User Guide for the Discrete Dipole Approximation Code DDSCAT 7.1
Draine, B T
2010-01-01
DDSCAT 7.1 is an open-source Fortran-90 software package applying the discrete dipole approximation to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and complex refractive index. The targets may be isolated entities (e.g., dust particles), but may also be 1-d or 2-d periodic arrays of "target unit cells", allowing calculation of absorption, scattering, and electric fields around arrays of nanostructures. The theory of the DDA and its implementation in DDSCAT is presented in Draine (1988) and Draine & Flatau (1994), and its extension to periodic structures (and near-field calculations) in Draine & Flatau (2008). DDSCAT 7.1 includes support for MPI, OpenMP, and the Intel Math Kernel Library (MKL). DDSCAT supports calculations for a variety of target geometries. Target materials may be both inhomogeneous and anisotropic. It is straightforward for the user to "import" arbitrary target geometries into the code. DDSCAT automatically calculates total cross ...
User Guide for the Discrete Dipole Approximation Code DDSCAT (Version 5a10)
Draine, B T; Flatau, Piotr J.
2000-01-01
DDSCAT.5a is a freely available software package which applies the "discrete dipole approximation" (DDA) to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and complex refractive index. The DDA approximates the target by an array of polarizable points. DDSCAT.5a requires that these polarizable points be located on a cubic lattice. DDSCAT.5a10 allows accurate calculations of electromagnetic scattering from targets with "size parameters" 2 pi a/lambda < 15 provided the refractive index m is not large compared to unity (|m-1| < 1). The DDSCAT package is written in Fortran and is highly portable. The program supports calculations for a variety of target geometries (e.g., ellipsoids, regular tetrahedra, rectangular solids, finite cylinders, hexagonal prisms, etc.). Target materials may be both inhomogeneous and anisotropic. It is straightforward for the user to import arbitrary target geometries into the code, and relatively straightforward to add new target ...
User Guide for the Discrete Dipole Approximation Code DDSCAT 7.3
Draine, B T
2013-01-01
DDSCAT 7.3 is an open-source Fortran-90 software package applying the discrete dipole approximation to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and complex refractive index. The targets may be isolated entities (e.g., dust particles), but may also be 1-d or 2-d periodic arrays of "target unit cells", allowing calculation of absorption, scattering, and electric fields around arrays of nanostructures. The theory of the DDA and its implementation in DDSCAT is presented in Draine (1988) and Draine & Flatau (1994), and its extension to periodic structures in Draine & Flatau (2008), and efficient near-field calculations in Flatau & Draine (2012). DDSCAT 7.3 includes support for MPI, OpenMP, and the Intel Math Kernel Library (MKL). DDSCAT supports calculations for a variety of target geometries. Target materials may be both inhomogeneous and anisotropic. It is straightforward for the user to "import" arbitrary target geometries into the code. DDSCA...
User Guide for the Discrete Dipole Approximation Code DDSCAT.6.0
Draine, B T
2003-01-01
DDSCAT.6.0 is a freely available software package (http://www.astro.princeton.edu/~draine/DDSCAT.6.0.html) which applies the "discrete dipole approximation" (DDA) to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and complex refractive index. DDSCAT.6.0 allows accurate calculations of electromagnetic scattering from targets with ``size parameters'' 2*pi*a/lambda < 15 provided the refractive index m is not large compared to unity (|m-1| < 1). DDSCAT.6.0 includes the option of using the FFTW (Fastest Fourier Transform in the West) package. DDSCAT.6.0 also includes MPI support, permitting parallel calculations on multiprocessor systems. DDSCAT package is written in Fortran and is highly portable. The program supports calculations for a variety of target geometries (e.g., ellipsoids, regular tetrahedra, rectangular solids, finite cylinders, hexagonal prisms, etc.). Target materials may be both inhomogeneous and anisotropic. It is straightforward for the use...
User Guide for the Discrete Dipole Approximation Code DDSCAT 6.1
Draine, B T; Draine, Bruce T.; Flatau, Piotr J.
2004-01-01
DDSCAT 6.1 is a software package which applies the discrete dipole approximation (DDA) to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and complex refractive index. DDSCAT 6.1 allows accurate calculations of electromagnetic scattering from targets with size parameters 2 pi a_eff/lambda < 15 provided the refractive index m is not large compared to unity (|m-1| < 2). DDSCAT 6.1 includes support for MPI and FFTW. We also make available a "plain" distribution of DDSCAT 6.1 that does not include support for MPI, FFTW, or netCDF, but is much simpler to install than the full distribution. The DDSCAT package is written in Fortran and is highly portable. The program supports calculations for a variety of target geometries (e.g., ellipsoids, regular tetrahedra, rectangular solids, finite cylinders, hexagonal prisms, etc.). Target materials may be both inhomogeneous and anisotropic. It is straightforward for the user to import arbitrary target geometries into th...
User Guide for the Discrete Dipole Approximation Code DDSCAT 7.2
Draine, Bruce T
2012-01-01
DDSCAT 7.2 is a freely available open-source Fortran-90 software package applying the discrete dipole approximation (DDA) to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and complex refractive index. The targets may be isolated entities (e.g., dust particles), but may also be 1-d or 2-d periodic arrays of "target unit cells", which can be used to study absorption, scattering, and electric fields around arrays of nanostructures. The DDA approximates the target by an array of polarizable points. The theory of the DDA and its implementation in DDSCAT is presented in Draine (1988) and Draine & Flatau (1994), and its extension to periodic structures in Draine & Flatau (2008). Efficient near-field calculations are enabled following Flatau & Draine (2012). DDSCAT 7.2 allows accurate calculations of electromagnetic scattering from targets with size parameters 2*pi*aeff/lambda < 25 provided the refractive index m is not large compared to unity (|m-1| ...
DDscat.C++ User and programmer guide
Choliy, Vasyl
2014-01-01
DDscat.C++ 7.3.0 is a freely available open-source C++ software package applying the "discrete dipole approximation" (DDA) to calculate scattering and absorption of electromagnetic waves by targets with arbitrary geometries and a complex refractive index. DDscat.C++ is a clone of well known DDscat Fortran-90 software. We refer to DDscat as to the parent code in this document. Versions 7.3.0 of both codes have the identical functionality but the quite different implementation. Started as a teaching project, the DDscat.C++ code differs from the parent code DDscat in programming techniques and features, essential for C++ but quite seldom in Fortran. As DDscat.C++ in its current version is just a clone, usage of DDscat.C++ for electromagnetic calculations is the same as of DDscat. Please, refer to "User Guide for the Discrete Dipole Approximation Code DDSCAT 7.3" to start using the code(s). This document consists of two parts. In the first part we present Quick start guide for users who want to begin to use the c...
Improving Estimated Optical Constants With MSTM and DDSCAT Modeling
Pitman, K. M.; Wolff, M. J.
2015-12-01
We present numerical experiments to determine quantitatively the effects of mineral particle clustering on Mars spacecraft spectral signatures and to improve upon the values of refractive indices (optical constants n, k) derived from Mars dust laboratory analog spectra such as those from RELAB and MRO CRISM libraries. Whereas spectral properties for Mars analog minerals and actual Mars soil are dominated by aggregates of particles smaller than the size of martian atmospheric dust, the analytic radiative transfer (RT) solutions used to interpret planetary surfaces assume that individual, well-separated particles dominate the spectral signature. Both in RT models and in the refractive index derivation methods that include analytic RT approximations, spheres are also over-used to represent nonspherical particles. Part of the motivation is that the integrated effect over randomly oriented particles on quantities such as single scattering albedo and phase function are relatively less than for single particles. However, we have seen in previous numerical experiments that when varying the shape and size of individual grains within a cluster, the phase function changes in both magnitude and slope, thus the "relatively less" effect is more significant than one might think. Here we examine the wavelength dependence of the forward scattering parameter with multisphere T-matrix (MSTM) and discrete dipole approximation (DDSCAT) codes that compute light scattering by layers of particles on planetary surfaces to see how albedo is affected and integrate our model results into refractive index calculations to remove uncertainties in approximations and parameters that can lower the accuracy of optical constants. By correcting the single scattering albedo and phase function terms in the refractive index determinations, our data will help to improve the understanding of Mars in identifying, mapping the distributions, and quantifying abundances for these minerals and will address long
Low rank approximations for the DEPOSIT computer code
Litsarev, Mikhail; Oseledets, Ivan
2014-01-01
We present an efficient technique based on low-rank separated approximations for the computation of three-dimensional integrals in the computer code DEPOSIT that describes ion-atomic collision processes. Implementation of this technique decreases the total computational time by a factor of 1000. The general concept can be applied to more complicated models.
Jégou, Hervé; Douze, Matthijs; Schmid, Cordelia
2009-01-01
We propose an approximate nearest neighbor search method based on quantization. It uses, in particular, product quantizer to produce short codes and corresponding distance estimators approximating the Euclidean distance between the orginal vectors. The method is advantageously used in an asymmetric manner, by computing the distance between a vector and code, unlike competing techniques such as spectral hashing that only compare codes. Our approach approximates the Euclidean distance based on ...
Konoshonkin, Alexander V.; Kustova, Natalia V.; Borovoi, Anatoli G.
2015-10-01
The open-source beam-splitting code is described which implements the geometric-optics approximation to light scattering by convex faceted particles. This code is written in C++ as a library which can be easy applied to a particular light scattering problem. The code uses only standard components, that makes it to be a cross-platform solution and provides its compatibility to popular Integrated Development Environments (IDE's). The included example of solving the light scattering by a randomly oriented ice crystal is written using Qt 5.1, consequently it is a cross-platform solution, too. Both physical and computational aspects of the beam-splitting algorithm are discussed. Computational speed of the beam-splitting code is obviously higher compared to the conventional ray-tracing codes. A comparison of the phase matrix as computed by our code with the ray-tracing code by A. Macke shows excellent agreement.
International Nuclear Information System (INIS)
The open-source beam-splitting code is described which implements the geometric-optics approximation to light scattering by convex faceted particles. This code is written in C++ as a library which can be easy applied to a particular light scattering problem. The code uses only standard components, that makes it to be a cross-platform solution and provides its compatibility to popular Integrated Development Environments (IDE's). The included example of solving the light scattering by a randomly oriented ice crystal is written using Qt 5.1, consequently it is a cross-platform solution, too. Both physical and computational aspects of the beam-splitting algorithm are discussed. Computational speed of the beam-splitting code is obviously higher compared to the conventional ray-tracing codes. A comparison of the phase matrix as computed by our code with the ray-tracing code by A. Macke shows excellent agreement. - Highlights: • The beam-splitting code is presented as open-source software. • Both physical and computational aspects of the code are discussed. • Computational speed of the code is higher than ray-tracing codes. • A comparison with the ray-tracing Macke's code shows excellent agreement
Distributed Successive Approximation Coding using Broadcast Advantage: The Two-Encoder Case
Chen, Zichong; Vetterli, Martin
2010-01-01
Traditional distributed source coding rarely considers the possible link between separate encoders. However, the broadcast nature of wireless communication in sensor networks provides a free gossip mechanism which can be used to simplify encoding/decoding and reduce transmission power. Using this broadcast advantage, we present a new two-encoder scheme which imitates the ping-pong game and has a successive approximation structure. For the quadratic Gaussian case, we prove that this scheme is successively refinable on the {sum-rate, distortion pair} surface, which is characterized by the rate-distortion region of the distributed two-encoder source coding. A potential energy saving over conventional distributed coding is also illustrated. This ping-pong distributed coding idea can be extended to the multiple encoder case and provides the theoretical foundation for a new class of distributed image coding method in wireless scenarios.
DESIGN OF LDPC-CODED BICM USING A SEMI-GAUSSIAN APPROXIMATION
Institute of Scientific and Technical Information of China (English)
Huang Jie; Zhang Fan; Zhu Jinkang
2007-01-01
This paper investigates analysis and design of Low-Density Parity-Check (LDPC) coded BitInterleaved Coded Modulation (BICM) over Additive White Gaussian Noise (AWGN) channel. It focuses on Gray-labeled 8-ary Phase-Shift-Keying (8PSK) modulation and employs a Maximum A Posteriori (MAP) symbol-to-bit metric calculator at the receiver. An equivalent model of a BICM communication channel with ideal interleaving is presented. The probability distribution function of log-likelihood ratio messages from the MAP receiver can be approximated by a mixture of symmetric Gaussian densities. As a result semi-Gaussian approximation can be used to analyze the decoder.Extrinsic information transfer charts are employed to describe the convergence behavior of LDPC decoder. The design of irregular LDPC codes reduces to a linear programming problem on two-dimensional variable edge-degree distribution. This method allows irregular code design in a wider range of rates without any limit on the maximum node degree and can be used to design irregular codes having rates varying from 0.5275 to 0.9099. The designed convergence thresholds are only a few tenths,even a few hundredths of a decibel from the capacity limits. It is shown by Monte Carlo simulations that,when the block length is 30,000, these codes operate about 0.62-0.75 dB from the capacity limit at a bit error rate of 10-8.
BILAM: a composite laminate failure-analysis code using bilinear stress-strain approximations
Energy Technology Data Exchange (ETDEWEB)
McLaughlin, P.V. Jr.; Dasgupta, A.; Chun, Y.W.
1980-10-01
The BILAM code which uses constant strain laminate analysis to generate in-plane load/deformation or stress/strain history of composite laminates to the point of laminate failure is described. The program uses bilinear stress-strain curves to model layer stress-strain behavior. Composite laminates are used for flywheels. The use of this computer code will help to develop data on the behavior of fiber composite materials which can be used by flywheel designers. In this program the stress-strain curves are modelled by assuming linear response in axial tension while using bilinear approximations (2 linear segments) for stress-strain response to axial compressive, transverse tensile, transverse compressive and axial shear loadings. It should be noted that the program attempts to empirically simulate the effects of the phenomena which cause nonlinear stress-strain behavior, instead of mathematically modelling the micromechanics involved. This code, therefore, performs a bilinear laminate analysis, and, in conjunction with several user-defined failure interaction criteria, is designed to provide sequential information on all layer failures up to and including the first fiber failure. The modus operandi is described. Code BILAM can be used to: predict the load-deformation/stress-strain behavior of a composite laminate subjected to a given combination of in-plane loads, and make analytical predictions of laminate strength.
International Nuclear Information System (INIS)
The neutron noise, induced by a rod manoeuvring experiment in a pressurized water reactor, has been calculated by the incore fuel management code SIMULATE. The space- and frequency-dependent noise in the thermal group was calculated through the adiabatic approximation in three dimensions and two-group theory, with the spatial resolution of the nodal model underlying the SIMULATE algorithm. The calculated spatial noise profiles were interpreted on physical terms. They were also compared with model calculations in a 2-D one-group model, where various approximations as well as the full space-dependent response could be calculated. The adiabatic results obtained with SIMULATE can be regarded as reliable for sub-plateau frequencies (below 0.1 Hz). (orig.)
The discrete-dipole-approximation code ADDA: Capabilities and known limitations
International Nuclear Information System (INIS)
The open-source code ADDA is described, which implements the discrete dipole approximation (DDA), a method to simulate light scattering by finite 3D objects of arbitrary shape and composition. Besides standard sequential execution, ADDA can run on a multiprocessor distributed-memory system, parallelizing a single DDA calculation. Hence the size parameter of the scatterer is in principle limited only by total available memory and computational speed. ADDA is written in C99 and is highly portable. It provides full control over the scattering geometry (particle morphology and orientation, and incident beam) and allows one to calculate a wide variety of integral and angle-resolved scattering quantities (cross sections, the Mueller matrix, etc.). Moreover, ADDA incorporates a range of state-of-the-art DDA improvements, aimed at increasing the accuracy and computational speed of the method. We discuss both physical and computational aspects of the DDA simulations and provide a practical introduction into performing such simulations with the ADDA code. We also present several simulation results, in particular, for a sphere with size parameter 320 (100-wavelength diameter) and refractive index 1.05.
Schmit, L. A.; Miura, H.
1975-01-01
The creation of an efficient automated capability for minimum weight design of structures is reported. The ACCESS 1 computer program combines finite element analysis techniques and mathematical programming algorithms using an innovative collection of approximation concepts. Design variable linking, constraint deletion techniques and approximate analysis methods are used to generate a sequence of small explicit mathematical programming problems which retain the essential features of the design problem. Organization of the finite element analysis is carefully matched to the design optimization task. The efficiency of the ACCESS 1 program is demonstrated by giving results for several example problems.
Upgraded Approximation of Non-Binary Alphabets for Polar Code Construction
Ghayoori, Arash; Gulliver, T. Aaron
2013-01-01
An algorithm is presented for approximating a single-user channel with a prime input alphabet size. The result is an upgraded version of the channel with a reduced output alphabet size. It is shown that this algorithm can be used to reduce the output alphabet size to the input alphabet size in most cases.
ACCESS-2: Approximation Concepts Code for Efficient Structural Synthesis, user's guide
Miura, H.; Schmit, L. A., Jr.
1978-01-01
A user's guide is presented for the ACCESS-2 computer program. ACCESS-2 is a research oriented program which implements a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and general mathematical programming algorithms are applied in the design optimization procedure.
ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide
Fleury, C.; Schmit, L. A., Jr.
1980-01-01
A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.
Miura, H.; Schmit, L. A., Jr.
1976-01-01
The program documentation and user's guide for the ACCESS-1 computer program is presented. ACCESS-1 is a research oriented program which implements a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and general mathematical programming algorithms are applied in the design optimization procedure. Implementation of the computer program, preparation of input data and basic program structure are described, and three illustrative examples are given.
A computer code for beam optics calculation--third order approximation
Institute of Scientific and Technical Information of China (English)
L(U) Jianqin; LI Jinhai
2006-01-01
To calculate the beam transport in the ion optical systems accurately, a beam dynamics computer program of third order approximation is developed. Many conventional optical elements are incorporated in the program. Particle distributions of uniform type or Gaussian type in the ( x, y, z ) 3D ellipses can be selected by the users. The optimization procedures are provided to make the calculations reasonable and fast. The calculated results can be graphically displayed on the computer monitor.
Energy Technology Data Exchange (ETDEWEB)
Sagaidak, R.N., E-mail: sagaidak@nrmail.jinr.ru [Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region (Russian Federation); Utyonkov, V.K., E-mail: utyonkov@sungns.jinr.ru [Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region (Russian Federation); Scarlassara, F., E-mail: scarlassara@pd.infn.it [INFN Sezione di Padova and Universitá di Padova, Dipartimento di Fisica “Galileo Galilei”, 35131 Padova (Italy)
2013-02-01
A Monte Carlo approach has been developed for simulations of the angular and energy distributions for heavy evaporation residues (ER) produced in heavy ion fusion-evaporation reactions. The approach uses statistical model approximations of the HIVAP code for the calculations of initial angular and energy distributions inside a target, which are determined by neutron evaporation from an excited compound nucleus. Further step in the simulation of transmission of ER heavy atoms through a target layer is performed with the TRIM code that gives final angle and energy distributions at the exit from the target. Both the simulations (neutron evaporation and transmission through solid media) have been separately considered and good agreement has been obtained between the results of simulations and available experimental data. Some applications of the approach have been also considered.
Directory of Open Access Journals (Sweden)
B. Scarnato
2012-10-01
Full Text Available According to recent studies, internal mixing of black carbon (BC with other aerosol materials in the atmosphere alters its aggregate shape, absorption of solar radiation, and radiative forcing. These mixing state effects are not yet fully understood. In this study, we characterize the morphology and mixing state of bare BC and BC internally mixed with sodium chloride (NaCl using electron microscopy and examine the sensitivity of optical properties to BC mixing state and aggregate morphology using a discrete dipole approximation model (DDSCAT. DDSCAT predicts a higher mass absorption coefficient, lower single scattering albedo (SSA, and higher absorption Angstrom exponent (AAE for bare BC aggregates that are lacy rather than compact. Predicted values of SSA at 550 nm range between 0.18 and 0.27 for lacy and compact aggregates, respectively, in agreement with reported experimental values of 0.25 ± 0.05. The variation in absorption with wavelength does not adhere precisely to a power law relationship over the 200 to 1000 nm range. Consequently, AAE values depend on the wavelength region over which they are computed. In the 300 to 550 nm range, AAE values ranged in this study from 0.70 for compact to 0.95 for lacy aggregates. The SSA of BC internally mixed with NaCl (100–300 nm in radius is higher than for bare BC and increases with the embedding in the NaCl. Internally mixed BC SSA values decrease in the 200–400 nm wavelength range, a feature also common to the optical properties of dust and organics. Linear polarization features are also predicted in DDSCAT and are dependent on particle morphology. The bare BC (with a radius of 80 nm presents in the linear polarization a bell shape feature, which is a characteristic of the Rayleigh regime (for particles smaller than the wavelength of incident radiation. When BC is internally mixed with NaCl (100–300 nm in radius, strong depolarization features for near-VIS incident radiation are evident
Directory of Open Access Journals (Sweden)
B. V. Scarnato
2013-05-01
Full Text Available According to recent studies, internal mixing of black carbon (BC with other aerosol materials in the atmosphere alters its aggregate shape, absorption of solar radiation, and radiative forcing. These mixing state effects are not yet fully understood. In this study, we characterize the morphology and mixing state of bare BC and BC internally mixed with sodium chloride (NaCl using electron microscopy and examine the sensitivity of optical properties to BC mixing state and aggregate morphology using a discrete dipole approximation model (DDSCAT. DDSCAT is flexible in simulating the geometry and refractive index of particle aggregates. DDSCAT predicts a higher mass absorption coefficient (MAC, lower single scattering albedo (SSA, and higher absorption Angstrom exponent (AAE for bare BC aggregates that are lacy rather than compact. Predicted values of SSA at 550 nm range between 0.16 and 0.27 for lacy and compact aggregates, respectively, in agreement with reported experimental values of 0.25 ± 0.05. The variation in absorption with wavelength does not adhere precisely to a power law relationship over the 200 to 1000 nm range. Consequently, AAE values depend on the wavelength region over which they are computed. The MAC of BC (averaged over the 200–1000 nm range is amplified when internally mixed with NaCl (100–300 nm in radius by factors ranging from 1.0 for lacy BC aggregates partially immersed in NaCl to 2.2 for compact BC aggregates fully immersed in NaCl. The SSA of BC internally mixed with NaCl is higher than for bare BC and increases with the embedding in the NaCl. Internally mixed BC SSA values decrease in the 200–400 nm wavelength range, a feature also common to the optical properties of dust and organics. Linear polarization features are also predicted in DDSCAT and are dependent on particle size and morphology. This study shows that DDSCAT predicts complex morphology and mixing state dependent aerosol optical properties that have
Energy Technology Data Exchange (ETDEWEB)
Lindsay, Sean S. [Department of Earth and Planetary Sciences, University of Tennessee, 1421 Circle Drive, Knoxville, TN 37996-2366 (United States); Wooden, Diane H. [Space Science Division, NASA Ames Research Center, MS 245-3, Moffett Field, CA 94035-0001 (United States); Harker, David E. [Center for Astrophysics and Space Sciences, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0424 (United States); Kelley, Michael S. [Department of Astronomy, University of Maryland, College Park, MD 20742 (United States); Woodward, Charles E. [Minnesota Institute of Astrophysics, 116 Church Street S. E., University of Minnesota, Minneapolis, MN 55455 (United States); Murphy, Jim R., E-mail: slindsay@utk.edu, E-mail: diane.h.wooden@nasa.gov, E-mail: dharker@uscd.edu, E-mail: msk@astro.umd.edu, E-mail: chelsea@astro.umn.edu, E-mail: murphy@nmsu.edu [Department of Astronomy, New Mexico State University, P.O. Box 30001, MSC 4500, Las Cruces, NM 88003-8001 (United States)
2013-03-20
We compute the absorption efficiency (Q{sub abs}) of forsterite using the discrete dipole approximation in order to identify and describe what characteristics of crystal grain shape and size are important to the shape, peak location, and relative strength of spectral features in the 8-40 {mu}m wavelength range. Using the DDSCAT code, we compute Q{sub abs} for non-spherical polyhedral grain shapes with a{sub eff} = 0.1 {mu}m. The shape characteristics identified are (1) elongation/reduction along one of three crystallographic axes; (2) asymmetry, such that all three crystallographic axes are of different lengths; and (3) the presence of crystalline faces that are not parallel to a specific crystallographic axis, e.g., non-rectangular prisms and (di)pyramids. Elongation/reduction dominates the locations and shapes of spectral features near 10, 11, 16, 23.5, 27, and 33.5 {mu}m, while asymmetry and tips are secondary shape effects. Increasing grain sizes (0.1-1.0 {mu}m) shifts the 10 and 11 {mu}m features systematically toward longer wavelengths and relative to the 11 {mu}m feature increases the strengths and slightly broadens the longer wavelength features. Seven spectral shape classes are established for crystallographic a-, b-, and c-axes and include columnar and platelet shapes plus non-elongated or equant grain shapes. The spectral shape classes and the effects of grain size have practical application in identifying or excluding columnar, platelet, or equant forsterite grain shapes in astrophysical environs. Identification of the shape characteristics of forsterite from 8 to 40 {mu}m spectra provides a potential means to probe the temperatures at which forsterite formed.
Aschwanden, Markus J
2016-01-01
In this work we provide an updated description of the Vertical Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) code, which is designed to measure the evolution of the potential, nonpotential, free energies, and the dissipated magnetic energies during solar flares. This code provides a complementary and alternative method to existing traditional NLFFF codes. The chief advantages of the VCA-NLFFF code over traditional NLFFF codes are the circumvention of the unrealistic assumption of a force-free photosphere in the magnetic field extrapolation method, the capability to minimize the misalignment angles between observed coronal loops (or chromospheric fibril structures) and theoretical model field lines, as well as computational speed. In performance tests of the VCA-NLFFF code, by comparing with the NLFFF code of Wiegelmann (2004), we find agreement in the potential, nonpotential, and free energy within a factor of about 1.3, but the Wiegelmann code yields in the average a factor of 2 lower flare en...
Daura-Oller, Elias; Cabré, Maria; Montero, Miguel A.; Paternáin, José L.; Romeu, Antoni
2009-01-01
In the present study, a positive training set of 30 known human imprinted gene coding regions are compared with a set of 72 randomly sampled human nonimprinted gene coding regions (negative training set) to identify genomic features common to human imprinted genes. The most important feature of the present work is its ability to use multivariate analysis to look at variation, at coding region DNA level, among imprinted and non-imprinted genes. There is a force affecting genomic parameters that appears through the use of the appropriate multivariate methods (principle components analysis (PCA) and quadratic discriminant analysis (QDA)) to analyse quantitative genomic data. We show that variables, such as CG content, [bp]% CpG islands, [bp]% Large Tandem Repeats, and [bp]% Simple Repeats, are able to distinguish coding regions of human imprinted genes. PMID:19360135
Directory of Open Access Journals (Sweden)
Elias Daura-Oller
2009-01-01
Full Text Available In the present study, a positive training set of 30 known human imprinted gene coding regions are compared with a set of 72 randomly sampled human nonimprinted gene coding regions (negative training set to identify genomic features common to human imprinted genes. The most important feature of the present work is its ability to use multivariate analysis to look at variation, at coding region DNA level, among imprinted and non-imprinted genes. There is a force affecting genomic parameters that appears through the use of the appropriate multivariate methods (principle components analysis (PCA and quadratic discriminant analysis (QDA to analyse quantitative genomic data. We show that variables, such as CG content, [bp]% CpG islands, [bp]% Large Tandem Repeats, and [bp]% Simple Repeats, are able to distinguish coding regions of human imprinted genes.
Lu, Weihua; Chen, Xinjian; Zhu, Weifang; Yang, Lei; Cao, Zhaoyuan; Chen, Haoyu
2015-03-01
In this paper, we proposed a method based on the Freeman chain code to segment and count rhesus choroid-retinal vascular endothelial cells (RF/6A) automatically for fluorescence microscopy images. The proposed method consists of four main steps. First, a threshold filter and morphological transform were applied to reduce the noise. Second, the boundary information was used to generate the Freeman chain codes. Third, the concave points were found based on the relationship between the difference of the chain code and the curvature. Finally, cells segmentation and counting were completed based on the characteristics of the number of the concave points, the area and shape of the cells. The proposed method was tested on 100 fluorescence microscopic cell images, and the average true positive rate (TPR) is 98.13% and the average false positive rate (FPR) is 4.47%, respectively. The preliminary results showed the feasibility and efficiency of the proposed method.
Barbier, Jean
2015-01-01
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity method. We will also use the replica method of statistical physics of disordered systems which allows to associate to the studied problems a cost function referred as the potential of free entropy in physics. It allows to predict the different phases of typical ...
Directory of Open Access Journals (Sweden)
Apoorva Aggarwal
2015-12-01
Full Text Available In this paper, an optimal design of linear phase digital finite impulse response (FIR highpass (HP filter using the L1-norm based real-coded genetic algorithm (RCGA is investigated. A novel fitness function based on L1 norm is adopted to enhance the design accuracy. Optimized filter coefficients are obtained by defining the filter objective function in L1 sense using RCGA. Simulation analysis unveils that the performance of the RCGA adopting this fitness function is better in terms of signal attenuation ability of the filter, flatter passband and the convergence rate. Observations are made on the percentage improvement of this algorithm over the gradient-based L1 optimization approach on various factors by a large amount. It is concluded that RCGA leads to the best solution under specified parameters for the FIR filter design on account of slight unnoticeable higher transition width.
Engel, D.; Klews, M.; Wunner, G.
2009-02-01
We have developed a new method for the fast computation of wavelengths and oscillator strengths for medium-Z atoms and ions, up to iron, at neutron star magnetic field strengths. The method is a parallelized Hartree-Fock approach in adiabatic approximation based on finite-element and B-spline techniques. It turns out that typically 15-20 finite elements are sufficient to calculate energies to within a relative accuracy of 10-5 in 4 or 5 iteration steps using B-splines of 6th order, with parallelization speed-ups of 20 on a 26-processor machine. Results have been obtained for the energies of the ground states and excited levels and for the transition strengths of astrophysically relevant atoms and ions in the range Z=2…26 in different ionization stages. Catalogue identifier: AECC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECC_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.: 3845 No. of bytes in distributed program, including test data, etc.: 27 989 Distribution format: tar.gz Programming language: MPI/Fortran 95 and Python Computer: Cluster of 1-26 HP Compaq dc5750 Operating system: Fedora 7 Has the code been vectorised or parallelized?: Yes RAM: 1 GByte Classification: 2.1 External routines: MPI/GFortran, LAPACK, PyLab/Matplotlib Nature of problem: Calculations of synthetic spectra [1] of strongly magnetized neutron stars are bedevilled by the lack of data for atoms in intense magnetic fields. While the behaviour of hydrogen and helium has been investigated in detail (see, e.g., [2]), complete and reliable data for heavier elements, in particular iron, are still missing. Since neutron stars are formed by the collapse of the iron cores of massive stars, it may be assumed that their atmospheres contain an iron plasma. Our objective is to fill the gap
Niven, Ivan
2008-01-01
This self-contained treatment originated as a series of lectures delivered to the Mathematical Association of America. It covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both the fractional and integral parts.The author refrains from the use of continuous fractions and includes basic results in the complex case, a feature often neglected in favor of the real number discuss
2006-01-01
This interactive tutorial presents the following concepts of Approximation Techniques: Methods of Weighted Residual (MWR), Weak Formulatioin, Piecewise Continuous Function, Galerkin Finite Element FormulationExplanations especially for mathematical statements are provided using mouseover the highlight equations. ME4613 Finite Element Methods
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Schmidt, Wolfgang M
1980-01-01
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
Energy Technology Data Exchange (ETDEWEB)
Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)
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.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension....... Applications of our general framework include those from number theory (classical, complex, p-adic and formal power series) and dynamical systems (iterated function schemes, rational maps and Kleinian groups)....
International Nuclear Information System (INIS)
The brief description of the AZIMUT code for calculation the neutron flux in a cluster cell is presented. Code takes into account 1 and 2 azimuthal harmonics in the one-group P3-approximation and uses the heterogeneous approach. 2 refs
The Procions` code; Le code Procions
Energy Technology Data Exchange (ETDEWEB)
Deck, D.; Samba, G.
1994-12-19
This paper presents a new code to simulate plasmas generated by inertial confinement. This multi-kinds kinetic code is done with no angular approximation concerning ions and will work in plan and spherical geometry. First, the physical model is presented, using Fokker-Plank. Then, the numerical model is introduced in order to solve the Fokker-Plank operator under the Rosenbluth form. At the end, several numerical tests are proposed. (TEC). 17 refs., 27 figs.
Leike, Reimar H
2016-01-01
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a ranking function that quantifies how "embarrassing" it is to communicate a given approximation. We show that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. We find that this ranking is equivalent to the Kullback-Leibler divergence that is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. We hope that our elementary derivation settles the apparent confusion. We show for example that when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many su...
Bin Qin
2014-01-01
Relationships between fuzzy relations and fuzzy topologies are deeply researched. The concept of fuzzy approximating spaces is introduced and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained.
Rasin, A
1994-01-01
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 iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Institute of Scientific and Technical Information of China (English)
YueShihong; ZhangKecun
2002-01-01
In a dot product space with the reproducing kernel (r. k. S. ) ,a fuzzy system with the estimation approximation errors is proposed ,which overcomes the defect that the existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach. The structure of the new fuzzy approximator benefits a course got by other means.
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
The Karlqvist approximation revisited
Tannous, C.
2015-01-01
The Karlqvist approximation signaling the historical beginning of magnetic recording head theory is reviewed and compared to various approaches progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld edge condition at angular points and leads to exact results.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.;
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
Directory of Open Access Journals (Sweden)
Malvina Baica
1985-01-01
Full Text Available The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF, and defines it as Generalized Euclidean Algorithm (abbr. GEA to approximate irrationals.
Approximation Behooves Calibration
DEFF Research Database (Denmark)
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Directory of Open Access Journals (Sweden)
Fabio Burderi
2007-05-01
Full Text Available Motivated by the study of decipherability conditions for codes weaker than Unique Decipherability (UD, we introduce the notion of coding partition. Such a notion generalizes that of UD code and, for codes that are not UD, allows to recover the ``unique decipherability" at the level of the classes of the partition. By tacking into account the natural order between the partitions, we define the characteristic partition of a code X as the finest coding partition of X. This leads to introduce the canonical decomposition of a code in at most one unambiguouscomponent and other (if any totally ambiguouscomponents. In the case the code is finite, we give an algorithm for computing its canonical partition. This, in particular, allows to decide whether a given partition of a finite code X is a coding partition. This last problem is then approached in the case the code is a rational set. We prove its decidability under the hypothesis that the partition contains a finite number of classes and each class is a rational set. Moreover we conjecture that the canonical partition satisfies such a hypothesis. Finally we consider also some relationships between coding partitions and varieties of codes.
Directory of Open Access Journals (Sweden)
Ishac Bertran
2012-08-01
Full Text Available "Exploring the potential of code to communicate at the level of poetry," the code {poems} project solicited submissions from codewriters in response to the notion of a poem, written in a software language which is semantically valid. These selections reveal the inner workings, constitutive elements, and styles of both a particular software and its authors.
Diophantine approximations on fractals
Einsiedler, Manfred; Shapira, Uri
2009-01-01
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0,1]^2, possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod1 : n is a natural number} are uniformly eventually bounded.
Towards a Unified Framework for Approximate Quantum Error Correction
Mandayam, Prabha
2012-01-01
Operator quantum error correction extends the standard formalism of quantum error correction (QEC) to codes in which only a subsystem within a subspace of states is used to store information in a noise-resilient fashion. Motivated by recent work on approximate QEC, which has opened up the possibility of constructing subspace codes beyond the framework of perfect error correction, we investigate the problem of {\\it approximate} operator quantum error correction (AOQEC). We demonstrate easily checkable sufficient conditions for the existence of AOQEC codes. Furthermore, for certain classes of noise processes, we prove the efficacy of the transpose channel as a simple-to-construct recovery map that works nearly as well as the optimal recovery channel, with optimality defined in terms of worst-case fidelity over all code states. This work generalizes our earlier approach \\cite{aqecPRA} of using the transpose channel for approximate correction of subspace codes to the case of subsystem codes, and brings us closer ...
Plasma Physics Approximations in Ares
Energy Technology Data Exchange (ETDEWEB)
Managan, R. A.
2015-01-08
Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, F_{n}( μ/θ ), the chemical potential, μ or ζ = ln(1+e^{ μ/θ} ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A^{α} (ζ ),A^{β} (ζ ), ζ, f(ζ ) = (1 + e^{-μ/θ})F_{1/2}(μ/θ), F_{1/2}'/F_{1/2}, F_{c}^{α}, and F_{c}^{β}. In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.
Approximate and Incomplete Factorizations
Chan, T.F.; Vorst, H.A. van der
2001-01-01
In this chapter, we give a brief overview of a particular class of preconditioners known as incomplete factorizations. They can be thought of as approximating the exact LU factorization of a given matrix A (e.g. computed via Gaussian elimination) by disallowing certain ll-ins. As opposed to other PD
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
White, Martin
2014-01-01
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 3rd 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 ...
DEFF Research Database (Denmark)
Madsen, Rasmus Elsborg
2005-01-01
The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM that...
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Latorre, Jose I
2015-01-01
There exists a remarkable four-qutrit state that carries absolute maximal entanglement in all its partitions. Employing this state, we construct a tensor network that delivers a holographic many body state, the H-code, where the physical properties of the boundary determine those of the bulk. This H-code is made of an even superposition of states whose relative Hamming distances are exponentially large with the size of the boundary. This property makes H-codes natural states for a quantum memory. H-codes exist on tori of definite sizes and get classified in three different sectors characterized by the sum of their qutrits on cycles wrapped through the boundaries of the system. We construct a parent Hamiltonian for the H-code which is highly non local and finally we compute the topological entanglement entropy of the H-code.
Approximations to Euler's constant
International Nuclear Information System (INIS)
We study a problem of finding good approximations to Euler's constant γ=lim→∞ Sn, where Sn = Σk=Ln (1)/k-log(n+1), by linear forms in logarithms and harmonic numbers. In 1995, C. Elsner showed that slow convergence of the sequence Sn can be significantly improved if Sn is replaced by linear combinations of Sn with integer coefficients. In this paper, considering more general linear transformations of the sequence Sn we establish new accelerating convergence formulae for γ. Our estimates sharpen and generalize recent Elsner's, Rivoal's and author's results. (author)
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
The Compact Approximation Property does not imply the Approximation Property
Willis, George A.
1992-01-01
It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.
Interacting boson approximation
International Nuclear Information System (INIS)
Lectures notes on the Interacting Boson Approximation are given. Topics include: angular momentum tensors; properties of T/sub i//sup (n)/ matrices; T/sub i//sup (n)/ matrices as Clebsch-Gordan coefficients; construction of higher rank tensors; normalization: trace of products of two s-rank tensors; completeness relation; algebra of U(N); eigenvalue of the quadratic Casimir operator for U(3); general result for U(N); angular momentum content of U(3) representation; p-Boson model; Hamiltonian; quadrupole transitions; S,P Boson model; expectation value of dipole operator; S-D model: U(6); quadratic Casimir operator; an O(5) subgroup; an O(6) subgroup; properties of O(5) representations; quadratic Casimir operator; quadratic Casimir operator for U(6); decomposition via SU(5) chain; a special O(3) decomposition of SU(3); useful identities; a useful property of D/sub αβγ/(α,β,γ = 4-8) as coupling coefficients; explicit construction of T/sub x//sup (2)/ and d/sub αβγ/; D-coefficients; eigenstates of T3; and summary of T = 2 states
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Energy Technology Data Exchange (ETDEWEB)
Ravishankar, C., Hughes Network Systems, Germantown, MD
1998-05-08
Speech is the predominant means of communication between human beings and since the invention of the telephone by Alexander Graham Bell in 1876, speech services have remained to be the core service in almost all telecommunication systems. Original analog methods of telephony had the disadvantage of speech signal getting corrupted by noise, cross-talk and distortion Long haul transmissions which use repeaters to compensate for the loss in signal strength on transmission links also increase the associated noise and distortion. On the other hand digital transmission is relatively immune to noise, cross-talk and distortion primarily because of the capability to faithfully regenerate digital signal at each repeater purely based on a binary decision. Hence end-to-end performance of the digital link essentially becomes independent of the length and operating frequency bands of the link Hence from a transmission point of view digital transmission has been the preferred approach due to its higher immunity to noise. The need to carry digital speech became extremely important from a service provision point of view as well. Modem requirements have introduced the need for robust, flexible and secure services that can carry a multitude of signal types (such as voice, data and video) without a fundamental change in infrastructure. Such a requirement could not have been easily met without the advent of digital transmission systems, thereby requiring speech to be coded digitally. The term Speech Coding is often referred to techniques that represent or code speech signals either directly as a waveform or as a set of parameters by analyzing the speech signal. In either case, the codes are transmitted to the distant end where speech is reconstructed or synthesized using the received set of codes. A more generic term that is applicable to these techniques that is often interchangeably used with speech coding is the term voice coding. This term is more generic in the sense that the
Operators of Approximations and Approximate Power Set Spaces
Institute of Scientific and Technical Information of China (English)
ZHANG Xian-yong; MO Zhi-wen; SHU Lan
2004-01-01
Boundary inner and outer operators are introduced; and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.
DEFF Research Database (Denmark)
Cox, Geoff
development, Speaking Code unfolds an argument to undermine the distinctions between criticism and practice, and to emphasize the aesthetic and political aspects of software studies. Not reducible to its functional aspects, program code mirrors the instability inherent in the relationship of speech......; alternatives to mainstream development, from performances of the live-coding scene to the organizational forms of commons-based peer production; the democratic promise of social media and their paradoxical role in suppressing political expression; and the market’s emptying out of possibilities for free...... expression in the public realm. The book’s line of argument defends language against its invasion by economics, arguing that speech continues to underscore the human condition, however paradoxical this may seem in an era of pervasive computing....
Energy Technology Data Exchange (ETDEWEB)
Delbecq, J.M
1999-07-01
The Aster code is a 2D or 3D finite-element calculation code for structures developed by the R and D direction of Electricite de France (EdF). This dossier presents a complete overview of the characteristics and uses of the Aster code: introduction of version 4; the context of Aster (organisation of the code development, versions, systems and interfaces, development tools, quality assurance, independent validation); static mechanics (linear thermo-elasticity, Euler buckling, cables, Zarka-Casier method); non-linear mechanics (materials behaviour, big deformations, specific loads, unloading and loss of load proportionality indicators, global algorithm, contact and friction); rupture mechanics (G energy restitution level, restitution level in thermo-elasto-plasticity, 3D local energy restitution level, KI and KII stress intensity factors, calculation of limit loads for structures), specific treatments (fatigue, rupture, wear, error estimation); meshes and models (mesh generation, modeling, loads and boundary conditions, links between different modeling processes, resolution of linear systems, display of results etc..); vibration mechanics (modal and harmonic analysis, dynamics with shocks, direct transient dynamics, seismic analysis and aleatory dynamics, non-linear dynamics, dynamical sub-structuring); fluid-structure interactions (internal acoustics, mass, rigidity and damping); linear and non-linear thermal analysis; steels and metal industry (structure transformations); coupled problems (internal chaining, internal thermo-hydro-mechanical coupling, chaining with other codes); products and services. (J.S.)
Approximation algorithms and hardness of approximation for knapsack problems
Buhrman, H.; Loff, B.; Torenvliet, L.
2012-01-01
We show various hardness of approximation algorithms for knapsack and related problems; in particular we will show that unless the Exponential-Time Hypothesis is false, then subset-sum cannot be approximated any better than with an FPTAS. We also give a simple new algorithm for approximating knapsac
Optimal codes as Tanner codes with cyclic component codes
DEFF Research Database (Denmark)
Høholdt, Tom; Pinero, Fernando; Zeng, Peng
2014-01-01
In this article we study a class of graph codes with cyclic code component codes as affine variety codes. Within this class of Tanner codes we find some optimal binary codes. We use a particular subgraph of the point-line incidence plane of A(2,q) as the Tanner graph, and we are able to describe...... the codes succinctly using Gröbner bases....
International Nuclear Information System (INIS)
The MCNP code is the major Monte Carlo coupled neutron-photon transport research tool at the Los Alamos National Laboratory, and it represents the most extensive Monte Carlo development program in the United States which is available in the public domain. The present code is the direct descendent of the original Monte Carlo work of Fermi, von Neumaum, and Ulam at Los Alamos in the 1940s. Development has continued uninterrupted since that time, and the current version of MCNP (or its predecessors) has always included state-of-the-art methods in the Monte Carlo simulation of radiation transport, basic cross section data, geometry capability, variance reduction, and estimation procedures. The authors of the present code have oriented its development toward general user application. The documentation, though extensive, is presented in a clear and simple manner with many examples, illustrations, and sample problems. In addition to providing the desired results, the output listings give a a wealth of detailed information (some optional) concerning each state of the calculation. The code system is continually updated to take advantage of advances in computer hardware and software, including interactive modes of operation, diagnostic interrupts and restarts, and a variety of graphical and video aids
International Nuclear Information System (INIS)
This report describes ANIMAL, a two-dimensional Eulerian magnetohydrodynamic computer code. ANIMAL's physical model also appears. Formulated are temporal and spatial finite-difference equations in a manner that facilitates implementation of the algorithm. Outlined are the functions of the algorithm's FORTRAN subroutines and variables
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2015-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
Approximate sine-Gordon solitons
Energy Technology Data Exchange (ETDEWEB)
Stratopoulos, G.N. (Dept. of Mathematical Sciences, Durham Univ. (United Kingdom)); Zakrzewski, W.J. (Dept. of Mathematical Sciences, Durham Univ. (United Kingdom))
1993-08-01
We look at the recently proposed scheme of approximating a sine-Gordon soliton by an expression derived from two dimensional instantons. We point out that the scheme of Sutcliffe in which he uses two dimensional instantons can be generalised to higher dimensions and that these generalisations produce even better approximations than the original approximation. We also comment on generalisations to other models. (orig.)
Wang, Jim Jing-Yan
2014-07-06
Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the manifold structure spanned by the data set of both labeled and unlabeled samples and the constraints provided by the labels of the labeled samples, we learn the variable class labels for all the samples. Furthermore, to improve the discriminative ability of the learned sparse codes, we assume that the class labels could be predicted from the sparse codes directly using a linear classifier. By solving the codebook, sparse codes, class labels and classifier parameters simultaneously in a unified objective function, we develop a semi-supervised sparse coding algorithm. Experiments on two real-world pattern recognition problems demonstrate the advantage of the proposed methods over supervised sparse coding methods on partially labeled data sets.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Legendre-tau approximations for functional differential equations
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.
NOVEL BIPHASE CODE -INTEGRATED SIDELOBE SUPPRESSION CODE
Institute of Scientific and Technical Information of China (English)
Wang Feixue; Ou Gang; Zhuang Zhaowen
2004-01-01
A kind of novel binary phase code named sidelobe suppression code is proposed in this paper. It is defined to be the code whose corresponding optimal sidelobe suppression filter outputs the minimum sidelobes. It is shown that there do exist sidelobe suppression codes better than the conventional optimal codes-Barker codes. For example, the sidelobe suppression code of length 11 with filter of length 39 has better sidelobe level up to 17dB than that of Barker code with the same code length and filter length.
From concatenated codes to graph codes
DEFF Research Database (Denmark)
Justesen, Jørn; Høholdt, Tom
2004-01-01
We consider codes based on simple bipartite expander graphs. These codes may be seen as the first step leading from product type concatenated codes to more complex graph codes. We emphasize constructions of specific codes of realistic lengths, and study the details of decoding by message passing...... in trees....
Concatenated codes with convolutional inner codes
DEFF Research Database (Denmark)
Justesen, Jørn; Thommesen, Christian; Zyablov, Viktor
1988-01-01
The minimum distance of concatenated codes with Reed-Solomon outer codes and convolutional inner codes is studied. For suitable combinations of parameters the minimum distance can be lower-bounded by the product of the minimum distances of the inner and outer codes. For a randomized ensemble of...... concatenated codes a lower bound of the Gilbert-Varshamov type is proved...
Approximate solutions for the skyrmion
Ponciano, J A; Fanchiotti, H; Canal-Garcia, C A
2001-01-01
We reconsider the Euler-Lagrange equation for the Skyrme model in the hedgehog ansatz and study the analytical properties of the solitonic solution. In view of the lack of a closed form solution to the problem, we work on approximate analytical solutions. We show that Pade approximants are well suited to continue analytically the asymptotic representation obtained in terms of a power series expansion near the origin, obtaining explicit approximate solutions for the Skyrme equations. We improve the approximations by applying the 2-point Pade approximant procedure whereby the exact behaviour at spatial infinity is incorporated. An even better convergence to the exact solution is obtained by introducing a modified form for the approximants. The new representations share the same analytical properties with the exact solution at both small and large values of the radial variable r.
BDD Minimization for Approximate Computing
Soeken, Mathias; Grosse, Daniel; Chandrasekharan, Arun; Drechsler, Rolf
2016-01-01
We present Approximate BDD Minimization (ABM) as a problem that has application in approximate computing. Given a BDD representation of a multi-output Boolean function, ABM asks whether there exists another function that has a smaller BDD representation but meets a threshold w.r.t. an error metric. We present operators to derive approximated functions and present algorithms to exactly compute the error metrics directly on the BDD representation. An experimental evaluation demonstrates the app...
Dutta, Sagarmoy
2010-01-01
In this paper, we define and study \\emph{quantum cyclic codes}, a generalisation of cyclic codes to the quantum setting. Previously studied examples of quantum cyclic codes were all quantum codes obtained from classical cyclic codes via the CSS construction. However, the codes that we study are much more general. In particular, we construct cyclic stabiliser codes with parameters $[[5,1,3
Nonlinear approximation with redundant dictionaries
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, M.; Gribonval, R.
2005-01-01
In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general...
Approximate Inference in Probabilistic Models
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2004-01-01
We present a framework for approximate inference in probabilistic data models which is based on free energies. The free energy is constructed from two approximating distributions which encode different aspects of the intractable model. Consistency between distributions is required on a chosen set...
The Logic of Approximate Dependence
Väänänen, Jouko
2014-01-01
We extend the treatment of functional dependence, the basic concept of dependence logic, to include the possibility of dependence with a limited number of exceptions. We call this approximate dependence. The main result of the paper is a Completeness Theorem for approximate dependence atoms. We point out some problematic features of this which suggests that we should consider multi-teams, not just teams.
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
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.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
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.
N-variable rational approximants
International Nuclear Information System (INIS)
''Desirable properties'' of a two-variable generalization of Pade approximants are laid down. The ''Chisholm approximants'' are defined and are shown to obey nearly all of these properties; the alternative ways of completing a unique definition are discussed, and the ''prong structure'' of the defining equations is elucidated. Several generalizations and variants of Chisholm approximants are described: N-variable diagonal, 2-variable simple off-diagonal, N-variable simple and general off-diagonal, and rotationally covariant 2-variable approximants. All of the 2-variable approximants are capable of representing singularities of functions of two variables, and of analytically continuing beyond the polycylinder of convergence of the double series. 8 figures
Yoshida, Shin'ichirou
2012-01-01
We present a new numerical code to compute non-axisymmetric eigenmodes of rapidly rotating relativistic stars by adopting spatially conformally flat approximation of general relativity. The approximation suppresses the radiative degree of freedom of relativistic gravity and the field equations are cast into a set of elliptic equations. The code is tested against the low-order f- and p-modes of slowly rotating stars for which a good agreement is observed in frequencies computed by our new code...
The efficiency of Flory approximation
International Nuclear Information System (INIS)
The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)
Binary nucleation beyond capillarity approximation
Kalikmanov, V.I.
2010-01-01
Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Approximate maximizers of intricacy functionals
Buzzi, Jerome
2009-01-01
G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. This functional is a special case of intricacy, i.e., an average of the mutual information of subsystems whose weights have good mathematical properties. Moreover, its maximum value grows at a definite speed with the size of the system. In this work, we compute exactly this speed of growth by building "approximate maximizers" subject to an entropy condition. These approximate maximizers work simultaneously for all intricacies. We also establish some properties of arbitrary approximate maximizers, in particular the existence of a threshold in the size of subsystems of approximate maximizers: most smaller subsystems are almost equidistributed, most larger subsystems determine the full system. The main ideas are a random construction of almost maximizers with a high statistical symmetry and the consideration of entropy profiles, i.e., the average entropies of sub-systems of a given size. ...
Reinforcement Learning via AIXI Approximation
Veness, Joel; Ng, Kee Siong; Hutter, Marcus; Silver, David
2010-01-01
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To deve...
Binary nucleation beyond capillarity approximation
Kalikmanov, V.I.
2010-01-01
Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption is taken into account within Gibbsian approximation. Binary clusters are treated by means of statistical-mechanical considerations: tracing out the molecular degrees of freedom of the more volatil...
Fundamentals of convolutional coding
Johannesson, Rolf
2015-01-01
Fundamentals of Convolutional Coding, Second Edition, regarded as a bible of convolutional coding brings you a clear and comprehensive discussion of the basic principles of this field * Two new chapters on low-density parity-check (LDPC) convolutional codes and iterative coding * Viterbi, BCJR, BEAST, list, and sequential decoding of convolutional codes * Distance properties of convolutional codes * Includes a downloadable solutions manual
Diffusion approximation for modeling of 3-D radiation distributions
International Nuclear Information System (INIS)
A three-dimensional transport code DIF3D, based on the diffusion approximation, is used to model the spatial distribution of radiation energy arising from volumetric isotropic sources. Future work will be concerned with the determination of irradiances and modeling of realistic scenarios, relevant to the battlefield conditions. 8 refs., 4 figs
Twisted inhomogeneous Diophantine approximation and badly approximable sets
Harrap, Stephen
2010-01-01
For any real pair i, j geq 0 with i+j=1 let Bad(i, j) denote the set of (i, j)-badly approximable pairs. That is, Bad(i, j) consists of irrational vectors x:=(x_1, x_2) in R^2 for which there exists a positive constant c(x) such that max {||qx_1||^(-i), ||qx_2||^(-j)} > c(x)/q for all q in N. Building on a result of Kurzweil, a new characterization of the set Bad(i, j) in terms of `well-approximable' vectors in the area of `twisted' inhomogeneous Diophantine approximation is established. In addition, it is shown that Bad^x(i, j), the `twisted' inhomogeneous analogue of Bad(i, j), has full Hausdorff dimension 2 when x is chosen from the set Bad(i, j).
Comparing numerical and analytic approximate gravitational waveforms
Afshari, Nousha; Lovelace, Geoffrey; SXS Collaboration
2016-03-01
A direct observation of gravitational waves will test Einstein's theory of general relativity under the most extreme conditions. The Laser Interferometer Gravitational-Wave Observatory, or LIGO, began searching for gravitational waves in September 2015 with three times the sensitivity of initial LIGO. To help Advanced LIGO detect as many gravitational waves as possible, a major research effort is underway to accurately predict the expected waves. In this poster, I will explore how the gravitational waveform produced by a long binary-black-hole inspiral, merger, and ringdown is affected by how fast the larger black hole spins. In particular, I will present results from simulations of merging black holes, completed using the Spectral Einstein Code (black-holes.org/SpEC.html), including some new, long simulations designed to mimic black hole-neutron star mergers. I will present comparisons of the numerical waveforms with analytic approximations.
Strong Trinucleotide Circular Codes
Directory of Open Access Journals (Sweden)
Christian J. Michel
2011-01-01
Full Text Available Recently, we identified a hierarchy relation between trinucleotide comma-free codes and trinucleotide circular codes (see our previous works. Here, we extend our hierarchy with two new classes of codes, called DLD and LDL codes, which are stronger than the comma-free codes. We also prove that no circular code with 20 trinucleotides is a DLD code and that a circular code with 20 trinucleotides is comma-free if and only if it is a LDL code. Finally, we point out the possible role of the symmetric group ∑4 in the mathematical study of trinucleotide circular codes.
Wavelet Sparse Approximate Inverse Preconditioners
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.
The structure of approximate groups
Breuillard, Emmanuel; Tao, Terence
2011-01-01
Let K >= 1 be a parameter. A K-approximate group is a finite set A in a (local) group which contains the identity, is symmetric, and such that A^2 is covered by K left translates of A. The main result of this paper is a qualitative description of approximate groups as being essentially finite-by-nilpotent, answering a conjecture of H. Helfgott and E. Lindenstrauss. This may be viewed as a generalisation of the Freiman-Ruzsa theorem on sets of small doubling in the integers to arbitrary groups. We begin by establishing a correspondence principle between approximate groups and locally compact (local) groups that allows us to recover many results recently established in a fundamental paper of Hrushovski. In particular we establish that approximate groups can be approximately modeled by Lie groups. To prove our main theorem we apply some additional arguments essentially due to Gleason. These arose in the solution of Hilbert's fifth problem in the 1950s. Applications of our main theorem include a finitary refineme...
Relativistic regular approximations revisited: An infinite-order relativistic approximation
International Nuclear Information System (INIS)
The concept of the regular approximation is presented as the neglect of the energy dependence of the exact Foldy - 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 - Wouthuysen transformation, which results in the ZORA Hamiltonian and a non-unit metric. This infinite-order regular approximation, IORA, has eigenvalues which differ from the Dirac eigenvalues by order E3/c4 for a hydrogen-like system, which is a considerable improvement over the ZORA eigenvalues, and similar to the non-variational 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 1999 American Institute of Physics
Approximating Graphic TSP by Matchings
Mömke, Tobias
2011-01-01
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a decreased cost. For the TSP on graphic metrics (graph-TSP), the approach yields a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted to a class of graphs that contains degree three bounded and claw-free graphs, we show that the integrality gap of the Held-Karp relaxation matches the conjectured ratio 4/3. The framework allows for generalizations in a natural way and also leads to a 1.586-approximation algorithm for the traveling salesman path problem on graphic metrics where the start and end vertices are prespecified.
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Reinforcement Learning via AIXI Approximation
Veness, Joel; Hutter, Marcus; Silver, David
2010-01-01
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.
Concept Approximation between Fuzzy Ontologies
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Fuzzy ontologies are efficient tools to handle fuzzy and uncertain knowledge on the semantic web; but there are heterogeneity problems when gaining interoperability among different fuzzy ontologies. This paper uses concept approximation between fuzzy ontologies based on instances to solve the heterogeneity problems. It firstly proposes an instance selection technology based on instance clustering and weighting to unify the fuzzy interpretation of different ontologies and reduce the number of instances to increase the efficiency. Then the paper resolves the problem of computing the approximations of concepts into the problem of computing the least upper approximations of atom concepts. It optimizes the search strategies by extending atom concept sets and defining the least upper bounds of concepts to reduce the searching space of the problem. An efficient algorithm for searching the least upper bounds of concept is given.
An Approximation Ratio for Biclustering
Puolamäki, Kai; Hanhijärvi, Sami; Garriga, Gemma C
2007-01-01
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worst-case approximation ratio of 1+sqrt(2) under L1-norm for 0-1 valued matrices, and of 2...
An Approximation Ratio for Biclustering
Puolamäki, Kai; Garriga, Gemma C
2007-01-01
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution yields a worst-case approximation ratio of 1+sqrt(2) under L1-norm for 0-1 valued matrices, and of 2 under L2-norm for real valued matrices.
Joint source channel coding using arithmetic codes
Bi, Dongsheng
2009-01-01
Based on the encoding process, arithmetic codes can be viewed as tree codes and current proposals for decoding arithmetic codes with forbidden symbols belong to sequential decoding algorithms and their variants. In this monograph, we propose a new way of looking at arithmetic codes with forbidden symbols. If a limit is imposed on the maximum value of a key parameter in the encoder, this modified arithmetic encoder can also be modeled as a finite state machine and the code generated can be treated as a variable-length trellis code. The number of states used can be reduced and techniques used fo
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Baraniuk, R. G., DeVore, R. A., Kyriazis, G., Yu, X. M., Near best tree approximation, Adv. Comput. Math.,2002, 16: 357-373.[2]Cohen, A., Dahmen, W., Daubechies, I., DeVore, R., Tree approximation and optimal encoding, Appl. Comput.Harmonic Anal., 2001, 11: 192-226.[3]Dahmen, W., Schneider, R., Xu, Y., Nonlinear functionals of wavelet expansions-adaptive reconstruction and fast evaluation, Numer. Math., 2000, 86: 49-101.[4]DeVore, R. A., Nonlinear approximation, Acta Numer., 1998, 7: 51-150.[5]Davis, G., Mallat, S., Avellaneda, M., Adaptive greedy approximations, Const. Approx., 1997, 13: 57-98.[6]DeVore, R. A., Temlyakov, V. N., Some remarks on greedy algorithms, Adv. Comput. Math., 1996, 5: 173-187.[7]Kashin, B. S., Temlyakov, V. N., Best m-term approximations and the entropy of sets in the space L1, Mat.Zametki (in Russian), 1994, 56: 57-86.[8]Temlyakov, V. N., The best m-term approximation and greedy algorithms, Adv. Comput. Math., 1998, 8:249-265.[9]Temlyakov, V. N., Greedy algorithm and m-term trigonometric approximation, Constr. Approx., 1998, 14:569-587.[10]Hutchinson, J. E., Fractals and self similarity, Indiana. Univ. Math. J., 1981, 30: 713-747.[11]Binev, P., Dahmen, W., DeVore, R. A., Petruchev, P., Approximation classes for adaptive methods, Serdica Math.J., 2002, 28: 1001-1026.[12]Gilbarg, D., Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Berlin: Springer-Verlag,1983.[13]Ciarlet, P. G., The Finite Element Method for Elliptic Problems, New York: North Holland, 1978.[14]Birman, M. S., Solomiak, M. Z., Piecewise polynomial approximation of functions of the class Wαp, Math. Sb.,1967, 73: 295-317.[15]DeVore, R. A., Lorentz, G. G., Constructive Approximation, New York: Springer-Verlag, 1993.[16]DeVore, R. A., Popov, V., Interpolation of Besov spaces, Trans. Amer. Math. Soc., 1988, 305: 397-414.[17]Devore, R., Jawerth, B., Popov, V., Compression of wavelet decompositions, Amer. J. Math., 1992, 114: 737-785.[18]Storozhenko, E
Truthful approximations to range voting
DEFF Research Database (Denmark)
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...
Shearlets and Optimally Sparse Approximations
DEFF Research Database (Denmark)
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
2012-01-01
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
Analytical Approximations to Galaxy Clustering
Mo, H. J.
1997-01-01
We discuss some recent progress in constructing analytic approximations to the galaxy clustering. We show that successful models can be constructed for the clustering of both dark matter and dark matter haloes. Our understanding of galaxy clustering and galaxy biasing can be greatly enhanced by these models.
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
2013-01-01
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
Approximation by Penultimate Stable Laws
L.F.M. de Haan (Laurens); L. Peng (Liang); H. Iglesias Pereira
1997-01-01
textabstractIn certain cases partial sums of i.i.d. random variables with finite variance are better approximated by a sequence of stable distributions with indices \\\\alpha_n \\\\to 2 than by a normal distribution. We discuss when this happens and how much the convergence rate can be improved by using
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...
Impact of inflow transport approximation on light water reactor analysis
Choi, Sooyoung; Smith, Kord; Lee, Hyun Chul; Lee, Deokjung
2015-10-01
The impact of the inflow transport approximation on light water reactor analysis is investigated, and it is verified that the inflow transport approximation significantly improves the accuracy of the transport and transport/diffusion solutions. A methodology for an inflow transport approximation is implemented in order to generate an accurate transport cross section. The inflow transport approximation is compared to the conventional methods, which are the consistent-PN and the outflow transport approximations. The three transport approximations are implemented in the lattice physics code STREAM, and verification is performed for various verification problems in order to investigate their effects and accuracy. From the verification, it is noted that the consistent-PN and the outflow transport approximations cause significant error in calculating the eigenvalue and the power distribution. The inflow transport approximation shows very accurate and precise results for the verification problems. The inflow transport approximation shows significant improvements not only for the high leakage problem but also for practical large core problem analyses.
Low Rank Approximation in $G_0W_0$ Approximation
Shao, Meiyue; Yang, Chao; Liu, Fang; da Jornada, Felipe H; Deslippe, Jack; Louie, Steven G
2016-01-01
The single particle energies obtained in a Kohn--Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The $G_0W_0$ approximation is a widely used technique in which the self energy is expressed as the convolution of a non-interacting Green's function ($G_0$) and a screened Coulomb interaction ($W_0$) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating $W_0$ at multiple frequencies. In this paper, we discuss how the cos...
New Mexico Univ., Albuquerque. American Indian Law Center.
The Model Children's Code was developed to provide a legally correct model code that American Indian tribes can use to enact children's codes that fulfill their legal, cultural and economic needs. Code sections cover the court system, jurisdiction, juvenile offender procedures, minor-in-need-of-care, and termination. Almost every Code section is…
Usage of burnt fuel isotopic compositions from engineering codes in Monte-Carlo code calculations
Energy Technology Data Exchange (ETDEWEB)
Aleshin, Sergey S.; Gorodkov, Sergey S.; Shcherenko, Anna I. [Nuclear Research Centre ' ' Kurchatov Institute' ' , Moscow (Russian Federation)
2015-09-15
A burn-up calculation of VVER's cores by Monte-Carlo code is complex process and requires large computational costs. This fact makes Monte-Carlo codes usage complicated for project and operating calculations. Previously prepared isotopic compositions are proposed to use for the Monte-Carlo code (MCU) calculations of different states of VVER's core with burnt fuel. Isotopic compositions are proposed to calculate by an approximation method. The approximation method is based on usage of a spectral functionality and reference isotopic compositions, that are calculated by engineering codes (TVS-M, PERMAK-A). The multiplication factors and power distributions of FA and VVER with infinite height are calculated in this work by the Monte-Carlo code MCU using earlier prepared isotopic compositions. The MCU calculation data were compared with the data which were obtained by engineering codes.
Hydrogen Beyond the Classic Approximation
Scivetti, I
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
formally proof that the pq-gram index can be incrementally updated based on the log of edit operations without reconstructing intermediate tree versions. The incremental update is independent of the data size and scales to a large number of changes in the data. We introduce windowed pq-grams for the......-gram based distance between streets, introduces a global greedy matching that guarantees stable pairs, and links addresses that are stored with different granularity. The connector has been successfully tested with public administration databases. Our extensive experiments on both synthetic and real world......The goal of this thesis is to design, develop, and evaluate new methods for the approximate matching of hierarchical data represented as labeled trees. In approximate matching scenarios two items should be matched if they are similar. Computing the similarity between labeled trees is hard as in...
Validity of the eikonal approximation
Kabat, D
1992-01-01
We summarize results on the reliability of the eikonal approximation in obtaining the high energy behavior of a two particle forward scattering amplitude. Reliability depends on the spin of the exchanged field. For scalar fields the eikonal fails at eighth order in perturbation theory, when it misses the leading behavior of the exchange-type diagrams. In a vector theory the eikonal gets the exchange diagrams correctly, but fails by ignoring certain non-exchange graphs which dominate the asymptotic behavior of the full amplitude. For spin--2 tensor fields the eikonal captures the leading behavior of each order in perturbation theory, but the sum of eikonal terms is subdominant to graphs neglected by the approximation. We also comment on the eikonal for Yang-Mills vector exchange, where the additional complexities of the non-abelian theory may be absorbed into Regge-type modifications of the gauge boson propagators.
Approximate Privacy: Foundations and Quantification
Feigenbaum, Joan; Schapira, Michael
2009-01-01
Increasing use of computers and networks in business, government, recreation, and almost all aspects of daily life has led to a proliferation of online sensitive data about individuals and organizations. Consequently, concern about the privacy of these data has become a top priority, particularly those data that are created and used in electronic commerce. There have been many formulations of privacy and, unfortunately, many negative results about the feasibility of maintaining privacy of sensitive data in realistic networked environments. We formulate communication-complexity-based definitions, both worst-case and average-case, of a problem's privacy-approximation ratio. We use our definitions to investigate the extent to which approximate privacy is achievable in two standard problems: the second-price Vickrey auction and the millionaires problem of Yao. For both the second-price Vickrey auction and the millionaires problem, we show that not only is perfect privacy impossible or infeasibly costly to achieve...
Hydrogen: Beyond the Classic Approximation
International Nuclear Information System (INIS)
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Concentration Bounds for Stochastic Approximations
Frikha, Noufel
2012-01-01
We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic time and its empirical mean obtained by the Monte-Carlo procedure. We then give some estimates concerning the deviation between the value at a given time-step of a stochastic approximation algorithm and its target. Under suitable assumptions both concentration bounds turn out to be Gaussian. The key tool consists in exploiting accurately the concentration properties of the increments of the schemes. For the first case, as opposed to the previous work of Lemaire and Menozzi (EJP, 2010), we do not have any systematic bias in our estimates. Also, no specific non-degeneracy conditions are assumed.
Variance approximation under balanced sampling
Deville, Jean-Claude; Tillé, Yves
2016-01-01
A balanced sampling design has the interesting property that Horvitz–Thompson estimators of totals for a set of balancing variables are equal to the totals we want to estimate, therefore the variance of Horvitz–Thompson estimators of variables of interest are reduced in function of their correlations with the balancing variables. Since it is hard to derive an analytic expression for the joint inclusion probabilities, we derive a general approximation of variance based on a residual technique....
Approximate maximizers of intricacy functionals
Buzzi, Jerome; Zambotti, Lorenzo
2009-01-01
G. Edelman, O. Sporns, and G. Tononi introduced in theoretical biology the neural complexity of a family of random variables. This functional is a special case of intricacy, i.e., an average of the mutual information of subsystems whose weights have good mathematical properties. Moreover, its maximum value grows at a definite speed with the size of the system. In this work, we compute exactly this speed of growth by building "approximate maximizers" subject to an entropy condition. These appr...
Approximating Metal-Insulator Transitions
Danieli, C.; Rayanov, K.; Pavlov, B.; Martin, G.; Flach, S
2014-01-01
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 ed...
Park, Brooke Anderson; Wright, Henry
2012-01-01
PatCon code was developed to help mission designers run trade studies on launch and arrival times for any given planet. Initially developed in Fortran, the required inputs included launch date, arrival date, and other orbital parameters of the launch planet and arrival planets at the given dates. These parameters include the position of the planets, the eccentricity, semi-major axes, argument of periapsis, ascending node, and inclination of the planets. With these inputs, a patched conic approximation is used to determine the trajectory. The patched conic approximation divides the planetary mission into three parts: (1) the departure phase, in which the two relevant bodies are Earth and the spacecraft, and where the trajectory is a departure hyperbola with Earth at the focus; (2) the cruise phase, in which the two bodies are the Sun and the spacecraft, and where the trajectory is a transfer ellipse with the Sun at the focus; and (3) the arrival phase, in which the two bodies are the target planet and the spacecraft, where the trajectory is an arrival hyperbola with the planet as the focus.
Radiative transfer in disc galaxies $-$ V. The accuracy of the KB approximation
Lee, Dukhang; Seon, Kwang-Il; Camps, Peter; Verstocken, Sam; Han, Wonyong
2016-01-01
We investigate the accuracy of an approximate radiative transfer technique that was first proposed by Kylafis & Bahcall (hereafter the KB approximation) and has been popular in modelling dusty late-type galaxies. We compare realistic galaxy models calculated with the KB approximation with those of a three-dimensional Monte Carlo radiative transfer code SKIRT. The SKIRT code fully takes into account of the contribution of multiple scattering whereas the KB approximation calculates only single scattered intensity and multiple scattering components are approximated. We find that the KB approximation gives fairly accurate results if optically thin, face-on galaxies are considered. However, for highly inclined ($i \\gtrsim 85^{\\circ}$) and/or optically thick (central face-on optical depth $\\gtrsim1$) galaxy models, the approximation can give rise to substantial errors, sometimes, up to $\\gtrsim 40\\%$. Moreover, it is also found that the KB approximation is not always physical, sometimes producing infinite inten...
Robust hashing with local models for approximate similarity search.
Song, Jingkuan; Yang, Yi; Li, Xuelong; Huang, Zi; Yang, Yang
2014-07-01
Similarity search plays an important role in many applications involving high-dimensional data. Due to the known dimensionality curse, the performance of most existing indexing structures degrades quickly as the feature dimensionality increases. Hashing methods, such as locality sensitive hashing (LSH) and its variants, have been widely used to achieve fast approximate similarity search by trading search quality for efficiency. However, most existing hashing methods make use of randomized algorithms to generate hash codes without considering the specific structural information in the data. In this paper, we propose a novel hashing method, namely, robust hashing with local models (RHLM), which learns a set of robust hash functions to map the high-dimensional data points into binary hash codes by effectively utilizing local structural information. In RHLM, for each individual data point in the training dataset, a local hashing model is learned and used to predict the hash codes of its neighboring data points. The local models from all the data points are globally aligned so that an optimal hash code can be assigned to each data point. After obtaining the hash codes of all the training data points, we design a robust method by employing l2,1 -norm minimization on the loss function to learn effective hash functions, which are then used to map each database point into its hash code. Given a query data point, the search process first maps it into the query hash code by the hash functions and then explores the buckets, which have similar hash codes to the query hash code. Extensive experimental results conducted on real-life datasets show that the proposed RHLM outperforms the state-of-the-art methods in terms of search quality and efficiency.
Eric M. Rains
1997-01-01
We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional global symmetries. From this standpoint, the analogues of Calderbank-Shor-Steane codes and of GF(4)-linear codes turn out to be special cases of the same construction. This allows us to construct families of quantum codes from certain codes over number fields...
DEFF Research Database (Denmark)
Sørensen, Jesper Hemming; Koike-Akino, Toshiaki; Orlik, Philip
2012-01-01
This paper proposes a concept called rateless feedback coding. We redesign the existing LT and Raptor codes, by introducing new degree distributions for the case when a few feedback opportunities are available. We show that incorporating feedback to LT codes can significantly decrease both...... the coding overhead and the encoding/decoding complexity. Moreover, we show that, at the price of a slight increase in the coding overhead, linear complexity is achieved with Raptor feedback coding....
DEFF Research Database (Denmark)
Høholdt, Tom; Beelen, Peter; Ghorpade, Sudhir Ramakant
2010-01-01
We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes.We determine the length, dimension, and the minimum distance of any affine Grassmann code. Moreover, we show that...... affine Grassmann codes have a large automorphism group and determine the number of minimum weight codewords....
Product Approximation of Grade and Precision
Institute of Scientific and Technical Information of China (English)
ZHANG Xian-yong; MO Zhi-wen
2005-01-01
The normal graded approximation and variable precision approximation are defined in approximate space. The relationship between graded approximation and variable precision approximation is studied, and an important formula of conversion between them is achieved. The product approximation of gradeand precision is defined and its basic properties are studied.
Abraham, Nikhil
2015-01-01
Hands-on exercises help you learn to code like a pro No coding experience is required for Coding For Dummies,your one-stop guide to building a foundation of knowledge inwriting computer code for web, application, and softwaredevelopment. It doesn't matter if you've dabbled in coding or neverwritten a line of code, this book guides you through the basics.Using foundational web development languages like HTML, CSS, andJavaScript, it explains in plain English how coding works and whyit's needed. Online exercises developed by Codecademy, a leading online codetraining site, help hone coding skill
Gao, Wen
2015-01-01
This comprehensive and accessible text/reference presents an overview of the state of the art in video coding technology. Specifically, the book introduces the tools of the AVS2 standard, describing how AVS2 can help to achieve a significant improvement in coding efficiency for future video networks and applications by incorporating smarter coding tools such as scene video coding. Topics and features: introduces the basic concepts in video coding, and presents a short history of video coding technology and standards; reviews the coding framework, main coding tools, and syntax structure of AV
Directory of Open Access Journals (Sweden)
M. Markkanen
2008-08-01
Full Text Available We present a new class of alternating codes. Instead of the customary binary phase codes, the new codes utilize either p or p–1 phases, where p is a prime number. The first class of codes has code length p^{m}, where m is a positive integer, the second class has code length p–1. We give an actual construction algorithm, and explain the principles behind it. We handle a few specific examples in detail. The new codes offer an enlarged collection of code lengths for radar experiments.
Coupling CFD code with system code and neutron kinetic code
International Nuclear Information System (INIS)
Highlights: • Coupling interface between CFD code Fluent and system code Athlet was created. • Athlet code is internally coupled with neutron kinetic code Dyn3D. • Explicit coupling of overlapped computational domains was used. • A coupled system of Athlet/Dyn3D+Fluent codes was successfully tested on a real case. - Abstract: The aim of this work was to develop the coupling interface between CFD code Fluent and system code Athlet internally coupled with neutron kinetic code Dyn3D. The coupling interface is intended for simulation of complex transients such as Main Steam Line Break scenarios, which cannot be modeled separately first by system and neutron kinetic code and then by CFD code, because of the feedback between the codes. In the first part of this article, the coupling method is described. Explicit coupling of overlapped computational domains is used in this work. The second part of the article presents a demonstration simulation performed by the coupled system of Athlet/Dyn3D and Fluent. The “Opening a Steam Dump to the Atmosphere” test carried out at the Temelin NPP (VVER-1000) was simulated by the coupled system. In this simulation, the primary and secondary circuits were modeled by Athlet, mixing in downcomer and lower plenum was simulated by Fluent and heat generation in the core was calculated by Dyn3D. The results of the simulation with Athlet/Dyn3D+Fluent were compared with the experimental data and the results from a calculation performed with Athlet/Dyn3D without Fluent
Rollout Sampling Approximate Policy Iteration
Dimitrakakis, Christos
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions which focus on policy representation using classifiers and address policy learning as a supervised learning problem. This paper proposes variants of an improved policy iteration scheme which addresses the core sampling problem in evaluating a policy through simulation as a multi-armed bandit machine. The resulting algorithm offers comparable performance to the previous algorithm achieved, however, with significantly less computational effort. An order of magnitude improvement is demonstrated experimentally in two standard reinforcement learning domains: inverted pendulum and mountain-car.
Quantum Tunneling Beyond Semiclassical Approximation
Banerjee, Rabin
2008-01-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.
Quantum tunneling beyond semiclassical approximation
Banerjee, Rabin; Ranjan Majhi, Bibhas
2008-06-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.
Fermion Tunneling Beyond Semiclassical Approximation
Majhi, Bibhas Ranjan
2008-01-01
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in \\cite{Majhi3} for the scalar particle, Hawking radiation as tunneling of Dirac particle through an event horizon is analysed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.
Fermion tunneling beyond semiclassical approximation
Majhi, Bibhas Ranjan
2009-02-01
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in R. Banerjee and B. R. Majhi, J. High Energy Phys.JHEPFG1029-8479 06 (2008) 09510.1088/1126-6708/2008/06/095 for the scalar particle, Hawking radiation as tunneling of the Dirac particle through an event horizon is analyzed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.
The distorted wave Glauber approximation
International Nuclear Information System (INIS)
A solution of the Pauli equation with non-zero potentials defines quantum scalar and vector potentials and magnetic fields and quantum trajectories. If a line integral of perturbing potentials and fields along these quantum trajectories is added to the phase of this solution, an approximate solution of the perturbed equation is found. Glauber theory is a special case and the conditions of applicability are similar. Applications given start from the harmonic oscillator and from a homogeneous magnetic field and add a perturbation. (author)
Approximation of Surfaces by Cylinders
DEFF Research Database (Denmark)
Randrup, Thomas
1998-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points...
Wavelet Approximation in Data Assimilation
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.
Locally Orderless Registration Code
DEFF Research Database (Denmark)
2012-01-01
This is code for the TPAMI paper "Locally Orderless Registration". The code requires intel threadding building blocks installed and is provided for 64 bit on mac, linux and windows.......This is code for the TPAMI paper "Locally Orderless Registration". The code requires intel threadding building blocks installed and is provided for 64 bit on mac, linux and windows....
Approximation Error Based Suitable Domain Search for Fractal Image Compression
Directory of Open Access Journals (Sweden)
Vijayshri Chaurasia
2010-02-01
Full Text Available Fractal Image compression is a very advantageous technique in the field of image compression. The coding phase of this technique is very time consuming because of computational expenses of suitable domain search. In this paper we have proposed an approximation error based speed-up technique with the use of feature extraction. Proposed scheme reduces the number of range-domain comparisons with significant amount and gives improved time performance.
Analytical approximations to the spectra of quark-antiquark potentials
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); De Pace, Arturo [Istituto Nazionale di Fisica Nucleare, Sezione di Torino, via Giuria 1, I-10125 Turin (Italy); Lopez, Jorge [Physics Department, University of Texas at El Paso, El Paso, TX (United States)
2006-07-15
A method recently devised to obtain analytical approximations to certain classes of integrals is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of our results is verified by comparing them both with the literature on the subject and with the numerical results obtained with a Fortran code. As an application of the method that we propose, we consider meson spectroscopy with various phenomenological potentials.
Users' guide to CACECO containment analysis code. [LMFBR
Energy Technology Data Exchange (ETDEWEB)
Peak, R.D.
1979-06-01
The CACECO containment analysis code was developed to predict the thermodynamic responses of LMFBR containment facilities to a variety of accidents. The code is included in the National Energy Software Center Library at Argonne National Laboratory as Program No. 762. This users' guide describes the CACECO code and its data input requirements. The code description covers the many mathematical models used and the approximations used in their solution. The descriptions are detailed to the extent that the user can modify the code to suit his unique needs, and, indeed, the reader is urged to consider code modification acceptable.
Simple approximations for condensational growth
Energy Technology Data Exchange (ETDEWEB)
Kostinski, A B [Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1200 (United States)], E-mail: alex.kostinski@mtu.edu
2009-01-15
A simple geometric argument relating to the liquid water content of clouds is given. The phase relaxation time and the nature of the quasi-steady approximation for the diffusional growth of cloud drops are elucidated directly in terms of water vapor concentration. Spatial gradients of vapor concentration, inherent in the notion of quasi-steady growth, are discussed and we argue for an occasional reversal of the traditional point of view: rather than a drop growing in response to a given supersaturation, the observed values of the supersaturation in clouds are the result of a vapor field adjusting to droplet growth. Our perspective is illustrated by comparing the exponential decay of condensation trails with a quasi-steady regime of cirrus clouds. The role of aerosol loading in decreasing relaxation times and increasing the rate of growth of the liquid water content is also discussed.
Strong shock implosion, approximate solution
Fujimoto, Y.; Mishkin, E. A.; Alejaldre, C.
1983-01-01
The self-similar, center-bound motion of a strong spherical, or cylindrical, shock wave moving through an ideal gas with a constant, γ= cp/ cv, is considered and a linearized, approximate solution is derived. An X, Y phase plane of the self-similar solution is defined and the representative curved of the system behind the shock front is replaced by a straight line connecting the mappings of the shock front with that of its tail. The reduced pressure P(ξ), density R(ξ) and velocity U1(ξ) are found in closed, quite accurate, form. Comparison with numerically obtained results, for γ= {5}/{3} and γ= {7}/{5}, is shown.
Diophantine approximations and Diophantine equations
Schmidt, Wolfgang M
1991-01-01
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
Stochastic Approximation with Averaging Innovation
Laruelle, Sophie
2010-01-01
The aim of the paper is to establish a convergence theorem for multi-dimensional stochastic approximation in a setting with innovations satisfying some averaging properties and to study some applications. The averaging assumptions allow us to unify the framework where the innovations are generated (to solve problems from Numerical Probability) and the one with exogenous innovations (market data, output of "device" $e.g.$ an Euler scheme) with stationary or ergodic properties. We propose several fields of applications with random innovations or quasi-random numbers. In particular we provide in both setting a rule to tune the step of the algorithm. At last we illustrate our results on five examples notably in Finance.
Benchmarking Declarative Approximate Selection Predicates
Hassanzadeh, Oktie
2009-01-01
Declarative data quality has been an active research topic. The fundamental principle behind a declarative approach to data quality is the use of declarative statements to realize data quality primitives on top of any relational data source. A primary advantage of such an approach is the ease of use and integration with existing applications. Several similarity predicates have been proposed in the past for common quality primitives (approximate selections, joins, etc.) and have been fully expressed using declarative SQL statements. In this thesis, new similarity predicates are proposed along with their declarative realization, based on notions of probabilistic information retrieval. Then, full declarative specifications of previously proposed similarity predicates in the literature are presented, grouped into classes according to their primary characteristics. Finally, a thorough performance and accuracy study comparing a large number of similarity predicates for data cleaning operations is performed.
Approximating metal-insulator transitions
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.
Crompton, Helen; LaFrance, Jason; van 't Hooft, Mark
2012-01-01
A QR (quick-response) code is a two-dimensional scannable code, similar in function to a traditional bar code that one might find on a product at the supermarket. The main difference between the two is that, while a traditional bar code can hold a maximum of only 20 digits, a QR code can hold up to 7,089 characters, so it can contain much more…
Markkanen, Markku
2007-01-01
This work introduces a method for constructing polyphase alternating codes in which the length of a code transmission cycle can be $p^m$ or $p-1$, where $p$ is a prime number and $m$ is a positive integer. The relevant properties leading to the construction alternating codes and the algorithm for generating alternating codes is described. Examples of all practical and some not that practical polyphase code lengths are given.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Quantum error correcting codes are indispensable for quantum information processing and quantum computation.In 1995 and 1996,Shor and Steane gave first several examples of quantum codes from classical error correcting codes.The construction of efficient quantum codes is now an active multi-discipline research field.In this paper we review the known several constructions of quantum codes and present some examples.
The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego; Lesgourgues, Julien [Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland); Tram, Thomas, E-mail: diego.blas@epfl.ch, E-mail: julien.lesgourgues@cern.ch, E-mail: tram@phys.au.dk [CERN, Theory Division, CH-1211 Geneva 23 (Switzerland)
2011-07-01
Boltzmann codes are used extensively by several groups for constraining cosmological parameters with Cosmic Microwave Background and Large Scale Structure data. This activity is computationally expensive, since a typical project requires from 10{sup 4} to 10{sup 5} Boltzmann code executions. The newly released code CLASS (Cosmic Linear Anisotropy Solving System) incorporates improved approximation schemes leading to a simultaneous gain in speed and precision. We describe here the three approximations used by CLASS for basic ΛCDM models, namely: a baryon-photon tight-coupling approximation which can be set to first order, second order or to a compromise between the two; an ultra-relativistic fluid approximation which had not been implemented in public distributions before; and finally a radiation streaming approximation taking reionisation into account.
Turbo Codes Extended with Outer BCH Code
DEFF Research Database (Denmark)
Andersen, Jakob Dahl
1996-01-01
The "error floor" observed in several simulations with the turbo codes is verified by calculation of an upper bound to the bit error rate for the ensemble of all interleavers. Also an easy way to calculate the weight enumerator used in this bound is presented. An extended coding scheme is proposed...
A Fast Fractal Image Compression Coding Method
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Fast algorithms for reducing encoding complexity of fractal image coding have recently been an important research topic. Search of the best matched domain block is the most computation intensive part of the fractal encoding process. In this paper, a fast fractal approximation coding scheme implemented on a personal computer based on matching in range block's neighbours is presented. Experimental results show that the proposed algorithm is very simple in implementation, fast in encoding time and high in compression ratio while PSNR is almost the same as compared with Barnsley's fractal block coding .
Rains, E M
1997-01-01
We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional global symmetries. From this standpoint, the analogues of Calderbank-Shor-Steane codes and of GF(4)-linear codes turn out to be special cases of the same construction. This allows us to construct families of quantum codes from certain codes over number fields; in particular, we get analogues of quadratic residue codes, including a single-error correcting code encoding one letter in five, for any alphabet size. We also consider the problem of fault-tolerant computation through such codes, generalizing ideas of Gottesman.
Rateless Coding for MIMO Block Fading Channels
Fan, Yijia; Erkip, Elza; Poor, H Vincent
2008-01-01
In this paper the performance limits and design principles of rateless codes over fading channels are studied. The diversity-multiplexing tradeoff (DMT) is used to analyze the system performance for all possible transmission rates. It is revealed from the analysis that the design of such rateless codes follows the design principle of approximately universal codes for parallel multiple-input multiple-output (MIMO) channels, in which each sub-channel is a MIMO channel. More specifically, it is shown that for a single-input single-output (SISO) channel, the previously developed permutation codes of unit length for parallel channels having rate LR can be transformed directly into rateless codes of length L having multiple rate levels (R, 2R, . . ., LR), to achieve the DMT performance limit.
Topological Code Architectures for Quantum Computation
Cesare, Christopher Anthony
This dissertation is concerned with quantum computation using many-body quantum systems encoded in topological codes. The interest in these topological systems has increased in recent years as devices in the lab begin to reach the fidelities required for performing arbitrarily long quantum algorithms. The most well-studied system, Kitaev's toric code, provides both a physical substrate for performing universal fault-tolerant quantum computations and a useful pedagogical tool for explaining the way other topological codes work. In this dissertation, I first review the necessary formalism for quantum information and quantum stabilizer codes, and then I introduce two families of topological codes: Kitaev's toric code and Bombin's color codes. I then present three chapters of original work. First, I explore the distinctness of encoding schemes in the color codes. Second, I introduce a model of quantum computation based on the toric code that uses adiabatic interpolations between static Hamiltonians with gaps constant in the system size. Lastly, I describe novel state distillation protocols that are naturally suited for topological architectures and show that they provide resource savings in terms of the number of required ancilla states when compared to more traditional approaches to quantum gate approximation.
Multidimensional stochastic approximation Monte Carlo.
Zablotskiy, Sergey V; Ivanov, Victor A; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g(E), of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g(E_{1},E_{2}). We show when and why care has to be exercised when obtaining the microcanonical density of states g(E_{1}+E_{2}) from g(E_{1},E_{2}). PMID:27415383
Randomized approximate nearest neighbors algorithm.
Jones, Peter Wilcox; Osipov, Andrei; Rokhlin, Vladimir
2011-09-20
We present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {x(j)} in R(d), the algorithm attempts to find k nearest neighbors for each of x(j), where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T·N·(d·(log d) + k·(d + log k)·(log N)) + N·k(2)·(d + log k), with T the number of iterations performed. The memory requirements of the procedure are of the order N·(d + k). A by-product of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among {x(j)} for an arbitrary point x ∈ R(d). The cost of each such query is proportional to T·(d·(log d) + log(N/k)·k·(d + log k)), and the memory requirements for the requisite data structure are of the order N·(d + k) + T·(d + N). The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme's behavior for certain types of distributions of {x(j)} and illustrate its performance via several numerical examples.
M. Markkanen; Vierinen, J.; Markkanen, J.
2007-01-01
We present a new class of alternating codes. Instead of the customary binary phase codes, the new codes utilize either p or p–1 phases, where p is a prime number. The first class of codes has code length p^{m}, where m is a positive integer, the second class has code length p–1. We give an actual construction algorithm, and explain the principles behind it. We ...
Network coding for computing: Linear codes
Appuswamy, Rathinakumar; Karamchandani, Nikhil; Zeger, Kenneth
2011-01-01
In network coding it is known that linear codes are sufficient to achieve the coding capacity in multicast networks and that they are not sufficient in general to achieve the coding capacity in non-multicast networks. In network computing, Rai, Dey, and Shenvi have recently shown that linear codes are not sufficient in general for solvability of multi-receiver networks with scalar linear target functions. We study single receiver networks where the receiver node demands a target function of the source messages. We show that linear codes may provide a computing capacity advantage over routing only when the receiver demands a `linearly-reducible' target function. % Many known target functions including the arithmetic sum, minimum, and maximum are not linearly-reducible. Thus, the use of non-linear codes is essential in order to obtain a computing capacity advantage over routing if the receiver demands a target function that is not linearly-reducible. We also show that if a target function is linearly-reducible,...
Construction of Codes for Network Coding
Elsenhans, Andreas-Stephan; Wassermann, Alfred
2010-01-01
Based on ideas of K\\"otter and Kschischang we use constant dimension subspaces as codewords in a network. We show a connection to the theory of q-analogues of a combinatorial designs, which has been studied in Braun, Kerber and Laue as a purely combinatorial object. For the construction of network codes we successfully modified methods (construction with prescribed automorphisms) originally developed for the q-analogues of a combinatorial designs. We then give a special case of that method which allows the construction of network codes with a very large ambient space and we also show how to decode such codes with a very small number of operations.
National Oceanic and Atmospheric Administration, Department of Commerce — Coded items are entered in the tiponline data entry program. The codes and their explanations are necessary in order to use the data
International Nuclear Information System (INIS)
This user's manual contains all the necessary information concerning the use of SEVERO code. This computer code is related to the statistics of extremes = extreme winds, extreme precipitation and flooding hazard risk analysis. (A.C.A.S.)
Fuzzy Set Approximations in Fuzzy Formal Contexts
Institute of Scientific and Technical Information of China (English)
Mingwen Shao; Shiqing Fan
2006-01-01
In this paper, a kind of multi-level formal concept is introduced. Based on the proposed multi-level formal concept, we present a pair of rough fuzzy set approximations within fuzzy formal contexts. By the proposed rough fuzzy set approximations, we can approximate a fuzzy set according to different precision level. We discuss the properties of the proposed approximation operators in detail.
Obtaining exact value by approximate computations
Institute of Scientific and Technical Information of China (English)
2007-01-01
Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.
Kubica, Aleksander; Yoshida, Beni; Pastawski, Fernando
2015-01-01
The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation. Here we show that the color code on a $d$-dimensional closed manifold is equivalent to multiple decoupled copies of the $d$-dimensional toric code up to local unitary transformations and adding or removing ancilla qubits. Our result not only generalizes the proven equivalence for $d=2$, but also provides an explicit recipe of how to decouple independent components of the ...
DEFF Research Database (Denmark)
Soon, Winnie
2014-01-01
to understand the socio-technical side of a changing network environment. Through the study of code, including but not limited to source code, technical specifications and other materials in relation to the artwork production, I would like to explore the materiality of code that goes beyond technical...
Bergstra, J. A.
2010-01-01
General definitions as well as rules of reasoning regarding control code production, distribution, deployment, and usage are described. The role of testing, trust, confidence and risk analysis is considered. A rationale for control code testing is sought and found for the case of safety critical embedded control code.
Deursen, A. van; Moonen, L.M.F.; Bergh, A. van den; Kok, G.
2001-01-01
Two key aspects of extreme programming (XP) are unit testing and merciless refactoring. Given the fact that the ideal test code / production code ratio approaches 1:1, it is not surprising that unit tests are being refactored. We found that refactoring test code is different from refactoring product
Bergstra, Jan A
2010-01-01
General definitions as well as rules of reasoning regarding control code production, distribution, deployment, and usage are described. The role of testing, trust, confidence and risk analysis is considered. A rationale for control code testing is sought and found for the case of safety critical embedded control code.
DEFF Research Database (Denmark)
Bombin Palomo, Hector
2015-01-01
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a generalized, subsystem version of color codes. In 3D they allow the...
Rapid Prototyping of Field Programmable Gate Array-Based Discrete Cosine Transform Approximations
Directory of Open Access Journals (Sweden)
Trevor W. Fox
2003-05-01
Full Text Available A method for the rapid design of field programmable gate array (FPGA-based discrete cosine transform (DCT approximations is presented that can be used to control the coding gain, mean square error (MSE, quantization noise, hardware cost, and power consumption by optimizing the coefficient values and datapath wordlengths. Previous DCT design methods can only control the quality of the DCT approximation and estimates of the hardware cost by optimizing the coefficient values. It is shown that it is possible to rapidly prototype FPGA-based DCT approximations with near optimal coding gains that satisfy the MSE, hardware cost, quantization noise, and power consumption specifications.
ARC Code TI: CODE Software Framework
National Aeronautics and Space Administration — CODE is a software framework for control and observation in distributed environments. The basic functionality of the framework allows a user to observe a...
ARC Code TI: ROC Curve Code Augmentation
National Aeronautics and Space Administration — ROC (Receiver Operating Characteristic) curve Code Augmentation was written by Rodney Martin and John Stutz at NASA Ames Research Center and is a modification of...
Universal Rateless Codes From Coupled LT Codes
Aref, Vahid
2011-01-01
It was recently shown that spatial coupling of individual low-density parity-check codes improves the belief-propagation threshold of the coupled ensemble essentially to the maximum a posteriori threshold of the underlying ensemble. We study the performance of spatially coupled low-density generator-matrix ensembles when used for transmission over binary-input memoryless output-symmetric channels. We show by means of density evolution that the threshold saturation phenomenon also takes place in this setting. Our motivation for studying low-density generator-matrix codes is that they can easily be converted into rateless codes. Although there are already several classes of excellent rateless codes known to date, rateless codes constructed via spatial coupling might offer some additional advantages. In particular, by the very nature of the threshold phenomenon one expects that codes constructed on this principle can be made to be universal, i.e., a single construction can uniformly approach capacity over the cl...
Spike Code Flow in Cultured Neuronal Networks.
Tamura, Shinichi; Nishitani, Yoshi; Hosokawa, Chie; Miyoshi, Tomomitsu; Sawai, Hajime; Kamimura, Takuya; Yagi, Yasushi; Mizuno-Matsumoto, Yuko; Chen, Yen-Wei
2016-01-01
We observed spike trains produced by one-shot electrical stimulation with 8 × 8 multielectrodes in cultured neuronal networks. Each electrode accepted spikes from several neurons. We extracted the short codes from spike trains and obtained a code spectrum with a nominal time accuracy of 1%. We then constructed code flow maps as movies of the electrode array to observe the code flow of "1101" and "1011," which are typical pseudorandom sequence such as that we often encountered in a literature and our experiments. They seemed to flow from one electrode to the neighboring one and maintained their shape to some extent. To quantify the flow, we calculated the "maximum cross-correlations" among neighboring electrodes, to find the direction of maximum flow of the codes with lengths less than 8. Normalized maximum cross-correlations were almost constant irrespective of code. Furthermore, if the spike trains were shuffled in interval orders or in electrodes, they became significantly small. Thus, the analysis suggested that local codes of approximately constant shape propagated and conveyed information across the network. Hence, the codes can serve as visible and trackable marks of propagating spike waves as well as evaluating information flow in the neuronal network.
Institute of Scientific and Technical Information of China (English)
XIONG ChengYi; TIAN JinWen; LIU Jian
2008-01-01
This paper introduced a novel high performance algorithm and VLSI architectures for achieving bit plane coding (BPC) in word level sequential and parallel mode. The proposed BPC algorithm adopts the techniques of coding pass prediction and par-allel & pipeline to reduce the number of accessing memory and to increase the ability of concurrently processing of the system, where all the coefficient bits of a code block could be coded by only one scan. A new parallel bit plane architecture (PA) was proposed to achieve word-level sequential coding. Moreover, an efficient high-speed architecture (HA) was presented to achieve multi-word parallel coding. Compared to the state of the art, the proposed PA could reduce the hardware cost more efficiently, though the throughput retains one coefficient coded per clock. While the proposed HA could perform coding for 4 coefficients belonging to a stripe column at one intra-clock cycle, so that coding for an N×N code-block could be completed in approximate N2/4 intra-clock cycles. Theoretical analysis and ex-perimental results demonstrate that the proposed designs have high throughput rate with good performance in terms of speedup to cost, which can be good alter-natives for low power applications.
Boulagouaz, M.; Leroy, A
2013-01-01
In this paper we introduce the notion of cyclic ($f(t),\\sigma,\\delta$)-codes for $f(t)\\in \\Ore$. These codes generalize the $\\theta$-codes as introduced by D. Boucher, F. Ulmer, W. Geiselmann \\cite{BGU}. We construct generic and control matrices for these codes. As a particular case the ($\\si,\\de$)-$W$-code associated to a Wedderburn polynomial are defined and we show that their control matrices are given by generalized Vandermonde matrices. All the Wedderburn polynomials of $\\mathbb F_q[t;\\t...
Benchmark study between FIDAP and a cellular automata code
Akau, R. L.; Stockman, H. W.
A fluid flow benchmark exercise was conducted to compare results between a cellular automata code and FIDAP. Cellular automata codes are free from gridding constraints, and are generally used to model slow (Reynolds number approximately 1) flows around complex solid obstacles. However, the accuracy of cellular automata codes at higher Reynolds numbers, where inertial terms are significant, is not well-documented. In order to validate the cellular automata code, two fluids problems were investigated. For both problems, flow was assumed to be laminar, two-dimensional, isothermal, incompressible and periodic. Results showed that the cellular automata code simulated the overall behavior of the flow field.
Testing algebraic geometric codes
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Property testing was initially studied from various motivations in 1990’s. A code C GF (r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector’s coordinates. The problem of testing codes was firstly studied by Blum, Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs). How to characterize locally testable codes is a complex and challenge problem. The local tests have been studied for Reed-Solomon (RS), Reed-Muller (RM), cyclic, dual of BCH and the trace subcode of algebraicgeometric codes. In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions). We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
Lim, Sung Hoon; Gamal, Abbas El; Chung, Sae-Young
2010-01-01
A noisy network coding scheme for sending multiple sources over a general noisy network is presented. For multi-source multicast networks, the scheme naturally extends both network coding over noiseless networks by Ahlswede, Cai, Li, and Yeung, and compress-forward coding for the relay channel by Cover and El Gamal to general discrete memoryless and Gaussian networks. The scheme also recovers as special cases the results on coding for wireless relay networks and deterministic networks by Avestimehr, Diggavi, and Tse, and coding for wireless erasure networks by Dana, Gowaikar, Palanki, Hassibi, and Effros. The scheme involves message repetition coding, relay signal compression, and simultaneous decoding. Unlike previous compress--forward schemes, where independent messages are sent over multiple blocks, the same message is sent multiple times using independent codebooks as in the network coding scheme for cyclic networks. Furthermore, the relays do not use Wyner--Ziv binning as in previous compress-forward sch...
Testing algebraic geometric codes
Institute of Scientific and Technical Information of China (English)
CHEN Hao
2009-01-01
Property testing was initially studied from various motivations in 1990's.A code C (∩)GF(r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector's coordinates.The problem of testing codes was firstly studied by Blum,Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs).How to characterize locally testable codes is a complex and challenge problem.The local tests have been studied for Reed-Solomon (RS),Reed-Muller (RM),cyclic,dual of BCH and the trace subcode of algebraicgeometric codes.In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions).We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
Institute of Scientific and Technical Information of China (English)
ZHANG Aili; LIU Xiufeng
2006-01-01
Chinese remainder codes are constructed by applying weak block designs and the Chinese remainder theorem of ring theory.The new type of linear codes take the congruence class in the congruence class ring R/I1 ∩ I2 ∩…∩ In for the information bit,embed R/Ji into R/I1 ∩ I2 ∩…∩ In,and assign the cosets of R/Ji as the subring of R/I1 ∩ I2 ∩…∩ In and the cosets of R/Ji in R/I1 ∩ I2 ∩…∩ In as check lines.Many code classes exist in the Chinese remainder codes that have high code rates.Chinese remainder codes are the essential generalization of Sun Zi codes.
Institute of Scientific and Technical Information of China (English)
张爱丽; 刘秀峰; 靳蕃
2004-01-01
Chinese Remainder Codes are constructed by applying weak block designs and Chinese Remainder Theorem of ring theory. The new type of linear codes take the congruence class in the congruence class ring R/I1∩I2∩…∩In for the information bit, embed R/Ji into R/I1∩I2∩…∩In, and asssign the cosets of R/Ji as the subring of R/I1∩I2∩…∩In and the cosets of R/Ji in R/I1∩I2∩…∩In as check lines. There exist many code classes in Chinese Remainder Codes, which have high code rates. Chinese Remainder Codes are the essential generalization of Sun Zi Codes.
Benchmarking the starting points of the GW approximation for molecules
International Nuclear Information System (INIS)
The GW approximation is nowadays being used to obtain accurate quasiparticle energies of atoms and molecules. In practice, the GW approximation is generally evaluated perturbatively, based on a prior self-consistent calculation within a simpler approximation. The final result thus depends on the choice of the self-consistent mean-field chosen as a starting point. Using a recently developed GW code based on Gaussian basis functions, we benchmark a wide range of starting points for perturbative GW, including Hartree-Fock, LDA, PBE, PBE0, B3LYP, HSE06, BH and HLYP, CAM-B3LYP, and tuned CAM-B3LYP. In the evaluation of the ionization energy, the hybrid functionals are clearly superior results starting points when compared to Hartree-Fock, to LDA, or to the semi local approximations. Furthermore, among the hybrid functionals, the ones with the highest proportion of exact-exchange usually perform best. Finally, the reliability of the frozen-core approximation, that allows for a considerable speedup of the calculations, is demonstrated. (authors)
APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION
Institute of Scientific and Technical Information of China (English)
杨守志; 程正兴; 唐远炎
2003-01-01
An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function.
Logical error rate in the Pauli twirling approximation.
Katabarwa, Amara; Geller, Michael R
2015-09-30
The performance of error correction protocols are necessary for understanding the operation of potential quantum computers, but this requires physical error models that can be simulated efficiently with classical computers. The Gottesmann-Knill theorem guarantees a class of such error models. Of these, one of the simplest is the Pauli twirling approximation (PTA), which is obtained by twirling an arbitrary completely positive error channel over the Pauli basis, resulting in a Pauli channel. In this work, we test the PTA's accuracy at predicting the logical error rate by simulating the 5-qubit code using a 9-qubit circuit with realistic decoherence and unitary gate errors. We find evidence for good agreement with exact simulation, with the PTA overestimating the logical error rate by a factor of 2 to 3. Our results suggest that the PTA is a reliable predictor of the logical error rate, at least for low-distance codes.
Reduction of Linear Programming to Linear Approximation
Vaserstein, Leonid N.
2006-01-01
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
Legendre rational approximation on the whole line
Institute of Scientific and Technical Information of China (English)
GUO; Benyu; WANG; Zhongqing
2004-01-01
The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numerical results show the efficiency of this new approach.
Validation of TNXY code with reference problems
International Nuclear Information System (INIS)
In this paper, the validation process for TNXY code, as well as the rference problems used in the same (Wagner and Benchmark 14 problems) are described. TNXY code is based on a polynomial type nodal method known as RTN-0. Several numerical results obtained with such code and others frequently illustrated in the literature related with numerical calculus for nuclear reactors are presented. Tests were done with different size meshes and different SN approximations. Several conclusions based on comparisons among different results obtained, as well as the present state of the already mentioned code and its almost inmediate applications to fuel assemblies as the used in the nuclear reactor of Laguna Verde are given. (Author)
An approximation technique for jet impingement flow
Energy Technology Data Exchange (ETDEWEB)
Najafi, Mahmoud; Fincher, Donald [Kent State University Ashtabula Department of Mathematical Sciences (United States); Rahni, Taeibi; Javadi, KH. [Department of Aerospace Engineering, Sharif University of Technology (Iran, Islamic Republic of); Massah, H. [Acoustic Research Center, Institute of Applied Physics (Iran, Islamic Republic of)
2015-03-10
The analytical approximate solution of a non-linear jet impingement flow model will be demonstrated. We will show that this is an improvement over the series approximation obtained via the Adomian decomposition method, which is itself, a powerful method for analysing non-linear differential equations. The results of these approximations will be compared to the Runge-Kutta approximation in order to demonstrate their validity.
Diophantine approximation and special Liouville numbers
Schleischitz, Johannes
2013-01-01
This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers $\\zeta_{1},\\zeta_{2},...,\\zeta_{k}$. The approach relies on results on the connection between the set of all $s$-adic expansions ($s\\geq 2$) of $\\zeta_{1},\\zeta_{2},...,\\zeta_{k}$ and their associated approximation constants. As an application, explicit construction of real numbers $\\zeta_{1},\\zeta_{2},...,\\zeta_{k}$ with prescribed approximation properties are dedu...
Nonlinear approximation with bi-framelets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten; Gribonval, Rémi
2005-01-01
We study the approximation in Lebesgue spaces of wavelet bi-frame systems given by translations and dilations of a finite set of generators. A complete characterization of the approximation spaces associated with best m-term approximation of wavelet bi-framelet systems is given. The characterizat...
Some relations between entropy and approximation numbers
Institute of Scientific and Technical Information of China (English)
郑志明
1999-01-01
A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.
Axiomatic Characterizations of IVF Rough Approximation Operators
Directory of Open Access Journals (Sweden)
Guangji Yu
2014-01-01
Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
Benyin Fu
2016-05-01
In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use the techniques of Ozawa’s to prove that a fine hyperbolic graph has the metric invariant translation approximation property.
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
$-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space...
Approximate Nearest Neighbor Queries among Parallel Segments
DEFF Research Database (Denmark)
Emiris, Ioannis Z.; Malamatos, Theocharis; Tsigaridas, Elias
2010-01-01
We develop a data structure for answering efficiently approximate nearest neighbor queries over a set of parallel segments in three dimensions. We connect this problem to approximate nearest neighbor searching under weight constraints and approximate nearest neighbor searching on historical data...
Truth Approximation, Social Epistemology, and Opinion Dynamics
Douven, Igor; Kelp, Christoph
2011-01-01
This paper highlights some connections between work on truth approximation and work in social epistemology, in particular work on peer disagreement. In some of the literature on truth approximation, questions have been addressed concerning the efficiency of research strategies for approximating the
Upper Bounds on Numerical Approximation Errors
DEFF Research Database (Denmark)
Raahauge, Peter
2004-01-01
This paper suggests a method for determining rigorous upper bounds on approximationerrors of numerical solutions to infinite horizon dynamic programming models.Bounds are provided for approximations of the value function and the policyfunction as well as the derivatives of the value function...... to approximations of a standard (strictly concave)growth model.KEYWORDS: Numerical approximation errors, Bellman contractions, Error bounds...
Casting Polymer Nets to Optimize Noisy Molecular Codes
Tlusty, Tsvi
2010-01-01
Life relies on the efficient performance of molecular codes, which relate symbols and meanings via error-prone molecular recognition. We describe how optimizing a code to withstand the impact of molecular recognition noise may be approximated by the statistics of a two-dimensional network made of polymers. The noisy code is defined by partitioning the space of symbols into regions according to their meanings. The "polymers" are the boundaries between these regions and their statistics defines...
Relativistic quasiparticle random phase approximation in deformed nuclei
Energy Technology Data Exchange (ETDEWEB)
Pena Arteaga, D.
2007-06-25
Covariant density functional theory is used to study the influence of electromagnetic radiation on deformed superfluid nuclei. The relativistic Hartree-Bogolyubov equations and the resulting diagonalization problem of the quasiparticle random phase approximation are solved for axially symmetric systems in a fully self-consistent way by a newly developed parallel code. Three different kinds of high precision energy functionals are investigated and special care is taken for the decoupling of the Goldstone modes. This allows the microscopic investigation of Pygmy and scissor resonances in electric and magnetic dipole fields. Excellent agreement with recent experiments is found and new types of modes are predicted for deformed systems with large neutron excess. (orig.)
Approximate Schur complement preconditioning of the lowest order nodal discretizations
Energy Technology Data Exchange (ETDEWEB)
Moulton, J.D.; Ascher, U.M. [Univ. of British Columbia, Vancouver, British Columbia (Canada); Morel, J.E. [Los Alamos National Lab., NM (United States)
1996-12-31
Particular classes of nodal methods and mixed hybrid finite element methods lead to equivalent, robust and accurate discretizations of 2nd order elliptic PDEs. However, widespread popularity of these discretizations has been hindered by the awkward linear systems which result. The present work exploits this awkwardness, which provides a natural partitioning of the linear system, by defining two optimal preconditioners based on approximate Schur complements. Central to the optimal performance of these preconditioners is their sparsity structure which is compatible with Dendy`s black box multigrid code.
Modified approximate 8-point multiplier less DCT like transform
Directory of Open Access Journals (Sweden)
Siddharth Pande
2015-05-01
Full Text Available Discrete Cosine Transform (DCT is widely usedtransformation for compression in image and video standardslike H.264 or MPEGv4, JPEG etc. Currently the new standarddeveloped Codec is Highly Efficient Video Coding (HEVC orH.265. With the help of the transformation matrix the computational cost can be dynamically reduce. This paper proposesa novel approach of multiplier-less modified approximate DCT like transformalgorithm and also comparison with exact DCT algorithm and theapproximate DCT like transform. This proposed algorithm willhave lower computational complexity. Furthermore, the proposedalgorithm will be modular in approach, and suitable for pipelinedVLSI implementation.
DEFF Research Database (Denmark)
Steensig, Jakob; Heinemann, Trine
2015-01-01
doing formal coding and when doing more “traditional” conversation analysis research based on collections. We are more wary, however, of the implication that coding-based research is the end result of a process that starts with qualitative investigations and ends with categories that can be coded....... Instead we propose that the promise of coding-based research lies in its ability to open up new qualitative questions.......We welcome Tanya Stivers’s discussion (Stivers, 2015/this issue) of coding social interaction and find that her descriptions of the processes of coding open up important avenues for discussion, among other things of the precise ad hoc considerations that researchers need to bear in mind, both when...
Yu, Jiun-Hung
2012-01-01
Polynomial remainder codes are a large class of codes derived from the Chinese remainder theorem that includes Reed-Solomon codes as a special case. In this paper, we revisit these codes and study them more carefully than in previous work. We explicitly allow the code symbols to be polynomials of different degrees, which leads to two different notions of weight and distance. Algebraic decoding is studied in detail. If the moduli are not irreducible, the notion of an error locator polynomial is replaced by an error factor polynomial. We then obtain a collection of gcd-based decoding algorithms, some of which are not quite standard even when specialized to Reed-Solomon codes.
DEFF Research Database (Denmark)
Andersen, Christian Ulrik
2007-01-01
avant-garde’. In line with Cramer, the artists Alex McLean and Adrian Ward (aka Slub) declare: “art-oriented programming needs to acknowledge the conditions of its own making – its poesis.” By analysing the Live Coding performances of Slub (where they program computer music live), the presentation......Computer art is often associated with computer-generated expressions (digitally manipulated audio/images in music, video, stage design, media facades, etc.). In recent computer art, however, the code-text itself – not the generated output – has become the artwork (Perl Poetry, ASCII Art, obfuscated...... code, etc.). The presentation relates this artistic fascination of code to a media critique expressed by Florian Cramer, claiming that the graphical interface represents a media separation (of text/code and image) causing alienation to the computer’s materiality. Cramer is thus the voice of a new ‘code...
Generating code adapted for interlinking legacy scalar code and extended vector code
Gschwind, Michael K
2013-06-04
Mechanisms for intermixing code are provided. Source code is received for compilation using an extended Application Binary Interface (ABI) that extends a legacy ABI and uses a different register configuration than the legacy ABI. First compiled code is generated based on the source code, the first compiled code comprising code for accommodating the difference in register configurations used by the extended ABI and the legacy ABI. The first compiled code and second compiled code are intermixed to generate intermixed code, the second compiled code being compiled code that uses the legacy ABI. The intermixed code comprises at least one call instruction that is one of a call from the first compiled code to the second compiled code or a call from the second compiled code to the first compiled code. The code for accommodating the difference in register configurations is associated with the at least one call instruction.
Kapsalis, Ioannis
2013-01-01
The 2-dimensional barcodes known as QR (Quick Response) Codesare increasing their popularity as they appear in more places in theurban environment. QR Codes can be considered as physical hyper-linksthat give the ability to users to access, through their mobile devicesthat are able to scan QR Codes, additional information located in aweb-page. Apart from marketing, QR Codes have been also adopted indifferent areas such as the on-line payments. This development alongwith the trend that some of ...
Practices in Code Discoverability
Teuben, Peter; Allen, Alice; Nemiroff, Robert J.; Shamir, Lior
2012-01-01
Much of scientific progress now hinges on the reliability, falsifiability and reproducibility of computer source codes. Astrophysics in particular is a discipline that today leads other sciences in making useful scientific components freely available online, including data, abstracts, preprints, and fully published papers, yet even today many astrophysics source codes remain hidden from public view. We review the importance and history of source codes in astrophysics and previous efforts to d...
Energy Technology Data Exchange (ETDEWEB)
Visser, B. [Stork Product Eng., Amsterdam (Netherlands)
1996-09-01
To support the discussion on aeroelastic codes, a description of the code FLEXLAST was given and experiences within benchmarks and measurement programmes were summarized. The code FLEXLAST has been developed since 1982 at Stork Product Engineering (SPE). Since 1992 FLEXLAST has been used by Dutch industries for wind turbine and rotor design. Based on the comparison with measurements, it can be concluded that the main shortcomings of wind turbine modelling lie in the field of aerodynamics, wind field and wake modelling. (au)
Kopilovic, Ivan; Saupe, Dietmar; Hamzaoui, Raouf
2001-01-01
Progressive coding is an important feature of compression schemes. Wavelet coders are well suited for this purpose because the wavelet coefficients can be naturally ordered according to decreasing importance. Progressive fractal coding is feasible, but it was proposed only for hybrid fractal-wavelet schemes. We introduce a progressive fractal image coder in the spatial domain. A Lagrange optimization based on rate-distortion performance estimates determines an optimal ordering of the code bit...
Polygonal Approximation of Contour Shapes Using Corner Detectors
Directory of Open Access Journals (Sweden)
Hermilo Sánchez‐Cruz
2009-12-01
Full Text Available A great amount of corner detectors that appear in literature are based on using the Freeman chain code of eight directions,which is used to represent contour shapes. We propose a new method for corner detection based on a three‐symbol chain coderepresentation, which requires lower storage memory and an easy way to obtain shape corners. We compare it with fiveexisting methods, which are well known in the literature, giving our method a better performance. Furthermore, in order toreconstruct the original shapes through polygonal approximations, we propose an error parameter to quantify the efficiency.This can be accomplished by considering the redundancy of points produced when looking for corners and when computing thedifference between the original region and the approximated polygon.
APPROXIMATE AMENABILITY OF CERTAIN INVERSE SEMIGROUP ALGEBRAS
Institute of Scientific and Technical Information of China (English)
Mehdi ROSTAMI; Abdolrasoul POURABBAS; Morteza ESSMAILI
2013-01-01
In this article,the approximate amenability of semigroup algebra e1(S) is investigated,where S is a uniformly locally finite inverse semigroup.Indeed,we show that for a uniformly locally finite inverse semigroup S,the notions of amenability,approximate amenability and bounded approximate amenability of e1 (S) are equivalent.We use this to give a direct proof of the approximate amenability of e1(S) for a Brandt semigroup S.Moreover,we characterize the approximate amenability of e1(S),where S is a uniformly locally finite band semigroup.
International Nuclear Information System (INIS)
The FEDC Tokamak Systems Code calculates tokamak performance, cost, and configuration as a function of plasma engineering parameters. This version of the code models experimental tokamaks. It does not currently consider tokamak configurations that generate electrical power or incorporate breeding blankets. The code has a modular (or subroutine) structure to allow independent modeling for each major tokamak component or system. A primary benefit of modularization is that a component module may be updated without disturbing the remainder of the systems code as long as the imput to or output from the module remains unchanged
Waters, Joe
2012-01-01
Find out how to effectively create, use, and track QR codes QR (Quick Response) codes are popping up everywhere, and businesses are reaping the rewards. Get in on the action with the no-nonsense advice in this streamlined, portable guide. You'll find out how to get started, plan your strategy, and actually create the codes. Then you'll learn to link codes to mobile-friendly content, track your results, and develop ways to give your customers value that will keep them coming back. It's all presented in the straightforward style you've come to know and love, with a dash of humor thrown
National Aeronautics and Space Administration — ACCEPT consists of an overall software infrastructure framework and two main software components. The software infrastructure framework consists of code written to...
Mapping moveout approximations in TI media
Stovas, Alexey
2013-11-21
Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.
On Gakerkin approximations for the quasigeostrophic equations
Rocha, Cesar B; Grooms, Ian
2015-01-01
We study the representation of approximate solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes. In particular, we show that standard modes are compatible with nonzero buoyancy at the surfaces and can be used to solve the Eady problem. We extend two existing Galerkin approaches (A and B) and develop a new Galerkin approximation (C). Approximation A, due to Flierl (1978), represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith (2009b), represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series, but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the b...
Research on universal combinatorial coding.
Lu, Jun; Zhang, Zhuo; Mo, Juan
2014-01-01
The conception of universal combinatorial coding is proposed. Relations exist more or less in many coding methods. It means that a kind of universal coding method is objectively existent. It can be a bridge connecting many coding methods. Universal combinatorial coding is lossless and it is based on the combinatorics theory. The combinational and exhaustive property make it closely related with the existing code methods. Universal combinatorial coding does not depend on the probability statistic characteristic of information source, and it has the characteristics across three coding branches. It has analyzed the relationship between the universal combinatorial coding and the variety of coding method and has researched many applications technologies of this coding method. In addition, the efficiency of universal combinatorial coding is analyzed theoretically. The multicharacteristic and multiapplication of universal combinatorial coding are unique in the existing coding methods. Universal combinatorial coding has theoretical research and practical application value.
Nymeyer, A.; Katoen, J.P.; Westra, Y.; Alblas, H.; Gyimóthy, T.
1996-01-01
A system called BURS that is based on term rewrite systems and a search algorithm A* are combined to produce a code generator that generates optimal code. The theory underlying BURS is re-developed, formalised and explained in this work. The search algorithm uses a cost heuristic that is derived fro
Thieren, Michel; Mauron, Alex
2007-01-01
This month marks sixty years since the Nuremberg code – the basic text of modern medical ethics – was issued. The principles in this code were articulated in the context of the Nuremberg trials in 1947. We would like to use this anniversary to examine its ability to address the ethical challenges of our time.
Division for Early Childhood, Council for Exceptional Children, 2009
2009-01-01
The Code of Ethics of the Division for Early Childhood (DEC) of the Council for Exceptional Children is a public statement of principles and practice guidelines supported by the mission of DEC. The foundation of this Code is based on sound ethical reasoning related to professional practice with young children with disabilities and their families…
Million, June
2004-01-01
Most schools have a code of conduct, pledge, or behavioral standards, set by the district or school board with the school community. In this article, the author features some schools that created a new vision of instilling code of conducts to students based on work quality, respect, safety and courtesy. She suggests that communicating the code…
SC Secretariat
2004-01-01
Please note that the revised safety code A1 entitled 'MEDICAL CODE' is available on the web at the following url: https://edms.cern.ch/document/335476/last_released Paper copies can also be obtained from the SC Secretariat, e-mail : sc.secretariat@cern.ch SC Secretariat
SC Secretariat
2005-01-01
Please note that the Safety Code A12 (Code A12) entitled "THE SAFETY COMMISSION (SC)" is available on the web at the following url: https://edms.cern.ch/document/479423/LAST_RELEASED Paper copies can also be obtained from the SC Unit Secretariat, e-mail: sc.secretariat@cern.ch SC Secretariat
Computerized mega code recording.
Burt, T W; Bock, H C
1988-04-01
A system has been developed to facilitate recording of advanced cardiac life support mega code testing scenarios. By scanning a paper "keyboard" using a bar code wand attached to a portable microcomputer, the person assigned to record the scenario can easily generate an accurate, complete, timed, and typewritten record of the given situations and the obtained responses. PMID:3354937
BIALEK, W; RIEKE, F; VANSTEVENINCK, RRD; WARLAND, D
1991-01-01
Traditional approaches to neural coding characterize the encoding of known stimuli in average neural responses. Organisms face nearly the opposite task - extracting information about an unknown time-dependent stimulus from short segments of a spike train. Here the neural code was characterized from
One Twenty Phase Code Design for Radar
Directory of Open Access Journals (Sweden)
E.N.V. Purna Chandra Rao
2013-12-01
Full Text Available Sequences with good autocorrelation Properties are useful for radar and communication applications. In this paper One Twenty Phase sequences are synthesized using Modified Genetic Algorithm (MGA. MGA is used as a statistical technique for obtaining approximate solutions to combinatorial optimization problems. This algorithm combines the good methodologies of the two algorithms like global minimum converging property of Genetic Algorithm (GA and fast convergence rate of Hamming scan algorithm. The synthesized sequences have autocorrelation Properties better than well-known binary MPS code and Frank codes. The synthesized sequences also have complex signal structure which is difficult to detect and analyze by enemy electronics support measure.
RF cavity evaluation with the code SUPERFISH
International Nuclear Information System (INIS)
The computer code SUPERFISH calculates axisymmetric rf fields and is most applicable to re-entrant cavities of an Alvarez linac. Some sample results are shown for the first Alvarez's in NUMATRON project. On the other hand the code can also be effectivily applied to TE modes excited in an RFQ linac when the cavity is approximately considered as positioning at an infinite distance from the symmetry axis. The evaluation was made for several RFQ cavities, models I, II and a test linac named LITL, and useful results for the resonator design were obtained. (author)
Astrophysics Source Code Library
Allen, Alice; Berriman, Bruce; Hanisch, Robert J; Mink, Jessica; Teuben, Peter J
2012-01-01
The Astrophysics Source Code Library (ASCL), founded in 1999, is a free on-line registry for source codes of interest to astronomers and astrophysicists. The library is housed on the discussion forum for Astronomy Picture of the Day (APOD) and can be accessed at http://ascl.net. The ASCL has a comprehensive listing that covers a significant number of the astrophysics source codes used to generate results published in or submitted to refereed journals and continues to grow. The ASCL currently has entries for over 500 codes; its records are citable and are indexed by ADS. The editors of the ASCL and members of its Advisory Committee were on hand at a demonstration table in the ADASS poster room to present the ASCL, accept code submissions, show how the ASCL is starting to be used by the astrophysics community, and take questions on and suggestions for improving the resource.
International Nuclear Information System (INIS)
The hydrology of the SCV site will be modelled utilizing discrete fracture flow models. These models are complex, and can not be fully cerified by comparison to analytical solutions. The best approach for verification of these codes is therefore cross-verification between different codes. This is complicated by the variation in assumptions and solution techniques utilized in different codes. Cross-verification procedures are defined which allow comparison of the codes developed by Harwell Laboratory, Lawrence Berkeley Laboratory, and Golder Associates Inc. Six cross-verification datasets are defined for deterministic and stochastic verification of geometric and flow features of the codes. Additional datasets for verification of transport features will be documented in a future report. (13 figs., 7 tabs., 10 refs.) (authors)
Combustion chamber analysis code
Przekwas, A. J.; Lai, Y. G.; Krishnan, A.; Avva, R. K.; Giridharan, M. G.
1993-05-01
A three-dimensional, time dependent, Favre averaged, finite volume Navier-Stokes code has been developed to model compressible and incompressible flows (with and without chemical reactions) in liquid rocket engines. The code has a non-staggered formulation with generalized body-fitted-coordinates (BFC) capability. Higher order differencing methodologies such as MUSCL and Osher-Chakravarthy schemes are available. Turbulent flows can be modeled using any of the five turbulent models present in the code. A two-phase, two-liquid, Lagrangian spray model has been incorporated into the code. Chemical equilibrium and finite rate reaction models are available to model chemically reacting flows. The discrete ordinate method is used to model effects of thermal radiation. The code has been validated extensively against benchmark experimental data and has been applied to model flows in several propulsion system components of the SSME and the STME.
Transformation invariant sparse coding
DEFF Research Database (Denmark)
Mørup, Morten; Schmidt, Mikkel Nørgaard
2011-01-01
Sparse coding is a well established principle for unsupervised learning. Traditionally, features are extracted in sparse coding in specific locations, however, often we would prefer invariant representation. This paper introduces a general transformation invariant sparse coding (TISC) model....... The model decomposes images into features invariant to location and general transformation by a set of specified operators as well as a sparse coding matrix indicating where and to what degree in the original image these features are present. The TISC model is in general overcomplete and we therefore invoke...... sparse coding to estimate its parameters. We demonstrate how the model can correctly identify components of non-trivial artificial as well as real image data. Thus, the model is capable of reducing feature redundancies in terms of pre-specified transformations improving the component identification....
Validity of the Aluminum Equivalent Approximation in Space Radiation Shielding
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 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
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...
A Conditional Saddlepoint Approximation for Testing Problems
Gatto, R.; Jammalamadaka, SR
1999-01-01
A saddlepoint approximation is provided for the distribution function of one M statistic conditional on another M statistic. Many interesting statistics based on dependent quantities (e.g., spacings, multinomial frequencies, rank differences) can be expressed in terms of independent identically distributed random variables conditioned on their sum, so that this conditional saddlepoint approximation yields accurate approximations for the distribution of such statistics. This saddlepoint approx...
Approximation Resistant Predicates From Pairwise Independence
Austrin, Per
2008-01-01
We study the approximability of predicates on $k$ variables from a domain $[q]$, and give a new sufficient condition for such predicates to be approximation resistant under the Unique Games Conjecture. Specifically, we show that a predicate $P$ is approximation resistant if there exists a balanced pairwise independent distribution over $[q]^k$ whose support is contained in the set of satisfying assignments to $P$.
Weak approximation of second-order BSDEs
Possamaï, Dylan; Tan, Xiaolu
2013-01-01
We study the weak approximation of the second-order backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time martingales. We establish a convergence result for a class of 2BSDEs, using both robustness properties of BSDEs, as proved in Briand, Delyon and M\\'{e}min [Stochastic Process. Appl. 97 (2002) 229-253], and tightness of solutions to discrete time BSDEs. In particular, when the approximating martingales are given by some particular controlled Mark...
A Note on Generalized Approximation Property
Directory of Open Access Journals (Sweden)
Antara Bhar
2013-01-01
Full Text Available We introduce a notion of generalized approximation property, which we refer to as --AP possessed by a Banach space , corresponding to an arbitrary Banach sequence space and a convex subset of , the class of bounded linear operators on . This property includes approximation property studied by Grothendieck, -approximation property considered by Sinha and Karn and Delgado et al., and also approximation property studied by Lissitsin et al. We characterize a Banach space having --AP with the help of -compact operators, -nuclear operators, and quasi--nuclear operators. A particular case for ( has also been characterized.
Application of RS Codes in Decoding QR Code
Institute of Scientific and Technical Information of China (English)
Zhu Suxia(朱素霞); Ji Zhenzhou; Cao Zhiyan
2003-01-01
The QR Code is a 2-dimensional matrix code with high error correction capability. It employs RS codes to generate error correction codewords in encoding and recover errors and damages in decoding. This paper presents several QR Code's virtues, analyzes RS decoding algorithm and gives a software flow chart of decoding the QR Code with RS decoding algorithm.
International Nuclear Information System (INIS)
This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name
DEFF Research Database (Denmark)
2015-01-01
Fulcrum network codes, which are a network coding framework, achieve three objectives: (i) to reduce the overhead per coded packet to almost 1 bit per source packet; (ii) to operate the network using only low field size operations at intermediate nodes, dramatically reducing complexity in the net...... the number of dimensions seen by the network using a linear mapping. Receivers can tradeoff computational effort with network delay, decoding in the high field size, the low field size, or a combination thereof.......Fulcrum network codes, which are a network coding framework, achieve three objectives: (i) to reduce the overhead per coded packet to almost 1 bit per source packet; (ii) to operate the network using only low field size operations at intermediate nodes, dramatically reducing complexity...... in the network; and (iii) to deliver an end-to-end performance that is close to that of a high field size network coding system for high-end receivers while simultaneously catering to low-end ones that can only decode in a lower field size. Sources may encode using a high field size expansion to increase...
Energy Technology Data Exchange (ETDEWEB)
Nelson, R.N. (ed.)
1985-05-01
This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name.
2014-01-01
While cracking a code might seem like something few of us would encounter in our daily lives, it is actually far more prevalent than we may realize. Anyone who has had personal information taken because of a hacked email account can understand the need for cryptography and the importance of encryption-essentially the need to code information to keep it safe. This detailed volume examines the logic and science behind various ciphers, their real world uses, how codes can be broken, and the use of technology in this oft-overlooked field.
International Nuclear Information System (INIS)
The FERDOR method is widely used to unfold neutron energy spectra from pulse-height distributions measured with NE-213 spectrometers. Two unfolding codes COOLC (developed at ORNL) and FORIST (modified version of COOLC developed at UIUC) implement the FERDOR method and are distributed by RSIC. Each code package contains an NE-213 response matrix, sample input data, and sample output. The smoothing (window) widths which are distributed with COOLC are not the most appropriate for all neutron spectrum measurements. The FORIST code determines an optimum set of window widths according to the desired statistical error in the smoothed spectrum
Brehm, Enrico M
2016-01-01
In this work, we introduce classical holographic codes. These can be understood as concatenated probabilistic codes and can be represented as networks uniformly covering hyperbolic space. In particular, classical holographic codes can be interpreted as maps from bulk degrees of freedom to boundary degrees of freedom. Interestingly, they are shown to exhibit features similar to those expected from the AdS/CFT correspondence. Among these are a version of the Ryu-Takayanagi formula and intriguing properties regarding bulk reconstruction and boundary representations of bulk operations. We discuss the relation of our findings with expectations from AdS/CFT and, in particular, with recent results from quantum error correction.
Distributed multiple description coding
Bai, Huihui; Zhao, Yao
2011-01-01
This book examines distributed video coding (DVC) and multiple description coding (MDC), two novel techniques designed to address the problems of conventional image and video compression coding. Covering all fundamental concepts and core technologies, the chapters can also be read as independent and self-sufficient, describing each methodology in sufficient detail to enable readers to repeat the corresponding experiments easily. Topics and features: provides a broad overview of DVC and MDC, from the basic principles to the latest research; covers sub-sampling based MDC, quantization based MDC,
Rockower, Edward B.
1985-01-01
A number of laser propagation codes have been assessed as to their suitability for modeling Army High Energy Laser (HEL) weapons used in an anti- sensor mode. We identify a number of areas in which systems analysis HEL codes are deficient. Most notably, available HEL scaling law codes model the laser aperture as circular, possibly with a fixed (e.g. 10%) obscuration. However, most HELs have rectangular apertures with up to 30% obscuration. We present a beam-quality/aperture shape scaling rela...
Pulliam, T. H.; Steger, J. L.
1985-01-01
In 1977 and 1978, general purpose centrally space differenced implicit finite difference codes in two and three dimensions have been introduced. These codes, now called ARC2D and ARC3D, can run either in inviscid or viscous mode for steady or unsteady flow. Since the introduction of the ARC2D and ARC3D codes, overall computational efficiency could be improved by making use of a number of algorithmic changes. These changes are related to the use of a spatially varying time step, the use of a sequence of mesh refinements to establish approximate solutions, implementation of various ways to reduce inversion work, improved numerical dissipation terms, and more implicit treatment of terms. The present investigation has the objective to describe the considered improvements and to quantify advantages and disadvantages. It is found that using established and simple procedures, a computer code can be maintained which is competitive with specialized codes.
INVARIANT RANDOM APPROXIMATION IN NONCONVEX DOMAIN
Directory of Open Access Journals (Sweden)
R. Shrivastava
2012-05-01
Full Text Available Random fixed point results in the setup of compact and weakly compact domain of Banach spaces which is not necessary starshaped have been obtained in the present work. Invariant random approximation results have also been determined asits application. In this way, random version of invariant approximation results due toMukherjee and Som [13] and Singh [17] have been given.
On approximating multi-criteria TSP
Manthey, Bodo; Albers, S.; Marion, J.-Y.
2009-01-01
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP), whose performances are independent of the number $k$ of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized app
A case where BO Approximation breaks down
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
@@ The Bom-Oppenheimer (BO)Approximation is ubiquitous in molecular physics,quantum physics and quantum chemistry. However, CAS researchers recently observed a breakdown of the Approximation in the reaction of fluorine with deuterium atoms.The result has been published in the August 24 issue of Science.
Computing Functions by Approximating the Input
Goldberg, Mayer
2012-01-01
In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…
Approximation of the Inverse -Frame Operator
Indian Academy of Sciences (India)
M R Abdollahpour; A Najati
2011-05-01
In this paper, we introduce the concept of (strong) projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.
Two Point Pade Approximants and Duality
Banks, Tom
2013-01-01
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a strong/weak duality, when the symmetries do not determine exact expressions for some quantity.
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2004-01-01
with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a comple...
Improved Approximation for the Directed Spanner Problem
Bhattacharyya, Arnab; Makarychev, Konstantin
2010-01-01
We prove that the size of the sparsest directed k-spanner of a graph can be approximated in polynomial time to within a factor of $\\tilde{O}(\\sqrt{n})$, for all k >= 3. This improves the $\\tilde{O}(n^{2/3})$-approximation recently shown by Dinitz and Krauthgamer.
On the closedness of approximation spectra
Parkkonen, Jouni; Paulin, Frédéric
2008-01-01
Generalizing Cusick's theorem on the closedness of the classical Lagrange spectrum for the approximation of real numbers by rational ones, we prove that various approximation spectra are closed, using penetration properties of the geodesic flow in cusp neighbourhoods in negatively curved manifolds and a result of Maucourant.
Inverse scattering problem in relativistic quasiclassical approximation
International Nuclear Information System (INIS)
Inverse scattering problem is solved on the basis of quasipotential approach in quantum field theory within the framework of relativistic quasiclassical approximation. Formulas of quasipotential restoration by phase shifts are derived. Cases of non-relativistic and ultra-relativistic approximations are investigated
Approximations for stop-loss reinsurance premiums
Reijnen, Rajko; Albers, Willem; Kallenberg, Wilbert C.M.
2005-01-01
Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are use
Approximations for stop-loss reinsurance premiums
Reijnen, R.; Albers, W.; Kallenberg, W.C.M.
2003-01-01
Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are use
On approximating multi-criteria TSP
Manthey, Bodo
2012-01-01
We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multicriteria maximum traveling salesman problems (Max-TSP). For multicriteria Max-STSP where the edge weights have to be symmet
Metadata for Approximate Query Answering Systems
Directory of Open Access Journals (Sweden)
Francesco Di Tria
2012-01-01
Full Text Available In business intelligence systems, data warehouse metadata management and representation are getting more and more attention by vendors and designers. The standard language for the data warehouse metadata representation is the Common Warehouse Metamodel. However, business intelligence systems include also approximate query answering systems, since these software tools provide fast responses for decision making on the basis of approximate query processing. Currently, the standard meta-model does not allow to represent the metadata needed by approximate query answering systems. In this paper, we propose an extension of the standard metamodel, in order to define the metadata to be used in online approximate analytical processing. These metadata have been successfully adopted in ADAP, a web-based approximate query answering system that creates and uses statistical data profiles.
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-01-01
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400--407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305--320]. The application of the trajectory averaging estimator to other stochastic approximation MCMC algorithms, for example, a stochastic approximation MLE al...
An improved proximity force approximation for electrostatics
Fosco, C D; Mazzitelli, F D
2012-01-01
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 to 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 contribution of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied to 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 to discuss the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction i...
Transfer reaction code with nonlocal interactions
Titus, L J; Nunes, F M
2016-01-01
We present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, $(d,N)$ or $(N,d)$, including nonlocal nucleon-target interactions, within the adiabatic distorted wave approximation. For this purpose, we implement an iterative method for solving the second order nonlocal differential equation, for both scattering and bound states. The final observables that can be obtained with NLAT are differential angular distributions for the cross sections of $A(d,N)B$ or $B(N,d)A$. Details on the implementation of the T-matrix to obtain the final cross sections within the adiabatic distorted wave approximation method are also provided. This code is suitable to be applied for deuteron induced reactions in the range of $E_d=10-70$ MeV, and provides cross sections with $4\\%$ accuracy.
Transfer reaction code with nonlocal interactions
Titus, L. J.; Ross, A.; Nunes, F. M.
2016-10-01
We present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, (d , N) or (N , d) , including nonlocal nucleon-target interactions, within the adiabatic distorted wave approximation. For this purpose, we implement an iterative method for solving the second order nonlocal differential equation, for both scattering and bound states. The final observables that can be obtained with NLAT are differential angular distributions for the cross sections of A(d , N) B or B(N , d) A. Details on the implementation of the T-matrix to obtain the final cross sections within the adiabatic distorted wave approximation method are also provided. This code is suitable to be applied for deuteron induced reactions in the range of Ed =10-70 MeV, and provides cross sections with 4% accuracy.
Montgomery County of Maryland — The Office of the County Attorney (OCA) processes Code Violation Citations issued by County agencies. The citations can be viewed by issued department, issued date...
Alloa, Emmanuel
2015-01-01
In allen Bereichen der Gesellschaft werden gegenwärtig Forderungen nach mehr Transparenz laut. Was steht hinter diesem Wort? Für Emmanuel Alloa wohnt der Transparenzforderung die Paradoxie inne, ein "codefreier Code" sein zu wollen.
Energy Technology Data Exchange (ETDEWEB)
Freeman, L.N.; Wilson, R.E. [Oregon State Univ., Dept. of Mechanical Engineering, Corvallis, OR (United States)
1996-09-01
The FAST Code which is capable of determining structural loads on a flexible, teetering, horizontal axis wind turbine is described and comparisons of calculated loads with test data are given at two wind speeds for the ESI-80. The FAST Code models a two-bladed HAWT with degrees of freedom for blade bending, teeter, drive train flexibility, yaw, and windwise and crosswind tower motion. The code allows blade dimensions, stiffnesses, and weights to differ and models tower shadow, wind shear, and turbulence. Additionally, dynamic stall is included as are delta-3 and an underslung rotor. Load comparisons are made with ESI-80 test data in the form of power spectral density, rainflow counting, occurrence histograms, and azimuth averaged bin plots. It is concluded that agreement between the FAST Code and test results is good. (au)
DEFF Research Database (Denmark)
2015-01-01
Fulcrum network codes, which are a network coding framework, achieve three objectives: (i) to reduce the overhead per coded packet to almost 1 bit per source packet; (ii) to operate the network using only low field size operations at intermediate nodes, dramatically reducing complexity...... in the network; and (iii) to deliver an end-to-end performance that is close to that of a high field size network coding system for high-end receivers while simultaneously catering to low-end ones that can only decode in a lower field size. Sources may encode using a high field size expansion to increase...... the number of dimensions seen by the network using a linear mapping. Receivers can tradeoff computational effort with network delay, decoding in the high field size, the low field size, or a combination thereof....
Volodymyr Kuznetsov; Laszlo Szekeres; Mathias Payer; George Candea; Sekar, R.; Dawn Song
2014-01-01
Systems code is often written in low-level languages like C/C++, which offer many benefits but also delegate memory management to programmers. This invites memory safety bugs that attackers can exploit to divert control flow and compromise the system. Deployed defense mechanisms (e.g., ASLR, DEP) are incomplete, and stronger defense mechanisms (e.g., CFI) often have high overhead and limited guarantees [19, 15, 9]. We introduce code-pointer integrity (CPI), a new design point that guarantees...
Lian, Shiguo
2007-01-01
In recent work, various fractal image coding methods are reported, which adopt the self-similarity of images to compress the size of images. However, till now, no solutions for the security of fractal encoded images have been provided. In this paper, a secure fractal image coding scheme is proposed and evaluated, which encrypts some of the fractal parameters during fractal encoding, and thus, produces the encrypted and encoded image. The encrypted image can only be recovered by the correct ke...
Coded Splitting Tree Protocols
DEFF Research Database (Denmark)
Sørensen, Jesper Hemming; Stefanovic, Cedomir; Popovski, Petar
2013-01-01
This paper presents a novel approach to multiple access control called coded splitting tree protocol. The approach builds on the known tree splitting protocols, code structure and successive interference cancellation (SIC). Several instances of the tree splitting protocol are initiated, each...... as possible. Evaluations show that the proposed protocol provides considerable gains over the standard tree splitting protocol applying SIC. The improvement comes at the expense of an increased feedback and receiver complexity....
Konishi, Masakazu
2003-01-01
Behavioral, anatomical, and physiological approaches can be integrated in the study of sound localization in barn owls. Space representation in owls provides a useful example for discussion of place and ensemble coding. Selectivity for space is broad and ambiguous in low-order neurons. Parallel pathways for binaural cues and for different frequency bands converge on high-order space-specific neurons, which encode space more precisely. An ensemble of broadly tuned place-coding neurons may conv...
GAPCON-THERMAL-3 code description
Energy Technology Data Exchange (ETDEWEB)
Lanning, D.D.; Mohr, C.L.; Panisko, F.E.; Stewart, K.B.
1978-01-01
GAPCON-3 is a computer program that predicts the thermal and mechanical behavior of an operating fuel rod during its normal lifetime. The code calculates temperatures, dimensions, stresses, and strains for the fuel and the cladding in both the radial and axial directions for each step of the user specified power history. The method of weighted residuals is for the steady state temperature calculation, and is combined with a finite difference approximation of the time derivative for transient conditions. The stress strain analysis employs an iterative axisymmetric finite element procedure that includes plasticity and creep for normal and pellet-clad mechanical interaction loads. GAPCON-3 can solve steady state and operational transient problems. Comparisons of GAPCON-3 predictions to both closed form analytical solutions and actual inpile instrumented fuel rod data have demonstrated the ability of the code to calculate fuel rod behavior. GAPCON-3 features a restart capability and an associated plot package unavailable in previous GAPCON series codes.
Axially symmetric pseudo-Newtonian hydrodynamics code
Kim, Jinho; Choptuik, Matthew William; Lee, Hyung Mok
2012-01-01
We develop a numerical hydrodynamics code using a pseudo-Newtonian formulation that uses the weak field approximation for the geometry, and a generalized source term for the Poisson equation that takes into account relativistic effects. The code was designed to treat moderately relativistic systems such as rapidly rotating neutron stars. The hydrodynamic equations are solved using a finite volume method with High Resolution Shock Capturing (HRSC) techniques. We implement several different slope limiters for second order reconstruction schemes and also investigate higher order reconstructions. We use the method of lines (MoL) to convert the mixed spatial-time partial differential equations into ordinary differential equations (ODEs) that depend only on time. These ODEs are solved using 2nd and 3rd order Runge-Kutta methods. The Poisson equation for the gravitational potential is solved with a multigrid method. In order to confirm the validity of our code, we carry out four different tests including one and two...
SPQR: a Monte Carlo reactor kinetics code
International Nuclear Information System (INIS)
The SPQR Monte Carlo code has been developed to analyze fast reactor core accident problems where conventional methods are considered inadequate. The code is based on the adiabatic approximation of the quasi-static method. This initial version contains no automatic material motion or feedback. An existing Monte Carlo code is used to calculate the shape functions and the integral quantities needed in the kinetics module. Several sample problems have been devised and analyzed. Due to the large statistical uncertainty associated with the calculation of reactivity in accident simulations, the results, especially at later times, differ greatly from deterministic methods. It was also found that in large uncoupled systems, the Monte Carlo method has difficulty in handling asymmetric perturbations
Radiation hydrodynamics integrated in the code PLUTO
Stefan, M. Kolb; Matthias, Stute; Wilhelm, Kley; Andrea, Mignone
2013-01-01
The transport of energy through radiation is very important in many astrophysical phenomena. In dynamical problems the time-dependent equations of radiation hydrodynamics have to be solved. We present a newly developed radiation-hydrodynamics module specifically designed for the versatile MHD code PLUTO. The solver is based on the flux-limited diffusion approximation in the two-temperature approach. All equations are solved in the co-moving frame in the frequency independent (grey) approximat...
International Nuclear Information System (INIS)
The KENO-V code is the current release of the Oak Ridge multigroup Monte Carlo criticality code development. The original KENO, with 16 group Hansen-Roach cross sections and P1 scattering, was one ot the first multigroup Monte Carlo codes and it and its successors have always been a much-used research tool for criticality studies. KENO-V is able to accept large neutron cross section libraries (a 218 group set is distributed with the code) and has a general P/sub N/ scattering capability. A supergroup feature allows execution of large problems on small computers, but at the expense of increased calculation time and system input/output operations. This supergroup feature is activated automatically by the code in a manner which utilizes as much computer memory as is available. The primary purpose of KENO-V is to calculate the system k/sub eff/, from small bare critical assemblies to large reflected arrays of differing fissile and moderator elements. In this respect KENO-V neither has nor requires the many options and sophisticated biasing techniques of general Monte Carlo codes
New generalizations of cosmography inspired by the Pade approximant
Energy Technology Data Exchange (ETDEWEB)
Zhou, Ya-Nan; Zou, Xiao-Bo; Wei, Hao [Beijing Institute of Technology, School of Physics, Beijing (China); Liu, De-Zi [Peking University, Department of Astronomy, Beijing (China)
2016-05-15
The current accelerated expansion of the universe has been one of the most important fields in physics and astronomy since 1998. Many cosmological models have been proposed in the literature to explain this mysterious phenomenon. Since the nature and cause of the cosmic acceleration are still unknown, model-independent approaches to study the evolution of the universe are welcome. One of the powerful model-independent approaches is the so-called cosmography. It only relies on the cosmological principle, without postulating any underlying theoretical model. However, there are several shortcomings in the usual cosmography. For instance, it is plagued with the problem of divergence (or an unacceptably large error), and it fails to predict the future evolution of the universe. In the present work, we try to overcome or at least alleviate these problems, and we propose two new generalizations of cosmography inspired by the Pade approximant. One is to directly parameterize the luminosity distance based on the Pade approximant, while the other is to generalize cosmography with respect to a so-called y{sub β}-shift y{sub β} =z/(1 + βz), which is also inspired by the Pade approximant. Then we confront them with the observational data with the help of the Markov chain Monte Carlo (MCMC) code emcee, and find that they work fairly well. (orig.)
Frankenstein's glue: transition functions for approximate solutions
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.
Analysis of the optimality of the standard genetic code.
Kumar, Balaji; Saini, Supreet
2016-07-19
Many theories have been proposed attempting to explain the origin of the genetic code. While strong reasons remain to believe that the genetic code evolved as a frozen accident, at least for the first few amino acids, other theories remain viable. In this work, we test the optimality of the standard genetic code against approximately 17 million genetic codes, and locate 29 which outperform the standard genetic code at the following three criteria: (a) robustness to point mutation; (b) robustness to frameshift mutation; and (c) ability to encode additional information in the coding region. We use a genetic algorithm to generate and score codes from different parts of the associated landscape, which are, as a result, presumably more representative of the entire landscape. Our results show that while the genetic code is sub-optimal for robustness to frameshift mutation and the ability to encode additional information in the coding region, it is very strongly selected for robustness to point mutation. This coupled with the observation that the different performance indicator scores for a particular genetic code are negatively correlated makes the standard genetic code nearly optimal for the three criteria tested in this work. PMID:27327359
Orthorhombic rational approximants for decagonal quasicrystals
Indian Academy of Sciences (India)
S Ranganathan; Anandh Subramaniam
2003-10-01
An important exercise in the study of rational approximants is to derive their metric, especially in relation to the corresponding quasicrystal or the underlying clusters. Kuo’s model has been the widely accepted model to calculate the metric of the decagonal approximants. Using an alternate model, the metric of the approximants and other complex structures with the icosahedral cluster are explained elsewhere. In this work a comparison is made between the two models bringing out their equivalence. Further, using the concept of average lattices, a modified model is proposed.
DIFFERENCE SCHEMES BASING ON COEFFICIENT APPROXIMATION
Institute of Scientific and Technical Information of China (English)
MOU Zong-ze; LONG Yong-xing; QU Wen-xiao
2005-01-01
In respect of variable coefficient differential equations, the equations of coefficient function approximation were more accurate than the coefficient to be frozen as a constant in every discrete subinterval. Usually, the difference schemes constructed based on Taylor expansion approximation of the solution do not suit the solution with sharp function.Introducing into local bases to be combined with coefficient function approximation, the difference can well depict more complex physical phenomena, for example, boundary layer as well as high oscillatory, with sharp behavior. The numerical test shows the method is more effective than the traditional one.
Approximately Liner Phase IIR Digital Filter Banks
Directory of Open Access Journals (Sweden)
J. D. Ćertić
2013-11-01
Full Text Available In this paper, uniform and nonuniform digital filter banks based on approximately linear phase IIR filters and frequency response masking technique (FRM are presented. Both filter banks are realized as a connection of an interpolated half-band approximately linear phase IIR filter as a first stage of the FRM design and an appropriate number of masking filters. The masking filters are half-band IIR filters with an approximately linear phase. The resulting IIR filter banks are compared with linear-phase FIR filter banks exhibiting similar magnitude responses. The effects of coefficient quantization are analyzed.
The Boussinesq approximation in rapidly rotating flows
Lopez, Jose M; Avila, Marc
2013-01-01
In the classical formulation of the Boussinesq approximation centrifugal buoyancy effects related to differential rotation, as well as strong vortices in the flow, are neglected. However, these may play an important role in rapidly rotating flows, such as in astrophysical and geophysical applications, and also in turbulent convection. We here provide a straightforward approach resulting in a Boussinesq-type approximation that consistently accounts for centrifugal effects. We further compare our new approach to the classical one in fluid flows confined between two differentially heated and rotating cylinders. The results justify the need of using the proposed approximation in rapidly rotating flows.
Mathematical analysis, approximation theory and their applications
Gupta, Vijay
2016-01-01
Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Approximate equivalence in von Neumann algebras
Institute of Scientific and Technical Information of China (English)
DING Huiru; Don Hadwin
2005-01-01
One formulation of D. Voiculescu's theorem on approximate unitary equivalence is that two unital representations π and ρ of a separable C*-algebra are approximately unitarily equivalent if and only if rank o π = rank o ρ. We study the analog when the ranges of π and ρ are contained in a von Neumann algebra R, the unitaries inducing the approximate equivalence must come from R, and "rank" is replaced with "R-rank" (defined as the Murray-von Neumann equivalence of the range projection).
Regression with Sparse Approximations of Data
DEFF Research Database (Denmark)
Noorzad, Pardis; Sturm, Bob L.
2012-01-01
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected by a...... sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based on the...
Relativistic stellar pulsations in the Cowling approximation
International Nuclear Information System (INIS)
Much that is known about the general pulsational properties of non-rotating Newtonian stars is traceable to the fact that in the Cowling approximation, the stellar pulsation equations can be cast in a nearly Sturm-Liouville form. In this paper, the relativistic Cowling approximation is investigated, and it is shown that in this approximation the equations for non-radial relativistic stellar pulsations are also of nearly Sturm-Liouville character. The consequences of this are discussed as a series of theorems regarding the eigenfrequencies and eigenfunctions of g-, f- and p-modes in relativistic stars. (author)
Approximation of the semi-infinite interval
Directory of Open Access Journals (Sweden)
A. McD. Mercer
1980-01-01
Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.
Accumulative Landings System Code Tables
National Oceanic and Atmospheric Administration, Department of Commerce — Code Tables Used In Landings System. These tables assign meanings to the codes that appear in the data tables. Code tables exist for species, gear, state, county,...
Product Codes for Optical Communication
DEFF Research Database (Denmark)
Andersen, Jakob Dahl
2002-01-01
Many optical communicaton systems might benefit from forward-error-correction. We present a hard-decision decoding algorithm for the "Block Turbo Codes", suitable for optical communication, which makes this coding-scheme an alternative to Reed-Solomon codes.......Many optical communicaton systems might benefit from forward-error-correction. We present a hard-decision decoding algorithm for the "Block Turbo Codes", suitable for optical communication, which makes this coding-scheme an alternative to Reed-Solomon codes....
Algebraic geometric codes with applications
Institute of Scientific and Technical Information of China (English)
CHEN Hao
2007-01-01
The theory of linear error-correcting codes from algebraic geomet-ric curves (algebraic geometric (AG) codes or geometric Goppa codes) has been well-developed since the work of Goppa and Tsfasman, Vladut, and Zink in 1981-1982. In this paper we introduce to readers some recent progress in algebraic geometric codes and their applications in quantum error-correcting codes, secure multi-party computation and the construction of good binary codes.
Low Rank Approximation Algorithms, Implementation, Applications
Markovsky, Ivan
2012-01-01
Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Seismic wave extrapolation using lowrank symbol approximation
Fomel, Sergey
2012-04-30
We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.
Approximation concepts for efficient structural synthesis
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.
Broadband Approximations for Doubly Curved Reflector Antenna
Directory of Open Access Journals (Sweden)
V. Schejbal
2010-12-01
Full Text Available The broadband approximations for shaped-beam doubly curved reflector antennas with primary feed (rectangular horn producing uniform amplitude and phase aperture distribution are derived and analyzed. They are very valuable for electromagnetic compatibility analyses both from electromagnetic interference and susceptibility point of view, because specialized more accurate methods such as physical optics are only used by antenna designers. To allow quick EMC analyses, typical values, beamwidth changes, sidelobe levels and aperture efficiencies are given for frequency changes approximately up to four times operating frequency. A comparison of approximated and measured patterns of doubly curved reflector antennas shows that the given approximation could be reliably used for analyses of pattern changes due to very broad frequency changes.
Optical coding theory with Prime
Kwong, Wing C
2013-01-01
Although several books cover the coding theory of wireless communications and the hardware technologies and coding techniques of optical CDMA, no book has been specifically dedicated to optical coding theory-until now. Written by renowned authorities in the field, Optical Coding Theory with Prime gathers together in one volume the fundamentals and developments of optical coding theory, with a focus on families of prime codes, supplemented with several families of non-prime codes. The book also explores potential applications to coding-based optical systems and networks. Learn How to Construct
Polynomial weights and code constructions
DEFF Research Database (Denmark)
Massey, J; Costello, D; Justesen, Jørn
1973-01-01
that are subcodes of the binary Reed-Muller codes and can be very simply instrumented, 3) a new class of constacyclic codes that are subcodes of thep-ary "Reed-Muller codes," 4) two new classes of binary convolutional codes with large "free distance" derived from known binary cyclic codes, 5) two new classes...... of long constraint length binary convolutional codes derived from2^r-ary Reed-Solomon codes, and 6) a new class ofq-ary "repeated-root" constacyclic codes with an algebraic decoding algorithm....
Lattice quantum chromodynamics with approximately chiral fermions
Energy Technology Data Exchange (ETDEWEB)
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Selfconsistent approximations, symmetries and choice of representation
Leupold, Stefan
2006-01-01
In thermal field theory selfconsistent (Phi-derivable) approximations are used to improve (resum) propagators at the level of two-particle irreducible diagrams. At the same time vertices are treated at the bare level. Therefore such approximations typically violate the Ward identities connected to internal symmetries. Examples are presented how such violations can be tamed by a proper choice of representation for the fields which describe the system under consideration. These examples cover t...
Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
Mostafazadeh, Ali
2014-01-01
arXiv:1401.4315v3 [quant-ph] 27 Feb 2014 Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility Ali Mostafazadeh∗ Department of Mathematics, Ko¸c University, 34450 Sarıyer, Istanbul, Turkey Abstract The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the S-matrix of a two-level time-dependent non-Hermitian Hamiltonian H( ). We show that the application of the adiabatic approximation ...
Approximate Bayesian computation in population genetics.
Beaumont, Mark A; Zhang, Wenyang; Balding, David J.
2002-01-01
We propose a new method for approximate Bayesian statistical inference on the basis of summary statistics. The method is suited to complex problems that arise in population genetics, extending ideas developed in this setting by earlier authors. Properties of the posterior distribution of a parameter, such as its mean or density curve, are approximated without explicit likelihood calculations. This is achieved by fitting a local-linear regression of simulated parameter values on simulated summ...
Approximation by Semigroups of Spherical Operators
Wang, Yuguang; Cao, Feilong
2011-01-01
This paper discusses the approximation by %semigroups of operators of class ($\\mathscr{C}_0$) on the sphere and focuses on a class of so called exponential-type multiplier operators. It is proved that such operators form a strongly continuous semigroup of contraction operators of class ($\\mathscr{C}_0$), from which the equivalence between approximation for these operators and $K$-functionals introduced by the operators is given. As examples, the constructed $r$-th Boolean of generalized spher...
Polynomial approximation of functions in Sobolev spaces
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.
Introduction to the Maxwell Garnett approximation: tutorial.
Markel, Vadim A
2016-07-01
This tutorial is devoted to the Maxwell Garnett approximation and related theories. Topics covered in this first, introductory part of the tutorial include the Lorentz local field correction, the Clausius-Mossotti relation and its role in the modern numerical technique known as the discrete dipole approximation, the Maxwell Garnett mixing formula for isotropic and anisotropic media, multicomponent mixtures and the Bruggeman equation, the concept of smooth field, and Wiener and Bergman-Milton bounds. PMID:27409680
A Ballistic Monte Carlo Approximation of {\\pi}
Dumoulin, Vincent
2014-01-01
We compute a Monte Carlo approximation of {\\pi} using importance sampling with shots coming out of a Mossberg 500 pump-action shotgun as the proposal distribution. An approximated value of 3.136 is obtained, corresponding to a 0.17% error on the exact value of {\\pi}. To our knowledge, this represents the first attempt at estimating {\\pi} using such method, thus opening up new perspectives towards computing mathematical constants using everyday tools.
Time Stamps for Fixed-Point Approximation
DEFF Research Database (Denmark)
Damian, Daniela
2001-01-01
Time stamps were introduced in Shivers's PhD thesis for approximating the result of a control-flow analysis. We show them to be suitable for computing program analyses where the space of results (e.g., control-flow graphs) is large. We formalize time-stamping as a top-down, fixed......-point approximation algorithm which maintains a single copy of intermediate results. We then prove the correctness of this algorithm....
Parallel local approximation MCMC for expensive models
Conrad, Patrick; Davis, Andrew; Marzouk, Youssef; Pillai, Natesh; Smith, Aaron
2016-01-01
Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In recent work [Conrad et al. JASA 2015, arXiv:1402.1694] we described a framework for constructing and refining local approximations of such models during an MCMC simulation. These posterior--adapted approximations harness regularity of the model to reduce the c...
The Actinide Transition Revisited by Gutzwiller Approximation
Xu, Wenhu; Lanata, Nicola; Yao, Yongxin; Kotliar, Gabriel
2015-03-01
We revisit the problem of the actinide transition using the Gutzwiller approximation (GA) in combination with the local density approximation (LDA). In particular, we compute the equilibrium volumes of the actinide series and reproduce the abrupt change of density found experimentally near plutonium as a function of the atomic number. We discuss how this behavior relates with the electron correlations in the 5 f states, the lattice structure, and the spin-orbit interaction. Our results are in good agreement with the experiments.
Lattice quantum chromodynamics with approximately chiral fermions
International Nuclear Information System (INIS)
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ+ pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Staying Thermal with Hartree Ensemble Approximations
Salle, M; Vink, Jeroen C
2000-01-01
Using Hartree ensemble approximations to compute the real time dynamics of scalar fields in 1+1 dimension, we find that with suitable initial conditions, approximate thermalization is achieved much faster than found in our previous work. At large times, depending on the interaction strength and temperature, the particle distribution slowly changes: the Bose-Einstein distribution of the particle densities develops classical features. We also discuss variations of our method which are numerically more efficient.
Approximations for the Erlang Loss Function
DEFF Research Database (Denmark)
Mejlbro, Leif
1998-01-01
Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error <1E-2, and methods are indicated for improving this bound.......Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error
Approximate Assertional Reasoning Over Expressive Ontologies
Tserendorj, Tuvshintur
2010-01-01
In this thesis, approximate reasoning methods for scalable assertional reasoning are provided whose computational properties can be established in a well-understood way, namely in terms of soundness and completeness, and whose quality can be analyzed in terms of statistical measurements, namely recall and precision. The basic idea of these approximate reasoning methods is to speed up reasoning by trading off the quality of reasoning results against increased speed.
Phase Transitions for Greedy Sparse Approximation Algorithms
Blanchard, Jeffrey D.; Cartis, Coralia; Tanner, Jared; Thompson, Andrew
2010-01-01
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many such algorithms have now been proven to have optimal-order uniform recovery guarantees using the ubiquitous Restricted Isometry Property (RIP) (Candes and Tao (2005) [11]). However, without specifying a matrix, or class of matrices, it is unclear when the ...
Limitations of the acoustic approximation for seismic crosshole tomography
Marelli, Stefano; Maurer, Hansruedi
2010-05-01
Modelling and inversion of seismic crosshole data is a challenging task in terms of computational resources. Even with the significant increase in power of modern supercomputers, full three-dimensional elastic modelling of high-frequency waveforms generated from hundreds of source positions in several boreholes is still an intractable task. However, it has been recognised that full waveform inversion offers substantially more information compared with traditional travel time tomography. A common strategy to reduce the computational burden for tomographic inversion is to approximate the true elastic wave propagation by acoustic modelling. This approximation assumes that the solid rock units can be treated like fluids (with no shear wave propagation) and is generally considered to be satisfactory so long as only the earliest portions of the recorded seismograms are considered. The main assumption is that most of the energy in the early parts of the recorded seismograms is carried by the faster compressional (P-) waves. Although a limited number of studies exist on the effects of this approximation for surface/marine synthetic reflection seismic data, and show it to be generally acceptable for models with low to moderate impedance contrasts, to our knowledge no comparable studies have been published on the effects for cross-borehole transmission data. An obvious question is whether transmission tomography should be less affected by elastic effects than surface reflection data when only short time windows are applied to primarily capture the first arriving wavetrains. To answer this question we have performed 2D and 3D investigations on the validity of the acoustic approximation for an elastic medium and using crosshole source-receiver configurations. In order to generate consistent acoustic and elastic data sets, we ran the synthetic tests using the same finite-differences time-domain elastic modelling code for both types of simulations. The acoustic approximation was
DEFF Research Database (Denmark)
Sadegh, Payman
1997-01-01
This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...
Noble, Viveca K.
1993-01-01
There are various elements such as radio frequency interference (RFI) which may induce errors in data being transmitted via a satellite communication link. When a transmission is affected by interference or other error-causing elements, the transmitted data becomes indecipherable. It becomes necessary to implement techniques to recover from these disturbances. The objective of this research is to develop software which simulates error control circuits and evaluate the performance of these modules in various bit error rate environments. The results of the evaluation provide the engineer with information which helps determine the optimal error control scheme. The Consultative Committee for Space Data Systems (CCSDS) recommends the use of Reed-Solomon (RS) and convolutional encoders and Viterbi and RS decoders for error correction. The use of forward error correction techniques greatly reduces the received signal to noise needed for a certain desired bit error rate. The use of concatenated coding, e.g. inner convolutional code and outer RS code, provides even greater coding gain. The 16-bit cyclic redundancy check (CRC) code is recommended by CCSDS for error detection.
Shengli, Zhang; Lam, Patrick P K
2007-01-01
A main distinguishing feature of a wireless network compared with a wired network is its broadcast nature, in which the signal transmitted by a node may reach several other nodes, and a node may receive signals from several other nodes simultaneously. Rather than a blessing, this feature is treated more as an interference-inducing nuisance in most wireless networks today (e.g., IEEE 802.11). This paper shows that the concept of network coding can be applied at the physical layer to turn the broadcast property into a capacity-boosting advantage in wireless ad hoc networks. Specifically, we propose a physical-layer network coding (PNC) scheme to coordinate transmissions among nodes. In contrast to straightforward network coding which performs coding arithmetic on digital bit streams after they have been received, PNC makes use of the additive nature of simultaneously arriving electromagnetic (EM) waves for equivalent coding operation. And in doing so, PNC can potentially achieve 100% and 50% throughput increase...
Optimizing ATLAS code with different profilers
International Nuclear Information System (INIS)
After the current maintenance period, the LHC will provide higher energy collisions with increased luminosity. In order to keep up with these higher rates, ATLAS software needs to speed up substantially. However, ATLAS code is composed of approximately 6M lines, written by many different programmers with different backgrounds, which makes code optimisation a challenge. To help with this effort different profiling tools and techniques are being used. These include well known tools, such as the Valgrind suite and Intel Amplifier; less common tools like Pin, PAPI, and GOoDA; as well as techniques such as library interposing. In this paper we will mainly focus on Pin tools and GOoDA. Pin is a dynamic binary instrumentation tool which can obtain statistics such as call counts, instruction counts and interrogate functions' arguments. It has been used to obtain CLHEP Matrix profiles, operations and vector sizes for linear algebra calculations which has provided the insight necessary to achieve significant performance improvements. Complimenting this, GOoDA, an in-house performance tool built in collaboration with Google, which is based on hardware performance monitoring unit events, is used to identify hot-spots in the code for different types of hardware limitations, such as CPU resources, caches, or memory bandwidth. GOoDA has been used in improvement of the performance of new magnetic field code and identification of potential vectorization targets in several places, such as Runge-Kutta propagation code
Nested Quantum Error Correction Codes
Wang, Zhuo; Fan, Hen; Vedral, Vlatko
2009-01-01
The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are available in constructing new quantum error correction codes from old codes. Here we exhibit a simple and general method to construct new quantum error correction codes by nesting certain quantum codes together. The problem of finding long quantum error correction codes is reduced to that of searching several short length quantum codes with certain properties. Our method works for all length and all distance codes, and is quite efficient to construct optimal or near optimal codes. Two main known methods in constructing new codes from old codes in quantum error-correction theory, the concatenating and pasting, can be understood in the framework of nested quantum error correction codes.
Graph Codes with Reed-Solomon Component Codes
DEFF Research Database (Denmark)
Høholdt, Tom; Justesen, Jørn
2006-01-01
We treat a specific case of codes based on bipartite expander graphs coming from finite geometries. The code symbols are associated with the branches and the symbols connected to a given node are restricted to be codewords in a Reed-Solomon code. We give results on the parameters of the codes and...
Phase-coded pulse aperiodic transmitter coding
Directory of Open Access Journals (Sweden)
I. I. Virtanen
2009-07-01
Full Text Available Both ionospheric and weather radar communities have already adopted the method of transmitting radar pulses in an aperiodic manner when measuring moderately overspread targets. Among the users of the ionospheric radars, this method is called Aperiodic Transmitter Coding (ATC, whereas the weather radar users have adopted the term Simultaneous Multiple Pulse-Repetition Frequency (SMPRF. When probing the ionosphere at the carrier frequencies of the EISCAT Incoherent Scatter Radar facilities, the range extent of the detectable target is typically of the order of one thousand kilometers – about seven milliseconds – whereas the characteristic correlation time of the scattered signal varies from a few milliseconds in the D-region to only tens of microseconds in the F-region. If one is interested in estimating the scattering autocorrelation function (ACF at time lags shorter than the F-region correlation time, the D-region must be considered as a moderately overspread target, whereas the F-region is a severely overspread one. Given the technical restrictions of the radar hardware, a combination of ATC and phase-coded long pulses is advantageous for this kind of target. We evaluate such an experiment under infinitely low signal-to-noise ratio (SNR conditions using lag profile inversion. In addition, a qualitative evaluation under high-SNR conditions is performed by analysing simulated data. The results show that an acceptable estimation accuracy and a very good lag resolution in the D-region can be achieved with a pulse length long enough for simultaneous E- and F-region measurements with a reasonable lag extent. The new experiment design is tested with the EISCAT Tromsø VHF (224 MHz radar. An example of a full D/E/F-region ACF from the test run is shown at the end of the paper.
International Nuclear Information System (INIS)
with high precision the neutron flux, burnup and concentration of every isotope, fissile, fissionable or fertile, gaseous or solid, all of them as functions of radius and time. But this formidable task is not suitable to be included in a fuel performance code, which must attend the great number of thermomechanical and thermochemical processes within the fuel rod. To accommodate both requirements, a simplified treatment is adopted consisting of restricting the balance equations to more relevant nuclides and reducing the energy spectrum to a single group. The purpose is to obtain empirical expressions to represent, with the higher possible approximation degree, the absorption, capture and fission cross sections of these isotopes as functions of the initial enrichment in 235U, the average burnup and the radial coordinate. The curves obtained with a so drastic simplification demand a careful testing before incorporation in the general fuel behaviour code. This testing is performed via comparison with the reliable reactor codes. The first antecedent in this type of analysis is found in the RADAR model [4] which was validated against the WIMS [5,6] code. The TUBRNP model, included in the TRANSURANUS code [7] and the RAPID model [8] are also based on the same concept. In this work curves fitted for the cross sections of 235U, 236U, 238U, 239Pu, 240Pu, 241Pu and 242Pu are obtained from the predictions of the reactor cell codes HUEMUL [9] and CONDOR [10] for an average burnup ranging from fresh fuel to 120 MWd/kgHM and for an initial enrichment ranging from natural uranium to 12%. The final purpose is to extend the application range of the DIONISIO code [11,12,13] (originally designed to predict the fuel behavior in normal operation conditions) to the high burnup domain. The predictions of DIONISIO were compared with a large number of experimental data, obtaining an excellent agreement
Institute of Scientific and Technical Information of China (English)
CHENG Qiang; CAO JianWen; WANG Bin; ZHANG HaiBin
2009-01-01
The adjoint code generator (ADG) is developed to produce the adjoint codes, which are used to analytically calculate gradients and the Hessian-vector products with the costs independent of the number of the independent variables. Different from other automatic differentiation tools, the implementation of ADG has advantages of using the least program behavior decomposition method and several static dependence analysis techniques. In this paper we first address the concerned concepts and fundamentals, and then introduce the functionality and the features of ADG. In particular, we also discuss the design architecture of ADG and implementation details including the recomputation and storing strategy and several techniques for code optimization. Some experimental results in several applications are presented at the end.
Frutos-Alfaro, Francisco
2015-01-01
A program to generate codes in Fortran and C of the full Magnetohydrodynamic equations is shown. The program used the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the MHD equations to obtain a code that can be used as a seed for a MHD code for numerical applications. As an example, we present part of output of our programs for Cartesian coordinates and how to do the discretization.
Vaucouleur, Sebastien
2011-02-01
We introduce code query by example for customisation of evolvable software products in general and of enterprise resource planning systems (ERPs) in particular. The concept is based on an initial empirical study on practices around ERP systems. We motivate our design choices based on those empirical results, and we show how the proposed solution helps with respect to the infamous upgrade problem: the conflict between the need for customisation and the need for upgrade of ERP systems. We further show how code query by example can be used as a form of lightweight static analysis, to detect automatically potential defects in large software products. Code query by example as a form of lightweight static analysis is particularly interesting in the context of ERP systems: it is often the case that programmers working in this field are not computer science specialists but more of domain experts. Hence, they require a simple language to express custom rules.
Approximate design calculation methods for radiation streaming in shield irregularities
Energy Technology Data Exchange (ETDEWEB)
Miura, Toshimasa; Hirao, Yoshihiro [Ship Research Inst., Mitaka, Tokyo (Japan); Yoritsune, Tsutomu
1997-10-01
Investigation and assessment are made for approximate design calculation methods of radiation streaming in shield irregularities. Investigation is made for (1) source, (2) definition of streaming radiation components, (3) calculation methods of streaming radiation, (4) streaming formulas for each irregularity, (5) difficulties in application of streaming formulas, etc. Furthermore, investigation is made for simple calculation codes and albedo data. As a result, it is clarified that streaming calculation formulas are not enough to cover various irregularities and their accuracy or application limit is not sufficiently clear. Accurate treatment is not made in the formulas with respect to the radiation behavior for slant incidence, bend part, offset etc., that results in too much safety factors in the design calculation and distrust of the streaming calculation. To overcome the state and improve the accuracy of the design calculation for shield irregularities, it is emphasized to assess existing formulas and develop better formulas based on systematic experimental studies. (author)
Gliebe, P; Mani, R.; Shin, H.; Mitchell, B.; Ashford, G.; Salamah, S.; Connell, S.; Huff, Dennis (Technical Monitor)
2000-01-01
This report describes work performed on Contract NAS3-27720AoI 13 as part of the NASA Advanced Subsonic Transport (AST) Noise Reduction Technology effort. Computer codes were developed to provide quantitative prediction, design, and analysis capability for several aircraft engine noise sources. The objective was to provide improved, physics-based tools for exploration of noise-reduction concepts and understanding of experimental results. Methods and codes focused on fan broadband and 'buzz saw' noise and on low-emissions combustor noise and compliment work done by other contractors under the NASA AST program to develop methods and codes for fan harmonic tone noise and jet noise. The methods and codes developed and reported herein employ a wide range of approaches, from the strictly empirical to the completely computational, with some being semiempirical analytical, and/or analytical/computational. Emphasis was on capturing the essential physics while still considering method or code utility as a practical design and analysis tool for everyday engineering use. Codes and prediction models were developed for: (1) an improved empirical correlation model for fan rotor exit flow mean and turbulence properties, for use in predicting broadband noise generated by rotor exit flow turbulence interaction with downstream stator vanes: (2) fan broadband noise models for rotor and stator/turbulence interaction sources including 3D effects, noncompact-source effects. directivity modeling, and extensions to the rotor supersonic tip-speed regime; (3) fan multiple-pure-tone in-duct sound pressure prediction methodology based on computational fluid dynamics (CFD) analysis; and (4) low-emissions combustor prediction methodology and computer code based on CFD and actuator disk theory. In addition. the relative importance of dipole and quadrupole source mechanisms was studied using direct CFD source computation for a simple cascadeigust interaction problem, and an empirical combustor
Energy Technology Data Exchange (ETDEWEB)
Link, Hamilton E.; Schroeppel, Richard Crabtree; Neumann, William Douglas; Campbell, Philip LaRoche; Beaver, Cheryl Lynn; Pierson, Lyndon George; Anderson, William Erik
2004-10-01
If software is designed so that the software can issue functions that will move that software from one computing platform to another, then the software is said to be 'mobile'. There are two general areas of security problems associated with mobile code. The 'secure host' problem involves protecting the host from malicious mobile code. The 'secure mobile code' problem, on the other hand, involves protecting the code from malicious hosts. This report focuses on the latter problem. We have found three distinct camps of opinions regarding how to secure mobile code. There are those who believe special distributed hardware is necessary, those who believe special distributed software is necessary, and those who believe neither is necessary. We examine all three camps, with a focus on the third. In the distributed software camp we examine some commonly proposed techniques including Java, D'Agents and Flask. For the specialized hardware camp, we propose a cryptographic technique for 'tamper-proofing' code over a large portion of the software/hardware life cycle by careful modification of current architectures. This method culminates by decrypting/authenticating each instruction within a physically protected CPU, thereby protecting against subversion by malicious code. Our main focus is on the camp that believes that neither specialized software nor hardware is necessary. We concentrate on methods of code obfuscation to render an entire program or a data segment on which a program depends incomprehensible. The hope is to prevent or at least slow down reverse engineering efforts and to prevent goal-oriented attacks on the software and execution. The field of obfuscation is still in a state of development with the central problem being the lack of a basis for evaluating the protection schemes. We give a brief introduction to some of the main ideas in the field, followed by an in depth analysis of a technique called &apos
Ogunfunmi, Tokunbo
2010-01-01
It is becoming increasingly apparent that all forms of communication-including voice-will be transmitted through packet-switched networks based on the Internet Protocol (IP). Therefore, the design of modern devices that rely on speech interfaces, such as cell phones and PDAs, requires a complete and up-to-date understanding of the basics of speech coding. Outlines key signal processing algorithms used to mitigate impairments to speech quality in VoIP networksOffering a detailed yet easily accessible introduction to the field, Principles of Speech Coding provides an in-depth examination of the
A minimum-error, energy-constrained neural code is an instantaneous-rate code.
Johnson, Erik C; Jones, Douglas L; Ratnam, Rama
2016-04-01
Sensory neurons code information about stimuli in their sequence of action potentials (spikes). Intuitively, the spikes should represent stimuli with high fidelity. However, generating and propagating spikes is a metabolically expensive process. It is therefore likely that neural codes have been selected to balance energy expenditure against encoding error. Our recently proposed optimal, energy-constrained neural coder (Jones et al. Frontiers in Computational Neuroscience, 9, 61 2015) postulates that neurons time spikes to minimize the trade-off between stimulus reconstruction error and expended energy by adjusting the spike threshold using a simple dynamic threshold. Here, we show that this proposed coding scheme is related to existing coding schemes, such as rate and temporal codes. We derive an instantaneous rate coder and show that the spike-rate depends on the signal and its derivative. In the limit of high spike rates the spike train maximizes fidelity given an energy constraint (average spike-rate), and the predicted interspike intervals are identical to those generated by our existing optimal coding neuron. The instantaneous rate coder is shown to closely match the spike-rates recorded from P-type primary afferents in weakly electric fish. In particular, the coder is a predictor of the peristimulus time histogram (PSTH). When tested against in vitro cortical pyramidal neuron recordings, the instantaneous spike-rate approximates DC step inputs, matching both the average spike-rate and the time-to-first-spike (a simple temporal code). Overall, the instantaneous rate coder relates optimal, energy-constrained encoding to the concepts of rate-coding and temporal-coding, suggesting a possible unifying principle of neural encoding of sensory signals.
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-10-01
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.
Tree-fold loop approximation of AMD
Energy Technology Data Exchange (ETDEWEB)
Ono, Akira [Tohoku Univ., Sendai (Japan). Faculty of Science
1997-05-01
AMD (antisymmetrized molecular dynamics) is a frame work for describing a wave function of nucleon multi-body system by Slater determinant of Gaussian wave flux, and a theory for integrally describing a wide range of nuclear reactions such as intermittent energy heavy ion reaction, nucleon incident reaction and so forth. The aim of this study is induction on approximation equation of expected value, {nu}, in correlation capable of calculation with time proportional A (exp 3) (or lower), and to make AMD applicable to the heavier system such as Au+Au. As it must be avoided to break characteristics of AMD, it needs not to be anxious only by approximating the {nu}-value. However, in order to give this approximation any meaning, error of this approximation will have to be sufficiently small in comparison with bond energy of atomic nucleus and smaller than 1 MeV/nucleon. As the absolute expected value in correlation may be larger than 50 MeV/nucleon, the approximation is required to have a high accuracy within 2 percent. (G.K.)
An Approximation Algorithm for #k-SAT
Thurley, Marc
2011-01-01
We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k >= 3 within a running time that is not only non-trivial, but also significantly better than that of the currently fastest exact algorithms for the problem. More precisely, our algorithm is a randomized approximation scheme whose running time depends polynomially on the error tolerance and is mildly exponential in the number n of variables of the input formula. For example, even stipulating sub-exponentially small error tolerance, the number of solutions to 3-CNF input formulas can be approximated in time O(1.5366^n). For 4-CNF input the bound increases to O(1.6155^n). We further show how to obtain upper and lower bounds on the number of solutions to a CNF formula in a controllable way. Relaxing the requirements on the quality of the approximation, on k-CNF input we obtain sign...
New code match strategy for wideband code division multiple access code tree management
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Orthogonal variable spreading factor channelization codes are widely used to provide variable data rates for supporting different bandwidth requirements in wideband code division multiple access (WCDMA) systems. A new code match scheme for WCDMA code tree management was proposed. The code match scheme is similar to the existing crowed-first scheme. When choosing a code for a user, the code match scheme only compares the one up layer of the allocated codes, unlike the crowed-first scheme which perhaps compares all up layers. So the operation of code match scheme is simple, and the average time delay is decreased by 5.1%. The simulation results also show that the code match strategy can decrease the average code blocking probability by 8.4%.
Gradient-based Kriging approximate model and its application research to optimization design
Institute of Scientific and Technical Information of China (English)
XUAN Ying; XIANG JunHua; ZHANG WeiHua; ZHANG YuLin
2009-01-01
In the process of multidisciplinary design optimization, there exits the calculation complexity problem due to frequently calling high fidelity system analysis models. The high fidelity system analysis models can be surrogated by approximate models. The sensitivity analysis and numerical noise filtering can be done easily by coupling approximate models to optimization. Approximate models can reduce the number of executions of the problem's simulation code during optimization, so the solution efficiency of the multidisciplinary design optimization problem can be improved. Most optimization methods are based on gradient. The gradients of the objective and constrain functions are gained easily. The gradient-based Kriging (GBK) approximate model can be constructed by using system response value and its gradients. The gradients can greatly improve prediction precision of system response. The hybrid optimization method is constructed by coupling GBK approximate models to gradient-based optimization methods. An aircraft aerodynamics shape optimization design example indicates that the methods of this paper can achieve good feasibility and validity.
Fast wavelet based sparse approximate inverse preconditioner
Energy Technology Data Exchange (ETDEWEB)
Wan, W.L. [Univ. of California, Los Angeles, CA (United States)
1996-12-31
Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.
Approximating light rays in the Schwarzschild field
Semerak, Oldrich
2014-01-01
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 practical solving of the ray-deflection exercise.
On the approximate zero of Newton method
Institute of Scientific and Technical Information of China (English)
黄正达
2003-01-01
A judgment criterion to guarantee a point to be a Chen' s approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen' s approximate zero may not be a Smale' s approximate zero. The error estimate obtained indicated the convergent order when we use |f(x) | < ε to stop computation in software.The result can also be applied for solving partial derivative and integration equations.
Large scale systems approximation: Analysis and control
International Nuclear Information System (INIS)
This work concerns the study of the approximation of high dimensional systems by low order models. This approximation is defined by aggregation methods, the method based on singular perturbations and a relatively recent method. This later one is formulated in a particular representation of the system and is called balanced realisation method. The application of the approximation is then studied in the case of suboptimal control theory for the several defined models. The results of numerical simulation for the analysis and control are carried on two examples defined by a model of a nuclear reactor core of order nine and a steam generator of a fuel station of order twenty and permitted to develop a comparative study of the performances of the different methods analysed in the case of open loop and closed loop models
Numerical approximation of partial differential equations
Bartels, Sören
2016-01-01
Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular ...
Approximate Bayesian Computation: a nonparametric perspective
Blum, Michael
2010-01-01
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics s_obs from the data and simulating summary statistics for different values of the parameter theta. The posterior distribution is then approximated by an estimator of the conditional density g(theta|s_obs). In this paper, we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment. Additionally, we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a fewer number of terms than the estimator with linear adjustment. Although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling, we find that they can achieve better perfor...
On approximation of Markov binomial distributions
Xia, Aihua; 10.3150/09-BEJ194
2010-01-01
For a Markov chain $\\mathbf{X}=\\{X_i,i=1,2,...,n\\}$ with the state space $\\{0,1\\}$, the random variable $S:=\\sum_{i=1}^nX_i$ is said to follow a Markov binomial distribution. The exact distribution of $S$, denoted $\\mathcal{L}S$, is very computationally intensive for large $n$ (see Gabriel [Biometrika 46 (1959) 454--460] and Bhat and Lal [Adv. in Appl. Probab. 20 (1988) 677--680]) and this paper concerns suitable approximate distributions for $\\mathcal{L}S$ when $\\mathbf{X}$ is stationary. We conclude that the negative binomial and binomial distributions are appropriate approximations for $\\mathcal{L}S$ when $\\operatorname {Var}S$ is greater than and less than $\\mathbb{E}S$, respectively. Also, due to the unique structure of the distribution, we are able to derive explicit error estimates for these approximations.
The unitary convolution approximation for heavy ions
Grande, P L
2002-01-01
The convolution approximation for the impact-parameter dependent energy loss is reviewed with emphasis on the determination of the stopping force for heavy projectiles. In this method, the energy loss in different impact-parameter regions is well determined and interpolated smoothly. The physical inputs of the model are the projectile-screening function (in the case of dressed ions), the electron density and oscillators strengths of the target atoms. Moreover, the convolution approximation, in the perturbative mode (called PCA), yields remarkable agreement with full semi-classical-approximation (SCA) results for bare as well as for screened ions at all impact parameters. In the unitary mode (called UCA), the method contains some higher-order effects (yielding in some cases rather good agreement with full coupled-channel calculations) and approaches the classical regime similar as the Bohr model for large perturbations (Z/v>>1). The results are then used to compare with experimental values of the non-equilibri...
DEFF Research Database (Denmark)
Paolini, Enrico; Stefanovic, Cedomir; Liva, Gianluigi;
2015-01-01
as waste. However, if the common receiver (e.g., base station) is capable to store the collision slots and use them in a transmission recovery process based on successive interference cancellation, the design space for access protocols is radically expanded. We present the paradigm of coded random access...
Anaïs Schaeffer
2013-01-01
This summer, CERN took part in the Google Summer of Code programme for the third year in succession. Open to students from all over the world, this programme leads to very successful collaborations for open source software projects. Image: GSoC 2013. Google Summer of Code (GSoC) is a global programme that offers student developers grants to write code for open-source software projects. Since its creation in 2005, the programme has brought together some 6,000 students from over 100 countries worldwide. The students selected by Google are paired with a mentor from one of the participating projects, which can be led by institutes, organisations, companies, etc. This year, CERN PH Department’s SFT (Software Development for Experiments) Group took part in the GSoC programme for the third time, submitting 15 open-source projects. “Once published on the Google Summer for Code website (in April), the projects are open to applications,” says Jakob Blomer, one of the o...
DEFF Research Database (Denmark)
Fukui, Hironori; Yomo, Hironori; Popovski, Petar
2013-01-01
Physical layer network coding (PLNC) has the potential to improve throughput of multi-hop networks. However, most of the works are focused on the simple, three-node model with two-way relaying, not taking into account the fact that there can be other neighboring nodes that can cause...
Laëtitia Pedroso
2010-01-01
During his talk to the staff at the beginning of the year, the Director-General mentioned that a new code of conduct was being drawn up. What exactly is it and what is its purpose? Anne-Sylvie Catherin, Head of the Human Resources (HR) Department, talked to us about the whys and wherefores of the project. Drawing by Georges Boixader from the cartoon strip “The World of Particles” by Brian Southworth. A code of conduct is a general framework laying down the behaviour expected of all members of an organisation's personnel. “CERN is one of the very few international organisations that don’t yet have one", explains Anne-Sylvie Catherin. “We have been thinking about introducing a code of conduct for a long time but lacked the necessary resources until now”. The call for a code of conduct has come from different sources within the Laboratory. “The Equal Opportunities Advisory Panel (read also the "Equal opportuni...
Approximately-Balanced Drilling in Daqing Oilfield
Institute of Scientific and Technical Information of China (English)
Xia Bairu; Zheng Xiuhua; Li Guoqing; Tian Tuo
2004-01-01
The Daqing oilfield is a multilayered heterogeneous oil field where the pressure are different in the same vertical profile causing many troubles to the adjustment well drillings. The approximately-balanced drilling technique has been developed and proved to be efficient and successful in Daqing oilfield. This paper discusses the application of approximately-balanced drilling technique under the condition of multilayered pressure in Daqing oilfield, including the prediction of formation pressure, the pressure discharge technique for the drilling well and the control of the density of drilling fluid.
Local density approximations from finite systems
Entwistle, Mike; Wetherell, Jack; Longstaff, Bradley; Ramsden, James; Godby, Rex
2016-01-01
The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We introduce an alternative set of LDAs constructed from slab-like systems of one, two and three electrons that resemble the HEG within a finite region, and illustrate the concept in one dimension. Comparing with the exact densities and Kohn-Sham potentials for various test systems, we find that the LDAs give a good account of the self-interaction correction, but are less reliable when correlation is stronger or currents flow.
Weisskopf--Wigner approximation in atomic physics
International Nuclear Information System (INIS)
Several approximations involved in the usual Weisskopf-Wigner treatment of the emission of light by an atom are investigated. The system considered is a recoilless, nonrelativistic hydrogen atom interacting with a quantized electromagnetic field, in dipole approximation (with a nonrelativistic cutoff in momentum space). Since only electric dipole waves interact with the atom, the Hamiltonian can be expressed in a simple one-dimensional form. The time evolution of the system is determined by resolvent operator techniques. The method goes beyond the analysis by Van Hove and Hugenholtz, allowing one to treat also fields of finite intensity in the infinite-volume limit. A comparison between this and other techniques is made
Extending the Eikonal Approximation to Low Energy
Capel, Pierre; Ogata, Kazuyuki
2014-01-01
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.
Computing Nash Equilibria: Approximation and Smoothed Complexity
Chen, Xi; Deng, Xiaotie; Teng, Shang-Hua
2006-01-01
We show that the BIMATRIX game does not have a fully polynomial-time approximation scheme, unless PPAD is in P. In other words, no algorithm with time polynomial in n and 1/\\epsilon can compute an \\epsilon-approximate Nash equilibrium of an n by nbimatrix game, unless PPAD is in P. Instrumental to our proof, we introduce a new discrete fixed-point problem on a high-dimensional cube with a constant side-length, such as on an n-dimensional cube with side-length 7, and show that they are PPAD-co...
Generalized companion matrix for approximate GCD
Boito, Paola
2011-01-01
We study a variant of the univariate approximate GCD problem, where the coe?- cients of one polynomial f(x)are known exactly, whereas the coe?cients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which describes the operator of multiplication by gin the quotient ring C[x]=(f). In particular, the structure of the null space of the multiplication matrix contains all the essential information about GCD(f; g). Moreover, the multiplication matrix exhibits a displacement structure that allows us to design a fast algorithm for approximate GCD computation with quadratic complexity w.r.t. polynomial degrees.
Static correlation beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly...... for intermediate binding distances. A Hubbard model for the dimer allows us to obtain exact analytical results for the various approximations, which is readily compared with the exact diagonalization of the model. Moreover, the model is shown to reproduce all the qualitative results from the ab initio...
BEST APPROXIMATION BY DOWNWARD SETS WITH APPLICATIONS
Institute of Scientific and Technical Information of China (English)
H.Mohebi; A. M. Rubinov
2006-01-01
We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs (W,x), where x ∈ X and W is a closed downward subset of X.
Development of a New Monte Carlo reactor physics code
Leppänen, Jaakko
2007-01-01
Monte Carlo neutron transport codes are widely used in various reactor physics applications, traditionally related to criticality safety analyses, radiation shielding problems, detector modelling and validation of deterministic transport codes. The main advantage of the method is the capability to model geometry and interaction physics without major approximations. The disadvantage is that the modelling of complicated systems is very computing-intensive, which restricts the applications to so...
On Asymmetric Quantum MDS Codes
Ezerman, Martianus Frederic; Ling, San
2010-01-01
Assuming the validity of the MDS Conjecture, the weight distribution of all MDS codes is known. Using a recently-established characterization of asymmetric quantum error-correcting codes, linear MDS codes can be used to construct asymmetric quantum MDS codes with $d_{z} \\geq d_{x}\\geq 2$ for all possible values of length $n$ for which linear MDS codes over $\\F_{q}$ are known to exist.
Evaluation Codes from an Affine Veriety Code Perspective
DEFF Research Database (Denmark)
Geil, Hans Olav
2008-01-01
Evaluation codes (also called order domain codes) are traditionally introduced as generalized one-point geometric Goppa codes. In the present paper we will give a new point of view on evaluation codes by introducing them instead as particular nice examples of affine variety codes. Our study inclu...... includes a reformulation of the usual methods to estimate the minimum distances of evaluation codes into the setting of affine variety codes. Finally we describe the connection to the theory of one-pointgeometric Goppa codes. Contents 4.1 Introduction...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 4.2 Affine variety codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 4.3 Some Gr¨obner basis theoretical tools . . . . . . . . . . . . . . . . . . . . . . . 155 4.4 A bound on the minimum distance of C(I,L) . . . . . . . . . . . . . . . . . . 157 4.5 The Feng-Rao bound...... for C(I,L)? . . . . . . . . . . . . . . . . . . . . . . . . 160 4.6 Using weighted degree orderings . . . . . . . . . . . . . . . . . . . . . . . . . 163 4.7 The order domain conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 4.8 Weight functions and order domains...
Rate-adaptive BCH codes for distributed source coding
DEFF Research Database (Denmark)
Salmistraro, Matteo; Larsen, Knud J.; Forchhammer, Søren
2013-01-01
This paper considers Bose-Chaudhuri-Hocquenghem (BCH) codes for distributed source coding. A feedback channel is employed to adapt the rate of the code during the decoding process. The focus is on codes with short block lengths for independently coding a binary source X and decoding it given its...... correlated side information Y. The proposed codes have been analyzed in a high-correlation scenario, where the marginal probability of each symbol, Xi in X, given Y is highly skewed (unbalanced). Rate-adaptive BCH codes are presented and applied to distributed source coding. Adaptive and fixed checking...... strategies for improving the reliability of the decoded result are analyzed, and methods for estimating the performance are proposed. In the analysis, noiseless feedback and noiseless communication are assumed. Simulation results show that rate-adaptive BCH codes achieve better performance than low...
Improved algorithms for approximate string matching (extended abstract
Directory of Open Access Journals (Sweden)
Papamichail Georgios
2009-01-01
Full Text Available Abstract Background The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants of the problem, including comparison of two strings, approximate pattern identification in a string or calculation of the longest common subsequence that two strings share. Results We designed an output sensitive algorithm solving the edit distance problem between two strings of lengths n and m respectively in time O((s - |n - m|·min(m, n, s + m + n and linear space, where s is the edit distance between the two strings. This worst-case time bound sets the quadratic factor of the algorithm independent of the longest string length and improves existing theoretical bounds for this problem. The implementation of our algorithm also excels in practice, especially in cases where the two strings compared differ significantly in length. Conclusion We have provided the design, analysis and implementation of a new algorithm for calculating the edit distance of two strings with both theoretical and practical implications. Source code of our algorithm is available online.
ASPHERICAL SURFACES APPROXIMATION IN AUTOMATED DESIGN OF OPTICAL SYSTEMS
Directory of Open Access Journals (Sweden)
T. V. Ivanova
2015-07-01
Full Text Available Subject of Research. The paper deals with the problems of higher order aspherical surfaces approximation using different equation types. The objects of research are two types of equations for higher order aspherical surfaces description used in different software for optical systems design (SАRО, OPAL, ZEMAX, CODE-V, etc. and dependent on z-coordinate or on a radial coordinate on the surface. Conversion from one type of equations to another is considered in view of application in different software for optical systems design. Methods. The subject matter of the method lies in usage of mean square method approximation for recalculation of high-order aspherical surface. Iterative algorithm for recalculation is presented giving the possibility to recalculate coefficients for different types of equations with required accuracy. Recommendations are given for choosing recalculation parameters such as the number of result equation coefficients, the number of points for recalculation and point allocation on a surface. Main Results. Example of recalculation for aspherical surface and accuracy estimation, including result aberration comparison between initial surface and recalculated surface are presented. The example has shown that required accuracy of surface representation was obtained. Practical Relevance. This technique is usable for recalculation of higher order aspherical surfaces in various types of software for optical systems design and also for research of optimal higher order aspherical surfaces description.
Improved Algorithms for Approximate String Matching (Extended Abstract)
Papamichail, Dimitris
2008-01-01
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants of the problem, including comparison of two strings, approximate pattern identification in a string or calculation of the longest common subsequence that two strings share. We designed an output sensitive algorithm solving the edit distance problem between two strings of lengths n and m respectively in time O((s-|n-m|)min(m,n,s)+m+n) and linear space, where s is the edit distance between the two strings. This worst-case time bound sets the quadratic factor of the algorithm independent of the longest string length and improves existing theoretical bounds for this problem. The implementation of our algorithm excels also in practice, especially in cases where the two strings compared differ significantly in length. Source code of our algorithm is available at http://www.cs.mia...
Nonlinear approximation in alpha-modulation spaces
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2006-01-01
The α-modulation spaces are a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that brushlet bases can be constructed to form unconditional and even greedy bases for the α-modulation spaces. We study m -term nonlinear approximation with brushlet...
An approximate classical unimolecular reaction rate theory
Zhao, Meishan; Rice, Stuart A.
1992-05-01
We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.
Approximate Equilibrium Problems and Fixed Points
Directory of Open Access Journals (Sweden)
H. Mazaheri
2013-01-01
Full Text Available We find a common element of the set of fixed points of a map and the set of solutions of an approximate equilibrium problem in a Hilbert space. Then, we show that one of the sequences weakly converges. Also we obtain some theorems about equilibrium problems and fixed points.
Median Approximations for Genomes Modeled as Matrices.
Zanetti, Joao Paulo Pereira; Biller, Priscila; Meidanis, Joao
2016-04-01
The genome median problem is an important problem in phylogenetic reconstruction under rearrangement models. It can be stated as follows: Given three genomes, find a fourth that minimizes the sum of the pairwise rearrangement distances between it and the three input genomes. In this paper, we model genomes as matrices and study the matrix median problem using the rank distance. It is known that, for any metric distance, at least one of the corners is a [Formula: see text]-approximation of the median. Our results allow us to compute up to three additional matrix median candidates, all of them with approximation ratios at least as good as the best corner, when the input matrices come from genomes. We also show a class of instances where our candidates are optimal. From the application point of view, it is usually more interesting to locate medians farther from the corners, and therefore, these new candidates are potentially more useful. In addition to the approximation algorithm, we suggest a heuristic to get a genome from an arbitrary square matrix. This is useful to translate the results of our median approximation algorithm back to genomes, and it has good results in our tests. To assess the relevance of our approach in the biological context, we ran simulated evolution tests and compared our solutions to those of an exact DCJ median solver. The results show that our method is capable of producing very good candidates. PMID:27072561
WEIGHTED APPROXIMATION ON SZASZ-TYPE OPERATORS
Institute of Scientific and Technical Information of China (English)
Feng Guo
2003-01-01
In this paper, we use weighted modules ω2φλ (f,t)w to study the pointwise approximation on Szász-type operators, and obtain the direct and converse theorem, as well as characterizations of the pointwise approxi- mation of Jacobi-weighted Szász-type operators.
Semi-classical approximation and microcanonical ensemble
International Nuclear Information System (INIS)
For quantum mechanical systems with spherically symmetric potential the improved W.K.B. approximation of Elworthy and Truman corresponds to the classical microcanonical ensemble in the limit where (h/2π) goes to zero, at least for small time. (orig.)
Eignets for function approximation on manifolds
Mhaskar, H N
2009-01-01
Let $\\XX$ be a compact, smooth, connected, Riemannian manifold without boundary, $G:\\XX\\times\\XX\\to \\RR$ be a kernel. Analogous to a radial basis function network, an eignet is an expression of the form $\\sum_{j=1}^M a_jG(\\circ,y_j)$, where $a_j\\in\\RR$, $y_j\\in\\XX$, $1\\le j\\le M$. We describe a deterministic, universal algorithm for constructing an eignet for approximating functions in $L^p(\\mu;\\XX)$ for a general class of measures $\\mu$ and kernels $G$. Our algorithm yields linear operators. Using the minimal separation amongst the centers $y_j$ as the cost of approximation, we give modulus of smoothness estimates for the degree of approximation by our eignets, and show by means of a converse theorem that these are the best possible for every \\emph{individual function}. We also give estimates on the coefficients $a_j$ in terms of the norm of the eignet. Finally, we demonstrate that if any sequence of eignets satisfies the optimal estimates for the degree of approximation of a smooth function, measured in ter...
Approximating the Balanced Minimum Evolution Problem
Fiorini, Samuel
2011-01-01
We prove a strong inapproximability result for the Balanced Minimum Evolution Problem. Our proof also implies that the problem remains NP-hard even when restricted to metric instances. Furthermore, we give a MST-based 2-approximation algorithm for the problem for such instances.
Optical bistability without the rotating wave approximation
Energy Technology Data Exchange (ETDEWEB)
Sharaby, Yasser A., E-mail: Yasser_Sharaby@hotmail.co [Physics Department, Faculty of Applied Sciences, Suez Canal University, Suez (Egypt); Joshi, Amitabh, E-mail: ajoshi@eiu.ed [Department of Physics, Eastern Illinois University, Charleston, IL 61920 (United States); Hassan, Shoukry S., E-mail: Shoukryhassan@hotmail.co [Mathematics Department, College of Science, University of Bahrain, P.O. Box 32038 (Bahrain)
2010-04-26
Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.
Kravchuk functions for the finite oscillator approximation
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.
An approximate analytical approach to resampling averages
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, M.
2004-01-01
Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr...
Approximations in the PE-method
DEFF Research Database (Denmark)
Arranz, Marta Galindo
1996-01-01
Two differenct sources of errors may occur in the implementation of the PE methods; a phase error introduced in the approximation of a pseudo-differential operator and an amplitude error generated from the starting field. First, the inherent phase errors introduced in the solution are analyzed...
Quantum electrodynamics in a classical approximation, 1
International Nuclear Information System (INIS)
Quantum electrodynamics is formulated in a classical approximation. A quantum mechanical proper-time is employed as a useful parameter, which enables us to elucidate the relationship between quantum electrodynamics and classical electrodynamics. The classical motion of a charged particle is realized as an asymptotic limit of quantum electrodynamics. (author)
Revisiting Twomey's approximation for peak supersaturation
Directory of Open Access Journals (Sweden)
B. J. Shipway
2014-10-01
Full Text Available Twomey's seminal 1959 paper provided lower and upper bound approximations to the estimation of peak supersaturation within an updraft and thus provides the first closed expression for the number of nucleated cloud droplets. The form of this approximation is simple, but provides a surprisingly good estimate and has subsequently been employed in more sophisticated treatments of nucleation parametrization. In the current paper, we revisit the lower bound approximation of Twomey and make a small adjustment which can be used to obtain a more accurate calculation of peak supersaturation under all potential aerosol loadings and thermodynamic conditions. In order to make full use of this improved approximation, the underlying integro-differential equation for supersaturation evolution and the condition for calculating peak supersaturation are examined. A simple rearrangement of the algebra allows for an expression to be written down which can then be solved with a single lookup table with only one independent variable for an underlying lognormal aerosol population. Multimode aerosol with only N different dispersion characteristics require only N of these one-dimensional lookup tables. No additional information is required in the lookup table to deal with additional chemical, physical or thermodynamic properties. The resulting implementation provides a relatively simple, yet computationally cheap and very accurate physically-based parametrization of droplet nucleation for use in climate and NWP models.
On operators with bounded approximation property
Reinov, Oleg
2013-01-01
It is known that any separable Banach space with BAP is a complemented subspace of a Banach space with a basis. We show that every operator with bounded approximation property, acting from a separable Banach space, can be factored through a Banach space with a basis.
Approximation by Penultimate Extreme Value Distributions
L.F.M. de Haan (Laurens)
1998-01-01
textabstractn certain cases the distribution of the normalized maximum of a sample can be better approximated by a sequence of different extreme value distributions than by the final one. We show that these cases are rather restricted and that the possible improvement is not spectacular.
Approximate fixed point of Reich operator
Directory of Open Access Journals (Sweden)
M. Saha
2013-01-01
Full Text Available In the present paper, we study the existence of approximate fixed pointfor Reich operator together with the property that the ε-fixed points are concentrated in a set with the diameter tends to zero if ε $to$ > 0.
An Approximation of Ultra-Parabolic Equations
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2012-01-01
Full Text Available The first and second order of accuracy difference schemes for the approximate solution of the initial boundary value problem for ultra-parabolic equations are presented. Stability of these difference schemes is established. Theoretical results are supported by the result of numerical examples.
Approximation Algorithms for Model-Based Diagnosis
Feldman, A.B.
2010-01-01
Model-based diagnosis is an area of abductive inference that uses a system model, together with observations about system behavior, to isolate sets of faulty components (diagnoses) that explain the observed behavior, according to some minimality criterion. This thesis presents greedy approximation a
Neutral kaons without Weisskopf-Wigner approximation
International Nuclear Information System (INIS)
The model-independent formalism is constructed to describe decays of mixed particles without using the Weisskopf-Wigner approximation (WWA). Limitations due to various symmetries are traced for neutral K mesons. As an application we show that effects of CPT violation and going beyond WWA may be separated and studied independently. 16 refs
Neutral Kaons without Weisskopf-Wigner Approximation
Azimov, Ya. I.
1995-01-01
The model-independent formalism is constructed to describe decays of mixed particles without using the Weisskopf-Wigner approximation. Limitations due to various symmetries are traced for neutral $K-$mesons. As an application we show that effects of $CPT-$violation and going beyond WWA may be separated and studied independently.
Approximating the DGP of China's Quarterly GDP
Ph.H.B.F. Franses (Philip Hans); H. Mees (Heleen)
2010-01-01
textabstractWe demonstrate that the data generating process (DGP) of China’s cumulated quarterly Gross Domestic Product (GDP, current prices), as it is reported by the National Bureau of Statistics of China, can be (very closely) approximated by a simple rule. This rule is that annual growth in any
Empirical progress and nomic truth approximation revisited
Kuipers, Theodorus
2014-01-01
In my From Instrumentalism to Constructive Realism (2000) I have shown how an instrumentalist account of empirical progress can be related to nomic truth approximation. However, it was assumed that a strong notion of nomic theories was needed for that analysis. In this paper it is shown, in terms of
Image Compression Via a Fast DCT Approximation
Bayer, F. M.; Cintra, R. J.
2010-01-01
Discrete transforms play an important role in digital signal processing. In particular, due to its transform domain energy compaction properties, the discrete cosine transform (DCT) is pivotal in many image processing problems. This paper introduces a numerical approximation method for the DCT based
Double unresolved approximations to multiparton scattering amplitudes
International Nuclear Information System (INIS)
We present approximations to tree-level multiparton scattering amplitudes which are appropriate when two partons are unresolved. These approximations are required for the analytic isolation of infrared singularities of n+2 parton scattering processes contributing to the next-to-next-to-leading order corrections to n jet cross sections. In each case the colour ordered matrix elements factorise and yield a function containing the singular factors multiplying the n-parton amplitudes. When the unresolved particles are colour unconnected, the approximations are simple products of the familiar eikonal and Altarelli-Parisi splitting functions used to describe single unresolved emission. However, when the unresolved particles are colour connected the factorisation is more complicated and we introduce new and general functions to describe the triple collinear and soft/collinear limits in addition to the known double soft gluon limits of Berends and Giele. As expected the triple collinear splitting functions obey an N=1 SUSY identity. To illustrate the use of these double unresolved approximations, we have examined the singular limits of the tree-level matrix elements for e+e- →5 partons when only three partons are resolved. When integrated over the unresolved regions of phase space, these expressions will be of use in evaluating the O(αs3) corrections to the three-jet rate in electron-positron annihilation. (orig.)
$\\Phi$-derivable approximations in gauge theories
Arrizabalaga, A
2003-01-01
We discuss the method of $\\Phi$-derivable approximations in gauge theories. There, two complications arise, namely the violation of Bose symmetry in correlation functions and the gauge dependence. For the latter we argue that the error introduced by the gauge dependent terms is controlled, therefore not invalidating the method.
Approximate Furthest Neighbor in High Dimensions
DEFF Research Database (Denmark)
Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen;
2015-01-01
-dimensional Euclidean space. We build on the technique of Indyk (SODA 2003), storing random projections to provide sublinear query time for AFN. However, we introduce a different query algorithm, improving on Indyk’s approximation factor and reducing the running time by a logarithmic factor. We also present a variation...
Virial expansion coefficients in the harmonic approximation
DEFF Research Database (Denmark)
R. Armstrong, J.; Zinner, Nikolaj Thomas; V. Fedorov, D.;
2012-01-01
The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated...
ON BEST SIMULTANEOUS APPROXIMATION IN QUOTIENT SPACES
Institute of Scientific and Technical Information of China (English)
M. Iranmanesh; H. Mohebi
2007-01-01
We assume that X is a normed linear space, W and M are subspaces of X.We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W + M and the quotient space W/M.
Markov operators, positive semigroups and approximation processes
Altomare, Francesco; Leonessa, Vita; Rasa, Ioan
2015-01-01
In recent years several investigations have been devoted to the study of large classes of (mainly degenerate) initial-boundary value evolution problems in connection with the possibility to obtain a constructive approximation of the associated positive C_0-semigroups. In this research monograph we present the main lines of a theory which finds its root in the above-mentioned research field.
Improved Approximations for Multiprocessor Scheduling Under Uncertainty
Crutchfield, Christopher; Fineman, Jeremy T; Karger, David R; Scott, Jacob
2008-01-01
This paper presents improved approximation algorithms for the problem of multiprocessor scheduling under uncertainty, or SUU, in which the execution of each job may fail probabilistically. This problem is motivated by the increasing use of distributed computing to handle large, computationally intensive tasks. In the SUU problem we are given n unit-length jobs and m machines, a directed acyclic graph G of precedence constraints among jobs, and unrelated failure probabilities q_{ij} for each job j when executed on machine i for a single timestep. Our goal is to find a schedule that minimizes the expected makespan, which is the expected time at which all jobs complete. Lin and Rajaraman gave the first approximations for this NP-hard problem for the special cases of independent jobs, precedence constraints forming disjoint chains, and precedence constraints forming trees. In this paper, we present asymptotically better approximation algorithms. In particular, we give an O(loglog min(m,n))-approximation for indep...
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, S.;
1998-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G_1 surface consisting of pieces of cones or cylinders of revolution or a G_r NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, s.;
1999-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G(1) surface consisting of pieces of cones or cylinders of revolution or a G(r) NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal...
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Counting independent sets using the Bethe approximation
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Laboratory; Chandrasekaran, V [MIT; Gamarmik, D [MIT; Shah, D [MIT; Sin, J [MIT
2009-01-01
The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques.
Hybrid diffusion approximation in highly absorbing media and its effects of source approximation
Institute of Scientific and Technical Information of China (English)
Huijuan Tian; Ying Liu; Lijun Wang; Yuhui Zhang; Lifeng Xiao
2009-01-01
A modified diffusion approximation model called the hybrid diffusion approximation that can be used for highly absorbing media is investigated.The analytic solution of the hybrid diffusion approximation for reflectance in two-source approximation and steady-state case with extrapolated boundary is obtained.The effects of source approximation on the analytic solution are investigated,and it is validated that two-source approximation in highly absorbing media to describe the optical properties of biological tissue is necessary.Monte Carlo simulation of recovering optical parameters from reflectant data is done with the use of this model.The errors of recovering μa and μ's are smaller than 15% for the reduced albedo between 0.77 and 0.5 with the source-detector separation of 0.4-3 ram.
Chen, Wei; Huang, Dayu; Kulkarni, Ankur A.; Unnikrishnan, Jayakrishnan; Zhu, Quanyan; Mehta, Prashant; Meyn, Sean; Wierman, Adam
2013-01-01
Neuro-dynamic programming is a class of powerful techniques for approximating the solution to dynamic programming equations. In their most computationally attractive formulations, these techniques provide the approximate solution only within a prescribed finite-dimensional function class. Thus, the question that always arises is how should the function class be chosen? The goal of this paper is to propose an approach using the solutions to associated fluid and diffusion approximations. In ord...
Energy Technology Data Exchange (ETDEWEB)
Chudnovsky, D.V.; Chudnovsky, G.V. [Columbia Univ., New York, NY (United States)
1995-12-01
High precision solution of extremal and (complex analytic) approximations problems that can be represented in terms of multiple integrals or integral equations involving hypergeornetric functions are examined. Fast algorithms of computations of (approximate) solutions are presented that are well suited for parallelization. Among problems considered are: WKB and adelic asymptotics of multidimensional hypergeometric Pade approximations to classical functions, and high accuracy computations of high order eigenvalues and eigenstates for 2D and 3D domains of complex geometry.
Polynomial approximation and cubature at approximate Fekete and Leja points of the cylinder
De Marchi, Stefano
2011-01-01
The paper deals with polynomial interpolation, least-square approximation and cubature of functions defined on the rectangular cylinder, $K=D\\times [-1,1]$, with $D$ the unit disk. The nodes used for these processes are the {\\it Approximate Fekete Points} (AFP) and the {\\it Discrete Leja Points} (DLP) extracted from suitable {\\it Weakly Admissible Meshes} (WAMs) of the cylinder. From the analysis of the growth of the Lebesgue constants, approximation and cubature errors, we show that the AFP and the DLP extracted from WAM are good points for polynomial approximation and numerical integration of functions defined on the cylinder.
Decoding Generalized Concatenated Codes Using Interleaved Reed-Solomon Codes
Senger, Christian; Bossert, Martin; Zyablov, Victor
2008-01-01
Generalized Concatenated codes are a code construction consisting of a number of outer codes whose code symbols are protected by an inner code. As outer codes, we assume the most frequently used Reed-Solomon codes; as inner code, we assume some linear block code which can be decoded up to half its minimum distance. Decoding up to half the minimum distance of Generalized Concatenated codes is classically achieved by the Blokh-Zyablov-Dumer algorithm, which iteratively decodes by first using the inner decoder to get an estimate of the outer code words and then using an outer error/erasure decoder with a varying number of erasures determined by a set of pre-calculated thresholds. In this paper, a modified version of the Blokh-Zyablov-Dumer algorithm is proposed, which exploits the fact that a number of outer Reed-Solomon codes with average minimum distance d can be grouped into one single Interleaved Reed-Solomon code which can be decoded beyond d/2. This allows to skip a number of decoding iterations on the one...
Recent advances in neutral particle transport methods and codes
Energy Technology Data Exchange (ETDEWEB)
Azmy, Y.Y.
1996-06-01
An overview of ORNL`s three-dimensional neutral particle transport code, TORT, is presented. Special features of the code that make it invaluable for large applications are summarized for the prospective user. Advanced capabilities currently under development and installation in the production release of TORT are discussed; they include: multitasking on Cray platforms running the UNICOS operating system; Adjacent cell Preconditioning acceleration scheme; and graphics codes for displaying computed quantities such as the flux. Further developments for TORT and its companion codes to enhance its present capabilities, as well as expand its range of applications are disucssed. Speculation on the next generation of neutron particle transport codes at ORNL, especially regarding unstructured grids and high order spatial approximations, are also mentioned.
Massey, Richard; Stoughton, Chris; Leauthaud, Alexie; Rhodes, Jason; Koekemoer, Anton; Ellis, Richard; Shaghoulian, Edgar
2013-07-01
Charge Transfer Inefficiency (CTI) due to radiation damage above the Earth's atmosphere creates spurious trailing in images from Charge-Coupled Device (CCD) imaging detectors. Radiation damage also creates unrelated warm pixels, which can be used to measure CTI. This code provides pixel-based correction for CTI and has proven effective in Hubble Space Telescope Advanced Camera for Surveys raw images, successfully reducing the CTI trails by a factor of ~30 everywhere in the CCD and at all flux levels. The core is written in java for speed, and a front-end user interface is provided in IDL. The code operates on raw data by returning individual electrons to pixels from which they were unintentionally dragged during readout. Correction takes about 25 minutes per ACS exposure, but is trivially parallelisable to multiple processors.
Schnack, D. D.; Glasser, A. H.
1996-11-01
NIMROD is a new code system that is being developed for the analysis of modern fusion experiments. It is being designed from the beginning to make the maximum use of massively parallel computer architectures and computer graphics. The NIMROD physics kernel solves the three-dimensional, time-dependent two-fluid equations with neo-classical effects in toroidal geometry of arbitrary poloidal cross section. The NIMROD system also includes a pre-processor, a grid generator, and a post processor. User interaction with NIMROD is facilitated by a modern graphical user interface (GUI). The NIMROD project is using Quality Function Deployment (QFD) team management techniques to minimize re-engineering and reduce code development time. This paper gives an overview of the NIMROD project. Operation of the GUI is demonstrated, and the first results from the physics kernel are given.
Mcaulay, Robert J.; Quatieri, Thomas F.
1988-01-01
It has been shown that an analysis/synthesis system based on a sinusoidal representation of speech leads to synthetic speech that is essentially perceptually indistinguishable from the original. Strategies for coding the amplitudes, frequencies and phases of the sine waves have been developed that have led to a multirate coder operating at rates from 2400 to 9600 bps. The encoded speech is highly intelligible at all rates with a uniformly improving quality as the data rate is increased. A real-time fixed-point implementation has been developed using two ADSP2100 DSP chips. The methods used for coding and quantizing the sine-wave parameters for operation at the various frame rates are described.
Epetra developers coding guidelines.
Energy Technology Data Exchange (ETDEWEB)
Heroux, Michael Allen; Sexton, Paul Michael
2003-12-01
Epetra is a package of classes for the construction and use of serial and distributed parallel linear algebra objects. It is one of the base packages in Trilinos. This document describes guidelines for Epetra coding style. The issues discussed here go beyond correct C++ syntax to address issues that make code more readable and self-consistent. The guidelines presented here are intended to aid current and future development of Epetra specifically. They reflect design decisions that were made in the early development stages of Epetra. Some of the guidelines are contrary to more commonly used conventions, but we choose to continue these practices for the purposes of self-consistency. These guidelines are intended to be complimentary to policies established in the Trilinos Developers Guide.
Confocal coded aperture imaging
Energy Technology Data Exchange (ETDEWEB)
Tobin, Jr., Kenneth William (Harriman, TN); Thomas, Jr., Clarence E. (Knoxville, TN)
2001-01-01
A method for imaging a target volume comprises the steps of: radiating a small bandwidth of energy toward the target volume; focusing the small bandwidth of energy into a beam; moving the target volume through a plurality of positions within the focused beam; collecting a beam of energy scattered from the target volume with a non-diffractive confocal coded aperture; generating a shadow image of said aperture from every point source of radiation in the target volume; and, reconstructing the shadow image into a 3-dimensional image of the every point source by mathematically correlating the shadow image with a digital or analog version of the coded aperture. The method can comprise the step of collecting the beam of energy scattered from the target volume with a Fresnel zone plate.
International Nuclear Information System (INIS)
This Code of Practice introduces accepted safety procedures associated with the use of alpha, beta, gamma and X-radiation in secondary schools (pupils aged 12 to 18) in Ireland, and summarises good practice and procedures as they apply to radiation protection. Typical dose rates at various distances from sealed sources are quoted, and simplified equations are used to demonstrate dose and shielding calculations. The regulatory aspects of radiation protection are outlined, and references to statutory documents are given
Approximate input physics for stellar modelling
Pols, O R; Eggleton, P P; Han, Z; Pols, O R; Tout, C A; Eggleton, P P; Han, Z
1995-01-01
We present a simple and efficient, yet reasonably accurate, equation of state, which at the moderately low temperatures and high densities found in the interiors of stars less massive than the Sun is substantially more accurate than its predecessor by Eggleton, Faulkner & Flannery. Along with the most recently available values in tabular form of opacities, neutrino loss rates, and nuclear reaction rates for a selection of the most important reactions, this provides a convenient package of input physics for stellar modelling. We briefly discuss a few results obtained with the updated stellar evolution code.
International Nuclear Information System (INIS)
MELCOR is a fully integrated, engineering-level computer code that models the progression of severe accidents in light water reactor nuclear power plants. MELCOR is being developed at Sandia National Laboratories for the U.S. Nuclear Regulatory Commission as a second-generation plant risk assessment tool and the successor to the Source Term Code Package. A broad spectrum of severe accident phenomena in both boiling and pressurized water reactors is treated in MELCOR in a unified framework. These include: thermal-hydraulic response in the reactor coolant system, reactor cavity, containment, and confinement buildings; core heatup, degradation, and relocation; core-concrete attack; hydrogen production, transport, and combustion; fission product release and transport; and the impact of engineered safety features on thermal-hydraulic and radionuclide behavior. Current uses of MELCOR include estimation of severe accident source terms and their sensitivities and uncertainties in a variety of applications. This publication of the MELCOR computer code manuals corresponds to MELCOR 1.8.3, released to users in August, 1994. Volume 1 contains a primer that describes MELCOR's phenomenological scope, organization (by package), and documentation. The remainder of Volume 1 contains the MELCOR Users Guides, which provide the input instructions and guidelines for each package. Volume 2 contains the MELCOR Reference Manuals, which describe the phenomenological models that have been implemented in each package
Energy Technology Data Exchange (ETDEWEB)
Summers, R.M.; Cole, R.K. Jr.; Smith, R.C.; Stuart, D.S.; Thompson, S.L. [Sandia National Labs., Albuquerque, NM (United States); Hodge, S.A.; Hyman, C.R.; Sanders, R.L. [Oak Ridge National Lab., TN (United States)
1995-03-01
MELCOR is a fully integrated, engineering-level computer code that models the progression of severe accidents in light water reactor nuclear power plants. MELCOR is being developed at Sandia National Laboratories for the U.S. Nuclear Regulatory Commission as a second-generation plant risk assessment tool and the successor to the Source Term Code Package. A broad spectrum of severe accident phenomena in both boiling and pressurized water reactors is treated in MELCOR in a unified framework. These include: thermal-hydraulic response in the reactor coolant system, reactor cavity, containment, and confinement buildings; core heatup, degradation, and relocation; core-concrete attack; hydrogen production, transport, and combustion; fission product release and transport; and the impact of engineered safety features on thermal-hydraulic and radionuclide behavior. Current uses of MELCOR include estimation of severe accident source terms and their sensitivities and uncertainties in a variety of applications. This publication of the MELCOR computer code manuals corresponds to MELCOR 1.8.3, released to users in August, 1994. Volume 1 contains a primer that describes MELCOR`s phenomenological scope, organization (by package), and documentation. The remainder of Volume 1 contains the MELCOR Users Guides, which provide the input instructions and guidelines for each package. Volume 2 contains the MELCOR Reference Manuals, which describe the phenomenological models that have been implemented in each package.
Structural coding versus free-energy predictive coding.
van der Helm, Peter A
2016-06-01
Focusing on visual perceptual organization, this article contrasts the free-energy (FE) version of predictive coding (a recent Bayesian approach) to structural coding (a long-standing representational approach). Both use free-energy minimization as metaphor for processing in the brain, but their formal elaborations of this metaphor are fundamentally different. FE predictive coding formalizes it by minimization of prediction errors, whereas structural coding formalizes it by minimization of the descriptive complexity of predictions. Here, both sides are evaluated. A conclusion regarding competence is that FE predictive coding uses a powerful modeling technique, but that structural coding has more explanatory power. A conclusion regarding performance is that FE predictive coding-though more detailed in its account of neurophysiological data-provides a less compelling cognitive architecture than that of structural coding, which, for instance, supplies formal support for the computationally powerful role it attributes to neuronal synchronization. PMID:26407895
Approximate inverse preconditioners for general sparse matrices
Energy Technology Data Exchange (ETDEWEB)
Chow, E.; Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)
1994-12-31
Preconditioned Krylov subspace methods are often very efficient in solving sparse linear matrices that arise from the discretization of elliptic partial differential equations. However, for general sparse indifinite matrices, the usual ILU preconditioners fail, often because of the fact that the resulting factors L and U give rise to unstable forward and backward sweeps. In such cases, alternative preconditioners based on approximate inverses may be attractive. We are currently developing a number of such preconditioners based on iterating on each column to get the approximate inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., we must use sparse-matrix by sparse-vector type operatoins. We will discuss a few options and compare their performance on standard problems from the Harwell-Boeing collection.
Flow past a porous approximate spherical shell
Srinivasacharya, D.
2007-07-01
In this paper, the creeping flow of an incompressible viscous liquid past a porous approximate spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier Stokes equation. The flow within the porous annulus region of the shell is governed by Darcy’s Law. The boundary conditions used at the interface are continuity of the normal velocity, continuity of the pressure and Beavers and Joseph slip condition. An exact solution for the problem is obtained. An expression for the drag on the porous approximate spherical shell is obtained. The drag experienced by the shell is evaluated numerically for several values of the parameters governing the flow.
Traveltime approximations for inhomogeneous HTI media
Alkhalifah, Tariq Ali
2011-01-01
Traveltimes information is convenient for parameter estimation especially if the medium is described by an anisotropic set of parameters. This is especially true if we could relate traveltimes analytically to these medium parameters, which is generally hard to do in inhomogeneous media. As a result, I develop traveltimes approximations for horizontaly transversely isotropic (HTI) media as simplified and even linear functions of the anisotropic parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to η and the azimuthal symmetry direction (usually used to describe the fracture direction) from a generally inhomogeneous elliptically anisotropic background medium. The resulting approximations can provide accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations out there. These equations will allow us to readily extend the inhomogenous background elliptical anisotropic model to an HTI with a variable, but smoothly varying, η and horizontal symmetry direction values. © 2011 Society of Exploration Geophysicists.
Adaptive approximate Bayesian computation for complex models
Lenormand, Maxime; Deffuant, Guillaume
2011-01-01
Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fit a model to data without relying on the computation of the model likelihood. They instead require to simulate a large number of times the model to be fitted. A number of refinements to the original rejection-based ABC scheme have been proposed, including the sequential improvement of posterior distributions. This technique allows to decrease the number of model simulations required, but it still presents several shortcomings which are particularly problematic for costly to simulate complex models. We here provide a new algorithm to perform adaptive approximate Bayesian computation, which is shown to perform better on both a toy example and a complex social model.
Seismic modeling using the frozen Gaussian approximation
Yang, Xu; Fomel, Sergey
2013-01-01
We adopt the frozen Gaussian approximation (FGA) for modeling seismic waves. The method belongs to the category of ray-based beam methods. It decomposes seismic wavefield into a set of Gaussian functions and propagates these Gaussian functions along appropriate ray paths. As opposed to the classic Gaussian-beam method, FGA keeps the Gaussians frozen (at a fixed width) during the propagation process and adjusts their amplitudes to produce an accurate approximation after summation. We perform the initial decomposition of seismic data using a fast version of the Fourier-Bros-Iagolnitzer (FBI) transform and propagate the frozen Gaussian beams numerically using ray tracing. A test using a smoothed Marmousi model confirms the validity of FGA for accurate modeling of seismic wavefields.
An Origami Approximation to the Cosmic Web
Neyrinck, Mark C
2014-01-01
The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in 'polygonal' or 'polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls ...
Improved Approximations for Some Polymer Extension Models
Petrosyan, Rafayel
2016-01-01
We propose approximations for force-extension dependencies for the freely jointed chain (FJC) and worm-like chain (WLC) models as well as for extension-force dependence for the WLC model. Proposed expressions show less than 1% relative error in the useful range of the corresponding variables. These results can be applied for fitting force-extension curves obtained in molecular force spectroscopy experiments. Particularly they can be useful for cases where one has geometries of springs in series and/or in parallel where particular combination of expressions should be used for fitting the data. All approximations have been obtained following the same procedure of determining the asymptotes and then reducing the relative error of that expression by adding an appropriate term obtained from fitting its absolute error.
On spline approximation of sliced inverse regression
Institute of Scientific and Technical Information of China (English)
Li-ping ZHU; Zhou YU
2007-01-01
The dimension reduction is helpful and often necessary in exploring the nonparametric regression structure. In this area, Sliced inverse regression (SIR) is a promising tool to estimate the central dimension reduction (CDR) space. To estimate the kernel matrix of the SIR, we herein suggest the spline approximation using the least squares regression. The heteroscedasticity can be incorporated well by introducing an appropriate weight function. The root-n asymptotic normality can be achieved for a wide range choice of knots. This is essentially analogous to the kernel estimation. Moreover,we also propose a modified Bayes information criterion (BIC) based on the eigenvalues of the SIR matrix. This modified BIC can be applied to any form of the SIR and other related methods. The methodology and some of the practical issues are illustrated through the horse mussel data. Empirical studies evidence the performance of our proposed spline approximation by comparison of the existing estimators.
Approximated solutions to Born-Infeld dynamics
Ferraro, Rafael; Nigro, Mauro
2016-02-01
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.
Approximate Lesion Localization in Dermoscopy Images
Celebi, M Emre; Schaefer, Gerald; Stoecker, William V; 10.1111/j.1600-0846.2009.00357.x
2010-01-01
Background: Dermoscopy is one of the major imaging modalities used in the diagnosis of melanoma and other pigmented skin lesions. Due to the difficulty and subjectivity of human interpretation, automated analysis of dermoscopy images has become an important research area. Border detection is often the first step in this analysis. Methods: In this article, we present an approximate lesion localization method that serves as a preprocessing step for detecting borders in dermoscopy images. In this method, first the black frame around the image is removed using an iterative algorithm. The approximate location of the lesion is then determined using an ensemble of thresholding algorithms. Results: The method is tested on a set of 428 dermoscopy images. The localization error is quantified by a metric that uses dermatologist determined borders as the ground truth. Conclusion: The results demonstrate that the method presented here achieves both fast and accurate localization of lesions in dermoscopy images.
Approximate locality for quantum systems on graphs.
Osborne, Tobias J
2008-10-01
In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis [Theory Comput. 1, 47 (2005)]: we show that if U is a sparse unitary operator with a gap Delta in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Delta increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk. PMID:18851512
Quasi-chemical approximation for polyatomic mixtures
Dávila, M V; Matoz-Fernandez, D A; Ramirez-Pastor, A J
2016-01-01
The statistical thermodynamics of binary mixtures of polyatomic species was developed on a generalization in the spirit of the lattice-gas model and the quasi-chemical approximation (QCA). The new theoretical framework is obtained by combining: (i) the exact analytical expression for the partition function of non-interacting mixtures of linear $k$-mers and $l$-mers (species occupying $k$ sites and $l$ sites, respectively) adsorbed in one dimension, and its extension to higher dimensions; and (ii) a generalization of the classical QCA for multicomponent adsorbates and multisite-occupancy adsorption. The process is analyzed through the partial adsorption isotherms corresponding to both species of the mixture. Comparisons with analytical data from Bragg-Williams approximation (BWA) and Monte Carlo simulations are performed in order to test the validity of the theoretical model. Even though a good fitting is obtained from BWA, it is found that QCA provides a more accurate description of the phenomenon of adsorpti...
Analytical Ballistic Trajectories with Approximately Linear Drag
Directory of Open Access Journals (Sweden)
Giliam J. P. de Carpentier
2014-01-01
Full Text Available This paper introduces a practical analytical approximation of projectile trajectories in 2D and 3D roughly based on a linear drag model and explores a variety of different planning algorithms for these trajectories. Although the trajectories are only approximate, they still capture many of the characteristics of a real projectile in free fall under the influence of an invariant wind, gravitational pull, and terminal velocity, while the required math for these trajectories and planners is still simple enough to efficiently run on almost all modern hardware devices. Together, these properties make the proposed approach particularly useful for real-time applications where accuracy and performance need to be carefully balanced, such as in computer games.
Numerical and approximate solutions for plume rise
Krishnamurthy, Ramesh; Gordon Hall, J.
Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585-590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).
Some approximation concepts for structural synthesis
Schmit, L. A., Jr.; Farshi, B.
1974-01-01
An efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles. Static stress and displacement constraints under alternative loading conditions are considered. The optimization algorithm is an adaptation of the method of inscribed hyperspheres and high efficiency is achieved by using several approximation concepts including temporary deletion of noncritical constraints, design variable linking, and Taylor series expansions for response variables in terms of design variables. Optimum designs for several planar and space truss examples problems are presented. The results reported support the contention that the innovative use of approximation concepts in structural synthesis can produce significant improvements in efficiency.
Approximate Solutions in Planted 3-SAT
Hsu, Benjamin; Laumann, Christopher; Moessner, Roderich; Sondhi, Shivaji
2013-03-01
In many computational settings, there exists many instances where finding a solution requires a computing time that grows exponentially in the number of variables. Concrete examples occur in combinatorial optimization problems and cryptography in computer science or glassy systems in physics. However, while exact solutions are often known to require exponential time, a related and important question is the running time required to find approximate solutions. Treating this problem as a problem in statistical physics at finite temperature, we examine the computational running time in finding approximate solutions in 3-satisfiability for randomly generated 3-SAT instances which are guaranteed to have a solution. Analytic predictions are corroborated by numerical evidence using stochastic local search algorithms. A first order transition is found in the running time of these algorithms.
Rough Sets in Approximate Solution Space
Institute of Scientific and Technical Information of China (English)
Hui Sun; Wei Tian; Qing Liu
2006-01-01
As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and in complete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set. A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.
Pade approximants of random Stieltjes series
Marklof, Jens; Wolowski, Lech
2007-01-01
We consider the random continued fraction S(t) := 1/(s_1 + t/(s_2 + t/(s_3 + >...))) where the s_n are independent random variables with the same gamma distribution. For every realisation of the sequence, S(t) defines a Stieltjes function. We study the convergence of the finite truncations of the continued fraction or, equivalently, of the diagonal Pade approximants of the function S(t). By using the Dyson--Schmidt method for an equivalent one-dimensional disordered system, and the results of Marklof et al. (2005), we obtain explicit formulae (in terms of modified Bessel functions) for the almost-sure rate of convergence of these approximants, and for the almost-sure distribution of their poles.
SOME CONVERSE RESULTS ON ONESIDED APPROXIMATION: JUSTIFICATIONS
Institute of Scientific and Technical Information of China (English)
Wang Jianli; Zhou Songping
2003-01-01
The present paper deals with best onesided approximation rate in Lp spaces ～En (f)Lp of f ∈ C2π. Although it is clear that the estimate ～En(f)Lp≤C ‖f‖ Lp cannot be correct for all f ∈ Lp2π in case p＜∞, the question whether ～En (f)Lp ≤Cω (f, n-1 )Lp or ～En(f)Lp ≤CEn(f)Lp holds for f ∈ C2π remains totally untouched.Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.
Decoding of concatenated codes with interleaved outer codes
DEFF Research Database (Denmark)
Justesen, Jørn; Thommesen, Christian; Høholdt, Tom
2004-01-01
Recently Bleichenbacher et al. proposed a decoding algorithm for interleaved Reed/Solomon codes, which allows close to errors to be corrected in many cases. We discuss the application of this decoding algorithm to concatenated codes. (NK) N-K......Recently Bleichenbacher et al. proposed a decoding algorithm for interleaved Reed/Solomon codes, which allows close to errors to be corrected in many cases. We discuss the application of this decoding algorithm to concatenated codes. (NK) N-K...
Coding Opportunity Densification Strategies for Instantly Decodable Network Coding
Sorour, Sameh; Valaee, Shahrokh
2012-01-01
In this paper, we aim to identify the strategies that can maximize and monotonically increase the density of the coding opportunities in instantly decodable network coding (IDNC).Using the well-known graph representation of IDNC, first derive an expression for the exact evolution of the edge set size after the transmission of any arbitrary coded packet. From the derived expressions, we show that sending commonly wanted packets for all the receivers can maximize the number of coding opportunit...
TASS code topical report. V.1 TASS code technical manual
International Nuclear Information System (INIS)
TASS 1.0 code has been developed at KAERI for the initial and reload non-LOCA safety analysis for the operating PWRs as well as the PWRs under construction in Korea. TASS code will replace various vendor's non-LOCA safety analysis codes currently used for the Westinghouse and ABB-CE type PWRs in Korea. This can be achieved through TASS code input modifications specific to each reactor type. The TASS code can be run interactively through the keyboard operation. A simimodular configuration used in developing the TASS code enables the user easily implement new models. TASS code has been programmed using FORTRAN77 which makes it easy to install and port for different computer environments. The TASS code can be utilized for the steady state simulation as well as the non-LOCA transient simulations such as power excursions, reactor coolant pump trips, load rejections, loss of feedwater, steam line breaks, steam generator tube ruptures, rod withdrawal and drop, and anticipated transients without scram (ATWS). The malfunctions of the control systems, components, operator actions and the transients caused by the malfunctions can be easily simulated using the TASS code. This technical report describes the TASS 1.0 code models including reactor thermal hydraulic, reactor core and control models. This TASS code models including reactor thermal hydraulic, reactor core and control models. This TASS code technical manual has been prepared as a part of the TASS code manual which includes TASS code user's manual and TASS code validation report, and will be submitted to the regulatory body as a TASS code topical report for a licensing non-LOCA safety analysis for the Westinghouse and ABB-CE type PWRs operating and under construction in Korea. (author). 42 refs., 29 tabs., 32 figs
Approximation of Marginal Abatement Cost Curve
Olga Kiuila; Rutherford, Thomas F.
2011-01-01
Top-down models usually include piecewise-smooth functions to describe marginal cost curves, while bottom-up models describe those curves with a step function. When a bottom-up cost curve is available, we can explicitly represent this curve with a top-down model in order to replicate its shape instead of arbitrary assumptions. We propose methods to approximate a piecewise function from a step function using constant elasticity of substitution technologies. Specifically, we consider a pollutio...
Approximate Bayesian inference for complex ecosystems
Michael P H Stumpf
2014-01-01
Mathematical models have been central to ecology for nearly a century. Simple models of population dynamics have allowed us to understand fundamental aspects underlying the dynamics and stability of ecological systems. What has remained a challenge, however, is to meaningfully interpret experimental or observational data in light of mathematical models. Here, we review recent developments, notably in the growing field of approximate Bayesian computation (ABC), that allow us to calibrate mathe...
Relativistic point interactions: Approximation by smooth potentials
Hughes, Rhonda J.
1997-06-01
We show that the four-parameter family of one-dimensional relativistic point interactions studied by Benvegnu and Dąbrowski may be approximated in the strong resolvent sense by smooth, local, short-range perturbations of the Dirac Hamiltonian. In addition, we prove that the nonrelativistic limits correspond to the Schrödinger point interactions studied extensively by the author and Paul Chernoff.
Dynamic Approximate Vertex Cover and Maximum Matching
Onak, Krzysztof; Rubinfeld, Ronitt
2010-01-01
We consider the problem of maintaining a large matching or a small vertex cover in a dynamically changing graph. Each update to the graph is either an edge deletion or an edge insertion. We give the first randomized data structure that simultaneously achieves a constant approximation factor and handles a sequence of k updates in k. polylog(n) time. Previous data structures require a polynomial amount of computation per update. The starting point of our construction is a distributed algorit...
Approximating viability kernels with support vector machines
Deffuant, G.; Chapel, L.; Martin, S.
2007-01-01
We propose an algorithm which performs a progressive approximation of a viability kernel, iteratively using a classification method. We establish the mathematical conditions that the classification method should fulfill to guarantee the convergence to the actual viability kernel. We study more particularly the use of support vector machines (SVMs) as classification techniques. We show that they make possible to use gradient optimisation techniques to find a viable control at each time step, a...
Solving Math Problems Approximately: A Developmental Perspective.
Directory of Open Access Journals (Sweden)
Dana Ganor-Stern
Full Text Available Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults' ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger than the exact answer and when it was far (vs. close from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner.
Gaussian Approximation Potentials: a brief tutorial introduction
Bart?k, Albert P.; Cs?nyi, G?bor
2015-01-01
We present a swift walk-through of our recent work that uses machine learning to t interatomic potentials based on quantum mechanical data. We describe our Gaussian Approximation Potentials (GAP) framework, discuss a variety of descriptors, how to train the model on total energies and derivatives and the simultaneous use of multiple models of di erent complexity. We also show a small example using QUIP, the software sandbox implementation of GAP that is available for non-comme...
Dual Control for Approximate Bayesian Reinforcement Learning
Klenske, Edgar D.; Hennig, Philipp
2015-01-01
Control of non-episodic, finite-horizon dynamical systems with uncertain dynamics poses a tough and elementary case of the exploration-exploitation trade-off. Bayesian reinforcement learning, reasoning about the effect of actions and future observations, offers a principled solution, but is intractable. We review, then extend an old approximate approach from control theory---where the problem is known as dual control---in the context of modern regression methods, specifically generalized line...
Space-Time Approximation with Sparse Grids
Energy Technology Data Exchange (ETDEWEB)
Griebel, M; Oeltz, D; Vassilevski, P S
2005-04-14
In this article we introduce approximation spaces for parabolic problems which are based on the tensor product construction of a multiscale basis in space and a multiscale basis in time. Proper truncation then leads to so-called space-time sparse grid spaces. For a uniform discretization of the spatial space of dimension d with O(N{sup d}) degrees of freedom, these spaces involve for d > 1 also only O(N{sup d}) degrees of freedom for the discretization of the whole space-time problem. But they provide the same approximation rate as classical space-time Finite Element spaces which need O(N{sup d+1}) degrees of freedoms. This makes these approximation spaces well suited for conventional parabolic and for time-dependent optimization problems. We analyze the approximation properties and the dimension of these sparse grid space-time spaces for general stable multiscale bases. We then restrict ourselves to an interpolatory multiscale basis, i.e. a hierarchical basis. Here, to be able to handle also complicated spatial domains {Omega}, we construct the hierarchical basis from a given spatial Finite Element basis as follows: First we determine coarse grid points recursively over the levels by the coarsening step of the algebraic multigrid method. Then, we derive interpolatory prolongation operators between the respective coarse and fine grid points by a least squares approach. This way we obtain an algebraic hierarchical basis for the spatial domain which we then use in our space-time sparse grid approach. We give numerical results on the convergence rate of the interpolation error of these spaces for various space-time problems with two spatial dimensions. Also implementational issues, data structures and questions of adaptivity are addressed to some extent.
APPROXIMATION MULTIDIMENSION FUCTION WITH FUNCTIONAL NETWORK
Institute of Scientific and Technical Information of China (English)
Li Weibin; Liu Fang; Jiao Licheng; Zhang Shuling; Li Zongling
2006-01-01
The functional network was introduced by E.Catillo, which extended the neural network. Not only can it solve the problems solved, but also it can formulate the ones that cannot be solved by traditional network.This paper applies functional network to approximate the multidimension function under the ridgelet theory.The method performs more stable and faster than the traditional neural network. The numerical examples demonstrate the performance.
Microscopic justification of the Equal Filling approximation
Perez-Martin, Sara
2008-01-01
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.
On the diagonal approximation of full matrices
Lioen, W.M.
1996-01-01
In this paper the construction of diagonal matrices, in some sense approximating the inverse of a given square matrix, is described. The matrices are constructed using the well-known computer algebra system Maple. The techniques we show are applicable to square matrices in general. Results are given for use in Parallel diagonal-implicit Runge-Kutta (PDIRK) methods. For an s-stage Radau IIA corrector we conjecture $s!$ possibilities for the diagonal matrices.
Fast approximate convex decomposition using relative concavity
Ghosh, Mukulika
2013-02-01
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 also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.
Broadband Approximations for Doubly Curved Reflector Antenna
V. Schejbal; J. Pidanic
2010-01-01
The broadband approximations for shaped-beam doubly curved reflector antennas with primary feed (rectangular horn) producing uniform amplitude and phase aperture distribution are derived and analyzed. They are very valuable for electromagnetic compatibility analyses both from electromagnetic interference and susceptibility point of view, because specialized more accurate methods such as physical optics are only used by antenna designers. To allow quick EMC analyses, typical values, beamwidth ...
Neutrino Mass Matrix with Approximate Flavor Symmetry
Riazuddin, M
2003-01-01
Phenomenological implications of neutrino oscillations implied by recent experimental data on pattern of neutrino mass matrix are disscussed. It is shown that it is possible to have a neutrino mass matrix which shows approximate flavor symmetry; the neutrino mass differences arise from flavor violation in off-diagonal Yukawa couplings. Two modest extensions of the standard model, which can embed the resulting neutrino mass matix have also been discussed.
Discrete least squares approximation with polynomial vectors
Van Barel, Marc; Bultheel, Adhemar
1993-01-01
We give a solution of a discrete least squares approximation problem in terms of orthogonal polynomial vectors. The degrees of the polynomial elements of these vectors can be different. An algorithm is constructed computing the coefficients of recurrence relations for the orthogonal polynomial vectors. In case the function values are prescribed in points on the real line or on the unit circle variants of the original algorithm can be designed which are an order of magnitude more efficient. Al...
Relativistic impulse approximation for nuclear inelastic scattering
International Nuclear Information System (INIS)
The Relativistic Impulse Approximation (RIA) for proton-nucleus elastic and inelastic scattering is contrasted with its non-relativistic counterpart (the NRIA). Differences between the two approaches are examined with special emphasis on the nuclear convection current and its generalizations which may show signatures of strong relativistic nuclear potentials. A simple extension of the RIA to meson-nucleus scattering based on the linear, spin-zero Duffin-Kemmer wave equation is considered
Sparse and silent coding in neural circuits
L\\Horincz, András; Szirtes, Gábor
2010-01-01
Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an important role in neural information processing. However, due to the computational complexity of the task, only approximate solutions provide the required efficiency (in terms of time). As new results show, under particular conditions there exist efficient solutions by minimizing the magnitude of the coefficients (`$l_1$-norm') instead of minimizing the size of the active subset of features (`$l_0$-norm'). Straightforward neural implementation of these solutions is not likely, as they require \\emph{a priori} knowledge of the number of active features. Furthermore, these methods utilize iterative re-evaluation of the reconstruction error, which in turn implies that final sparse forms (featuring `population sparseness') can only be reached through the formation of a series of non-...
Sparsity in Linear Predictive Coding of Speech
DEFF Research Database (Denmark)
Giacobello, Daniele
This thesis deals with developing improved techniques for speech coding based on the recent developments in sparse signal representation. In particular, this work is motivated by the need to address some of the limitations of the well- known linear prediction (LP) model currently applied in many...... modern speech coders. In the first part of the thesis, we provide an overview of Sparse Linear Predic- tion, a set of speech processing tools created by introducing sparsity constraints into the LP framework. This approach defines predictors that look for a sparse residual rather than a minimum variance...... of the effectiveness of their application in audio processing. The second part of the thesis deals with introducing sparsity directly in the linear prediction analysis-by-synthesis (LPAS) speech coding paradigm. We first propose a novel near-optimal method to look for a sparse approximate excitation using a compressed...
Containment Code Validation Matrix
International Nuclear Information System (INIS)
The Committee on the Safety of Nuclear Installations (CSNI) formed the CCVM (Containment Code Validation Matrix) task group in 2002. The objective of this group was to define a basic set of available experiments for code validation, covering the range of containment (ex-vessel) phenomena expected in the course of light and heavy water reactor design basis accidents and beyond design basis accidents/severe accidents. It was to consider phenomena relevant to pressurised heavy water reactor (PHWR), pressurised water reactor (PWR) and boiling water reactor (BWR) designs of Western origin as well as of Eastern European VVER types. This work would complement the two existing CSNI validation matrices for thermal hydraulic code validation (NEA/CSNI/R(1993)14) and In-vessel core degradation (NEA/CSNI/R(2001)21). The report initially provides a brief overview of the main features of a PWR, BWR, CANDU and VVER reactors. It also provides an overview of the ex-vessel corium retention (core catcher). It then provides a general overview of the accident progression for light water and heavy water reactors. The main focus is to capture most of the phenomena and safety systems employed in these reactor types and to highlight the differences. This CCVM contains a description of 127 phenomena, broken down into 6 categories: - Containment Thermal-hydraulics Phenomena; - Hydrogen Behaviour (Combustion, Mitigation and Generation) Phenomena; - Aerosol and Fission Product Behaviour Phenomena; - Iodine Chemistry Phenomena; - Core Melt Distribution and Behaviour in Containment Phenomena; - Systems Phenomena. A synopsis is provided for each phenomenon, including a description, references for further information, significance for DBA and SA/BDBA and a list of experiments that may be used for code validation. The report identified 213 experiments, broken down into the same six categories (as done for the phenomena). An experiment synopsis is provided for each test. Along with a test description
The Complexity of Approximately Counting Stable Matchings
Chebolu, Prasad; Martin, Russell
2010-01-01
We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances between "preference points" and "attribute points". Irving and Leather proved that counting the number of stable matchings in the general case is $#P$-complete. Counting the number of stable matchings is reducible to counting the number of downsets in a (related) partial order and is interreducible, in an approximation-preserving sense, to a class of problems that includes counting the number of independent sets in a bipartite graph ($#BIS$). It is conjectured that no FPRAS exists for this class of problems. We show this approximation-preserving interreducibilty remains even in the restricted $k$-attribute setting when $k \\geq 3$ (dot products) or $k \\geq 2$ (Euclidean distances). Finally, we show it is easy to count the number of stable matchings in the 1-attribute dot-product ...
Development of the relativistic impulse approximation
International Nuclear Information System (INIS)
This talk contains three parts. Part I reviews the developments which led to the relativistic impulse approximation for proton-nucleus scattering. In Part II, problems with the impulse approximation in its original form - principally the low energy problem - are discussed and traced to pionic contributions. Use of pseudovector covariants in place of pseudoscalar ones in the NN amplitude provides more satisfactory low energy results, however, the difference between pseudovector and pseudoscalar results is ambiguous in the sense that it is not controlled by NN data. Only with further theoretical input can the ambiguity be removed. Part III of the talk presents a new development of the relativistic impulse approximation which is the result of work done in the past year and a half in collaboration with J.A. Tjon. A complete NN amplitude representation is developed and a complete set of Lorentz invariant amplitudes are calculated based on a one-meson exchange model and appropriate integral equations. A meson theoretical basis for the important pair contributions to proton-nucleus scattering is established by the new developments. 28 references
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.
2011-05-12
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
CMB-lensing beyond the Born approximation
Marozzi, Giovanni; Fanizza, Giuseppe; Di Dio, Enea; Durrer, Ruth
2016-09-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles l lesssim 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.
Cylindrical Helix Spline Approximation of Spatial Curves
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, we present a new method for approximating spatial curves with a G1 cylindrical helix spline within a prescribed tolerance. We deduce the general formulation of a cylindrical helix,which has 11 freedoms. This means that it needs 11 restrictions to determine a cylindrical helix. Given a spatial parametric curve segment, including the start point and the end point of this segment, the tangent and the principal normal of the start point, we can always find a cylindrical segment to interpolate the given direction and position vectors. In order to approximate the known parametric curve within the prescribed tolerance, we adopt the trial method step by step. First, we must ensure the helix segment to interpolate the given two end points and match the principal normal and tangent of the start point, and then, we can keep the deviation between the cylindrical helix segment and the known curve segment within the prescribed tolerance everywhere. After the first segment had been formed, we can construct the next segment. Circularly, we can construct the G1 cylindrical helix spline to approximate the whole spatial parametric curve within the prescribed tolerance. Several examples are also given to show the efficiency of this method.
Green-Ampt approximations: A comprehensive analysis
Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K.
2016-04-01
Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems.
Generalized Quasilinear Approximation: Application to Zonal Jets
Marston, J. B.; Chini, G. P.; Tobias, S. M.
2016-05-01
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems.
A coastal ocean model with subgrid approximation
Walters, Roy A.
2016-06-01
A wide variety of coastal ocean models exist, each having attributes that reflect specific application areas. The model presented here is based on finite element methods with unstructured grids containing triangular and quadrilateral elements. The model optimizes robustness, accuracy, and efficiency by using semi-implicit methods in time in order to remove the most restrictive stability constraints, by using a semi-Lagrangian advection approximation to remove Courant number constraints, and by solving a wave equation at the discrete level for enhanced efficiency. An added feature is the approximation of the effects of subgrid objects. Here, the Reynolds-averaged Navier-Stokes equations and the incompressibility constraint are volume averaged over one or more computational cells. This procedure gives rise to new terms which must be approximated as a closure problem. A study of tidal power generation is presented as an example of this method. A problem that arises is specifying appropriate thrust and power coefficients for the volume averaged velocity when they are usually referenced to free stream velocity. A new contribution here is the evaluation of three approaches to this problem: an iteration procedure and two mapping formulations. All three sets of results for thrust (form drag) and power are in reasonable agreement.