NASA Astrophysics Data System (ADS)
Bieg, Bohdan; Chrzanowski, Janusz; Kravtsov, Yury A.; Orsitto, Francesco
Basic principles and recent findings of quasi-isotropic approximation (QIA) of a geometrical optics method are presented in a compact manner. QIA was developed in 1969 to describe electromagnetic waves in weakly anisotropic media. QIA represents the wave field as a power series in two small parameters, one of which is a traditional geometrical optics parameter, equal to wavelength ratio to plasma characteristic scale, and the other one is the largest component of anisotropy tensor. As a result, "" QIA ideally suits to tokamak polarimetry/interferometry systems in submillimeter range, where plasma manifests properties of weakly anisotropic medium.
Kravtsov, Yu. A. [Space Research Institute, Profsoyuznaya St. 82/34, Moscow 117997 (Russian Federation); Institute of Physics, Maritime University of Szczecin, Waly Chrobrego 1/., 70-500 Szczecin (Poland); Bieg, B. [Institute of Physics, Maritime University of Szczecin, Waly Chrobrego 1/., 70-500 Szczecin (Poland); Bliokh, K. Yu. [Institute of Radio Astronomy, 4 Krasnoznamyonnaya St., Kharkov 61002 (Ukraine); Optical Engineering Laboratory, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000 (Israel); Hirsch, M. [Max Planck Institute for Plasma Physics, Greifswald, Wendelsteinstrasse D-17491 (Germany)
2008-03-19
Three different theoretical approaches are presented: quasi-isotropic approximation (QIA), Stokes vector formalism and complex polarization angle method, which allow describing polarization of electromagnetic waves in weakly anisotropic plasma. QIA stems directly from the Maxwell equations under assumption of weak anisotropy and has a form of coupled differential equations for the transverse components of the electromagnetic wave field. Being applied to high frequency (microwave or IR) electromagnetic waves in magnetized plasma, QIA describes combined action of Faraday and Cotton-Mouton phenomena. QIA takes into account curvature and torsion of the ray, describes normal modes conversion in the inhomogeneous plasma and allows specifying area of applicability of the method.In distinction to QIA, Stokes vector formalism (SVF) deals with quantities, quadratic in a wave field. It is shown (and this is the main result of the paper) that equation for Stokes vector evolution can be derived directly from QIA. This evidences deep unity of two seemingly different approaches. In fact QIA suggests somewhat more information than SVF; in particular, it describes the phases of both transverse components of the electromagnetic field, whereas SVF operates only with the phase difference.At last, the coupled equations of the quasi-isotropic approximation can be reduced to a single equation for complex polarization angle (CPA), which describes both the shape and orientation of the polarization ellipse. In turn, equation for CPA allows obtaining equations for traditional parameters of polarization ellipse, which in fact are equivalent to the equation for Stokes vector evolution. It is pointed out that every method under discussion has its own advantages plasma polarimetry.
Quasi-isotropic approximation in dynamical elasticity and some problems of geotomography
Sharafutdinov, Vladimir
factor that describes the accumulation, due to anisotropy, of the wave phase along a ray. Second this approximation was considered for electromagnetic waves. In these works a system of ordinary differential equations was obtained that describes the evolution of the wave polarization along a light ray. It was shown
A new quasi - isotropic antenna for ultra - wideband application
E. S. Pires; G. Fontgalland; M. A. B. de Melo; R. M. Valle; G. F. Aragao; T. P. Vuong
2007-01-01
In this paper, we propose a new compact antenna design for applications where an ultra-wideband (UWB) frequency range is needed. The main features of the proposed antenna is the capability of generate a quasi-isotropic radiation pattern. For this case, the proposed antenna is designed to operate from 2.17 GHz to 2.68 GHz. The construction details of the conceived antenna are
Impact-induced fracture in a quasi-isotropic laminate
NASA Technical Reports Server (NTRS)
Joshi, S. P.; Sun, C. T.
1987-01-01
A systematic study of impact-induced fracture in a quasi-isotropic laminated composite is carried out. The main focus of the study is to understand damage initiation when a laminate is subjected to the impact of a foreign object. The total incipient damage of a laminate subjected to impact at higher than threshold velocity is also presented. The incipient damage is restricted to small growth from the initiation of the damage. The experimentally collected data are interpreted using a two-dimensional plane-strain finite-element analysis. The qualitative comparison suggests that the skew cracks in the proximal layers are primarily due to transverse shear stress. Skew cracks in the middle layers are also due to transverse shear stress. Vertical cracks in the distal layer are due to flexural stress transverse to the fiber orientation of the layer.
Quasi-isotropic VHF antenna array design study for the International Ultraviolet Explorer satellite
NASA Technical Reports Server (NTRS)
Raines, J. K.
1975-01-01
Results of a study to design a quasi-isotropic VHF antenna array for the IUE satellite are presented. A free space configuration was obtained that has no nulls deeper than -6.4 dbi in each of two orthogonal polarizations. A computer program named SOAP that analyzes the electromagnetic interaction between antennas and complicated conducting bodies, such as satellites was developed.
Prediction of Damage Extension in CFRP Quasi-Isotropic Laminated Plates under Low-Velocity Impact
NASA Astrophysics Data System (ADS)
Zemba, Yutaka; Hu, Ning; Hara, Eiichi; Fukunaga, Hisao
In this paper, to understand the mechanism of delamination propagation in low-velocity impact problems, a weight-drop test is performed for quasi-isotropic composite plates of 32 plies. Due to the high computational cost, up to date, there have been almost no computational effects for simulating the damage propagations in quasi-isotropic composite laminates of 32 plies. This low-velocity impact problem is further numerically modeled and the damage propagation is simulated. A stress-based criterion is adopted for modeling various in-plane damages, such as transverse matrix cracking. A bi-linear cohesive interface model is employed for interface damages, such as delaminations. Moreover, to remove the numerical instability in simulations when using the traditional cohesive model, we propose a new technique, i.e., adaptive cohesive model. The effectiveness of this cohesive model is investigated using a DCB example. Then, it is applied to the low-velocity impact problem of quasi-isotropic composite laminates of 32 plies. The validity of the proposed numerical methodology is verified by comparing the numerical results with the experimental results.
NASA Astrophysics Data System (ADS)
Zeng, Chunmei; Yu, Xia; Guo, Peiji
2014-08-01
A regularization stiffness coefficient method was verified further to optimize lay-up sequences of quasi-isotropic laminates for carbon fiber reinforced polymer (CFRP) composite mirrors. Firstly, the deformation due to gravity of 1G and temperature difference of 20-100°C and the modal were analyzed by finite element method (FEM). Secondly, the influence of angle error of ply stacking on quasi-isotropic of bending stiffness was evaluated. Finally, an active support system of 49 actuators in circular arrangement is designed for a 500mm CFRP mirror, and its goal is to deform the spherical CFRP mirror to a parabolic. Therefore, the response functions of the actuators were gotten, and the surface form errors and stresses were calculated and analyzed. The results show that the CFRP mirrors designed by the method have a better symmetrical bending deformation under gravity and thermal load and a higher fundamental frequency, and the larger n the better symmetry (for ?/n quasi-isotropic laminates); the method reduces the sensitivity to misalignment of ply orientation for symmetric bending, and the mirror's maximum von Mises stress and maximum shear stress are less compared to those laminates not optimized in lay-up sequence.
NASA Technical Reports Server (NTRS)
Hyer, M. W.; Hagaman, J. A.
1979-01-01
The results of a series of tests of graphite-polyimide honeycomb sandwich panels are presented. The panels were 1.22 m long, 0.508 m wide, and approximately 13.3 m thick. The face sheets were a T-300/PMR-15 fabric in a quasi-isotropic layup and were 0.279 mm thick. The core was Hexcel HRH 327-3/16 - 4.0 glass reinforced polyimide honeycomb, 12.7 mm thick. Three panels were used in the test: one was cut into smaller pieces for testing as beam, compression, and shear specimens; a second panel was used for plate bending tests; the third panel was used for in-plane stability tests. Presented are the experimental results of four point bending tests, short block compression tests, core transverse shear modulus, three point bending tests, vibration tests, plate bending tests, and panel stability tests. The results of the first three tests are used to predict the results of some of the other tests. The predictions and experimental results are compared, and the agreement is quite good.
Thermomechanical fatigue behavior of a quasi-isotropic SCS-6/Ti-15-3 metal matrix composite
Hart, K.A.; Mall, S. (Air Force Inst. of Technology, Wright Patterson Air Force Base, OH (United States). Dept. of Aeronautics and Astronautics)
1995-01-01
As the speed of new aerospace vehicles pushes the supersonic and hypersonic envelopes, aerodynamic heating and structural strength and weight are becoming even greater design factors. Here, the response of a quasi-isotropic laminate of metal matrix composite, SCS-6/Ti-15-3 in a thermomechanical fatigue (TMF) environment was investigated. To achieve this, three sets of fatigue tests were conducted: (1) in-phase TMF (IP-TMF), (2) out-of-phase TMF (OP-TMF), and (3) isothermal fatigue (IF). The fatigue response was dependent on the test condition and the maximum stress level during cycling. The IF, IP-TMF, and OP-TMF conditions yielded shortest fatigue life at higher, intermediate and lower stress levels, respectively. Examination of the failure mode through the variation of strain or modulus during cycling, and post-mortem microscopic evaluation revealed that it was dependent on the fatigue condition and applied stress level. Higher stresses, mostly with IP-TMF and IF conditions, produced a primarily fiber dominated failure. Lower stresses, mostly with the OP-TMF condition, produced a matrix dominated failure. Also, an empirical model based on the observed damage mechanisms was developed to represent the fatigue lives for the three conditions examined here.
Zhongqing Su; Lin Ye
2005-01-01
Active transducer networks using distributed piezoelectric actuator\\/sensor were designed in terms of a concept of ‘Standard Sensor Unit’ (SSU). Functionally integrating the artificial neural networks well-trained by Damage Parameters Database (DPD) developed in Part I, an active online structural health monitoring (SHM) system was configured on a VXI platform, which was then validated by quantitatively identifying hole-type defects in quasi-isotropic
Zhongqing Su; Lin Ye
2005-01-01
A guided Lamb wave-based damage identification scheme and an online structural health monitoring (online-SHM) system with an integrated piezoelectric actuator-sensor network are developed. The proposed methodology is applied to the quantitative diagnosis of through-hole-type defect in the CF-EP quasi-isotropic laminate with the aid of an artificial neural network algorithm. For this purpose, a variety of composite laminates with stochastic damages
Hergt, Steven; Schaefer, Gerhard [Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, 07743 Jena (Germany)
2008-05-15
The Kerr metric outside the ergosphere is transformed into Arnowitt-Deser-Misner coordinates up to the orders 1/r{sup 4} and a{sup 2}, respectively, in radial coordinate r and reduced angular momentum variable a, starting from the Kerr solution in quasi-isotropic as well as harmonic coordinates. The distributional source terms for the approximate solution are calculated. To leading order in linear momenta, higher-order-in-spin interaction Hamiltonians for black hole binaries are derived.
Har-Peled, Sariel
, slow, and not robust nZ1,000,000 n 2 =10 12 O n 2 #12; Approximation Algorithms: Approximation the Polytope A Features of the polytope partition sphere into regions A Voronoi Diagram induced by features
An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program
NASA Technical Reports Server (NTRS)
Rose, Cheryl A.; Herakovich, Carl T.
1992-01-01
An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.
Gautam, Natarajan
Approximations for system performance under selfsimilar traffic N. Gautam Department of Industrial) in networks are Leland et al [13] in ethernet LAN traffic. Ever since, several experiments and measurements
Design and Measurements of a quasi-isotropic UWB micro-strip antenna
Paris-Sud XI, Université de
, integration of an UWB antenna requires the latter to be isotropic (almost) and matched over a wide band disturbing other neighboring wireless communications that share part of the UWB band. Antennas dedicated-dispersive and wideband. Power matching should be realized continuously on the whole 7.5 GHz wide frequency band
Hsu, T.L.
1998-09-01
This study primarily investigated the electro-mechanical fatigue behavior of the embedded piezoelectric actuators in graphite/epoxy laminate with a lay-up of 0/ {+-} 45 / 90s. A secondary focus was the investigation of the mechanical fatigue effects of the 0 / 0 / {+-} 45 / 0 / 0 / 90s laminate with embedded PZT under tensile loading. All the fatigue tests were conducted with a triangular loading waveform which had a frequency of 10 Hz and with R = 0.1. In the electro-mechanical testing, the embedded actuator was excited by a {minus}10 V to {minus}100 V or a 10 V to 100 V voltage input, which resulted in either in-phase or out-of-phase electrically induced strain waveform with respect to the mechanical loading or strain. It was found that the embedded PZTs performed very well during the out-of-phase electro-mechanical and low stress fatigue conditions when the applied strain was within the operating range of PZT. Beyond the upper strain limit, the voltage output of the PZT was primarily influenced by the mechanical fatigue loading. Results from the high stress fatigue tests showed that the embedded piezoelectric actuators did not have significant effect on the tensile strength of the laminates.
Flexural Stiffnesses of and Dimensional Stability in Circular Quasi-isotropic Laminate Mirrors
Kim, Kyungpyo
2009-01-01
to Hank Blazek, Bennett Optical Research, for providing me a very special and valuable mirror specimen for my dissertation. I could never have been able to finish without the help. Finally, I would like to thank my wife and my kids (Eunja Kim, Aaron K.... Kim, Andrew K. Kim, and my lovely daughter) who have never failed to stand beside me and my decisions. Your faith and support are a constant source of comport and inspiration. v DEDICATION to my wife Eunja Kim...
Self-amplification of the field of velocity derivatives in quasi-isotropic turbulence
NASA Astrophysics Data System (ADS)
Galanti, B.; Tsinober, A.
2000-12-01
We report results of direct numerical simulations of the Navier-Stokes equations regarding the role of self-amplification of the field of velocity derivatives, i.e., involving both vorticity and strain. The main result is that even at rather moderate values of the Reynolds number the self-amplification totally dominates the process of production of the field of velocity derivatives. The role of external forcing in this process is negligible. This dominance occurs not only in the mean, but practically pointwise throughout the whole flow field. The property of self-amplification possesses a number of quantitative universal properties which are independent of the details of forcing.
Wissenschaftliches Approximation
Auzinger, Winfried
' am Digitalcomputer Archimedes und die Berechnung von = 3.14159 . . . Das leidige Integral Das Einleitung: `Alles ist Zahl' am Digitalcomputer Archimedes und die Berechnung von = 3.14159 . . . Das Approximation als Sparmaßnahme Anhang Überblick Einleitung: `Alles ist Zahl' am Digitalcomputer Archimedes und
Irina Perfilieva
2002-01-01
The principle approach to the construction of approximating formulas is discussed. We suggest the generalized definition\\u000a of normal forms in predicate BL-logic and prove the conditional equivalence between a formula and each of its normal forms.\\u000a Some mutual relations between normal forms will be also established.
Fast Approximate Convex Decomposition
Ghosh, Mukulika
2012-10-19
Approximate convex decomposition (ACD) is a technique that partitions an input object into "approximately convex" components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can...
Approximate Information Theory
Penny, Will
Approximate Inference Will Penny Information Theory Information Entropy Kullback-Liebler Divergence Approximate Inference Will Penny 31st March 2011 #12;Approximate Inference Will Penny Information Theory Will Penny Information Theory Information Entropy Kullback-Liebler Divergence Gaussians Asymmetry
Interpolation and Approximation Theory.
ERIC Educational Resources Information Center
Kaijser, Sten
1991-01-01
Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH)
Umar Farooq; Karl Gregory
This study was aimed at improving the understanding of the barely visible internal impact damage (BVID), its initiation, growth and tolerance in fibrous composites under low velocity impact through developing a computational model to perform damage assessment, and visualize the damage morphology. Instead of inducing damage in the form of ply the selected areas equal to the size of the
Verre, Ruggero; Antosiewicz, Tomasz J; Svedendahl, Mikael; Lodewijks, Kristof; Shegai, Timur; Käll, Mikael
2014-09-23
Quasicrystals are structures that possess long-range order without being periodic. We investigate the unique characteristics of a photonic quasicrystal that consists of plasmonic Ag nanodisks arranged in a Penrose pattern. The quasicrystal scatters light in a complex but spectacular diffraction pattern that can be directly imaged in the back focal plane of an optical microscope, allowing us to assess the excitation efficiency of the various diffraction modes. Furthermore, surface plasmon polaritons can be launched almost isotropically through near-field grating coupling when the quasicrystal is positioned close to a homogeneous silver surface. We characterize the dispersion relation of the different excited plasmon modes by reflection measurements and simulations. It is demonstrated that the quasicrystal in-coupling efficiency is strongly enhanced compared to a nanoparticle array with the same particle density but only short-range lateral order. We envision that the system can be useful for a number of advanced light harvesting and optoelectronic applications. PMID:25182843
HIERARCHICAL GEOMETRIC APPROXIMATIONS
North Carolina at Chapel Hill, University of
HIERARCHICAL GEOMETRIC APPROXIMATIONS TR-050 1994 Amitabh Varshney Department of Computer Science;HIERARCHICAL GEOMETRIC APPROXIMATIONS by Amitabh Varshney A Dissertation submitted to the faculty Advisor Reader Reader Reader #12;@1994 Amitabh Varshney ALL RIGHTS RESERVED #12;AMITABH VARSHNEY
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Quasicrystals and crystalline approximants
A. I. Goldman; R. F. Kelton
1993-01-01
Over the past seven years, many examples of periodic crystals closely related to quasicrystalline alloys have been discovered. These crystals have been termed approximants, since the arrangements of atoms within their unit cells closely approximate the local atomic structures in quasicrystals. This colloquium focuses on these approximant structures, their description, and their relationship to quasicrystals.
Approximate solution in gasdynamics
NASA Technical Reports Server (NTRS)
Sirovich, L.; Chong, T. H.
1980-01-01
One-dimensional unsteady gasdynamics is considered. An approximation based mainly on the interaction of simple and entropy waves is adopted. A discussion supporting this approximation, based in part on shock expansion theory, is given. By the use of certain transformations the approximation leads to solution in terms of quadratures. Excellent agreement with exact numerical results is obtained over a wide range of cases.
Geometric Approximation via Coresets
PANKAJ K. AGARWAL; SARIEL HAR-PELED; KASTURI R. VARADARAJAN
The paradigm of coresets has recently emerged as a powerful tool for eciently approximating various extent measures of a point set P. Using this paradigm, one quickly computes a small subset Q of P, called a coreset, that approximates the original set P and and then solves the problem on Q using a relatively inecient algorithm. The solution for Q
Steven M. Pincus
1992-01-01
A common framework of finite state approximating Markov chains is developed for discrete time deterministic and stochastic processes. Two types of approximating chains are introduced: (i) those based on stationary conditional probabilities (time averaging) and (ii) transient, based on the percentage of the Lebesgue measure of the image of cells intersecting any given cell. For general dynamical systems, stationary measures
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.
Mikkel Thorup; Uri Zwick
2005-01-01
Let G = (V,E) be an undirected weighted graph with |V| = n and |E| = m. Let k ? 1 be an integer. We show that G = (V,E) can be preprocessed in O(kmn1\\/k) expected time, constructing a data structure of size O(kn1+1\\/k), such that any subsequent distance query can be answered, approximately, in O(k) time. The approximate distance
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. PMID:25528318
Covariant approximation averaging
NASA Astrophysics Data System (ADS)
Shintani, Eigo; Arthur, Rudy; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2015-06-01
We present a new class of statistical error reduction techniques for Monte Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in Nf=2 +1 lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte Carlo calculations over conventional methods for the same cost.
Mikkel Thorup; Uri Zwick
2001-01-01
Let G=(V,E) be an undirected weighted graph with |V|=n and |E|=m. Let k\\\\ge 1 be an integer. We show that G=(V,E) can be preprocessed in O(kmn^{1\\/k}) expected time, constructing a data structure of size O(kn^{1+1\\/k}), such that any subsequent distance query can be answered, approximately, in O(k) time. The approximate distance returned is of stretch at most 2k-1, i.e., the
Approximation Algorithms Tandy Warnow
Warnow,Tandy
CS 331 Approximation Algorithms Tandy Warnow #12;Princeton University · COS 423 · Theory-SAT 3-SAT DIR-HAM-CYCLEINDEPENDENT SET VERTEX COVER GRAPH 3-COLOR HAM-CYCLE TSP SUBSET of DNA sequences) Travelling Salesman (finding a minimum cost tour in an edge-weighted graph) #12;Vertex
Complexity of Approximating the
Fomin, Fedor V.
Complexity of Approximating the Oriented Diameter of Chordal Graphs Fedor V. Fomin,1 Marti the diameters of strongly connected orientations of G. We study algorithmic aspects of determining the oriented chordal bcu graph G, finds a strongly connected orientation of G with diameter at most one plus twice
Social choice Approximate MAX CUT
Pansu, Pierre
Social choice Un-friends Approximate MAX CUT Unique games Hardness of approximation P. Pansu;Social choice Un-friends Approximate MAX CUT Unique games Today's menu: A theorem in social choice theory-Sud Hardness of approximation #12;Social choice Un-friends Approximate MAX CUT Unique games Influences Noise
Optimizing the Zeldovich approximation
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Pellman, Todd F.; Shandarin, Sergei F.
1994-01-01
We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment of phases in the nonlinear regime. We also report on the accuracy of particle positions and velocities produced by TZA.
Variational truncated Wigner approximation.
Sels, Dries; Brosens, Fons
2014-04-01
In this paper we reconsider the notion of an optimal effective Hamiltonian for the semiclassical propagation of the Wigner distribution in phase space. An explicit expression for the optimal effective Hamiltonian is obtained in the short-time limit by minimizing the Hilbert-Schmidt distance between the semiclassical approximation and the real state of the system. The method is illustrated for the quartic oscillator. PMID:24827193
Alessandra Di Pierro; Chris Hankin; Herbert Wiklicky
2004-01-01
We address the problem of characterising the security of a program,against unauthorised information flows. Classical approaches,are based on non-interference models which depend,ultimately on the notion of process equivalence. In these models confidentiality is an absolute property statin g the absence of any illegal information flow. We present a model,in which the notion of non-interference is approximated in the sense that
Approximation of Time-Dependent, Viscoelastic Fluid Flow: SUPG Approximation
Ervin, Vincent J.
Approximation of Time-Dependent, Viscoelastic Fluid Flow: SUPG Approximation Vincent J. Ervin equations with an Oldroyd B constitutive equation. The approximation is stabilized by using a SUPG, the numerical approximations. Key words. viscoelasticity, finite element method, fully discrete, SUPG AMS
Approximation of Time-Dependent Viscoelastic Fluid Flow: SUPG Approximation
Vincent J. Ervin; William W. Miles
2003-01-01
In this article we consider the numerical approximation to the time dependent vis- coelasticity equations with an Oldroyd B constitutive equation. The approximation is stabilized by using a SUPG approximation for the constitutive equation. We analyse both the semi-discrete and fully discrete numerical approximations. For both discretizations we prove the existence of, and derive a priori error estimates for, the
Toward Approximate Moving Least Squares Approximation with Irregularly Spaced
Heller, Barbara
-order moving least squares approximations. In this paper we focus our interest on practical implementationsToward Approximate Moving Least Squares Approximation with Irregularly Spaced Centers Gregory E.S.A. Abstract By combining the well known moving least squares approximation method and the theory
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.
Efficient polynomial L -approximations
Brisebarre, Nicolas
Dr P. Michelon, 42023 St-Â´Etienne Cedex 02 and Projet ArÂ´enaire, LIP, 46 allÂ´ee d'Italie, 69364 Lyon are the supremum norm (or L norm or absolute error) ||p - f||,[a,b] = sup axb |p(x) - f(x)|, or the relative error ||p - f||rel,[a,b] = sup axb 1 |f(x)| |p(x) - f(x)| or least squares approximations norm ||p-f||2,[a,b
Approximate Bayesian Computation
Sunnåker, Mikael; Corander, Jukka; Foll, Matthieu; Dessimoz, Christophe
2013-01-01
Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology). PMID:23341757
Exploring Machin's Approximation of Exploring Machin's Approximation of
Knaust, Helmut
#12;Exploring Machin's Approximation of Precursors Method of Exhaustion `a la Archimedes Archimedes of Precursors Method of Exhaustion `a la Archimedes Archimedes of Syracuse ( 287212 BC) approximated la Archimedes Archimedes of Syracuse ( 287212 BC) approximated by the Method of Exhaustion: 3
Approximate nonlinear self-adjointness and approximate conservation laws
Zhi-Yong Zhang
2013-04-03
In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed by means of the method. As an application, a class of perturbed nonlinear wave equations is considered to illustrate the effectiveness.
On uniform approximation of elliptic functions by Pade approximants
Khristoforov, Denis V [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2009-06-30
Diagonal Pade approximants of elliptic functions are studied. It is known that the absence of uniform convergence of such approximants is related to them having spurious poles that do not correspond to any singularities of the function being approximated. A sequence of piecewise rational functions is proposed, which is constructed from two neighbouring Pade approximants and approximates an elliptic function locally uniformly in the Stahl domain. The proof of the convergence of this sequence is based on deriving strong asymptotic formulae for the remainder function and Pade polynomials and on the analysis of the behaviour of a spurious pole. Bibliography: 23 titles.
Structural optimization with approximate sensitivities
S. N Patnaik; D. A Hopkins; R Coroneos
1996-01-01
Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with a small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients
Taylor Approximations and Definite Integrals
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2007-01-01
We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)
Approximate equivalence and approximate synchronization of metric transition systems
A. Agung Julius; George J. Pappas
2006-01-01
In this paper, we consider metric transition systems which are transition systems equipped with metrics for observation and synchronization labels. The existence of metrics leads to the introduction of two new concepts, (i) (epsi, delta)-approximate (bi)simulation of transition systems and (ii) approximate synchronization of transition systems. We show that the notion of (epsi, delta)-approximate (bi)simulation can be thought of as
NASA Technical Reports Server (NTRS)
Harris, C. E.; Morris, D. H.
1983-01-01
Notched and unnotched geometries at 16, 32, and 64-ply thicknesses of a 90/45/0-45 (ns) laminate and a 45/0/-45/90 (ns) laminate were tested in compression-compression fatigue. The fatigue life and the initiation, type, and progression of damage were determined. Interlaminar stresses generated at straight, free edges of axially loaded laminates were used to interpret the test results. The fatigue lives of the notched specimens did not appear to be a strong function of laminate stacking sequence or specimen thickness. The stress concentration at the hole dominated over the interlaminar stresses at the straight free edge. The unnotched specimens of the 90/45/0/-45 (ns) laminate with tensile interlaminar normal stresses delaminated more readily than did the 45/0/-45/90 (ns) laminate with compressive interlaminar normal stress. The life of the 16-ply unnotched specimens was lower than the 32- and 64-ply specimens. Delaminations were located at the interface where the maximum shear stress occurred regardless of the sense or magnitude of the interlaminar normal stress. An antibuckling fixture was effective in preventing out-of-plane motion without overconstraining the specimen.
NASA Technical Reports Server (NTRS)
Harris, C. E.; Morris, D. H.
1985-01-01
Notched and unnotched geometries at 16, 32, and 64-ply thicknesses of a 90/45/0-45 (ns) laminate and a 45/0/-45/90 (ns) laminate were tested in compression-compression fatigue. The fatigue life and the initiation, type, and progression of damage were determined. Interlaminar stresses generated at straight, free edges of axially loaded laminates were used to interpret the test results. The fatigue lives of the notched specimens did not appear to be a strong function of laminate stacking sequence or specimen thickness. The stress concentration at the hole dominated over the interlaminar stresses at the straight free edge. The unnotched specimens of the 90/45/0/-45 (ns) laminate with tensile interlaminar normal stresses delaminated more readily than did the 45/0/-45/90 (ns) laminate with compressive interlaminar normal stress. The life of the 16-ply unnotched specimens was lower than the 32and 64-ply specimens. Delaminations were located at the interface where the maximum shear stress occurred regardless of the sense or magnitude of the interlaminar normal stress. An antibuckling fixture was effective in preventing out-of-plane motion without overconstraining the specimen.
R. Basri; W. K. Chiu
2004-01-01
This paper investigates how Lamb waves respond to the presence of material degradation in a plate-like structure using a series of finite element analyses. To facilitate this study, the propagation of these guided waves was interpreted with the dispersion characteristics and displacement profiles were analysed in the frequency and wave number domain. The results show that the material degradation simulated
Very badly approximable matrix functions
V. V. Peller; S. R. Treil
2005-01-01
. We study in this paper very badly approximable matrix functions on the unit circle\\u000a $$ \\\\mathbb{T}, $$ i.e., matrix functions ? such that the zero function is a superoptimal approximation of ?. The purpose of this paper is to\\u000a obtain a characterization of the continuous very badly approximable functions.\\u000a \\u000a Our characterization is more geometric than algebraic characterizations earlier obtained in
Superresolution by structured matrix approximation
Ramdas Kumaresan; Arnab K. Shaw
1988-01-01
The bearing estimation problem is formulated as a matrix-approximation problem. The columns of a matrix X are formed by the snapshot vectors from an N-element array. The matrix X is then approximated by a matrix in the least-square sense. The rank as well as the partial structure of the space spanned by the columns of the approximated X matrix are
Algorithms for Polytope Covering and Approximation, and for Approximate
Clarkson, Kenneth L.
Algorithms for Polytope Covering and Approximation, and for Approximate Closest-point Queries draft a data structure so that given a query point q, the closest site to q can be found quickly. The algorithm the ratio of the distance between the farthest pair of sites to the distance between the closest pair
Algorithms for Polytope Covering and Approximation, and for Approximate
Clarkson, Kenneth L.
Algorithms for Polytope Covering and Approximation, and for Approximate Closest-point Queries draft points (called sites) in d dimensions, build a data structure so that given a query point q, the closest to the distance between the closest pair of sites. The algorithm builds a data structure of size O(n(log )/ d/2
Approximate Sensor Interpretation Norman Carver
Carver III, Norman
problems: vehicle monitoring and tracking, robot map making, sound understanding for robotic hearing in adapting ideas from the belief network community about approximate probablistic inference. A critical issue
Discrete Approximations of Probability Distributions
Allen C. Miller III; Thomas R. Rice
1983-01-01
Practical limits on the size of most probabilistic models require that probability distributions be approximated by a few representative values and associated probabilities. This paper demonstrates that methods commonly used to determine discrete approximations of probability distributions systematically underestimate the moments of the original distribution. A new procedure based on gaussian quadrature is developed in this paper. It can be
Approximating Functions with Exponential Functions
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2005-01-01
The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…
Computer Science Approximately Uniform Random
Massachusetts at Amherst, University of
Computer Science Approximately Uniform Random Sampling in Sensor Networks Boulat A. Bash, John W Science Outline Exact uniform random sampling Previous work Approximately uniform random sampling Naïve Preliminary simulations Conclusions and future work #12;Computer Science Sampling Problem Exact uniform random
Cavity approximation for graphical models.
Rizzo, T; Wemmenhove, B; Kappen, H J
2007-07-01
We reformulate the cavity approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our formulation, which allows for the treatment of multivalued variables, a further generalization to factor graphs with arbitrary order of interaction factors is explicitly carried out, and a message passing algorithm that implements the first order correction to the Bethe approximation is described. Furthermore, we investigate an implementation of the CA for pairwise interactions. In all cases considered we could confirm that CA[k] with increasing k provides a sequence of approximations of markedly increasing precision. Furthermore, in some cases we could also confirm the general expectation that the approximation of order k , whose computational complexity is O(N(k+1)) has an error that scales as 1/N(k+1) with the size of the system. We discuss the relation between this approach and some recent developments in the field. PMID:17677405
Goddard, Wayne
;Introduction problems Ideas Light Spanners Approximation Schemes Summary Approximation Algorithms Many;Introduction problems Ideas Light Spanners Approximation Schemes Summary Approximation Algorithms ManyIntroduction problems Ideas Light Spanners Approximation Schemes Summary Faster Approximations
The electroneutrality approximation in electrochemistry
Edmund J. F. Dickinson; Juan G. Limon-Petersen; Richard G. Compton
The electroneutrality approximation assumes that charge separation is impossible in electrolytic solutions. It has a long\\u000a and successful history dating back to 1889 and may be justified because of the small absolute values for the permittivities\\u000a of typical solvents. Dimensional analysis shows that the approximation becomes invalid only at nanosecond and nanometre scales.\\u000a Recent work, however, has taken advantage of
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Approximate entropy of network parameters
NASA Astrophysics Data System (ADS)
West, James; Lacasa, Lucas; Severini, Simone; Teschendorff, Andrew
2012-04-01
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.
Approximate entropy of network parameters.
West, James; Lacasa, Lucas; Severini, Simone; Teschendorff, Andrew
2012-04-01
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches. PMID:22680542
Wavelet Sparse Approximate Inverse Preconditioners
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Tang, W.-P.; Wan, W. L.
1996-01-01
There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.
Measure fields for function approximation.
Marroquin, J L
1995-01-01
The computation of a piecewise smooth function that approximates a finite set of data points may be decomposed into two decoupled tasks: 1) the computation of the locally smooth models, and hence, the segmentation of the data into classes that consist of the sets of points best approximated by each model; 2) the computation of the normalized discriminant functions for each induced class (which maybe interpreted as relative probabilities). The approximating function may then be computed as the optimal estimator with respect to this measure field. For the first step, we propose a scheme that involves both robust regression and spatial localization using Gaussian windows. The discriminant functions are obtained fitting Gaussian mixture models for the data distribution inside each class. We give an efficient procedure for effecting both computations and for the determination of the optimal number of components. Examples of the application of this scheme to image filtering, surface reconstruction and time series prediction are presented. PMID:18263399
Approximations to camera sensor noise
NASA Astrophysics Data System (ADS)
Jin, Xiaodan; Hirakawa, Keigo
2013-02-01
Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.
Gadgets, approximation, and linear programming
Trevisan, L. [Universita degli Studi Di Roma La Sapienza, Rome (Italy); Sudan, M.; Sorkin, G.B.; Williamson, D.P. [IBM T.J. Watson Research Center, Yorktown Heights, NY (United States)
1996-12-31
We present a linear-programming based method for finding {open_quotes}gadgets{close_quotes}, i.e., combinatorial structures reducing constraints of one optimization problems to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method we present a number of new, computer-constructed gadgets for several different reductions. This method also answers a question posed by on how to prove the optimality of gadgets-we show how LP duality gives such proofs. The new gadgets improve hardness results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 60/61 and 44/45 respectively is N P-hard. We also use the gadgets to obtain an improved approximation algorithm for MAX 3SAT which guarantees an approximation ratio of .801. This improves upon the previous best bound of .7704.
Approximate dynamic programming for management
Powell, Warren B.
inventory levels in a distributed warehouse network. Keywords Inventory management, Warehousing, Spare partsApproximate dynamic programming for management of high-value spare parts Hugo Simao and Warren to a set of distributed warehouses in response to random, nonstationary demands. There is particular
Hardness of Approximation Subhash Khot
Khot, Subhash
Q17. Keywords. NP-completeness, Approximation algorithms, Inapproximability, Proba- bilistically Checkable Proofs, Discrete Fourier analysis. 1. Introduction The P = NP hypothesis says that a large class of computational problems known as NP-complete problems do not have efficient algorithms. An algorithm is called
Pythagorean Approximations and Continued Fractions
ERIC Educational Resources Information Center
Peralta, Javier
2008-01-01
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
Approximations to wire grid inductance.
Warne, Larry Kevin; Johnson, William Arthur; Merewether, Kimball O.
2004-06-01
By using a multipole-conformal mapping expansion for the wire currents we examine the accuracy of approximations for the transfer inductance of a one dimensional array of wires (wire grid). A simple uniform fit is constructed by introduction of the decay factor from bipolar coordinates into existing formulas for this inductance.
Approximate Proximity Drawings$ William Evans
Evans, Will
Approximate Proximity Drawings$ William Evans University of British Columbia, Canada, Emden Gansner proximity drawings, called (1, 2)-proximity drawings. Intuitively, given a defi- nition of proximity and two real numbers 1 0 and 2 0, an (1, 2)-proximity drawing of a graph is a planar straight-line drawing
Introduction to Normal Multiresolution Approximation
Runborg, Olof
Introduction to Normal Multiresolution Approximation Olof Runborg Department of Numerical Analysis and Computer Science, KTH, S--100 44 Stockholm, Sweden olofr@nada.kth.se Summary. A multiresolution analysis general schemes. Key words: subdivision, wavelet, normal mesh, normal multiresolution 1 Introduction
Speech Compression by Polynomial Approximation
Sorin Dusan; James L. Flanagan; Amod Karve; Mridul Balaraman
2007-01-01
Methods for speech compression aim at reducing the transmission bit rate while preserving the quality and intelligibility of speech. These objectives are antipodal in nature since higher compression presupposes preserving less information about the original speech signal. This paper presents a method for compressing speech based on polynomial approximations of the trajectories in time of various speech features (i.e., spectrum,
Approximation of maps by diffeomorphisms
Yann Brenier; Wilfrid Gangbo
2003-01-01
. It is shown that if then every map of class can be approximated in the -norm by a sequence of orientation-preserving diffeomorphims These conclusions hold provided that is open, bounded, and that In addition, is contained in the -neighborhood of the convex hull of All these conclusions fail for The main ingredients of the proof are the polar factorization
Normal Approximation to Poisson Distribution
NSDL National Science Digital Library
Dinov, Ivo
This applet, created by Ivo Dinov of the University of California, Los Angeles, demonstrates the normal approximation to the Poisson distribution. Users can set the rate, lambda, and the number of trials, n, and observe how the shape of the distribution changes. The Poisson distribution is shown in blue, and the Normal distribution is shown in red.
Best Monotone Approximation Using a Peak Norm
D. A. Legg; D. W. Townsend
1997-01-01
Monotone approximation relative to peak norms is studied both on an interval and in the discrete case. Existence and some structure results are obtained which demonstrate that peak norm approximation has similar properties toL1approximation. In particular, sup's and inf's of best approximants are best approximants (in the discrete case) and a half-above, half-below property is demonstrated.
Reflectance Function Approximation for Material Classification
Dyer, Charles R.
Reflectance Function Approximation for Material Classification Edward Wild CS 766 Final Project Report Abstract Reflectance functions are approximated from data using kernel re- gression and used results show that some reflectance functions can be approximated quite accurately with kernel regression
One sign ion mobile approximation
NASA Astrophysics Data System (ADS)
Barbero, G.
2011-12-01
The electrical response of an electrolytic cell to an external excitation is discussed in the simple case where only one group of positive and negative ions is present. The particular case where the diffusion coefficients of the negative ions, Dm, is very small with respect to that of the positive ions, Dp, is considered. In this framework, it is discussed under what conditions the one mobile approximation, in which the negative ions are assumed fixed, works well. The analysis is performed by assuming that the external excitation is sinusoidal with circular frequency ?, as that used in the impedance spectroscopy technique. In this framework, we show that there exists a circular frequency, ?*, such that for ? > ?*, the one mobile ion approximation works well. We also show that for Dm ? Dp, ?* is independent of Dm.
Waveless Approximation Theories of Gravity
James A. Isenberg
2007-02-20
The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability -- are associated with the presence of gravitational waves. We have developed a number of ``waveless approximation theories'' (WAT) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.
On approximation of quantum channels
M. E. Shirokov; A. S. Holevo
2007-01-01
We develop an approximation approach to infinite dimensional quantum channels\\u000abased on detailed investigation of the continuity properties of entropic\\u000acharacteristics of quantum channels and operations (trace-nonincreasing\\u000acompletely positive maps) as functions of a pair ``channel, input state''. The\\u000aobtained results are then applied to the following problems: continuity of the\\u000a$\\\\chi$-capacity as function of a channel; strong additivity of
Waveless Approximation Theories of Gravity
James A. Isenberg
2007-01-01
The analysis of a general multibody physical system governed by Einstein's\\u000aequations in quite difficult, even if numerical methods (on a computer) are\\u000aused. Some of the difficulties -- many coupled degrees of freedom, dynamic\\u000ainstability -- are associated with the presence of gravitational waves. We have\\u000adeveloped a number of ``waveless approximation theories'' (WAT) which repress\\u000athe gravitational radiation
Approximating extent measures of points
Pankaj K. Agarwal; Sariel Har-Peled; Kasturi R. Varadarajan
2004-01-01
We present a general technique for approximating various descriptors of the extent of a set P of n points in Rd when the dimension d is an arbitrary fixed constant. For a given extent measure ? and a parameter ϵ > 0, it computes in time O(n + 1\\/ϵO(1)) a subset Q ? P of size 1\\/ϵO(1), with the property
Networks and the Best Approximation Property
Girosi, Federico
1989-10-01
Networks can be considered as approximation schemes. Multilayer networks of the backpropagation type can approximate arbitrarily well continuous functions (Cybenko, 1989; Funahashi, 1989; Stinchcombe and White, 1989). We ...
Approximate reasoning using terminological models
NASA Technical Reports Server (NTRS)
Yen, John; Vaidya, Nitin
1992-01-01
Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.
Approximate Counting of Graphical Realizations.
Erd?s, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erd?s and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erd?s and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994
Approximate Counting of Graphical Realizations
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erd?s and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erd?s and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations. PMID:26161994
Generalized Gradient Approximation Made Simple
Perdew, J.P.; Burke, K.; Ernzerhof, M. [Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118 (United States)] [Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118 (United States)
1996-10-01
Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
The Monostatic/Bistatic Approximation
NASA Technical Reports Server (NTRS)
Schuh, Michael J.; Woo, Alex C.; Simon, Michael P.
1994-01-01
Many Radar Cross Section (RCS) prediction codes are limited to one monostatic return per run. However, such codes can calculate multiple bistatic returns per incident angle for a relatively small amount of additional computer resources. This note describes a method of using bistatic returns to generate multiple monostatic predictions for each incident angle computed. Typical results are presented and show the accuracy is initially good and then degrades as the separation angle between the incident and viewing angles becomes large. Introduction Since 1990, the monostatic/bistatic approximation has been used to reduce the number of runs required by finite-volume time-domain (FVTD) codes for making RCS versus azimuth plots. This approximation was spawned by the observation of a range test where the transmit and receive antennas were separated by a few degrees to prevent cross talk between the antennas. The measurements from this range are presented as monostatic RCS rather than bistatic: RCS. The procedure of reporting experimental bistatic RCS as the monostatic RCS at the angle bisecting the transmit and receive antennas was extended to FVTD codes and produces excellent results.
On approximations to generalized Poisson distributions
V. E. Bening; V. Yu. Korolev; S. Ya. Shorgin
1997-01-01
In this paper three methods of the construction of approximations to generalized Poisson distributions are considered: approximation\\u000a by a normal law, approximation by asymptotic distributions, the so-called Robbins mixtures, and approximation with the help\\u000a of asymptotic expansions. Uniform and (for the first two methods) nonuniform estimates of the accuracy of the corresponding\\u000a approximations are given. Some estimates for the concentration
The Velocity of Compressional Waves in Rocks to 10 Kilobars, Part 2
Francis Birch
1961-01-01
The measurements of the velocity of compressional waves up to 10 kilobars for some 250 specimens of rock, reported in part 1, are discussed with respect to the effects of porosity, alteration, anisotropy, and composition. The relations of isotropic elasticity are shown to be approximately valid for a number of examples. Reasonable agreement with theoretical values for quasi-isotropic aggregates is
Reconstruction within the Zeldovich approximation
NASA Astrophysics Data System (ADS)
White, Martin
2015-07-01
The Zeldovich approximation, first-order Lagrangian perturbation theory, provides a good description of the clustering of matter and galaxies on large scales. The acoustic feature in the large-scale correlation function of galaxies imprinted by sound waves in the early Universe has been successfully used as a `standard ruler' to constrain the expansion history of the Universe. The standard ruler can be improved if a process known as density field reconstruction is employed. In this paper, we develop the Zeldovich formalism to compute the correlation function of biased tracers in both real and redshift space using the simplest reconstruction algorithm with a Gaussian kernel and compare to N-body simulations. The model qualitatively describes the effects of reconstruction on the simulations, though its quantitative success depends upon how redshift-space distortions are handled in the reconstruction algorithm.
Interplay of approximate planning strategies.
Huys, Quentin J M; Lally, Níall; Faulkner, Paul; Eshel, Neir; Seifritz, Erich; Gershman, Samuel J; Dayan, Peter; Roiser, Jonathan P
2015-03-10
Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and hierarchically decompose hard tasks into simpler subtasks. Theoretical and cognitive research has revealed several such strategies; however, little is known about their establishment, interaction, and efficiency. Here, we use model-based behavioral analysis to provide a detailed examination of the performance of human subjects in a moderately deep planning task. We find that subjects exploit the structure of the domain to establish subgoals in a way that achieves a nearly maximal reduction in the cost of computing values of choices, but then combine partial searches with greedy local steps to solve subtasks, and maladaptively prune the decision trees of subtasks in a reflexive manner upon encountering salient losses. Subjects come idiosyncratically to favor particular sequences of actions to achieve subgoals, creating novel complex actions or "options." PMID:25675480
Analytical approximations for spiral waves
Löber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald [Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin (Germany)] [Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin (Germany)
2013-12-15
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency ? and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent ?(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
Indexing the approximate number system.
Inglis, Matthew; Gilmore, Camilla
2014-01-01
Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects. PMID:24361686
Producing approximate answers to database queries
NASA Technical Reports Server (NTRS)
Vrbsky, Susan V.; Liu, Jane W. S.
1993-01-01
We have designed and implemented a query processor, called APPROXIMATE, that makes approximate answers available if part of the database is unavailable or if there is not enough time to produce an exact answer. The accuracy of the approximate answers produced improves monotonically with the amount of data retrieved to produce the result. The exact answer is produced if all of the needed data are available and query processing is allowed to continue until completion. The monotone query processing algorithm of APPROXIMATE works within the standard relational algebra framework and can be implemented on a relational database system with little change to the relational architecture. We describe here the approximation semantics of APPROXIMATE that serves as the basis for meaningful approximations of both set-valued and single-valued queries. We show how APPROXIMATE is implemented to make effective use of semantic information, provided by an object-oriented view of the database, and describe the additional overhead required by APPROXIMATE.
IONIS: Approximate atomic photoionization intensities
NASA Astrophysics Data System (ADS)
Heinäsmäki, Sami
2012-02-01
A program to compute relative atomic photoionization cross sections is presented. The code applies the output of the multiconfiguration Dirac-Fock method for atoms in the single active electron scheme, by computing the overlap of the bound electron states in the initial and final states. The contribution from the single-particle ionization matrix elements is assumed to be the same for each final state. This method gives rather accurate relative ionization probabilities provided the single-electron ionization matrix elements do not depend strongly on energy in the region considered. The method is especially suited for open shell atoms where electronic correlation in the ionic states is large. Program summaryProgram title: IONIS Catalogue identifier: AEKK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1149 No. of bytes in distributed program, including test data, etc.: 12 877 Distribution format: tar.gz Programming language: Fortran 95 Computer: Workstations Operating system: GNU/Linux, Unix Classification: 2.2, 2.5 Nature of problem: Photoionization intensities for atoms. Solution method: The code applies the output of the multiconfiguration Dirac-Fock codes Grasp92 [1] or Grasp2K [2], to compute approximate photoionization intensities. The intensity is computed within the one-electron transition approximation and by assuming that the sum of the single-particle ionization probabilities is the same for all final ionic states. Restrictions: The program gives nonzero intensities for those transitions where only one electron is removed from the initial configuration(s). Shake-type many-electron transitions are not computed. The ionized shell must be closed in the initial state. Running time: Few seconds for a large problem with a few thousand configurations.
Signal and System Approximation from General Measurements
Boche, Holger
2014-01-01
In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley–Wiener space PW[1 over ?]. We consider approximation processes, where the input ...
Laplace Approximation Thursday, September 11, 2008
Cevher, Volkan
Laplace Approximation Thursday, September 11, 2008 Rice University STAT 631 / ELEC 639: Graphical distribution we want to represent (blue), with its Gaussian approximation (red) obtained by using the Laplace
Partial equilibrium approximations in Apoptosis
Huang, Ya-Jing
2012-01-01
Apoptosis is one of the most basic biological processes. In apoptosis, tens of species are involved in many biochemical reactions with times scales of widely differing orders of magnitude. By the law of mass action, the process is mathematically described with a large and stiff system of ODEs (ordinary differential equations). The goal of this work is to simplify such systems of ODEs with the PEA (partial equilibrium approximation) method. In doing so, we propose a general framework of the PEA method together with some conditions, under which the PEA method can be justified rigorously. The main condition is the principle of detailed balance for fast reactions as a whole. With the justified method as a tool, we made many attempts via numerical tests to simplify the Fas-signaling pathway model due to Hua et al. (2005) and found that nine of reactions therein can be well regarded as relatively fast. This paper reports our simplification of Hua at el.'s model with the PEA method based on the fastness of the nine ...
Decision analysis with approximate probabilities
NASA Technical Reports Server (NTRS)
Whalen, Thomas
1992-01-01
This paper concerns decisions under uncertainty in which the probabilities of the states of nature are only approximately known. Decision problems involving three states of nature are studied. This is due to the fact that some key issues do not arise in two-state problems, while probability spaces with more than three states of nature are essentially impossible to graph. The primary focus is on two levels of probabilistic information. In one level, the three probabilities are separately rounded to the nearest tenth. This can lead to sets of rounded probabilities which add up to 0.9, 1.0, or 1.1. In the other level, probabilities are rounded to the nearest tenth in such a way that the rounded probabilities are forced to sum to 1.0. For comparison, six additional levels of probabilistic information, previously analyzed, were also included in the present analysis. A simulation experiment compared four criteria for decisionmaking using linearly constrained probabilities (Maximin, Midpoint, Standard Laplace, and Extended Laplace) under the eight different levels of information about probability. The Extended Laplace criterion, which uses a second order maximum entropy principle, performed best overall.
Femtolensing: Beyond the semiclassical approximation
NASA Technical Reports Server (NTRS)
Ulmer, Andrew; Goodman, Jeremy
1995-01-01
Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.
Energy conservation - A test for scattering approximations
NASA Technical Reports Server (NTRS)
Acquista, C.; Holland, A. C.
1980-01-01
The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.
Abel inversion using Legendre polynomials approximations
Shuiliang Ma; Hongming Gao; Lin Wu; Guangjun Zhang
2008-01-01
An improved Abel inversion method based on Legendre polynomials approximations is presented for reconstructing the original radial distribution of plasma emission coefficients from projected intensities. The method uses the technique of overlapping two near segments for obtaining an excellent approximation of the intensity distribution. The approximated function of the intensity profile is a combination of various shifted Legendre polynomials which
Polyhedral approximations of strictly convex compacta
Balashov, Maxim V
2011-01-01
We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the Hausdorff metric. We also obtain new estimates of an approximate algorithm for finding the convex hulls.
On the hardness of approximating minimization problems
Carsten Lund; Mihalis Yannakakis
1993-01-01
We prove results indicating that it is hard to compute efficiently good approximate solutions to the Graph Coloring, Set Covering and other related minimization problems. Specifi- cally, there is an E > 0 such that Graph Coloring cannot be approximated with ratio n' unless P = NP. Set Covering cannot be approximated with ratio c log n for any c
Efficient Analytic Approximation of American Option Values
Giovanni Barone-Adesi; Robert E. Whaley
1987-01-01
This paper provides simple analytic approximations for pricing exchange-traded American call and put options written on commodities and commodity futures contracts. These approximations are accurate and considerably more computationally efficient than finite- difference, binomial, or compound-option approximation methods. Copyright 1987 by American Finance Association.
An approximation to the KBKZ constitutive equation
P Olley; P. D Coates
1997-01-01
This work describes an approximation to a KBKZ based equation which completely separates shear and elongational contributions to visco-elastic stresses. This approximation has two significant advantages over a normal KBKZ implementation: (i) computationally intensive procedures associated with computing the Finger-strain tensor are largely avoided, and (ii) the approximation is relatively easy to understand intuitively, hence illustrating some important mechanisms implicit
On the Approximation of Complicated Dynamical Behavior
On the Approximation of Complicated Dynamical Behavior Michael Dellnitz and Oliver Junge techniques for the numerical approximation of compli- cated dynamical behavior. In particular, we develop numerical methods which allow to approximate SBR-measures as well as (almost) cyclic behavior of a dynamical
Best Quadratic Approximations of Cubic Boolean Functions
, n). Key words: Bent functions; boolean functions; covering radius; lower order approximationsBest Quadratic Approximations of Cubic Boolean Functions Nicholas Kolokotronis1,2, Konstantinos of Boolean functions is treated in this paper. We focus on the case of best quadratic approximations
Approximate Group Analysis and Multiple Time Scales Method for the Approximate Boussinesq Equation
Svetlana A. Kordyukova
2006-01-01
This paper is devoted to investigation of the approximate Boussinesq equation by methods of the approximate symmetry analysis of partial differential equations with a small parameter developed by Baikov, Gazizov and Ibragimov. We combine these methods with the method of multiple time scales to extend the domain of definition of approximate group invariant solutions of the approximate Boussinesq equation.
Comparison of some approximations for isotropic turbulence.
NASA Technical Reports Server (NTRS)
Herring, J. R.; Kraichnan, R. H.
1972-01-01
Study of several related turbulence approximations with regard to dynamical properties and agreement of numerical predictions with laboratory and computer experiments. The approximations considered include the direct-interaction equations (Kraichnan, 1964), Herring's (1966) self-consistent-field theory, a generalization of Edwards' (1964) theory, the abridged Lagrangian-history, direct-interaction approximation (Kraichnan, 1966), the test-field model (Kraichnan, 1971), and an approximation, not previously described, in which one velocity field passively suffers convection by another. Most of the cited approximations are representable by stochastic model equations for the velocity amplitude. Explicit constructions are given for the stochastic models, in a form that can be approximated on a digital computer. These constructions are used to discuss the physical and mathematical differences between the model dynamics and actual Navier-Stokes dynamics.-
Variationally consistent approximation scheme for charge transfer
NASA Technical Reports Server (NTRS)
Halpern, A. M.
1978-01-01
The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groups of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximation to the amplitude.
Approximation Algorithms for 3D Orthogonal Knapsack
Florian Diedrich; Rolf Harren; Klaus Jansen; Ralf Thöle; Henning Thomas
2008-01-01
Abstract. We study non-overlapping axis-parallel packings of 3D boxes with profits into a dedicated bigger box where rotation is forbidden; we wish to maximize,the total profit. Since this optimization problem,is NP-hard, we focus on approximation algorithms. We obtain fast and simple algorithms with approximation ratios 9 + ? and 8 + ? as well as an algorithm with approximation ratio
Bent approximations to synchrotron radiation optics
Heald, S.
1981-01-01
Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors.
Normal Approximation to the Binomial Distribution
NSDL National Science Digital Library
Lane, David M.
This demonstration, by David M. Lane of Rice University, allows you to view the binomial distribution and the normal approximation to it as a function of the probability of a success on a given trial and the number of trials. It can be used to compute binomial probabilities and normal approximations of those probabilities.
Efficient Real Root Approximation Michael Kerber
Efficient Real Root Approximation Michael Kerber IST (Institute of Science and Technology) Austria real roots of a square- free polynomial f. Given isolating intervals, our algorithm refines each of them to a certain width 2-L, that is, each of the roots is approximated to L bits after the binary
Efficient Real Root Approximation Michael Kerber
Efficient Real Root Approximation Michael Kerber IST (Institute of Science and Technology) Austria real roots of a square- free polynomial f . Given isolating intervals, our algorithm refines each of them to a width at most 2-L, that is, each of the roots is approximated to L bits after the binary
Spline approximations for nonlinear hereditary control systems
P. K. Lamm
1984-01-01
A spline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Boson Star Rotation: A Newtonian Approximation
Vanda Silveira; Claudio M. G. de Sousa
1995-08-08
Using the Newtonian approximation, we study rotating compact bosonic objects. The equations which describe stationary states with non-zero angular momentum are constructed and some numerical results are presented as examples. Limits on the applicability of the Newtonian approximation are discussed.
Approximating lapped transforms through unitary postprocessing
Ricardo L. de Queiroz
2001-01-01
We deal with the approximation of a nonsquare lapped transform matrix by another matrix. This second matrix is constrained to be the product of two stages: one lapped transform and a unitary postprocessing step, in such a way that approximation is accomplished by modifying the postprocessing stage alone. Viewing both matrices as transforms, the goal is to minimize the variance
Diagonal Pade approximations for initial value problems
Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.
1987-06-01
Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab.
Approximating Dynamic Global Illumination in Image Space
Tobias Ritschel; Thorsten Grosch; Hans-Peter Seidel
2009-01-01
Physically plausible illumination at real-time framerates is often achieved using approximations. One popular example is ambient occlusion (AO), for which very simple and efficient implementations are used extensively in production. Recent methods approximate AO between nearby geometry in screen space (SSAO). The key observation described in this paper is, that screen-space occlusion methods can be used to compute many more
Uniform harmonic approximation on Riemannian manifolds
Thomas Bagby; Pierre Blanchet
1994-01-01
In this paper we study uniform approximation by harmonic functions on arbitrary closed subsets of a Riemannian manifold. Thus our goal is to extend a number of results obtained in earlier papers concerning uniform harmonic approximation on unbounded closed subsets of Riemann surfaces or regions in Euclidean space R n. In this setting we obtain a localization theorem, and extensions
Approximations in Canonical Electrostatic MEMS Models
John A. Pelesko; Tobin A. Driscoll
2004-01-01
The mathematical modeling and analysis of electrostatically actuated micro- and nanoelectromechanical systems (MEMS and NEMS) has typically relied upon simplied electrostatic eld approximations to facilitate the analysis. Usually, the small aspect ratio of typical MEMS and NEMS devices is used to simplify Laplace's equation. Terms small in this aspect ratio are ignored. Unfortunately, such an approximation is not uniformly valid
Raftery, Adrian
___________________________________________________________________________________________________ Approximate Bayes Factors for Image Segmentation: The Pseudolikelihood Information Criterion (PLIC) Derek C of colors or true gray levels in an image; this allows fully automatic segmentation of images. Our as corresponding to a statistical model for the image, and the resulting models are compared via approximate Bayes
February 13, 2012 Diophantine approximation and
Waldschmidt, Michel
;Diophantus of Alexandria (250 ±50) #12;Rational approximation The rational numbers are dense in the real : starting from the rational numbers, compute the maximal number of digits of x with the minimum;Rational approximation The rational numbers are dense in the real numbers : For any x in R and any > 0
Approximate option valuation for arbitrary stochastic processes
Robert Jarrow; Andrew Rudd
1982-01-01
We show how a given probability distribution can be approximated by an arbitrary distribution in terms of a series expansion involving second and higher moments. This theoretical development is specialized to the problem of option valuation where the underlying security distribution, if not lognormal, can be approximated by a lognormally distributed random variable. The resulting option price is expressed as
Kirchhoff approximation for diffusive waves Jorge Ripoll*
Lorenzo, Jorge Ripoll
Laboratoire d'Energetique Moleculaire et Macroscopique, Combustion, Ecole Centrale Paris, Centre National de. The accuracy of this approximation is evaluated on comparison with results from a rigorous numerical technique calculated for an arbitrary geometry. Performance of the approximation as a function of the optical
Approximate Euclidean Ramsey theorems Adrian Dumitrescu
Dumitrescu, Adrian
an arbitrary long approximate arithmetic progression, if L is large enough. (ii) every dense separated set condition is needed in this case. Keywords: Euclidean Ramsey theory, approximate arithmetic progression of a geometric nature is Van der Waerden's theorem on arithmetic progressions: Theorem 2 (Van der Waerden [31
Join Synopses for Approximate Query Answering
Swarup Acharya; Phillip B. Gibbons; Viswanath Poosala; Sridhar Ramaswamy
1999-01-01
In large data warehousing environments, it is often advantageous to provide fast, approximate answers to complex aggregate queries based on statistical summaries of the full data. In this paper, we demonstrate the difficulty of providing good approximate answers for join-queries using only statistics (in particular, samples) from the base relations. We propose join synopses as an effective solution for this
Blood Management Using Approximate Linear Programming
Shenoy, Prashant
Blood Management Using Approximate Linear Programming Marek Petrik and Shlomo Zilberstein January 13th, 2009 Marek Petrik and Shlomo Zilberstein () Blood Management Using Approximate Linear ProgrammingJanuary 13th, 2009 1 / 36 #12;Blood Inventory Management Problem Regional blood banks: Aggregate
SUPERCONVERGENT APPROXIMATION OF SINGULARLY PERTURBED PROBLEMS
Zhang, Zhimin
SUPERCONVERGENT APPROXIMATION OF SINGULARLY PERTURBED PROBLEMS Zhimin Zhang Abstract. In this work, superconvergent approximation of singularly perturbed twopoint boundary value problems of reactiondiffusion type bounds are uniformly valid with respect to the singular perturbation parameter. Numerical tests indicate
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Approximating edge dominating set in dense graphs
Richard Schmied; Claus Viehmann
We study the approximation complexity of the Minimum Edge Dominating Set problem in everywhere ?-dense and average ??-dense graphs. More precisely, we consider the computational complexity of approximating a generalization of the Minimum Edge Dominating Set problem, the so called Minimum Subset Edge Dominating Set problem. As a direct result, we obtain for the special case of the Minimum Edge
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
A simple approximation algorithm for WIS based on the approximability in k-partite graphs
Paris-Sud XI, Université de
A simple approximation algorithm for WIS based on the approximability in k-partite graphs J show how an optimum weighted indepen- dent set in bipartite graphs and a -approximation of WIS in k Set; k-partite graphs. 1 Introduction In the Maximum Weighted Independent Set problem (WIS, for short
The Gaussian Approximation to Homogeneous Bose Gas
NASA Astrophysics Data System (ADS)
Paolini, Fabio; Pires, M. O. C.
2013-04-01
We study low-lying excitations of a spinless homogeneous Bose gas with repulsive interaction at zero temperature in terms of the Gaussian mean field approximation. The dynamical equations of this approximation have been derived for small displacements from the static Hartree-Fock-Bogoliubov solution. We obtain a gapped continuous band of excitations above a discrete branch with phonon behavior at long wavelength regime. We also discuss the available forms of excitations and conclude that there are constraints on the first order deviations of the Gaussian approximation parameters and they are generated by an infinitesimal unitary transformation.
Efficient approximation concepts using second order information
NASA Technical Reports Server (NTRS)
Fleury, Claude
1988-01-01
The application of second derivative information for solving structural optimization problems is considered. In the present method, rather than building approximate nonlinear forms for the objective function and constraints, only linear approximations are used. A separable quadratic approximation of the Lagrangian function is included in the subproblem statement. The method has been successfully used for simple problems that can be solved in closed form, in addition to the sizing optimization of trusses, and it is shown to converge faster than the convex linearization method or the method of moving asymptotes.
A Monte-Carlo AIXI Approximation
Silver, David
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. Our approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement ...
Approximate inference in Gaussian graphical models
Malioutov, Dmitry M., 1981-
2008-01-01
The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a ...
On Padé approximants to virial series.
Guerrero, André O; Bassi, Adalberto B M S
2008-07-28
Padé approximants have long been used to predict virial series coefficients and to provide equations of state for low and high density materials. However, some justified criticism has appeared about this procedure. Although we agree to impose several restrictions on the use of Padé approximants, we indicate that the Padé approximant is still an excellent way to predict the first unknown virial series coefficients. As an example, we report a calculation of the B11=128.6 and B12=155 virial coefficients of the three dimensional hard sphere model that are in excellent agreement with the two most recent estimates. We also consider that the commonly used method to choose among Padé approximants is not completely reliable for this specific application and suggest an alternative new method. PMID:18681662
Workshop on Semiclassical Approximation and Vacuum Energy
Kuchment, Peter
Workshop on Semiclassical Approximation and Vacuum Energy Texas A&M University January 1216, 2005 with induced arc length coor- dinates along the edges. #12;Quantum graph: a metric graph equipped with a self
On Ensemble Techniques for AIXI Approximation
Hutter, Marcus
On Ensemble Techniques for AIXI Approximation Joel Veness1 , Peter Sunehag2 , and Marcus Hutter2 1 compression performance across many well-known benchmarks. Within reinforcement learning (Sutton and Barto
Approximate Confidence Intervals for Effect Sizes.
ERIC Educational Resources Information Center
Algina, James; Keselman, H. J.
2003-01-01
Investigated the approximate confidence intervals for effect sizes developed by K. Bird (2002) and proposed a more accurate method developed through simulation studies. The average coverage probability for the new method was 0.959. (SLD)
SAMPLE AVERAGE APPROXIMATION METHOD FOR COMPOUND ...
2013-06-30
Jun 30, 2013 ... Sample Average Approximation (SAA) method (also known as ..... ? ? X, with rate (of a numerical sequence) 1/?n and distribution ?, if there is a ...... In [32] this property was attached a status ...... tics Reports, 34 (1990), pp.
Learning Approximate Sequential Patterns for Classification
Syed, Zeeshan
In this paper, we present an automated approach to discover patterns that can distinguish between sequences belonging to different labeled groups. Our method searches for approximately conserved motifs that occur with ...
Energy-efficient approximate computation in Topaz
Achour, Sara
2015-01-01
The increasing prominence of energy consumption as a first-order concern in contemporary computing systems has motivated the design of energy-efficient approximate computing platforms. These computing platforms feature ...
Local graph partitions for approximation and testing
Hassidim, Avinatan
We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of bounded-degree graphs with an excluded minor, and in general, for any ...
Computational aspects of pseudospectral Laguerre approximations
NASA Technical Reports Server (NTRS)
Funaro, Daniele
1989-01-01
Pseudospectral approximations in unbounded domains by Laguerre polynomials lead to ill-conditioned algorithms. Introduced are a scaling function and appropriate numerical procedures in order to limit these unpleasant phenomena.
Signal approximation using the bilinear transform
Venkataraman, Archana, Ph. D. Massachusetts Institute of Technology
2007-01-01
This thesis explores the approximation properties of a unique basis expansion. The expansion implements a nonlinear frequency warping between a continuous-time signal and its discrete-time representation according to the ...
Approximated Theorem Proving Marcelo Finger Renata Wassermann
Ayala-Rincón, Mauricio
are mammals. Mammals are vertebrate. Vertebrates are animals. Brazil is in South America. Volcanic soil@ime.usp.br Department of Computer Science University of S~ao Paulo Brazil c Marcelo Finger Approximated Theorem Proving
Linear source approximation in CASMO5
Ferrer, R.; Rhodes, J. [Studsvik Scandpower, Inc., 504 Shoup Ave., Idaho Falls, ID 83402 (United States); Smith, K. [Dept. of Nuclear Science and Engineering, Massachusetts Inst. of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States)
2012-07-01
A Linear Source (LS) approximation has been implemented in the two-dimensional Method of Characteristics (MOC) transport solver in a prototype version of CASMO5. The LS approximation, which relies on the computation of trajectory-based spatial moments over source regions to obtain the linear source expansion coefficients, improves the solution accuracy relative to the 'flat' or constant source approximation. In addition, the LS formulation is capable of treating arbitrarily-shaped source regions and is compatible with standard Coarse-Mesh Finite Difference (CMFD) acceleration. Numerical tests presented in this paper for the C5G7 MOX benchmark show that, for comparable accuracy with respect to the reference solution, the LS approximation can reduce the run time by a factor of four and the memory requirements by a factor often relative to the FS scheme. (authors)
Continuous and discrete N-convex approximations
D. Legg; D. Townsend
1992-01-01
We show that the best Lp-approximant to continuous functions by n-convex functions is the limit of discrete n-convex approximations. The techniques\\u000a of the proof are then used to show the existence of near interpolants to discrete n-convex data by continuous n-convex functions\\u000a if the data points are close.
Approximate algorithms for Space Station Maneuver Optimization
Mur-Dongil, Andres
1998-01-01
APPROXIMATE ALGORITHMS FOR SPACE STATION MANEUVER OPTIMIZATION A Thesis by ANDRE S MUR-DONGIL Submitted to the OAice of Graduate Studies of Texas ARM University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE... August 1998 Major Subject: Aerospace Engineering APPROXIMATE ALGORITHMS FOR SPACE STATION MANEUVER OPTIMIZATION A Thesis by ANDRES MUR-DONGIL Submitted to Texas A&M University in partial fulfillment of the requirements for the degree of MASTER...
Polynomial approximation of functions in Sobolev spaces
NASA Technical Reports Server (NTRS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
On the approximation of invariant measures
Fern Y. Hunt; Walter M. Miller
1992-01-01
Given a discrete dynamical system defined by the map t:X ?X, the density of the absolutely continuous (a.c.) invariant measure (if it exists) is the fixed point of the Frobenius-Perron operator defined on L1(X). Ulam proposed a numerical method for approximating such densities based on the computation of a fixed point of a matrix approximation of the operator. T. Y.
Approximate searches: k-neighbors + precision
Sid-Ahmed Berrani; Laurent Amsaleg; Patrick Gros
2003-01-01
It is known that all multi-dimensional index structures fail to accelerate content-based similarity searches when the feature vectors describing images are high-dimensional. It is possible to circumvent this problem by relying on approximate search-schemes trading-off result quality for reduced query execution time. Most approximate schemes, however, provide none or only complex control on the precision of the searches, especially when
The approximability of NP-hard problems
Sanjeev Arora
1998-01-01
IntroductionMany problems in combinatorial optimization areNP-hard (see [60]). This has forced researchers toexplore techniques for dealing with NP-completeness.Some have considered algorithms that solve "typical" or "average" instances instead of worst-case instances[86, 100]. In practice, however, identifying"typical" instances is not easy. Other researchershave tried to design approximation algorithms. Analgorithm achieves an approximation ratio # for amaximization problem if,...
Approximations for the range of ballistic missiles
NASA Astrophysics Data System (ADS)
Snyder, Ralph
1987-05-01
The actual range, flight time, and maximum height of an ICBM are compared to the predictions of five simple approximations that are more sophisticated than the standard flat-Earth-with-constant-gravity problem but more elementary than the full Keplerian solution. The simplest of these approximations is accessible to first-year students and gives results in closed form whose range predictions are in good agreement with the Keplerian ranges at typical ICBM speeds.
Approximating Edge Dominating Set in Dense Graphs
Richard Schmiedand; Claus Viehmann
2011-01-01
\\u000a We study the approximation complexity of the Minimum Edge Dominating Set problem in everywhere ?-dense and average [`<\\/font\\u000a>(e<\\/font\\u000a>)]\\\\bar{\\\\epsilon}-dense graphs. More precisely, we consider the computational complexity of approximating a generalization of the Minimum Edge\\u000a Dominating Set problem, the so called Minimum Subset Edge Dominating Set problem. As a direct result, we obtain for the special case of the
Approximate clustering via core-sets
Mihai B?doiu; Sariel Har-Peled; Piotr Indyk
2002-01-01
In this paper, we show that for several clustering problems one can extract a small set of points, so that using those core-sets enable us to perform approximate clustering efficiently. The surprising property of those core-sets is that their size is independent of the dimension.Using those, we present a (1+ ?)-approximation algorithms for the k-center clustering and k-median clustering problems
The Actinide Transition Revisited by Gutzwiller Approximation
NASA Astrophysics Data System (ADS)
Xu, Wenhu; Lanata, Nicola; Yao, Yongxin; Kotliar, Gabriel
2015-03-01
We revisit the problem of the actinide transition using the Gutzwiller approximation (GA) in combination with the local density approximation (LDA). In particular, we compute the equilibrium volumes of the actinide series and reproduce the abrupt change of density found experimentally near plutonium as a function of the atomic number. We discuss how this behavior relates with the electron correlations in the 5 f states, the lattice structure, and the spin-orbit interaction. Our results are in good agreement with the experiments.
Adiabatic approximation in open quantum systems
M. S. Sarandy; D. A. Lidar
2005-02-01
We generalize the standard quantum adiabatic approximation to the case of open quantum systems. We define the adiabatic limit of an open quantum system as the regime in which its dynamical superoperator can be decomposed in terms of independently evolving Jordan blocks. We then establish validity and invalidity conditions for this approximation and discuss their applicability to superoperators changing slowly in time. As an example, the adiabatic evolution of a two-level open system is analysed.
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.
Green's functions for inhomogeneous weakly anisotropic media
1998-01-01
Formulae for the zeroth-order principal term plus the first-order additional term of the qP- and qS-wave Green's functions in the so-called quasi-isotropic (QI) approximation are derived for an unbounded inhomogeneous weakly anisotropic medium. The basic idea of this approximation is to seek the asymptotic solution of the elastodynamic equation as an expansion with respect to two small parameters of the
Fast piecewise-constant approximation of images
NASA Astrophysics Data System (ADS)
Radha, Hayder; Vetterli, Martin; Leonardi, Riccardo
1991-11-01
In this work, we present a Least-Square-Error (LSE), recursive method for generating piecewise-constant approximations of images. The method is developed using an optimization approach to minimize a cost function. The cost function, proposed here, is based on segmenting the image, recursively, using Binary Space Partitionings (BSPs) of the image domain. We derive a LSE necessary condition for the optimum piecewise-constant approximation, and use this condition to develop an algorithm for generating the LSE, BSP- based approximation. The proposed algorithm provides a significant reduction in the computational expense when compared with a brute force method. As shown in the paper, the LSE algorithm generates efficient segmentations of simple as well as complex images. This shows the potential of the LSE approximation approach for image coding applications. Moreover, the BSP-based segmentation provides a very simple (yet flexible) description of the regions resulting from the partitioning. This makes the proposed approximation method useful for performing image affine transformations (e.g., rotation and scaling) which are common in computer graphics applications.
Cabbibo Angle Approximation of the CKM Matrix
NASA Astrophysics Data System (ADS)
Dannon, Vic
1999-10-01
(1) The Wolfenstein approximation for the CKM matrix is constrained by theory to be real, and an inaccurate measure of CP violation. (2)The matrix [matrix\\cos ? C & sin ? C & sin ^4? _C?-sin ? _C\\cos ? _C^2 & \\cos ? _C\\cos ? _C^2 & sin ^2? _C?sin ^3? C & -sin ^2? _C\\cos ? C & \\cos ? _C^2] is a very good approximation to the real part of the CKM matrix. (3) This approximation is equivalent to assuming, sin ? _2? sin ^2? C and, , sin ? _3? sin ^3? C where the CKM matrix is the product of four rotation matrices, based on four mixing angles, ? _1, ? _2, ? _3, and ? , [matrix1 & 0 & 0 ?0 & c2 & s2 ?0 & -s2 & c_2][matrixc1 & s1 & 0 ?-s1 & c1 & 0 ?0 & 0 & 1][matrix1 &0 & 0 ?0 & 1 & 0 ?0 & 0 & exp i? ][matrix1 & 0 & 0 ?0 & c3 & s3 ?0 & s3 & c_3], and where c_i=\\cos ? _i, and s_i=sin ? _i. (4) The Wolfenstein approximation real part, reduces to our approximation for ? ? sin ? _C\\over 1+sin ? C and A? 1+sin ? _C. For sin ? _C? 0.23, ? ? 0.187 and A? 1.23.
Approximate Flavor Symmetry in Supersymmetric Model
Zhijian Tao
1998-10-28
We investigate the maximal approximate flavor symmetry in the framework of generic minimal supersymmetric standard model. We consider the low energy effective theory of the flavor physics with all the possible operators included. Spontaneous flavor symmetry breaking leads to the approximate flavor symmetry in Yukawa sector and the supersymmetry breaking sector. Fermion mass and mixing hierachies are the results of the hierachy of the flavor symmetry breaking. It is found that in this theory it is possible to solve the flavor changing problems. Furthermore baryogenesis of the universe can be well described and neutron electric dipole moment is closely below it experimental bound by assuming approximate CP violating phase $\\sim 10^{-2}$ and superpartner mass around 100 GeV.
The Cell Cycle Switch Computes Approximate Majority
NASA Astrophysics Data System (ADS)
Cardelli, Luca; Csikász-Nagy, Attila
2012-09-01
Both computational and biological systems have to make decisions about switching from one state to another. The `Approximate Majority' computational algorithm provides the asymptotically fastest way to reach a common decision by all members of a population between two possible outcomes, where the decision approximately matches the initial relative majority. The network that regulates the mitotic entry of the cell-cycle in eukaryotes also makes a decision before it induces early mitotic processes. Here we show that the switch from inactive to active forms of the mitosis promoting Cyclin Dependent Kinases is driven by a system that is related to both the structure and the dynamics of the Approximate Majority computation. We investigate the behavior of these two switches by deterministic, stochastic and probabilistic methods and show that the steady states and temporal dynamics of the two systems are similar and they are exchangeable as components of oscillatory networks.
Eight-moment approximation solar wind models
NASA Technical Reports Server (NTRS)
Olsen, Espen Lyngdal; Leer, Egil
1995-01-01
Heat conduction from the corona is important in the solar wind energy budget. Until now all hydrodynamic solar wind models have been using the collisionally dominated gas approximation for the heat conductive flux. Observations of the solar wind show particle distribution functions which deviate significantly from a Maxwellian, and it is clear that the solar wind plasma is far from collisionally dominated. We have developed a numerical model for the solar wind which solves the full equation for the heat conductive flux together with the conservation equations for mass, momentum, and energy. The equations are obtained by taking moments of the Boltzmann equation, using an 8-moment approximation for the distribution function. For low-density solar winds the 8-moment approximation models give results which differ significantly from the results obtained in models assuming the gas to be collisionally dominated. The two models give more or less the same results in high density solar winds.
Ancilla-approximable quantum state transformations
NASA Astrophysics Data System (ADS)
Blass, Andreas; Gurevich, Yuri
2015-04-01
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ?, but also address the question of arbitrarily close approximation.
Approximation methods in gravitational-radiation theory
NASA Technical Reports Server (NTRS)
Will, C. M.
1986-01-01
The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
Approximate Killing Fields as an Eigenvalue Problem
Christopher Beetle
2008-08-12
Approximate Killing vector fields are expected to help define physically meaningful spins for non-symmetric black holes in general relativity. However, it is not obvious how such fields should be defined geometrically. This paper relates a definition suggested recently by Cook and Whiting to an older proposal by Matzner, which seems to have been overlooked in the recent literature. It also describes how to calculate approximate Killing fields based on these proposals using an efficient scheme that could be of immediate practical use in numerical relativity.
Excluded-volume approximation for supernova matter
NASA Astrophysics Data System (ADS)
Yudin, A. V.
2011-08-01
A general scheme of the excluded-volume approximation as applied to multicomponent systems with an arbitrary degree of degeneracy has been developed. This scheme also admits an allowance for additional interactions between the components of a system. A specific form of the excluded-volume approximation for investigating supernova matter at subnuclear densities has been found from comparison with the hard-sphere model. The possibility of describing the phase transition to uniform nuclear matter in terms of the formalism under consideration is discussed.
Extending the Eikonal Approximation to Low Energy
Pierre Capel; Tokuro Fukui; Kazuyuki Ogata
2014-11-21
E-CDCC and DEA, two eikonal-based reaction models are compared to CDCC at low energy (e.g. 20AMeV) to study their behaviour in the regime at which the eikonal approximation is supposed to fail. We confirm that these models lack the Coulomb deflection of the projectile by the target. We show that a hybrid model, built on the CDCC framework at low angular momenta and the eikonal approximation at larger angular momenta gives a perfect agreement with CDCC. An empirical shift in impact parameter can also be used reliably to simulate this missing Coulomb deflection.
Approximating Likelihood Ratios with Calibrated Discriminative Classifiers
Cranmer, Kyle
2015-01-01
In particle physics likelihood ratio tests are established tools for statistical inference. These tests are complicated by the fact that computer simulators are used as a generative model for the data, but they do not provide a way to evaluate the likelihood function. We demonstrate how discriminative classifiers can be used to approximate the likelihood function when a generative model for the data is available for training and calibration. This offers an approach to parametric inference when simulators are used that is complementary to approximate Bayesian computation.
Bronchopulmonary segments approximation using anatomical atlas
NASA Astrophysics Data System (ADS)
Busayarat, Sata; Zrimec, Tatjana
2007-03-01
Bronchopulmonary segments are valuable as they give more accurate localization than lung lobes. Traditionally, determining the segments requires segmentation and identification of segmental bronchi, which, in turn, require volumetric imaging data. In this paper, we present a method for approximating the bronchopulmonary segments for sparse data by effectively using an anatomical atlas. The atlas is constructed from a volumetric data and contains accurate information about bronchopulmonary segments. A new ray-tracing based image registration is used for transferring the information from the atlas to a query image. Results show that the method is able to approximate the segments on sparse HRCT data with slice gap up to 25 millimeters.
The Exact Renormalization Group and Approximate Solutions
NASA Astrophysics Data System (ADS)
Morris, Tim R.
We investigate the structure of Polchinski’s formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff Green’s functions are given. A promising nonperturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in “irrelevancy” of operators. We illustrate with two simple models of four-dimensional ??4 theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.
ANALOG QUANTUM NEURON FOR FUNCTIONS APPROXIMATION
A. EZHOV; A. KHROMOV; G. BERMAN
2001-05-01
We describe a system able to perform universal stochastic approximations of continuous multivariable functions in both neuron-like and quantum manner. The implementation of this model in the form of multi-barrier multiple-silt system has been earlier proposed. For the simplified waveguide variant of this model it is proved, that the system can approximate any continuous function of many variables. This theorem is also applied to the 2-input quantum neural model analogical to the schemes developed for quantum control.
Rational approximations and quantum algorithms with postselection
Urmila Mahadev; Ronald de Wolf
2014-08-23
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We give optimal (up to constant factors) quantum algorithms with postselection for the Majority function, slightly improving upon an earlier algorithm of Aaronson. Finally we show how Newman's classic theorem about low-degree rational approximation of the absolute-value function follows from these algorithms.
Characterizing inflationary perturbations: The uniform approximation
Habib, Salman [T-8, Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Heinen, Andreas [Institut fuer Physik, Universitaet Dortmund, D - 44221 Dortmund (Germany); Heitmann, Katrin [ISR-1, ISR-Division, MS D436, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Jungman, Gerard [T-6, Theoretical Division, MS B227, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Molina-Paris, Carmen [Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT (United Kingdom)
2004-10-15
The spectrum of primordial fluctuations from inflation can be obtained using a mathematically controlled, and systematically extendable, uniform approximation. Closed-form expressions for power spectra and spectral indices may be found without making explicit slow-roll assumptions. Here we provide details of our previous calculations, extend the results beyond leading-order in the approximation, and derive general error bounds for power spectra and spectral indices. Already at next-to-leading-order, the errors in calculating the power spectrum are less than a percent. This meets the accuracy requirement for interpreting next-generation cosmic microwave background observations.
Faddeev Random Phase Approximation for Molecules
Degroote, Matthias; Barbieri, Carlo
2010-01-01
The Faddeev Random Phase Approximation is a Green's function technique that makes use of Faddeev-equations to couple the motion of a single electron to the two-particle--one-hole and two-hole--one-particle excitations. This method goes beyond the frequently used third-order Algebraic Diagrammatic Construction method: all diagrams involving the exchange of phonons in the particle-hole and particle-particle channel are retained, but the phonons are described at the level of the Random Phase Approximation. This paper presents the first results for diatomic molecules at equilibrium geometry. The behavior of the method in the dissociation limit is also investigated.
Improved Approximation Algorithms for Relay Placement
the sensors is performed by wireless radio with very limited range, e.g., via the Bluetooth protocol. To make (going directly from a sensor to a sensor is forbidden). Previous Work. The current best approximation. In the relay placement problem the input is a set of sensors and a number r 1, the communication range
Approximation of the Quadratic Knapsack Problem
2013-12-04
stead an edge weighted graph G = (V,E) whose vertices represent the knapsack .... shown in the last years, mostly by using and developing very involved tech- ... ness assumption on random k-AND formulas, there will not exist any constant ... These two contributions are the first meaningful approximation results for QKP.
UNIFORM SEMICLASSICAL APPROXIMATION IN QUANTUM STATISTICAL MECHANICS.
De Carvalho, C.A.A.; Cavalcanit, R.M.; Fraga, E.S.; Joras, S.E.
2000-10-23
We present a simple method to deal with caustics in the semiclassical approximation to the partition function of a one-dimensional quantum system. The procedure, which makes use of complex trajectories, is applied to the quartic double-well potential.
Approximate Killing Vectors on S^2
Gregory B. Cook; Bernard F. Whiting
2007-06-01
We present a new method for computing the best approximation to a Killing vector on closed 2-surfaces that are topologically S^2. When solutions of Killing's equation do not exist, this method is shown to yield results superior to those produced by existing methods. In addition, this method appears to provide a new tool for studying the horizon geometry of distorted black holes.
Pixel Approximation Errors in Common Watershed Algorithms
Hamprecht, Fred A.
Pixel Approximation Errors in Common Watershed Algorithms Hans Meine1 , Peer Stelldinger1 for Image Processing, University of Heidelberg, Germany Abstract. The exact, subpixel watershed algorithm delivers very accu- rate watershed boundaries based on a spline interpolation, but is slow and only works
Research Memorandum No.674 Mean Field Approximation
Iba, Yukito
Iba The Institute of Statistical Mathematics 1068569, MinamiAzabu, Minatoku, Tokyo, Japan Email: iba@ism.ac.jp URL: http://www.ism.ac.jp/~iba/ KEYWORDS Probabilistic and Statistical Methods, Learning and Gener to ICONIP'98 ) #12; Mean Field Approximation in Bayesian Variable Selection Yukito Iba Email:iba
Neuro-fuzzy systems for function approximation
Detlef Nauck; Rudolf Kruse
1999-01-01
We present a neuro-fuzzy architecture for function approximation based on supervised learning. The learning algorithm is able to determine the structure and the parameters of a fuzzy system. The approach is an extension to our already published NEFCON and NEFCLASS models which are used for control or classification purposes. The proposed extended model, which we call NEFPROX, is more general
Improved Approximation Algorithms for Resource Allocation
Gruia Calinescu; Amit Chakrabarti; Howard J. Karloff; Yuval Rabani
2002-01-01
Abstract: We study the problem ofnding a most protable subset of n given tasks, each with a givenstart andnish time as well as prot and resource requirement, that at no time exceeds thequantity B of available resource. We show that this NP-hard Resource Allocation problemcan be (1=2 ")-approximated in polynomial time, which improves upon earlier approximationresults for this problem, the
Approximating Kinematics for Tracked Mobile Robots
J. L. Martínez; A. Mandow; J. Morales; S. Pedraza; A. García-Cerezo
2005-01-01
In this paper we propose a kinematic approach for tracked mobile robots in order to improve motion control and pose estimation. Complex dynamics due to slippage and track–soil interactions make it difficult to predict the exact motion of the vehicle on the basis of track velocities. Nevertheless, real-time computations for autonomous navigation require an effective kinematics approximation without introducing dynamics
Approximating Minimum Manhattan Networks (Extended Abstract)
Approximating Minimum Manhattan Networks (Extended Abstract) Joachim Gudmundsson 1 ? , Christos them. A Minimum Manhattan Network on S is a Manhat- tan network of minimum possible length. A Manhattan connecting points in S [S 0 . A Manhattan network can also be thought of as a 1-spanner (for the L1-metric
Approximating Minimum Manhattan Networks in Higher Dimensions
Kobourov, Stephen G.
Approximating Minimum Manhattan Networks in Higher Dimensions Aparna Das1 , Emden R. Gansner2Â¨urzburg, Germany Abstract. We consider the minimum Manhattan network problem, which is defined as follows. Given's Manhattan (that is, L1-) distance. The problem is NP-hard in 2D and there is no PTAS for 3D (unless P = NP
Approximating Minimum Manhattan Networks (Extended Abstract)
Narasimhan, Giri
Approximating Minimum Manhattan Networks (Extended Abstract) Joachim Gudmundsson 1 ? , Christos, USA Abstract. Given a set S of n points in the plane, we define a Manhattan Network the shortest rectilinear path between them. A Minimum Manhattan Network on S is a Manhattan network of minimum
Approximating the Generalized Minimum Manhattan Network Problem
Kobourov, Stephen G.
Approximating the Generalized Minimum Manhattan Network Problem Aparna Das1 , Krzysztof Fleszar2Â¨urzburg, Germany Abstract. We consider the generalized minimum Manhattan network problem (GMMN). The input-length rectilinear network that connects every pair in R by a Manhattan path, that is, a path of axis-parallel line
On approximating the TSP with intersecting neighborhoods
Elbassioni, Khaled
that goes through all the regions. We give two approxiÂ mation algorithms for the case when the regions are allowed to intersect: We give the first O(1)Âfactor approximation algorithm for intersecting convex fat points. The proof follows from two packing lemmas that are of independent interest. For the problem
Approximate Method for FMR in Metals
A. Yelon; G. Spronken; T. Bui-Thieu; R. C. Barker; Y.-J. Liu; T. Kobayashi
1974-01-01
We have developed a powerful technique for approximate calculation of ferromagnetic resonance in isotropic metal plates. The key step in this calculation is a transformation previously applied to magnetoelastic insulators, which permits the separation of the resonant and nonresonant senses of polarization. This separation is exact for perpendicular resonance (so that the entire calculation is exact in this case), and
Approximation Algorithms for NP-Hard Problems
1997-01-01
Approximation algorithms have developed in response to the impossibility of solving a great variety of important optimization problems. Too frequently, when attempting to get a solution for a problem, one is confronted with the fact that the problem is NP-hard. This, in the words of Garey and Johnson, means \\
Quantitative Evaluation of Poisson Point Process Approximation
Shozo Mori; Chee-Yee Chong
This papers is generally concerned with random finite sets or finite point processes that arise from the multiple target tracking problems, more specifically with quantitative evaluation of approximation of a random finite set by a Poisson point process in such an environment. As one of the first attempts in such efforts, we will consider a simple single-scan problem with a
Magnus approximation in the adiabatic picture
NASA Astrophysics Data System (ADS)
Klarsfeld, S.; Oteo, J. A.
1992-03-01
We describe a simple approximate nonperturbative method for treating time-dependent problems that works well in the intermediate regime far from both the sudden and the adiabatic limits. The method consists of applying the Magnus expansion after transforming to the adiabatic basis defined by the eigenstates of the instantaneous Hamiltonian.
Numerical approximation of SDE with explosions.
Groisman, Pablo
Numerical approximation of SDE with explosions. Joint work with JuÂ´an DÂ´avila, U. de Chile Juli of the largest crack. The explosion time corresponds to the time of ultimate damage or fatigue failure in the material. #12;The Feller Test for Explosions provides a precise criteria to de- termine, in terms of b
A Trichromatic Approximation Method Surface Illumination
Borges, Carlos F.
A Trichromatic Approximation Method for Surface Illumination Appears in: Journal of the Optical are interested in determining the color appearance of an illuminated Lambertian surface. In an ideal physical to P â?? ae(â??), the product of the spectral radiant power of the illuminant, P â?? , and the spectral
Discussion of "Regularization of Wavelets Approximations"
Cai, T. Tony
discussion both a single index i and the more conventional double indices (j, k) for wavelet coefficients and the sample size is a power of 2, then the matrix A is the inverse discrete wavelet transform W-1 and (1) canDiscussion of "Regularization of Wavelets Approximations" by A. Antoniadis and J. Fan T. Tony Cai
Self-Intersection Problems and Approximate Implicitization
Jüttler, Bert
. 1 Introduction Self-intersection algorithms are important for many applications within CAD/ CAM. Suppose we try to create an offset surface within a CAD system with an offset distance larger than, and it is therefore necessary to make a NURBS approximation. In a typical CAD-system, surfaces are often represented
Syntactic approximations to computational complexity classes
Argimiro Arratia; Carlos E. Ortiz
We present a formal syntax of approximate formulas suited for the logic with counting quantifiers SOLP. This logic was studied by us in (1) where, among other properties, we showed: (i) In the presence of a built-in (linear) order, SOLP can describe NP-complete problems and fragments of it capture classes like P and NL; (ii) weakening the ordering relation to
Asymptotic approximation of hyperbolic weakly nonlinear systems
A. Krylovas; R. Ciegis
2002-01-01
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems. We consider the resonance conditions for some classes of solutions. The averaged system can be solved numerically in the resonance case. The shallow water problem is considered as an
Approximation and compression with sparse orthonormal transforms.
Sezer, Osman Gokhan; Guleryuz, Onur G; Altunbasak, Yucel
2015-08-01
We propose a new transform design method that targets the generation of compression-optimized transforms for next-generation multimedia applications. The fundamental idea behind transform compression is to exploit regularity within signals such that redundancy is minimized subject to a fidelity cost. Multimedia signals, in particular images and video, are well known to contain a diverse set of localized structures, leading to many different types of regularity and to nonstationary signal statistics. The proposed method designs sparse orthonormal transforms (SOTs) that automatically exploit regularity over different signal structures and provides an adaptation method that determines the best representation over localized regions. Unlike earlier work that is motivated by linear approximation constructs and model-based designs that are limited to specific types of signal regularity, our work uses general nonlinear approximation ideas and a data-driven setup to significantly broaden its reach. We show that our SOT designs provide a safe and principled extension of the Karhunen-Loeve transform (KLT) by reducing to the KLT on Gaussian processes and by automatically exploiting non-Gaussian statistics to significantly improve over the KLT on more general processes. We provide an algebraic optimization framework that generates optimized designs for any desired transform structure (multiresolution, block, lapped, and so on) with significantly better n -term approximation performance. For each structure, we propose a new prototype codec and test over a database of images. Simulation results show consistent increase in compression and approximation performance compared with conventional methods. PMID:25823033
The case for approximate Distance Transforms
Antoni Moore
Starting with a binary raster, the calculation of exact Euclidean distance from the foreground pixels (1-elements) to the background pixels (0-elements) is a simple yet time-consuming operation. Elsewhere it is argued that for some applications (such as pattern recognition and robotics for example) the calculation of approximate Euclidean distance is a viable, quick and efficient alternative solution. There has been
Methods and approximations for strongly coupled plasmas
G. Kalman
1978-01-01
The theory of strongly coupled plasmas is examined in terms of response functions, sum rules, and fluctuation-dissipation theorems. Particular consideration is given to the development of a nonlinear fluctuation-dissipation theorem. Several approximation schemes for strongly coupled plasmas are considered, including (1) the scheme of Singwi, Tosi, Land and Sjolander (1968); (2) the scheme of Totsuji and Ichimaru (1973, 1974); and
Can Distributional Approximations Give Exact Answers?
ERIC Educational Resources Information Center
Griffiths, Martin
2013-01-01
Some mathematical activities and investigations for the classroom or the lecture theatre can appear rather contrived. This cannot, however, be levelled at the idea given here, since it is based on a perfectly sensible question concerning distributional approximations that was posed by an undergraduate student. Out of this simple question, and…
Improved approximation algorithms for geometric set cover
Kenneth L. Clarkson; Kasturi R. Varadarajan
2005-01-01
Given a collection S of subsets of some set U, and M ? U, the set cover problem is to find the smallest subcollection C ? S such that M is a subset of the union of the sets in C. While the general problem is NP-hard to solve, even approximately, here we consider some geometric special cases, where usually
Symbolic Test Selection Based on Approximate Analysis
Paris-Sud XI, Université de
Symbolic Test Selection Based on Approximate Analysis Bertrand Jeannet, Thierry J´eron, Vlad Rusu}@irisa.fr Abstract. This paper addresses the problem of generating symbolic test cases for testing the conformance. The challenge we consider is the selection of test cases according to a test purpose, which is here a set
Approximating Border Length for DNA Microarray Synthesis
Wong, Prudence W.H.
Approximating Border Length for DNA Microarray Synthesis Cindy Y. Li1 Prudence W.H. Wong1 Qin Xin2 Introduction DNA microarrays [9] have become a very important research tool which have proved to benefit areas about the pres- ence or absence of biological target sequences in a sample. A DNA microarray ("chip
Approximating Power Indices --Theoretical and Empirical Analysis
Rosenschein, Jeff
Approximating Power Indices -- Theoretical and Empirical Analysis Yoram Bachrach School power indices. This version contains new empirical analysis of the performance of these methods of these domains, agents are unequal in their power to affect the outcome of the game. Prior research on weighted
Approximation of electron stopping powers of materials
Davydov, M.G.; Potetyunko, G.N. [Rostov State Univ. (Russian Federation)
1994-06-01
The objective of this study was to develop a simple analytic expression for electron stopping power for application to a beam of accelerated electrons. Based on a previously proposed approximation for ions, a result was obtained that gave good results over the electron range 1 to 30 MeV.
FRACTAL APPROXIMATION AND COMPRESSION USING PROJECTED IFS
Baskurt, Atilla
FRACTAL APPROXIMATION AND COMPRESSION USING PROJECTED IFS Ã?ric GuÃ©rin, Ã?ric Tosan and Atilla, or images) with fractal models is an important center of interest for research. The general inverse problem.The most known of them is the fractal image compression method introduced by Jacquin. Generally speaking
Alternative approximation concepts for space frame synthesis
NASA Technical Reports Server (NTRS)
Lust, R. V.; Schmit, L. A.
1985-01-01
A structural synthesis methodology for the minimum mass design of 3-dimensionall frame-truss structures under multiple static loading conditions and subject to limits on displacements, rotations, stresses, local buckling, and element cross-sectional dimensions is presented. A variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses. Available options include: (A) formulation of the nonlinear mathematcal programming problem in either reciprocal section property (RSP) or cross-sectional dimension (CSD) space; (B) two alternative approximate problem structures in each design space; and (C) three distinct assumptions about element end-force variations. Fixed element, design element linking, and temporary constraint deletion features are also included. The solution of each approximate problem, in either its primal or dual form, is obtained using CONMIN, a feasible directions program. The frame-truss synthesis methodology is implemented in the COMPASS computer program and is used to solve a variety of problems. These problems were chosen so that, in addition to exercising the various approximation concepts options, the results could be compared with previously published work.
Extending a Blackboard Architecture for Approximate Processing
Keith Decker; Victor R. Lesser; Robert Whitehair
1990-01-01
Abstract Approximate processing is an approach to real-time AI problem solving systems in domains where there are a range of acceptable answers in terms of cert ainty, accuracy, and completeness. Such a system needs to evaluate the current situation, make time predictions about the likelihood of achieving current objectives, monitor the processing and p ursuit of those objectives, and if
APPROXIMATE REASONING IN TRANSPORT PROJECT EVALUATION
P. N. SMITH
1997-01-01
The paper illustrates the potential of approximate reasoning and fuzzy logic in the evaluation of transport projects where projects are characterised in terms of multiple factors or characteristics. A method is illustrated which incorporates fragments of imprecise information (conditional propositions, implications). The antecedents in each fragment involve factors of environmental significance and the consequent is a measure of satisfaction associated
DISTRIBUTED VERIFICATION AND HARDNESS OF DISTRIBUTED APPROXIMATION
DISTRIBUTED VERIFICATION AND HARDNESS OF DISTRIBUTED APPROXIMATION ATISH DAS SARMA, STEPHAN HOLZER Abstract. We study the verification problem in distributed networks, stated as follows. Let H be a subgraph in a decentralized fashion via a distributed algorithm. The time complexity of verification is measured as the number
Distributed Verification and Hardness of Distributed Approximation
Distributed Verification and Hardness of Distributed Approximation Atish Das Sarma Google wattenhofer@tik.ee.ethz.ch ABSTRACT We study the verification problem in distributed networks, stated like to perform this verification in a decentralized fashion via a distributed algorithm. The time
Polynomial spline-approximation of Clarke's model
Yuriy V. Zakharov; Tim C. Tozer; Jonathan F. Adlard
2004-01-01
We investigate polynomial spline approximation of stationary random processes on a uniform grid applied to Clarke's model of time variations of path amplitudes in multipath fading channels with Doppler scattering. The integral mean square error (MSE) for optimal and interpolation splines is presented as a series of spectral moments. The optimal splines outperform the interpolation splines; however, as the sampling
Fourier series approximation of separable models
U. Amato; A. Antoniadis; I. De Feis
2002-01-01
The approximation of a function affected by noise in several dimensions suffers from the so-called “curse of dimensionality”. In this paper a Fourier series method based on regularization is developed both for uniform and random design when a restriction on the complexity of the curve such as additivity is considered in order to circumvent the problem. Optimal convergence theorems are
COUNTING INDEPENDENT SETS USING THE BETHE APPROXIMATION*
to have at least one fixed point, where each fixed point corresponds to a stationary point of the Bethe point (or BP fixed point) leads to the Bethe approximation for the number of independent sets free energy (introduced by Yedidia, Freeman, and Weiss [IEEE Trans. Inform. Theory, 51 (2004), pp. 2282
ON THE LANDAU APPROXIMATION IN PLASMA PHYSICS
Villani, CÃ©dric
ON THE LANDAU APPROXIMATION IN PLASMA PHYSICS R. ALEXANDRE AND C. VILLANI Abstract. This paper of his important works in plasma physics, established the kinetic equation which is now called after him interacting through binary collisions. Since then, this equation has been widely in use in plasma physics, see
Approximate mode filtering Kathleen E. Wage
Wage, Kathleen
email: kwage@gmu.edu Abstract-- Normal modes, the eigenfunctions of the ocean waveguide, are useful by using the approximate modeshapes are analyzed. I. INTRODUCTION Normal modes are the eigenfunctions of this paper applies Miller and Good's approach to generate modes for the ocean waveguide and examines
Theory of generalized least pth approximation
J. Bandler; C. Charalambous
1972-01-01
A unified discussion of leastpth approximation as it relates to optimal computer-aided design of networks and systems is presented. General objective functions are proposed and their properties discussed. The main result is that a wider variety of design problems and a wider range of specifications than appear to have been considered previously from the least pth point of view should
Generalized Nonnegative Matrix Approximations with Bregman Divergences
Inderjit S. Dhillon; Suvrit Sra
2005-01-01
Nonnegative matrix approximation (NNMA) is a recent technique for di- mensionality reduction and data analysis that yields a part s based, sparse nonnegative representation for nonnegative input data. NNMA has found a wide variety of applications, including text analysis, do cument cluster- ing, face\\/image recognition, language modeling, speech processing and many others. Despite these numerous applications, the algorithmic de- velopment
Nonnegative Matrix Approximation: Algorithms and Applications
Suvrit Sra; Inderjit S. Dhillon
Low dimensional data representations are crucial to numerous applications in machine learning, statis- tics, and signal processing. Nonnegative matrix approximation (NNMA) is a method for dimensionality reduction that respects the nonnegativity of the input data while constructin g a low-dimensional approx- imation. NNMA has been used in a multitude of applications, though without commensurate theoretical development. In this report we
Approximate join processing over data streams
Abhinandan Das; Johannes Gehrke; Mirek Riedewald
2003-01-01
We consider the problem of approximating sliding window joins over data streams in a data stream processing system with limited resources. In our model, we deal with resource constraints by shedding load in the form of dropping tuples from the data streams. We first discuss alternate architectural models for data stream join processing, and we survey suitable measures for the
Quickly Approximating the Distance Between Two Objects
NASA Technical Reports Server (NTRS)
Hammen, David
2009-01-01
A method of quickly approximating the distance between two objects (one smaller, regarded as a point; the other larger and complexly shaped) has been devised for use in computationally simulating motions of the objects for the purpose of planning the motions to prevent collisions.
Real-time creased approximate subdivision surfaces
Denis Kovacs; Jason Mitchell; Shanon Drone; Denis Zorin
2009-01-01
We present an extension of recently developed Loop and Schaefer's approximation of Catmull-Clark surfaces (ACC) for surfaces with creases and corners which are essential for most applications. We discuss the integration of ACC into Valve's Source game engine and analyze performance of our implementation.
Cross-Domain Approximate String Matching
Daniel P. Lopresti; Gordon T. Wilfong
1999-01-01
Approximate string matching is an important paradigm in domains ranging from speech recognition to information retrieval and molecular biology. In this paper, we introduce a new formalism for a class of applications that takes two strings as input, each specified in terms of a particular do- main, and performs a comparison motivated by constraints derived from a third, possibly different
Approximating Value Trees in Structured Dynamic Programming
Craig Boutilier; Richard Dearden
1996-01-01
We propose and examine a method of approximate dynamic programming for Markov decision processes based on structured problem representations. We as- sume an MDP is represented using a dynamic Bayesian network, and construct value functions using decision trees as our function representation. The size of the representation is kept within acceptable limits by prun- ing these value trees so that
An optimized version of the Approximating
A. Juan; E. Vidal
The Approximating and Eliminating Search Algorithm (AESA) and re- lated AESA-based techniques are among the fastest methods for ( -)Nearest Neighbour(s) searching in general metric spaces. These techniques can be optimized for the (easier) ( -)Nearest Neighbour(s) classification problem. In particular, an optimized version of the AESA is proposed here which is shown to be significantly faster than the AESA,
Rational Approximation on the Complex Plane
Geest, Harm G. van der
developed. Bent Fuglede ([4]) shows that a finely holomorphic function and its finely derivatives of all point derivations . . . . . . . . . . 15 3 Finely Holomorphic Functions 18 3.1 Definition and some properties of finely holomorphic functions 18 3.2 Rational approximation of finely holomorphic functions
Approximate Frequency Counts over Data Streams
Gurmeet Singh Manku; Rajeev Motwani
2002-01-01
We present algorithms for computing frequency counts exceeding a user-specified threshold over data streams. Our algorithms are simple and have provably small memory footprints. Although the output is approximate, the error is guaranteed not to exceed a user-specified parameter. Our algo- rithms can easily be deployed for streams of single- ton items like those found in IP network monitor- ing.
On approximating the depth and related problems
Boris Aronovt; Sariel Har-Peled
2005-01-01
In this paper, we study the problem of finding a disk covering the largest number of red points, while avoiding all the blue points. We reduce it to the question of finding a deepest point in an arrangement of pseudodisks and provide a near-linear expected-time randomized approximation algorithm for this problem. As an application of our techniques, we show how
Approximating vertex covers in anonymous networks
Suomela, Jukka
of nodes · Minimum-weight vertex cover: · Vertex cover with the smallest total weight #12;Vertex coverApproximating vertex covers in anonymous networks Jukka Suomela Helsinki Institute for Information;Vertex cover problem 2 · Vertex cover for a graph G: · Subset C of nodes that "covers" all edges: each
Approximate Range Searching Department of Computer Science
Mount, David
Approximate Range Searching Sunil Arya Department of Computer Science The Hong Kong University by the National Science Foun- dation under grant CCR9712379 . 1 #12;convex ranges, we tighten this to O(log n of Science and Technology Clear Water Bay, Kowloon, Hong Kong David M. Mount Department of Computer Science
Approximate Range Searching Department of Computer Science
Arya, Sunil
Approximate Range Searching Sunil Arya Department of Computer Science The Hong Kong University by the National Science Foun- dation under grant CCR9712379 . 1 #12;1 Introduction. The range searching problem of Science and Technology Clear Water Bay, Kowloon, Hong Kong David M. Mount Department of Computer Science
THE MATRIX CUBE PROBLEM: Approximations and Applications
Nemirovski, Arkadi
THE MATRIX CUBE PROBLEM: Approximations and Applications Arkadi Nemirovski, Stieltjes Visiting with A. Ben-Tal 1. Matrix Cube · The problem: formulation and moti- vation · Main result · Back to applications · Sketch of the proof 2. From Matrix Cube to Computing Ma- trix Norms · The problem · Main result
On Functional Approximation with Normalized Gaussian Units
Michel Benaïm
1994-01-01
Feedforward neural networks with a single hidden layer using normalized gaussian units are studied. It is proved that such neural networks are capable of universal approximation in a satisfactory sense. Then, a hybrid learning rule as per Moody and Darken that combines unsupervised learning of hidden units and supervised learning of output units is considered. By using the method of
Fast Approximation of the Shape Diameter Function
Fabio Guggeri; Stefano Marras; Riccardo Scateni
2010-01-01
In this paper we propose an optimization of the Shape Diameter Function (SDF) that we call Accelerated SDF (ASDF). We discuss in detail the advantages and disadvantages of the original SDF definition, proposing theoretical and practical approaches for speedup and approximation. Using Poisson-based interpolation we compute the SDF value for a small subset of randomly distributed faces and ...
A numerical approximation of the rotation number
R. Pavani
1995-01-01
The rotation number of a circle map is approximated by an efficient numerical method. The method works well for both irrational rotation numbers and rational ones. Moreover, it allows us to distinguish between the two cases. Numerical results are presented; they are mainly related to the standard circle map and the delayed logistic map.
Some approximate equations for the standard atmosphere
NASA Technical Reports Server (NTRS)
Diehl, Walter S
1932-01-01
This report contains the derivation of a series of simple approximate equations for density ratios and for the pressure ratio in the standard atmosphere. The accuracy of the various equations is discussed and the limits of applications are given. Several of these equations are in excellent agreement with the standard values.
CLASS NUMBER APPROXIMATION IN CUBIC FUNCTION FIELDS
RENATE SCHEIDLER; ANDREAS STEIN
2007-01-01
We develop explicitly computable bounds for the order of the Jacobian of a cubic function eld. We use approximations via trun- cated Euler products and thus derive eectiv e methods of computing the order of the Jacobian of a cubic function eld. Also, a detailed discussion of the zeta function of a cubic function eld extension is included. 1. Introduction
Gadgets, Approximation, and Linear Programming [Extended Abstract
Trevisan, Luca
Gadgets, Approximation, and Linear Programming [Extended Abstract] Luca Trevisan \\Lambda Gregory B at FOCS. Abstract We present a linearÂprogramming based method for finding ``gadgets'', i this new method we present a number of new, computerÂconstructed gadgets for several difÂ ferent reductions
Kravchuk functions for the finite oscillator approximation
NASA Technical Reports Server (NTRS)
Atakishiyev, Natig M.; Wolf, Kurt Bernardo
1995-01-01
Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.
Fast approximate 2D inversion of airborne TEM data: Born approximation and empirical approach
Paris-Sud XI, UniversitÃ© de
Fast approximate 2D inversion of airborne TEM data: Born approximation and empirical approach surveying provides data sections with a sufficient coverage to perform 2D imaging of electrical conductivity within the ground. Full 2D inversion using numerical modeling with finite differences or finite elements
Approximating Mathematical Semantic Web Services Using Approximation Formulas and Numerical Methods
Paris-Sud XI, Université de
Approximating Mathematical Semantic Web Services Using Approximation Formulas and Numerical Methods.andreica@cs.pub.ro) Abstract: Mathematical semantic web services are very useful in practice, but only a small number of a mathematical semantic web service, from its semantic description, using existing mathematical semantic web
Kurt Hornik; Maxwell B. Stinchcombe; Halbert White; Peter Auer
1994-01-01
Recently Barron (1993) has given rates for hidden layer feedforward networks with sigmoid activation functions approximating a class of functions satisfying a certain smoothness condition. These rates do not depend on the dimension of the input space. We extend Barron's results to feedforward networks with possibly nonsigmoid activation functions approximating mappings and their derivatives simultaneously. Our conditions are similar but
Counting independent sets using the Bethe approximation
Chertkov, Michael [Los Alamos National Laboratory; Chandrasekaran, V [MIT; Gamarmik, D [MIT; Shah, D [MIT; Sin, J [MIT
2009-01-01
The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques.
VISCOSITY AND RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
Tzavaras, Athanasios E.
VISCOSITY AND RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS deal with the approximation of conservation * *laws via viscosity or relaxation. The following topics are covered: The general structure of viscosity and relaxation approximations is discu
Rindler approximation to Kerr black hole
H. A. Camargo; M. Socolovsky
2014-10-23
We show that the Rindler approximation to the time-radial part of the Kerr and Kerr-Newman metrics near their external $h_+$ and internal $h_-$ horizons {\\bf only} holds {\\bf outside} $h_+$ and {\\bf inside} $h_-$, so respectively inside and outside the external and internal ergospheres, regions where, in Boyer-Lindquist coordinates, both $g_{tt}$ and $g_{rr}$ are negative, but preserving the Lorentzian character of the metric, and $r>0$ i.e. outside the region $r<0$ where closed timelike curves exist. At each point, the choice of Rindler coordinates is not trivial, but depends on the polar angle $\\theta$. The approximation, as is known, automatically gives the absolute values of the surface gravities $\\kappa_\\pm$ as the corresponding proper accelerations, and therefore the Hawking temperatures $\\tau_\\pm$ at $h_\\pm$.
Numerical and approximate solutions for plume rise
NASA Astrophysics Data System (ADS)
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).
Thick domain walls in a polynomial approximation
H. Arodz
1995-01-18
Relativistic domain walls are studied in the framework of a polynomial approximation to the field interpolating between different vacua and forming the domain wall. In this approach we can calculate evolution of a core and of a width of the domain wall. In the single, cubic polynomial approximation used in this paper, the core obeys Nambu-Goto equation for a relativistic membrane. The width of the domain wall obeys a nonlinear equation which is solved perturbatively. There are two types of corrections to the constant zeroth order width: the ones oscillating in time, and the corrections directly related to curvature of the core. We find that curving a static domain wall is associated with an increase of its width. As an example, evolution of a toroidal domain wall is investigated.
Comparison of quasilinear and WKB approximations
Mandelzweig, V.B. [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)]. E-mail: victor@phys.huji.ac.il
2006-12-15
It is shown that the quasilinearization method (QLM) sums the WKB series. The method approaches solution of the Riccati equation (obtained by casting the Schroedinger equation in a nonlinear form) by approximating the nonlinear terms by a sequence of the linear ones, and is not based on the existence of a smallness parameter. Each pth QLM iterate is expressible in a closed integral form. Its expansion in powers of h reproduces the structure of the WKB series generating an infinite number of the WKB terms. Coefficients of the first 2 {sup p} terms of the expansion are exact while coefficients of a similar number of the next terms are approximate. The quantization condition in any QLM iteration, including the first, leads to exact energies for many well known physical potentials such as the Coulomb, harmonic oscillator, Poeschl-Teller, Hulthen, Hyleraas, Morse, Eckart, etc.
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 ...
Second derivatives for approximate spin projection methods
NASA Astrophysics Data System (ADS)
Thompson, Lee M.; Hratchian, Hrant P.
2015-02-01
The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical second derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.
Algorithmic survey of parametric value function approximation.
Geist, Matthieu; Pietquin, Olivier
2013-06-01
Reinforcement learning (RL) is a machine learning answer to the optimal control problem. It consists of learning an optimal control policy through interactions with the system to be controlled, the quality of this policy being quantified by the so-called value function. A recurrent subtopic of RL concerns computing an approximation of this value function when the system is too large for an exact representation. This survey reviews state-of-the-art methods for (parametric) value function approximation by grouping them into three main categories: bootstrapping, residual, and projected fixed-point approaches. Related algorithms are derived by considering one of the associated cost functions and a specific minimization method, generally a stochastic gradient descent or a recursive least-squares approach. PMID:24808468
Approximating a Global Passive Adversary Against Tor
Sambuddho Chakravarty; Angelos Stavrou; Angelos D. Keromytis
We present a novel, practical, and eective mecha- nism for exposing the IP address of Tor relays, clients and hidden services. We approximate an almost-global passive adversary (GPA) capable of eavesdropping any- where in the network by using LinkWidth. LinkWidth allows network edge-attached entities to estimate the available bandwidth in an arbitrary Internet link with- out a cooperating peer host,
Approximate earth mover's distance in linear time
Sameer Shirdhonkar; David W. Jacobs
2008-01-01
The earth moverpsilas distance (EMD) is an important perceptually meaningful metric for comparing histograms, but it suffers from high (O(N3 logN)) computational complexity. We present a novel linear time algorithm for approximating the EMD for low dimensional histograms using the sum of absolute values of the weighted wavelet coefficients of the difference histogram. EMD computation is a special case of
An approximation algorithm for manhattan routing
Brenda S. Baker; Sandeep N. Bhatt; Frank Thomson Leighton
1983-01-01
A linear-time approximation algorithm for routing multipoint net channels is presented. The algorithm uses at most a constant factor times the optimal number of tracks required. The notion of channel fluxis introduced and shown, like channel density, to be a lower bound for channel width. Every multipoint net channel having density d and flux f is routed within 2d+O(f) tracks,
Sparse greedy matrix approximation for machine learning
Alex J. Smola; B. Scholkopf
2000-01-01
In kernel based methods such as RegularizationNetworks large datasets pose signi-cant problems since the number of basis functionsrequired for an optimal solution equalsthe number of samples. We present a sparsegreedy approximation technique to constructa compressed representation of the designmatrix. Experimental results are given andconnections to Kernel-PCA, Sparse KernelFeature Analysis, and Matching Pursuit arepointed out.1. IntroductionMany recent advances in...
An Intrinsic Characterization of Approximate Probabilistic Bisimulation
van Breugel, Franck
An Intrinsic Characterization of Approximate Probabilistic Bisimulation Franck van Breugel, Michael Mislove, JoÂ¨el Ouaknine and James Worrell Technical Report CS-2003-01 January 2003 Department of Computer"Â§Â¦3145Â¡6487 @9A98Â¨B42CDEF"Â§Â¦)(GHÂ¨B45I#"AIPRQS1TÂ¦31VUW1EYXAQ1"Â§Â¦314`Â¡ Franck van Breugel York University
Approximations to the plasma dispersion function
NASA Technical Reports Server (NTRS)
Brinca, A. L.
1972-01-01
Linear wave propagation in hot collisionless plasmas is described by the linearized Vlasov and Maxwell equations. In uniform media, the utilization of spatial and temporal transforms of those equations leads to the consideration of integrals of the Hilbert transform type. Analysis and comparison of two simple approximations are provided based on the utilization of resonance velocity distributions. Application is then made to the Landau and whistler waves, along with a discussion of the results, and commentary on possible improvements.
Viscosity approximation methods for nonexpansive mappings
Hong-Kun Xu
2004-01-01
Viscosity approximation methods for nonexpansive mappings are studied. Consider a nonexpansive self-mapping T of a closed convex subset C of a Banach space X. Suppose that the set Fix(T) of fixed points of T is nonempty. For a contraction f on C and t?(0,1), let xt?C be the unique fixed point of the contraction x?tf(x)+(1?t)Tx. Consider also the iteration process
Asymptotic Approximation of Hyperbolic Weakly Nonlinear Systems
A. Krylovas; R. Ciegis
2001-01-01
An averaging method for getting uniformly valid asymptotic approximations of\\u000athe solution of hyperbolic systems of equations is presented. The averaged\\u000asystem of equations disintegrates into independent equations for non-resonance\\u000asystems. We consider the resonance conditions for some classes of solutions.\\u000aThe averaged system can be solved numerically in the resonance case. The\\u000ashallow water problem is considered as an
The concept of the approximants of quasicrystals
Dong, C. [Beijing Lab. of Electron Microscopy, Beijing (China)] [Beijing Lab. of Electron Microscopy, Beijing (China); [Dalian Univ. of Technology (China). Dept. of Materials Engineering
1995-07-15
The study of quasicrystals has always been associated with the research of related crystalline phases. Quasicrystalline alloys are rarely single phase and the secondary phases are usually crystalline. For example, in melt-spun ribbons of Ti{sub 2}Fe alloys, the following phases are observed: an icosahedral phase, Ti{sub 2}Fe (Ti{sub 2}Ni type), {alpha}-Ti{sub 2}Fe ({alpha}-AlMnSi type), TiFe (CsCl type, or B2 structure) and {beta}-Ti (W type, or A3 structure). Similar phases were also observed in Ti-Ni alloys. In Al-Cu-Fe quasicrystalline alloys, one finds {lambda}-Al{sub 13}Fe{sub 4}, a cubic phase (a B2 superstructure), {omega}-Al{sub 7}Cu{sub 2}Fe, {phi}-Al{sub 10}Cu{sub 10}Fe, {theta}-Al{sub 2}Cu, etc. Valence electron concentration has been proposed as a new criterion to define the approximants to quasicrystals: these should satisfy two basic requirements: (1) they possess approximately the same valence electron concentration as that of the corresponding quasicrystal; (2) they arise from the projection of a hyper crystal along rational directions. The first criterion indicates that the approximants are Hume-Rothery phases existing in an e/a-constant band in the phase diagrams; the second implies that their atomic structures are related to those of quasicrystals. According to their positions in the phase diagrams, they can be classified into two groups: the phases to the left of quasicrystal composition are complex approximants retaining some local quasi-periodic structure; those to the right include B2 and its superstructures.
Approximating node connectivity problems via set covers
Guy Kortsarz; Zeev Nutov
2000-01-01
Given a graph (directed or undirected) with costs on the edges, and an integer k, we consider the problem of finding a k-node connected spanning subgraph of minimum cost. For the general instance of the problem (directed or undirected), there is a simple 2k-approximation algorithm. Better algorithms are known for various ranges of n,k. For undirected graphs with metric costs
Online Learning of Approximate Dependency Parsing Algorithms
Ryan T. Mcdonald; Fernando C. N. Pereira
2006-01-01
In this paper we extend the maximum spanning tree (MST) dependency parsing framework of McDonald et al. (2005c) to incorporate higher-order feature rep- resentations and allow dependency struc- tures with multiple parents per word. We show that those extensions can make the MST framework computationally in- tractable, but that the intractability can be circumvented with new approximate pars- ing algorithms.
Parameter Biases Introduced by Approximate Gravitational Waveforms
NASA Astrophysics Data System (ADS)
Farr, Benjamin; Coughlin, Scott; Le, John; Skeehan, Connor; Kalogera, Vicky
2013-04-01
The production of the most accurate gravitational waveforms from compact binary mergers require Einstein's equations to be solved numerically, a process far too expensive to produce the ˜10^7 waveforms necessary to estimate the parameters of a measured gravitational wave signal. Instead, parameter estimation depends on approximate or phenomenological waveforms to characterize measured signals. As part of the Ninja collaboration, we study the biases introduced by these methods when estimating the parameters of numerically produced waveforms.
Photonic crystal heterostructures and the envelope approximation
E. Istrate; E. H. Sargent
2002-01-01
Photonic crystal heterostructures are concatenations of photonic crystals having different bandstructures. Examples include controlled defects, type-I and type-II heterostructures, and superlattices. These novel and prospectively powerful functional devices rely on computationally intensive analysis in a conventional fully numerical treatment. We have developed an envelope approximation method to explain and compute the frequency-dependent behaviour of photonic crystal heterostructures. The method begins
Approximation algorithms for restless bandit problems
Sudipto Guha; Kamesh Munagala; Peng Shi
2009-01-01
Abstract In this paper, we consider the restless bandit problem, which is one of the most well-studied generalizations of the cel- ebrated stochastic multi-armed bandit problem in decision theory. In its ultimate generality, the restless bandit prob- lem is known,to be PSPACE-Hard to approximate to any non-trivial factor, and little progress has been made on this problem despite its signicance,in
Approximation by superpositions of a sigmoidal function
G. Cybenko
1989-01-01
In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of\\u000a affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results\\u000a settle an open question about representability in the class of single hidden
Constant-time distributed dominating set approximation
Fabian Kuhn; Roger Wattenhofer
2003-01-01
Finding a small dominating set is one of the most fundamental problems of traditional graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary parameter k and maximum degree ?, our algorithm computes a dominating set of expected size O(k?2\\/k log ?|DSOPT|) in O(k2) rounds where each node has
Approximation methods for stochastic petri nets
NASA Technical Reports Server (NTRS)
Jungnitz, Hauke Joerg
1992-01-01
Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists.
ARTICLE IN PRESS Journal of Approximation Theory ( )
Berndt, Bruce C.
. E-mail addresses: nayan@tezu.ernet.in (N.D. Baruah), berndt@illinois.edu (B.C. Berndt). 1 Research rights reserved. doi:10.1016/j.jat.2008.04.002 Please cite this article as: N.D. Baruah, B.C. Berndt (2008), doi:10.1016/j.jat.2008.04.002 #12;2 N.D. Baruah, B.C. Berndt / Journal of Approximation Theory
Microscopic justification of the equal filling approximation
Perez-Martin, Sara; Robledo, L. M. [Departamento de Fisica Teorica C-XI, Facultad de Ciencias, Universidad Autonoma de Madrid, 28049 Madrid (Spain)
2008-07-15
The equal filling approximation, a procedure widely used in mean-field calculations to treat the dynamics of odd nuclei in a time-reversal invariant way, is justified as the consequence of a variational principle over an average energy functional. The ideas of statistical quantum mechanics are employed in the justification. As an illustration of the method, the ground and lowest-lying states of some octupole deformed radium isotopes are computed.
Approximation in Model-Based Learning
Leonid Kuvayev Rich Sutton
1997-01-01
Model-based reinforcement learning, inwhich a model of the environment's dynamicsis learned and used to supplement directlearning from experience, has been proposedas a general approach to learning and planning.We present experiments with this ideain which the model of the environment's dynamicsis both approximate and learned online.These experiments involve the MountainCar task, which requires approximationof both value function and model because ithas
Gaussian Approximation Potentials: a brief tutorial introduction
Bartók, Albert P
2015-01-01
We present a swift walk-through of our recent work that uses machine learning to fit interatomic potentials based on quantum mechanical data. We describe our Gaussian Approximation Potentials (GAP) framework, discussing a variety of descriptors, how to train the model on total energies and derivatives and the simultaneous use of multiple models. We also show a small example using QUIP, the software sandbox implementation of GAP that is available for non-commercial use.
Quasicrystalline decagonal and related crystalline approximant structures
Daulton, T.L.
1992-01-01
The icosahedral phase is a condensed phase of matter that has a noncrystallographic point group with long range orientational and translational order but lacks strict periodicity. Periodicity is replaced in all dimensions by a mathematically well defined quasiperiodicity. Two and one dimensional quasicrystals also form in the same metallic-alloy systems as does the icosahedral quasicrystal. The decagonal phase is an example of a two-dimensional quasicrystal that occurs with dicrete one dimensional periodicites of approximately 4 [angstrom] x (1, 2, 3, and 4). The different periodicity decagonal phases are studied with an analytical transmission electron microscope (TEM), using high resolution electron microscopy (HREM), convergent beam electron diffraction (CBED), selected area diffraction (SAD), energy-dispersive x-ray spectroscopy (EDXS), and electron energy-loss spectroscopy (EELS). X-ray powder diffraction studies are also presented. Closely related crystalline structures that approximate well the noncrystallographic symmetries of quasicrystals, were also studied. These crystals also exhibit the same discrete periodicities present in the decagonal phases. The striking similarities between the different periodicity decagonal phases, the icosahedral phase, and the crystalline approximant structures suggest that they all contain similar fundamental atomic clusters. Further, the discrete decagonal periodicities observed suggest that the decagonal structures are formed by different stacking sequences of similar atomic clusters. An atomic model that is based on distorted icosahedrally symmetric clusters that are stacked with different interpenentration depths to form the different periodicity decagonal phases is presented.
Strong washout approximation to resonant leptogenesis
NASA Astrophysics Data System (ADS)
Garbrecht, Björn; Gautier, Florian; Klaric, Juraj
2014-09-01
We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ?=Xsin(2varphi)/(X2+sin2varphi), where X=8??/(|Y1|2+|Y2|2), ?=4(M1-M2)/(M1+M2), varphi=arg(Y2/Y1), and M1,2, Y1,2 are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y1,2|2gg ?, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.
Heuer, Norbert
Galerkin (SUPG) approximation for the constitutive equation. In this paper we analyze a Crank discretization with a SUPG discretization of the constitutive equation and showed that, in IR #19; d , the method
Ervin, Vincent J.
],[3],[14], or by using a Streamline Upwind Petrov Galerkin (SUPG) [7],[16] approximation for the constitutive equation discretization with a SUPG discretization of the constitutive equation and showed that, in IR ´d , the method
A simple approximation algorithm for WIS based on the approximability in k-partite
Paris-Sud XI, Université de
A simple approximation algorithm for WIS based on the approximability in k-partite graphs Jérôme}@lamsade.dauphine.fr Cahiers du LAMSADE 1 #12;1 Introduction In the Maximum Weighted Independent Set problem (WIS, for short of vertices, we denote by w(S) = vS w(v) the sum of the weights of the elements in S. The goal of WIS
Quantum entropic security and approximate quantum encryption
Simon Pierre Desrosiers; Frédéric Dupuis
2010-04-15
We present full generalisations of entropic security and entropic indistinguishability to the quantum world where no assumption but a limit on the knowledge of the adversary is made. This limit is quantified using the quantum conditional min-entropy as introduced by Renato Renner. A proof of the equivalence between the two security definitions is presented. We also provide proofs of security for two different cyphers in this model and a proof for a lower bound on the key length required by any such cypher. These cyphers generalise existing schemes for approximate quantum encryption to the entropic security model.
Quantum entropic security and approximate quantum encryption
Desrosiers, Simon Pierre
2007-01-01
We present full generalisations of entropic security and entropic indistinguishability to the quantum world where no assumption but a limit on the knowledge of the adversary is made. This limit is quantified using the quantum conditional min-entropy as introduced by Renato Renner. A proof of the equivalence between the two security definitions is presented. We also provide proofs of security for two different cyphers in this model and a proof for a lower bound on the key length required by any such cypher. These cyphers generalise existing schemes for approximate quantum encryption to the entropic security model.
Casimir forces beyond the proximity approximation
Bimonte, G; Jaffe, R L; Kardar, M
2011-01-01
The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Pad\\'e extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere-plate Casimir force at all separations.
Approximate string matching using phase correlation.
Alba, Alfonso; Rodriguez-Kessler, Margarita; Arce-Santana, Edgar R; Mendez, Martin O
2012-01-01
A novel method for approximate string matching with applications to bioinformatics is presented in this paper. Unlike most methods in the literature, the proposed method does not depend on the computation of the edit distance between two sequences, but uses instead a similarity index obtained by applying the phase correlation method. The resulting algorithm provides a finer control over the false positive rate, allowing users to pick out relevant matchings in less time, and can be applied for both offline and online processing. PMID:23367371
[Bond selective chemistry beyond the adiabatic approximation
Butler, L.J.
1993-02-28
The adiabatic Born-Oppenheimer potential energy surface approximation is not valid for reaction of a wide variety of energetic materials and organic fuels; coupling between electronic states of reacting species plays a key role in determining the selectivity of the chemical reactions induced. This research program initially studies this coupling in (1) selective C-Br bond fission in 1,3- bromoiodopropane, (2) C-S:S-H bond fission branching in CH[sub 3]SH, and (3) competition between bond fission channels and H[sub 2] elimination in CH[sub 3]NH[sub 2].
Fuzzy systems with defuzzification are universal approximators.
Castro, J L; Delgado, M
1996-01-01
In this paper, we consider a fundamental theoretical question: Is it always possible to design a fuzzy system capable of approximating any real continuous function on a compact set with arbitrary accuracy? Moreover, we research whether the answer to the above question is positive when we restrict to a fixed (but arbitrary) type of fuzzy reasoning and to a subclass of fuzzy relations. This result can be viewed as an existence theorem of an optimal fuzzy system for a wide variety of problems. PMID:18263015
Asphericity and approximation properties of crossed modules
NASA Astrophysics Data System (ADS)
Mikhailov, R. V.
2007-04-01
This paper is devoted to the study of the Baer invariants and approximation properties of crossed modules and cat ^1-groups. Conditions are considered under which the kernels of crossed modules coincide with the intersection of the lower central series. An algebraic criterion for asphericity is produced for two-dimensional complexes having aspherical plus-construction. As a consequence it is shown that a subcomplex of an aspherical two-dimensional complex is aspherical if and only if its fundamental cat ^1-group is residually soluble. Thus, a new formulation in group-theoretic terms is given to the Whitehead asphericity conjecture.Bibliography: 25 titles.
Relativistic mean field approximation to baryons
Dmitri Diakonov
2005-02-01
We stress the importance of the spontaneous chiral symmetry breaking for understanding the low-energy structure of baryons. The Mean Field Approximation to baryons is formulated, which solves several outstanding paradoxes of the naive quark models, and which allows to compute parton distributions at low virtuality in a consistent way. We explain why this approach to baryons leads to the prediction of relatively light exotic pentaquark baryons, in contrast to the constituent models which do not take seriously the importance of chiral symmetry breaking. We briefly discuss why, to our mind, it is easier to produce exotic pentaquarks at low than at high energies.
Modeling error in Approximate Deconvolution Models
Adrian Dunca; Roger Lewandowski
2012-10-09
We investigate the assymptotic behaviour of the modeling error in approximate deconvolution model in the 3D periodic case, when the order $N$ of deconvolution goes to $\\infty$. We consider successively the generalised Helmholz filters of order $p$ and the Gaussian filter. For Helmholz filters, we estimate the rate of convergence to zero thanks to energy budgets, Gronwall's Lemma and sharp inequalities about Fouriers coefficients of the residual stress. We next show why the same analysis does not allow to conclude convergence to zero of the error modeling in the case of Gaussian filter, leaving open issues.
Casimir forces beyond the proximity approximation
NASA Astrophysics Data System (ADS)
Bimonte, G.; Emig, T.; Jaffe, R. L.; Kardar, M.
2012-03-01
The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Padé extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere/plate Casimir force at all separations.
Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems
R. Ravi; Amitabh Sinha
2004-01-01
We study the design of approximation algorithms for stoch- astic combinatorial optimization problems. We formulate the problems in the framework of two-stage stochastic optimization, and provide nearly tight approximations. Our problems range from the simple (shortest path, vertex cover, bin packing) to complex (facility location, set cover), and contain representatives with different approximation ratios. The approximation ratio of the stochastic
Approximation properties of a multilayered feedforward artificial neural network
Hrushikesh Narhar Mhaskar
1993-01-01
We prove that an artificial neural network with multiple hidden layers and akth-order sigmoidal response function can be used to approximate any continuous function on any compact subset of a Euclidean space so as to achieve the Jackson rate of approximation. Moreover, if the function to be approximated has an analytic extension, then a nearly geometric rate of approximation can
Comparison of Approximate Symmetry Methods for Differential Equations
M. Pakdemirli; M. Yürüsoy; ?. T. Dolapç?
2004-01-01
Two current approximate symmetry methods and a modified new one are contrasted. Approximate symmetries of potential Burgers equation and non-Newtonian creeping flow equations are calculated using different methods. Approximate solutions corresponding to the approximate symmetries are derived for each method. Symmetries and solutions are compared and advantages and disadvantages of each method are discussed in detail.
Space-efficient Online Approximation of Time Series Data
California at Santa Barbara, University of
Space-efficient Online Approximation of Time Series Data: Streams, Amnesia, and Out-of-order Luca Luca Foschini (UCSB) Time Series Approximation ICDE 2010 1 / 21 #12;Outline 1 Time Series Approximation and Future Work Luca Foschini (UCSB) Time Series Approximation ICDE 2010 2 / 21 #12;Time Series
Variance reduction in sample approximations of stochastic programs
Matti Koivu
2005-01-01
This paper studies the use of randomized Quasi-Monte Carlo methods (RQMC) in sam- ple approximations of stochastic programs. In high dimensional numerical integration, RQMC methods often substantially reduce the variance of sample approximations compared to MC. It seems thus natural to use RQMC methods in sample approximations of stochastic programs. It is shown, that RQMC methods produce epi-convergent approximations of
FLEXIBLE IMPLEMENTATION OF APPROXIMATION CONCEPTS IN AN MDO FRAMEWORK
Oleg Golovidov; Srinivas Kodiyalam; Peter Marineau; Liping Wang; Peter Rohl
1998-01-01
This paper describes the flexible implementation of approximation concepts in an MDO framework offered by the commercial-off-the- shelf software package iSIGHT. Three different types of approximation models - Response Surface Modeling, Taylor Series Approximations, and Variable Complexity Modeling - are implemented in such a way that they may be used interchangeably in any combination to approximate any segment of an
The validity of the Background Field Approximation
R. Parentani
1997-10-10
In the absence of a tractable theory of quantum gravity, quantum matter field effects have been so far computed by treating gravity at the Background Field Approximation. The principle aim of this paper is to investigate the validity of this approximation which is not specific to gravity. To this end, for reasons of simplicity and clarity, we shall compare the descriptions of thermal processes induced by constant acceleration (i.e. the Unruh effect) in four dynamical frameworks. In this problem, the position of the ``heavy'' accelerated system plays the role of gravity. In the first framework, the trajectory is treated at the BFA: it is given from the outset and unaffected by radiative processes. In the second one, recoil effects induced by these emission processes are taken into account by describing the system's position by WKB wave functions. In the third one, the accelerated system is described by second quantized fields and in the fourth one, gravity is turned on. It is most interesting to see when and why transitions amplitudes evaluated in different frameworks but describing the same process do agree. It is indeed this comparison that determines the validity of the BFA. It is also interesting to notice that the abandonment of the BFA delivers new physical insights concerning the processes. For instance, in the fourth framework, the ``recoils'' of gravity show that the acceleration horizon area acts as an entropy in delivering heat to accelerated systems.
Exact and Approximate Sizes of Convex Datacubes
NASA Astrophysics Data System (ADS)
Nedjar, Sébastien
In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.
Revisiting approximate dynamic programming and its convergence.
Heydari, Ali
2014-12-01
Value iteration-based approximate/adaptive dynamic programming (ADP) as an approximate solution to infinite-horizon optimal control problems with deterministic dynamics and continuous state and action spaces is investigated. The learning iterations are decomposed into an outer loop and an inner loop. A relatively simple proof for the convergence of the outer-loop iterations to the optimal solution is provided using a novel idea with some new features. It presents an analogy between the value function during the iterations and the value function of a fixed-final-time optimal control problem. The inner loop is utilized to avoid the need for solving a set of nonlinear equations or a nonlinear optimization problem numerically, at each iteration of ADP for the policy update. Sufficient conditions for the uniqueness of the solution to the policy update equation and for the convergence of the inner-loop iterations to the solution are obtained. Afterwards, the results are formed as a learning algorithm for training a neurocontroller or creating a look-up table to be used for optimal control of nonlinear systems with different initial conditions. Finally, some of the features of the investigated method are numerically analyzed. PMID:24846687
Conservative buffering of approximate nonlinear constraints
NASA Technical Reports Server (NTRS)
Thomas, H. L.; Schmit, L. A.
1990-01-01
In engineering design practice behavior is usually predicted based on some known nominal design. However, when the design is fabricated it will differ from the nominal design because of manufacturing tolerances. In order to generate nominal designs that will still satisfy behavior constraints in the presence of manufacturing tolerances, engineers resort to the use of safety factors, over and above those introduced to account for other uncertainties (e.g., in load conditions, material properties, analysis modeling). The accurate selection of the values of these manufacturing tolerances safety factors is dependent on the capability of the engineer to determine the sensitivity of the critical constraints to changes in the design variables. This process usually leads to overly conservative designs. The task of choosing safety factors is much more difficult in structural synthesis because: (1) it is not known which constraints will be active at the final design, (2) as the design changes during the synthesis process the sensitivities of the constraints with respect to the design variables also change, and (3) the imposition of the safety factors themselves may change the set of critical constraints. These difficulties can be overcome with the approximation concepts approach to structural synthesis by buffering the approximate constraints with quantities that are related to the design variable tolerances and the accurate sensitivities of the constraints with respect to the design variable. Designs generated by this approach tend to be feasible but not overly conservative.
Approximate discrete dynamics of EMG signal
Sayan Mukherjee; Sanjay Kumar Palit; D. K. Bhattacharya
2014-09-23
Approximation of a continuous dynamics by discrete dynamics in the form of Poincare map is one of the fascinating mathematical tool, which can describe the approximate behaviour of the dynamics of the dynamical system in lesser dimension than the embedding diemnsion. The present article considers a very rare biomedical signal like Electromyography (EMG) signal. It determines suitable time delay and reconstruct the attractor of embedding diemnsion three. By measuring its Lyapunov exponent, the attractor so reconstructed is found to be chaotic. Naturally the Poincare map obtained by corresponding Poincare section is to be chaotic too. This may be verified by calculation of Lyapunov exponent of the map. The main objective of this article is to show that Poincare map exists in this case as a 2D map for a suitable Poincare section only. In fact, the article considers two Poincare sections of the attractor for construction of the Poincare map. It is seen that one such map is chaotic but the other one is not so, both are verified by calculation of Lyapunov exponent of the map.
Spectrally Invariant Approximation within Atmospheric Radiative Transfer
NASA Technical Reports Server (NTRS)
Marshak, A.; Knyazikhin, Y.; Chiu, J. C.; Wiscombe, W. J.
2011-01-01
Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These spectrally invariant relationships are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.
Approximation of Failure Probability Using Conditional Sampling
NASA Technical Reports Server (NTRS)
Giesy. Daniel P.; Crespo, Luis G.; Kenney, Sean P.
2008-01-01
In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.
Approximating Markov Chains: What and why
Pincus, S. [990 Moose Hill Road, Guilford, Connecticut 06437 (United States)
1996-06-01
Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to {open_quote}{open_quote}solve,{close_quote}{close_quote} or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the {ital attractor}, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. {copyright} {ital 1996 American Institute of Physics.}
Approximate conservation laws of perturbed partial differential equations
Yani Gan; Changzheng Qu
2010-01-01
This paper presents a general result on approximate conservation laws of perturbed partial differential equations. A method\\u000a of constructing approximate conservation laws to systems of perturbed partial differential equations is given, which is based\\u000a on approximate Noether symmetries of approximate and standard adjoint systems of the original system. The relationship between\\u000a the Noether symmetry operators of approximate and standard adjoint
Transient queueing approximations for computer networks
Baker, William A.
1986-01-01
24. te 15. 4 IN IJ N \\2. 0. 15. 30. 45. SO. 75. 90. 7laa. aec. 0. 10. 20. 30. ~ 0. 50. TIae, aec. A. TYPE f: RHO = 0. 7, Np 0 B TYPE 2 RHO 0 9 NO= 5 15. 4. 4 4 N S. al M M 2 N 4. 5 4 al O S. 12. Cl 4 ta 9. ! al el 12. N...'(P?, (t) ? P?(t)) = 2M(t) y1 n=1 (7) P n' (P?+, (t) ? P?(t)) = -2M(t) + 1 ? P, (t). Tl ? 1 Substituting (5), (7), (8), and (4) into (6) yields (8) A + P (2M(t) + 1) I1Pp(t) dV(t) dt (9) The closure approximations use the equations derived above...
Nonlocal Gravity: The General Linear Approximation
B. Mashhoon
2014-12-09
The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field equations is derived. The linear approximation of nonlocal gravity (NLG) is thoroughly examined and the solutions of the corresponding field equations are discussed. It is shown that nonlocality, with a characteristic length scale of order 1 kpc, simulates dark matter in the linear regime while preserving causality. Light deflection in linearized nonlocal gravity is studied in connection with gravitational lensing; in particular, the propagation of light in the weak gravitational field of a uniformly moving source is investigated. The astrophysical implications of the results are briefly mentioned.
Approximate Bayesian inference for complex ecosystems
2014-01-01
Mathematical models have been central to ecology for nearly a century. Simple models of population dynamics have allowed us to understand fundamental aspects underlying the dynamics and stability of ecological systems. What has remained a challenge, however, is to meaningfully interpret experimental or observational data in light of mathematical models. Here, we review recent developments, notably in the growing field of approximate Bayesian computation (ABC), that allow us to calibrate mathematical models against available data. Estimating the population demographic parameters from data remains a formidable statistical challenge. Here, we attempt to give a flavor and overview of ABC and its applications in population biology and ecology and eschew a detailed technical discussion in favor of a general discussion of the advantages and potential pitfalls this framework offers to population biologists. PMID:25152812
Improved Approximation Algorithms for Geometric Set Cover
Kenneth L. Clarkson; Kasturi R. Varadarajan
2007-01-01
Given a collection S of subsets of some set \\u000a \\u000a and \\u000a \\u000a the set cover problem is to find the smallest subcollection \\u000a \\u000a that covers \\u000a \\u000a that is, \\u000a \\u000a where \\u000a \\u000a denotes \\u000a \\u000a We assume of course that S covers \\u000a \\u000a While the general problem is NP-hard to solve, even approximately, here we consider some geometric special cases, where usually\\u000a \\u000a \\u000a Combining previously known techniques [4], [5], we show
An approximate CPHD filter for superpositional sensors
NASA Astrophysics Data System (ADS)
Mahler, Ronald; El-Fallah, Adel
2012-06-01
Most multitarget tracking algorithms, such as JPDA, MHT, and the PHD and CPHD filters, presume the following measurement model: (a) targets are point targets, (b) every target generates at most a single measurement, and (c) any measurement is generated by at most a single target. However, the most familiar sensors, such as surveillance and imaging radars, violate assumption (c). This is because they are actually superpositional-that is, any measurement is a sum of signals generated by all of the targets in the scene. At this conference in 2009, the first author derived exact formulas for PHD and CPHD filters that presume general superpositional measurement models. Unfortunately, these formulas are computationally intractable. In this paper, we modify and generalize a Gaussian approximation technique due to Thouin, Nannuru, and Coates to derive a computationally tractable superpositional-CPHD filter. Implementation requires sequential Monte Carlo (particle filter) techniques.
Anisotropic local likelihood approximations: theory, algorithms, applications
NASA Astrophysics Data System (ADS)
Katkovnik, Vladimir; Foi, Alessandro; Egiazarian, Karen O.; Astola, Jaakko T.
2005-03-01
We consider a signal restoration from observations corrupted by random noise. The local maximum likelihood technique allows to deal with quite general statistical models of signal dependent observations, relaxes the standard parametric modelling of the standard maximum likelihood, and results in flexible nonparametric regression estimation of the signal. We deal with the anisotropy of the signal using multi-window directional sectorial local polynomial approximation. The data-driven sizes of the sectorial windows, obtained by the intersection of confidence interval (ICI) algorithm, allow to form starshaped adaptive neighborhoods used for the pointwise estimation. The developed approach is quite general and is applicable for multivariable data. A fast adaptive algorithm implementation is proposed. It is applied for photon-limited imaging with the Poisson distribution of data. Simulation experiments and comparison with some of the best results in the field demonstrate an advanced performance of the developed algorithms.
Improved approximations for control augmented structural synthesis
NASA Technical Reports Server (NTRS)
Thomas, H. L.; Schmit, L. A.
1990-01-01
A methodology for control-augmented structural synthesis is presented for structure-control systems which can be modeled as an assemblage of beam, truss, and nonstructural mass elements augmented by a noncollocated direct output feedback control system. Truss areas, beam cross sectional dimensions, nonstructural masses and rotary inertias, and controller position and velocity gains are treated simultaneously as design variables. The structural mass and a control-system performance index can be minimized simultaneously, with design constraints placed on static stresses and displacements, dynamic harmonic displacements and forces, structural frequencies, and closed-loop eigenvalues and damping ratios. Intermediate design-variable and response-quantity concepts are used to generate new approximations for displacements and actuator forces under harmonic dynamic loads and for system complex eigenvalues. This improves the overall efficiency of the procedure by reducing the number of complete analyses required for convergence. Numerical results which illustrate the effectiveness of the method are given.
Sivers function in the quasiclassical approximation
NASA Astrophysics Data System (ADS)
Kovchegov, Yuri V.; Sievert, Matthew D.
2014-03-01
We calculate the Sivers function in semi-inclusive deep inelastic scattering (SIDIS) and in the Drell-Yan process (DY) by employing the quasiclassical Glauber-Mueller/McLerran-Venugopalan approximation. Modeling the hadron as a large "nucleus" with nonzero orbital angular momentum (OAM), we find that its Sivers function receives two dominant contributions: one contribution is due to the OAM, while another one is due to the local Sivers function density in the nucleus. While the latter mechanism, being due to the "lensing" interactions, dominates at large transverse momentum of the produced hadron in SIDIS or of the dilepton pair in DY, the former (OAM) mechanism is leading in saturation power counting and dominates when the above transverse momenta become of the order of the saturation scale. We show that the OAM channel allows for a particularly simple and intuitive interpretation of the celebrated sign flip between the Sivers functions in SIDIS and DY.
Diffractive structure function in a quasiclassical approximation
Kovchegov, Y.V.; McLerran, L. [School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455 (United States)] [School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455 (United States)
1999-09-01
We derive an expression for the diffractive F{sub 2} structure function which should be valid at small {ital x} for quasielastic scattering on a hadron and for quasielastic scattering on a large nucleus. This expression includes multiple rescatterings of the quark-antiquark pair produced by the virtual photon off the sources of color charge in a quasiclassical approximation. We find that there is a relation between such diffractive production and inclusive processes. In the former, one averages over all colors of sources before squaring the amplitude, and in the latter one first squares the amplitude and then averages it in the hadron or nuclear wave function. We show that in the limit of a large virtuality of the photon Q{sup 2} the diffractive structure function becomes linearly proportional to the gluon distribution of the hadron or nucleus, therefore proving that in this sense diffraction is a leading twist effect. {copyright} {ital 1999} {ital The American Physical Society}
Convergence of approximate solutions to conservation laws
NASA Astrophysics Data System (ADS)
Diperna, R. J.
The general setting considered is a system of n conservation laws in one space dimension. It includes a smooth nonlinear mapping, which is strictly hyperbolic in the sense that its Jacobian has n real and distinct eigenvalues. In a study of suitable approaches for an approximation, attention is given to associated parabolic systems and finite difference schemes which are conservative according to the definitions employed by Lax and Wendroff (1960). In the context of conservation laws, the maximum norm and the total variation norm provide a natural pair of metrics for the investigation of stab ility. The maximum norm serves as a measure of the amplitude of the solution, while the total variation norm represents a measure of the gradient of the solution. Attention is also given to finite difference schemes in the strong topology, the finite scale features of the solution, and the problem of providing stability in the total variation norm.
Gutzwiller approximation in strongly correlated electron systems
NASA Astrophysics Data System (ADS)
Li, Chunhua
Gutzwiller wave function is an important theoretical technique for treating local electron-electron correlations nonperturbatively in condensed matter and materials physics. It is concerned with calculating variationally the ground state wave function by projecting out multi-occupation configurations that are energetically costly. The projection can be carried out analytically in the Gutzwiller approximation that offers an approximate way of calculating expectation values in the Gutzwiller projected wave function. This approach has proven to be very successful in strongly correlated systems such as the high temperature cuprate superconductors, the sodium cobaltates, and the heavy fermion compounds. In recent years, it has become increasingly evident that strongly correlated systems have a strong propensity towards forming inhomogeneous electronic states with spatially periodic superstrutural modulations. A good example is the commonly observed stripes and checkerboard states in high- Tc superconductors under a variety of conditions where superconductivity is weakened. There exists currently a real challenge and demand for new theoretical ideas and approaches that treats strongly correlated inhomogeneous electronic states, which is the subject matter of this thesis. This thesis contains four parts. In the first part of the thesis, the Gutzwiller approach is formulated in the grand canonical ensemble where, for the first time, a spatially (and spin) unrestricted Gutzwiller approximation (SUGA) is developed for studying inhomogeneous (both ordered and disordered) quantum electronic states in strongly correlated electron systems. The second part of the thesis applies the SUGA to the t-J model for doped Mott insulators which led to the discovery of checkerboard-like inhomogeneous electronic states competing with d-wave superconductivity, consistent with experimental observations made on several families of high-Tc superconductors. In the third part of the thesis, new concepts and techniques are developed to study the Mott transition in inhomogeneous electronic superstructures. The latter is termed "SuperMottness" which is shown to be a general framework that unifies the two paradigms in the physics of strong electronic correlation: Mott transition and Wigner crystallization. A cluster Gutzwiller approximation (CGA) approach is developed that treats the local ( U) and extended Coulomb interactions (V) on equal footing. It is shown with explicit calculations that the Mott-Wigner metal-insulator transition can take place far away from half-filling. The mechanism by which a superlattice potential enhances the correlation effects and the tendency towards local moment formation is investigated and the results reveal a deeper connection among the strongly correlated inhomogeneous electronic states, the Wigner-Mott physics, and the multiorbital Mott physics that can all be united under the notion of SuperMottness. It is proposed that doping into a superMott insulator can lead to coexistence of local moment and itinerant carriers. The last part of the thesis studies the possible Kondo effect that couples the local moment and the itinerant carriers. In connection to the sodium rich phases of the cobaltates, a new Kondo lattice model is proposed where the itinerant carriers form a Stoner ferromagnet. The competition between the Kondo screening and the Stoner ferromagnetism is investigated when the conduction band is both at and away from half-filling.
Improved binary collision approximation ion implant simulators
NASA Astrophysics Data System (ADS)
Hernández-Mangas, J. M.; Arias, J.; Bailón, L.; Jaraíz, M.; Barbolla, J.
2002-01-01
An efficient binary collision approximation (BCA) ion implant code with good prediction capabilities for semiconductor materials (Si, GaAs, SiC) with only one fitting parameter for low implantation doses is presented. It includes specific interatomic potentials and recent improvements in physical models for inelastic stopping. A periodic ab initio full bond electron density for the target is used. Damage accumulation is supported using a modified Kinchin-Pease model [G. H. Kinchin and R. S. Pease, Rep. Prog. Phys. 18, 1 (1955)]. Also, some of the BCA integration algorithms and target selection procedure have been refined. An algorithm commonly used for statistical noise reduction has been modified to also improve the noise reduction in the lateral and shallow zones. The agreement with experiments is good, even under channeling conditions and for different target materials. A comparison with experimental secondary ion mass spectroscopy results for several projectiles and targets is presented.
WKB approximation for abruptly varying potential wells
NASA Astrophysics Data System (ADS)
Amthong, Attapon
2014-11-01
We present an approach to obtain eigenfunctions and eigenenergies for abruptly varying potentials in the framework of the Wentzel-Kramers-Brillouin (WKB) approximation. To illustrate it, two examples of the potentials are studied. The first one is the combination of a step barrier and a harmonic oscillator potential, and the second one consists of a step barrier and a linear potential. The formulation of a WKB quantization rule is proposed. Our approach shows that WKB energies and those from numerical calculation are in good agreement. According to matching conditions used, WKB wavefunctions in this present work are violated at only one classical turning point, but they behave well at another point where the potentials are discontinuous.
Approximate spacetime symmetries and conservation laws
Abraham I Harte
2008-08-29
A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincare and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these objects are discussed for both geodesics and extended matter distributions. One example is a generalized Komar integral that may be taken to define the linear and angular momenta of a spacetime volume as seen by a particular observer. This is evaluated explicitly for a gravitational plane wave spacetime.
Approximate flavor symmetries in the lepton sector
Rasin, A. (Department of Physics, University of California, Berkeley and Theoretical Physics Group, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (United States)); Silva, J.P. (Physics Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States))
1994-01-01
Approximate flavor symmetries in the quark sector have been used as a handle on physics beyond the standard model. Because of the great interest in neutrino masses and mixings and the wealth of existing and proposed neutrino experiments it is important to extend this analysis to the leptonic sector. We show that in the seesaw mechanism the neutrino masses and mixing angles do not depend on the details of the right-handed neutrino flavor symmetry breaking, and are related by a simple formula. We propose several [ital Ansa]$[ital uml]---[ital tze] which relate different flavor symmetry-breaking parameters and find that the MSW solution to the solar neutrino problem is always easily fit. Further, the [nu][sub [mu]-][nu][sub [tau
Fast approximate quadratic programming for graph matching.
Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624
The random phase approximation applied to ice
NASA Astrophysics Data System (ADS)
Macher, M.; Klimeš, J.; Franchini, C.; Kresse, G.
2014-02-01
Standard density functionals without van der Waals interactions yield an unsatisfactory description of ice phases, specifically, high density phases occurring under pressure are too unstable compared to the common low density phase Ih observed at ambient conditions. Although the description is improved by using functionals that include van der Waals interactions, the errors in relative volumes remain sizable. Here we assess the random phase approximation (RPA) for the correlation energy and compare our results to experimental data as well as diffusion Monte Carlo data for ice. The RPA yields a very balanced description for all considered phases, approaching the accuracy of diffusion Monte Carlo in relative energies and volumes. This opens a route towards a concise description of molecular water phases on surfaces and in cavities.
The random phase approximation applied to ice.
Macher, M; Klimeš, J; Franchini, C; Kresse, G
2014-02-28
Standard density functionals without van der Waals interactions yield an unsatisfactory description of ice phases, specifically, high density phases occurring under pressure are too unstable compared to the common low density phase Ih observed at ambient conditions. Although the description is improved by using functionals that include van der Waals interactions, the errors in relative volumes remain sizable. Here we assess the random phase approximation (RPA) for the correlation energy and compare our results to experimental data as well as diffusion Monte Carlo data for ice. The RPA yields a very balanced description for all considered phases, approaching the accuracy of diffusion Monte Carlo in relative energies and volumes. This opens a route towards a concise description of molecular water phases on surfaces and in cavities. PMID:24588180
Approximation Preserving Reductions among Item Pricing Problems
NASA Astrophysics Data System (ADS)
Hamane, Ryoso; Itoh, Toshiya; Tomita, Kouhei
When a store sells items to customers, the store wishes to determine the prices of the items to maximize its profit. Intuitively, if the store sells the items with low (resp. high) prices, the customers buy more (resp. less) items, which provides less profit to the store. So it would be hard for the store to decide the prices of items. Assume that the store has a set V of n items and there is a set E of m customers who wish to buy those items, and also assume that each item i ? V has the production cost di and each customer ej ? E has the valuation vj on the bundle ej ? V of items. When the store sells an item i ? V at the price ri, the profit for the item i is pi = ri - di. The goal of the store is to decide the price of each item to maximize its total profit. We refer to this maximization problem as the item pricing problem. In most of the previous works, the item pricing problem was considered under the assumption that pi ? 0 for each i ? V, however, Balcan, et al. [In Proc. of WINE, LNCS 4858, 2007] introduced the notion of “loss-leader, ” and showed that the seller can get more total profit in the case that pi < 0 is allowed than in the case that pi < 0 is not allowed. In this paper, we derive approximation preserving reductions among several item pricing problems and show that all of them have algorithms with good approximation ratio.
Stone, Peter
Approximation via Tile Coding: Automating Parameter Choice Alexander A. Sherstov and Peter Stone Department. The success of RL on real- world problems with large, often continuous state and action spaces hinges of parameter choices and provide guidance to their setting. We further illustrate that no single
Convergence of RB Approximations Model Order Reduction Techniques
Noelle, Sebastian
Convergence of RB Approximations Model Order Reduction Techniques RB: Convergence of RB for Advanced Study in Computational Engineering Science (AICES) RWTH Aachen Sommersemester 2013 1 / 38 #12;Convergence of RB Approximations Preliminaries Convergence (P = 1) Sampling Strategies Convergence Results: P
On the complexity of approximating a nash equilibrium
Daskalakis, Constantinos
2011-01-01
We show that computing a relative---that is, multiplicative as opposed to additive---approximate Nash equilibrium in two-player games is PPAD-complete, even for constant values of the approximation. Our result is the first ...
Efficient Nonparametric Bayesian Modelling with Sparse Gaussian Process Approximations
Seeger, Matthias
Efficient Nonparametric Bayesian Modelling with Sparse Gaussian Process Approximations Matthias W. 7 J J Thomson Ave, Cambridge, UK Editor: ?? Abstract Sparse approximations to Bayesian inference for nonparametric Gaussian Process models scale linearly in the number of training points, allowing
An asymptotic homogenized neutron diffusion approximation. II. Numerical comparisons
Trahan, T. J.; Larsen, E. W. [Dept. of Nuclear Engineering and Radiological Sciences, Univ. of Michigan, 2355 Bonisteel Blvd., Ann Arbor, MI 48109 (United States)
2012-07-01
In a companion paper, a monoenergetic, homogenized, anisotropic diffusion equation is derived asymptotically for large, 3-D, multiplying systems with a periodic lattice structure [1]. In the present paper, this approximation is briefly compared to several other well known diffusion approximations. Although the derivation is different, the asymptotic diffusion approximation matches that proposed by Deniz and Gelbard, and is closely related to those proposed by Benoist. The focus of this paper, however, is a numerical comparison of the various methods for simple reactor analysis problems in 1-D. The comparisons show that the asymptotic diffusion approximation provides a more accurate estimate of the eigenvalue than the Benoist diffusion approximations. However, the Benoist diffusion approximations and the asymptotic diffusion approximation provide very similar estimates of the neutron flux. The asymptotic method and the Benoist methods both outperform the standard homogenized diffusion approximation, with flux weighted cross sections. (authors)
Structured total least norm and approximate GCDs of inexact polynomials
NASA Astrophysics Data System (ADS)
Winkler, Joab R.; Allan, John D.
2008-05-01
The determination of an approximate greatest common divisor (GCD) of two inexact polynomials f=f(y) and g=g(y) arises in several applications, including signal processing and control. This approximate GCD can be obtained by computing a structured low rank approximation S*(f,g) of the Sylvester resultant matrix S(f,g). In this paper, the method of structured total least norm (STLN) is used to compute a low rank approximation of S(f,g), and it is shown that important issues that have a considerable effect on the approximate GCD have not been considered. For example, the established works only yield one matrix S*(f,g), and therefore one approximate GCD, but it is shown in this paper that a family of structured low rank approximations can be computed, each member of which yields a different approximate GCD. Examples that illustrate the importance of these and other issues are presented.
VISCOSITY AND RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
Tzavaras, Athanasios E.
VISCOSITY AND RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS Athanasios E. Tzavaras Abstract. These lecture notes deal with the approximation of conservation laws via viscosity or relaxation. The following topics are covered: The general structure of viscosity and relaxation
Non-Parametric Approximate Dynamic Programming via the Kernel Method
Bhat, Nikhil
This paper presents a novel non-parametric approximate dynamic programming (ADP) algorithm that enjoys graceful approximation and sample complexity guarantees. In particular, we establish both theoretically and computationally ...
Approximate Dynamic Programming via a Smoothed Linear Program
Desai, Vijay V.
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural ...
Discrete Approximations for Singularly Perturbed Boundary Value Problems with
Farrell, Paul A.
Discrete Approximations for Singularly Perturbed Boundary Value Problems with Parabolic Layers, I Kent, Ohio 44242. #12;Discrete Approximations for Singularly Perturbed Boundary Value Problems we study singularly perturbed SP bound- ary value problems for equations of elliptic and parabolic
Discrete Approximations for Singularly Perturbed Boundary Value Problems with
Farrell, Paul A.
Discrete Approximations for Singularly Perturbed Boundary Value Problems with Parabolic Layers, III Kent, Ohio 44242. #12;Discrete Approximations for Singularly Perturbed Boundary Value Problems papers we study singularly perturbed SP bound- ary value problems for equations of elliptic and parabolic
Discrete Approximations for Singularly Perturbed Boundary Value Problems with
Farrell, Paul A.
Discrete Approximations for Singularly Perturbed Boundary Value Problems with Parabolic Layers, II, Ohio 44242. #12;Discrete Approximations for Singularly Perturbed Boundary Value Problems with Parabolic study singularly perturbed SP bound- ary value problems for equations of elliptic and parabolic type
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1982-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1984-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589
Grover's quantum search algorithm and Diophantine approximation
Dolev, Shahar; Pitowsky, Itamar; Tamir, Boaz [Edelstein Center, Levi Building, The Hebrew University, Givat Ram, Jerusalem (Israel); Department of Philosophy of Science, Bar-Ilan University, Ramat-Gan (Israel)
2006-02-15
In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O({radical}(N)) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using iterations of Grover's basic step only, and no other algorithm. Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m<2{radical}(N)/({radical}(K)-{radical}(M)) obtains. This bound reproduces previous results based on more elaborate algorithms, and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.
Improved Discrete Approximation of Laplacian of Gaussian
NASA Technical Reports Server (NTRS)
Shuler, Robert L., Jr.
2004-01-01
An improved method of computing a discrete approximation of the Laplacian of a Gaussian convolution of an image has been devised. The primary advantage of the method is that without substantially degrading the accuracy of the end result, it reduces the amount of information that must be processed and thus reduces the amount of circuitry needed to perform the Laplacian-of- Gaussian (LOG) operation. Some background information is necessary to place the method in context. The method is intended for application to the LOG part of a process of real-time digital filtering of digitized video data that represent brightnesses in pixels in a square array. The particular filtering process of interest is one that converts pixel brightnesses to binary form, thereby reducing the amount of information that must be performed in subsequent correlation processing (e.g., correlations between images in a stereoscopic pair for determining distances or correlations between successive frames of the same image for detecting motions). The Laplacian is often included in the filtering process because it emphasizes edges and textures, while the Gaussian is often included because it smooths out noise that might not be consistent between left and right images or between successive frames of the same image.
Approximate theory for radial filtration/consolidation
Tiller, F.M. [Univ. of Houston, TX (United States)] [Univ. of Houston, TX (United States); Kirby, J.M. [Commonwealth Scientific and Industrial Research Organization, Canberra (Australia). Soils Div.] [Commonwealth Scientific and Industrial Research Organization, Canberra (Australia). Soils Div.; Nguyen, H.L. [Veteran`s Hospital, Los Angeles, CA (United States)] [Veteran`s Hospital, Los Angeles, CA (United States)
1996-10-01
Approximate solutions are developed for filtration and subsequent consolidation of compactible cakes on a cylindrical filter element. Darcy`s flow equation is coupled with equations for equilibrium stress under the conditions of plane strain and axial symmetry for radial flow inwards. The solutions are based on power function forms involving the relationships of the solidosity {epsilon}{sub s} (volume fraction of solids) and the permeability K to the solids effective stress p{sub s}. The solutions allow determination of the various parameters in the power functions and the ratio k{sub 0} of the lateral to radial effective stress (earth stress ratio). Measurements were made of liquid and effective pressures, flow rates, and cake thickness versus time. Experimental data are presented for a series of tests in a radial filtration cell with a central filter element. Slurries prepared from two materials (Microwate, which is mainly SrSO{sub 4}, and kaolin) were used in the experiments. Transient deposition of filter cakes was followed by static (i.e., no flow) conditions in the cake. The no-flow condition was accomplished by introducing bentonite which produced a nearly impermeable layer with negligible flow. Measurement of the pressure at the cake surface and the transmitted pressure on the central element permitted calculation of k{sub 0}.
Femtolensing: Beyond the Semi-Classical Approximation
A. Ulmer; J. Goodman
1994-06-16
Femtolensing is a gravitational lensing effect in which the magnification is a function not only of the positions and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of $(10^{-13}-10^{-16} M_{\\sun})$ dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculations in general potentials. The physical-optics results presented here differ at low frequencies from the semi-classical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semi-classical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to $10^{-11}$ solar masses, much larger than previously believed. Additionally, we discuss the possibility of a search for femtolensing of white dwarfs in the LMC at optical wavelengths.
Adaptive approximation of higher order posterior statistics
Lee, Wonjung, E-mail: leew@maths.ox.ac.uk
2014-02-01
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively.
Methods for local gravity field approximation
NASA Technical Reports Server (NTRS)
Sailor, R. V.; Tait, K. S.; Leschack, A. R.
1989-01-01
The most widely known modern method for estimating gravity field values from observed data is least-squares collocation. Its advantages are that it can make estimates at arbitrary locations based on irregularly spaced observations, and that it makes use of statistical information about errors in the input data while providing corresponding information about the quality of the output estimates. Disadvantages of collocation include the necessity of inverting square matrices of dimension equal to the number of data values and the need to assume covariance models for the gravity field and the data errors. Fourier methods are an important alternative to collocation; having the advantage of greater computational efficiency, but requiring data estimates to be on a regular grid and not using or providing statistical accuracy information. The GEOFAST algorithm is an implementation of collocation that achieves high computational efficiency by transforming the estimation equations into the frequency domain where an accurate approximation may be made to reduce the workload. The forward and inverse Fast Fourier Transforms (FFTs) are utilized. The accuracy and computational efficiency of the GEOFAST algorithm is demonstrated using two sets of synthetic gravity data: marine gravity for an ocean trench region including wavelengths longer than 200 km; and local land gravity containing wavelengths as short as 5 km. These results are discussed along with issues such as the advantages of first removing reference field models before carrying out the estimation algorithm.
Multilayer Perceptrons to Approximate Quaternion Valued Functions.
Xibilia, M G.; Muscato, G; Fortuna, L; Arena, P
1997-03-01
In this paper a new type of multilayer feedforward neural network is introduced. Such a structure, called hypercomplex multilayer perceptron (HMLP), is developed in quaternion algebra and allows quaternionic input and output signals to be dealt with, requiring a lower number of neurons than the real MLP, thus providing a reduced computational complexity. The structure introduced represents a generalization of the multilayer perceptron in the complex space (CMLP) reported in the literature. The fundamental result reported in the paper is a new density theorem which makes HMLPs universal interpolators of quaternion valued continuous functions. Moreover the proof of the density theorem can be restricted in order to formulate a density theorem in the complex space. Due to the identity between the quaternion and the four-dimensional real space, such a structure is also useful to approximate multidimensional real valued functions with a lower number of real parameters, decreasing the probability of being trapped in local minima during the learning phase. A numerical example is also reported in order to show the efficiency of the proposed structure. Copyright 1997 Elsevier Science Ltd. All Rights Reserved. PMID:12662531
A new approximation method for stress constraints in structural synthesis
NASA Technical Reports Server (NTRS)
Vanderplaats, Garret N.; Salajegheh, Eysa
1987-01-01
A new approximation method for dealing with stress constraints in structural synthesis is presented. The finite element nodal forces are approximated and these are used to create an explicit, but often nonlinear, approximation to the original problem. The principal motivation is to create the best approximation possible, in order to reduce the number of detailed finite element analyses needed to reach the optimum. Examples are offered and compared with published results, to demonstrate the efficiency and reliability of the proposed method.
Regular Type III and Type N Approximate Solutions
Philip Downes; Paul MacAllevey; Bogdan Nita; Ivor Robinson
2001-05-18
New type III and type N approximate solutions which are regular in the linear approximation are shown to exist. For that, we use complex transformations on self-dual Robinson-Trautman metrics rather then the classical approach. The regularity criterion is the boundedness and vanishing at infinity of a scalar obtained by saturating the Bel-Robinson tensor of the first approximation by a time-like vector which is constant with respect to the zeroth approximation.
The hard pulse approximation for the AKNS 2 2-system
scattering transform for this hard pulse approximation converge to the expected continuum potential pointwiseThe hard pulse approximation for the AKNS 2 Ã? 2-system Charles L. Epstein and Jeremy Magland LSNI, 2005 Abstract In the hard pulse approximation, commonly used in nuclear magnetic reso- nance, one
Accepted Manuscript A rounding algorithm for approximating minimum Manhattan
Chepoi, Victor
Accepted Manuscript A rounding algorithm for approximating minimum Manhattan networks Victor Chepoi algorithm for approximating minimum Manhattan networks, Theoretical Computer Science (2007), doi:10.1016/j MANUSCRIPT A rounding algorithm for approximating minimum Manhattan networks1 Victor Chepoi, Karim Nouioua
Approximate conditions for the offaxis triplication in transversely isotropic media
Cerveny, Vlastislav
in transversely isotropic media. The formulas are simple and approximate the exact solution with a high accuracy91 Approximate conditions for the offÂaxis triplication in transversely isotropic media 9iFODY##9. The best results are obtained by the thirdÂorder approximation, which yields accuracy at least 20 times
Explicitly solvable complex Chebyshev approximation problems related to sine polynomials
NASA Technical Reports Server (NTRS)
Freund, Roland
1989-01-01
Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.
Policy Gradient Methods for Reinforcement Learning with Function Approximation
Richard S. Sutton; David A. Mcallester; Satinder P. Singh; Yishay Mansour
1999-01-01
Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and deter- mining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly represented by its own function approximator, indepen- dent of the value function, and is updated according to
Approximations and Consistency of Bayes Factors as Model Dimension Grows
Berger, Jim
Approximations and Consistency of Bayes Factors as Model Dimension Grows James O. Berger Duke. Note, however, that BIC was developed as an asymptotic approximation to Bayes factors between models in which BIC is not an adequate approxima- tion. We develop some new approximations to Bayes factors
Approximating the mapping between systems exhibiting generalized synchronization
Reggie Brown
1998-09-02
We present methods for approximating the mapping that defines the invariant manifold for two systems exhibiting generalized synchronization. If the equations of motion are known then an analytic approximation to the mapping can be found. If time series data is used then a numerical approximation can be found.
Improved Approximations for Max Set Splitting and Max NAE SAT
Ye, Yinyu
Improved Approximations for Max Set Splitting and Max NAE SAT #3; Jiawei Zhang and Yinyu Ye y. 1 #12; Abstract We present a 0:7499-approximation algorithm for Max-Set-Splitting in this paper words. Max Set Splitting, Max NAE SAT, approximation algorithm, semidef- inite programming relaxation. 2
Viscosity and Relaxation Approximation for Hyperbolic Systems of Conservation Laws
Tzavaras, Athanasios E.
Viscosity and Relaxation Approximation for Hyperbolic Systems of Conservation Laws Athanasios E with the approximation of conservation laws via viscosity or relaxation. The following topics are covered: The general structure of viscosity and relaxation approximations is discussed, as suggested by the second law
Detection of Approximal Caries with a New Laser Fluorescence Device
A. Lussi; A. Hack; I. Hug; H. Heckenberger; B. Megert; H. Stich
2006-01-01
The laser device DIAGNOdent developed for the detection of occlusal caries has limited value on approximal surfaces. The aim of this study was to develop and to test a new laser fluorescence (LF) device for the detection of approximal caries. Light with a wavelength of 655 nm was transported to the approximal surface using two different sapphire fibre tips. Seventy-five
Edinburgh Research Explorer Static Approximation of MPI Communication Graphs for
Millar, Andrew J.
Edinburgh Research Explorer Static Approximation of MPI Communication Graphs for Optimized Process Approximation of MPI Communication Graphs for Optimized Process Placement'. in LCPC 2014: The 27th International immediately and investigate your claim. Download date: 11. Dec. 2014 #12;Static Approximation of MPI
Nonlinear n-term Approximation from Hierarchical Spline Bases
Petrushev, Pencho
Nonlinear n-term Approximation from Hierarchical Spline Bases Pencho Petrushev This article is a survey of some recent developments which concern two multilevel approximation schemes: (a) Nonlinear n-term approximation from piecewise polynomials generated by anisotropic dyadic partitions in Rd , and (b) Nonlinear n
Approximating the Bandwidth for Asteroidal Triple-Free Graphs
Ton Kloks; Dieter Kratsch; Haiko Müller
1995-01-01
We show that there is an algorithm to approximate the bandwidth of an AT-free graph with worst case performance ratio 2. Alternatively, at the cost of the approximation factor, we can also obtain an log algorithm to approximate the bandwidth of an AT-free graph within a factor 4 and an algorithm with a factor 6. For the special cases of
The MVA Pre-empt resume priority approximation
Raymond M. Bryant; Anthony E. Krzesinski; Peter Teunissen
1983-01-01
A Mean Value Analysis (MVA) approximation is presented for computing the average performance measures of closed multiclass queueing networks containing non pre-emptive Head Of Line (HOL) and Pre-empt Resume (PR) priority centers. The approximation has the same storage and computational requirements as MVA thus allowing computationally efficient solutions of large priority queueing networks. The accuracy of the MVA PR approximation
Fast and precise approximations of the joint spectral radius
VINCENT D. BLONDEL; YURII NESTEROV
2003-01-01
In this paper, we introduce a procedure for approximating the joint spectral radius of a finite set of matrices with arbitrary precision. Our approximation procedure is based on semidefinite liftings and can be implemented in a recursive way. For two matrices even the first step of the procedure gives an approximation, whose relative quality is at least 1\\/sq.2, that is,
Approximations for the probability of ruin within finite time
Søren Asmussen
1984-01-01
A number of approximations for the probability of ruin before time T are surveyed, some new ones are suggested and numerical comparisons with the exact values are given for the Poisson\\/Exponential case. The approximations include normal ones and diffusion types. A variant and refinement of the classical diffusion approximation is derived and found to have a quite remarkable fit in
On Approximation Complexity of Edge Dominating Set Problem
Eckmiller, Rolf
On Approximation Complexity of Edge Dominating Set Problem in Dense Graphs Richard Schmied Claus Viehmann Abstract We study the approximation complexity of the Minimum Edge Dominating Set problem of approximating a generalization of the Minimum Edge Dominating Set problem, the so called Minimum Subset Edge
On Approximation Complexity of Edge Dominating Set Problem
Eckmiller, Rolf
On Approximation Complexity of Edge Dominating Set Problem in Dense Graphs Richard Schmied # Claus Viehmann + Abstract We study the approximation complexity of the Minimum Edge Dominating Set problem of approximating a generalization of the Minimum Edge Dominating Set problem, the so called Minimum Subset Edge
Open-channel flow model approximation for controller design
R. Brouwer
1995-01-01
In this paper, open-channel flow is analyzed using the linearized St. Venant equations. A method is presented to derive an approximation model for an open channel with backwater effects; the approximation model consists of functions that allow the application of effective control synthesis methods. The accuracy of the approximation models is demonstrated by two examples.
Rapid approximate inversion of airborne TEM
NASA Astrophysics Data System (ADS)
Fullagar, Peter K.; Pears, Glenn A.; Reid, James E.; Schaa, Ralf
2015-11-01
Rapid interpretation of large airborne transient electromagnetic (ATEM) datasets is highly desirable for timely decision-making in exploration. Full solution 3D inversion of entire airborne electromagnetic (AEM) surveys is often still not feasible on current day PCs. Therefore, two algorithms to perform rapid approximate 3D interpretation of AEM have been developed. The loss of rigour may be of little consequence if the objective of the AEM survey is regional reconnaissance. Data coverage is often quasi-2D rather than truly 3D in such cases, belying the need for `exact' 3D inversion. Incorporation of geological constraints reduces the non-uniqueness of 3D AEM inversion. Integrated interpretation can be achieved most readily when inversion is applied to a geological model, attributed with lithology as well as conductivity. Geological models also offer several practical advantages over pure property models during inversion. In particular, they permit adjustment of geological boundaries. In addition, optimal conductivities can be determined for homogeneous units. Both algorithms described here can operate on geological models; however, they can also perform `unconstrained' inversion if the geological context is unknown. VPem1D performs 1D inversion at each ATEM data location above a 3D model. Interpretation of cover thickness is a natural application; this is illustrated via application to Spectrem data from central Australia. VPem3D performs 3D inversion on time-integrated (resistive limit) data. Conversion to resistive limits delivers a massive increase in speed since the TEM inverse problem reduces to a quasi-magnetic problem. The time evolution of the decay is lost during the conversion, but the information can be largely recovered by constructing a starting model from conductivity depth images (CDIs) or 1D inversions combined with geological constraints if available. The efficacy of the approach is demonstrated on Spectrem data from Brazil. Both separately and in combination, these programs provide new options to exploration and mining companies for rapid interpretation of ATEM surveys.
Mappings and accuracy for Chebyshev pseudo-spectral approximations
NASA Technical Reports Server (NTRS)
Bayliss, Alvin; Turkel, Eli
1990-01-01
The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed.
Mappings and accuracy for Chebyshev pseudo-spectral approximations
NASA Technical Reports Server (NTRS)
Bayliss, Alvin; Turkel, Eli
1992-01-01
The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed.
Approximation Set of the Interval Set in Pawlak's Space
Wang, Jin; Wang, Guoyin
2014-01-01
The interval set is a special set, which describes uncertainty of an uncertain concept or set Z with its two crisp boundaries named upper-bound set and lower-bound set. In this paper, the concept of similarity degree between two interval sets is defined at first, and then the similarity degrees between an interval set and its two approximations (i.e., upper approximation set R¯(Z) and lower approximation set R_(Z)) are presented, respectively. The disadvantages of using upper-approximation set R¯(Z) or lower-approximation set R_(Z) as approximation sets of the uncertain set (uncertain concept) Z are analyzed, and a new method for looking for a better approximation set of the interval set Z is proposed. The conclusion that the approximation set R 0.5(Z) is an optimal approximation set of interval set Z is drawn and proved successfully. The change rules of R 0.5(Z) with different binary relations are analyzed in detail. Finally, a kind of crisp approximation set of the interval set Z is constructed. We hope this research work will promote the development of both the interval set model and granular computing theory. PMID:25177721
A Lattice-Theoretic Approach to Multigranulation Approximation Space
He, Xiaoli
2014-01-01
In this paper, we mainly investigate the equivalence between multigranulation approximation space and single-granulation approximation space from the lattice-theoretic viewpoint. It is proved that multigranulation approximation space is equivalent to single-granulation approximation space if and only if the pair of multigranulation rough approximation operators (?i=1nRi¯,?i=1nRi_) forms an order-preserving Galois connection, if and only if the collection of lower (resp., upper) definable sets forms an (resp., union) intersection structure, if and only if the collection of multigranulation upper (lower) definable sets forms a distributive lattice when n = 2, and if and only if ?X?U,???i=1nRi_(X)=?i=1nRi_(X). The obtained results help us gain more insights into the mathematical structure of multigranulation approximation spaces. PMID:25243226
Approximate equivalence and synchronization of metric transition systems
A. Agung Julius; Alessandro D’Innocenzo; Maria Domenica Di Benedetto; George J. Pappas
2009-01-01
In this paper, we consider metric transition systems which are transition systems equipped with metrics for observation and synchronization labels. The existence of metrics leads to the introduction of two new concepts, (i) (?,?)-approximate (bi)simulation of transition systems and (ii) approximate synchronization of transition systems.We show that the notion of (?,?)-approximate (bi)simulation can be thought of as a generalization or
Multijet final states: exact results and the leading pole approximation
Ellis, R.K.; Owens, J.F.
1984-09-01
Exact results for the process gg ..-->.. ggg are compared with those obtained using the leading pole approximation. Regions of phase space where the approximation breaks down are discussed. A specific example relevant for background estimates to W boson production is presented. It is concluded that in this instance the leading pole approximation may underestimate the standard QCD background by more than a factor of two in certain kinematic regions of physical interest.
Disorder and size effects in the envelope-function approximation
T. G. Dargam; R. B. Capaz; Belita Koiller
1997-01-01
We investigate the validity and limitations of the envelope-function approximation (EFA), widely accepted for the description of the electronic states of semiconductor heterostructures. We consider narrow quantum wells of GaAs confined by AlxGa1-xAs barriers. Calculations performed within the tight-binding approximation using ensembles of supercells are compared to the EFA results. Results for miniband widths in superlattices obtained in different approximations
Simulations of 2D Turbulence in the Anelastic Approximation
T. M. Rogers; G. A. Glatzmaier; S. E. Woosley
2002-01-01
High resolution simulations of two-dimensional convection using the Anelastic approximation are presented. These calculations span Rayleigh numbers from 108}-10{12 for Prandtl number equal to unity. This range covers several decades in the hard turbulent regime. While many studies of this sort have been conducted for the Boussinesq approximation, these are the first to use the Anelastic Approximation in this turbulent
New approximant phases in Al–Cr–Fe
V Demange; J. S Wu; V Brien; F Machizaud; J. M Dubois
2000-01-01
Recently, new approximant phases were pointed out in the Al–Cr–Fe system, namely orthorhombic O-Al–Cr–Fe, hexagonal H-Al–Cr–Fe and monoclinic M-Al–Cr–Fe. In the corresponding analysed samples, the new approximant phases were always coexisting with metallic aluminium. We have studied the Al–Cr–Fe system within a broad composition range. In one alloy with composition Al81Cr11Fe8, two new crystalline approximants of the decagonal phase were
Orthogonal polynomial approximation in higher dimensions: Applications in astrodynamics
NASA Astrophysics Data System (ADS)
Bani Younes, Ahmad Hani Abd Alqader
We propose novel methods to utilize orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical differential equation solvers to perform high precision, long-term orbit propagation. These methods have immediate application to efficient propagation of catalogs of Resident Space Objects (RSOs) and improved accounting for the uncertainty in the ephemeris of these objects. More fundamentally, the methodology promises to be of broad utility in solving initial and two point boundary value problems from a wide class of mathematical representations of problems arising in engineering, optimal control, physical sciences and applied mathematics. We unify and extend classical results from function approximation theory and consider their utility in astrodynamics. Least square approximation, using the classical Chebyshev polynomials as basis functions, is reviewed for discrete samples of the to-be-approximated function. We extend the orthogonal approximation ideas to n-dimensions in a novel way, through the use of array algebra and Kronecker operations. Approximation of test functions illustrates the resulting algorithms and provides insight into the errors of approximation, as well as the associated errors arising when the approximations are differentiated or integrated. Two sets of applications are considered that are challenges in astrodynamics. The first application addresses local approximation of high degree and order geopotential models, replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. A method is introduced which adapts the approximation degree radially, compatible with the truth that the highest degree approximations (to ensure maximum acceleration error < 10-9 ms-2, globally) are required near the Earths surface, whereas lower degree approximations are required as radius increases. We show that a four order of magnitude speedup is feasible, with both speed and storage efficiency op- timized using radial adaptation. The second class of problems addressed includes orbit propagation and solution of associated boundary value problems. The successive Chebyshev-Picard path approximation method is shown well-suited to solving these problems with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. Used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss.
Approximation functions for airblast environments from buried charges
Reichenbach, H.; Behrens, K. [Fraunhofer-Institut fuer Kurzzeitdynamik - Ernst-Mach-Institut (EMI), Freiburg im Breisgau (Germany); Kuhl, A.L. [Lawrence Livermore National Lab., El Segundo, CA (United States)
1993-11-01
In EMI report E 1/93, ``Airblast Environments from Buried HE-Charges,`` fit functions were used for the compact description of blastwave parameters. The coefficients of these functions were approximated by means of second order polynomials versus DOB. In most cases, the agreement with the measured data was satisfactory; to reduce remaining noticeable deviations, an approximation by polygons (i.e., piecewise-linear approximation) was used instead of polynomials. The present report describes the results of the polygon approximation and compares them to previous data. We conclude that the polygon representation leads to a better agreement with the measured data.
Bethe free-energy approximations for disordered quantum systems
NASA Astrophysics Data System (ADS)
Biazzo, I.; Ramezanpour, A.
2014-06-01
Given a locally consistent set of reduced density matrices, we construct approximate density matrices which are globally consistent with the local density matrices we started from when the trial density matrix has a tree structure. We employ the cavity method of statistical physics to find the optimal density matrix representation by slowly decreasing the temperature in an annealing algorithm, or by minimizing an approximate Bethe free energy depending on the reduced density matrices and some cavity messages originated from the Bethe approximation of the entropy. We obtain the classical Bethe expression for the entropy within a naive (mean-field) approximation of the cavity messages, which is expected to work well at high temperatures. In the next order of the approximation, we obtain another expression for the Bethe entropy depending only on the diagonal elements of the reduced density matrices. In principle, we can improve the entropy approximation by considering more accurate cavity messages in the Bethe approximation of the entropy. We compare the annealing algorithm and the naive approximation of the Bethe entropy with exact and approximate numerical simulations for small and large samples of the random transverse Ising model on random regular graphs.
Legendre-Tau approximations for functional differential equations
NASA Technical Reports Server (NTRS)
Ito, K.; Teglas, R.
1983-01-01
The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.
An approximation based global optimization strategy for structural synthesis
NASA Technical Reports Server (NTRS)
Sepulveda, A. E.; Schmit, L. A.
1991-01-01
A global optimization strategy for structural synthesis based on approximation concepts is presented. The methodology involves the solution of a sequence of highly accurate approximate problems using a global optimization algorithm. The global optimization algorithm implemented consists of a branch and bound strategy based on the interval evaluation of the objective function and constraint functions, combined with a local feasible directions algorithm. The approximate design optimization problems are constructed using first order approximations of selected intermediate response quantities in terms of intermediate design variables. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure setforth.
Better approximation guarantees for job-shop scheduling
Goldberg, L.A.; Paterson, M. [Univ. of Warwick, Conventry (United Kingdom); Srinivasan, A. [National Univ. of Singapore (Singapore)] [and others
1997-06-01
Job-shop scheduling is a classical NP-hard problem. Shmoys, Stein & Wein presented the first polynomial-time approximation algorithm for this problem that has a good (polylogarithmic) approximation guarantee. We improve the approximation guarantee of their work, and present further improvements for some important NP-hard special cases of this problem (e.g., in the preemptive case where machines can suspend work on operations and later resume). We also present NC algorithms with improved approximation guarantees for some NP-hard special cases.
Diffusion approximation of stochastic master equations with jumps
Pellegrini, C.; Petruccione, F. [School of Physics, National Institute for Theoretical Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa)
2009-12-15
In the presence of quantum measurements with direct photon detection, the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, diffusion models can be obtained from these equations as an approximation. A condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using techniques for Markov processes, which are based on the convergence of Markov generators and martingale problems. This result is illustrated by rigorously obtaining the diffusion approximation for homodyne and heterodyne detection.
Approximating the physical inner product of Loop Quantum Cosmology
Benjamin Bahr; Thomas Thiemann
2006-07-19
In this article, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: Firstly, we compute it analytically via a trick, secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We will find that the approximation is able to recover the analytic solution of the problem, which solidifies hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity.
Monotonically improving approximate answers to relational algebra queries
NASA Technical Reports Server (NTRS)
Smith, Kenneth P.; Liu, J. W. S.
1989-01-01
We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined.
Embedding impedance approximations in the analysis of SIS mixers
NASA Technical Reports Server (NTRS)
Kerr, A. R.; Pan, S.-K.; Withington, S.
1992-01-01
Future millimeter-wave radio astronomy instruments will use arrays of many SIS receivers, either as focal plane arrays on individual radio telescopes, or as individual receivers on the many antennas of radio interferometers. Such applications will require broadband integrated mixers without mechanical tuners. To produce such mixers, it will be necessary to improve present mixer design techniques, most of which use the three-frequency approximation to Tucker's quantum mixer theory. This paper examines the adequacy of three approximations to Tucker's theory: (1) the usual three-frequency approximation which assumes a sinusoidal LO voltage at the junction, and a short-circuit at all frequencies above the upper sideband; (2) a five-frequency approximation which allows two LO voltage harmonics and five small-signal sidebands; and (3) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R(sub N)C for the SIS junctions used. For large omega R(sub N)C, all three approximations approach the eight-harmonic solution. For omega R(sub N)C values in the range 0.5 to 10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, and should be suitable for much design work. For the realistic SIS mixers considered here, the five-frequency approximation gives results very close to those of the eight-harmonic solution. Use of these approximations, where appropriate, considerably reduces the computational effort needed to analyze an SIS mixer, and allows the design and optimization of mixers using a personal computer.
A Padé approximant to the inverse Langevin function
A. Cohen
1991-01-01
Application of the methodology of Pade approximants to a Taylor expansion of the inverse Langevin function led to an accurate analytical expression. The approximation, retaining a finite extendibility of the Langevin spring, enables a convenient analysis of experimental data and analytical manipulations of material models.
A New and Simpler Approximation for ANOVA under Variance Heterogeneity.
ERIC Educational Resources Information Center
Alexander, Ralph A.; Govern, Diane M.
1994-01-01
A new approximation is proposed for testing the equality of "k" independent means in the face of heterogeneity of variance. Monte Carlo simulations show that the new procedure has nearly nominal Type I error rates and Type II error rates that are close to those produced by James's second-order approximation. (SLD)
Complex Band Structures: From Parabolic to Elliptic Approximation
Ximeng Guan; Donghyun Kim; Krishna C. Saraswat; H.-S. Philip Wong
2011-01-01
We show that the conventional nonparabolic approx- imation of real band structures can be modified and generalized to approximate the complex band structures of common semicon- ductors with a significant improvement of accuracy against the parabolic approximation. The improvement is due to the inherent elliptic nature of the complex band structures in the vicinity of the bandgap, which has a
Approximate Killing Vectors for Computing Spin in Black-Hole
Cook, Greg
Approximate Killing Vectors for Computing Spin in Black-Hole Initial Data and Evolutions Gregory B-local definition: e.g. Brown & York[2] or Ashtekar & Krishnan[1] S = - 1 8 BH Kiji sj hd2 x i = i CK : Killing vector of ~hij conformal Killing vector of hij i AKV : Approximate Killing vector of hij Greg Cook
Approximate Killing Vectors and Black-Hole Diagnostics
Cook, Greg
Approximate Killing Vectors and Black-Hole Diagnostics Gregory B. Cook Wake Forest University[2] or Ashtekar & Krishnan[1] S = - 1 8 BH Kiji sj hd2 x i = i CK : Killing vector of ~hij conformal Killing vector of hij i AKV : Approximate Killing vector of hij Greg Cook (WFU Physics) 1 #12
Information capacity in the weak-signal approximation
Lubomir Kostal
2010-01-01
We derive an approximate expression for mutual information in a broad class of discrete-time stationary channels with continuous input, under the constraint of vanishing input amplitude or power. The approximation describes the input by its covariance matrix, while the channel properties are described by the Fisher information matrix. This separation of input and channel properties allows us to analyze the
Inner approximations for polynomial matrix inequalities and robust ...
2011-04-26
Apr 26, 2011 ... controller design purposes, inner approximations are essential ... On the practical and computational sides, the quality of the approximation of P depends ...... where x ?? 1A(x) denotes the indicator function of set A and B(Rn) ...
Makespan minimization in job shops: a polynomial time approximation scheme
Solis-Oba, Roberto
Makespan minimization in job shops: a polynomial time approximation scheme Klaus Jansen \\Lambda present a polynomial time approximation scheme for the job shop scheduling problem with fixed number to the case of job shop problems with release and delivery times, multiprocessor job shops, and dag job shops
Approximability and inapproximability results for nowait shop scheduling
Atkinson, Katie
Approximability and inapproximability results for nowait shop scheduling MAXIM SVIRIDENKO IBM Twait shop scheduling problems under the makespan criterion. In a flow shop, all jobs pass through the machines in the same ordering. In the more general job shop, the routes of the jobs are jobdependent. We
Approximate probability distributions for stochastic systems: maximum entropy method
K. Sobczyk; J. Trcebicki
1999-01-01
The effective analytical methods for stochastic nonlinear dynamical systems are applicable only in some simple cases. If one deals with more complex systems and with the so-called real life applications the approximate methods and numerical integration are necessary. In this paper we present the possible approaches to approximate characterization of the probability distributions of stochastic nonlinear systems. Starting from the
What About Wednesday? Approximation Algorithms for Multistage Stochastic Optimization
Anupam Gupta; Martin Pál; Ramamoorthi Ravi; Amitabh Sinha
2005-01-01
The field of stochastic optimization studies decision making under uncertainty, when only probabilistic information about the future is available. Finding approximate solutions to well-studied optimization problems (such as Steiner tree, Vertex Cover, and Facility Location, to name but a few) presents new challenges when investigated in this frame- work, which has promoted much research in approximation algorithms. There has been
ADAPTIVE EXPERIMENTAL DESIGN FOR CONSTRUCTION OF RESPONSE SURFACE APPROXIMATIONS
Victor M. P ´; John E. Renaud; Layne T. Watson
2001-01-01
Sequential Approximate Optimization (SAO) is a class of methods available for the multidisciplinary de- sign optimization (MDO) of complex systems that are composed of several disciplines coupled together. One of the approaches used for SAO, is based on a quadratic response surface approximation, where zero and first or- der information are required. In these methods, designers must generate and query
A Fast Approximation for Influence Maximization in Large Social Networks
Chung, Chin-Wan
A Fast Approximation for Influence Maximization in Large Social Networks Jong-Ryul Lee Dept the spread of influence in a social network for a given parameter k. A social net- work is represented number of influenced users on a social network, and it is usually approximated by Monte-Carlo simulations
Non-approximability Results for Scheduling Problems with Minsum Criteria
Han Hoogeveen; Petra Schuurman; Gerhard J. Woeginger
1998-01-01
We provide several non-approximability results for deterministic scheduling problems whose objective is to minimize the total job completion time. Unless P = NP, none of the problems under consideration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by Max SNP hardness proofs. Among the investigated problems are: scheduling unrelated machines with job
On Approximation of Max-Vertex-Cover Qiaoming Han y
Ye, Yinyu
, The University of Iowa. 1 #12; Abstract We consider the Max-Vertex-Cover (MVC) problem, i.e., #12;nd k vertices that the existence of a (1 #15;)- approximation algorithm for MVC implies P=NP for some #15; > 0. There is a 3=4-approximation algorithm for MVC, based on a linear programming (LP) relaxation. We illustrate
Single-frequency approximation of the coupling ray theory
Cerveny, Vlastislav
Single-frequency approximation of the coupling ray theory Ludek Klimes & Petr Bulant Departmentraytheory Green tensor is frequency dependent, and is usually calculated for many frequencies. This frequency this frequency dependence. In the vicinity of a given prevailing frequency, we approximate the frequency domain
Linear approximations to the quadratic almost ideal demand system
Toshinobu Matsuda
2006-01-01
This paper investigates linear approximations to the recently popular quadratic almost ideal demand system (QUAIDS) by proposing a new composite variable and conducting a simulation study. The linear approximations are especially useful when one uses nonstationary time series, to which nonlinear systems are difficult to apply properly. The new composite variable performs well in combination with the price indices appropriate
Polynomial approximation on pyramids, cones and solids of rotation
Vianello, Marco
Polynomial approximation on pyramids, cones and solids of rotation S. De Marchi and M. Vianello 1 sets for polynomial interpolation on solid (even truncated) cones with base (with pyramids interpolation and approximation, pyramids, cones, solids of rotation, weakly admissible meshes (WAMs
Sensitivity, Approximation and Uncertainty in Power System Dynamic Simulation
1 Sensitivity, Approximation and Uncertainty in Power System Dynamic Simulation Ian A. Hiskens sensitivities can be used to generate accurate first-order approximations of trajecto- ries that arise from perturbed parameter sets. The computational cost of obtaining the sensitivities and perturbed trajectories
Approximate methods in Bayesian point process spatial models
Andrew B. Lawson
2009-01-01
A range of point process models which are commonly used in spatial epidemiology applications for the increased incidence of disease are compared. The models considered vary from approximate methods to an exact method. The approximate methods include the Poisson process model and methods that are based on discretization of the study window. The exact method includes a marked point process
A study of the effects of state transition matrix approximations
J. A. May
1980-01-01
The effects of using an approximate state transition matrix in orbit estimation are investigated. The approximate state transition matrix results when higher order geopotential terms in the equations of motion are ignored in the formation of the variational equations. Two methods of orbit estimation are considered: the differential correction procedure (DC) and the extended Kalman filter (EKF). The system used
Approximating Hu man Codes in Parallel (Revised Version)
Eckmiller, Rolf
Approximating Hu man Codes in Parallel (Revised Version) Piotr Berman Marek Karpinskiy Yakov Nekrichz Abstract In this paper we present new results on the approximate parallel construction of Hu man approach with the best known parallel sorting algo- rithms we can construct an almost optimal Hu man tree
Topologically Reliable Approximation of Trimmed Polynomial Surface Patches
Wonjoon Cho; Takashi Maekawa; Nicholas M. Patrikalakis; Jaime Peraire
1999-01-01
We present an unstructured triangular mesh generation algorithm that approximates a set of mu- tually nonintersecting simple trimmed polynomial parametric surface patches within a user specied geometric tolerance. The proposed method uses numerically robust interval geometric representa- tions\\/computations and also addresses the problem of topological consistency (homeomorphism) be- tween the exact geometry and its approximation. Those are among the most
Energy Content of Colliding Plane Waves using Approximate Noether Symmetries
M. Sharif; Saira Waheed
2011-09-19
This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. It is shown that in both cases, there does not exist
Detecting and approximating fault lines from randomly scattered data
Andrew Crampton; John C. Mason
2005-01-01
Discretely defined surfaces that exhibit vertical displacements across unknown fault lines can be difficult to approximate accurately unless a representation of the faults is known. Accurate representations of these faults enable the construction of constrained approximation models that can successfully overcome common problems such as over-smoothing.
Function Approximation via Tile Coding: Automating Parameter Choice
Stone, Peter
of the state action space. A variety of function approximation methods for RL have been proposed, includingFunction Approximation via Tile Coding: Automating Parameter Choice Alexander A. Sherstov and Peter of small, simulated domains. The success of RL on real world problems with large, often continuous state
Calculating reactor transfer functions by Pade approximation via Lanczos algorithm
Pázsit, Imre
Calculating reactor transfer functions by PadeÂ approximation via Lanczos algorithm Zhifeng Kuang a in this paper, the so-called PadeÂ approximation via Lanczos algorithm (PVL). The advantage of the PVL method by other authors. The PVL algorithm is demonstrated through the solution of the problem and its advantages
The orthogonal approximation of an oblique structure in factor analysis
Bert F. Green
1952-01-01
A procedure is derived for obtaining an orthogonal transformation which most nearly transforms one given matrix into another given matrix, according to some least-squares criterion of fit. From this procedure, three analytic methods are derived for obtaining an orthogonal factor matrix which closely approximates a given oblique factor matrix. The case is considered of approximating a specified subset of oblique
MULTIPLE ZETA VALUES, PADE APPROXIMATION AND VASILYEV'S CONJECTURE
Paris-Sud XI, Université de
MULTIPLE ZETA VALUES, PAD´E APPROXIMATION AND VASILYEV'S CONJECTURE S. FISCHLER AND T. RIVOAL´e approximation problem involving certain multiple polylogarithms, which evaluated at the point 1 are multiple a rational linear combination of 1 and multiple zeta values in an extended sense that turn out to be values
Approximate Counting Scheme for m n Contingency Tables
Yamamoto, Hirosuke
data from sample surveys. The problem of exactly counting the number of contingency tables with fixedApproximate Counting Scheme for m × n Contingency Tables Shuji Kijima and Tomomi Matsui METR 2003-01 JANUARY 2003 #12;Approximate Counting Scheme for m × n Contingency Tables Shuji Kijima and Tomomi Matsui
Approximate Belief Updating in Max-2-Connected Bayes Networks is
Beimel, Amos
Approximate Belief Updating in Max-2-Connected Bayes Networks is NP-Hard Erez Karpas Faculty}@cs.bgu.ac.il Abstract A max-2-connected Bayes network is one where there are at most 2 distinct di- rected paths between to approximate. Key words: Bayes network, Complexity, Max-k-connected 1 Introduction Bayes networks are a compact
Approximate Belief Updating in Max2Connected Bayes Networks is
Beimel, Amos
Approximate Belief Updating in Max2Connected Bayes Networks is NPHard Erez Karpas Faculty}@cs.bgu.ac.il Abstract A max2connected Bayes network is one where there are at most 2 distinct di rected paths between to approximate. Key words: Bayes network, Complexity, Maxkconnected 1 Introduction Bayes networks are a compact
On the Approximations of Multiple target filtering P. Del Moral
Del Moral , Pierre
On the Approximations of Multiple target filtering equations P. Del Moral Centre INRIA de Bordeaux (2010). To appear in Stochastic Analysis and Applications (2011). P. Del Moral (INRIA) INRIA Bordeaux Approximation models P. Del Moral (INRIA) INRIA Bordeaux-Sud Ouest 2 / 25 #12;Some notation : E measurable space
On the Approximations of Multiple target filtering P. Del Moral
Del Moral , Pierre
On the Approximations of Multiple target filtering equations P. Del Moral Centre INRIA Bordeaux (2010). To appear in Stochastic Analysis and Applications (2011). Del Moral (INRIA) INRIA Centre models 7 Approximation models Del Moral (INRIA) INRIA Centre Bordeaux-Sud Ouest, France 2 / 25 #12;Some
Hybrid approximation of stochastic process algebras for systems biology
Bortolussi, Luca
Hybrid approximation of stochastic process algebras for systems biology Luca Bortolussi Alberto: We present a technique to approximate models of biological systems written in a "distilled" version of stochastic Concurrent Constraint Programming (sCCP), a stochastic programming methodology based on logic
Maintaining Approximate Extent Measures of Moving Points Pankaj K. Agarwaly
Agarwal, Pankaj K.
. As the points move continuously, the extent measure of interest changes continuously as well, though its comMaintaining Approximate Extent Measures of Moving Points Pankaj K. Agarwaly Sariel Har-Peledz Abstract We present approximation algorithms for maintaining various descriptors of the extent of moving
The Density of Alternation Points in Rational Approximation
P. B. Borwein; A. Kroo; R. Grothmann; E. B. Saff
1989-01-01
We investigate the behavior of the equioscillation (alternation) points for the error in best uniform rational approximation on (-1, 1). In the context of the Walsh table (in which the best rational approximant with numerator degree < m , denominator degree < n, is displayed in the nth row and the mth column), we show that these points are dense
Approximation of a Digital Signal Using Estimate Wavelet Transform
Archit Yajnik
2011-01-01
This article presents a general outline of the approximation of digital signal using Discrete Wavelet. The technique used in (1) is a new attitude to a multiresolution digital signal analysis by discrete wavelet transforms. This article demonstrates an approximation of a digital signal using Daubechies D4 wavelets. The present technique exhibits a revised procedure of removing distortion (loss) generated from
Approximate continuous wavelet transform with an application to noise reduction
James M. Lewis; C. Sidney Burrus
1998-01-01
We describe a generalized scale-redundant wavelet transform which approximates a dense sampling of the continuous wavelet transform (CWT) in both time and scale. The dyadic scaling requirement of the usual wavelet transform is relaxed in favor of an approximate scaling relationship which in the case of a Gaussian scaling function is known to be asymptotically exact and irrational. This scheme
A fast approximation to the continuous wavelet transform with applications
Kathrin Berkner; Raymond O. Wells
1997-01-01
We propose an approximation of a continuous wavelet transform (CWT) which is based on a hierarchical scheme, similar to the fast discrete wavelet transform. This approximation keeps redundancies in time and scale. Furthermore, it preserves properties of the CWT regarding the characterization of singularities and leads to efficient applications in detection and characterization of singularities
Alpha Theory to Certify Roots 1 Approximate Zeroes
Verschelde, Jan
Newton's method in projective space Analytic Symbolic Computation (MCS 563) Alpha Theory to certify roots Newton's method in projective space Analytic Symbolic Computation (MCS 563) Alpha Theory to certify rootsAlpha Theory to Certify Roots 1 Approximate Zeroes what is an approximate zero? a criterion
Democracy functions and optimal embeddings for approximation spaces
Garrigós, Gustavo; de Natividade, Maria
2009-01-01
We prove optimal embeddings for nonlinear approximation spaces in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions of the basis. As applications we recover known embeddings for $N$-term wavelet approximation in Lebesgue, Orlicz, and Lorentz norms. We also study the "greedy classes" introduced by Gribonval and Nielsen.
Dimensionality Reduction and Similarity Computation by Inner Product Approximations
Egecioglu, Ömer
as universal weights based on the moments of the probability density function as- sumed for the distribution be accurately approximated by a signi cantly lower dimensional representation. Keywords: Distance approximation - cient high dimensional similarity searching in large-scale sys- This work was partially supported
Continuation of Approximate Transformation Groups via Multiple Time Scales Method
V. A. Baikov; N. H. Ibragimov
2000-01-01
Recently, the theory of approximate symmetries was developedfor tackling differential equations with a small parameter. This theoryfurnishes us with a tool, e.g. for constructing approximate groupinvariant solutions. Usually, these solutions are determined by powerseries in the small parameter and hence they are well defined only in asmall region of independent variables. In this paper, we modify theapproximate symmetry analysis by
On approximate phasor models in dissipative bilinear systems
Gilead Tadmor
2002-01-01
Dynamic phasors models capture transients in (main) harmonic coefficients of periodically dominated systems, and their utility in state approximations is supported by machine and power systems case studies. The author explores analytical plausibility arguments, and inherent restrictions of such approximations in dissipative systems with quadratically nonlinear lossless components.
Reaching Approximate Agreement in the Presence of Faults
Danny Dolev; Nancy A. Lynch
1985-01-01
This paper considers a variant on the Byzantine Generals problem, in which processes start with arbitrary real values rather than Boolean values or values from some bounded range, and in which approximate, rather than exact, agreement is the desired goal. Algorithms are presented to reach approximate agreement in asynchronous, as well as synchronous systems. The asynchronous agreement algorithm is an
Quasicrystal approximants with novel compositions and structures M. Mihalkovic1
Widom, Michael
Quasicrystal approximants with novel compositions and structures M. Mihalkovic1 and M. Widom, Slovak Academy of Sciences, 84228 Bratislava, Slovakia ABSTRACT We identify several new quasicrystal approximants in alloy systems in which quasicrystals have not been previously reported. Some occur in alloys
Linear-Work Greedy Parallel Approximate Set Cover and Variants
Blelloch, Guy E.
Linear-Work Greedy Parallel Approximate Set Cover and Variants Guy E. Blelloch Richard Peng Kanat approximation algorithms for set cover and related problems. These algorithms build on an algorithm for solving of a key component in existing work on parallel set cover. We derive a randomized algorithm for Ma
Approximation of the Quadratic Set Covering Bruno Escoffier
Paris-Sud XI, Université de
Approximation of the Quadratic Set Covering Problem§ Bruno Escoffier , Peter L. Hammer Résumé Nous Set Covering problem. This problem, which arises in many applications, is a natural generaliza- tion of the usual Set Covering problem. We show that this problem is very hard to approximate in the general case
Splitting Methods for SU(N) Loop Approximation Peter Oswald
Oswald. Peter
groups [8], but also occurs in a more practical context. For example, polarization mode dispersion and operating optical FIR filter architectures for polarization mode dispersion compensation [7]. The classical approximation: constructive approximation of manifold-valued functions. This field is currently fueled
Computing Approximate Extended Krylov Subspaces without Explicit Inversion
Matijevic, Domagoj
Computing Approximate Extended Krylov Subspaces without Explicit Inversion Thomas Mach Miroslav S the matrix of recurrences. In practice, however, for large dimensions computing time is saved by making use can lead to time savings when approximating, e.g., matrix functions. The research was partially
The blind leading the blind: Mutual refinement of approximate theories
NASA Technical Reports Server (NTRS)
Kedar, Smadar T.; Bresina, John L.; Dent, C. Lisa
1991-01-01
The mutual refinement theory, a method for refining world models in a reactive system, is described. The method detects failures, explains their causes, and repairs the approximate models which cause the failures. The approach focuses on using one approximate model to refine another.
The approximate controllability of a model for mutant selection
Weinberger, Hans
: parabolic system, population genetics, evolutionary selec- tion, approximate controllability AMS with population control to evolve in a re- actor with impenetrable walls is approximately controllable. 1 that the model contains no population control, which makes it unrealistic. In fact it was shown by T. Malthus
Fast Polygonal Approximation of Terrains and Height Fields
Garland, Michael
Fast Polygonal Approximation of Terrains and Height Fields Michael Garland and Paul S. Heckbert Several algorithms for approximating terrains and other height fields using polygonal meshes are described, compared, and optimized. These algorithms take a height field as input, typically a rectangular grid
Fast Polygonal Approximation of Terrains and Height Fields
Garland, Michael
Fast Polygonal Approximation of Terrains and Height Fields Michael Garland and Paul S. Heckbert. #12; Abstract Several algorithms for approximating terrains and other height fields using polygonal meshes are described, compared, and optimized. These algorithms take a height field as input, typically
Approximate Solutions of Nonlinear Heat Equation for Given Flow
Mikhail A. Chmykhov; Nikolai A. Kudryashov
2005-08-01
The one-dimensional problem of the nonlinear heat equation is considered. We assume that the heat flow in the origin of coordinates is the power function of time and the initial temperature is zero. Approximate solutions of the problem are given. Convergence of approximate solutions is discussed.
Pade Approximations in Inverse Homogenization and Numerical Simulation of Electromagnetic
Cherkaev, Elena
Pad´e Approximations in Inverse Homogenization and Numerical Simulation of Electromagnetic Fields and in numerical simulation of time- domain electromagnetic fields in composites. It is assumed that the scale governing the electromagnetic fields are of convolution type. We use rational Pad´e approximation to derive
Expectation-Maximization Gaussian-Mixture Approximate Message Passing
Schniter, Philip
Expectation-Maximization Gaussian-Mixture Approximate Message Passing Jeremy Vila and Philip). If this distribution was apriori known, one could use efficient approximate message passing (AMP) techniques for nearly.i.d from the marginal pdf pX (x) = fX (x) + (1 - )(x), (2) where (·) is the Dirac delta, f
Expectation-Maximization Bernoulli-Gaussian Approximate Message Passing
Schniter, Philip
Expectation-Maximization Bernoulli-Gaussian Approximate Message Passing Jeremy Vila and Philip@ece.osu.edu) Abstract--The approximate message passing (AMP) algorithm originally proposed by Donoho, Maleki. probabilistic viewpoint where the elements of x are drawn i.i.d from the marginal pdf pX (x) = f(x)+(1-)(x
APPROXIMATE ROOTS OF A VALUATION AND THE PIERCEBIRKHOFF CONJECTURE
APPROXIMATE ROOTS OF A VALUATION AND THE PIERCEBIRKHOFF CONJECTURE F. Lucas D´epartement de Math. Abstract In this paper, we construct an object, called a system of approximate roots of a valuation, centered in a regular local ring, which describes the fine structure of the valuation (namely, its
An Approach to Designing Very Fast Approximate String Matching Algorithms
M.-W. Du; S. C. Chang
1994-01-01
An approach to designing very fast algorithms for approximate string matching in a dictionary is proposed. Multiple spelling errors corresponding to insert, delete, change, and transpose operations on character strings are considered in the fault model. The design of very fast approximate string matching algorithms through a four-step reduction procedure is described. The final and most effective step uses hashing
Approximate Fault-Tree Analysis with Prescribed Accuracy
W. Schneeweiss
1987-01-01
Unavailability or Unreliability of a system can be found with a given error-bound by a proper approximate fault-tree analysis. In essence: Using a given maximum error, the set of mincuts is reduced, and the rest of the mincuts are processed such that at the end an approximate value of system unavailability or unreliability is found, which is too high by
Transport approximations in partially diffusive media Guillaume Bal
Bal, Guillaume
Transport approximations in partially diffusive media Guillaume Bal Department of Applied Physics concerns the analysis of approximations of transport equations in diffusive media. Firstly, we consider a variational formulation for the first-order transport equation that has the correct diffusive behavior
The Role of Intuitive Approximation Skills for School Math Abilities
ERIC Educational Resources Information Center
Libertus, Melissa E.
2015-01-01
Research has shown that educated children and adults have access to two ways of representing numerical information: an approximate number system (ANS) that is present from birth and allows for quick approximations of numbers of objects encountered in one's environment, and an exact number system (ENS) that is acquired through experience and…
Variational approximations for categorical causal modeling with latent variables
K. Humphreys; D. M. Titterington
2003-01-01
Latent class models in the social and behavioral sciences have remained structurally simple. One reason for this is that inference in statistical models can be computationally difficult. Methods for approximate inference, known as variational approximations, which have been developed in the machine learning, graphical modeling and statistical physics literatures, can be used to alleviate the computational difficulties of inference for
Diffusion, P 1, and other approximate forms of radiation transport
Gordon L. Olson; Lawrence H. Auer; Michael L. Hall
2000-01-01
Full transport solutions of time-dependent problems can be computationally very expensive. Therefore, considerable effort has been devoted to developing approximate solution techniques that are much faster computationally and yet are accurate enough for a particular application. Many of these approximate solutions have been used in isolated problems and have not been compared to each other. This paper presents two test
Efficient Approximate Visibility Query in Large Dynamic Environments
Shahabi, Cyrus
, the answer to an AVQ for the viewpoint v is an approximate visibility set such that its difference and online mapping systems to computer games. Most recently the marriage of spatial queries and visibility is defined in terms of the cosine similarity between the two visibility vectors. Approximation
Approximating conductive ellipsoid inductive responses using static quadrupole moments
J. Torquil
2008-01-01
Smith and Morrison (2006) developed an approximation for the inductive response of conducting magnetic (permeable) spheroids (e.g., steel spheroids) based on the inductive response of conducting magnetic spheres of related dimensions. Spheroids are axially symmetric objects with elliptical cross-sections along the axis of symmetry and circular cross sections perpendicular to the axis of symmetry. Spheroids are useful as an approximation
Finding the Best Quadratic Approximation of a Function
ERIC Educational Resources Information Center
Yang, Yajun; Gordon, Sheldon P.
2011-01-01
This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…
CrossDomain Approximate String Matching Daniel Lopresti
Wilfong, Gordon
CrossDomain Approximate String Matching Daniel Lopresti Gordon Wilfong Bell Labs, Lucent an #12; CrossDomain Approximate String Matching 2 Speech Recognition Optical Character Recognition Retrieval Model Figure 1: An example of crossdomain retrieval. intricate chemical decryption algorithm
Approximating linear restrictions of Boolean functions Yaoyun Shi 1
Shi, Yaoyun
subject that has many fascinating applications in Boolean function complexity. In the #12;rst direction and the approximate degree with other im- portant measures of Boolean function complexity, such as the decision treeApproximating linear restrictions of Boolean functions Yaoyun Shi 1 Abstract We initiate two new
POINTWISE ERROR ESTIMATES FOR RELAXATION APPROXIMATIONS TO CONSERVATION LAWS
Soatto, Stefano
POINTWISE ERROR ESTIMATES FOR RELAXATION APPROXIMATIONS TO CONSERVATION LAWS EITAN TADMOR AND TAO that the maximum principle can be applied. Key words. conservation laws, error estimates, relaxation method@fisher.math.hkbu.edu.hk). 870 #12;RELAXATION APPROXIMATIONS TO CONSERVATION LAWS 871 dissipative mechanism for discontinuities
Approximate reduction of multiregional models with environmental stochasticity
Luis Sanz; Rafael Bravo de la Parra
2007-01-01
In this work we extend previous results regarding the use of approximate aggregation techniques to simplify the study of discrete time models for populations that live in an environment that changes randomly with time. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a
Approximating Minimum Independent Dominating Sets in Wireless Networks
Al Hanbali, Ahmad
Approximating Minimum Independent Dominating Sets in Wireless Networks Johann L. Hurink, Tim-time approximation scheme (PTAS) for the Mini- mum Independent Dominating Set problem in graphs of polynomially. An independent dominating set is a dominating set in a graph that is also independent. It thus combines
Rational approximation and universality for a quasilinear parabolic equation
P. M. Gauthier; N. Tarkhanov
2008-01-01
Approximation theorems, analogous to results known for linear elliptic equations, are obtained for solutions of the heat equation.\\u000a Via the Cole-Hopf transformation, this gives rise to approximation theorems for one of the simplest examples of a nonlinear\\u000a partial differential equation, Burgers’ equation.
Polyhedral approximation of the second-order cone
Glineur, François
#20; x 2 0 o General SOCO problem : min c T x s.t. ( b l #20; Ax #20; b u ; x l #20; x #20; x u ; x Ik: Computational experiments ' & $ % Observation SOCO software #28; LO software w.r.t. capability (size) and availability (commercial packages) Idea: try to approximate SOCO with LO, i.e. approximate L n
Cascaded centralized TSK fuzzy system: universal approximator and high interpretation
Shitong Wang; Fu-lai Chung; Hong-bin Shen; Dewen Hu
2005-01-01
When applying fuzzy systems for data analysis, their approximation and interpretation capabilities are two important aspects. Cascaded fuzzy system (CFS) is a new special class of hierarchical fuzzy systems in architectures proposed by Duan and Chung [IEEE Trans. Fuzzy Syst. 9 (2) (2001) 293] but its universal approximation capability is still not proved. When CFS is utilized in fuzzy data
Learning Approximate Thematic Maps from Labeled Geospatial Data
Shahabi, Cyrus
Learning Approximate Thematic Maps from Labeled Geospatial Data (Extended Abstract) Mehdi of these geospatial datasets is a promising ap- proach towards building approximate thematic maps. More- over spatial datasets. We study how factors such as distribution of the training data, neighborhood
Approximate Linear Programming for Network Control: Column Generation and Subproblems
Veatch, Michael H.
Approximate Linear Programming for Network Control: Column Generation and Subproblems Michael H.veatch@gordon.edu nathan.walker@gordon.edu February 26, 2008 Subject classifications: Dynamic programming/optimal control: approximations/large-scale problems. Queues: control of queueing networks. Production/scheduling: dynamic
Model-Based Reinforcement Learning with an Approximate, Learned Model
Sutton, Richard S.
Model-Based Reinforcement Learning with an Approximate, Learned Model Leonid Kuvayev Rich Sutton that model-based methods do indeed perform better than model-free reinforcement learning. Keywords: Reinforcement learning, planning, model-based learning, function approximation, CMAC networks. 1 Introduction
Numerical Approximation of the Exact Control for the String Equation
Cabral, Marco
Numerical Approximation of the Exact Control for the String Equation M. A. Rincon1 , M. Zegarra the results obtained by Vasilyev et al [11] on the numerical approximation of the exact control for the string us consider a flexible elastic string of length L. Then its small transversal vibration can
Improved Approximate String Matching using Compressed Suffix Data Structures
Sung, Wing-Kin Ken"
Improved Approximate String Matching using Compressed Suffix Data Structures TakÂWah Lam 2 , Wing twlam@cs.hku.hk Abstract. Approximate string matching is about finding a given string pattern in a text, respectively. 1 Introduction Consider a text T of length n and a pattern P of length m, both strings over
Properties of the Boltzmann equation in the classical approximation
Tanji, Naoto [Nishina Center, RIKEN, Wako (Japan). Theoretical Research Division; Brookhaven National Lab. (BNL), Upton, NY (United States); Epelbaum, Thomas [Institut de Physique Theorique (France); Gelis, Francois [Institut de Physique Theorique (France); Wu, Bin [Institut de Physique Theorique (France)
2014-12-01
We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.
Properties of the Boltzmann equation in the classical approximation
Tanji, Naoto; Epelbaum, Thomas; Gelis, Francois; Wu, Bin
2014-12-01
We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since onemore »has also access to the non-approximated result for comparison.« less
An approximation theory for the identification of linear thermoelastic systems
NASA Technical Reports Server (NTRS)
Rosen, I. G.; Su, Chien-Hua Frank
1990-01-01
An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.
Recent advances in approximation concepts for optimum structural design
NASA Technical Reports Server (NTRS)
Barthelemy, Jean-Francois M.; Haftka, Raphael T.
1991-01-01
The basic approximation concepts used in structural optimization are reviewed. Some of the most recent developments in that area since the introduction of the concept in the mid-seventies are discussed. The paper distinguishes between local, medium-range, and global approximations; it covers functions approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It also appears that some new methodologies are emerging which could greatly benefit from the introduction of new computer architecture.
Padé and rational approximations to systems of functions and their arithmetic applications
D. Chudnovsky; G. Chudnovsky
Introduction. In this lecture we study the algebraic properties of Pad~ approximations to systems of analytic functions~ and Pad~-type approximations and consider applications of Pad6 approximations to diophantine approximations to numbers. One of the problems we consider in detail, is the existence of recurrences that relate contiguous Pad~ approximations (and Pad6 approximants). This part of Pad~ approximation studies is especially
Approximate number word knowledge before the cardinal principle.
Gunderson, Elizabeth A; Spaepen, Elizabet; Levine, Susan C
2015-02-01
Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge. PMID:25462030
Hiroyuki Kuwahara; Chris J. Myers
2007-01-01
Given the substantial computational requirements of stochas- tic simulation, approximation is essential for efficient analysis of any re- alistic biochemical system. This paper introduces a new approximation method to reduce the computational cost of stochastic simulations of an enzymatic reaction scheme which in biochemical systems often includes rapidly changing fast reactions with enzyme and enzyme-substrate com- plex molecules present in
A test of the adhesion approximation for gravitational clustering
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.
1993-01-01
We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.
Approximate Coulomb distortion effects in (e,e'p) reactions
K. S. Kim; L. E. Wright
2005-03-30
In this paper we apply a well-tested approximation of electron Coulomb distortion effects to the exclusive reaction (e,e'p) in the quasielastic region. We compare the approximate treatment of Coulomb distortion effects to the exact distorted wave Born approximation evaluated by means of partial wave analysis to gauge the quality of our approximate treatment. We show that the approximate M\\"oller potential has a plane-wave-like structure and hence permits the separation of the cross section into five terms which depend on bilinear products of transforms of the transition four current elements. These transforms reduce to Fourier transforms when Coulomb distortion is not present, but become modified with the inclusion of Coulomb distortion. We investigate the application of the approximate formalism to a model of 208Pb(e,e'p) using Dirac-Hartree single particle wave functions for the ground state and relativistic optical model wave functions for the continuum proton. We show that it is still possible to extract, albeit with some approximation, the various structure functions from the experimentally measured data even for heavy nuclei.
Meromorphic approximants to complex Cauchy transforms with polar singularities
Baratchart, Laurent; Yattselev, Maxim L [Institut National de Recherche en Informatique et en Automatique, Sophia Antipolis - Mediterranee (France)
2009-10-31
We study AAK-type meromorphic approximants to functions of the form F(z)={integral}(d{lambda}(t))/(z-t)+R(z), where R is a rational function and {lambda} is a complex measure with compact regular support included in (-1,1), whose argument has bounded variation on the support. The approximation is understood in the L{sup p}-norm of the unit circle, p{>=}2. We dwell on the fact that the denominators of such approximants satisfy certain non-Hermitian orthogonal relations with varying weights. They resemble the orthogonality relations that arise in the study of multipoint Pade approximants. However, the varying part of the weight implicitly depends on the orthogonal polynomials themselves, which constitutes the main novelty and the main difficulty of the undertaken analysis. We obtain that the counting measures of poles of the approximants converge to the Green equilibrium distribution on the support of {lambda} relative to the unit disc, that the approximants themselves converge in capacity to F, and that the poles of R attract at least as many poles of the approximants as their multiplicity and not much more. Bibliography: 35 titles.
Convergence of multipoint Pade approximants of piecewise analytic functions
Buslaev, Viktor I [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)] [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2013-02-28
The behaviour as n{yields}{infinity} of multipoint Pade approximants to a function which is (piecewise) holomorphic on a union of finitely many continua is investigated. The convergence of multipoint Pade approximants is proved for a function which extends holomorphically from these continua to a union of domains whose boundaries have a certain symmetry property. An analogue of Stahl's theorem is established for two-point Pade approximants to a pair of functions, either of which is a multivalued analytic function with finitely many branch points. Bibliography: 11 titles.
Usefulness of bound-state approximations in reaction theory
Adhikari, S.K.
1981-08-01
A bound-state approximation when applied to certain operators, such as the many-body resolvent operator for a two-body fragmentation channel, in many-body scattering equations, reduces such equations to equivalent two-body scattering equations which are supposed to provide a good description of the underlying physical process. In this paper we test several variants of bound-state approximations in the soluble three-boson Amado model and find that such approximations lead to weak and unacceptable kernels for the equivalent two-body scattering equations and hence to a poor description of the underlying many-body process.
Existence of best N-convex approximants in L 1
R. Huotari; D. Legg; D. Townsend
1989-01-01
We consider here best approximation by n-convex functions. We first show that if f?L1[0,1], then there is, a best L1-approximant to f by functions which are n-convex on (0,1). We then show that if f?L?[0,1], then any best Lp-approximant, fp, to f by n-convex, functions is bounded and hence, f has the Pólya-one property, i.e., fp converges a.e. as p
Bethe approximation in the Ising model with mobile impurities
NASA Astrophysics Data System (ADS)
Semkin, S. V.; Smagin, V. P.
2015-05-01
The Bethe approximation as applied to a system consisting of magnetic and nonmagnetic atoms in the thermodynamic equilibrium has been considered. In this approximation, the dependences of the magnetization and Curie temperature on the concentration of magnetic atoms for the Ising model with mobile nonmagnetic impurities have been constructed and the limiting concentrations of the appearance of spontaneous magnetization in the ground state have been obtained. It has been established that the considered approximation for a one-dimensional chain is the exact solution.