - di. The goal of the store is to decide the price of each item to maximize its total profit. We refer to this maximization problem as the item pricing problem. In most of the previous works, the item pricing problem was considered under the assumption that pi ? 0 for each i ? V, however, Balcan, et al. [In Proc. of WINE, LNCS 4858, 2007] introduced the notion of “loss-leader, ” and showed that the seller can get more total profit in the case that pi < 0 is allowed than in the case that pi < 0 is not allowed. In this paper, we derive approximation preserving reductions among several item pricing problems and show that all of them have algorithms with good approximation ratio.
Suetin, S P
2002-12-31
A non-linear system of differential equations ('generalized Dubrovin system') is obtained to describe the behaviour of the zeros of polynomials orthogonal on several intervals that lie in lacunae between the intervals. The same system is shown to describe the dynamical behaviour of zeros of this kind for more general orthogonal polynomials: the denominators of the diagonal Pade approximants of meromorphic functions on a real hyperelliptic Riemann surface. On the basis of this approach several refinements of Rakhmanov's results on the convergence of diagonal Pade approximants for rational perturbations of Markov functions are obtained.
Differential equation based method for accurate approximations in optimization
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.
1990-01-01
A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.
Finite volume approximation of elliptic problems and convergence of an approximate gradient
Herbin, RaphaÃ¨le
of vertexÂcentered finite volume schemes, studies were carried out by [34] in the case of Cartesian meshes] and [35] in the case of quadrilateral meshes in two space dimensions. CellÂcentered finite volume schemes method, [13] and [12] with a pure finite volume scheme. Since the approximate solution constructed
Protein alignment: Exact versus approximate. An illustration.
Randi?, Milan; Pisanski, Tomaž
2015-05-30
We illustrate solving the protein alignment problem exactly using the algorithm VESPA (very efficient search for protein alignment). We have compared our result with the approximate solution obtained with BLAST (basic local alignment search tool) software, which is currently the most widely used for searching for protein alignment. We have selected human and mouse proteins having around 170 amino acids for comparison. The exact solution has found 78 pairs of amino acids, to which one should add 17 individual amino acid alignments giving a total of 95 aligned amino acids. BLAST has identified 64 aligned amino acids which involve pairs of more than two adjacent amino acids. However, the difference between the two outputs is not as large as it may appear, because a number of amino acids that are adjacent have been reported by BLAST as single amino acids. So if one counts all amino acids, whether isolated (single) or in a group of two and more amino acids, then the count for BLAST is 89 and for VESPA is 95, a difference of only six. PMID:25800773
Phase estimation using an approximate eigenstate
Avatar Tulsi
2015-10-20
A basic building block of many quantum algorithms is the Phase Estimation algorithm (PEA). It estimates an eigenphase $\\phi$ of a unitary operator $U$ using a copy of the corresponding eigenstate $|\\phi\\rangle$. Suppose, in place of $|\\phi\\rangle$, we have a copy of an approximate eigenstate $|\\psi\\rangle$ whose overlap magnitude with $|\\phi\\rangle$ is at least $\\sqrt{2/3}$. Then PEA fails with a constant probability. However, using multiple copies of $|\\psi\\rangle$, the failure probaility can be made to decrease exponentially with the number of copies. In this paper, we show that as long as we can perform a selective inversion of $|\\psi\\rangle$, a single copy is sufficient to estimate $\\phi$. An important application is to improve the spatial complexity of eigenpath traversal algorithm, a "digital" analogue of quantum adiabatic evolution, having applications ranging from quantum physics simulation to optimization. Here the goal is to travel a path of eigenstates of $n$ different unitary operators satisfying some conditions. The fastest algorithm is due to Boixo, Knill and Somma (BKS) which needs $\\Theta(\\ln n)$ copies of the eigenstate. Using our algorithm, BKS algorithm can work using just a single copy of the eigenstate.
Improved Discrete Approximation of Laplacian of Gaussian
NASA Technical Reports Server (NTRS)
Shuler, Robert L., Jr.
2004-01-01
An improved method of computing a discrete approximation of the Laplacian of a Gaussian convolution of an image has been devised. The primary advantage of the method is that without substantially degrading the accuracy of the end result, it reduces the amount of information that must be processed and thus reduces the amount of circuitry needed to perform the Laplacian-of- Gaussian (LOG) operation. Some background information is necessary to place the method in context. The method is intended for application to the LOG part of a process of real-time digital filtering of digitized video data that represent brightnesses in pixels in a square array. The particular filtering process of interest is one that converts pixel brightnesses to binary form, thereby reducing the amount of information that must be performed in subsequent correlation processing (e.g., correlations between images in a stereoscopic pair for determining distances or correlations between successive frames of the same image for detecting motions). The Laplacian is often included in the filtering process because it emphasizes edges and textures, while the Gaussian is often included because it smooths out noise that might not be consistent between left and right images or between successive frames of the same image.
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.
The time-dependent Gutzwiller approximation
NASA Astrophysics Data System (ADS)
Fabrizio, Michele
2015-03-01
The time-dependent Gutzwiller Approximation (t-GA) is shown to be capable of tracking the off-equilibrium evolution both of coherent quasiparticles and of incoherent Hubbard bands. The method is used to demonstrate that the sharp dynamical crossover observed by time-dependent DMFT in the quench-dynamics of a half-filled Hubbard model can be identified within the t-GA as a genuine dynamical transition separating two distinct physical phases. This result, strictly variational for lattices of infinite coordination number, is intriguing as it actually questions the occurrence of thermalization. Next, we shall present how t-GA works in a multi-band model for V2O3 that displays a first-order Mott transition. We shall show that a physically accessible excitation pathway is able to collapse the Mott gap down and drive off-equilibrium the insulator into a metastable metal phase. Work supported by the European Union, Seventh Framework Programme, under the project GO FAST, Grant Agreement No. 280555.
Approximate stoichiometry for rich hydrocarbon mixtures
Beans, E.W. )
1993-03-01
The stoichiometry of lean mixtures can readily and accurately be determined from the assumption that all the carbon oxidizes to carbon dioxide and all the hydrogen oxidizes to water. This assumption is valid up to an equivalence ratio ([sigma]) of 0.8 and can be used with little error up to [sigma] = 1. The composition of the products of a hydrocarbon burnt in air under the foregoing assumption can be obtained from simple carbon, hydrogen, oxygen and nitrogen balances. Given the composition, one can determine the energy released and/or the adiabatic flame temperature. For rich mixtures, the foregoing assumption, of course, is not valid. Hence, there is no easy way to determine the stoichiometry of the products of a rich mixture. The objective of this note is to present an equation' which will allow one to readily determine the composition of the products of rich hydrocarbon mixtures. The equation is based on equilibrium composition calculations and some assumptions regarding the characteristics of hydrocarbons. The equation gives approximate results. However, the results are sufficiently accurate for many situations. If more accuracy is wanted, one should use an equilibrium combustion program like the one by Gordon and McBride.
Magnetic reconnection under anisotropic magnetohydrodynamic approximation
Hirabayashi, K.; Hoshino, M.
2013-11-15
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless MHD codes based on the double adiabatic approximation and the Landau closure model. We bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observations. Our results showed that once magnetic reconnection takes place, a firehose-sense (p{sub ?}>p{sub ?}) pressure anisotropy arises in the downstream region, and the generated slow shocks are quite weak comparing with those in an isotropic MHD. In spite of the weakness of the shocks, however, the resultant reconnection rate is 10%–30% higher than that in an isotropic case. This result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere.
Grover's quantum search algorithm and Diophantine approximation
Dolev, Shahar; Pitowsky, Itamar; Tamir, Boaz
2006-02-15
In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O({radical}(N)) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using iterations of Grover's basic step only, and no other algorithm. Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m<2{radical}(N)/({radical}(K)-{radical}(M)) obtains. This bound reproduces previous results based on more elaborate algorithms, and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.
Adaptive approximation of higher order posterior statistics
Lee, Wonjung
2014-02-01
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively.
Approximate 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.
An asymptotic homogenized neutron diffusion approximation. II. Numerical comparisons
Trahan, T. J.; Larsen, E. W.
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)
ON NUMBERS BADLY APPROXIMABLE BY Q-ADIC RATIONALS
Nilsson, Johan
1. Diophantine Approximation and BAN . . . . . . . . 9 - q-adically Badly Approximable Numbers. One-sided q-adically BAN 3. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 II. Two-sided q-adically BAN 9. Introduction
The use of the labiodental approximant in Indian English
Dinkar, Tanvi
2013-11-27
The use of the labiodental approximant /?/ in place of bilabial /w/ and fricative /v/ is a phonetic feature commonly found in Indian English (IndE). This essay aims to track the specific environments that the labiodental approximant occurs...
Approximate Dynamic Programming via a Smoothed Linear Program
Desai, Vijay V.
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural ...
On the complexity of approximating a nash equilibrium
Daskalakis, Constantinos
2011-01-01
We show that computing a relative---that is, multiplicative as opposed to additive---approximate Nash equilibrium in two-player games is PPAD-complete, even for constant values of the approximation. Our result is the first ...
Model-Based Reinforcement Learning with an Approximate, Learned Model
Sutton, Richard S.
and learned online. These experiments involve the Mountain Car task, which requires approximation of both will generalize nat- urally and easily to the use of learned, approximate environmental models
A STOCHASTIC APPROXIMATION APPROACH TO LOAD SHEDDING IN POWER NETWORKS
Marques, Antonio Garcia
A STOCHASTIC APPROXIMATION APPROACH TO LOAD SHEDDING IN POWER NETWORKS Nikolaos Gatsis-time decisions with respect to user load shedding, energy procurement, and battery charging or discharging need shedding, smart grid, stochastic approximation. 1. INTRODUCTION Environmental concerns and requirements
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
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1982-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1984-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589
On Curved Simplicial Elements and Best Quadratic Spline Approximation for
Hamann, Bernd
On Curved Simplicial Elements and Best Quadratic Spline Approximation for Hierarchical Data a method for hierarchical data approximation using curved quadratic simplicial elements for domain- cial elements make possible a better representation of curved geometry, domain boundaries
Least-squares Finite Element Approximations for the Reissner ...
1999-11-05
three-stage algorithm for approximating the Reissner–Mindlin plate model with ... two simple Poisson equations and the second stage approximates a perturbed Stokes equation. ... using the mixed finite element method which is subject to the '
Borel's Conjectures, Complexity of Words Transcendence, Diophantine Approximation
Waldschmidt, Michel
, Diophantine Approximation Continued Fractions First decimals of 2 http://wims.unice.fr/wims/wims.cgi 1 of Words Transcendence, Diophantine Approximation Continued Fractions First binary digits of 2 http://wims.unice.fr/wims/wims
ON SPECTRAL APPROXIMATIONS IN ELLIPTICAL GEOMETRIES USING MATHIEU FUNCTIONS
Shen, Jie
functions. A first set of optimal error estimates are derived for the approximation of periodic functions approximations to partial differential equations. Given a PDE in an elliptic or elliptic cylindrical geometry
Pawlak Algebra and Approximate Structure on Fuzzy Lattice
Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai
2014-01-01
The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties. PMID:25152922
Pawlak algebra and approximate structure on fuzzy lattice.
Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai
2014-01-01
The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties. PMID:25152922
Rapid approximate inversion of airborne TEM
NASA Astrophysics Data System (ADS)
Fullagar, Peter K.; Pears, Glenn A.; Reid, James E.; Schaa, Ralf
2015-11-01
Rapid interpretation of large airborne transient electromagnetic (ATEM) datasets is highly desirable for timely decision-making in exploration. Full solution 3D inversion of entire airborne electromagnetic (AEM) surveys is often still not feasible on current day PCs. Therefore, two algorithms to perform rapid approximate 3D interpretation of AEM have been developed. The loss of rigour may be of little consequence if the objective of the AEM survey is regional reconnaissance. Data coverage is often quasi-2D rather than truly 3D in such cases, belying the need for `exact' 3D inversion. Incorporation of geological constraints reduces the non-uniqueness of 3D AEM inversion. Integrated interpretation can be achieved most readily when inversion is applied to a geological model, attributed with lithology as well as conductivity. Geological models also offer several practical advantages over pure property models during inversion. In particular, they permit adjustment of geological boundaries. In addition, optimal conductivities can be determined for homogeneous units. Both algorithms described here can operate on geological models; however, they can also perform `unconstrained' inversion if the geological context is unknown. VPem1D performs 1D inversion at each ATEM data location above a 3D model. Interpretation of cover thickness is a natural application; this is illustrated via application to Spectrem data from central Australia. VPem3D performs 3D inversion on time-integrated (resistive limit) data. Conversion to resistive limits delivers a massive increase in speed since the TEM inverse problem reduces to a quasi-magnetic problem. The time evolution of the decay is lost during the conversion, but the information can be largely recovered by constructing a starting model from conductivity depth images (CDIs) or 1D inversions combined with geological constraints if available. The efficacy of the approach is demonstrated on Spectrem data from Brazil. Both separately and in combination, these programs provide new options to exploration and mining companies for rapid interpretation of ATEM surveys.
Bond selective chemistry beyond the adiabatic approximation
Butler, L.J.
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.
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
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
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
BUILDING SURROGATE MODELS BASED ON DETAILED AND APPROXIMATE SIMULATIONS
Seepersad, Carolyn Conner
- Page 1 - BUILDING SURROGATE MODELS BASED ON DETAILED AND APPROXIMATE SIMULATIONS Zhiguang Qian is taken to integrate data from approximate and detailed simulations to build a surrogate model approximate simulations form the bulk of the data, and they are used to build a model based on a Gaussian
Constructing analytic approximate solutions to the Lane-Emden equation
NASA Astrophysics Data System (ADS)
Iacono, R.; De Felice, M.
2015-09-01
We derive analytic approximations to the solutions of the Lane-Emden equation, a basic equation in Astrophysics that describes the Newtonian equilibrium structure of a self-gravitating polytropic fluid sphere. After recalling some basic results, we focus on the construction of rational approximations, discussing the limitations of previous attempts, and providing new accurate approximate solutions.
Solving infinite-dimensional optimization problems by polynomial approximation
Glineur, François
2010/29 Solving infinite-dimensional optimization problems by polynomial approximation Olivier DISCUSSION PAPER 2010/29 Solving infinite-dimensional optimization problems by polynomial approximation of convex infinite-dimensional optimization problems using a numerical approximation method that does
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.
Comparison of synthetic seismograms calculated by QI approximations of the
Cerveny, Vlastislav
Comparison of synthetic seismograms calculated by QI approximations of the coupling ray theory.tessmer@dkrz.de Summary The quasiÂisotropic (QI) approximation of the coupling ray theory is numerically comÂ pared, in which they coincide (kiss singularity). Keywords Weak anisotropy, qS waves, QI approximation, coupling
SPATIAL FINITE DIFFERENCE APPROXIMATIONS FOR WAVE-TYPE EQUATIONS
Fornberg, Bengt
SPATIAL FINITE DIFFERENCE APPROXIMATIONS FOR WAVE-TYPE EQUATIONS BENGT FORNBERG AND MICHELLE GHRIST in space that occur in many wave-type PDEs. Key words. finite differences, implicit approximation, compact130 Abstract. The simplest finite difference approximations for spatial derivatives are centered, explicit
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.
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.
Approximating the spin distributions in capture reactions between spherical nuclei
NASA Astrophysics Data System (ADS)
Chushnyakova, M. V.; Gontchar, I. I.
2015-09-01
Twenty years ago an approximation for the spin distribution of the dinuclear systems formed in capture reactions with heavy ions was proposed. This approximation is used nowadays. However, since that time the experimental errors of the measured capture cross sections were reduced drastically. We show that the accuracy of the old spin distribution approximation is certainly out of date and propose a new approximation built on the dynamical modeling of the capture process. Results suggest that this new approximation might be useful especially for performing modeling of decay of excited dinuclear systems (compound nuclei) formed during heavy-ion collisions.
Sorin A. Lusceac; Markus Rosenstihl; Michael Vogel; Catalin Gainaru; Ariane Fillmer; Roland Böhmer
2010-04-23
Using a combination of dielectric spectroscopy and solid-state deuteron NMR, the hydration water dynamics of connective tissue proteins is studied at sub-ambient temperatures. In this range, the water dynamics follows an Arrhenius law. A scaling analysis of dielectric losses, 'two-phase' NMR spectra, and spin-lattice relaxation times consistently yield evidence for a Gaussian distribution of energy barriers. With the dielectric data as input, random-walk simulations of a large-angle, quasi-isotropic water reorientation provide an approximate description of stimulated-echo data on hydrated elastin. This secondary process takes place in an essentially rigid energy landscape, but in contrast to typical {\\beta}-relaxations it is quasi-isotropic and delocalized. The delocalization is inferred from previous NMR diffusometry experiments. To emphasize the distinction from conventional {\\beta}-processes, for aqueous systems such a matrix-decoupled relaxation was termed a {\
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.
Hybrid adaptive methods for approximating a nonconvex multidimensional Pareto frontier
NASA Astrophysics Data System (ADS)
Berezkin, V. E.; Kamenev, G. K.; Lotov, A. V.
2006-11-01
New hybrid methods for approximating the Pareto frontier of the feasible set of criteria vectors in nonlinear multicriteria optimization problems with nonconvex Pareto frontiers are considered. Since the approximation of the Pareto frontier is an ill-posed problem, the methods are based on approximating the Edgeworth-Pareto hull (EPH), i.e., the maximum set having the same Pareto frontier as the original feasible set of criteria vectors. The EPH approximation also makes it possible to visualize the Pareto frontier and to estimate the quality of the approximation. In the methods proposed, the statistical estimation of the quality of the current EPH approximation is combined with its improvement based on a combination of random search, local optimization, adaptive compression of the search region, and genetic algorithms.
Approximation Algorithms and Heuristics for a Heterogeneous Traveling Salesman Problem
Rangarajan, Rahul
2011-08-08
] present an approximation algorithm that runs in O(log n) steps. 2.2.2 Multiple vehicle problems In [18], Malik et al., develop a 2 - approximation algorithm for a symmetric generalized MDMTSP where they obtain the feasible solution using a degree..., vol. 3, no. 1, pp. 197{209, 2007. [18] S. Rathinam W. Malik and S. Darbha, \\An approximation algorithm for a symmetric generalized multiple depot, multiple travelling salesman problem," Operations Research Letters, vol. 35, no. 6, pp. 747 { 753...
Differential equation based method for accurate approximations in optimization
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.
1990-01-01
This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.
Legendre-Tau approximations for functional differential equations
NASA Technical Reports Server (NTRS)
Ito, K.; Teglas, R.
1983-01-01
The numerical approximation of solutions to linear 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 approximations is made.
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.
Diffusion approximation of stochastic master equations with jumps
Pellegrini, C.; Petruccione, F.
2009-12-15
In the presence of quantum measurements with direct photon detection, the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, diffusion models can be obtained from these equations as an approximation. A condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using techniques for Markov processes, which are based on the convergence of Markov generators and martingale problems. This result is illustrated by rigorously obtaining the diffusion approximation for homodyne and heterodyne detection.
Integrating Approximation and Interactive Decision Making in Multicriteria Optimization
Klamroth, Kathrin
Integrating Approximation and Interactive Decision Making in Multicriteria Optimization KATHRIN. In a priori meth- ods, the decision maker first specifies preferences and hopes and after that a solution
Approximation functions for airblast environments from buried charges
Reichenbach, H.; Behrens, K.; Kuhl, A.L.
1993-11-01
In EMI report E 1/93, ``Airblast Environments from Buried HE-Charges,`` fit functions were used for the compact description of blastwave parameters. The coefficients of these functions were approximated by means of second order polynomials versus DOB. In most cases, the agreement with the measured data was satisfactory; to reduce remaining noticeable deviations, an approximation by polygons (i.e., piecewise-linear approximation) was used instead of polynomials. The present report describes the results of the polygon approximation and compares them to previous data. We conclude that the polygon representation leads to a better agreement with the measured data.
An approximation based global optimization strategy for structural synthesis
NASA Technical Reports Server (NTRS)
Sepulveda, A. E.; Schmit, L. A.
1991-01-01
A global optimization strategy for structural synthesis based on approximation concepts is presented. The methodology involves the solution of a sequence of highly accurate approximate problems using a global optimization algorithm. The global optimization algorithm implemented consists of a branch and bound strategy based on the interval evaluation of the objective function and constraint functions, combined with a local feasible directions algorithm. The approximate design optimization problems are constructed using first order approximations of selected intermediate response quantities in terms of intermediate design variables. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure setforth.
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.
Master's Thesis Approximation and analysis of confluent hypergeometric differential
Kim, Yong Jung
the calculation cost of computer loaded at missile, we will find simple approximation of solution of confluent to air missile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Missile
Rigorous Polynomial Approximation Using Taylor Models in Coq
Mayero, Micaela
in C. This is a milestone in our long-term goal of providing fully formally proved and efficient TaylorRigorous Polynomial Approximation Using Taylor Models in Coq Nicolas Brisebarre1 , Mioara Jolde4 for a specific kind of rigorous polynomial approximation called Taylor model. We carry out this work in the Coq
Technical Note Variational free energy and the Laplace approximation
Penny, Will
Technical Note Variational free energy and the Laplace approximation Karl Friston,a, Jérémie the variational free energy under the Laplace approximation, with a focus on accounting for additional model complexity induced by increasing the number of model parameters. This is relevant when using the free energy
Approximate reduction of multiregional models with environmental stochasticity
Bravo de la Parra, Rafael
-struc- tured populations living in a multipatch environment. By manipulating the original system of the knowledge of the behavior of the reduced system. Approximate aggregation techniques have been widely studied extend previous results regarding the use of approximate aggregation techniques to sim- plify the study
Leaky Quantum Graphs: Approximations by Point Interaction Hamiltonians
Leaky Quantum Graphs: Approximations by Point Interaction Hamiltonians P. Exner, 1,2 K. NÅ¸emcovâ??a 1 of various graphÂtype nanosÂ tructures which in distinction to the usual description [KS] take quantum with coe#cients containing values of the free Green function. Hence an approximation of the mentioned type
A Fast Algorithm for Approximate String Matching on Gene Sequences
Chen, Xin
A Fast Algorithm for Approximate String Matching on Gene Sequences Zheng Liu1 , Xin Chen1 , James Department of Plant Pathology, University of California, Riverside Abstract. Approximate string matching is a fundamental and challeng- ing problem in computer science, for which a fast algorithm is highly demanded
INTEREST ZONE MATRIX APPROXIMATION GIL SHABAT AND AMIR AVERBUCH
Averbuch, Amir
ELA INTEREST ZONE MATRIX APPROXIMATION GIL SHABAT AND AMIR AVERBUCH Abstract. An algorithm, and is a pointwise multiplication. This setup is also called Interest-Zone- Matrix-Approximation (IZMA). We show is known as the Eckart-Young Theorem [8] and it is given by the singular value decomposition (SVD
Motivation and Outline Hatree-Fock Theory and KLI Approximation
Holzwarth, Natalie
Motivation and Outline Hatree-Fock Theory and KLI Approximation Frozen core orbital approximation March 24, 2011 Xiao Xu, N. A. W. Holzwarth PAW + HF & KLI #12;Motivation and Outline Hatree-Fock Theory of HF and KLI Conclusion Outline 1 Motivation of this work: Why? orbital dependent functionals + PAW 2
Front Tracing Approximations for Slow Erosion Debora Amadori
. The function f is called the erosion function, which denotes the erosion rate per unit length in space coveredFront Tracing Approximations for Slow Erosion Debora Amadori and Wen Shen ( ): Dipartimento di erosion of granular flow. We construct piecewise constant approximate solutions, using a front tracing
Wavelet-domain Approximation and Compression of Piecewise Smooth Images
1 Wavelet-domain Approximation and Compression of Piecewise Smooth Images Michael B. Wakin,* Justin represen- tation for smooth images, enabling efficient approximation and compression using techniques such as zerotrees. Unfortunately, this sparsity does not extend to piecewise smooth images, where edge
43 CFR 2201.5 - Exchanges at approximately equal value.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 43 Public Lands: Interior 2 2012-10-01 2012-10-01 false Exchanges at approximately equal value... LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) EXCHANGES: GENERAL PROCEDURES Exchanges-Specific Requirements § 2201.5 Exchanges at approximately equal value. (a)...
43 CFR 2201.5 - Exchanges at approximately equal value.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 43 Public Lands: Interior 2 2014-10-01 2014-10-01 false Exchanges at approximately equal value... LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) EXCHANGES: GENERAL PROCEDURES Exchanges-Specific Requirements § 2201.5 Exchanges at approximately equal value. (a)...
43 CFR 2201.5 - Exchanges at approximately equal value.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 43 Public Lands: Interior 2 2011-10-01 2011-10-01 false Exchanges at approximately equal value... LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) EXCHANGES: GENERAL PROCEDURES Exchanges-Specific Requirements § 2201.5 Exchanges at approximately equal value. (a)...
Nucleon Properties from Approximating Chiral Quark Sigma Model
M. Abu-Shady
2009-12-18
We apply the approximating chiral quark model. This chiral quark model is based on an effective Lagrangian which the interactions between quarks via sigma and pions mesons. The field equations have been solved in the mean field approximation for the hedgehog baryon state. Good results are obtained for nucleon properties in comparison with original model.
Generalization of Ramanujan Method of Approximating root of an equation
Muthumalai, Ramesh Kumar
2011-01-01
We generalize Ramanujan method of approximating the smallest root of an equation which is found in Ramanujan Note books, Part-I. We provide simple analytical proof to study convergence of this method. Moreover, we study iterative approach of this method on approximating a root with arbitrary order of convergence.
Approximate Minimum-Energy Multicasting in Wireless Ad Hoc Networks
Liang, Weifa
Approximate Minimum-Energy Multicasting in Wireless Ad Hoc Networks Weifa Liang, Senior Member, IEEE Abstract--A wireless ad hoc network consists of mobile nodes that are equipped with energy-limited a constant factor of the best-possible approximation achievable unless P = NP. Index Terms
On the Approximations of Multiple target filtering P. Del Moral
Del Moral , Pierre
On the Approximations of Multiple target filtering equations P. Del Moral Centre INRIA Bordeaux (2010). To appear in Stochastic Analysis and Applications (2011). Del Moral (INRIA) INRIA Centre models 7 Approximation models Del Moral (INRIA) INRIA Centre Bordeaux-Sud Ouest, France 2 / 25 #12;Some
On the Approximations of Multiple target filtering P. Del Moral
Del Moral , Pierre
On the Approximations of Multiple target filtering equations P. Del Moral Centre INRIA de Bordeaux (2010). To appear in Stochastic Analysis and Applications (2011). P. Del Moral (INRIA) INRIA Bordeaux Approximation models P. Del Moral (INRIA) INRIA Bordeaux-Sud Ouest 2 / 25 #12;Some notation : E measurable space
The blind leading the blind: Mutual refinement of approximate theories
NASA Technical Reports Server (NTRS)
Kedar, Smadar T.; Bresina, John L.; Dent, C. Lisa
1991-01-01
The mutual refinement theory, a method for refining world models in a reactive system, is described. The method detects failures, explains their causes, and repairs the approximate models which cause the failures. The approach focuses on using one approximate model to refine another.
Error Estimates for the Approximation of the Effective Hamiltonian
Camilli, Fabio Capuzzo Dolcetta, Italo Gomes, Diogo A.
2008-02-15
We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting.
An Analysis of the Morris Loe Angle Trisection Approximation.
ERIC Educational Resources Information Center
Aslan, Farhad,; And Others
1992-01-01
Presents the Morris Loe Angle Trisection Approximation Method to introduce students to areas of mathematics where approximations are used when exact answers are difficult or impossible to obtain. Examines the accuracy of the method using the laws of sines and cosines and a BASIC computer program that is provided. (MDH)
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…
Control of implicit chaotic maps using nonlinear approximations
NASA Astrophysics Data System (ADS)
Hill, D. L.
2000-09-01
The technique of using nonlinear approximations to design controllers for chaotic dynamical systems introduced by Yagasaki and Uozumi is extended in order to enable it to be used to design controllers for chaotic dynamical systems that are described by implicit maps and is then used to control the well-known bouncing ball system without recourse to the high-bounce approximation.
Matching Pursuit Video Coding Part I: Dictionary Approximation
Zakhor, Avideh
1 Matching Pursuit Video Coding Part I: Dictionary Approximation Ralph Neff and Avideh Zakhor Electrical Engineering and Computer Science University of California, Berkeley Abstract We have shown. The key to the method is an algorithm which takes an arbitrary 2D dictionary and generates approximations
New approximation for free surface flow of groundwater: capillarity correction
New approximation for free surface flow of groundwater: capillarity correction D.-S. Jeng a,*, B capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal
A new approximation for the dynamics of topographic Rossby waves
Ashkenazy, Yossi "Yosef"
A new approximation for the dynamics of topographic Rossby waves By YOSEF ASHKENAZY1 *, NATHAN theory of non-harmonic topographic Rossby waves over a slowly varying bottom depth of arbitrary, 1-D explicit approximate expressions for the phase speed and non-harmonic cross-slope structure of waves
Practical Experiments with Regular Approximation of Context-Free Languages
implemented a large number of meth- ods, and where necessary, refined them with an analysis of the grammar. We. The nature of this processing differs for the respective approximation meth- ods. For other parts several meth- ods to approximate the language generated by a grammar if the sufficient condition mentioned
Approximate Killing Vectors for Computing Spin in Black-Hole
Cook, Greg
Approximate Killing Vectors for Computing Spin in Black-Hole Initial Data and Evolutions Gregory B-local definition: e.g. Brown & York[2] or Ashtekar & Krishnan[1] S = - 1 8 BH Kiji sj hd2 x i = i CK : Killing vector of ~hij conformal Killing vector of hij i AKV : Approximate Killing vector of hij Â Greg Cook
Approximate Killing Vectors and Black-Hole Diagnostics
Cook, Greg
Approximate Killing Vectors and Black-Hole Diagnostics Gregory B. Cook Wake Forest University[2] or Ashtekar & Krishnan[1] S = - 1 8 BH Kiji sj hd2 x i = i CK : Killing vector of ~hij conformal Killing vector of hij i AKV : Approximate Killing vector of hij Â Greg Cook Â (WFU Physics) 1 #12
Atomic Structure Schrdinger equation has approximate solutions for multi-
Zakarian, Armen
Atomic Structure Schrödinger equation has approximate solutions for multi- electron atoms, which indicate that all atoms are like hydrogen Atomic Structure Schrödinger equation has approximate solutions 3s 3p 3d Energy hydrogen multi-electron #12;Atomic Structure · orbitals are populated by electrons
Hybrid Least-Squares Algorithms for Approximate Policy Evaluation
Mahadevan, Sridhar
Hybrid Least-Squares Algorithms for Approximate Policy Evaluation Jeff Johns, Marek Petrik of approximate policy evaluation is to "best" represent a target value function according to a specific criterion suggest hybrid algorithms can find solutions that lead to better policies when performing policy iteration
APPROXIMATE ROOTS OF A VALUATION AND THE PIERCEBIRKHOFF CONJECTURE
APPROXIMATE ROOTS OF A VALUATION AND THE PIERCEBIRKHOFF CONJECTURE F. Lucas D´epartement de Math. Abstract In this paper, we construct an object, called a system of approximate roots of a valuation, centered in a regular local ring, which describes the fine structure of the valuation (namely, its
Approximating the Minimum Weight Steiner Triangulation David Eppstein
Eppstein, David
Approximating the Minimum Weight Steiner Triangulation David Eppstein Department of Information that the length of the minimum weight Steiner triangulation (MWST) of a point set can be approximated within a constant factor by a triangulation algorithm based on quadtrees. In O(n log n) time we can compute
Approximation of Minimum Triangulation for Polyhedron with Bounded Degrees
Fung, Stanley P. Y.
Approximation of Minimum Triangulation for Polyhedron with Bounded Degrees Francis Y. L. Chin, Hong Kong. fchin, pyfungg @csis.hku.hk Abstract. Finding minimum triangulations of convex polyhedra the approximation ratio of #12;nding minimum triangulations for some special classes of 3-dimensional convex
Improving Local Convergence in Particle Swarms by Fitness Approximation Using
Li, Xiaodong
Chapter 11 Improving Local Convergence in Particle Swarms by Fitness Approximation Using Regression. A least-squares regression is used to estimate the shape of the local fit- ness landscape. From this shape using a polynomial regression model. This chapter presents a fitness approximation technique that helps
Thermodynamics of the ?^4 theory in tadpole approximation
A. Peshier; B. Kämpfer; O. P. Pavlenko; G. Soff
1998-01-19
Relying on the Luttinger-Ward theorem we derive a thermodynamically selfconsistent and scale independent approximation of the thermodynamic potential for the scalar $\\phi^4$ theory in the tadpole approximation. The resulting thermodynamic potential as a function of the temperature is similar to the one of the recently proposed screened perturbation theory.
An Approximate Inference Approach to Temporal Optimization in Optimal Control
Toussaint, Marc
An Approximate Inference Approach to Temporal Optimization in Optimal Control Konrad C. Rawlik on iterative local approximations present a practical approach to optimal control in robotic systems. However optimizing the temporal parameters in addition to the control command profiles. The presented approach
Approximate distributed Kalman filtering for cooperative multi-agent
Hespanha, João Pedro
Approximate distributed Kalman filtering for cooperative multi-agent localization Prabir Barooah1 an algorithm that computes an approximation of the central- ized optimal (Kalman filter) estimates with nearby agents. The problem of distributed Kalman filtering for this application is reformulated
Approximating Fault-Tolerant Steiner Subgraphs in Heterogeneous Wireless Networks
Erlebach, Thomas
and Thomas Erlebach Department of Computer Science University of Leicester University Road, Leicester LE1 7RH spanning a given set of terminals, and we propose a constant-factor approximation algorithm subgraphs in UDG and quasi-UDG. We propose a constant-factor approximation algorithm for this problem. A
Function approximation using combined unsupervised and supervised learning.
Andras, Peter
2014-03-01
Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data. PMID:24807446
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.
Krylov Space Approximate Kalman Filtering Johnathan M. Bardsleya
Bardsley, John
Krylov Space Approximate Kalman Filtering Johnathan M. Bardsleya , Albert Parkerb , Antti Solonenc Institute, Helsinki, Finland. Abstract The Kalman filter is a technique for estimating a time-varying state requirements of the Kalman filter are prohibitive, and hence, approximations must be made. In this paper, we
Properties of the Boltzmann equation in the classical approximation
Epelbaum, Thomas; Gelis, François; Tanji, Naoto; Wu, Bin
2014-12-30
We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.
Properties of the Boltzmann equation in the classical approximation
Epelbaum, Thomas; Gelis, François; Tanji, Naoto; Wu, Bin
2014-12-30
We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since onemore »has also access to the non-approximated result for comparison.« less
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.
NASA Astrophysics Data System (ADS)
Zhou, Shi-Qi
2007-04-01
A universal theoretical approach is proposed which enables all hard sphere density functional approximations (DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.
Finite state approximation for continuous-time Markov games with ergodic payoffs Finite state-Rumeau and O. Hern´andez-Lerma. #12;Finite state approximation for continuous-time Markov games with ergodic the state process evolves in time as a Markov process. If time parameter evolves in an interval, then we
Mapping biological entities using the longest approximately common prefix method
2014-01-01
Background The significant growth in the volume of electronic biomedical data in recent decades has pointed to the need for approximate string matching algorithms that can expedite tasks such as named entity recognition, duplicate detection, terminology integration, and spelling correction. The task of source integration in the Unified Medical Language System (UMLS) requires considerable expert effort despite the presence of various computational tools. This problem warrants the search for a new method for approximate string matching and its UMLS-based evaluation. Results This paper introduces the Longest Approximately Common Prefix (LACP) method as an algorithm for approximate string matching that runs in linear time. We compare the LACP method for performance, precision and speed to nine other well-known string matching algorithms. As test data, we use two multiple-source samples from the Unified Medical Language System (UMLS) and two SNOMED Clinical Terms-based samples. In addition, we present a spell checker based on the LACP method. Conclusions The Longest Approximately Common Prefix method completes its string similarity evaluations in less time than all nine string similarity methods used for comparison. The Longest Approximately Common Prefix outperforms these nine approximate string matching methods in its Maximum F1 measure when evaluated on three out of the four datasets, and in its average precision on two of the four datasets. PMID:24928653
Meromorphic approximants to complex Cauchy transforms with polar singularities
Baratchart, Laurent; Yattselev, Maxim L
2009-10-31
We study AAK-type meromorphic approximants to functions of the form F(z)={integral}(d{lambda}(t))/(z-t)+R(z), where R is a rational function and {lambda} is a complex measure with compact regular support included in (-1,1), whose argument has bounded variation on the support. The approximation is understood in the L{sup p}-norm of the unit circle, p{>=}2. We dwell on the fact that the denominators of such approximants satisfy certain non-Hermitian orthogonal relations with varying weights. They resemble the orthogonality relations that arise in the study of multipoint Pade approximants. However, the varying part of the weight implicitly depends on the orthogonal polynomials themselves, which constitutes the main novelty and the main difficulty of the undertaken analysis. We obtain that the counting measures of poles of the approximants converge to the Green equilibrium distribution on the support of {lambda} relative to the unit disc, that the approximants themselves converge in capacity to F, and that the poles of R attract at least as many poles of the approximants as their multiplicity and not much more. Bibliography: 35 titles.
Comparison of approximate and numerical analyses of nonlinear combustion instability
NASA Technical Reports Server (NTRS)
Culick, F. E. C.; Levine, J. N.
1974-01-01
At the present time, there are three general analytical techniques available to study problems of unsteady motions in rocket motors: linear stability analysis; approximate nonlinear analysis, founded on examining the behavior of coupled normal modes; and numerical calculations based on the conservation equations for one-dimensional flows. The last two yield the linear results as a limit. It is the main purpose of this paper to check the accuracy of the approximate analysis against the numerical analysis for some special cases. The results provide some justification for using the approximate analysis to study three-dimensional problems.
Quadrupole Collective Inertia in Nuclear Fission: Cranking Approximation
Baran, A.; Sheikh, J. A.; Dobaczewski, J.; Nazarewicz, Witold
2011-01-01
Collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian Overlap Approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in ^{256}Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and perturbative cranking approximations to ATDHFB, and within GOA, are discussed.
Approximate Quantum Cloaking and Almost-Trapped States
Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
2008-11-28
We describe potentials which act as approximate cloaks for matter waves. These potentials are derived from ideal cloaks for the conductivity and Helmholtz equations. At most energies E, if a potential is surrounded by an approximate cloak, then it becomes almost undetectable and unaltered by matter waves originating externally to the cloak. For certain E, however, the approximate cloaks are resonant, supporting wave functions almost trapped inside the cloaked region and negligible outside. Applications include dc or magnetically tunable ion traps and beam switches.
Communication: Improved pair approximations in local coupled-cluster methods
Schwilk, Max; Werner, Hans-Joachim; Usvyat, Denis
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.
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.
Analytic Approximate Solution for Falkner-Skan Equation
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
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.
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.
Baby Skyrme Model, Near-BPS Approximations and Supersymmetric Extensions
Bolognesi, S
2014-01-01
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 which, however, involves 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 ${\\cal N}=1$ and the particular ones with extended ${\\cal N}=2$ supersymmetries and relate this to the above mentioned almost-BPS approximation.
A similarity theory of approximate deconvolution models of turbulence
NASA Astrophysics Data System (ADS)
Layton, William; Neda, Monika
2007-09-01
We apply the phenomenology of homogeneous, isotropic turbulence to the family of approximate deconvolution models proposed by Stolz and Adams. In particular, we establish that the models themselves have an energy cascade with two asymptotically different inertial ranges. Delineation of these gives insight into the resolution requirements of using approximate deconvolution models. The approximate deconvolution model's energy balance contains both an enhanced energy dissipation and a modification to the model's kinetic energy. The modification of the model's kinetic energy induces a secondary energy cascade which accelerates scale truncation. The enhanced energy dissipation completes the scale truncation by reducing the model's micro-scale from the Kolmogorov micro-scale.
Nernst effect beyond the relaxation-time approximation
NASA Astrophysics Data System (ADS)
Pikulin, D. I.; Hou, Chang-Yu; Beenakker, C. W. J.
2011-07-01
Motivated by recent interest in the Nernst effect in cuprate superconductors, we calculate this magnetothermoelectric effect for an arbitrary (anisotropic) quasiparticle dispersion relation and elastic-scattering rate. The exact solution of the linearized Boltzmann equation is compared with the commonly used relaxation-time approximation. We find qualitative deficiencies in this approximation to the extent that it can get the sign wrong of the Nernst coefficient. Ziman’s improvement of the relaxation-time approximation, which becomes exact when the Fermi surface is isotropic, also cannot capture the combined effects of anisotropy in dispersion and scattering.
Berkel, M. van; Hogeweij, G. M. D.; Tamura, N.; Ida, K.; Zwart, H. J.; Inagaki, S.; Baar, M. R. de
2014-11-15
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.
8. BUILDING 223 INTERIOR, EASTERN MAIN STOREROOM, FROM APPROXIMATE CENTER, ...
8. BUILDING 223 INTERIOR, EASTERN MAIN STOREROOM, FROM APPROXIMATE CENTER, LOOKING SOUTHEAST, WITH VALUABLES CAGE AT LEFT BEHIND FORKLIFT. - Oakland Naval Supply Center, Pier Transit Sheds, North Marginal Wharf, between First & Third Streets, Oakland, Alameda County, CA
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
6. BUILDING 123 INTERIOR, FROM APPROXIMATE CENTER OF BUILDING, LOOKING ...
6. BUILDING 123 INTERIOR, FROM APPROXIMATE CENTER OF BUILDING, LOOKING WEST, WITH OFFICE MEZZANINE AT WESTERN END. - Oakland Naval Supply Center, Pier Transit Sheds, North Marginal Wharf, between First & Third Streets, Oakland, Alameda County, CA
Numerical Approximations of Stochastic Optimal Stopping and Control Problems
Siska, David
2007-01-01
We study numerical approximations for the payoff function of the stochastic optimal stopping and control problem. It is known that the payoff function of the optimal stopping and control problem corresponds to the solution ...
Sensitivity, Approximation and Uncertainty in Power System Dynamic Simulation
1 Sensitivity, Approximation and Uncertainty in Power System Dynamic Simulation Ian A. Hiskens the influence of uncertainty in simulations of power system dynamic behaviour. It is shown that trajectory uncertainty; power system dynamic performance assessment; power system simulation; trajectory sensitivity
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
Approximating Terminological Queries Heiner Stuckenschmidt, Frank van Harmelen
van Harmelen, Frank
of approximate reasoning using the example of building and maintaining semantic cat- alogues that can be used/no oracles, but that instead display anytime behaviour [3]. It is tempting to conclude that symbolic, formal
Born approximation in linear-time invariant system
Gumjudpai, Burin
2015-01-01
Linear-time invariant (LTI) oscillation systems such as forced mechanical vibration, series RLC and parallel RLC circuits can be solved by using simplest initial conditions or employing of Green's function of which knowledge of initial condition of the force term is needed. Here we show a mathematical connection of the LTI system and the Helmholtz equation form of the time-independent Schr\\"{o}dinger equation in quantum mechanical scattering problem. We apply Born approximation in quantum mechanics to obtain LTI general solution in form of infinite Born series which can be expressed as a series of one-dimensional Feynman graphs. Conditions corresponding to the approximation are given for the case of harmonic driving force. The Born series of the harmonic forced oscillation case are derived by directly applying the approximation to the LTI system or by transforming the LTI system to Helmholtz equation prior to doing the approximation.
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 ...
An approximate dynamic programming approach to solving dynamic oligopoly models
Farias, Vivek F.
In this article, we introduce a new method to approximate Markov perfect equilibrium in large-scale Ericson and Pakes (1995)-style dynamic oligopoly models that are not amenable to exact solution due to the curse of ...
Sparse Multinomial Logistic Regression via Approximate Message Passing
Schniter, Philip
Sparse Multinomial Logistic Regression via Approximate Message Passing A Thesis Presented Generalized Ap- proximate Message Passing (Hybrid-GAMP) to train a multinomial logistic regression model. We classifier . . . . . . . . . . . . . . . . . . . . 6 1.3.3 Justification for the multinomial logistic
DEMOCRACY FUNCTIONS AND OPTIMAL EMBEDDINGS FOR APPROXIMATION SPACES
Hernández, Eugenio
DEMOCRACY FUNCTIONS AND OPTIMAL EMBEDDINGS FOR APPROXIMATION SPACES GUSTAVO GARRIG´OS, EUGENIO HERN , in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions
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 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 ...
Numerical Stability and Convergence of Approximate Methods for Conservation Laws
NASA Astrophysics Data System (ADS)
Galkin, V. A.
We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.
Hybrid approximation of stochastic process algebras for systems biology
Bortolussi, Luca
of stochastic Concurrent Constraint Programming (sCCP), a stochastic programming methodology based on logic programming. Our technique automatically associates to a stochastic model an hybrid automaton, i. Keywords: Stochastic programming, Hybrid systems, Approximate analysis, Computer simulation, Biosystems 1
Generalized eikonal approximation for strong-field ionization
NASA Astrophysics Data System (ADS)
Cajiao Vélez, F.; Krajewska, K.; Kami?ski, J. Z.
2015-05-01
We develop the eikonal perturbation theory to describe the strong-field ionization by finite laser pulses. This approach in the first order with respect to the binding potential (the so-called generalized eikonal approximation) avoids a singularity at the potential center. Thus, in contrast to the ordinary eikonal approximation, it allows one to treat rescattering phenomena in terms of quantum trajectories. We demonstrate how the first Born approximation and its domain of validity follow from eikonal perturbation theory. Using this approach, we study the coherent interference patterns in photoelectron energy spectra and their modifications induced by the interaction of photoelectrons with the atomic potential. Along with these first results, we discuss the prospects of using the generalized eikonal approximation to study strong-field ionization from multicentered atomic systems and to study other strong-field phenomena.
4. BUILDING 422, WEST SIDE, FROM APPROXIMATELY 25 FEET SOUTHWEST ...
4. BUILDING 422, WEST SIDE, FROM APPROXIMATELY 25 FEET SOUTHWEST OF SOUTHWEST CORNER, LOOKING NORTHEAST. - Oakland Naval Supply Center, Aeronautical Materials Storehouses, Between E & G Streets, between Fourth & Sixth Streets, Oakland, Alameda County, CA
6. BUILDING 522, INTERIOR, STOREROOM, FROM APPROXIMATELY TWOTHIRDS OF DISTANCE ...
6. BUILDING 522, INTERIOR, STOREROOM, FROM APPROXIMATELY TWO-THIRDS OF DISTANCE FROM EAST END, LOOKING WEST. - Oakland Naval Supply Center, Aeronautical Materials Storehouses, Between E & G Streets, between Fourth & Sixth Streets, Oakland, Alameda County, CA
5. BUILDING 522, INTERIOR, STOREROOM, FROM APPROXIMATELY 50 FEET SOUTHEAST ...
5. BUILDING 522, INTERIOR, STOREROOM, FROM APPROXIMATELY 50 FEET SOUTHEAST OF NORTHWEST CORNER, LOOKING EAST. - Oakland Naval Supply Center, Aeronautical Materials Storehouses, Between E & G Streets, between Fourth & Sixth Streets, Oakland, Alameda County, CA
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.
Appendix to "Approximating perpetuities" Margarete Knape and Ralph Neininger
Neininger, Ralph
Appendix to "Approximating perpetuities" Margarete Knape and Ralph Neininger Institute: Perfect simulation, perpetuity, Quickselect, coupling from the past, multigamma coupler, key exchanges. 1 of distributions, the Vervaat perpetuities. Devroye and Fawzi [3] presented a different multigamma cou- pler
Lecture 4: Approximate Wray Buntine and Petri Myllymaki
Myllymäki, Petri
· General maximisation on the Almond tree is essentially an "all solutions" approach. What if we want just one solution? · What if our graph is too big for Almond trees? Can an approximation be developed
Queueing systems subject to random server failures: an approximation
Matis, Timothy
1998-01-01
are arbitrary), and yet maintains computational simplicity and efficiency. This method will be obtained through the implementation of a stationary delayed renewal process and simple modifications of common approximation formulas for a G/G/m queue. Through...
Multiscale Approximation S. Dahlke, K. Koch, M. Werner1
Teschke, Gerd
Multiscale Approximation S. Dahlke, K. Koch, M. Werner1 , P. Maaß, D. Lorenz, S. Schiffler2 , G,dlorenz,schiffi}@math.uni-bremen.de 3 Konrad-Zuse-Zentrum f¨ur Informationstechnik Berlin (ZIB) Takustraße 7, D-14195 Berlin
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Benzi, M.; Tuma, M.
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
Approximate translation : media, narrative, and experience in urban design
Crisman, Jonathan
2013-01-01
Approximate translation is developed as a design process through which the place-embedded history of an urban environment can be understood, allowing for better design and intervention in that urban environment. Generally, ...
Explicit bounds for the approximation error in Benford's law
Duembgen, Lutz
2007-01-01
Benford's law states that for many random variables X > 0 the leading digit D = D(X) satisfies approximately the equation P(D = d) = log_{10}(1 + 1/d) for d = 1,2,...,9. This phenomenon follows from another, maybe more intuitive fact, applied to Y := log_{10}(X): For many real random variables Y, the remainder U = U(Y) := Y - floor(Y) is approximately uniformly distributed on [0,1). The present paper provides new explicit bounds for the latter approximation in terms of the total variation of the density of Y or some derivative of it. These bounds are an interesting alternative to traditional Fourier methods which yield mostly qualitative results. As a by-product we obtain explicit bounds for the approximation error in Benford's law.
Approximate Algebraic Methods for Curves and Surfaces and their Applications
Jüttler, Bert
of these techniques, such as detection of selfintersections, ray tracing, footpoint computation and parameterization: approximation, implicitization, parameterization, distance bounds, intersections and selfintersections, raytracing
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
Decidable Approximations on Generalized and Parameterized Discrete Timed Automata
Dang, Zhe
specification written in ASTRAL is used to run a number of experiments using one of the approximation techniques in the realtime specification language ASTRAL [6] use generalized clock constraints and parameterized
Generalized Discrete Timed Automata: Decidable Approximations for Safety Verification ?
Dang, Zhe
specification written in ASTRAL is used to run a number of experiments using one of the approximation techniques ASTRAL [6] use generalized clock constraints and parameterized durations in almost every specification
Generalized Discrete Timed Automata: Decidable Approximations for Safety Verification
Dang, Zhe
specification written in ASTRAL is used to run a number of experiments using one of the approximation techniques-world speci- fications [6, 8, 10, 21] written in the real-time specification language ASTRAL [6] use
Approximate inference : decomposition methods with applications to networks
Jung, Kyomin
2009-01-01
Markov random field (MRF) model provides an elegant probabilistic framework to formulate inter-dependency between a large number of random variables. In this thesis, we present a new approximation algorithm for computing ...
Second post-Newtonian approximation of Einstein-aether theory
Yi Xie; Tian-Yi Huang
2008-07-02
In this paper, second post-Newtonian approximation of Einstein-aether theory is obtained by Chandrasekhar's approach. Five parameterized post-Newtonian parameters in first post-Newtonian approximation are presented after a time transformation and they are identical with previous works, in which $\\gamma=1$, $\\beta=1$ and two preferred-frame parameters remain. Meanwhile, in second post-Newtonian approximation, a parameter, which represents third order nonlinearity for gravity, is zero the same as in general relativity. For an application for future deep space laser ranging missions, we reduce the metric coefficients for light propagation in a case of $N$ point masses as a simplified model of the solar system. The resulting light deflection angle in second post-Newtonian approximation poses another constraint on the Einstein-aether theory.
Pade Approximations in Inverse Homogenization and Numerical Simulation of Electromagnetic
Cherkaev, Elena
and residues of the corresponding partial fraction decompositions stem from the properties of Pad fractions of the constituents in the composite. Diagonal PadÂ´e approximants for inverse homog- enization
Approximate Mechanism Design Without Money Ariel D. Procaccia
Procaccia, Ariel
, and (more often than not) approximation is a necessary evil that is required to circumvent computational our results in two natural directions: a domain where two fa- cilities must be located, and a domain
Equivalence between Approximate Dynamic Inversion and Proportion-Integral Control
Teo, Justin
2008-09-29
Approximate Dynamic Inversion (ADI) has been established as a method to control minimum-phase, nonaffine-in-control systems. Previous results have shown that for single-input nonaffine-in-control systems, every ADI controller ...
Approximate Solutions for Galvanostatic Discharge of Spherical Particles
Approximate Solutions for Galvanostatic Discharge of Spherical Particles I. Constant Diffusion of an electrochemically active species in a spherical electrode particle. Analytical expressions are obtained during the galvanostatic discharge of an electrode particle. Based on a comparison with an exact
VIDEO SYNTHESIS OF ARBITRARY VIEWS FOR APPROXIMATELY PLANAR SCENES
Kale, Amit
VIDEO SYNTHESIS OF ARBITRARY VIEWS FOR APPROXIMATELY PLANAR SCENES Amit K. Roy Chowdhury, Amit KaleÂ¡ amitrc,kale,ramaÂ¢ @cfar.umd.edu ABSTRACT In this paper, we propose a method to synthesize arbitrary views
The Uniform Hardcore Lemma via Approximate Bregman Projections
Barak, Boaz
The Uniform Hardcore Lemma via Approximate Bregman Projections Boaz Barak Moritz Hardt Satyen Kale Microsoft Way, Redmond, WA 98052, satyen.kale@microsoft.com dependent interest. 1 Introduction Informally
Particle approximation of multiple object filtering problems P. Del Moral
Del Moral , Pierre
Particle association measures #12;Introduction/notation Defense Industrial Research project Some basic research project 1. Defense industrial Contract : ALEA INRIA & DCNS Toulon (2009) 2. National ResearchParticle approximation of multiple object filtering problems P. Del Moral UNSW, School
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
Approximating the Helium Wavefunction in Positronium-Helium Scattering
NASA Technical Reports Server (NTRS)
DiRienzi, Joseph; Drachman, Richard J.
2003-01-01
In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.
Approximating the ground state of gapped quantum spin systems
Michalakis, Spyridon; Hamza, Eman; Nachtergaele, Bruno; Sims, Robert
2009-01-01
We consider quantum spin systems defined on finite sets V equipped with a metric. In typical examples, V is a large, but finite subset of Z{sup d}. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset {chi} {contained_in} V the ground state projector can be approximated by the product of two projections, one supported on {chi} and one supported on {chi}{sup c}, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue.
An approximation for homogeneous freezing temperature of water droplets
NASA Astrophysics Data System (ADS)
O, K.-T.; Wood, R.
2015-11-01
In this work, based on the well-known formulae of classical nucleation theory (CNT), the temperature TNc = 1 at which the mean number of critical embryos inside a droplet is unity is derived and proposed as a new approximation for homogeneous freezing temperature of water droplets. Without consideration of time dependence and stochastic nature of the ice nucleation process, the approximation TNc = 1 is able to reproduce the dependence of homogeneous freezing temperature on drop size and water activity of aqueous drops observed in a wide range of experimental studies. We use the TNc = 1 approximation to argue that the distribution of homogeneous freezing temperatures observed in the experiments may largely be explained by the spread in the size distribution of droplets used in the particular experiment. It thus appears that this approximation is useful for predicting homogeneous freezing temperatures of water droplets in the atmosphere.
An Approximate Inference Approach to Temporal Optimization in Optimal Control
Rawlik, Konrad; Toussaint, Marc; Vijayakumar, Sethu
2011-01-28
Algorithms based on iterative local approximations present a practical approach to optimal control in robotic systems. However, they generally require the temporal parameters (for e.g. the movement duration or the time ...
1. WEST AND SOUTH SIDES, FROM APPROXIMATELY 25 FEET SOUTH ...
1. WEST AND SOUTH SIDES, FROM APPROXIMATELY 25 FEET SOUTH OF SOUTHEASTERN CORNER OF BUILDING 441-B, LOOKING NORTHEAST. - Oakland Naval Supply Center, Heating Plant, On Northwest Corner of K Street & Fifth Street, Oakland, Alameda County, CA
1. WEST AND SOUTH SIDES, FROM APPROXIMATELY 75 FEET SOUTHWEST ...
1. WEST AND SOUTH SIDES, FROM APPROXIMATELY 75 FEET SOUTHWEST OF BUILDING, LOOKING EAST-NORTHEAST. - Oakland Naval Supply Center, Heating Plant, North of B Street & West of Third Street, Oakland, Alameda County, CA
Nonlinear adaptive control using radial basis function approximants
Petersen, Jerry Lee
1993-01-01
equations used for the tracking control problem are then introduced, and the stability of the system is investigated employing a Lyapunov stability analysis. The extension of the radial basis function approximation method for the adaptive tracking control...
Approximate Distributed Kalman Filtering for Cooperative Multi-agent Localization
Hespanha, JoÃ£o Pedro
Approximate Distributed Kalman Filtering for Cooperative Multi-agent Localization Wm. Joshua filter, to fuse both odometry data and robot-to-robot relative distance measurements (Mourikis & Roumeliotis, 2006; Roumeliotis & Bekey, 2002). However, computing the Kalman filter estimates requires all
86. View of elevator approximately three feet below ground, air ...
86. View of elevator approximately three feet below ground, air exhaust vent and escape hatch visible at far left, pit "B", looking northwest - Nike Missile Battery MS-40, County Road No. 260, Farmington, Dakota County, MN
87. View of elevator approximately six feet below ground, air ...
87. View of elevator approximately six feet below ground, air exhaust vent and escape hatch visible at far left, pit "B", looking northwest - Nike Missile Battery MS-40, County Road No. 260, Farmington, Dakota County, MN
Approximate Momentum Conservation for Spatial Semidiscretizations of Semilinear Wave Equations
Oliver, Marcel
second order finite difference uniform space discretization of the semilinear wave equation with periodic wave equation and modified system . . . . . . . . . . . . . 30 7.5 Difference between discreteApproximate Momentum Conservation for Spatial Semidiscretizations of Semilinear Wave Equations
Superconvergence of the Mixed Finite Element Approximations to parabolic equations
Ewing, Richard E.
\\Lambda Richard Ewing \\Lambda Raytcho Lazarov y Abstract Semidiscrete mixed finite element approximation by many other authors; see, e.g., Duran [7], Douglas and Wang [6], Wang [18], and Ewing, Lazarov, and Wang
Superconvergence of the mixed nite element approximations to parabolic equations
Ewing, Richard E.
Richard Ewing Raytcho Lazarov y Abstract Semidiscrete mixed nite element approximation to parabolic, see, e.g., Duran 7], Douglas and Wang 6], Wang 18], and Ewing, Lazarov and Wang 9]. The corresponding
FINITE VOLUME ELEMENT APPROXIMATIONS OF INTEGRODIFFERENTIAL PARABOLIC PROBLEMS
Ewing, Richard E.
FINITE VOLUME ELEMENT APPROXIMATIONS OF INTEGRODIFFERENTIAL PARABOLIC PROBLEMS RICHARD E. EWING Institute for Scientific Computation, Texas A&M University, College Station, TX 778433404, Email: ewing
Duplicate view to show interior of the gymnasium from approximately ...
Duplicate view to show interior of the gymnasium from approximately the same vantage point as in MD-1109-S-12 - National Park Seminary, Gymnasium, North of Linden Lane, south of Aloha House, Silver Spring, Montgomery County, MD
Orthogonal Polynomial Approximation in Higher Dimensions: Applications in Astrodynamics
Bani Younes, Ahmad H.
2013-08-05
-1 ORTHOGONAL POLYNOMIAL APPROXIMATION IN HIGHER DIMENSIONS: APPLICATIONS IN ASTRODYNAMICS A Dissertation by AHMAD HANI ABD ALQADER BANI YOUNES Submitted to the O ce of Graduate Studies of Texas A&M University in partial ful llment of the requirements... Engineering Copyright 2013 Ahmad Hani Abd Alqader Bani Younes ABSTRACT We propose novel methods to utilize orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical di erential equation solvers to perform high...
Comment on 'Approximate formula of weak oblique shock wave angle'
NASA Astrophysics Data System (ADS)
Powers, Joseph M.
1992-11-01
Dou and Teng (1992) give an approximation of flow of a supersonic gas with constant specific heats over a wedge in the case where the wedge angle is much less than unity. It is presently noted that, for higher Mach numbers, the Liepmann and Roshko (1957) approximation is simpler and superior. Dou and Teng reply that their linear equation is only applicable to very small wedge angles, and that Liepmann and Roshko exhibits advantages only at very high Mach number conditions.
Convex approximation to the likelihood criterion for aperture synthesis imaging.
Meimon, Serge; Mugnier, Laurent M; Le Besnerais, Guy
2005-11-01
Aperture synthesis allows one to measure visibilities at very high resolutions by coupling telescopes of reasonable diameters. We consider the case where visibility amplitudes and phase are measured separately. It leads to an estimation problem where the noise model yields a nonconvex data-likelihood criterion. We show how to optimally approximate the noise model while keeping the criterion convex. This approximation has been validated both on simulations and on experimental data. PMID:16302388
Breakdown of the dipole approximation in core losses
Löffler, S.; Ennen, I.; Tian, F.; Schattschneider, P.; Jaouen, N.
2011-01-01
The validity of the dipole approximations commonly used in the inelastic scattering theory for transmission electron microscopy is reviewed. Both experimental and numerical arguments are presented, emphasizing that the dipole approximations cause significant errors of the order of up to 25% even at small momentum transfer. This behavior is attributed mainly to non-linear contributions to the dynamic form factor due to the overlap of wave functions. PMID:21741917
Quantum Adiabatic Approximation, Quantum Action, and Berry's Phase
Ali Mostafazadeh
1996-06-19
An alternative interpretation of the quantum adiabatic approximation is presented. This interpretation is based on the ideas originally advocated by David Bohm in his quest for establishing a hidden variable alternative to quantum mechanics. It indicates that the validity of the quantum adiabatic approximation is a sufficient condition for the separability of the quantum action function in the time variable. The implications of this interpretation for Berry's adiabatic phase and its semi-classical limit are also discussed.
Mean field approximation for noisy delay coupled excitable neurons
Nikola Buric; Dragana Rankovic; Kristina Todorovic; Nebojsa Vasovic
2010-03-26
Mean field approximation of a large collection of FitzHugh-Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by $N\\gg 1$ stochastic delay-differential equations is derived. The resulting approximation contains only two deterministic delay-differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system.
Approximate analysis for failure probability of structural systems
NASA Astrophysics Data System (ADS)
Cai, Yin-Lin; Zhou, Jian-Sheng
1992-03-01
An approximate formula for calculating failure probability of structural systems is presented, which uses the lower and upper bounds of the first simple bounds to estimate the failure probability. In this formula, the correlation between each of the two failure modes of a structure is considered, but only the first failure probability of the failure modes is contained. Computations using the approximate formula are quite simple and accurate, with maximum error being within 5 percent.
A Modica-Mortola Approximation for Branched Transport and Applications
NASA Astrophysics Data System (ADS)
Oudet, Edouard; Santambrogio, Filippo
2011-07-01
The M ? energy which is usually minimized in branched transport problems among singular one-dimensional rectifiable vector measures is approximated by means of a sequence of elliptic energies defined on more regular vector fields. The procedure recalls the one of Modica-Mortola related to the approximation of the perimeter. In our context, the double-well potential is replaced by a concave term. The paper contains a proof of ?-convergence and numerical simulations of optimal networks based on that previous result.
Simple Approximations for Epidemics with Exponential and Fixed Infectious Periods.
Fowler, A C; Déirdre Hollingsworth, T
2015-08-01
Analytical approximations have generated many insights into the dynamics of epidemics, but there is only one well-known approximation which describes the dynamics of the whole epidemic. In addition, most of the well-known approximations for different aspects of the dynamics are for the classic susceptible-infected-recovered model, in which the infectious period is exponentially distributed. Whilst this assumption is useful, it is somewhat unrealistic. Equally reasonable assumptions are that the infectious period is finite and fixed or that there is a distribution of infectious periods centred round a nonzero mean. We investigate the effect of these different assumptions on the dynamics of the epidemic by deriving approximations to the whole epidemic curve. We show how the well-known sech-squared approximation for the infective population in 'weak' epidemics (where the basic reproduction rate [Formula: see text]) can be extended to the case of an arbitrary distribution of infectious periods having finite second moment, including as examples fixed and gamma-distributed infectious periods. Further, we show how to approximate the time course of a 'strong' epidemic, where [Formula: see text], demonstrating the importance of estimating the infectious period distribution early in an epidemic. PMID:26337289
APPLICATION OF SYMBOLIC PIECEWISE AGGREGATE APPROXIMATION (PAA) ANALYSIS TO ECG SIGNALS
Kumova, Bora
Approximation (PAA), Symbolic Aggregate Approximation (SAX), ECG, Coarse Graining 1. Introduction The studiesAPPLICATION OF SYMBOLIC PIECEWISE AGGREGATE APPROXIMATION (PAA) ANALYSIS TO ECG SIGNALS Burcu, and anomaly detection. This study involves symbolization through Symbolic Aggregate Approximation (SAX
Validity of the Aluminum Equivalent Approximation in Space Radiation Shielding
NASA Technical Reports Server (NTRS)
Badavi, Francis F.; Adams, Daniel O.; Wilson, John W.
2009-01-01
The origin of the aluminum equivalent shield approximation in space radiation analysis can be traced back to its roots in the early years of the NASA space programs (Mercury, Gemini and Apollo) wherein the primary radiobiological concern was the intense sources of ionizing radiation causing short term effects which was thought to jeopardize the safety of the crew and hence the mission. Herein, it is shown that the aluminum equivalent shield approximation, although reasonably well suited for that time period and to the application for which it was developed, is of questionable usefulness to the radiobiological concerns of routine space operations of the 21 st century which will include long stays onboard the International Space Station (ISS) and perhaps the moon. This is especially true for a risk based protection system, as appears imminent for deep space exploration where the long-term effects of Galactic Cosmic Ray (GCR) exposure is of primary concern. The present analysis demonstrates that sufficiently large errors in the interior particle environment of a spacecraft result from the use of the aluminum equivalent approximation, and such approximations should be avoided in future astronaut risk estimates. In this study, the aluminum equivalent approximation is evaluated as a means for estimating the particle environment within a spacecraft structure induced by the GCR radiation field. For comparison, the two extremes of the GCR environment, the 1977 solar minimum and the 2001 solar maximum, are considered. These environments are coupled to the Langley Research Center (LaRC) deterministic ionized particle transport code High charge (Z) and Energy TRaNsport (HZETRN), which propagates the GCR spectra for elements with charges (Z) in the range I <= Z <= 28 (H -- Ni) and secondary neutrons through selected target materials. The coupling of the GCR extremes to HZETRN allows for the examination of the induced environment within the interior' of an idealized spacecraft as approximated by a spherical shell shield, and the effects of the aluminum equivalent approximation for a good polymeric shield material such as genetic polyethylene (PE). The shield thickness is represented by a 25 g/cm spherical shell. Although one could imagine the progression to greater thickness, the current range will be sufficient to evaluate the qualitative usefulness of the aluminum equivalent approximation. Upon establishing the inaccuracies of the aluminum equivalent approximation through numerical simulations of the GCR radiation field attenuation for PE and aluminum equivalent PE spherical shells, we Anther present results for a limited set of commercially available, hydrogen rich, multifunctional polymeric constituents to assess the effect of the aluminum equivalent approximation on their radiation attenuation response as compared to the generic PE.
Berkel, M. van; Zwart, H. J.; Tamura, N.; Ida, K.; Hogeweij, G. M. D.; Inagaki, S.; Baar, M. R. de
2014-11-15
In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (?), convectivity (V), and damping (?) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of ? under the influence of V and ? based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate ? well in cylindrical geometry, the relationships between heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate ?, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which ?, V, and ? can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and ? in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and ? based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.
Structural Reliability Analysis and Optimization: Use of Approximations
NASA Technical Reports Server (NTRS)
Grandhi, Ramana V.; Wang, Liping
1999-01-01
This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.
Comparison of the Radiative Two-Flux and Diffusion Approximations
NASA Technical Reports Server (NTRS)
Spuckler, Charles M.
2006-01-01
Approximate solutions are sometimes used to determine the heat transfer and temperatures in a semitransparent material in which conduction and thermal radiation are acting. A comparison of the Milne-Eddington two-flux approximation and the diffusion approximation for combined conduction and radiation heat transfer in a ceramic material was preformed to determine the accuracy of the diffusion solution. A plane gray semitransparent layer without a substrate and a non-gray semitransparent plane layer on an opaque substrate were considered. For the plane gray layer the material is semitransparent for all wavelengths and the scattering and absorption coefficients do not vary with wavelength. For the non-gray plane layer the material is semitransparent with constant absorption and scattering coefficients up to a specified wavelength. At higher wavelengths the non-gray plane layer is assumed to be opaque. The layers are heated on one side and cooled on the other by diffuse radiation and convection. The scattering and absorption coefficients were varied. The error in the diffusion approximation compared to the Milne-Eddington two flux approximation was obtained as a function of scattering coefficient and absorption coefficient. The percent difference in interface temperatures and heat flux through the layer obtained using the Milne-Eddington two-flux and diffusion approximations are presented as a function of scattering coefficient and absorption coefficient. The largest errors occur for high scattering and low absorption except for the back surface temperature of the plane gray layer where the error is also larger at low scattering and low absorption. It is shown that the accuracy of the diffusion approximation can be improved for some scattering and absorption conditions if a reflectance obtained from a Kubelka-Munk type two flux theory is used instead of a reflection obtained from the Fresnel equation. The Kubelka-Munk reflectance accounts for surface reflection and radiation scattered back by internal scattering sites while the Fresnel reflection only accounts for surface reflections.
?-convergence Approximation of Fracture and Cavitation in Nonlinear Elasticity
NASA Astrophysics Data System (ADS)
Henao, Duvan; Mora-Corral, Carlos; Xu, Xianmin
2015-06-01
Our starting point is a variational model in nonlinear elasticity that allows for cavitation and fracture that was introduced by Henao and Mora-Corral (Arch Rational Mech Anal 197:619-655, 2010). The total energy to minimize is the sum of the elastic energy plus the energy produced by crack and surface formation. It is a free discontinuity problem, since the crack set and the set of new surface are unknowns of the problem. The expression of the functional involves a volume integral and two surface integrals, and this fact makes the problem numerically intractable. In this paper we propose an approximation (in the sense of ?-convergence) by functionals involving only volume integrals, which makes a numerical approximation by finite elements feasible. This approximation has some similarities to the Modica-Mortola approximation of the perimeter and the Ambrosio-Tortorelli approximation of the Mumford-Shah functional, but with the added difficulties typical of nonlinear elasticity, in which the deformation is assumed to be one-to-one and orientation-preserving.
An optimized semiclassical approximation for vibrational response functions
Gerace, Mallory; Loring, Roger F.
2013-01-01
The observables of multidimensional infrared spectroscopy may be calculated from nonlinear vibrational response functions. Fully quantum dynamical calculations of vibrational response functions are generally impractical, while completely classical calculations are qualitatively incorrect at long times. These challenges motivate the development of semiclassical approximations to quantum mechanics, which use classical mechanical information to reconstruct quantum effects. The mean-trajectory (MT) approximation is a semiclassical approach to quantum vibrational response functions employing classical trajectories linked by deterministic transitions representing the effects of the radiation-matter interaction. Previous application of the MT approximation to the third-order response function R(3)(t3, t2, t1) demonstrated that the method quantitatively describes the coherence dynamics of the t3 and t1 evolution times, but is qualitatively incorrect for the waiting-time t2 period. Here we develop an optimized version of the MT approximation by elucidating the connection between this semiclassical approach and the double-sided Feynman diagrams (2FD) that represent the quantum response. Establishing the direct connection between 2FD and semiclassical paths motivates a systematic derivation of an optimized MT approximation (OMT). The OMT uses classical mechanical inputs to accurately reproduce quantum dynamics associated with all three propagation times of the third-order vibrational response function. PMID:23556706
Approximate approaches to the one-dimensional finite potential well
NASA Astrophysics Data System (ADS)
Singh, Shilpi; Pathak, Praveen; Singh, Vijay A.
2011-11-01
The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (mi) is taken to be distinct from mass outside (mo). A relevant parameter is the mass discontinuity ratio ? = mi/mo. To correctly account for the mass discontinuity, we apply the BenDaniel-Duke boundary condition. We obtain approximate solutions for two cases: when the well is shallow and when the well is deep. We compare the approximate results with the exact results and find that higher-order approximations are quite robust. For the shallow case, the approximate solution can be expressed in terms of a dimensionless parameter ?l = 2moV0L2/planck2 (or ? = ?2?l for the deep case). We show that the lowest-order results are related by a duality transform. We also discuss how the energy upscales with L (E~1/L?) and obtain the exponent ?. Exponent ? ? 2 when the well is sufficiently deep and ? ? 1. The ratio of the masses dictates the physics. Our presentation is pedagogical and should be useful to students on a first course on elementary quantum mechanics or low-dimensional semiconductors.
Rational trigonometric approximations using Fourier series partial sums
NASA Technical Reports Server (NTRS)
Geer, James F.
1993-01-01
A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented.
Anisotropic Homogeneous Cosmologies in the Post-Newtonian Approximation
Tamath Rainsford
2000-07-23
In this paper we explore how far the post-Newtonian theory goes in overcoming the difficulties associated with anisotropic homogeneous cosmologies in the Newtonian approximation. It will be shown that, unlike in the Newtonian case, the cosmological equations of the post-Newtonian approximation are much more in the spirit of general relativity with regard to the nine Bianchi types and issues of singularities. The situations of vanishing rotation and vanishing shear are treated separately. The homogeneous Bianchi I model is considered as an example of a rotation-free cosmology with anisotropy. It is found in the Newtonian approximation that there are arbitrary functions that need to be given for all time if the initial value problem is to be well-posed, while in the post-Newtonian case there is no such need. For the general case of a perfect fluid only the post-Newtonian theory can satisfactorily describe the effects of pressure. This is in accordance with findings in an earlier paper where the post-Newtonian approximation was applied to homogeneous cosmologies. For a shear-free anisotropic homogeneous cosmology the Newtonian theory of Heckmann and Sch\\"ucking is explored. Comparisons with its relativistic and post-Newtonian counterparts are made. In the Newtonian theory solutions exist to which there are no analogues in general relativity. The post-Newtonian approximation may provide a way out.
Space-angle approximations in the variational nodal method.
Lewis, E. E.; Palmiotti, G.; Taiwo, T.
1999-03-12
The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared.
Continuous Approximations of a Class of Piecewise Continuous Systems
NASA Astrophysics Data System (ADS)
Danca, Marius-F.
In this paper, we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piecewise continuous functions. By using techniques from the theory of differential inclusions, the underlying piecewise functions can be locally or globally approximated. The approximation results can be used to model piecewise continuous-time dynamical systems of integer or fractional-order. In this way, by overcoming the lack of numerical methods for differential equations of fractional-order with discontinuous right-hand side, unattainable procedures for systems modeled by this kind of equations, such as chaos control, synchronization, anticontrol and many others, can be easily implemented. Several examples are presented and three comparative applications are studied.
Analytical approximations of the diffusive dispersion in fluid flows
NASA Astrophysics Data System (ADS)
Karedla, N.; Gregor, I.; Enderlein, J.
2014-11-01
We present a path-integral approach for finding solutions of the convection-diffusion equation with inhomogeneous fluid flow, which are notoriously difficult to solve. We derive a general approximate analytical solution of the convection-diffusion equation which is in principle applicable to arbitrary flow profiles. As examples, we apply this approximation to the diffusion in a linear shear flow and in a parabolic flow in infinite space, and to the diffusion in a linear shear flow over an impenetrable interface. This last case is particularly important for problems involving diffusive transport towards an interface with advection. We compare the analytical approximation with numerical solutions which are obtained from a conventional finite-element time-difference method.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Global uniform semiclassical approximation for Clebsch-Gordan coefficients
NASA Astrophysics Data System (ADS)
Engel, Hamutal; Kay, Kenneth G.
2008-03-01
Semiclassical integral representations, analogous to initial value expressions for the propagator, are presented for the Clebsch-Gordan angular momentum coupling coefficients. Two forms (L and R types) of the approximation are presented. For each form, new non-Gaussian expressions, which are specifically adapted to the nature of angular momentum variables, are proposed in place of the familiar Gaussian coherent state functions. With these non-Gaussian kernels, it is found that the present treatments are capable of accuracy similar to that obtained from a uniform Airy approximation. Although the present semiclassical approximations involve only real-valued angle variables, associated with sets of angular momenta that are related by ordinary, real, classical transformations, the treatments produce accurate results not only for classically allowed choices of quantum numbers but also for very strongly classically forbidden values.
Global uniform semiclassical approximation for Clebsch-Gordan coefficients.
Engel, Hamutal; Kay, Kenneth G
2008-03-01
Semiclassical integral representations, analogous to initial value expressions for the propagator, are presented for the Clebsch-Gordan angular momentum coupling coefficients. Two forms (L and R types) of the approximation are presented. For each form, new non-Gaussian expressions, which are specifically adapted to the nature of angular momentum variables, are proposed in place of the familiar Gaussian coherent state functions. With these non-Gaussian kernels, it is found that the present treatments are capable of accuracy similar to that obtained from a uniform Airy approximation. Although the present semiclassical approximations involve only real-valued angle variables, associated with sets of angular momenta that are related by ordinary, real, classical transformations, the treatments produce accurate results not only for classically allowed choices of quantum numbers but also for very strongly classically forbidden values. PMID:18331084
Local density approximation for the relativistic nucleon-nucleus potential
Jaminon, M.
1982-10-01
We investigate the relativistic Hartree-Fock single-particle potential in the framework of a local density approximation and of an improved local density approximation. In most cases the latter yields a better agreement between theoretical and experimental results for quantities which are characteristic of the nuclear surface. In the case of /sup 40/Ca, the energy dependence of the ratio of the strengths of the scalar and vector components of the relativistic potential in the center-of-mass system is in good agreement with that determined by the elastic scattering data analyses. In keeping with recent experimental evidence, the calculated central part of the optical-model potential has a wine-bottle bottom shape at intermediate energy. Both approximations provide a strong spin-orbit component.
Non-perturbative QCD amplitudes in quenched and eikonal approximations
Fried, H.M.; Grandou, T.; Sheu, Y.-M.
2014-05-15
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. - Highlights: • We discuss the physical insight of effective locality to QCD fermionic amplitudes. • We show that an unavoidable delta function goes along with the effective locality property. • The generic structure of QCD fermion amplitudes is obtained through Random Matrix calculus.
An approximate method for residual stress calculation infunctionally graded materials
Becker, T.L.
1999-06-02
Thermal residual stresses in functionally graded materials(FGMs) arise primarily from nonlinear spatial variations in the thermalexpansion coefficient, but can be significantly adjusted by variations inmodulus. Thermoelastic analysis of FGMs is complicated by such modulusgradients. A class of problems for which thermal stress solutions formaterials with constant modulus can be used as a basis for approximationsfor FGMs is discussed. The size of the error in this approximation due togradients in elastic modulus is investigated. Analytical and finiteelement solutions for the thermal stresses in various FGM geometries arecompared to results from this approximate method. In a geometry ofpractical interest, a right cylinder graded along the z-axis, the errorfor a Ni-Al2O3 FGM was found to be within 15 percent for all gradientsconsidered. The form of the approximation makes it easier to identifydesirable types of spatial nonlinearity in expansion coefficient andvariations in modulus: this would allow the manipulation of the locationof compressive stresses.
Integral approximants for functions of higher monodromic dimension
Baker, G.A. Jr.
1987-01-01
In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.
On current sheet approximations in models of eruptive flares
NASA Technical Reports Server (NTRS)
Bungey, T. N.; Forbes, T. G.
1994-01-01
We consider an approximation sometimes used for current sheets in flux-rope models of eruptive flares. This approximation is based on a linear expansion of the background field in the vicinity of the current sheet, and it is valid when the length of the current sheet is small compared to the scale length of the coronal magnetic field. However, we find that flux-rope models which use this approximation predict the occurrence of an eruption due to a loss of ideal-MHD equilibrium even when the corresponding exact solution shows that no such eruption occurs. Determination of whether a loss of equilibrium exists can only be obtained by including higher order terms in the expansion of the field or by using the exact solution.
Approximate Noether symmetries from geodetic Lagrangian for plane symmetric spacetimes
NASA Astrophysics Data System (ADS)
Ali, Farhad; Feroze, Tooba
2015-09-01
Noether symmetries from geodetic Lagrangian for time-conformal plane symmetric spacetime are presented. Here, time-conformal factor is used to find the approximate Noether symmetries. This is a generalization of the idea discussed,5-6 where they obtained approximate Noether symmetries from Lagrangian for a particular plane symmetric static spacetime. In the present paper, the most general plane symmetric static spacetime is considered and perturbed it by introducing a general time-conformal factor e?f(t), where ? is very small which causes the perturbation in the spacetime. Taking the perturbation up to the first-order, we find all Lagrangian for plane symmetric spacetimes for which approximate Noether symmetries exist.
Approximate Bisimulation-Based Reduction of Power System Dynamic Models
Stankovic, AM; Dukic, SD; Saric, AT
2015-05-01
In this paper we propose approximate bisimulation relations and functions for reduction of power system dynamic models in differential- algebraic (descriptor) form. The full-size dynamic model is obtained by linearization of the nonlinear transient stability model. We generalize theoretical results on approximate bisimulation relations and bisimulation functions, originally derived for a class of constrained linear systems, to linear systems in descriptor form. An algorithm for transient stability assessment is proposed and used to determine whether the power system is able to maintain the synchronism after a large disturbance. Two benchmark power systems are used to illustrate the proposed algorithm and to evaluate the applicability of approximate bisimulation relations and bisimulation functions for reduction of the power system dynamic models.
Efficient algorithm for approximating one-dimensional ground states
Aharonov, Dorit; Arad, Itai; Irani, Sandy
2010-07-15
The density-matrix renormalization-group method is very effective at finding ground states of one-dimensional (1D) quantum systems in practice, but it is a heuristic method, and there is no known proof for when it works. In this article we describe an efficient classical algorithm which provably finds a good approximation of the ground state of 1D systems under well-defined conditions. More precisely, our algorithm finds a matrix product state of bond dimension D whose energy approximates the minimal energy such states can achieve. The running time is exponential in D, and so the algorithm can be considered tractable even for D, which is logarithmic in the size of the chain. The result also implies trivially that the ground state of any local commuting Hamiltonian in 1D can be approximated efficiently; we improve this to an exact algorithm.
Moment-closure approximations for mass-action models.
Gillespie, C S
2009-01-01
Although stochastic population models have proved to be a powerful tool in the study of process generating mechanisms across a wide range of disciplines, all too often the associated mathematical development involves nonlinear mathematics, which immediately raises difficult and challenging analytic problems that need to be solved if useful progress is to be made. One approximation that is often employed to estimate the moments of a stochastic process is moment closure. This approximation essentially truncates the moment equations of the stochastic process. A general expression for the marginal- and joint-moment equations for a large class of stochastic population models is presented. The generalisation of the moment equations allows this approximation to be applied easily to a wide range of models. Software is available from http://pysbml.googlecode.com/ to implement the techniques presented here. PMID:19154084
Best Slater approximation of a fermionic wave function
Alex D. Gottlieb; Norbert J. Mauser; J. M. Zhang
2015-10-26
We study the best Slater approximation of an $N$-fermion wave function analytically. That is, we seek the Slater determinant (constructed out of $N$ orthonormal single-particle orbitals) wave function having largest overlap with a given $N$-fermion wave function. Some simple lemmas have been established and their usefulness is demonstrated on some structured states, such as the GHZ state. In the simplest nontrivial case of three fermions in six orbitals, which the celebrated Borland-Dennis discovery is about, the best Slater approximation wave function is proven to be built out of the natural orbitals in an interesting way. We also show that the Hadamard inequality is useful for finding the best Slater approximation of some special target wave functions.
Fast Gravitational Field Model Using Adaptive Orthogonal Finite Element Approximation
NASA Astrophysics Data System (ADS)
Younes, A.; Macomber, B.; Woollands, R.; Probe, A.; Bai, X.; Junkins, J.
2013-09-01
Recent research has addressed the issue that high degree and order gravity expansions involve tens of thousands of terms in a theoretically infinite order spherical harmonic expansion (some gravity models extend to degree and order 200 with over 30,000 terms) which in principle must be computed at every integration step to obtain the acceleration consistent with the gravity model. We propose to evaluate these gravity model interpolation models and use them in conjunction with the modified Picard path approximation methods. It was decided to consider analogous orthogonal approximation methods to interpolate, an FEM model, high (degree, order) gravity fields, by replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. Our preliminary results showed that time to compute the state of the art (degree and order 200) spherical harmonic gravity is reduced by 4 to 5 orders of magnitude while maintaining > 9 digits of accuracy. Most of the gain is due to adopting the orthogonal FEM approach, but radial adaptation of the approximation degree gains an additional order of magnitude speedup. The efficient data base storage/access of the local coefficients is studied, which utilizes porting the algorithm to the NVIDIA GPU. This paper will address the accuracy and efficiency in both a C++ serial PC architecture as well as a PC/GPU architecture. The Adaptive Orthogonal Finite Element Gravity Model (AOFEGM) is expected to have broad potential for speeding the trajectory propagation algorithms; for example, 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.
Trigonometric Pade approximants for functions with regularly decreasing Fourier coefficients
Labych, Yuliya A; Starovoitov, Alexander P
2009-08-31
Sufficient conditions describing the regular decrease of the coefficients of a Fourier series f(x)=a{sub 0}/2 + {sigma} a{sub n} cos kx are found which ensure that the trigonometric Pade approximants {pi}{sup t}{sub n,m}(x;f) converge to the function f in the uniform norm at a rate which coincides asymptotically with the highest possible one. The results obtained are applied to problems dealing with finding sharp constants for rational approximations. Bibliography: 31 titles.
A Poisson process approximation for generalized K-5 confidence regions
NASA Technical Reports Server (NTRS)
Arsham, H.; Miller, D. R.
1982-01-01
One-sided confidence regions for continuous cumulative distribution functions are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. To avoid tedious computation of confidence levels and critical values, an approximation based on the Poisson process is introduced. This aproximation provides a conservative confidence region; moreover, the approximation error decreases monotonically to 0 as sample size increases. Critical values necessary for implementation are given. Applications are made to the areas of risk analysis, investment modeling, reliability assessment, and analysis of fault tolerant systems.
On the approximation of crack shapes found during inservice inspection
Bhate, S.R.; Chawla, D.S.; Kushwaha, H.S.
1997-04-01
This paper addresses the characterization of axial internal flaw found during inservice inspection of a pipe. J-integral distribution for various flaw shapes is obtained using line spring finite, element method. The peak J-value and its distribution across the crack is found to be characteristic feature of each shape. The triangular shape yields peak J-value away from the center, the point of depth. The elliptic approximation results in large overestimate of J-value for unsymmetric flaws. Triangular approximation is recommended for such flaws so that further service can be obtained from the component.
Exponentially accurate approximations to piece-wise smooth periodic functions
NASA Technical Reports Server (NTRS)
Greer, James; Banerjee, Saheb
1995-01-01
A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.
Are there approximate relations among transverse momentum dependent distribution functions?
Harutyun AVAKIAN; Anatoli Efremov; Klaus Goeke; Andreas Metz; Peter Schweitzer; Tobias Teckentrup
2007-10-11
Certain {\\sl exact} relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into {\\sl approximate} ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the practical usefulness of one such ``Wandzura-Wilczek-type approximation'', namely of that connecting $h_{1L}^{\\perp(1)a}(x)$ to $h_L^a(x)$, and discuss how it can be further tested by future CLAS and COMPASS data.
Approximation of a general singular vertex coupling in quantum graphs
Cheon, Taksu Exner, Pavel Turek, Ondrej
2010-03-15
The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a {delta} potential and a vector potential coupled to the 'loose' edges by a {delta} coupling. It is shown that if the lengths of the connecting edges shrink to zero and the potentials are properly scaled, the limit can yield any prescribed singular vertex coupling, and moreover, that such an approximation converges in the norm-resolvent sense.
Integrable approximation of regular regions with a nonlinear resonance chain
NASA Astrophysics Data System (ADS)
Kullig, Julius; Löbner, Clemens; Mertig, Normann; Bäcker, Arnd; Ketzmerick, Roland
2014-11-01
Generic Hamiltonian systems have a mixed phase space where regions of regular and chaotic motion coexist. We present a method for constructing an integrable approximation to such regular phase-space regions including a nonlinear resonance chain. This approach generalizes the recently introduced iterative canonical transformation method. In the first step of the method a normal-form Hamiltonian with a resonance chain is adapted such that actions and frequencies match with those of the nonintegrable system. In the second step a sequence of canonical transformations is applied to the integrable approximation to match the shape of regular tori. We demonstrate the method for the generic standard map at various parameters.
Some special series in ultraspherical polynomials and their approximation properties
NASA Astrophysics Data System (ADS)
Sharapudinov, I. I.
2014-10-01
Using the explicit form of a limiting ultraspherical series \\sumk=0^? f_k-1\\widehat P_k-1(x), which was established by us in [1], we consider new, more general, special series in ultraspherical Jacobi polynomials and their approximation properties. We show that as an approximation tool, these series compare favourably with Fourier series in Jacobi polynomials. At the same time, they admit a simple construction, which in important particular cases enables one to use the fast Fourier transform for the numerical realization of their partial sums.
An approximate method for calculating aircraft downwash on parachute trajectories
Strickland, J.H.
1989-01-01
An approximate method for calculating velocities induced by aircraft on parachute trajectories is presented herein. A simple system of quadrilateral vortex panels is used to model the aircraft wing and its wake. The purpose of this work is to provide a simple analytical tool which can be used to approximate the effect of aircraft-induced velocities on parachute performance. Performance issues such as turnover and wake recontact may be strongly influenced by velocities induced by the wake of the delivering aircraft, especially if the aircraft is maneuvering at the time of parachute deployment. 7 refs., 9 figs.
Dynamical nonlocal coherent-potential approximation for itinerant electron magnetism.
Rowlands, D A; Zhang, Yu-Zhong
2014-11-26
A dynamical generalisation of the nonlocal coherent-potential approximation is derived based upon the functional integral approach to the interacting electron problem. The free energy is proven to be variational with respect to the self-energy provided a self-consistency condition on a cluster of sites is satisfied. In the present work, calculations are performed within the static approximation and the effect of the nonlocal physics on the formation of the local moment state in a simple model is investigated. The results reveal the importance of the dynamical correlations. PMID:25351678
Exterior view looking down through the approximate centerline of the ...
Exterior view looking down through the approximate centerline of the upper hatch and docking ring on the external airlock on the Orbiter Discovery. This photograph was take in the Orbiter Processing Facility at the Kennedy Space Center. - Space Transportation System, Orbiter Discovery (OV-103), Lyndon B. Johnson Space Center, 2101 NASA Parkway, Houston, Harris County, TX
Dentate Gyrus Circuitry Features Improve Performance of Sparse Approximation Algorithms
Petrantonakis, Panagiotis C.; Poirazi, Panayiota
2015-01-01
Memory-related activity in the Dentate Gyrus (DG) is characterized by sparsity. Memory representations are seen as activated neuronal populations of granule cells, the main encoding cells in DG, which are estimated to engage 2–4% of the total population. This sparsity is assumed to enhance the ability of DG to perform pattern separation, one of the most valuable contributions of DG during memory formation. In this work, we investigate how features of the DG such as its excitatory and inhibitory connectivity diagram can be used to develop theoretical algorithms performing Sparse Approximation, a widely used strategy in the Signal Processing field. Sparse approximation stands for the algorithmic identification of few components from a dictionary that approximate a certain signal. The ability of DG to achieve pattern separation by sparsifing its representations is exploited here to improve the performance of the state of the art sparse approximation algorithm “Iterative Soft Thresholding” (IST) by adding new algorithmic features inspired by the DG circuitry. Lateral inhibition of granule cells, either direct or indirect, via mossy cells, is shown to enhance the performance of the IST. Apart from revealing the potential of DG-inspired theoretical algorithms, this work presents new insights regarding the function of particular cell types in the pattern separation task of the DG. PMID:25635776
2. Photocopy of approximately 12' x 17' lithograph by Charlie ...
2. Photocopy of approximately 12' x 17' lithograph by Charlie C. Taylor from circa 1860 (Original in the Chester County Historical Society, West Chester, Pennsylvania) Photocopy taken by Ned Goode, July 1958 WEST AND SOUTH SIDE - Baptist Church of West Chester, 221 South High Street, West Chester, Chester County, PA
BLOCK DIAGONALLY DOMINANT POSITIVE DEFINITE APPROXIMATE FILTERS AND SMOOTHERS
BLOCK DIAGONALLY DOMINANT POSITIVE DEFINITE APPROXIMATE FILTERS AND SMOOTHERS Running title: BLOCK the transition matrix and the incremental information are nearly block diagonal. Kurt S. Riedel Courant Institute are nearly block diagonal. When H T R -1H is also nearly block diagonal, where R is the observation noise co
BLOCK DIAGONALLY DOMINANT POSITIVE DEFINITE APPROXIMATE FILTERS AND SMOOTHERS
BLOCK DIAGONALLY DOMINANT POSITIVE DEFINITE APPROXIMATE FILTERS AND SMOOTHERS Running title: BLOCK the transition matrix and the incremental information are nearly block diagonal. Kurt S. Riedel Courant Institute are nearly block diagonal. When H T R 1 H is also nearly block diagonal, where R is the observation noise co
New approximating results for data with errors in both variables
NASA Astrophysics Data System (ADS)
Bogdanova, N.; Todorov, S.
2015-05-01
We introduce new data from mineral water probe Lenovo Bulgaria, measured with errors in both variables. We apply our Orthonormal Polynomial Expansion Method (OPEM), based on Forsythe recurrence formula to describe the data in the new error corridor. The development of OPEM gives the approximating curves and their derivatives in optimal orthonormal and usual expansions including the errors in both variables with special criteria.
10. INTERIOR, NORTHEAST STORAGE AREA, FROM APPROXIMATELY 15 FEET SOUTHWEST ...
10. INTERIOR, NORTHEAST STORAGE AREA, FROM APPROXIMATELY 15 FEET SOUTHWEST OF NORTHEAST CORNER, LOOKING WEST-SOUTHWEST, WITH CONNECTING DOORWAYS IN FAR WALL. - Oakland Naval Supply Center, Pier Transit Shed, South of D Street between First & Second Streets, Oakland, Alameda County, CA
4. WEST PORTION OF SOUTH SIDE, OBLIQUE VIEW, FROM APPROXIMATELY ...
4. WEST PORTION OF SOUTH SIDE, OBLIQUE VIEW, FROM APPROXIMATELY 30 FEET WEST OF SOUTHWEST CORNER, LOOKING EAST, WITH WEST SIDE OF BUILDING 123 AT RIGHT BEYOND LIGHTING POLE. - Oakland Naval Supply Center, Pier Transit Shed, South of D Street between First & Second Streets, Oakland, Alameda County, CA
Approximating Radon measures on first--countable compact spaces
Plebanek, Grzegorz
Approximating Radon measures on first--countable compact spaces Grzegorz Plebanek (Wroc/law) Abstract The assertion every Radon measure defined on a first--countable compact space is uniformly regular under CH. In this note we consider some properties of finite Radon measures defined on compact spaces
Fast Incremental Maintenance of Approximate PHILLIP B. GIBBONS
Matias, Yossi
Fast Incremental Maintenance of Approximate Histograms PHILLIP B. GIBBONS Intel Research Pittsburgh' addresses: P. B. Gibbons, Intel Research Pittsburgh, 417 South Craig Street, Suite 300, Pittsburgh, PA 15213, e-mail: phillip.b.gibbons@intel.com; Y. Matias, Department of Computer Science, Tel Aviv Univer
A Fully Polynomial Time Approximation Scheme in Scheduling Deteriorating Jobs
Krovi, Venkat
A Fully Polynomial Time Approximation Scheme in Scheduling Deteriorating Jobs JinYi Cai \\Lambda Pu Cai y Yixin Zhu z Abstract We consider a scheduling problem with a single machine and a set of jobs which have to be processed sequentially. While waiting for processing, jobs may deteriorate, causing
Approximate Dynamic Programming for Communication-Constrained Sensor Network
Willsky, Alan S.
1 Approximate Dynamic Programming for Communication-Constrained Sensor Network Management Jason L (PDF), and transmitting the updated conditional PDF. Communications is commonly the highest contributor dynamic programming approach which integrates the value of information and the cost of transmitting data
Recycling Authorizations: Toward Secondary and Approximate Authorizations Model
1 Recycling Authorizations: Toward Secondary and Approximate Authorizations Model (SAAM) Konstantin. This paper establishes the concept of recycling previously made authorizations for serving new authorization by conventional authorization systems. #12;2 This paper introduces the concept of recycling previously made
Lorentz-invariant membranes and finite matrix approximations
Jens Hoppe; Maciej Trzetrzelewski
2011-01-23
The question of Lorentz invariance for finite N approximations of relativistic membranes is addressed. We find that one of the classical manifestations of Lorentz-invariance is not possible for NxN matrices (at least when N=2 or 3). How the symmetry is restored in the large N limit is studied numerically.
Diffusion Approximations for Ecological Models P.K. Pollett
Pollett, Phil
Diffusion Approximations for Ecological Models P.K. Pollett Department of Mathematics, The University of Queensland, Queensland 4072 Australia (pkp@maths.uq.edu.au) Abstract: Diffusion models to inaccurate predictions of critical quantities such as persistence times. This paper examines diffusion models
1. Photocopy of photograph, showing a view approximately northnorthwest of ...
1. Photocopy of photograph, showing a view approximately north-northwest of the sixteen original kilns. Photographer and date unknown, but believed to be ca. 1895. Courtesy of Felicia Nichols, Pocatello, Id. - Warren King Charcoal Kilns, 5 miles west of Idaho Highway 28, Targhee National Forest, Leadore, Lemhi County, ID
Hierarchical BOA, Cluster Exact Approximation, and Ising Spin Glasses
Peinke, Joachim
Hierarchical BOA, Cluster Exact Approximation, and Ising Spin Glasses Martin Pelikan 1 , Alexander the hierarchical Bayesian optimization algorithm (hBOA) on the problem of finding ground states of Ising spin glasses with ±J couplings in two and three dimensions. The perfor mance of hBOA is compared
Stochastic Approximation Methods for Latent Regression Item Response Models
ERIC Educational Resources Information Center
von Davier, Matthias; Sinharay, Sandip
2010-01-01
This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariates…
Approximate Dynamic Programming in Transportation and Logistics: A Unified Framework
Powell, Warren B.
Approximate Dynamic Programming in Transportation and Logistics: A Unified Framework Warren B Engineering Princeton University, Princeton, NJ 08544 European J. of Transportation and Logistics, Vol. 1, No optimization has enjoyed a rich place in transportation and logistics, where it repre- sents a mature field
On the Oberbeck-Boussinesq approximation on unbounded domains
Schonbek, Maria
Abstract We study the Oberbeck-Boussinesq approximation describing the mo- tion of an incompressible, heat-conducting deviation = (t,x). The symbol denotes the pressure, µ > 0 is the viscosity coefficient, > 0 the heat conductivity coefficient, > 0 stands for the fluid density, and > 0 is the reference temperature. Here, cp
Reconstruction of Outdoor Sculptures from Silhouettes under Approximate Circular Motion
Martin, Ralph R.
Reconstruction of Outdoor Sculptures from Silhouettes under Approximate Circular Motion, as opposed to previous works, the technique here does not require the camera motion to be perfectly circular (e.g., turntable sequence). It employs an image rectification step before the circular motion
Approximate Scaling Properties of RNA Free Energy Landscapes
Stadler, Peter F.
Approximate Scaling Properties of RNA Free Energy Landscapes By Subbiah Baskaran a;b;c , Peter F al: Scaling in RNA Landscapes Abstract RNA free energy landscapes are analyzed by means of ``time and the exponents characterizing selfÂaffinity. Key Words RNA Folding --- Excursion Sets --- Fractal Landscape
APPROXIMATE INVERSEDYNAMICS BASED ROBUST CONTROL USING STATIC AND DYNAMIC FEEDBACK
Szepesvari, Csaba
APPROXIMATE INVERSEDYNAMICS BASED ROBUST CONTROL USING STATIC AND DYNAMIC FEEDBACK CSABA SZEPESV the horizon of the optimal control problem. The process is then repeated indefinitely. Stability that the inversedynamic model is used in a mixed mode fashion, in that of a `Static and Dynamic' State
SMOOTH APPROXIMATIONS PETR H AJEK AND MICHAL JOHANIS
Johanis, Michal
SMOOTH APPROXIMATIONS PETR H ´AJEK AND MICHAL JOHANIS ABSTRACT. We prove, among other things) by smooth Lipschitz (resp. uniformly continuous) mapping, if X is a separable Banach space admitting a smooth Lipschitz bump and either X or Y is a separable C.K/ space (resp. super-reflexive space). Further
Approximate Bayesian Smoothing with Unknown Process and Measurement Noise Covariances
NASA Astrophysics Data System (ADS)
Ardeshiri, Tohid; Ozkan, Emre; Orguner, Umut; Gustafsson, Fredrik
2015-12-01
We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is computationally efficient, easy to implement, and can be applied to high dimensional linear systems. The performance of the algorithm is illustrated on a target tracking example.
43 CFR 2201.5 - Exchanges at approximately equal value.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 43 Public Lands: Interior 2 2013-10-01 2013-10-01 false Exchanges at approximately equal value. 2201.5 Section 2201.5 Public Lands: Interior Regulations Relating to Public Lands (Continued) BUREAU OF LAND MANAGEMENT, DEPARTMENT OF THE INTERIOR LAND RESOURCE MANAGEMENT (2000) EXCHANGES: GENERAL PROCEDURES Exchanges-Specific Requirements §...
Approximate bisimulation for a class of stochastic hybrid systems
Pappas, George J.
linear stochastic systems are widely applied, for example, in manufacturing systems, aircraft control- tems Engineering, University of Pennsylvania, Philadelphia, PA 19104 {agung,agirard,pappasg}@seas.upenn.edu discuss the idea of exact and approximate bisimulation for labelled Markov processes. Following a series