Institute of Scientific and Technical Information of China (English)
范洪义
2002-01-01
We study the Wentzel-Kramers-Brillouin (WKB) approximation for dynamic systems with kinetic couplings inentangled state representations. The result shows that the kinetic coupling will affect the position of classicalturning points where the condition of using the WKB approximation breaks down. The modified WKB approx-imation formula is derived in the entangled state representation, for example, the common eigenvector of therelative coordinate and the total momentum of two particles. The corresponding Bohr-Sommerfeld quantizationrule is also derived.
Paraxial Wentzel-Kramers-Brillouin method applied to the lower hybrid wave propagation
Energy Technology Data Exchange (ETDEWEB)
Bertelli, N.; Phillips, C. K.; Valeo, E.; Wilson, J. R. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Maj, O.; Poli, E. [Max Planck Institute for Plasma Physics, EURATOM Association, Boltzmannstr. 2, 85748, Garching (Germany); Harvey, R. [CompX, Del Mar, California 92014 (United States); Wright, J. C.; Bonoli, P. T. [MIT Plasma Science and Fusion Center, Cambridge, Massachusetts 02139 (United States); Smirnov, A. P. [Lomonosov Moscow State University, Moscow (Russian Federation)
2012-08-15
The paraxial Wentzel-Kramers-Brillouin (pWKB) approximation, also called beam tracing method, has been employed in order to study the propagation of lower hybrid waves in a tokamak plasma. Analogous to the well-know ray tracing method, this approach reduces Maxwell's equations to a set of ordinary differential equations, while, in addition, retains the effects of the finite beam cross-section, and, thus, the effects of diffraction. A new code, LHBEAM (lower hybrid BEAM tracing), is presented, which solves the pWKB equations in tokamak geometry for arbitrary launching conditions and for analytic and experimental plasma equilibria. In addition, LHBEAM includes linear electron Landau damping for the evaluation of the absorbed power density and the reconstruction of the wave electric field in both the physical and Fourier space. Illustrative LHBEAM calculations are presented along with a comparison with the ray tracing code GENRAY and the full wave solver TORIC-LH.
Isgur-Wise function in a QCD-inspired potential model with WKB approximation
Hazarika, Bhaskar Jyoti; Choudhury, D. K.
2017-03-01
We use Wentzel-Kramers-Brillouin (WKB) approximation for calculating the slope and curvature of Isgur-Wise function in a QCD-inspired potential model. This work is an extension of the approximation methods to the QCD-inspired potential model. The approach hints at an effective range of distance for calculating the slope and curvature of Isgur-Wise function. Comparison is also made with those of Dalgarno method and variationally improved perturbation theory (VIPT) as well as other models to show the advantages of using WKB approximation.
Approximation methods in gravitational-radiation theory
Will, C. M.
1986-02-01
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. The author summarizes recent developments in two areas in which approximations are important: (1) the quadrupole approximation, 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 (2) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
Wentzel-Kramers-Brillouin method in the Bargmann representation. [of quantum mechanics
Voros, A.
1989-01-01
It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.
New approach for alpha decay half-lives of superheavy nuclei and applicability of WKB approximation
Dong, Jianmin; Zuo, Wei; Scheid, Werner
2011-07-01
The α decay half-lives of recently synthesized superheavy nuclei (SHN) are calculated by applying a new approach which estimates them with the help of their neighbors based on some simple formulas. The estimated half-life values are in very good agreement with the experimental ones, indicating the reliability of the experimental observations and measurements to a large extent as well as the predictive power of our approach. The second part of this work is to test the applicability of the Wentzel-Kramers-Brillouin (WKB) approximation for the quantum mechanical tunneling probability. We calculated the accurate barrier penetrability for alpha decay along with proton and cluster radioactivity by numerically solving Schrödinger equation. The calculated results are compared with those of the WKB method to find that WKB approximation works well for the three physically analogical decay modes.
New approach for alpha decay half-lives of superheavy nuclei and applicability of WKB approximation
Energy Technology Data Exchange (ETDEWEB)
Dong Jianmin [Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000 (China); Graduate University of Chinese Academy of Sciences, Beijing 100049 (China); School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000 (China); Institute for Theoretical Physics, Justus Liebig University, D-35392 Giessen (Germany); China Institute of Atomic Energy, P.O. Box 275(18), Beijing 102413 (China); Zuo Wei, E-mail: zuowei@impcas.ac.cn [Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000 (China); School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000 (China); Scheid, Werner [Institute for Theoretical Physics, Justus Liebig University, D-35392 Giessen (Germany)
2011-07-01
The {alpha} decay half-lives of recently synthesized superheavy nuclei (SHN) are calculated by applying a new approach which estimates them with the help of their neighbors based on some simple formulas. The estimated half-life values are in very good agreement with the experimental ones, indicating the reliability of the experimental observations and measurements to a large extent as well as the predictive power of our approach. The second part of this work is to test the applicability of the Wentzel-Kramers-Brillouin (WKB) approximation for the quantum mechanical tunneling probability. We calculated the accurate barrier penetrability for alpha decay along with proton and cluster radioactivity by numerically solving Schroedinger equation. The calculated results are compared with those of the WKB method to find that WKB approximation works well for the three physically analogical decay modes.
New approach for alpha decay half-lives of superheavy nuclei and applicability of WKB approximation
Dong, Jianmin; Scheid, Werner; 10.1016/j.nuclphysa.2011.06.016
2011-01-01
The alpha decay half-lives of recently synthesized superheavy nuclei (SHN) are calculated by applying a new approach which estimates them with the help of their neighbors based on some simple formulas. The estimated half-life values are in very good agreement with the experimental ones, indicating the reliability of the experimental observations and measurements to a large extent as well as the predictive power of our approach. The second part of this work is to test the applicability of the Wentzel-Kramers-Brillouin (WKB) approximation for the quantum mechanical tunneling probability. We calculated the accurate barrier penetrability for alpha decay along with proton and cluster radioactivity by numerically solving Schr\\"odinger equation. The calculated results are compared with those of the WKB method to find that WKB approximation works well for the three physically analogical decay modes.
Ulhoa, S C; Capistrano, Abraão J S
2016-01-01
In this paper we investigate scalar perturbations of black holes embedded in a five dimensional bulk space. It is calculated the quasinormal frequencies of a such black holes using the third order of Wentzel, Kramers, Brillouin (WKB) approximation for scalar perturbations. The results are presented in tables along the text.
Lorentz symmetry breaking effects on relativistic EPR correlations
Energy Technology Data Exchange (ETDEWEB)
Belich, H. [Universidade Federal do Espirito Santo, Departamento de Fisica e Quimica, Vitoria, ES (Brazil); Furtado, C.; Bakke, K. [Universidade Federal da Paraiba, Departamento de Fisica, Caixa Postal 5008, Joao Pessoa, PB (Brazil)
2015-09-15
Lorentz symmetry breaking effects on relativistic EPR (Einstein-Podolsky-Rosen) correlations are discussed. From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the Lorentz symmetry violation and write an effective metric for the Minkowski spacetime. Then we obtain the Wigner rotation angle via the Fermi-Walker transport of spinors and consider the WKB (Wentzel-Kramers-Brillouin) approximation in order to study the influence of Lorentz symmetry breaking effects on the relativistic EPR correlations. (orig.)
One-dimensional wave propagation in rods of variable cross section: A WKBJ solution
Ochi, Simeon C. U.; Williams, James H., Jr.
1987-01-01
As an important step in the characterization of a particular dynamic surface displacement transducer (IQI Model 501), a one-dimensional wave propagation in isotropic nonpiezoelectric and piezoelectric rods of variable cross section are presented. With the use of the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximate solution technique, an approximate formula, which relates the ratio of the amplitudes of a propagating wave observed at any two locations along the rod to the ratio of the cross sectional radii at these respective locations, is derived. The domains of frequency for which the approximate solution is valid are discussed for piezoelectric and nonpiezoelectric materials.
Nonparallel stability of boundary layers
Nayfeh, Ali H.
1987-01-01
The asymptotic formulations of the nonparallel linear stability of incompressible growing boundary layers are critically reviewed. These formulations can be divided into two approaches. The first approach combines a numerical method with either the method of multiple scales, or the method of averaging, of the Wentzel-Kramers-Brillouin (WKB) approximation; all these methods yield the same result. The second approach combined a multi-structure theory with the method of multiple scales. The first approach yields results that are in excellent agreement with all available experimental data, including the growth rates as well as the neutral stability curve. The derivation of the linear stability of the incompressible growing boundary layers is explained.
Proton Radioactivity Within a Hybrid Metho d
Institute of Scientific and Technical Information of China (English)
张鸿飞
2016-01-01
The proton radioactivity half-lives are investigated theoretically within a hybrid method. The potential barriers preventing the emission of protons are determined in the quasimolecular shape path within a generalized liquid drop model (GLDM). The penetrability is calculated with the Wentzel-Kramers-Brillouin (WKB) approximation. The spectroscopic factor has been taken into account in half-life calculation, which is obtained by employing the relativistic mean field (RMF) theory combined with the Bardeen-Cooper-Schrieffer (BCS) method. The half-lives within the present hybrid method repro-duced the experimental data very well. Some predictions for proton radioactivity are made for future experiments.
Effect of Spin on Thermodynamical Quantities around Reissner-Nordstrom Black Holes
Institute of Scientific and Technical Information of China (English)
LI Zhong-Heng
2005-01-01
@@ Using the quantization procedure involving in the Boulware vacuum state and Killing time t, we evaluate the entropy density, energy density, pressure and equation of state around the Reissner-Nordstrom black hole by the Wentzel-Kramers-Brillouin approximation on the Teukolsky-type master equation. We find that, near the event horizon, there exist subleading order terms with spin dependence beyond the expected Minkowskian hightemperature contribution. In particular, the terms are important and cannot be neglected for near-extremal black hole cases. At large r, the Boulware state approaches the Minkowski vacuum and the theory agrees with that performed in Minkowski spacetime.
Quantum tunneling from rotating black holes with scalar hair in three dimensions
Energy Technology Data Exchange (ETDEWEB)
Sakalli, I.; Gursel, H. [Eastern Mediterranean University, Department of Physics, Mersin-10 (Turkey)
2016-06-15
We study the Hawking radiation of scalar and Dirac particles (fermions) emitted from a rotating scalar hair black hole (RSHBH) within the context of three dimensional (3D) Einstein gravity using non-minimally coupled scalar field theory. Amalgamating the quantum tunneling approach with the Wentzel-Kramers-Brillouin approximation, we obtain the tunneling rates of the outgoing particles across the event horizon. Inserting the resultant tunneling rates into the Boltzmann formula, we then obtain the Hawking temperature (T{sub H}) of the 3D RSHBH. (orig.)
Saleh, Mahamat; Bouetou, Bouetou Thomas; Kofane, Timoleon Crepin
2016-04-01
In this work, quasinormal modes (QNMs) of the Schwarzschild black hole are investigated by taking into account the quantum fluctuations. Gravitational and Dirac perturbations were considered for this case. The Regge-Wheeler gauge and the Dirac equation were used to derive the perturbation equations of the gravitational and Dirac fields respectively and the third order Wentzel-Kramers-Brillouin (WKB) approximation method is used for the computing of the quasinormal frequencies. The results show that due to the quantum fluctuations in the background of the Schwarzschild black hole, the QNMs of the black hole damp more slowly when increasing the quantum correction factor (a), and oscillate more slowly.
Quantum tunneling from rotating black holes with scalar hair in three dimensions
Sakalli, I
2015-01-01
We study the Hawking radiation (HR) of scalar and Dirac particles (fermions) emitted from a rotating scalar hair black hole (RSHBH) within the context of three dimensional ($3D$) Einstein gravity using non-minimally coupled scalar field theory. Amalgamating the quantum tunneling approach with the Wentzel--Kramers--Brillouin (WKB) approximation, we obtain the tunneling rates of the outgoing particles across the event horizon. Inserting the resultant tunneling rates into the Boltzmann formula, we then obtain the Hawking temperature ($T_{H}$) of the $3D$ RSHBH.
Quasinormal Modes of Electromagnetic Perturbation around a Stringy Black Hole
Institute of Scientific and Technical Information of China (English)
ZHANG Yu; GUI Yuan-Xing; YU Fei; WANG Fu-Jun
2007-01-01
We investigate the electromagnetic perturbation around a stringy black hole. A second-order differential equation is obtained for the perturbation. The variation of the effective potential with r is presented. The complex frequencies of the quasinormal modes of electromagnetic perturbation around a stringy black hole are computed by the third Wentzel-Kramers-Brillouin (WKB) approximation. The results show that the parameters resulted from the compactification of higher dimensions can influence the quasinormal complex frequencies, and the Maxwell field around a stringy black hole damps more slowly than that around a Schwarzschild black hole.
Institute of Scientific and Technical Information of China (English)
HAN Yi-Wen; LIU Shou-Yu
2005-01-01
@@ The new equation of state density is obtained by the utilization of the generalized uncertainty relation. With the help of coordinates and the Wentzel-Kramers-Brillouin approximation, direct calculation of the scalar field entropy of the non-state black hole with an internal global monopole is performed. The entropy obtained from the calculation is proportional to the horizon area. The calculation can be free from convergence if without any cutoff, which is different from the brick-wall method. However, the pertinent result is limited.
Hamiltonian theory of nonlinear waves in planetary rings
Stewart, G. R.
1987-01-01
The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.
Saleh, Mahamat; Crépin, Kofané Timoléon
2016-01-01
In this work, quasinormal modes (QNMs) of the Schwarzschild black hole are investigated by taking into account the quantum fluctuations. Gravitational and Dirac perturbations were considered for this case. The Regge-Wheeler gauge and the Dirac equation were used to derive the perturbation equations of the gravitational and Dirac fields respectively and the third order Wentzel-Kramers-Brillouin (WKB) approximation method is used for the computing of the quasinormal frequencies. The results show that due to the quantum fluctuations in the background of the Schwarzschild black hole, the QNMs of the black hole damp more slowly when increasing the quantum correction factor (a), and oscillate more slowly.
Quantum tunneling from rotating black holes with scalar hair in three dimensions
Sakalli, I.; Gursel, H.
2016-06-01
We study the Hawking radiation of scalar and Dirac particles (fermions) emitted from a rotating scalar hair black hole (RSHBH) within the context of three dimensional (3 D) Einstein gravity using non-minimally coupled scalar field theory. Amalgamating the quantum tunneling approach with the Wentzel-Kramers-Brillouin approximation, we obtain the tunneling rates of the outgoing particles across the event horizon. Inserting the resultant tunneling rates into the Boltzmann formula, we then obtain the Hawking temperature (T_H) of the 3 D RSHBH.
Afanasyev, A. N.; Uralov, A. M.
2012-10-01
We present the results of analytical modelling of fast-mode magnetohydrodynamic wave propagation near a 2D magnetic null point. We consider both a linear wave and a weak shock and analyse their behaviour in cold and warm plasmas. We apply the nonlinear geometrical acoustics method based on the Wentzel-Kramers-Brillouin approximation. We calculate the wave amplitude, using the ray approximation and the laws of solitary shock wave damping. We find that a complex caustic is formed around the null point. Plasma heating is distributed in space and occurs at a caustic as well as near the null point due to substantial nonlinear damping of the shock wave. The shock wave passes through the null point even in a cold plasma. The complex shape of the wave front can be explained by the caustic pattern.
Three Dimensional Confinement WKB Revisited
Sinha, A K
2002-01-01
We develop an alternate formalism for radially confined quantum mechanical systems, in the framework of Wentzel-Kramers-Brillouin (WKB) approximation, without considering the Langer correction for the centrifugal term. Rather, following the analysis the Hainz and Grabert, we expand the centrifugal term perturbatively (in powers of $\\hbar$), decomposing it into 2 terms -- the classical centrifugal potential and a quantum correction. To test the validity of our formalism, we apply it explicitly to study the energy spectrum of certain physically relevant, radially confined quantum mechanical systems, viz., the 3-dimensional harmonic oscillator, the hydrogen atom, and the Hulthen potential. As observed by Hainz and Grabert, this approach gives better estimates than the conventional WKB approximation technique (based on Langer modification), even for spatially confined systems.
Afanasyev, Andrey N
2012-01-01
We present the results of analytical modelling of fast-mode magnetohydrodynamic wave propagation near a 2D magnetic null point. We consider both a linear wave and a weak shock and analyse their behaviour in cold and warm plasmas. We apply the nonlinear geometrical acoustics method based on the Wentzel-Kramers-Brillouin approximation. We calculate the wave amplitude, using the ray approximation and the laws of solitary shock wave damping. We find that a complex caustic is formed around the null point. Plasma heating is distributed in space and occurs at a caustic as well as near the null point due to substantial nonlinear damping of the shock wave. The shock wave passes through the null point even in a cold plasma. The complex shape of the wave front can be explained by the caustic pattern.
Tunnelling effects for acoustic waves in slowly varying axisymmetric flow ducts
Nielsen, R. B.; Peake, N.
2016-10-01
The multiple-scales Wentzel-Kramers-Brillouin (WKB) approximation is used to model the propagation of acoustic waves in an axisymmetric duct with a constriction in the presence of mean flow. An analysis of the reflection/transmission process of modes tunnelling through the constriction is conducted, and the key mathematical feature is the presence of two turning points, located at either real axial locations or in the complex plane. The resulting asymptotic solution consists of WKB solutions in regions away from the constriction and an inner solution valid in the near vicinity of the constriction. A solution which is uniformly valid throughout the duct is also derived. A range of test cases are considered, and the importance of accounting for the inner region, even in cases in which the turning points lie away from the real axis, is demonstrated.
Optimum orientation versus orientation averaging description of cluster radioactivity
Seif, W M; Refaie, A I; Amer, L H
2016-01-01
Background: The deformation of the nuclei involved in the cluster decay of heavy nuclei affect seriously their half-lives against the decay. Purpose: We investigate the description of the different decay stages in both the optimum orientation and the orientation-averaged pictures of the cluster decay process. Method: We consider the decays of 232,233,234U and 236,238Pu isotopes. The quantum mechanical knocking frequency and penetration probability based on the Wentzel-Kramers-Brillouin approximation are used to find the decay width. Results: We found that the orientation-averaged decay width is one or two orders of magnitude less than its value along the non-compact optimum orientation. The difference between the two values increases with decreasing the mass number of the emitted cluster. Correspondingly, the extracted preformation probability based on the averaged decay width increases with the same orders of magnitude compared to its value obtained considering the optimum orientation. The cluster preformati...
Harmsen, G E; Cho, H T; Cornell, A S
2016-01-01
In June 2015 the Large Hadron Collider was able to produce collisions with an energy of 13TeV, where collisions at these energy levels may allow for the formation of higher dimensional black holes. In order to detect these higher dimensional black holes we require an understanding of their emission spectra. One way of determining this is by looking at the absorption probabilities associated with the black hole. In this proceedings we will look at the absorption probability for spin-3/2 particles near $N$-dimensional Schwarzschild black holes. We will show how the Unruh method is used to determine these probabilities for low energy particles. We then use the Wentzel-Kramers-Brillouin approximation in order to determine these absorption probabilities for the entire possible energy range.
Hawking Radiation from the Horowitz-Strominger Black Hole
Institute of Scientific and Technical Information of China (English)
FANG Heng-Zhong; HU Ya-Peng; ZHAO Zheng
2005-01-01
@@ When a black hole radiates particles, it losses energy and shrinks, the horizon contracts from its original radius to a new smaller radius. This leads to the separation between the initial and finalradii, which sets the barrier for the particles to tunnel. We develop the work of Parikh [Phys. Rev. Lett. 85 (2000) 5042; Gen. Rel. Gray.36 (2004) 2419] to a Horowitz-Strominger black hole, i.e. applying the Wentzel-Kramers-Brillouin approximation and semi-classical method to calculate the rate of the Hawking radiation. The result agrees with Γ～ e-2ImI =e△SBH. It is also proven that the energy spectrum deviates from exact thermality.
Comparing Ray-Based and Wave-Based Models of Cross-Beam Energy Transfer
Follett, R. K.; Edgell, D. H.; Shaw, J. G.; Froula, D. H.; Myatt, J. F.
2016-10-01
Ray-based models of cross-beam energy transfer (CBET) are used in radiation-hydrodynamics codes to calculate laser-energy deposition. The accuracy of ray-based CBET models is limited by assumptions about the polarization and phase of the interacting laser beams and by the use of a paraxial Wentzel-Kramers-Brillouin (WKB) approximation. A 3-D wave-based solver (LPSE-CBET) is used to study the nonlinear interaction between overlapping laser beams in underdense plasma. A ray-based CBET model is compared to the wave-based model and shows good agreement in simple geometries where the assumptions of the ray-based model are satisfied. Near caustic surfaces, the assumptions of the ray-based model break down and the calculated energy transfer deviates from wave-based calculations. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
Magnetohydrodynamic Shearing Waves
Johnson, B M
2006-01-01
I consider the nonaxisymmetric linear theory of an isothermal magnetohydrodynamic (MHD) shear flow. The analysis is performed in the shearing box, a local model appropriate for a thin disk geometry. Linear perturbations in this model can be decomposed in terms of shearing waves (shwaves), which appear spatially as plane waves in a frame comoving with the shear. The time dependence of these waves cannot in general be expressed in terms of a frequency eigenvalue as in a normal mode decomposition, and numerical integration of a set of first-order amplitude equations is required for a complete characterization of their behavior. Their generic time dependence, however, is oscillatory with slowly-varying frequency and amplitude, and one can construct accurate analytic solutions by applying the Wentzel-Kramers-Brillouin method to the full set of amplitude equations. For the bulk of wavenumber space, therefore, the shwaves are well-approximated as modes with time-dependent frequencies and amplitudes. The incompressiv...
Cluster decay half-lives of trans-lead nuclei based on a finite-range nucleon-nucleon interaction
Adel, A.; Alharbi, T.
2017-02-01
Nuclear cluster radioactivity is investigated using microscopic potentials in the framework of the Wentzel-Kramers-Brillouin approximation of quantum tunneling by considering the Bohr-Sommerfeld quantization condition. The microscopic cluster-daughter potential is numerically constructed in the well-established double-folding model. A realistic M3Y-Paris NN interaction with the finite-range exchange part as well as the ordinary zero-range exchange NN force is considered in the present work. The influence of nuclear deformations on the cluster decay half-lives is investigated. Based on the available experimental data, the cluster preformation factors are extracted from the calculated and the measured half lives of cluster radioactivity. Some useful predictions of cluster emission half-lives are made for emissions of known clusters from possible candidates, which may guide future experiments.
Singh, Navpreet; Gupta, Naveen; Singh, Arvinder
2016-12-01
This paper investigates second harmonic generation (SHG) of an intense Cosh-Gaussian (ChG) laser beam propagating through a preformed underdense collisional plasma with nonlinear absorption. Nonuniform heating of plasma electrons takes place due to the nonuniform irradiance of intensity along the wavefront of laser beam. This nonuniform heating of plasma leads to the self-focusing of the laser beam and thus produces strong density gradients in the transverse direction. The density gradients so generated excite an electron plasma wave (EPW) at pump frequency that interacts with the pump beam to produce its second harmonics. To envision the propagation dynamics of the ChG laser beam, moment theory in Wentzel-Kramers-Brillouin (W.K.B) approximation has been invoked. The effects of nonlinear absorption on self-focusing of the laser beam as well as on the conversion efficiency of its second harmonics have been theoretically investigated.
Asymptotic theory of gravity modes in rotating stars. I. Ray dynamics
Prat, Vincent; Ballot, Jérôme
2015-01-01
Context. The seismology of early-type stars is limited by our uncomplete understanding of gravito-inertial modes. Aims. We develop a short-wavelength asymptotic analysis for gravito-inertial modes in rotating stars. Methods. The Wentzel-Kramers-Brillouin approximation is applied to the equations governing adiabatic small perturbations about a model of uniformly rotating barotropic star. Results. A general eikonal equation, including the effect of the centrifugal deformation, is derived. The dynamics of axisymmetric gravito-inertial rays is solved numerically for polytropic stellar models of increasing rotation and analysed by describing the structure of the phase space. Three different types of phase space structures are distinguished. The first type results from the continuous evolution of structures of the non-rotating integrable phase space. It is predominant in the low-frequency part of the phase space. The second type of structures is island chains associated with stable periodic rays. The third type of ...
Nonideal Quantum Measurement Effects on the Switching Currents Distribution of Josephson Junctions
Pierro, Vincenzo
2016-01-01
The quantum character of Josephson junctions is ordinarily revealed through the analysis of the switching currents, i.e. the current at which a finite voltage appears: A sharp rise of the voltage signals the passage (tunnel) from a trapped state (the zero voltage solution) to a running state (the finite voltage solution). In this context, we investigate the probability distribution of the Josephson junctions switching current taking into account the effect of the bias sweeping rate and introducing a simple nonideal quantum measurements scheme. The measurements are modelled as repeated voltage samplings at discrete time intervals, that is with repeated projections of the time dependent quantum solutions on the static or the running states, to retrieve the probability distribution of the switching currents. The distribution appears to be immune of the quantum Zeno effect, and it is close to, but distinguishable from, the Wentzel-Kramers-Brillouin approximation. For energy barriers comparable to the quantum fund...
Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory.
Schmidt, Steffen; Klevansky, S P
2013-04-28
This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H=p(2)+x(2)(ix)(ε), H=p(2)+(x(2))(δ) and H=p(2)-(x(2))(μ). In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display PT symmetry. To do so, simple arguments that use the Wentzel-Kramers-Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and PT-symmetric quantum theory.
Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics
Bressloff, Paul C.
2010-11-03
We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N→∞, where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first consider a single excitatory population that exhibits bistability in the deterministic limit. The steady-state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network; the relative weighting of the two maxima depends on the system size. For large but finite N, we calculate the exponentially small rate of noise-induced transitions between the resulting metastable states using a Wentzel-Kramers- Brillouin (WKB) approximation and matched asymptotic expansions. We then consider a two-population excitatory or inhibitory network that supports limit cycle oscillations. Using a diffusion approximation, we reduce the dynamics to a neural Langevin equation, and show how the intrinsic noise amplifies subthreshold oscillations (quasicycles). © 2010 The American Physical Society.
Analytical fundamentals of migration in reflection seismics
Directory of Open Access Journals (Sweden)
Ray Arnab K.
2016-06-01
Full Text Available We consider migration in reflection seismics from a completely analytical perspective. We review the basic geometrical ray-path approach to understanding the subject of migration, and discuss the limitations of this method. We stress the importance of the linear differential wave equation in migration. We also review briefly how a wavefield, travelling with a constant velocity, is extrapolated from the differential wave equation, with the aid of Fourier transforms. Then we present a non-numerical treatment by which we derive an asymptotic solution for both the amplitude and the phase of a planar subsurface wavefield that has a vertical velocity variation. This treatment entails the application of the Wentzel-Kramers-Brillouin approximation, whose self-consistency can be established due to a very slow logarithmic variation of the velocity in the vertical direction, a feature that holds more firmly at increasingly greater subsurface depths. For a planar subsurface wavefield, we also demonstrate an equivalence between two apparently different migration algorithms, namely, the constant-velocity Stolt Migration algorithm and the stationary-phase approximation method.
The first-principle study on the stability of trans-HCOH in various solvents
Nur Fadilla, Rizka; Dwi Aisyah, Nufida; Dipojono, Hermawan K.; Rusydi, Febdian
2017-05-01
We attempt to study about the solvent effects of the stability of trans-HCOH molecules using the density-functional theory. Experimentally, trans-HCOH rearranges to H2CO with half-life of two hours [1] which we theoretically proved that it occurs through quantum tunneling. [2] In this work, we calculate the rearrangement rate of the molecules in various solvents. The solvents are selected based on their dielectric constant values, from lower to higher ones; they are benzene, dichloroethane, benzaldehyde, acetone, methanol, ethanediol, dimethylsulfoxide, formic acid, water, and formamide. We use polarizable continuum to model the solvents (PCM). We begin from determining the reaction path from trans-HCOH to H2CO and its corresponding energy barrier using intrinsic reaction coordinate calculation with PCM. Then, we use Wentzel-Kramers-Brillouin (WKB) approximation to calculate the rearrangement rates. The calculation results showed a general trend in which there were arrangement rate was decreasing inversely proportional to dielectric constant value.
Epidemic extinction in a generalized susceptible-infected-susceptible model
Chen, Hanshuang; Huang, Feng; Zhang, Haifeng; Li, Guofeng
2017-01-01
We study the extinction of epidemics in a generalized susceptible-infected-susceptible model, where a susceptible individual becomes infected at the rate λ when contacting m infective individual(s) simultaneously, and an infected individual spontaneously recovers at the rate μ. By employing the Wentzel-Kramers-Brillouin approximation for the master equation, the problem is reduced to finding the zero-energy trajectories in an effective Hamiltonian system, and the mean extinction time depends exponentially on the associated action S and the size of the population N, ˜ \\exp ≤ft(NS\\right) . Because of qualitatively different bifurcation features for m = 1 and m≥slant 2 , we derive independently the expressions of S as a function of the rescaled infection rate λ /μ . For the weak infection, S scales to the distance to the bifurcation with an exponent 2 for m = 1 and 3/2 for m≥slant 2 . Finally, a rare-event simulation method is used to validate the theory.
Ribstein, Bruno; Bölöni, Gergely; Muraschko, Jewgenija; Sgoff, Christine; Wei, Junhong; Achatz, Ulrich
2016-11-01
With the aim of contributing to the improvement of subgrid-scale gravity wave (GW) parameterizations in numerical-weather-prediction and climate models, the comparative relevance in GW drag of direct GW-mean-flow interactions and turbulent wave breakdown are investigated. Of equal interest is how well Wentzel-Kramer-Brillouin (WKB) theory can capture direct wave-mean-flow interactions, that are excluded by applying the steady-state approximation. WKB is implemented in a very efficient Lagrangian ray-tracing approach that considers wave action density in phasespace, thereby avoiding numerical instabilities due to caustics. It is supplemented by a simple wave-breaking scheme based on a static-instability saturation criterion. Idealized test cases of horizontally homogeneous GW packets are considered where wave-resolving Large-Eddy Simulations (LES) provide the reference. In all of theses cases the WKB simulations including direct GW-mean-flow interactions reproduce the LES data, to a good accuracy, already without wave-breaking scheme. The latter provides a next-order correction that is useful for fully capturing the total-energy balance between wave and mean flow. This is not the case when a steady-state WKB implementation is used, as used in present GW parameterizations.
Hassanzadeh, Abdollah; Nitsche, Michael; Armstrong, Souzan; Nabavi, Noushin; Harrison, Rene; Dixon, S. Jeffrey; Langbein, Uwe; Mittler, Silvia
2010-05-01
Planar glass waveguides with a specific number of modes were fabricated by Ag+-Na+ exchange in Schott SG11 glass. The effective refractive indices were determined using m-line spectroscopy in both s- and p-polarization. By using the reversed Wentzel-Kramers-Brillouin approximation, the index profiles were described by a nonlinear diffusion equation. The diffusion coefficients for Ag+ were established, as well as the penetration depth of the evanescent field in an aqueous environment for the different modes. The integrals of |E|2 fields for the evanescent-guided fields were investigated. These are important when evanescent fields are used for illumination in interface microscopy, an alternative method to total internal reflection fluorescence (TIRF) microscopy. The photoluminescent behavior of the waveguides was investigated as a function of ion exchange time and excitation wavelengths. Comparable images were obtained of fluorescently labeled HEK293 cells using TIRF microscopy and waveguide evanescent field fluorescence microscopy. Imaging was performed using HEK293 cells, delivering similar images and information.
Institute of Scientific and Technical Information of China (English)
TANG Jin-yun; TANG Jie; WANG Yuan
2007-01-01
A new analytical model was developed to predict the gravity wave drag (GWD) induced by an isolated 3-dimensional mountain, over which a stratified, nonrotating non-Boussinesq sheared flow is impinged. The model is confined to small amplitude motion and assumes the ambient velocity varying slowly with height. The modified Taylor-Goldstein equation with variable coefficients is solved with a Wentzel-KramersBrillouin (WKB) approximation, formally valid at high Richardson numbers. With this WKB solution, generic formulae of second order accuracy, for the GWD and surface pressure perturbation (both for hydrostatic and non-hydrostatic flow) are presented, enabling a rigorous treatment on the effects by vertical variations in wind profiles. In an ideal test to the circular bell-shaped mountain, it was found that when the wind is linearly sheared,that the GWD decreases as the Richardson number decreases. However, the GWD for a forward sheared wind (wind increases with height) decreases always faster than that for the backward sheared wind (wind deceases with height). This difference is evident whenever the model is hydrostatic or not.
Towards the quantization of Eddington-inspired-Born-Infeld theory
Bouhmadi-López, Mariam; Chen, Che-Yu
2016-11-01
The quantum effects close to the classical big rip singularity within the Eddington-inspired-Born-Infeld theory (EiBI) are investigated through quantum geometrodynamics. It is the first time that this approach is applied to a modified theory constructed upon Palatini formalism. The Wheeler-DeWitt (WDW) equation is obtained and solved based on an alternative action proposed in ref. [1], under two different factor ordering choices. This action is dynamically equivalent to the original EiBI action while it is free of square root of the spacetime curvature. We consider a homogeneous, isotropic and spatially flat universe, which is assumed to be dominated by a phantom perfect fluid whose equation of state is a constant. We obtain exact solutions of the WDW equation based on some specific conditions. In more general cases, we propose a qualitative argument with the help of a Wentzel-Kramers-Brillouin (WKB) approximation to get further solutions. Besides, we also construct an effective WDW equation by simply promoting the classical Friedmann equations. We find that for all the approaches considered, the DeWitt condition hinting singularity avoidance is satisfied. Therefore the big rip singularity is expected to be avoided through the quantum approach within the EiBI theory.
Effect of interface geometry on electron tunnelling in Al/Al2O3/Al junctions
Koberidze, M.; Feshchenko, A. V.; Puska, M. J.; Nieminen, R. M.; Pekola, J. P.
2016-04-01
We investigate how different interface geometries of an Al/Al2O3 junction, a common component of modern tunnel devices, affect electron transport through the tunnel barrier. We study six distinct Al/Al2O3 interfaces which differ in stacking sequences of the metal and the oxide surface atoms and the oxide termination. To construct model potential barrier profiles for each examined geometry, we rely on first-principles density-functional theory (DFT) calculations for the barrier heights and the shapes of the interface regions as well as on experimental data for the barrier widths. We show that even tiny variations in the atomic arrangement at the interface cause significant changes in the tunnel barrier parameters and, consequently, in electron transport properties. Especially, we find that variations in the crucial barrier heights and widths can be as large as 2 eV and 5 Å, respectively. Finally, to gain information about the average properties of the measured junction, we fit the conductance calculated within the Wentzel-Kramers-Brillouin approximation to the experimental data and interpret the fit parameters with the help of the DFT results.
Sausage Waves in Transversely Nonuniform Monolithic Coronal Tubes
Lopin, I.; Nagorny, I.
2015-09-01
We investigate fast sausage waves in a monolithic coronal magnetic tube, modeled as a local density inhomogeneity with a continuous radial profile. This work is a natural extension of our previous results, obtained for a slab loop model for the case of cylindrical geometry. Using Kneser’s oscillating theorem, we provided the criteria for the existence of trapped and leaky wave regimes as a function of the profile features. For a number of density profiles there are only trapped modes for the entire range of longitudinal wave numbers. The phase speed of these modes tends toward the external Alfvén speed in the long wavelength limit. The generalized results were supported by the analytic solution of the wave equation for the specific density profiles. The approximate Wentzel-Kramers-Brillouin solutions allowed us to obtain the desired dispersion relations and to study their properties as a function of the profile parameters. The multicomponent quasi-periodic pulsations in flaring loops, observed on 2001 May 2 and 2002 July 3, are interpreted in terms of the transversely fundamental trapped fast sausage mode with several longitudinal harmonics in a smooth coronal waveguide.
Elementary framework for cold field emission from quantum-confined, non-planar emitters
Energy Technology Data Exchange (ETDEWEB)
Patterson, A. A., E-mail: apatters@mit.edu; Akinwande, A. I. [Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA and Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2015-05-07
For suitably small field emitters, the effects of quantum confinement at the emitter tip may have a significant impact on the emitter performance and total emitted current density (ECD). Since the geometry of a quantum system uniquely determines the magnitude and distribution of its energy levels, a framework for deriving ECD equations from cold field electron emitters of arbitrary geometry and dimensionality is developed. In the interest of obtaining semi-analytical ECD equations, the framework is recast in terms of plane wave solutions to the Schrödinger equation via the use of the Jeffreys-Wentzel-Kramers-Brillouin approximation. To demonstrate the framework's consistency with our previous work and its capabilities in treating emitters with non-planar geometries, ECD equations were derived for the normally unconfined cylindrical nanowire (CNW) and normally confined (NC) CNW emitter geometries. As a function of the emitter radius, the NC CNW emitter ECD profile displayed a strong dependence on the Fermi energy and had an average ECD that exceeded the Fowler-Nordheim equation for typical values of the Fermi energy due to closely spaced, singly degenerate energy levels (excluding electron spin), comparatively large electron supply values, and the lack of a transverse, zero-point energy. Such characteristics suggest that emitters with non-planar geometries may be ideal for emission from both an electron supply and electrostatics perspective.
Asymptotic theory of gravity modes in rotating stars. I. Ray dynamics
Prat, V.; Lignières, F.; Ballot, J.
2016-03-01
Context. The seismology of early-type stars is limited by our incomplete understanding of gravito-inertial modes. Aims: We develop a short-wavelength asymptotic analysis for gravito-inertial modes in rotating stars. Methods: The Wentzel-Kramers-Brillouin approximation was applied to the equations governing adiabatic small perturbations about a model of a uniformly rotating barotropic star. Results: A general eikonal equation, including the effect of the centrifugal deformation, is derived. The dynamics of axisymmetric gravito-inertial rays is solved numerically for polytropic stellar models of increasing rotation and analysed by describing the structure of the phase space. Three different types of phase-space structures are distinguished. The first type results from the continuous evolution of structures of the non-rotating integrable phase space. It is predominant in the low-frequency region of the phase space. The second type of structures are island chains associated with stable periodic rays. The third type of structures are large chaotic regions that can be related to the envelope minimum of the Brunt-Väisälä frequency. Conclusions: Gravito-inertial modes are expected to follow this classification, in which the frequency spectrum is a superposition of sub-spectra associated with these different types of phase-space structures. The detailed confrontation between the predictions of this ray-based asymptotic theory and numerically computed modes will be presented in a companion paper.
The orientation distribution of tunneling-related quantities
Seif, W. M.; Refaie, A. I.; Botros, M. M.
2017-09-01
In the nuclear tunneling processes involving deformed nuclei, most of the tunneling-related quantities depend on the relative orientations of the participating nuclei. In the presence of different multipole deformations, we study the variation of a few relevant quantities for the α-decay and the sub-barrier fusion processes, in an orientation degree of freedom. The knocking frequency and the penetration probability are evaluated within the Wentzel-Kramers-Brillouin approximation. The interaction potential is calculated with Skyrme-type nucleon-nucleon interaction. We found that the width of the potential pocket, the Coulomb barrier radius, the penetration probability, the α-decay width, and the fusion cross-section follow consistently the orientation-angle variation of the radius of the deformed nucleus. The orientation distribution patterns of the pocket width, the barrier radius, the logarithms of the penetrability, the decay width, and the fusion cross-section are found to be highly analogous to pattern of the deformed-nucleus radius. The curve patterns of the orientation angle distributions of the internal pocket depth, the Coulomb barrier height and width, as well as the knocking frequency simulate inversely the variation of the deformed nucleus radius. The predicted orientation behaviors will be of a special interest in predicting the optimum orientations for the tunneling processes.
Towards the Quantization of Eddington-inspired-Born-Infeld Theory
Bouhmadi-López, Mariam
2016-01-01
The quantum effects close to the classical big rip singularity within the Eddington-inspired-Born-Infeld theory (EiBI) are investigated through quantum geometrodynamics. It is the first time that this approach is applied to a modified theory constructed upon Palatini formalism. The Wheeler-DeWitt (WDW) equation is obtained and solved based on an alternative action proposed in Ref.[1], under two different factor ordering choices. This action is dynamically equivalent to the original EiBI action while it is free of square root of the spacetime curvature. We consider a homogeneous, isotropic and spatially flat universe, which is assumed to be dominated by a phantom perfect fluid whose equation of state is a constant. We obtain exact solutions of the WDW equation based on some specific conditions. In more general cases, we propose a qualitative argument with the help of a Wentzel-Kramers-Brillouin (WKB) approximation to get further solutions. Besides, we also construct an effective WDW equation by simply promotin...
Complex Normal-mode Frequencies of External Perturbations in Generalized Schwarzschild Geometry
Institute of Scientific and Technical Information of China (English)
YUAN Ning-Yi; LI Xin-Zhou
2000-01-01
A moditied Wentzel-Kramers-Brillouin approach is used to determine the complex normal-mode frequencies of external perturbations in generalized Schwarzschild geometry. In the λ= 1 case (Schwarzschild geometry), the agreement with other methods is excellent for the low-lying modes. On the contrary, the λ ≠ 1 case of this geometry is unstable against external perturbations
Konosevich, B. I.
2014-07-01
The error of the Wentzel-Kramers-Brillouin solution of the equations describing the angular motion of the axis of symmetry of rotation of a rigid body (projectile) is estimated. It is established that order of this estimate does not depend on whether the low-frequency oscillations of the axis of symmetry are damped or not
Non-uniform Euler-Bernoulli beams’ natural frequencies
Directory of Open Access Journals (Sweden)
Hugo Aya
2011-05-01
Full Text Available This paper has studied the problem of natural frequencies for Euler-Bernoulli beams having non-uniform cross-section. The numerically-obtained solutions were compared to asymptotic solutions obtained by the Wentzel-Kramers-Brillouin (WKB method. It was established that WKB formula precision was higher than 3% for high frequencies (≥ 4 mode.
Wigner phase space distribution via classical adiabatic switching
Energy Technology Data Exchange (ETDEWEB)
Bose, Amartya [Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States); Makri, Nancy [Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States); Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801 (United States)
2015-09-21
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.
Kouznetsov, Igor; Lotko, William
1995-01-01
The 'radial' transport of energy by internal ULF waves, stimulated by dayside magnetospheric boundary oscillations, is analyzed in the framework of one-fluid magnetohydrodynamics. (the term radial is used here to denote the direction orthogonal to geomagnetic flux surfaces.) The model for the inhomogeneous magnetospheric plasma and background magnetic field is axisymmetric and includes radial and parallel variations in the magnetic field, magnetic curvature, plasma density, and low but finite plasma pressure. The radial mode structure of the coupled fast and intermediate MHD waves is determined by numerical solution of the inhomogeneous wave equation; the parallel mode structure is characterized by a Wentzel-Kramer-Brillouin (WKB) approximation. Ionospheric dissipation is modeled by allowing the parallel wave number to be complex. For boudnary oscillations with frequencies in the range from 10 to 48 mHz, and using a dipole model for the background magnetic field, the combined effects of magnetic curvature and finite plasma pressure are shown to (1) enhance the amplitude of field line resonances by as much as a factor of 2 relative to values obtained in a cold plasma or box-model approximation for the dayside magnetosphere; (2) increase the energy flux delivered to a given resonance by a factor of 2-4; and (3) broaden the spectral width of the resonance by a factor of 2-3. The effects are attributed to the existence of an 'Alfven buoyancy oscillation,' which approaches the usual shear mode Alfven wave at resonance, but unlike the shear Alfven mode, it is dispersive at short perpendicular wavelengths. The form of dispersion is analogous to that of an internal atmospheric gravity wave, with the magnetic tension of the curved background field providing the restoring force and allowing radial propagation of the mode. For nominal dayside parameters, the propagation band of the Alfven buoyancy wave occurs between the location of its (field line) resonance and that of the
Bölöni, Gergely; Ribstein, Bruno; Muraschko, Jewgenija; Sgoff, Christine; Wei, Junhong; Achatz, Ulrich
2017-04-01
With the aim of contributing to the improvement of subgrid-scale gravity wave (GW) parameterizations in numerical-weather-prediction and climate models, the comparative relevance in GW drag of direct GW-mean-flow interactions and turbulent wave breakdown are investigated. Of equal interest is how well Wentzel-Kramer-Brillouin (WKB) theory can capture direct wave-mean-flow interactions, that are excluded by applying the steady-state approximation. WKB is implemented in a very efficient Lagrangian ray-tracing approach that considers wave action density in phase-space, thereby avoiding numerical instabilities due to caustics (Muraschko et al., 2015, Quart. J. Roy. Meteor. Soc., 141, 676-697). It is supplemented by a simple wave-breaking scheme based on a static-instability saturation criterion. Idealized test cases of horizontally homogeneous GW packets are considered where wave-resolving Large-Eddy Simulations (LES) provide the reference. In all of theses cases the WKB simulations including direct GW-mean-flow interactions reproduce the LES data, to a good accuracy, already without wave-breaking scheme. The latter provides a next-order correction that is useful for fully capturing the total-energy balance between wave and mean flow. Moreover, a steady-state WKB implementation, as used in present GW parameterizations, and where turbulence provides, by the non-interaction paradigm, the only possibility to affect the mean flow, is much less able to yield reliable results. The GW energy is damped too strongly and induces an oversimplified mean flow. This argues for WKB approaches to GW parameterization that take wave transience into account (Bölöni et al., 2016 J. Atmos. Sci., 73, 4833-4852).
Trejos, Víctor M; Gil-Villegas, Alejandro
2012-05-14
Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); and ibid. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.
Nuclear spin of odd-odd α emitters based on the behavior of α -particle preformation probability
Ismail, M.; Adel, A.; Botros, M. M.
2016-05-01
The preformation probabilities of an α cluster inside radioactive parent nuclei for both odd-even and odd-odd nuclei are investigated. The calculations cover the isotopic chains from Ir to Ac in the mass regions 166 ≤A ≤215 and 77 ≤Z ≤89 . The calculations are employed in the framework of the density-dependent cluster model. A realistic density-dependent nucleon-nucleon (N N ) interaction with a finite-range exchange part is used to calculate the microscopic α -nucleus potential in the well-established double-folding model. The main effect of antisymmetrization under exchange of nucleons between the α and daughter nuclei has been included in the folding model through the finite-range exchange part of the N N interaction. The calculated potential is then implemented to find both the assault frequency and the penetration probability of the α particle by means of the Wentzel-Kramers-Brillouin approximation in combination with the Bohr-Sommerfeld quantization condition. The correlation of the α -particle preformation probability and the neutron and proton level sequences of the parent nucleus as obtained in our previous work is extended to odd-even and odd-odd nuclei to determine the nuclear spin and parities. Two spin coupling rules are used, namely, strong and weak rules to determine the nuclear spin for odd-odd isotopes. This work can be a useful reference for theoretical calculation of undetermined nuclear spin of odd-odd nuclei in the future.
Extinction rates of established spatial populations
Meerson, Baruch; Sasorov, Pavel V.
2011-01-01
This paper deals with extinction of an isolated population caused by intrinsic noise. We model the population dynamics in a “refuge” as a Markov process which involves births and deaths on discrete lattice sites and random migrations between neighboring sites. In extinction scenario I, the zero population size is a repelling fixed point of the on-site deterministic dynamics. In extinction scenario II, the zero population size is an attracting fixed point, corresponding to what is known in ecology as the Allee effect. Assuming a large population size, we develop a WKB (Wentzel-Kramers-Brillouin) approximation to the master equation. The resulting Hamilton’s equations encode the most probable path of the population toward extinction and the mean time to extinction. In the fast-migration limit these equations coincide, up to a canonical transformation, with those obtained, in a different way, by Elgart and Kamenev [Phys. Rev. EPHYADX1539-375510.1103/PhysRevE.70.041106 70, 041106 (2004)]. We classify possible regimes of population extinction with and without an Allee effect and for different types of refuge, and solve several examples analytically and numerically. For a very strong Allee effect, the extinction problem can be mapped into the overdamped limit of the theory of homogeneous nucleation due to Langer [Ann. Phys. (NY)APNYA60003-491610.1016/0003-4916(69)90153-5 54, 258 (1969)]. In this regime, and for very long systems, we predict an optimal refuge size that maximizes the mean time to extinction.
Basic data of ions in He-air mixtures for fluid modeling of low temperature plasma jets
Energy Technology Data Exchange (ETDEWEB)
Yousfi, M.; Benhenni, M.; Eichwald, O.; Merbahi, N. [University of Toulouse, Laplace, UMR CNRS 5213, UPS, 118 Route de Narbonne, 31062 Toulouse (France); Hennad, A. [University of Sciences and Technology of Oran Mohamed Boudiaf, USTO-MB, ETT-LMSE, BP 1505 El M' Naouer, 31000 Oran (Algeria)
2012-08-15
The basic ion data such as interaction potential parameters, elastic and inelastic collision cross sections, transport coefficients (reduced mobility and diffusion coefficients) and reaction coefficients have been analysed and determined for the case of He{sup +}, N{sub 2}{sup +}, and O{sub 2}{sup +} in He-dry air mixtures. The ion transport and reaction coefficients have been determined from an optimized Monte Carlo simulation using calculated elastic and experimentally fitted inelastic collision cross sections. The elastic momentum transfer cross sections have been calculated from a semi-classical JWKB (Jeffreys Wentzel Kramers Brillouin) approximation based on a (6-4) rigid core interaction potential model. The inelastic cross sections have been fitted using the measured reaction coefficients, such as, for instance, the non resonant charge transfer coefficients. The cross section sets involving elastic and inelastic processes were then validated using either the measured reduced mobility whenever available in the literature or the zero-field mobility calculated from Satoh's relation, and potential parameters available in the literature. From the sets of elastic and inelastic collision cross sections thus obtained for the first time for He{sup +}/N{sub 2}, He{sup +}/O{sub 2}, N{sub 2}{sup +}/He, and O{sub 2}{sup +}/He systems, the ion transport and reaction coefficients were calculated in the pure gases over a wide range of the density reduced electric field E/N. Then, from the present cross section and other literature sets, the ion mobility and the longitudinal and transverse diffusion coefficients were calculated for different concentrations of air in He in the case of He{sup +}, N{sub 2}{sup +}, O{sub 2}{sup +}, and also O{sup -} ions.
Electronic Transport Parameter of Carbon Nanotube Metal-Semiconductor On-Tube Heterojunction
Directory of Open Access Journals (Sweden)
Sukirno
2009-03-01
Full Text Available Carbon Nanotubes research is one of the top five hot research topics in physics since 2006 because of its unique properties and functionalities, which leads to wide-range applications. One of the most interesting potential applications is in term of nanoelectronic device. It has been modeled carbon nanotubes heterojunction, which was built from two different carbon nanotubes, that one is metallic and the other one is semiconducting. There are two different carbon nanotubes metal-semiconductor heterojunction. The first one is built from CNT(10,10 as metallic carbon nanotube and CNT (17,0 as semiconductor carbon nanotube. The other one is built from CNT (5,5 as metallic carbon nanotube and CNT (8,0. All of the semiconducting carbon nanotubes are assumed to be a pyridine-like N-doped. Those two heterojunctions are different in term of their structural shape and diameter. It has been calculated their charge distribution and potential profile, which would be useful for the simulation of their electronic transport properties. The calculations are performed by using self-consistent method to solve Non-Homogeneous Poisson’s Equation with aid of Universal Density of States calculation method for Carbon Nanotubes. The calculations are done by varying the doping fraction of the semiconductor carbon nanotubes The electron tunneling transmission coefficient, for low energy region, also has been calculated by using Wentzel-Kramer-Brillouin (WKB approximation. From the calculation results, it is obtained that the charge distribution as well as the potential profile of this device is doping fraction dependent. It is also inferred that the WKB method is fail to be used to calculate whole of the electron tunneling coefficient in this system. It is expected that further calculation for electron tunneling coefficient in higher energy region as well as current-voltage characteristic of this system will become an interesting issue for this carbon nanotube based
Trejos, Víctor M.; Gil-Villegas, Alejandro
2012-05-01
Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); Singh and Sinha J. Chem. Phys. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.
Energy Technology Data Exchange (ETDEWEB)
Nanda, Vikas; Kant, Niti, E-mail: nitikant@yahoo.com [Department of Physics, Lovely Professional University, Phagwara 144411, Punjab (India)
2014-04-15
Enhanced and early relativistic self-focusing of Hermite-cosh-Gaussian (HChG) beam in the plasmas under density transition has been investigated theoretically using Wentzel-Kramers-Brillouin and paraxial ray approximation for mode indices m=0, 1, and 2. The variation of beam width parameter with normalized propagation distance for m=0, 1, and 2 is reported, and it is observed that strong self-focusing occurs as the HChG beam propagates deeper inside the nonlinear medium as spot size shrinks due to highly dense plasmas and the results are presented graphically. A comparative study between self-focusing of HChG beam in the presence and absence of plasmas density transition is reported. The dependency of beam width parameter on the normalized propagation distance for different values of decentered parameter “b” has also been presented graphically. For m=0 and 1, strong self-focusing is reported for b=1.8, and for m=2 and b=1.8, beam gets diffracted. The results obtained indicate the dependency of the self-focusing of the HChG beam on the selected values of decentered parameter. Moreover, proper selection of decentered parameter results strong self-focusing of HChG beam. Stronger self-focusing of laser beam is observed due to the presence of plasma density transition which might be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, etc.
An Emergent Spin-Filter at the interface between Ferromagnetic and Insulating Layered Oxides
Liu, Yaohua
2014-03-01
Complex oxide heterostructures are of keen interest because modified bonding at the interfaces can give rise to fundamentally new phenomena and valuable functionalities. Particularly, an induced magnetization is widely observed at epitaxial interfaces between layered transition-metal oxides; however, much less effort has been spent on investigating how it affects the charge transport properties. To this end, we have studied magnetic tunneling junctions consisting of ferromagnetic manganite La0.7Ca0.3MnO3 (LCMO) and insulating cuprate PrBa2Cu3O7 (PBCO). Contrary to the typically observed steady increase of the tunnel magnetoresistance with decreasing temperature, this system exhibits an anomalous decrease at low temperatures. Polarized neutron reflectometry (PNR) and x-ray magnetic circular dichroism (XMCD) studies on LCMO/PBCO/LCMO trilayers show that the saturation magnetization of the LCMO contacts increase as the temperature decreases. In other words, degradation of the ferromagnetic contacts is ruled out as a cause. Interestingly, there exists induced net Cu moments, which indicates that the spin degeneracy of the conduction band of the PBCO barrier is lifted and thus the barrier becomes spin selective. Our calculations, within the Wentzel-Kramers-Brillouin approximation, show that the complex temperature dependence can arise from a competition between the high positive spin polarization of the manganite electrodes and a negative spin-filter effect from the interfacial Cu magnetization. This work illustrates that the interface-induced magnetization in layered oxide heterostructures can have non-trivial effects on the macroscopic transport properties. Work performed in collaboration with FA Cuellar, Z Sefrioui, C Leon, J Santamaria (Universidad Complutense de Madrid), JW Freeland, SGE te Velthuis (ANL) and MR Fitzsimmons (LANL). Work at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Basic Energy Sciences under contract no
Sanayei, Ali; Schopohl, Nils
2016-07-01
We present numerically accurate calculations of the bound-state spectrum of the highly excited valence electron in the heavy alkali-metal atoms solving the radial Schrödinger eigenvalue problem with a modern spectral collocation method that applies also for a large principal quantum number n ≫1 . As an effective single-particle potential we favor the reputable potential of Marinescu et al. [Phys. Rev. A 49, 982 (1994)], 10.1103/PhysRevA.49.982. Recent quasiclassical calculations of the quantum defect of the valence electron agree for orbital angular momentum l =0 ,1 ,2 ,... overall remarkably well with the results of the numerical calculations, but for the Rydberg states of rubidium and also cesium with l =3 this agreement is less fair. The reason for this anomaly is that in rubidium and cesium the potential acquires for l =3 deep inside the ionic core a second classical region, thus invalidating a standard Wentzel-Kramers-Brillouin (WKB) calculation with two widely spaced turning points. Comparing then our numerical solutions of the radial Schrödinger eigenvalue problem with the uniform analytic WKB approximation of Langer constructed around the remote turning point rn,j ,l (" close=")n -δ0)">+ we observe everywhere a remarkable agreement, apart from a tiny region around the inner turning point rn,j ,l (-). For s states the centrifugal barrier is absent and no inner turning point exists: rn,j ,0 (-)=0 . With the help of an ansatz proposed by Fock we obtain for the s states a second uniform analytic approximation to the radial wave function complementary to the WKB approximation of Langer, which is exact for r →0+ . From the patching condition, that is, for l =0 the Langer and Fock solutions should agree in the intermediate region 0 application we consider recent spectroscopic data for the hyperfine splittings of the isotopes 85Rb and 87Rb and find a remarkable agreement with the predicted scaling relation An,j ,0 (HFS )=const .
Yan, L.; Olsen, S. H.; Escobedo-Cousin, E.; O'Neill, A. G.
2008-05-01
This work presents a detailed study of ultrathin gate oxide integrity in strained Si metal oxide silicon field effect transistors (MOSFETs) fabricated on thin virtual substrates aimed at reducing device self-heating. The gate oxide quality and reliability of the devices are compared to those of simultaneously processed Si control devices and conventional thick virtual substrate devices that have the same Ge content (20%), strained Si channel thickness, and channel strain. The thin virtual substrates offer the same mobility enhancement as the thick virtual substrates (˜100% compared to universal mobility data) and are effective at reducing device self-heating. Up to 90% improvement in gate leakage current is demonstrated for the strained Si n-channel MOSFETs compared to that for the bulk Si controls. The lower leakage arises from the increased electron affinity in tensile strained Si and is significant due to the sizeable strain generated by using wafer-level stressors. The strain-induced leakage reductions also lead to major improvements in stress-induced leakage current (SILC) and oxide reliability. The lower leakage current of the thin and thick virtual substrate devices compares well to theoretical estimates based on the Wentzel-Kramers-Brillouin approximation. Breakdown characteristics also differ considerably between the devices, with the strained Si devices exhibiting a one order of magnitude increase in time to hard breakdown (THBD) compared to the Si control devices following high-field stressing at 17 MV cm-1. The strained Si devices are exempted from soft breakdown. Experimental based analytical leakage modeling has been carried out across the field range for the first time in thin oxides and demonstrates that Poole-Frenkel (PF) emissions followed by Fowler-Nordheim tunneling dominate gate leakage current at low fields in all of the devices. This contrasts to the frequently reported assumption that direct tunneling dominates gate leakage in ultrathin
Stochastic switching in biology: from genotype to phenotype
Bressloff, Paul C.
2017-03-01
There has been a resurgence of interest in non-equilibrium stochastic processes in recent years, driven in part by the observation that the number of molecules (genes, mRNA, proteins) involved in gene expression are often of order 1-1000. This means that deterministic mass-action kinetics tends to break down, and one needs to take into account the discrete, stochastic nature of biochemical reactions. One of the major consequences of molecular noise is the occurrence of stochastic biological switching at both the genotypic and phenotypic levels. For example, individual gene regulatory networks can switch between graded and binary responses, exhibit translational/transcriptional bursting, and support metastability (noise-induced switching between states that are stable in the deterministic limit). If random switching persists at the phenotypic level then this can confer certain advantages to cell populations growing in a changing environment, as exemplified by bacterial persistence in response to antibiotics. Gene expression at the single-cell level can also be regulated by changes in cell density at the population level, a process known as quorum sensing. In contrast to noise-driven phenotypic switching, the switching mechanism in quorum sensing is stimulus-driven and thus noise tends to have a detrimental effect. A common approach to modeling stochastic gene expression is to assume a large but finite system and to approximate the discrete processes by continuous processes using a system-size expansion. However, there is a growing need to have some familiarity with the theory of stochastic processes that goes beyond the standard topics of chemical master equations, the system-size expansion, Langevin equations and the Fokker-Planck equation. Examples include stochastic hybrid systems (piecewise deterministic Markov processes), large deviations and the Wentzel-Kramers-Brillouin (WKB) method, adiabatic reductions, and queuing/renewal theory. The major aim of this
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Li, Xu; Chen, Zhigang; Gong, Jianmin; Taflove, Allen; Backman, Vadim
2004-06-01
Understanding light scattering by nonspherical particles is crucial in modeling the transport of light in realistic structures such as biological tissues. We report the application of novel analytical approaches based on modified Wentzel-Kramers-Brillouin and equiphase-sphere methods that facilitate accurate characterization of light scattering by a wide range of irregularly shaped dielectric particles. We also demonstrate that these approaches have the potential to address the inverse-scattering problem by means of a spectral analysis of the total scattering cross section of arbitrarily shaped particles.
Cosmic Wave Functions with the Brans-Dicke Theory
Institute of Scientific and Technical Information of China (English)
ZHU Zong-Hong
2000-01-01
Using the standard Wentzel-Kramers-Brillouin method, the Wheeler-De Witt equation for the Brans-Dicke theory is solved under three kinds of boundary conditions (proposed by Hattie-Hawking, Vilenkin and Linde, respectively). It is found that, although the gravitational and cosmological"constants" are dynamical and timedependent in the classical models, they will acquire constant values when the universe comes from the quantum creation, and that in particular, the amplitude of the resulting wave function under Linde or Vilenkin boundary conditions reaches its maximum if the cosmological constant is the minimum.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Leike, Reimar H
2016-01-01
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a ranking function that quantifies how "embarrassing" it is to communicate a given approximation. We show that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. We find that this ranking is equivalent to the Kullback-Leibler divergence that is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. We hope that our elementary derivation settles the apparent confusion. We show for example that when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many su...
Rašin, Andrija
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
On Element SDD Approximability
Avron, Haim; Toledo, Sivan
2009-01-01
This short communication shows that in some cases scalar elliptic finite element matrices cannot be approximated well by an SDD matrix. We also give a theoretical analysis of a simple heuristic method for approximating an element by an SDD matrix.
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X...
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Achieser, N I
2004-01-01
A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of pr
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Microscopic theory of nuclear fission: a review
Schunck, N.; Robledo, L. M.
2016-11-01
This article reviews how nuclear fission is described within nuclear density functional theory. A distinction should be made between spontaneous fission, where half-lives are the main observables and quantum tunnelling the essential concept, and induced fission, where the focus is on fragment properties and explicitly time-dependent approaches are often invoked. Overall, the cornerstone of the density functional theory approach to fission is the energy density functional formalism. The basic tenets of this method, including some well-known tools such as the Hartree-Fock-Bogoliubov (HFB) theory, effective two-body nuclear potentials such as the Skyrme and Gogny force, finite-temperature extensions and beyond mean-field corrections, are presented succinctly. The energy density functional approach is often combined with the hypothesis that the time-scale of the large amplitude collective motion driving the system to fission is slow compared to typical time-scales of nucleons inside the nucleus. In practice, this hypothesis of adiabaticity is implemented by introducing (a few) collective variables and mapping out the many-body Schrödinger equation into a collective Schrödinger-like equation for the nuclear wave-packet. The region of the collective space where the system transitions from one nucleus to two (or more) fragments defines what are called the scission configurations. The inertia tensor that enters the kinetic energy term of the collective Schrödinger-like equation is one of the most essential ingredients of the theory, since it includes the response of the system to small changes in the collective variables. For this reason, the two main approximations used to compute this inertia tensor, the adiabatic time-dependent HFB and the generator coordinate method, are presented in detail, both in their general formulation and in their most common approximations. The collective inertia tensor enters also the Wentzel-Kramers-Brillouin (WKB) formula used to extract
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
Approximate calculation of integrals
Krylov, V I
2006-01-01
A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable.The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to t
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximating Stationary Statistical Properties
Institute of Scientific and Technical Information of China (English)
Xiaoming WANG
2009-01-01
It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. The result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.
Directory of Open Access Journals (Sweden)
Malvina Baica
1985-01-01
Full Text Available The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF, and defines it as Generalized Euclidean Algorithm (abbr. GEA to approximate irrationals.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
The Karlqvist approximation revisited
Tannous, C
2015-01-01
The Karlqvist approximation signaling the historical beginning of magnetic recording head theory is reviewed and compared to various approaches progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld edge condition at angular points and leads to exact results.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Approximation Behooves Calibration
DEFF Research Database (Denmark)
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
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.
Directory of Open Access Journals (Sweden)
Maksim Duškin
2015-11-01
Full Text Available Approximation and supposition This article compares exponents of approximation (expressions like Russian около, примерно, приблизительно, более, свыше and the words expressing supposition (for example Russian скорее всего, наверное, возможно. These words are often confused in research, in particular researchers often mention exponents of supposition in case of exponents of approximation. Such approach arouses some objections. The author intends to demonstrate in this article a notional difference between approximation and supposition, therefore the difference between exponents of these two notions. This difference could be described by specifying different attitude of approximation and supposition to the notion of knowledge. Supposition implies speaker’s ignorance of the exact number, while approximation does not mean such ignorance. The article offers examples proving this point of view.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
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 $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Diophantine approximations on fractals
Einsiedler, Manfred; Shapira, Uri
2009-01-01
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0,1]^2, possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod1 : n is a natural number} are uniformly eventually bounded.
Monotone Boolean approximation
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Norton, Andrew H.
1991-01-01
Local spline approximants offer a means for constructing finite difference formulae for numerical solution of PDEs. These formulae seem particularly well suited to situations in which the use of conventional formulae leads to non-linear computational instability of the time integration. This is explained in terms of frequency responses of the FDF.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
Macroscopic Quantum Coherence in Antiferromagnetic Molecular Magnets
Institute of Scientific and Technical Information of China (English)
HU Hui; LO Rong; ZHU Jia-Lin; XIONG Jia-Jiong
2001-01-01
The macroscopic quantum coherence in a biaxial antiferromagnetic molecular magnet in the presence of magnetic field acting parallel to its hard anisotropy axis is studied within the two-sublattice model. On the basis of instanton technique in the spin-coherent-state path-integral representation, both the rigorous Wentzel-Kramers-Brillouin exponent and pre-exponential factor for the ground-state tunnel splitting are obtained. We find that the quantum fluctuations around the classical paths can not only induce a new quantum phase previously reported by Chiolero and Loss (Phys. Rev. Lett. 80 (1998) 169), but also have great influence on the intensity of the ground-state tunnel splitting. Those features clearly have no analogue in the ferromagnetic molecular magnets. We suggest that they may be the universal behaviors in all antiferromagnetic molecular magnets. The analytical results are complemented by exact diagonalization calculation.
Black Hole Creation at the Birth of the Universe
Institute of Scientific and Technical Information of China (English)
Wu Zhong-Chao
2000-01-01
We study the quantum creation of black hole pairs in the (anti-)de Sitter space background. These black hole pairs in the Kerr-Newman family are created from constrained instantons. At the Wentzel-Kramers-Brillouin level, for the chargeless and nonrotating case, the relative creation probability is the exponential of (the negative of) the entropy of the universe. Also for the remaining cases of the family, the creation probability is the exponential of (the negative of) one quarter of the sum of the inner and outer black hole horizon areas. In the absence of a general no-boundary proposal for open universes, we treat the creations of the closed and the open universes in the same way.
Controlling the motion of solitons in BEC by a weakly periodic potential
Institute of Scientific and Technical Information of China (English)
Xi Yu-Dong; Wang Deng-Long; He Zhang-Ming; Ding Jian-Wen
2009-01-01
By developing multiple-scale method combined with Wentzel-Kramer-Brillouin expansion, this paper analytically studies the modulating effect of weakly periodic potential on the dynamical properties of the Bose-Einstein condensates (BEC) trapped in harmonic magnetic traps. A black-grey soliton transition is observed in the BEC trapped in harmonic magnetic potential, due to the weakly periodic potential modulating effect. Meanwhile, it finds that with the slight increase of the weakly periodic potential strength, the velocity of the soliton decreases, while its width firstly decreases then increases, a minimum exists there. These results show that the amplitude, velocity, and width of matter solitons can be effectively managed by means of a weakly periodic potential.
α-decay half-lives in medium mass nuclei
Qian, Yibin; Ren, Zhongzhou; Ni, Dongdong
2011-01-01
Systematical calculations on the α-decay half-lives of even-even medium mass nuclei with 82 cluster model using a two-potential approach. The decay width is achieved in terms of the bound state wavefunction, the scattering wavefunction and the outer potential, where the effective α-nucleus potential is obtained from the double-folded integral of the realistic nucleon-nucleon interaction with the mass distributions of α particle and daughter nucleus. Instead of the Wentzel-Kramers-Brillouin (WKB) barrier penetration probability, the numerical solution of the Schrödinger equation for the bound state is presented. In addition, the shell effect on the α-preformation factor has been taken into account for even-even N = 126 isotones. The calculated α-decay half-lives are found to agree with experimental data with a mean factor of less than 2.
Numerical Validation and Comparison of Three Solar Wind Heating Methods by the SIP-CESE MHD Model
Institute of Scientific and Technical Information of China (English)
YANG Li-Ping; FENG Xue-Shang; XIANG Chang-Qing; JIANG Chao-Wei
2011-01-01
We conduct simulations using the three-dimensional(3D) solar-interplanetary conservation element/solution element(SIP-CESE) maguetohydrodynamic(MHD) model and magnetogram data from a Carrington rotation (CR) 1897 to compare the three commonly used heating methods, I.e. The Wentzel-Kramers-Brillouin(WKB)Alfvén wave heating method, the turbulence heating method and the volumetric heating method. Our results show that all three heating models can basically reproduce the bimodal structure of the solar wind observed near the solar minimum. The results also demonstrate that the major acceleration interval terminates about 4Rs for the turbulence heating method and 1ORs for both the WKB Alfvén wave heating method and the volumetric heating method. The turbulence heating and the volumetric heating methods can capture the observed changing trends by the WIND satellite, while the WKB Alfvén wave heating method does not.
Macroscopic Quantum Coherence in Antiferromagnetic Molecular Magnets
Institute of Scientific and Technical Information of China (English)
HUHui; LURong; 等
2001-01-01
The macroscopic quantum coherence in a biaxial antiferromagnetic molecular magnet in the presence of magnetic field acting parallel to its hard anisotropy axis is studied within the two-sublattice model.On the basis of instanton technique in the spin-coherent-state path-integral representation,both the rigorous Wentzel-Kramers-Brillouin exponent and pre-exponential factor for the ground-state tunnel splitting are obtained.We find that the quantum fluctuations around the classical paths can not only induce a new quantum phase previously reported by Chiolero and Loss (Phys.Rev.Lett.80(1998)169),but also have great influence on the intensity of the ground-state tunnel splitting.Those features clearly have no analogue in the ferromagnetic molecular magnets.We suggest that they may be the universal behaviors in all antiferromagnetic molecular magnets.The analytical results are complemented by exact diagonalization calculation.
Kozyreff, Gregory; Acharyya, Nirmalendu
2016-12-12
We derive formulas for whispering gallery mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent waveguides. The derivation is based on a Wentzel-Kramers-Brillouin (WKB) treatment of Helmholtz equation and can in principle be extended to any number of concentric shells. A distinctive limit analytically arises in the analysis when two shells are brought at very close distance to one another. In that limit, the two shells act as a slot waveguide. If the two shells are sufficiently apart, we identify a structural resonance between the individual shells, which can either lead to a substantial enhancement or suppression of radiation losses.
InSb Nanowires with Built-In GaxIn1-xSb Tunnel Barriers for Majorana Devices
Car, Diana; Conesa-Boj, Sonia; Zhang, Hao; Op het Veld, Roy L. M.; de Moor, Michiel W. A.; Fadaly, Elham M. T.; Gül, Önder; Kölling, Sebastian; Plissard, Sebastien R.; Toresen, Vigdis; Wimmer, Michael T.; Watanabe, Kenji; Taniguchi, Takashi; Kouwenhoven, Leo P.; Bakkers, Erik P. A. M.
2017-02-01
Majorana zero modes (MZMs), prime candidates for topological quantum bits, are detected as zero bias conductance peaks (ZBPs) in tunneling spectroscopy measurements. Implementation of a narrow and high tunnel barrier in the next generation of Majorana devices can help to achieve the theoretically predicted quantized height of the ZBP. We propose a material-oriented approach to engineer a sharp and narrow tunnel barrier by synthesizing a thin axial segment of GaxIn1-xSb within an InSb nanowire. By varying the precursor molar fraction and the growth time, we accurately control the composition and the length of the barriers. The height and the width of the GaxIn1-xSb tunnel barrier are extracted from the Wentzel-Kramers-Brillouin (WKB)-fits to the experimental I-V traces.
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Optimization and approximation
Pedregal, Pablo
2017-01-01
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Energy Technology Data Exchange (ETDEWEB)
Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Approximate Bayesian computation.
Directory of Open Access Journals (Sweden)
Mikael Sunnåker
Full Text Available 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.
Roy, Swapnoneel; Thakur, Ashok Kumar
2008-01-01
Genome rearrangements have been modelled by a variety of primitives such as reversals, transpositions, block moves and block interchanges. We consider such a genome rearrangement primitive Strip Exchanges. Given a permutation, the challenge is to sort it by using minimum number of strip exchanges. A strip exchanging move interchanges the positions of two chosen strips so that they merge with other strips. The strip exchange problem is to sort a permutation using minimum number of strip exchanges. We present here the first non-trivial 2-approximation algorithm to this problem. We also observe that sorting by strip-exchanges is fixed-parameter-tractable. Lastly we discuss the application of strip exchanges in a different area Optical Character Recognition (OCR) with an example.
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points...... in the projection within a tolerance given by the reference curve, and the rulings are lines perpendicular to the projection plane. Application of the method in ship design is given....
S-Approximation: A New Approach to Algebraic Approximation
Directory of Open Access Journals (Sweden)
M. R. Hooshmandasl
2014-01-01
Full Text Available We intend to study a new class of algebraic approximations, called S-approximations, and their properties. We have shown that S-approximations can be used for applied problems which cannot be modeled by inclusion based approximations. Also, in this work, we studied a subclass of S-approximations, called Sℳ-approximations, and showed that this subclass preserves most of the properties of inclusion based approximations but is not necessarily inclusionbased. The paper concludes by studying some basic operations on S-approximations and counting the number of S-min functions.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Operators of Approximations and Approximate Power Set Spaces
Institute of Scientific and Technical Information of China (English)
ZHANG Xian-yong; MO Zhi-wen; SHU Lan
2004-01-01
Boundary inner and outer operators are introduced; and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.
International Conference Approximation Theory XV
Schumaker, Larry
2017-01-01
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Nonlinear Approximation Using Gaussian Kernels
Hangelbroek, Thomas
2009-01-01
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. Our scheme is sophisticated to a degree that it employs even locally Gaussians with varying tensions, and that it resolves local ...
Forms of Approximate Radiation Transport
Brunner, G
2002-01-01
Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.
Approximation by Multivariate Singular Integrals
Anastassiou, George A
2011-01-01
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last cha
Approximations of fractional Brownian motion
Li, Yuqiang; 10.3150/10-BEJ319
2012-01-01
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
BDD Minimization for Approximate Computing
Soeken, Mathias; Grosse, Daniel; Chandrasekharan, Arun; Drechsler, Rolf
2016-01-01
We present Approximate BDD Minimization (ABM) as a problem that has application in approximate computing. Given a BDD representation of a multi-output Boolean function, ABM asks whether there exists another function that has a smaller BDD representation but meets a threshold w.r.t. an error metric. We present operators to derive approximated functions and present algorithms to exactly compute the error metrics directly on the BDD representation. An experimental evaluation demonstrates the app...
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
XU Yuesheng; ZOU Qingsong
2005-01-01
We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.
Diophantine approximation and automorphic spectrum
Ghosh, Anish; Nevo, Amos
2010-01-01
The present paper establishes qunatitative estimates on the rate of diophantine approximation in homogeneous varieties of semisimple algebraic groups. The estimates established generalize and improve previous ones, and are sharp in a number of cases. We show that the rate of diophantine approximation is controlled by the spectrum of the automorphic representation, and is thus subject to the generalised Ramanujan conjectures.
Some results in Diophantine approximation
DEFF Research Database (Denmark)
the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered...
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...
Uniform approximation by (quantum) polynomials
Drucker, A.; de Wolf, R.
2011-01-01
We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectivel
Global approximation of convex functions
Azagra, D
2011-01-01
We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Rytov approximation in electron scattering
Krehl, Jonas; Lubk, Axel
2017-06-01
In this work we introduce the Rytov approximation in the scope of high-energy electron scattering with the motivation of developing better linear models for electron scattering. Such linear models play an important role in tomography and similar reconstruction techniques. Conventional linear models, such as the phase grating approximation, have reached their limits in current and foreseeable applications, most importantly in achieving three-dimensional atomic resolution using electron holographic tomography. The Rytov approximation incorporates propagation effects which are the most pressing limitation of conventional models. While predominately used in the weak-scattering regime of light microscopy, we show that the Rytov approximation can give reasonable results in the inherently strong-scattering regime of transmission electron microscopy.
Rollout sampling approximate policy iteration
Dimitrakakis, C.; Lagoudakis, M.G.
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a
Approximate common divisors via lattices
Cohn, Henry
2011-01-01
We analyze the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common divisor of size N^beta, this improves the size of the error tolerated from N^(beta^2) to N^(beta^((m+1)/m)), under a commonly used heuristic assumption. This gives a more detailed analysis of the hardness assumption underlying the recent fully homomorphic cryptosystem of van Dijk, Gentry, Halevi, and Vaikuntanathan. While these results do not challenge the suggested parameters, a 2^sqrt(n) approximation algorithm for lattice basis reduction in n dimensions could be used to break these parameters. We have implemented our algorithm, and it performs better in practice than the theoretical analysis suggests. Our results fit into a broader context of analogies between cryptanalysis and coding theory. The multivariate approximate common divisor problem is the number-theoretic analogue of noisy multivariate polynomial interpolation, and we ...
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Binary nucleation beyond capillarity approximation
Kalikmanov, V.I.
2010-01-01
Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Nonlinear approximation with redundant dictionaries
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, M.; Gribonval, R.
2005-01-01
In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general......, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non-oversampled wavelet bi-frames we...... can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion....
Mathematical algorithms for approximate reasoning
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
Twisted inhomogeneous Diophantine approximation and badly approximable sets
Harrap, Stephen
2010-01-01
For any real pair i, j geq 0 with i+j=1 let Bad(i, j) denote the set of (i, j)-badly approximable pairs. That is, Bad(i, j) consists of irrational vectors x:=(x_1, x_2) in R^2 for which there exists a positive constant c(x) such that max {||qx_1||^(-i), ||qx_2||^(-j)} > c(x)/q for all q in N. Building on a result of Kurzweil, a new characterization of the set Bad(i, j) in terms of `well-approximable' vectors in the area of `twisted' inhomogeneous Diophantine approximation is established. In addition, it is shown that Bad^x(i, j), the `twisted' inhomogeneous analogue of Bad(i, j), has full Hausdorff dimension 2 when x is chosen from the set Bad(i, j).
Reinforcement Learning via AIXI Approximation
Veness, Joel; Hutter, Marcus; Silver, David
2010-01-01
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
The goal of this thesis is to design, develop, and evaluate new methods for the approximate matching of hierarchical data represented as labeled trees. In approximate matching scenarios two items should be matched if they are similar. Computing the similarity between labeled trees is hard...... as in addition to the data values also the structure must be considered. A well-known measure for comparing trees is the tree edit distance. It is computationally expensive and leads to a prohibitively high run time. Our solution for the approximate matching of hierarchical data are pq-grams. The pq...... formally proof that the pq-gram index can be incrementally updated based on the log of edit operations without reconstructing intermediate tree versions. The incremental update is independent of the data size and scales to a large number of changes in the data. We introduce windowed pq...
Concept Approximation between Fuzzy Ontologies
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Fuzzy ontologies are efficient tools to handle fuzzy and uncertain knowledge on the semantic web; but there are heterogeneity problems when gaining interoperability among different fuzzy ontologies. This paper uses concept approximation between fuzzy ontologies based on instances to solve the heterogeneity problems. It firstly proposes an instance selection technology based on instance clustering and weighting to unify the fuzzy interpretation of different ontologies and reduce the number of instances to increase the efficiency. Then the paper resolves the problem of computing the approximations of concepts into the problem of computing the least upper approximations of atom concepts. It optimizes the search strategies by extending atom concept sets and defining the least upper bounds of concepts to reduce the searching space of the problem. An efficient algorithm for searching the least upper bounds of concept is given.
Approximating Graphic TSP by Matchings
Mömke, Tobias
2011-01-01
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a decreased cost. For the TSP on graphic metrics (graph-TSP), the approach yields a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted to a class of graphs that contains degree three bounded and claw-free graphs, we show that the integrality gap of the Held-Karp relaxation matches the conjectured ratio 4/3. The framework allows for generalizations in a natural way and also leads to a 1.586-approximation algorithm for the traveling salesman path problem on graphic metrics where the start and end vertices are prespecified.
Diophantine approximation and Dirichlet series
Queffélec, Hervé
2013-01-01
This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Approximate Sparse Regularized Hyperspectral Unmixing
Directory of Open Access Journals (Sweden)
Chengzhi Deng
2014-01-01
Full Text Available Sparse regression based unmixing has been recently proposed to estimate the abundance of materials present in hyperspectral image pixel. In this paper, a novel sparse unmixing optimization model based on approximate sparsity, namely, approximate sparse unmixing (ASU, is firstly proposed to perform the unmixing task for hyperspectral remote sensing imagery. And then, a variable splitting and augmented Lagrangian algorithm is introduced to tackle the optimization problem. In ASU, approximate sparsity is used as a regularizer for sparse unmixing, which is sparser than l1 regularizer and much easier to be solved than l0 regularizer. Three simulated and one real hyperspectral images were used to evaluate the performance of the proposed algorithm in comparison to l1 regularizer. Experimental results demonstrate that the proposed algorithm is more effective and accurate for hyperspectral unmixing than state-of-the-art l1 regularizer.
Transfinite Approximation of Hindman's Theorem
Beiglböck, Mathias
2010-01-01
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring of the integers there are arbitrarily long finite sets with the same property. We extend the finite form of Hindman's Theorem to a "transfinite" version for each countable ordinal, and show that Hindman's Theorem is equivalent to the appropriate transfinite approximation holding for every countable ordinal. We then give a proof of Hindman's Theorem by directly proving these transfinite approximations.
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Baraniuk, R. G., DeVore, R. A., Kyriazis, G., Yu, X. M., Near best tree approximation, Adv. Comput. Math.,2002, 16: 357-373.[2]Cohen, A., Dahmen, W., Daubechies, I., DeVore, R., Tree approximation and optimal encoding, Appl. Comput.Harmonic Anal., 2001, 11: 192-226.[3]Dahmen, W., Schneider, R., Xu, Y., Nonlinear functionals of wavelet expansions-adaptive reconstruction and fast evaluation, Numer. Math., 2000, 86: 49-101.[4]DeVore, R. A., Nonlinear approximation, Acta Numer., 1998, 7: 51-150.[5]Davis, G., Mallat, S., Avellaneda, M., Adaptive greedy approximations, Const. Approx., 1997, 13: 57-98.[6]DeVore, R. A., Temlyakov, V. N., Some remarks on greedy algorithms, Adv. Comput. Math., 1996, 5: 173-187.[7]Kashin, B. S., Temlyakov, V. N., Best m-term approximations and the entropy of sets in the space L1, Mat.Zametki (in Russian), 1994, 56: 57-86.[8]Temlyakov, V. N., The best m-term approximation and greedy algorithms, Adv. Comput. Math., 1998, 8:249-265.[9]Temlyakov, V. N., Greedy algorithm and m-term trigonometric approximation, Constr. Approx., 1998, 14:569-587.[10]Hutchinson, J. E., Fractals and self similarity, Indiana. Univ. Math. J., 1981, 30: 713-747.[11]Binev, P., Dahmen, W., DeVore, R. A., Petruchev, P., Approximation classes for adaptive methods, Serdica Math.J., 2002, 28: 1001-1026.[12]Gilbarg, D., Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Berlin: Springer-Verlag,1983.[13]Ciarlet, P. G., The Finite Element Method for Elliptic Problems, New York: North Holland, 1978.[14]Birman, M. S., Solomiak, M. Z., Piecewise polynomial approximation of functions of the class Wαp, Math. Sb.,1967, 73: 295-317.[15]DeVore, R. A., Lorentz, G. G., Constructive Approximation, New York: Springer-Verlag, 1993.[16]DeVore, R. A., Popov, V., Interpolation of Besov spaces, Trans. Amer. Math. Soc., 1988, 305: 397-414.[17]Devore, R., Jawerth, B., Popov, V., Compression of wavelet decompositions, Amer. J. Math., 1992, 114: 737-785.[18]Storozhenko, E
WKB Approximation in Noncommutative Gravity
Directory of Open Access Journals (Sweden)
Maja Buric
2007-12-01
Full Text Available We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the high-frequency waves on the flat background.
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
Truthful approximations to range voting
DEFF Research Database (Denmark)
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
2013-01-01
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...
Rational approximation of vertical segments
Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte
2007-08-01
In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.
Approximation on the complex sphere
Alsaud, Huda; Kushpel, Alexander; Levesley, Jeremy
2012-01-01
We develop new elements of harmonic analysis on the complex sphere on the basis of which Bernstein's, Jackson's and Kolmogorov's inequalities are established. We apply these results to get order sharp estimates of $m$-term approximations. The results obtained is a synthesis of new results on classical orthogonal polynomials, harmonic analysis on manifolds and geometric properties of Euclidean spaces.
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...
Pythagorean Approximations and Continued Fractions
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…
Approximation of Surfaces by Cylinders
DEFF Research Database (Denmark)
Randrup, Thomas
1998-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...
Low Rank Approximation in $G_0W_0$ Approximation
Shao, Meiyue; Yang, Chao; Liu, Fang; da Jornada, Felipe H; Deslippe, Jack; Louie, Steven G
2016-01-01
The single particle energies obtained in a Kohn--Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The $G_0W_0$ approximation is a widely used technique in which the self energy is expressed as the convolution of a non-interacting Green's function ($G_0$) and a screened Coulomb interaction ($W_0$) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating $W_0$ at multiple frequencies. In this paper, we discuss how the cos...
Approximate Inference for Wireless Communications
DEFF Research Database (Denmark)
Hansen, Morten
This thesis investigates signal processing techniques for wireless communication receivers. The aim is to improve the performance or reduce the computationally complexity of these, where the primary focus area is cellular systems such as Global System for Mobile communications (GSM) (and extensions...... complexity can potentially lead to limited power consumption, which translates into longer battery life-time in the handsets. The scope of the thesis is more specifically to investigate approximate (nearoptimal) detection methods that can reduce the computationally complexity significantly compared...... to the optimal one, which usually requires an unacceptable high complexity. Some of the treated approximate methods are based on QL-factorization of the channel matrix. In the work presented in this thesis it is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum...
Hydrogen Beyond the Classic Approximation
Scivetti, I
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Validity of the eikonal approximation
Kabat, D
1992-01-01
We summarize results on the reliability of the eikonal approximation in obtaining the high energy behavior of a two particle forward scattering amplitude. Reliability depends on the spin of the exchanged field. For scalar fields the eikonal fails at eighth order in perturbation theory, when it misses the leading behavior of the exchange-type diagrams. In a vector theory the eikonal gets the exchange diagrams correctly, but fails by ignoring certain non-exchange graphs which dominate the asymptotic behavior of the full amplitude. For spin--2 tensor fields the eikonal captures the leading behavior of each order in perturbation theory, but the sum of eikonal terms is subdominant to graphs neglected by the approximation. We also comment on the eikonal for Yang-Mills vector exchange, where the additional complexities of the non-abelian theory may be absorbed into Regge-type modifications of the gauge boson propagators.
Approximate Privacy: Foundations and Quantification
Feigenbaum, Joan; Schapira, Michael
2009-01-01
Increasing use of computers and networks in business, government, recreation, and almost all aspects of daily life has led to a proliferation of online sensitive data about individuals and organizations. Consequently, concern about the privacy of these data has become a top priority, particularly those data that are created and used in electronic commerce. There have been many formulations of privacy and, unfortunately, many negative results about the feasibility of maintaining privacy of sensitive data in realistic networked environments. We formulate communication-complexity-based definitions, both worst-case and average-case, of a problem's privacy-approximation ratio. We use our definitions to investigate the extent to which approximate privacy is achievable in two standard problems: the second-price Vickrey auction and the millionaires problem of Yao. For both the second-price Vickrey auction and the millionaires problem, we show that not only is perfect privacy impossible or infeasibly costly to achieve...
Validity of the Eikonal Approximation
Kabat, Daniel
1992-01-01
We summarize results on the reliability of the eikonal approximation in obtaining the high energy behavior of a two particle forward scattering amplitude. Reliability depends on the spin of the exchanged field. For scalar fields the eikonal fails at eighth order in perturbation theory, when it misses the leading behavior of the exchange-type diagrams. In a vector theory the eikonal gets the exchange diagrams correctly, but fails by ignoring certain non-exchange graphs which dominate the asymp...
Approximate Counting of Graphical Realizations.
Erdős, 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, Erdős 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, Erdős 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.
Approximate Counting of Graphical Realizations.
Directory of Open Access Journals (Sweden)
Péter L Erdős
Full Text Available 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, Erdős 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, Erdős 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.
Many Faces of Boussinesq Approximations
Vladimirov, Vladimir A
2016-01-01
The \\emph{equations of Boussinesq approximation} (EBA) for an incompressible and inhomogeneous in density fluid are analyzed from a viewpoint of the asymptotic theory. A systematic scaling shows that there is an infinite number of related asymptotic models. We have divided them into three classes: `poor', `reasonable' and `good' Boussinesq approximations. Each model can be characterized by two parameters $q$ and $k$, where $q =1, 2, 3, \\dots$ and $k=0, \\pm 1, \\pm 2,\\dots$. Parameter $q$ is related to the `quality' of approximation, while $k$ gives us an infinite set of possible scales of velocity, time, viscosity, \\emph{etc.} Increasing $q$ improves the quality of a model, but narrows the limits of its applicability. Parameter $k$ allows us to vary the scales of time, velocity and viscosity and gives us the possibility to consider any initial and boundary conditions. In general, we discover and classify a rich variety of possibilities and restrictions, which are hidden behind the routine use of the Boussinesq...
Rollout Sampling Approximate Policy Iteration
Dimitrakakis, Christos
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions which focus on policy representation using classifiers and address policy learning as a supervised learning problem. This paper proposes variants of an improved policy iteration scheme which addresses the core sampling problem in evaluating a policy through simulation as a multi-armed bandit machine. The resulting algorithm offers comparable performance to the previous algorithm achieved, however, with significantly less computational effort. An order of magnitude improvement is demonstrated experimentally in two standard reinforcement learning domains: inverted pendulum and mountain-car.
Approximate Deconvolution Reduced Order Modeling
Xie, Xuping; Wang, Zhu; Iliescu, Traian
2015-01-01
This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution(AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient(10^{-3})
Approximation for Bayesian Ability Estimation.
1987-02-18
posterior pdfs of ande are given by p(-[Y) p(F) F P((y lei’ j)P )d. SiiJ i (4) a r~d p(e Iy) - p(t0) 1 J i P(Yij ei, (5) As shown in Tsutakawa and Lin...inverse A Hessian of the log of (27) with respect to , evaulatedat a Then, under regularity conditions, the marginal posterior pdf of O is...two-way contingency tables. Journal of Educational Statistics, 11, 33-56. Lindley, D.V. (1980). Approximate Bayesian methods. Trabajos Estadistica , 31
Plasma Physics Approximations in Ares
Energy Technology Data Exchange (ETDEWEB)
Managan, R. A.
2015-01-08
Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, F_{n}( μ/θ ), the chemical potential, μ or ζ = ln(1+e^{ μ/θ} ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A^{α} (ζ ),A^{β} (ζ ), ζ, f(ζ ) = (1 + e^{-μ/θ})F_{1/2}(μ/θ), F_{1/2}'/F_{1/2}, F_{c}^{α}, and F_{c}^{β}. In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.
Rational approximations to fluid properties
Kincaid, J. M.
1990-05-01
The purpose of this report is to summarize some results that were presented at the Spring AIChE meeting in Orlando, Florida (20 March 1990). We report on recent attempts to develop a systematic method, based on the technique of rational approximation, for creating mathematical models of real-fluid equations of state and related properties. Equation-of-state models for real fluids are usually created by selecting a function tilde p(T,rho) that contains a set of parameters (gamma sub i); the (gamma sub i) is chosen such that tilde p(T,rho) provides a good fit to the experimental data. (Here p is the pressure, T the temperature and rho is the density). In most cases, a nonlinear least-squares numerical method is used to determine (gamma sub i). There are several drawbacks to this method: one has essentially to guess what tilde p(T,rho) should be; the critical region is seldom fit very well and nonlinear numerical methods are time consuming and sometimes not very stable. The rational approximation approach we describe may eliminate all of these drawbacks. In particular, it lets the data choose the function tilde p(T,rho) and its numerical implementation involves only linear algorithms.
Dodgson's Rule Approximations and Absurdity
McCabe-Dansted, John C
2010-01-01
With the Dodgson rule, cloning the electorate can change the winner, which Young (1977) considers an "absurdity". Removing this absurdity results in a new rule (Fishburn, 1977) for which we can compute the winner in polynomial time (Rothe et al., 2003), unlike the traditional Dodgson rule. We call this rule DC and introduce two new related rules (DR and D&). Dodgson did not explicitly propose the "Dodgson rule" (Tideman, 1987); we argue that DC and DR are better realizations of the principle behind the Dodgson rule than the traditional Dodgson rule. These rules, especially D&, are also effective approximations to the traditional Dodgson's rule. We show that, unlike the rules we have considered previously, the DC, DR and D& scores differ from the Dodgson score by no more than a fixed amount given a fixed number of alternatives, and thus these new rules converge to Dodgson under any reasonable assumption on voter behaviour, including the Impartial Anonymous Culture assumption.
Approximation by double Walsh polynomials
Directory of Open Access Journals (Sweden)
Ferenc Móricz
1992-01-01
Full Text Available We study the rate of approximation by rectangular partial sums, Cesàro means, and de la Vallée Poussin means of double Walsh-Fourier series of a function in a homogeneous Banach space X. In particular, X may be Lp(I2, where 1≦p<∞ and I2=[0,1×[0,1, or CW(I2, the latter being the collection of uniformly W-continuous functions on I2. We extend the results by Watari, Fine, Yano, Jastrebova, Bljumin, Esfahanizadeh and Siddiqi from univariate to multivariate cases. As by-products, we deduce sufficient conditions for convergence in Lp(I2-norm and uniform convergence on I2 as well as characterizations of Lipschitz classes of functions. At the end, we raise three problems.
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."
Approximate reduction of dynamical systems
Tabuada, Paulo; Julius, Agung; Pappas, George J
2007-01-01
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with mechanical systems with symmetry--which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a lower dimensional space. These concepts are illustrated on a series of examples.
Diophantine approximations and Diophantine equations
Schmidt, Wolfgang M
1991-01-01
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
Truthful approximations to range voting
DEFF Research Database (Denmark)
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...... maximization in this setting. With m being the number of alternatives, we exhibit a randomized truthful-in-expectation ordinal mechanism implementing an outcome whose expected social welfare is at least an Omega(m^{-3/4}) fraction of the social welfare of the socially optimal alternative. On the other hand, we...... show that for sufficiently many agents and any truthful-in-expectation ordinal mechanism, there is a valuation profile where the mechanism achieves at most an O(m^{-{2/3}) fraction of the optimal social welfare in expectation. We get tighter bounds for the natural special case of m = 3...
Approximation of Surfaces by Cylinders
DEFF Research Database (Denmark)
Randrup, Thomas
1998-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...... projection of the surface onto this plane, a reference curve is determined by use of methods for thinning of binary images. Finally, the cylinder surface is constructed as follows: the directrix of the cylinder surface is determined by a least squares method minimizing the distance to the points...... in the projection within a tolerance given by the reference curve, and the rulings are lines perpendicular to the projection plane. Application of the method in ship design is given....
Analytical approximations for spiral waves
Energy Technology Data Exchange (ETDEWEB)
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)
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 Ω 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 Ω(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.
On quantum and approximate privacy
Klauck, H
2001-01-01
This paper studies privacy in communication complexity. The focus is on quantum versions of the model and on protocols with only approximate privacy against honest players. We show that the privacy loss (the minimum divulged information) in computing a function can be decreased exponentially by using quantum protocols, while the class of privately computable functions (i.e., those with privacy loss 0) is not increased by quantum protocols. Quantum communication combined with small information leakage on the other hand makes certain functions computable (almost) privately which are not computable using quantum communication without leakage or using classical communication with leakage. We also give an example of an exponential reduction of the communication complexity of a function by allowing a privacy loss of o(1) instead of privacy loss 0.
IONIS: Approximate atomic photoionization intensities
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
Approximate analytic solutions to the NPDD: Short exposure approximations
Close, Ciara E.; Sheridan, John T.
2014-04-01
There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more 'opaque'. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects resulting from the photo-polymerisation process, and have accurately described these processes in a number of different materials. It is our aim to develop accessible mathematical expressions which provide physical insights and simple quantitative predictions of practical value to material designers and users. In this paper, starting with the Non-Local Photo-Polymerisation Driven Diffusion (NPDD) model coupled integro-differential equations, we first simplify these equations and validate the accuracy of the resulting approximate model. This new set of governing equations are then used to produce accurate analytic solutions (polynomials) describing the evolution of the monomer and polymer concentrations, and the grating refractive index modulation, in the case of short low intensity sinusoidal exposures. The physical significance of the results and their consequences for holographic data storage (HDS) are then discussed.
Randomized approximate nearest neighbors algorithm.
Jones, Peter Wilcox; Osipov, Andrei; Rokhlin, Vladimir
2011-09-20
We present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {x(j)} in R(d), the algorithm attempts to find k nearest neighbors for each of x(j), where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T·N·(d·(log d) + k·(d + log k)·(log N)) + N·k(2)·(d + log k), with T the number of iterations performed. The memory requirements of the procedure are of the order N·(d + k). A by-product of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among {x(j)} for an arbitrary point x ∈ R(d). The cost of each such query is proportional to T·(d·(log d) + log(N/k)·k·(d + log k)), and the memory requirements for the requisite data structure are of the order N·(d + k) + T·(d + N). The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme's behavior for certain types of distributions of {x(j)} and illustrate its performance via several numerical examples.
Obtaining exact value by approximate computations
Institute of Scientific and Technical Information of China (English)
Jing-zhong ZHANG; Yong FENG
2007-01-01
Numerical approximate computations can solve large and complex problems fast. They have the advantage of high efficiency. However they only give approximate results, whereas we need exact results in some fields. There is a gap between approximate computations and exact results.In this paper, we build a bridge by which exact results can be obtained by numerical approximate computations.
Fuzzy Set Approximations in Fuzzy Formal Contexts
Institute of Scientific and Technical Information of China (English)
Mingwen Shao; Shiqing Fan
2006-01-01
In this paper, a kind of multi-level formal concept is introduced. Based on the proposed multi-level formal concept, we present a pair of rough fuzzy set approximations within fuzzy formal contexts. By the proposed rough fuzzy set approximations, we can approximate a fuzzy set according to different precision level. We discuss the properties of the proposed approximation operators in detail.
Obtaining exact value by approximate computations
Institute of Scientific and Technical Information of China (English)
2007-01-01
Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2004-01-01
We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation...... with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
We study various approximation classes associated with $m$-term approximation by elements from a (possibly redundant) dictionary in a Banach space. The standard approximation class associated with the best $m$-term approximation is compared to new classes defined by considering $m......$-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space...
APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION
Institute of Scientific and Technical Information of China (English)
杨守志; 程正兴; 唐远炎
2003-01-01
An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function.
Bernstein-type approximations of smooth functions
Directory of Open Access Journals (Sweden)
Andrea Pallini
2007-10-01
Full Text Available The Bernstein-type approximation for smooth functions is proposed and studied. We propose the Bernstein-type approximation with definitions that directly apply the binomial distribution and the multivariate binomial distribution. The Bernstein-type approximations generalize the corresponding Bernstein polynomials, by considering definitions that depend on a convenient approximation coefficient in linear kernels. In the Bernstein-type approximations, we study the uniform convergence and the degree of approximation. The Bernstein-type estimators of smooth functions of population means are also proposed and studied.
Applications of Discrepancy Theory in Multiobjective Approximation
Glaßer, Christian; Witek, Maximilian
2011-01-01
We apply a multi-color extension of the Beck-Fiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1/2-approximable on directed graphs and randomized 2/3-approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiablilty problem is 1/2-approximable.
Fractal Trigonometric Polynomials for Restricted Range Approximation
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016-05-01
One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.
Axiomatic Characterizations of IVF Rough Approximation Operators
Directory of Open Access Journals (Sweden)
Guangji Yu
2014-01-01
Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.
Some relations between entropy and approximation numbers
Institute of Scientific and Technical Information of China (English)
郑志明
1999-01-01
A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
$-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space...
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
Advanced Concepts and Methods of Approximate Reasoning
1989-12-01
and L. Valverde. On mode and implication in approximate reasoning. In M.M. Gupta, A. Kandel, W. Bandler , J.B. Kiszka, editors, Approximate Reasoning and...190, 1981. [43] E. Trillas and L. Valverde. On mode and implication in approximate reasoning. In M.M. Gupta, A. Kandel, W. Bandler , J.B. Kiszka
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.
Approximate Nearest Neighbor Queries among Parallel Segments
DEFF Research Database (Denmark)
Emiris, Ioannis Z.; Malamatos, Theocharis; Tsigaridas, Elias
2010-01-01
We develop a data structure for answering efficiently approximate nearest neighbor queries over a set of parallel segments in three dimensions. We connect this problem to approximate nearest neighbor searching under weight constraints and approximate nearest neighbor searching on historical data...
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...... characterization of the approximation spaces is derived....
Nonlinear approximation with bi-framelets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten; Gribonval, Rémi
2005-01-01
We study the approximation in Lebesgue spaces of wavelet bi-frame systems given by translations and dilations of a finite set of generators. A complete characterization of the approximation spaces associated with best m-term approximation of wavelet bi-framelet systems is given...
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
Benyin Fu
2016-05-01
In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use the techniques of Ozawa’s to prove that a fine hyperbolic graph has the metric invariant translation approximation property.
Resonant-state expansion Born Approximation
Doost, M B
2015-01-01
The Born Approximation is a fundamental formula in Physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. I extend the Born Approximation by including in the formula the Fourier transform of a truncated basis of the infinite number of appropriately normalised resonant states. This extension of the Born Approximation is named the Resonant-State Expansion Born Approximation or RSE Born Approximation. The resonant-states of the system can be calculated using the recently discovered RSE perturbation theory for electrodynamics and normalised correctly to appear in spectral Green's functions via the flux volume normalisation.
Canonical Sets of Best L1-Approximation
Directory of Open Access Journals (Sweden)
Dimiter Dryanov
2012-01-01
Full Text Available In mathematics, the term approximation usually means either interpolation on a point set or approximation with respect to a given distance. There is a concept, which joins the two approaches together, and this is the concept of characterization of the best approximants via interpolation. It turns out that for some large classes of functions the best approximants with respect to a certain distance can be constructed by interpolation on a point set that does not depend on the choice of the function to be approximated. Such point sets are called canonical sets of best approximation. The present paper summarizes results on canonical sets of best L1-approximation with emphasis on multivariate interpolation and best L1-approximation by blending functions. The best L1-approximants are characterized as transfinite interpolants on canonical sets. The notion of a Haar-Chebyshev system in the multivariate case is discussed also. In this context, it is shown that some multivariate interpolation spaces share properties of univariate Haar-Chebyshev systems. We study also the problem of best one-sided multivariate L1-approximation by sums of univariate functions. Explicit constructions of best one-sided L1-approximants give rise to well-known and new inequalities.
Mapping moveout approximations in TI media
Stovas, Alexey
2013-11-21
Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.
An Approximate Approach to Automatic Kernel Selection.
Ding, Lizhong; Liao, Shizhong
2016-02-02
Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
On Gakerkin approximations for the quasigeostrophic equations
Rocha, Cesar B; Grooms, Ian
2015-01-01
We study the representation of approximate solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes. In particular, we show that standard modes are compatible with nonzero buoyancy at the surfaces and can be used to solve the Eady problem. We extend two existing Galerkin approaches (A and B) and develop a new Galerkin approximation (C). Approximation A, due to Flierl (1978), represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith (2009b), represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series, but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the b...
Improving biconnectivity approximation via local optimization
Energy Technology Data Exchange (ETDEWEB)
Ka Wong Chong; Tak Wah Lam [Univ. of Hong Kong (Hong Kong)
1996-12-31
The problem of finding the minimum biconnected spanning subgraph of an undirected graph is NP-hard. A lot of effort has been made to find biconnected spanning subgraphs that approximate to the minimum one as close as possible. Recently, new polynomial-time (sequential) approximation algorithms have been devised to improve the approximation factor from 2 to 5/3 , then 3/2, while NC algorithms have also been known to achieve 7/4 + {epsilon}. This paper presents a new technique which can be used to further improve parallel approximation factors to 5/3 + {epsilon}. In the sequential context, the technique reveals an algorithm with a factor of {alpha} + 1/5, where a is the approximation factor of any 2-edge connectivity approximation algorithm.
Frankenstein's Glue: Transition functions for approximate solutions
Yunes, N
2006-01-01
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate solutions together. In particular, we propose certain sufficient conditions on these functions and proof that these conditions guarantee that the joined solution still satisfies the Einstein equations to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the...
Floating-Point $L^2$-Approximations
Brisebarre, Nicolas; Hanrot, Guillaume
2007-01-01
International audience; Computing good polynomial approximations to usual functions is an important topic for the computer evaluation of those functions. These approximations can be good under several criteria, the most desirable being probably that the relative error is as small as possible in the $L^{\\infty}$ sense, i.e. everywhere on the interval under study. In the present paper, we investigate a simpler criterion, the $L^2$ case. Though finding a best polynomial $L^2$-approximation with ...
Metric Diophantine approximation on homogeneous varieties
Ghosh, Anish; Nevo, Amos
2012-01-01
We develop the metric theory of Diophantine approximation on homogeneous varieties of semisimple algebraic groups and prove results analogous to the classical Khinchin and Jarnik theorems. In full generality our results establish simultaneous Diophantine approximation with respect to several completions, and Diophantine approximation over general number fields using S-algebraic integers. In several important examples, the metric results we obtain are optimal. The proof uses quantitative equidistribution properties of suitable averaging operators, which are derived from spectral bounds in automorphic representations.
Approximately liner phase IIR digital filter banks
J. D. Ćertić; M. D. Lutovac; L. D. Milić
2013-01-01
In this paper, uniform and nonuniform digital filter banks based on approximately linear phase IIR filters and frequency response masking technique (FRM) are presented. Both filter banks are realized as a connection of an interpolated half-band approximately linear phase IIR filter as a first stage of the FRM design and an appropriate number of masking filters. The masking filters are half-band IIR filters with an approximately linear phase. The resulting IIR filter banks are compared with li...
A Note on Generalized Approximation Property
Directory of Open Access Journals (Sweden)
Antara Bhar
2013-01-01
Full Text Available We introduce a notion of generalized approximation property, which we refer to as --AP possessed by a Banach space , corresponding to an arbitrary Banach sequence space and a convex subset of , the class of bounded linear operators on . This property includes approximation property studied by Grothendieck, -approximation property considered by Sinha and Karn and Delgado et al., and also approximation property studied by Lissitsin et al. We characterize a Banach space having --AP with the help of -compact operators, -nuclear operators, and quasi--nuclear operators. A particular case for ( has also been characterized.
Upper Bounds on Numerical Approximation Errors
DEFF Research Database (Denmark)
Raahauge, Peter
2004-01-01
This paper suggests a method for determining rigorous upper bounds on approximationerrors of numerical solutions to infinite horizon dynamic programming models.Bounds are provided for approximations of the value function and the policyfunction as well as the derivatives of the value function....... The bounds apply to moregeneral problems than existing bounding methods do. For instance, since strict concavityis not required, linear models and piecewise linear approximations can bedealt with. Despite the generality, the bounds perform well in comparison with existingmethods even when applied...... to approximations of a standard (strictly concave)growth model.KEYWORDS: Numerical approximation errors, Bellman contractions, Error bounds...
TMB: Automatic differentiation and laplace approximation
DEFF Research Database (Denmark)
Kristensen, Kasper; Nielsen, Anders; Berg, Casper Willestofte
2016-01-01
computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects...... are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (approximate to 10(6)) and parameters (approximate to 10...
Single-electron tunneling by using a two-dimensional Corbino nano-scale disk
Energy Technology Data Exchange (ETDEWEB)
Taira, H., E-mail: taira.hisao@s.hokkyodai.ac.jp [Faculty of Education, Hokkaido University of Education, Kita-ku, Sapporo 002-8502 (Japan); Suzuki, A., E-mail: asuzuki@rs.kagu.tus.ac.jp [Department of Physics, Faculty of Science, Tokyo University of Science, Tokyo 162-8601 (Japan)
2015-09-15
We investigate a single-electron tunneling effect of two-dimensional electron systems formed in the Corbino nano-scale disk. By controlling bias and gate voltages, the transistor using this effect is able to control electrons one by one. The present study focuses on the electronic transmission probability affected by the charging energy in the Corbino-type single-electron transistor. We reformulated the Schrödinger equation for an electron in the Corbino disk in order to consider the effect of the curvature of the disk, taking into account the charging effect on the performance of the Corbino-type single-electron transistor. We formulated the transmission probability of the electron by applying the Wentzel-Kramers-Brillouin (WKB) method. The electron’s energy in the formula of the transmission probability is then associated to the energy eigenvalue of the Schrödinger equation for an electron in an effective confining potential. We numerically solved the Schrödinger equation to evaluate the transmission probability. Our results show that the transmission probability strongly depends on the charging energy stored in the Corbino disk depending on its size.
Asymptotic Laws of Thermovibrational Convecton in a Horizontal Fluid Layer
Smorodin, B. L.; Myznikova, B. I.; Keller, I. O.
2017-02-01
Theoretical study of convective instability is applied to a horizontal layer of incompressible single-component fluid subjected to the uniform steady gravity, longitudinal vibrations of arbitrary frequency and initial temperature difference. The mathematical model of thermovibrational convection has the form of initial boundary value problem for the Oberbeck-Boussinesq system of equations. The problems are solved using different simulation strategies, like the method of averaging, method of multiple scales, Galerkin approach, Wentzel-Kramers-Brillouin method and Floquet technique. The numerical analysis has shown that the effect of vibrations on the stability threshold is complex: vibrations can either stabilize or destabilize the basic state depending on values of the parameters. The influence of the Prandtl number on the instability thresholds is investigated. The asymptotic behaviour of critical values of the parameters is studied in two limiting cases: (i) small amplitude and (ii) low frequency of vibration. In case (i), the instability is due to the influence of thermovibrational mechanism on the classical Rayleigh-Benard convective instability. In case (ii), the nature of the instability is related to the instability of oscillating counter-streams with a cubic profile.
Jin, M; van der Holst, B; Sokolov, I; Toth, G; Vourlidas, A; de Koning, C A; Gombosi, T I
2016-01-01
We perform and analyze results of a global magnetohydrodyanmic (MHD) simulation of the fast coronal mass ejection (CME) that occurred on 2011 March 7. The simulation is made using the newly developed Alfv\\'en Wave Solar Model (AWSoM), which describes the background solar wind starting from the upper chromosphere and extends to 24 R$_{\\odot}$. Coupling AWSoM to an inner heliosphere (IH) model with the Space Weather Modeling Framework (SWMF) extends the total domain beyond the orbit of Earth. Physical processes included in the model are multi-species thermodynamics, electron heat conduction (both collisional and collisionless formulations), optically thin radiative cooling, and Alfv\\'en-wave turbulence that accelerates and heats the solar wind. The Alfv\\'en-wave description is physically self-consistent, including non-Wentzel-Kramers-Brillouin (WKB) reflection and physics-based apportioning of turbulent dissipative heating to both electrons and protons. Within this model, we initiate the CME by using the Gibson...
On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas
Energy Technology Data Exchange (ETDEWEB)
Nariyuki, Y. [Faculty of Human Development, University of Toyama, 3190 Toyama City, Toyama 930-8555 (Japan)
2015-02-15
A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation of Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.
Phase of shear vibrations within cochlear partition leads to activation of the cochlear amplifier.
Directory of Open Access Journals (Sweden)
Jessica S Lamb
Full Text Available Since Georg von Bekesy laid out the place theory of the hearing, researchers have been working to understand the remarkable properties of mammalian hearing. Because access to the cochlea is restricted in live animals, and important aspects of hearing are destroyed in dead ones, models play a key role in interpreting local measurements. Wentzel-Kramers-Brillouin (WKB models are attractive because they are analytically tractable, appropriate to the oblong geometry of the cochlea, and can predict wave behavior over a large span of the cochlea. Interest in the role the tectorial membrane (TM plays in cochlear tuning led us to develop models that directly interface the TM with the cochlear fluid. In this work we add an angled shear between the TM and reticular lamina (RL, which serves as an input to a nonlinear active force. This feature plus a novel combination of previous work gives us a model with TM-fluid interaction, TM-RL shear, a nonlinear active force and a second wave mode. The behavior we get leads to the conclusion the phase between the shear and basilar membrane (BM vibration is critical for amplification. We show there is a transition in this phase that occurs at a frequency below the cutoff, which is strongly influenced by TM stiffness. We describe this mechanism of sharpened BM velocity profile, which demonstrates the importance of the TM in overall cochlear tuning and offers an explanation for the response characteristics of the Tectb mutant mouse.
Li, Huan; Tang, Xiaobin; Hang, Shuang; Liu, Yunpeng; Chen, Da
2017-03-01
Rapid progress in exploiting X-ray science has fueled its potential application in communication networks as a carrier wave for transmitting information through a plasma sheath during spacecraft reentry into earth's atmosphere. In this study, we addressed the physical transmission process of X-rays in the reentry plasma sheath and near-earth space theoretically. The interactions between the X-rays and reentry plasma sheath were investigated through the theoretical Wentzel-Kramers-Brillouin method, and the Monte Carlo simulation was employed to explore the transmission properties of X-rays in the near-earth space. The simulation results indicated that X-ray transmission was not influenced by the reentry plasma sheath compared with regular RF signals, and adopting various X-ray energies according to different spacecraft reentry altitudes is imperative when using X-ray uplink communication especially in the near-earth space. Additionally, the performance of the X-ray communication system was evaluated by applying the additive white Gaussian noise, Rayleigh fading channel, and plasma sheath channel. The Doppler shift, as a result of spacecraft velocity changes, was also calculated through the Matlab Simulink simulation, and various plasma sheath environments have no significant influence on X-ray communication owing to its exceedingly high carrier frequency.
α-α folding cluster model for α-radioactivity
Soylu, A.; Bayrak, O.
2015-04-01
The -decay half-lives are calculated for heavy and superheavy nuclei for and from the ground state to ground state transitions within the framework of the Wentzel-Kramers-Brillouin (WKB) method and the Bohr-Sommerfeld quantization. In the calculations, the - single folding cluster potential obtained with the folded integral of the - potential with the -cluster density distributions is used in order to model the nuclear interaction between the -particle and core nucleus. While the results show very good agreement with the experimental ones in the heavy-nuclei region, especially for even-even nuclei, smaller values than the experimental ones are obtained for superheavy nuclei. As both the density of the core and the interaction term in the folding integral include the -clustering effects and, in this way, all cluster effects are taken into account in the model, the results of calculations are more physical and reasonable than the calculations done in the other models. The present method could be applied to light nuclei with different types of nuclear densities.
Effects of Arbitrarily Directed Field on Spin Phase Oscillations in Biaxial Molecular Magnets
Institute of Scientific and Technical Information of China (English)
HU Hui; ZHU JiaLin; LU Rong; XIONG JiaJiong
2001-01-01
Quantum phase interference and spin-parity effects are studied in biaxial molecular magnets in a magnetic field at an arbitrarily directed angle. The calculations of the ground-state tunnel splitting are performed on the basis of the instanton technique in the spin-coherent-state path-integral representation, and complemented by exactly numerical diagonalization. Both the Wentzel-Kramers-Brillouin exponent and the pre-exponential factor are obtained for the entire region of the direction of the field. Our results show that the tunnel splitting oscillates with the field for the small field angle, while for the large field angle the oscillation is completely suppressed. This distinct angular dependence, together with the dependence of the tunnel splitting on the field strength, provides an independent test for spin-parity effects in biaxial molecular magnets. The analytical results for the molecular Fes magnet are found to be in good agreement with the numerical simulations, which suggests that even the molecular magnet with total spin S = 10 is large enough to be treated as a giant spin system.``
Prieto-Blanco, Xesús; Montero-Orille, Carlos; Moreno, Vicente; Mateo, Eduardo F; Liñares, Jesús
2015-04-10
Mode-division multiplexing (MDM) in few-mode fibers is regarded as a promising candidate to increase optical network capacity. A fundamental element for MDM is a modal transformer to LP modes which can be implemented in a free-space basis by using multiregion phase plates, that is, LP plates. Likewise, several wavelengths have to be used due to wavelength multiplexing purposes, optical amplification tasks, and so on. In this work we show that efficient monolithic binary phase plates for different wavelengths can be fabricated by ion-exchange in glass and used for MDM tasks. We introduce an optical characterization method of the chromatic properties of such phase plates which combines the inverse Wentzel-Kramers-Brillouin (IWKB) together with Mach-Zehnder and Michelson-based interferometric techniques. The interferometric method provides a measurement of the phase step for several wavelengths, which characterizes the chromatic properties of the phase plate. Consequently, it is shown that the IWKB method allows us to design and characterize the phase plates in an easy and fast way.
Theoretical aspects of the use of pulsed reflectometry in a spheromak plasma
Energy Technology Data Exchange (ETDEWEB)
Cohen, B. J., LLNL
1998-06-11
Pulsed reflectometry using both ordinary (O) and extraordinary (X) modes has the potential of providing time and space-resolved measurements of the electron density, the magnitude of the magnetic field, and the magnetic shear as a function of radius. Such a diagnostic also yields the current profile from the curl of the magnetic field. This research addresses theoretical issues associated with the use of reflectometry in the SSPX spheromak experiment at the Lawrence Livermore National Laboratory. We have extended a reflectometry simulation model to accommodate O and X-mode mixed polarization and linear mode conversion between the two polarizations. A Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) formula for linear mode conversion agrees reasonably well with direct numerical solutions of the wave equation, and we have reconstructed the magnetic pitch-angle profile by matching the results of the WKBJ formula with the mode conversion data observed in simulations using a least-squares determination of coefficients in trial functions for the profile. The reflectometry data also yield information on fluctuations. Instrumental issues, e.g., the effects of microwave mixers and filters on model reflectometry pulses, have been examined to optimize the performance of the reflectometry diagnostics.
Brennan, K. F.; Summers, C. J.
1987-01-01
A theoretical study of resonant tunneling in multilayered heterostructures is presented based on an exact solution of the Schroedinger equation under the application of a constant electric field. By use of the transfer matrix approach, the transmissivity of the structure is determined as a function of the incident electron energy. The approach presented herein is easily extended to many layer structures where it is more accurate than other existing transfer matrix or Wentzel-Kramers-Brillouin (WKB) models. The transmission resonances are compared to the bound-state energies calculated for a finite square well under bias using either an asymmetric square-well model or the exact solution of an infinite square well under the application of an electric field. The results show good agreement with other existing models as well as with the bound-state energies. The calculations were then applied to a new superlattice structure, the variably spaced superlattice energy filter, which is designed such that under bias the spatial quantization levels fully align. Based on these calculations, a new class of resonant tunneling superlattice devices can be designed.
α-α folding cluster model for α-radioactivity
Energy Technology Data Exchange (ETDEWEB)
Soylu, A. [Nigde University, Department of Physics, Nigde (Turkey); Bayrak, O. [Akdeniz University, Department of Physics, Antalya (Turkey)
2015-04-01
The α-decay half-lives are calculated for heavy and superheavy nuclei for 52 ≤ Z ≤ 112 and 108 ≤ A ≤ 285 from the ground state to ground state α transitions within the framework of the Wentzel-Kramers-Brillouin (WKB) method and the Bohr-Sommerfeld quantization. In the calculations, the α-α single folding cluster potential obtained with the folded integral of the α-α potential with the α-cluster density distributions is used in order to model the nuclear interaction between the α-particle and core nucleus. While the results show very good agreement with the experimental ones in the heavy-nuclei region, especially for even-even nuclei, smaller values than the experimental ones are obtained for superheavy nuclei. As both the density of the core and the interaction term in the folding integral include the α-clustering effects and, in this way, all cluster effects are taken into account in the model, the results of calculations are more physical and reasonable than the calculations done in the other models. The present method could be applied to light nuclei with different types of nuclear densities. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lu, Jian [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Sun, Lantao [National Center for Atmospheric Research, Boulder, CO (United States); Wu, Yutian [New York Univ. (NYU), NY (United States); Chen, Gang [Cornell Univ., Ithaca, NY (United States)
2013-11-21
The atmospheric circulation response to the global warming-like tropical upper tropospheric heating is revisited using a dry atmospheric general circulation model (AGCM) in light of a new diagnostics based on the concept of finite-amplitude wave activity (FAWA) on equivalent latitude. For a given tropical heating profile, the linear Wentzel-Kramers-Brillouin (WKB) wave refraction analysis sometimes gives a very different and even opposite prediction of the eddy momentum flux response to that of the actual full model simulation, exposing the limitation of the traditional linear approach in understanding the full dynamics of the atmospheric response under global warming. The implementation of the FAWA diagnostics reveals that in response to the upper tropospheric heating, effective diffusivity, a measure of the mixing efficiency, increases and advances upward and poleward in the subtropics and the resultant enhancement and the poleward encroachment of eddy potential vorticity mixing leads to a poleward displaced potential vorticity (PV) gradient peak in the upper troposphere. The anomalous eddy PV flux, in balance with the PV dissipation, gives rise to a poleward shift in the eddy-driven jet and eddy-driven mean meridional circulation. Sensitivity experiments show that these irreversible dissipation processes in the upper troposphere are robust, regardless of the width of the tropical heating.
Hawking Radiation of Warped Anti de Sitter and Rotating Hairy Black Holes with Scalar Hair
Gursel, H
2015-01-01
This thesis mainly focuses on the Hawking radiation (HR) evacuating from the surface of the objects that have earned a reputation as the most extraordinary objects existing so far; the black holes (BHs). Throughout this study, quantum tunneling (QT) process serves as the model for the HR of scalar, vector and Dirac particles. The scalar and Dirac particles are anticipated to be tunneling through the horizon of rotating scalar hairy black holes (RHSBHs); whilst the vector particles are associated with a rotating warped anti de-Sitter black hole (WAdS3BH) embedded in a (2+1) dimensional fabric. It is no coincidence that for all three cases; the standard HT expression is derived. Additionally, the engagement of conformal field theory (CFT) with anti de-Sitter (AdS) space presents itself to the reader and the methodologies of Klein-Gordon equation (KGE), Dirac equation and Proca equations (PEs) are introduced. For all three cases, Hamilton-Jacobi (HJ) approach is used, together with Wentzel-Kramers-Brillouin (WKB...
Inversion and approximation of Laplace transforms
Lear, W. M.
1980-01-01
A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.
Computing Functions by Approximating the Input
Goldberg, Mayer
2012-01-01
In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Random Attractors of Stochastic Modified Boussinesq Approximation
Institute of Scientific and Technical Information of China (English)
郭春晓
2011-01-01
The Boussinesq approximation is a reasonable model to describe processes in body interior in planetary physics. We refer to [1] and [2] for a derivation of the Boussinesq approximation, and [3] for some related results of existence and uniqueness of solution.
Approximating a harmonizable isotropic random field
Directory of Open Access Journals (Sweden)
Randall J. Swift
2001-01-01
Full Text Available The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers a stochastic series approximation of a harmonizable isotropic random field. This approximation is useful for numerical simulation of such a field.
On approximating multi-criteria TSP
Manthey, Bodo; Albers, S.; Marion, J.-Y.
2009-01-01
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP), whose performances are independent of the number $k$ of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized app
Regression with Sparse Approximations of Data
DEFF Research Database (Denmark)
Noorzad, Pardis; Sturm, Bob L.
2012-01-01
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected by...
A case where BO Approximation breaks down
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
@@ The Bom-Oppenheimer (BO)Approximation is ubiquitous in molecular physics,quantum physics and quantum chemistry. However, CAS researchers recently observed a breakdown of the Approximation in the reaction of fluorine with deuterium atoms.The result has been published in the August 24 issue of Science.
Two Point Pade Approximants and Duality
Banks, Tom
2013-01-01
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a strong/weak duality, when the symmetries do not determine exact expressions for some quantity.
Function Approximation Using Probabilistic Fuzzy Systems
J.H. van den Berg (Jan); U. Kaymak (Uzay); R.J. Almeida e Santos Nogueira (Rui Jorge)
2011-01-01
textabstractWe consider function approximation by fuzzy systems. Fuzzy systems are typically used for approximating deterministic functions, in which the stochastic uncertainty is ignored. We propose probabilistic fuzzy systems in which the probabilistic nature of uncertainty is taken into account.
Approximation of the Inverse -Frame Operator
Indian Academy of Sciences (India)
M R Abdollahpour; A Najati
2011-05-01
In this paper, we introduce the concept of (strong) projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2004-01-01
with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...
Approximations for stop-loss reinsurance premiums
Reijnen, Rajko; Albers, Willem/Wim; Kallenberg, W.C.M.
2005-01-01
Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are use
Quirks of Stirling's Approximation
Macrae, Roderick M.; Allgeier, Benjamin M.
2013-01-01
Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…
INVARIANT RANDOM APPROXIMATION IN NONCONVEX DOMAIN
Directory of Open Access Journals (Sweden)
R. Shrivastava
2012-05-01
Full Text Available Random fixed point results in the setup of compact and weakly compact domain of Banach spaces which is not necessary starshaped have been obtained in the present work. Invariant random approximation results have also been determined asits application. In this way, random version of invariant approximation results due toMukherjee and Som [13] and Singh [17] have been given.
Approximability and Parameterized Complexity of Minmax Values
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Hansen, Thomas Dueholm; Miltersen, Peter Bro;
2008-01-01
We consider approximating the minmax value of a multi player game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of ε log n digits (for any constant ε > 0) is NP-hard, where n is the size of the game. On the other hand...
Hardness of approximation for strip packing
DEFF Research Database (Denmark)
Adamaszek, Anna Maria; Kociumaka, Tomasz; Pilipczuk, Marcin
2017-01-01
[SODA 2016] have recently proposed a (1.4 + ϵ)-approximation algorithm for this variant, thus showing that strip packing with polynomially bounded data can be approximated better than when exponentially large values are allowed in the input. Their result has subsequently been improved to a (4/3 + ϵ...
Approximations for stop-loss reinsurance premiums
Reijnen, Rajko; Albers, Willem; Kallenberg, Wilbert C.M.
2005-01-01
Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are use
Approximations for stop-loss reinsurance premiums
Reijnen, R.; Albers, W.; Kallenberg, W.C.M.
2003-01-01
Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are use
Lifetime of the Nonlinear Geometric Optics Approximation
DEFF Research Database (Denmark)
Binzer, Knud Andreas
The subject of the thesis is to study acertain approximation method for highly oscillatory solutions to nonlinear partial differential equations.......The subject of the thesis is to study acertain approximation method for highly oscillatory solutions to nonlinear partial differential equations....
Simple Lie groups without the approximation property
DEFF Research Database (Denmark)
Haagerup, Uffe; de Laat, Tim
2013-01-01
For a locally compact group G, let A(G) denote its Fourier algebra, and let M0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-∗ topology...
An improved proximity force approximation for electrostatics
Fosco, C D; Mazzitelli, F D
2012-01-01
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated to their shapes. Indeed, in the so called "proximity force approximation" the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contribution of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied to different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful to discuss the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction i...
Approximate Furthest Neighbor in High Dimensions
DEFF Research Database (Denmark)
Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen;
2015-01-01
Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries. We present a simple, fast, and highly practical data structure for answering AFN queries in high-dimensional Euclid......Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries. We present a simple, fast, and highly practical data structure for answering AFN queries in high......-dimensional Euclidean space. We build on the technique of Indyk (SODA 2003), storing random projections to provide sublinear query time for AFN. However, we introduce a different query algorithm, improving on Indyk’s approximation factor and reducing the running time by a logarithmic factor. We also present a variation...
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-01-01
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400--407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305--320]. The application of the trajectory averaging estimator to other stochastic approximation MCMC algorithms, for example, a stochastic approximation MLE al...
Approximating maximum clique with a Hopfield network.
Jagota, A
1995-01-01
In a graph, a clique is a set of vertices such that every pair is connected by an edge. MAX-CLIQUE is the optimization problem of finding the largest clique in a given graph and is NP-hard, even to approximate well. Several real-world and theory problems can be modeled as MAX-CLIQUE. In this paper, we efficiently approximate MAX-CLIQUE in a special case of the Hopfield network whose stable states are maximal cliques. We present several energy-descent optimizing dynamics; both discrete (deterministic and stochastic) and continuous. One of these emulates, as special cases, two well-known greedy algorithms for approximating MAX-CLIQUE. We report on detailed empirical comparisons on random graphs and on harder ones. Mean-field annealing, an efficient approximation to simulated annealing, and a stochastic dynamics are the narrow but clear winners. All dynamics approximate much better than one which emulates a "naive" greedy heuristic.
A systematic sequence of relativistic approximations.
Dyall, Kenneth G
2002-06-01
An approach to the development of a systematic sequence of relativistic approximations is reviewed. The approach depends on the atomically localized nature of relativistic effects, and is based on the normalized elimination of the small component in the matrix modified Dirac equation. Errors in the approximations are assessed relative to four-component Dirac-Hartree-Fock calculations or other reference points. Projection onto the positive energy states of the isolated atoms provides an approximation in which the energy-dependent parts of the matrices can be evaluated in separate atomic calculations and implemented in terms of two sets of contraction coefficients. The errors in this approximation are extremely small, of the order of 0.001 pm in bond lengths and tens of microhartrees in absolute energies. From this approximation it is possible to partition the atoms into relativistic and nonrelativistic groups and to treat the latter with the standard operators of nonrelativistic quantum mechanics. This partitioning is shared with the relativistic effective core potential approximation. For atoms in the second period, errors in the approximation are of the order of a few hundredths of a picometer in bond lengths and less than 1 kJ mol(-1) in dissociation energies; for atoms in the third period, errors are a few tenths of a picometer and a few kilojoule/mole, respectively. A third approximation for scalar relativistic effects replaces the relativistic two-electron integrals with the nonrelativistic integrals evaluated with the atomic Foldy-Wouthuysen coefficients as contraction coefficients. It is similar to the Douglas-Kroll-Hess approximation, and is accurate to about 0.1 pm and a few tenths of a kilojoule/mole. The integrals in all the approximations are no more complicated than the integrals in the full relativistic methods, and their derivatives are correspondingly easy to formulate and evaluate.
Frankenstein's glue: transition functions for approximate solutions
Yunes, Nicolás
2007-09-01
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate analytic solutions together. In particular, we propose certain sufficient conditions on these functions and prove that these conditions guarantee that the joined solution still satisfies the Einstein equations analytically to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the proposed conditions, then the joined solution does not contain any violations to the Einstein equations larger than those already inherent in the approximations. We further show that if these functions violate the proposed conditions, then the matter content of the spacetime is modified by the introduction of a matter shell, whose stress energy tensor depends on derivatives of these functions.
The tendon approximator device in traumatic injuries.
Forootan, Kamal S; Karimi, Hamid; Forootan, Nazilla-Sadat S
2015-01-01
Precise and tension-free approximation of two tendon endings is the key predictor of outcomes following tendon lacerations and repairs. We evaluate the efficacy of a new tendon approximator device in tendon laceration repairs. In a comparative study, we used our new tendon approximator device in 99 consecutive patients with laceration of 266 tendons who attend a university hospital and evaluated the operative time to repair the tendons, surgeons' satisfaction as well as patient's outcomes in a long-term follow-up. Data were compared with the data of control patients undergoing tendon repair by conventional method. Totally 266 tendons were repaired by approximator device and 199 tendons by conventional technique. 78.7% of patients in first group were male and 21.2% were female. In approximator group 38% of patients had secondary repair of cut tendons and 62% had primary repair. Patients were followed for a mean period of 3years (14-60 months). Time required for repair of each tendon was significantly reduced with the approximator device (2 min vs. 5.5 min, ptendon repair were identical in the two groups and were not significantly different. 1% of tendons in group A and 1.2% in group B had rupture that was not significantly different. The new nerve approximator device is cheap, feasible to use and reduces the time of tendon repair with sustained outcomes comparable to the conventional methods.
Entanglement in the Born-Oppenheimer Approximation
Izmaylov, Artur F
2016-01-01
The role of electron-nuclear entanglement on the validity of the Born-Oppenheimer (BO) approximation is investigated. While nonadiabatic couplings generally lead to entanglement and to a failure of the BO approximation, surprisingly the degree of electron-nuclear entanglement is found to be uncorrelated with the degree of validity of the BO approximation. This is because while the degree of entanglement of BO states is determined by their deviation from the corresponding states in the crude BO approximation, the accuracy of the BO approximation is dictated, instead, by the deviation of the BO states from the exact electron-nuclear states. In fact, in the context of a minimal avoided crossing model, extreme cases are identified where an adequate BO state is seen to be maximally entangled, and where the BO approximation fails but the associated BO state remains approximately unentangled. Further, the BO states are found to not preserve the entanglement properties of the exact electron-nuclear eigenstates, and t...
DIFFERENCE SCHEMES BASING ON COEFFICIENT APPROXIMATION
Institute of Scientific and Technical Information of China (English)
MOU Zong-ze; LONG Yong-xing; QU Wen-xiao
2005-01-01
In respect of variable coefficient differential equations, the equations of coefficient function approximation were more accurate than the coefficient to be frozen as a constant in every discrete subinterval. Usually, the difference schemes constructed based on Taylor expansion approximation of the solution do not suit the solution with sharp function.Introducing into local bases to be combined with coefficient function approximation, the difference can well depict more complex physical phenomena, for example, boundary layer as well as high oscillatory, with sharp behavior. The numerical test shows the method is more effective than the traditional one.
Approximate equivalence in von Neumann algebras
Institute of Scientific and Technical Information of China (English)
DING; Huiru; Don; Hadwin
2005-01-01
One formulation of D. Voiculescu's theorem on approximate unitary equivalence is that two unital representations π and ρ of a separable C*-algebra are approximately unitarily equivalent if and only if rank o π = rank o ρ. We study the analog when the ranges of π and ρ are contained in a von Neumann algebra R, the unitaries inducing the approximate equivalence must come from R, and "rank" is replaced with "R-rank" (defined as the Murray-von Neumann equivalence of the range projection).
Approximation of free-discontinuity problems
Braides, Andrea
1998-01-01
Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.
Mathematical analysis, approximation theory and their applications
Gupta, Vijay
2016-01-01
Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Regression with Sparse Approximations of Data
DEFF Research Database (Denmark)
Noorzad, Pardis; Sturm, Bob L.
2012-01-01
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...
Orthorhombic rational approximants for decagonal quasicrystals
Indian Academy of Sciences (India)
S Ranganathan; Anandh Subramaniam
2003-10-01
An important exercise in the study of rational approximants is to derive their metric, especially in relation to the corresponding quasicrystal or the underlying clusters. Kuo’s model has been the widely accepted model to calculate the metric of the decagonal approximants. Using an alternate model, the metric of the approximants and other complex structures with the icosahedral cluster are explained elsewhere. In this work a comparison is made between the two models bringing out their equivalence. Further, using the concept of average lattices, a modified model is proposed.
Approximation of the semi-infinite interval
Directory of Open Access Journals (Sweden)
A. McD. Mercer
1980-01-01
Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.
An overview on Approximate Bayesian computation*
Directory of Open Access Journals (Sweden)
Baragatti Meïli
2014-01-01
Full Text Available Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics.
Trigonometric Approximations for Some Bessel Functions
Muhammad Taher Abuelma'atti
1999-01-01
Formulas are obtained for approximating the tabulated Bessel functions Jn(x), n = 0–9 in terms of trigonometric functions. These formulas can be easily integrated and differentiated and are convenient for personal computers and pocket calculators.
Low Rank Approximation Algorithms, Implementation, Applications
Markovsky, Ivan
2012-01-01
Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...
Asynchronous stochastic approximation with differential inclusions
Directory of Open Access Journals (Sweden)
David S. Leslie
2012-01-01
Full Text Available The asymptotic pseudo-trajectory approach to stochastic approximation of Benaïm, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of an equivalent synchronous process. In addition, this allows many of the restrictive assumptions previously associated with asynchronous stochastic approximation to be removed. The framework is extended for a coupled asynchronous stochastic approximation process with set-valued mean fields. Two-timescales arguments are used here in a similar manner to the original work in this area by Borkar. The applicability of this approach is demonstrated through learning in a Markov decision process.
An approximate Expression for Viscosity of Nanosuspensions
Domostroeva, N G
2009-01-01
We consider liquid suspensions with dispersed nanoparticles. Using two-points Pade approximants and combining results of both hydrodynamic and molecular dynamics methods, we obtain the effective viscosity for any diameters of nanoparticles
On Approximating Four Covering and Packing Problems
Ashley, Mary; Berman, Piotr; Chaovalitwongse, Wanpracha; DasGupta, Bhaskar; Kao, Ming-Yang; 10.1016/j.jcss.2009.01.002
2011-01-01
In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and have applications in biology ranging from full-sibling reconstructions in wild populations to biomolecular clusterings; however, as this paper shows, their approximability properties differ considerably. Our inapproximability constant for the triangle packing problem improves upon the previous results; this is done by directly transforming the inapproximability gap of Haastad for the problem of maximizing the number of satisfied equations for a set of equations over GF(2) and is interesting in its own right. Our approximability results on the full siblings reconstruction problems answers questions originally posed by Berger-Wolf et al. and our results on the maximum profit coverage problem provides almost matching upper and lower bounds on the approximation ratio, answering a...
Staying thermal with Hartree ensemble approximations
Energy Technology Data Exchange (ETDEWEB)
Salle, Mischa E-mail: msalle@science.uva.nl; Smit, Jan E-mail: jsmit@science.uva.nl; Vink, Jeroen C. E-mail: jcvink@science.uva.nl
2002-03-25
We study thermal behavior of a recently introduced Hartree ensemble approximation, which allows for non-perturbative inhomogeneous field configurations as well as for approximate thermalization, in the phi (cursive,open) Greek{sup 4} model in 1+1 dimensions. Using ensembles with a free field thermal distribution as out-of-equilibrium initial conditions we determine thermalization time scales. The time scale for which the system stays in approximate quantum thermal equilibrium is an indication of the time scales for which the approximation method stays reasonable. This time scale turns out to be two orders of magnitude larger than the time scale for thermalization, in the range of couplings and temperatures studied. We also discuss simplifications of our method which are numerically more efficient and make a comparison with classical dynamics.
Approximations of solutions to retarded integrodifferential equations
Directory of Open Access Journals (Sweden)
Dhirendra Bahuguna
2004-11-01
Full Text Available In this paper we consider a retarded integrodifferential equation and prove existence, uniqueness and convergence of approximate solutions. We also give some examples to illustrate the applications of the abstract results.
APPROXIMATE DEVELOPMENTS FOR SURFACES OF REVOLUTION
Directory of Open Access Journals (Sweden)
Mădălina Roxana Buneci
2016-12-01
Full Text Available The purpose of this paper is provide a set of Maple procedures to construct approximate developments of a general surface of revolution generalizing the well-known gore method for sphere
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Seismic wave extrapolation using lowrank symbol approximation
Fomel, Sergey
2012-04-30
We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.
Approximate Flavor Symmetry in Supersymmetric Model
Tao, Zhijian
1998-01-01
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 i...
Pointwise approximation by elementary complete contractions
Magajna, Bojan
2009-01-01
A complete contraction on a C*-algebra A, which preserves all closed two sided ideals J, can be approximated pointwise by elementary complete contractions if and only if the induced map on the tensor product of B with A/J is contractive for every C*-algebra B, ideal J in A and C*-tensor norm on the tensor product. A lifting obstruction for such an approximation is also obtained.
Polynomial approximation of functions in Sobolev spaces
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Parallel local approximation MCMC for expensive models
Conrad, Patrick; Davis, Andrew; Marzouk, Youssef; Pillai, Natesh; Smith, Aaron
2016-01-01
Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In recent work [Conrad et al. JASA 2015, arXiv:1402.1694] we described a framework for constructing and refining local approximations of such models during an MCMC simulation. These posterior--adapted approximations harness regularity of the model to reduce the c...
The Actinide Transition Revisited by Gutzwiller Approximation
Xu, Wenhu; Lanata, Nicola; Yao, Yongxin; Kotliar, Gabriel
2015-03-01
We revisit the problem of the actinide transition using the Gutzwiller approximation (GA) in combination with the local density approximation (LDA). In particular, we compute the equilibrium volumes of the actinide series and reproduce the abrupt change of density found experimentally near plutonium as a function of the atomic number. We discuss how this behavior relates with the electron correlations in the 5 f states, the lattice structure, and the spin-orbit interaction. Our results are in good agreement with the experiments.
Intuitionistic Fuzzy Automaton for Approximate String Matching
Directory of Open Access Journals (Sweden)
K.M. Ravi
2014-03-01
Full Text Available This paper introduces an intuitionistic fuzzy automaton model for computing the similarity between pairs of strings. The model details the possible edit operations needed to transform any input (observed string into a target (pattern string by providing a membership and non-membership value between them. In the end, an algorithm is given for approximate string matching and the proposed model computes the similarity and dissimilarity between the pair of strings leading to better approximation.
Approximations for the Erlang Loss Function
DEFF Research Database (Denmark)
Mejlbro, Leif
1998-01-01
Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error <1E-2, and methods are indicated for improving this bound.......Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error
Staying Thermal with Hartree Ensemble Approximations
Salle, M; Vink, Jeroen C
2000-01-01
Using Hartree ensemble approximations to compute the real time dynamics of scalar fields in 1+1 dimension, we find that with suitable initial conditions, approximate thermalization is achieved much faster than found in our previous work. At large times, depending on the interaction strength and temperature, the particle distribution slowly changes: the Bose-Einstein distribution of the particle densities develops classical features. We also discuss variations of our method which are numerically more efficient.
Lattice quantum chromodynamics with approximately chiral fermions
Energy Technology Data Exchange (ETDEWEB)
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Nonlinear approximation in alpha-modulation spaces
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2006-01-01
The α-modulation spaces are a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that brushlet bases can be constructed to form unconditional and even greedy bases for the α-modulation spaces. We study m -term nonlinear approximation with brushlet...... bases, and give complete characterizations of the associated approximation spaces in terms of α-modulation spaces....
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, s.
1999-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G(1) surface consisting of pieces of cones or cylinders of revolution or a G(r) NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding. (C) 1999 Academic Press....
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, S.
1998-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G_1 surface consisting of pieces of cones or cylinders of revolution or a G_r NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding....
Differential geometry of proteins. Helical approximations.
Louie, A H; Somorjai, R L
1983-07-25
We regard a protein molecule as a geometric object, and in a first approximation represent it as a regular parametrized space curve passing through its alpha-carbon atoms (the backbone). In an earlier paper we argued that the regular patterns of secondary structures of proteins (morphons) correspond to geodesics on minimal surfaces. In this paper we discuss methods of recognizing these morphons on space curves that represent the protein backbone conformation. The mathematical tool we employ is the differential geometry of curves and surfaces. We introduce a natural approximation of backbone space curves in terms of helical approximating elements and present a computer algorithm to implement the approximation. Simple recognition criteria are given for the various morphons of proteins. These are incorporated into our helical approximation algorithm, together with more non-local criteria for the recognition of beta-sheet topologies. The method and the algorithm are illustrated with several examples of representative proteins. Generalizations of the helical approximation method are considered and their possible implications for protein energetics are sketched.
DEFF Research Database (Denmark)
Sadegh, Payman
1997-01-01
This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...
Ito, K.
1984-01-01
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
Ito, K.
1985-01-01
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A characteristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
Tree-fold loop approximation of AMD
Energy Technology Data Exchange (ETDEWEB)
Ono, Akira [Tohoku Univ., Sendai (Japan). Faculty of Science
1997-05-01
AMD (antisymmetrized molecular dynamics) is a frame work for describing a wave function of nucleon multi-body system by Slater determinant of Gaussian wave flux, and a theory for integrally describing a wide range of nuclear reactions such as intermittent energy heavy ion reaction, nucleon incident reaction and so forth. The aim of this study is induction on approximation equation of expected value, {nu}, in correlation capable of calculation with time proportional A (exp 3) (or lower), and to make AMD applicable to the heavier system such as Au+Au. As it must be avoided to break characteristics of AMD, it needs not to be anxious only by approximating the {nu}-value. However, in order to give this approximation any meaning, error of this approximation will have to be sufficiently small in comparison with bond energy of atomic nucleus and smaller than 1 MeV/nucleon. As the absolute expected value in correlation may be larger than 50 MeV/nucleon, the approximation is required to have a high accuracy within 2 percent. (G.K.)
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-10-01
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.
Approximation of Bivariate Functions via Smooth Extensions
Zhang, Zhihua
2014-01-01
For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of well-known approximation theorems, using our extension methods, the Fourier approximation and the wavelet approximation of the bivariate function on the general domain with small error are obtained. PMID:24683316
Approximation Limits of Linear Programs (Beyond Hierarchies)
Braun, Gábor; Pokutta, Sebastian; Steurer, David
2012-01-01
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any linear program as opposed to only programs generated by hierarchies. Using our framework, we prove that O(n^{1/2-eps})-approximations for CLIQUE require linear programs of size 2^{n^\\Omega(eps)}. (This lower bound applies to linear programs using a certain encoding of CLIQUE as a linear optimization problem.) Moreover, we establish a similar result for approximations of semidefinite programs by linear programs. Our main ingredient is a quantitative improvement of Razborov's rectangle corruption lemma for the high error regime, which gives strong lower bounds on the nonnegative rank of certain perturbations of the unique disjointness matrix.
Discontinuous Galerkin Methods with Trefftz Approximation
Kretzschmar, Fritz; Tsukerman, Igor; Weiland, Thomas
2013-01-01
We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space-time Trefftz-type basis functions that satisfy the underlying partial differential equations and the respective interface boundary conditions exactly in an element-wise fashion. The basis functions can be of arbitrary high order, and we demonstrate spectral convergence in the $\\Lebesgue_2$-norm. In this context, spectral convergence is obtained with respect to the approximation error in the entire space-time domain of interest, i.e. in space and time simultaneously. Formulating the approximation in terms of a space-time Trefftz basis makes high order time integration an inherent property of the method and clearly sets it apart from methods, that employ a high order approximation in space only.
Approximating light rays in the Schwarzschild field
Semerak, Oldrich
2014-01-01
A short formula is suggested which approximates photon trajectories in the Schwarzschild field better than other simple prescriptions from the literature. We compare it with various "low-order competitors", namely with those following from exact formulas for small $M$, with one of the results based on pseudo-Newtonian potentials, with a suitably adjusted hyperbola, and with the effective and often employed approximation by Beloborodov. Our main concern is the shape of the photon trajectories at finite radii, yet asymptotic behaviour is also discussed, important for lensing. An example is attached indicating that the newly suggested approximation is usable--and very accurate--for practical solving of the ray-deflection exercise.
On the approximate zero of Newton method
Institute of Scientific and Technical Information of China (English)
黄正达
2003-01-01
A judgment criterion to guarantee a point to be a Chen' s approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen' s approximate zero may not be a Smale' s approximate zero. The error estimate obtained indicated the convergent order when we use |f(x) | < ε to stop computation in software.The result can also be applied for solving partial derivative and integration equations.
On the approximate zero of Newton method
Institute of Scientific and Technical Information of China (English)
黄正达
2003-01-01
A judgment criterion to guarantee a point to be a Chen's approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen's approximate zero may not be a Smale's approximate zero. The error estimate obtained indicated the convergent order when we use |f(x)|<ε to stop computation in software. The result can also be applied for solving partial derivative and integration equations.
Optical pulse propagation with minimal approximations
Kinsler, Paul
2010-01-01
Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations—including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first-order propagation equation using a minimum of approximations and a straightforward “factorization” mathematical scheme. The approach generates exact coupled bidirectional equations, after which it is clear that the description can be reduced to a single unidirectional first-order wave equation by means of a simple “slow evolution” approximation, where the optical pulse changes little over the distance of one wavelength. It also allows a direct term-to-term comparison of an exact bidirectional theory with the approximate unidirectional theory.
Rough interfaces beyond the Gaussian approximation
Caselle, M; Gliozzi, F; Hasenbusch, M; Pinn, K; Vinti, S; Caselle, M; Gliozzi, F; Fiore, R; Hasenbusch, M; Pinn, K; Vinti, S
1994-01-01
We compare predictions of the Capillary Wave Model beyond its Gaussian approximation with Monte Carlo results for the energy gap and the surface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two--loop order ( one order beyond the Gaussian approximation). We compare predictions of the Capillary Wave Model with Monte Carlo results for the energy gap and the interface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two-loop order (one order beyond the Gaussian approximation).
Implementing regularization implicitly via approximate eigenvector computation
Mahoney, Michael W
2010-01-01
Regularization is a powerful technique for extracting useful information from noisy data. Typically, it is implemented by adding some sort of norm constraint to an objective function and then exactly optimizing the modified objective function. This procedure typically leads to optimization problems that are computationally more expensive than the original problem, a fact that is clearly problematic if one is interested in large-scale applications. On the other hand, a large body of empirical work has demonstrated that heuristics, and in some cases approximation algorithms, developed to speed up computations sometimes have the side-effect of performing regularization implicitly. Thus, we consider the question: What is the regularized optimization objective that an approximation algorithm is exactly optimizing? We address this question in the context of computing approximations to the smallest nontrivial eigenvector of a graph Laplacian; and we consider three random-walk-based procedures: one based on the heat ...
On approximation of Markov binomial distributions
Xia, Aihua; 10.3150/09-BEJ194
2010-01-01
For a Markov chain $\\mathbf{X}=\\{X_i,i=1,2,...,n\\}$ with the state space $\\{0,1\\}$, the random variable $S:=\\sum_{i=1}^nX_i$ is said to follow a Markov binomial distribution. The exact distribution of $S$, denoted $\\mathcal{L}S$, is very computationally intensive for large $n$ (see Gabriel [Biometrika 46 (1959) 454--460] and Bhat and Lal [Adv. in Appl. Probab. 20 (1988) 677--680]) and this paper concerns suitable approximate distributions for $\\mathcal{L}S$ when $\\mathbf{X}$ is stationary. We conclude that the negative binomial and binomial distributions are appropriate approximations for $\\mathcal{L}S$ when $\\operatorname {Var}S$ is greater than and less than $\\mathbb{E}S$, respectively. Also, due to the unique structure of the distribution, we are able to derive explicit error estimates for these approximations.
Fast wavelet based sparse approximate inverse preconditioner
Energy Technology Data Exchange (ETDEWEB)
Wan, W.L. [Univ. of California, Los Angeles, CA (United States)
1996-12-31
Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.
Numerical approximation of partial differential equations
Bartels, Sören
2016-01-01
Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular ...
On Born approximation in black hole scattering
Energy Technology Data Exchange (ETDEWEB)
Batic, D. [University of West Indies, Department of Mathematics, Kingston (Jamaica); Kelkar, N.G.; Nowakowski, M. [Universidad de los Andes, Departamento de Fisica, Bogota (Colombia)
2011-12-15
A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordstroem and Reissner-Nordstroem-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes. (orig.)
Time Stamps for Fixed-Point Approximation
DEFF Research Database (Denmark)
Damian, Daniela
2001-01-01
Time stamps were introduced in Shivers's PhD thesis for approximating the result of a control-flow analysis. We show them to be suitable for computing program analyses where the space of results (e.g., control-flow graphs) is large. We formalize time-stamping as a top-down, fixed-point approximat......Time stamps were introduced in Shivers's PhD thesis for approximating the result of a control-flow analysis. We show them to be suitable for computing program analyses where the space of results (e.g., control-flow graphs) is large. We formalize time-stamping as a top-down, fixed......-point approximation algorithm which maintains a single copy of intermediate results. We then prove the correctness of this algorithm....
Exponential Approximations Using Fourier Series Partial Sums
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Extending the Eikonal Approximation to Low Energy
Capel, Pierre; Ogata, Kazuyuki
2014-01-01
E-CDCC and DEA, two eikonal-based reaction models are compared to CDCC at low energy (e.g. 20AMeV) to study their behaviour in the regime at which the eikonal approximation is supposed to fail. We confirm that these models lack the Coulomb deflection of the projectile by the target. We show that a hybrid model, built on the CDCC framework at low angular momenta and the eikonal approximation at larger angular momenta gives a perfect agreement with CDCC. An empirical shift in impact parameter can also be used reliably to simulate this missing Coulomb deflection.
Approximately-Balanced Drilling in Daqing Oilfield
Institute of Scientific and Technical Information of China (English)
Xia Bairu; Zheng Xiuhua; Li Guoqing; Tian Tuo
2004-01-01
The Daqing oilfield is a multilayered heterogeneous oil field where the pressure are different in the same vertical profile causing many troubles to the adjustment well drillings. The approximately-balanced drilling technique has been developed and proved to be efficient and successful in Daqing oilfield. This paper discusses the application of approximately-balanced drilling technique under the condition of multilayered pressure in Daqing oilfield, including the prediction of formation pressure, the pressure discharge technique for the drilling well and the control of the density of drilling fluid.
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.
An Approximate Bayesian Fundamental Frequency Estimator
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2012-01-01
Joint fundamental frequency and model order estimation is an important problem in several applications such as speech and music processing. In this paper, we develop an approximate estimation algorithm of these quantities using Bayesian inference. The inference about the fundamental frequency...... and the model order is based on a probability model which corresponds to a minimum of prior information. From this probability model, we give the exact posterior distributions on the fundamental frequency and the model order, and we also present analytical approximations of these distributions which lower...
Approximate Controllability of Fractional Integrodifferential Evolution Equations
Directory of Open Access Journals (Sweden)
R. Ganesh
2013-01-01
Full Text Available This paper addresses the issue of approximate controllability for a class of control system which is represented by nonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory, p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results are established under the assumption that the corresponding linear system is approximately controllable and functions satisfy non-Lipschitz conditions. The results generalize and improve some known results.
Excluded-Volume Approximation for Supernova Matter
Yudin, A V
2014-01-01
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.
Generalized companion matrix for approximate GCD
Boito, Paola
2011-01-01
We study a variant of the univariate approximate GCD problem, where the coe?- cients of one polynomial f(x)are known exactly, whereas the coe?cients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which describes the operator of multiplication by gin the quotient ring C[x]=(f). In particular, the structure of the null space of the multiplication matrix contains all the essential information about GCD(f; g). Moreover, the multiplication matrix exhibits a displacement structure that allows us to design a fast algorithm for approximate GCD computation with quadratic complexity w.r.t. polynomial degrees.
An approximate analytical approach to resampling averages
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, M.
2004-01-01
Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr......Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach...
Static correlation beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
We investigate various approximations to the correlation energy of a H2 molecule in the dissociation limit, where the ground state is poorly described by a single Slater determinant. The correlation energies are derived from the density response function and it is shown that response functions...... derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly...
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A. V.
2016-08-01
We consider the eikonal approximation for moderately small scattering amplitudes. To find numerical estimates of these approximations, we derive formulas that contain no Bessel functions and consequently no rapidly oscillating integrands. To obtain these formulas, we study improper integrals of the first kind containing products of the Bessel functions J0(z). We generalize the expression with four functions J0(z) and also find expressions for the integrals with the product of five and six Bessel functions. We generalize a known formula for the improper integral with two functions Jυ (az) to the case with noninteger υ and complex a.
The exact renormalization group and approximation solutions
Morris, T R
1994-01-01
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 greens functions are given. A promising non-perturbative 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 $\\lambda \\varphi^4$ 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.
Approximating W projection as a separable kernel
Merry, Bruce
2016-02-01
W projection is a commonly used approach to allow interferometric imaging to be accelerated by fast Fourier transforms, but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show that they can be closely approximated by separable kernels. The error scales with the fourth power of the field of view, and so is small enough to be ignored at mid- to high frequencies. We also show that hybrid imaging algorithms combining W projection with either faceting, snapshotting, or W stacking allow the error to be made arbitrarily small, making the approximation suitable even for high-resolution wide-field instruments.
BEST APPROXIMATION BY DOWNWARD SETS WITH APPLICATIONS
Institute of Scientific and Technical Information of China (English)
H.Mohebi; A. M. Rubinov
2006-01-01
We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs (W,x), where x ∈ X and W is a closed downward subset of X.
Local density approximations from finite systems
Entwistle, Mike; Wetherell, Jack; Longstaff, Bradley; Ramsden, James; Godby, Rex
2016-01-01
The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We introduce an alternative set of LDAs constructed from slab-like systems of one, two and three electrons that resemble the HEG within a finite region, and illustrate the concept in one dimension. Comparing with the exact densities and Kohn-Sham potentials for various test systems, we find that the LDAs give a good account of the self-interaction correction, but are less reliable when correlation is stronger or currents flow.
Rational approximations and quantum algorithms with postselection
Mahadev, U.; de Wolf, R.
2015-01-01
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using post-selection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We gi
Kravchuk functions for the finite oscillator approximation
Atakishiyev, Natig M.; Wolf, Kurt Bernardo
1995-01-01
Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.
Optical bistability without the rotating wave approximation
Energy Technology Data Exchange (ETDEWEB)
Sharaby, Yasser A., E-mail: Yasser_Sharaby@hotmail.co [Physics Department, Faculty of Applied Sciences, Suez Canal University, Suez (Egypt); Joshi, Amitabh, E-mail: ajoshi@eiu.ed [Department of Physics, Eastern Illinois University, Charleston, IL 61920 (United States); Hassan, Shoukry S., E-mail: Shoukryhassan@hotmail.co [Mathematics Department, College of Science, University of Bahrain, P.O. Box 32038 (Bahrain)
2010-04-26
Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.
Improved Approximations for Multiprocessor Scheduling Under Uncertainty
Crutchfield, Christopher; Fineman, Jeremy T; Karger, David R; Scott, Jacob
2008-01-01
This paper presents improved approximation algorithms for the problem of multiprocessor scheduling under uncertainty, or SUU, in which the execution of each job may fail probabilistically. This problem is motivated by the increasing use of distributed computing to handle large, computationally intensive tasks. In the SUU problem we are given n unit-length jobs and m machines, a directed acyclic graph G of precedence constraints among jobs, and unrelated failure probabilities q_{ij} for each job j when executed on machine i for a single timestep. Our goal is to find a schedule that minimizes the expected makespan, which is the expected time at which all jobs complete. Lin and Rajaraman gave the first approximations for this NP-hard problem for the special cases of independent jobs, precedence constraints forming disjoint chains, and precedence constraints forming trees. In this paper, we present asymptotically better approximation algorithms. In particular, we give an O(loglog min(m,n))-approximation for indep...
Markov operators, positive semigroups and approximation processes
Altomare, Francesco; Leonessa, Vita; Rasa, Ioan
2015-01-01
In recent years several investigations have been devoted to the study of large classes of (mainly degenerate) initial-boundary value evolution problems in connection with the possibility to obtain a constructive approximation of the associated positive C_0-semigroups. In this research monograph we present the main lines of a theory which finds its root in the above-mentioned research field.
Image Compression Via a Fast DCT Approximation
Bayer, F. M.; Cintra, R. J.
2010-01-01
Discrete transforms play an important role in digital signal processing. In particular, due to its transform domain energy compaction properties, the discrete cosine transform (DCT) is pivotal in many image processing problems. This paper introduces a numerical approximation method for the DCT based
Approximation algorithms for planning and control
Boddy, Mark; Dean, Thomas
1989-01-01
A control system operating in a complex environment will encounter a variety of different situations, with varying amounts of time available to respond to critical events. Ideally, such a control system will do the best possible with the time available. In other words, its responses should approximate those that would result from having unlimited time for computation, where the degree of the approximation depends on the amount of time it actually has. There exist approximation algorithms for a wide variety of problems. Unfortunately, the solution to any reasonably complex control problem will require solving several computationally intensive problems. Algorithms for successive approximation are a subclass of the class of anytime algorithms, algorithms that return answers for any amount of computation time, where the answers improve as more time is allotted. An architecture is described for allocating computation time to a set of anytime algorithms, based on expectations regarding the value of the answers they return. The architecture described is quite general, producing optimal schedules for a set of algorithms under widely varying conditions.
Large hierarchies from approximate R symmetries
Energy Technology Data Exchange (ETDEWEB)
Kappl, Rolf; Ratz, Michael [Technische Univ. Muenchen, Garching (Germany). Physik Dept. T30; Nilles, Hans Peter [Bonn Univ. (Germany). Bethe Zentrum fuer Theoretische Physik und Physikalisches Inst.; Ramos-Sanchez, Saul; Schmidt-Hoberg, Kai [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Vaudrevange, Patrick K.S. [Ludwig-Maximilians-Univ. Muenchen (Germany). Arnold Sommerfeld Zentrum fuer Theoretische Physik
2008-12-15
We show that hierarchically small vacuum expectation values of the superpotential in supersymmetric theories can be a consequence of an approximate R symmetry. We briefly discuss the role of such small constants in moduli stabilization and understanding the huge hierarchy between the Planck and electroweak scales. (orig.)
Strong washout approximation to resonant leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Garbrecht, Bjoern; Gautier, Florian; Klaric, Juraj [Physik Department T70, James-Franck-Strasse, Techniche Universitaet Muenchen, 85748 Garching (Germany)
2016-07-01
We study resonant Leptogenesis with two sterile neutrinos with masses M{sub 1} and M{sub 2}, Yukawa couplings Y{sub 1} and Y{sub 2}, and a single active flavor. Specifically, we focus on the strong washout regime, where the decay width dominates the mass splitting of the two sterile neutrinos. We show that one can approximate the effective decay asymmetry by it's late time limit ε = X sin(2 φ)/(X{sup 2}+sin{sup 2}φ), where X=8 π Δ/(vertical stroke Y{sub 1} vertical stroke {sup 2}+ vertical stroke Y{sub 2} vertical stroke {sup 2}), Δ=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), and φ=arg(Y{sub 2}/Y{sub 1}), and establish criteria for the validity of this approximation. We compare the approximate results with numerical ones, obtained by solving the mixing and oscillations of the sterile neutrinos. We generalize the formula to the case of several active flavors, and demonstrate how it can be used to calculate the lepton asymmetry in phenomenological scenarios which are in agreement with the neutrino oscillation data. We find that that using the late time limit is an applicable approximation throughout the phenomenologically viable parameter space.
Lower Bound Approximation for Elastic Buckling Loads
Vrouwenvelder, A.; Witteveen, J.
1975-01-01
An approximate method for the elastic buckling analysis of two-dimensional frames is introduced. The method can conveniently be explained with reference to a physical interpretation: In the frame every member is replaced by two new members: - a flexural member without extensional rigidity to transmi
Approximate Equilibrium Problems and Fixed Points
Directory of Open Access Journals (Sweden)
H. Mazaheri
2013-01-01
Full Text Available We find a common element of the set of fixed points of a map and the set of solutions of an approximate equilibrium problem in a Hilbert space. Then, we show that one of the sequences weakly converges. Also we obtain some theorems about equilibrium problems and fixed points.
Approximations in diagnosis: motivations and techniques
Harmelen, van F.A.H.; Teije, A. ten
1995-01-01
We argue that diagnosis should not be seen as solving a problem with a unique definition, but rather that there exists a whole space of reasonable notions of diagnosis. These notions can be seen as mutual approximations. We present a number of reasons for choosing among different notions of diagnos
Eignets for function approximation on manifolds
Mhaskar, H N
2009-01-01
Let $\\XX$ be a compact, smooth, connected, Riemannian manifold without boundary, $G:\\XX\\times\\XX\\to \\RR$ be a kernel. Analogous to a radial basis function network, an eignet is an expression of the form $\\sum_{j=1}^M a_jG(\\circ,y_j)$, where $a_j\\in\\RR$, $y_j\\in\\XX$, $1\\le j\\le M$. We describe a deterministic, universal algorithm for constructing an eignet for approximating functions in $L^p(\\mu;\\XX)$ for a general class of measures $\\mu$ and kernels $G$. Our algorithm yields linear operators. Using the minimal separation amongst the centers $y_j$ as the cost of approximation, we give modulus of smoothness estimates for the degree of approximation by our eignets, and show by means of a converse theorem that these are the best possible for every \\emph{individual function}. We also give estimates on the coefficients $a_j$ in terms of the norm of the eignet. Finally, we demonstrate that if any sequence of eignets satisfies the optimal estimates for the degree of approximation of a smooth function, measured in ter...
Approximations in diagnosis: motivations and techniques
Harmelen, van F.A.H.; Teije, A. ten
1995-01-01
We argue that diagnosis should not be seen as solving a problem with a unique definition, but rather that there exists a whole space of reasonable notions of diagnosis. These notions can be seen as mutual approximations. We present a number of reasons for choosing among different notions of
Empirical progress and nomic truth approximation revisited
Kuipers, Theodorus
2014-01-01
In my From Instrumentalism to Constructive Realism (2000) I have shown how an instrumentalist account of empirical progress can be related to nomic truth approximation. However, it was assumed that a strong notion of nomic theories was needed for that analysis. In this paper it is shown, in terms of
Faddeev Random Phase Approximation applied to molecules
Degroote, Matthias
2012-01-01
This Ph.D. thesis derives the equations of the Faddeev Random Phase Approximation (FRPA) and applies the method to a set of small atoms and molecules. The occurence of RPA instabilities in the dissociation limit is addressed in molecules and by the study of the Hubbard molecule as a test system with reduced dimensionality.
Auction analysis by normal form game approximation
Kaisers, Michael; Tuyls, Karl; Thuijsman, Frank; Parsons, Simon
2008-01-01
Auctions are pervasive in todaypsilas society and provide a variety of real markets. This article facilitates a strategic choice between a set of available trading strategies by introducing a methodology to approximate heuristic payoff tables by normal form games. An example from the auction domain
Fostering Formal Commutativity Knowledge with Approximate Arithmetic.
Directory of Open Access Journals (Sweden)
Sonja Maria Hansen
Full Text Available How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2 and third graders (Experiment 3. Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school.
Approximate fixed point of Reich operator
Directory of Open Access Journals (Sweden)
M. Saha
2013-01-01
Full Text Available In the present paper, we study the existence of approximate fixed pointfor Reich operator together with the property that the ε-fixed points are concentrated in a set with the diameter tends to zero if ε $to$ > 0.
Approximation of Aggregate Losses Using Simulation
Directory of Open Access Journals (Sweden)
Mohamed A. Mohamed
2010-01-01
Full Text Available Problem statement: The modeling of aggregate losses is one of the main objectives in actuarial theory and practice, especially in the process of making important business decisions regarding various aspects of insurance contracts. The aggregate losses over a fixed time period is often modeled by mixing the distributions of loss frequency and severity, whereby the distribution resulted from this approach is called a compound distribution. However, in many cases, realistic probability distributions for loss frequency and severity cannot be combined mathematically to derive the compound distribution of aggregate losses. Approach: This study aimed to approximate the aggregate loss distribution using simulation approach. In particular, the approximation of aggregate losses was based on a compound Poisson-Pareto distribution. The effects of deductible and policy limit on the individual loss as well as the aggregate losses were also investigated. Results: Based on the results, the approximation of compound Poisson-Pareto distribution via simulation approach agreed with the theoretical mean and variance of each of the loss frequency, loss severity and aggregate losses. Conclusion: This study approximated the compound distribution of aggregate losses using simulation approach. The investigation on retained losses and insurance claims allowed an insured or a company to select an insurance contract that fulfills its requirement. In particular, if a company wants to have an additional risk reduction, it can compare alternative policies by considering the worthiness of the additional expected total cost which can be estimated via simulation approach.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-11-30
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
Approximations in the PE-method
DEFF Research Database (Denmark)
Arranz, Marta Galindo
1996-01-01
Two differenct sources of errors may occur in the implementation of the PE methods; a phase error introduced in the approximation of a pseudo-differential operator and an amplitude error generated from the starting field. First, the inherent phase errors introduced in the solution are analyzed...
Approximating the DGP of China's Quarterly GDP
Ph.H.B.F. Franses (Philip Hans); H. Mees (Heleen)
2010-01-01
textabstractWe demonstrate that the data generating process (DGP) of China’s cumulated quarterly Gross Domestic Product (GDP, current prices), as it is reported by the National Bureau of Statistics of China, can be (very closely) approximated by a simple rule. This rule is that annual growth in any
OPTICAL QUANTIFICATION OF APPROXIMAL CARIES INVITRO
VANDERIJKE, JW; HERKSTROTER, FM; TENBOSCH, JJ
1991-01-01
A fluorescent dye was applied to extracted premolars with either early artificial lesions or natural white-spot lesions. The teeth were placed in an approximal geometry, and with a specially designed fibre-optic probe the fluorescence of the dye was measured in the lesions. The same fibre-optic
Approximation Algorithms for Model-Based Diagnosis
Feldman, A.B.
2010-01-01
Model-based diagnosis is an area of abductive inference that uses a system model, together with observations about system behavior, to isolate sets of faulty components (diagnoses) that explain the observed behavior, according to some minimality criterion. This thesis presents greedy approximation a
An Approximation of Ultra-Parabolic Equations
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2012-01-01
Full Text Available The first and second order of accuracy difference schemes for the approximate solution of the initial boundary value problem for ultra-parabolic equations are presented. Stability of these difference schemes is established. Theoretical results are supported by the result of numerical examples.
Approximation Algorithms for Model-Based Diagnosis
Feldman, A.B.
2010-01-01
Model-based diagnosis is an area of abductive inference that uses a system model, together with observations about system behavior, to isolate sets of faulty components (diagnoses) that explain the observed behavior, according to some minimality criterion. This thesis presents greedy approximation a
Approximating the DGP of China's Quarterly GDP
Ph.H.B.F. Franses (Philip Hans); H. Mees (Heleen)
2010-01-01
textabstractWe demonstrate that the data generating process (DGP) of China’s cumulated quarterly Gross Domestic Product (GDP, current prices), as it is reported by the National Bureau of Statistics of China, can be (very closely) approximated by a simple rule. This rule is that annual growth in any
$\\Phi$-derivable approximations in gauge theories
Arrizabalaga, A
2003-01-01
We discuss the method of $\\Phi$-derivable approximations in gauge theories. There, two complications arise, namely the violation of Bose symmetry in correlation functions and the gauge dependence. For the latter we argue that the error introduced by the gauge dependent terms is controlled, therefore not invalidating the method.
Approximations of Two-Attribute Utility Functions
1976-09-01
Introduction to Approximation Theory, McGraw-Hill, New York, 1966. Faber, G., Uber die interpolatorische Darstellung stetiger Funktionen, Deutsche...Management Review 14 (1972b) 37-50. Keeney, R. L., A decision analysis with multiple objectives: the Mexico City airport, Bell Journal of Economics
Approximate Furthest Neighbor in High Dimensions
DEFF Research Database (Denmark)
Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen
2015-01-01
-dimensional Euclidean space. We build on the technique of Indyk (SODA 2003), storing random projections to provide sublinear query time for AFN. However, we introduce a different query algorithm, improving on Indyk’s approximation factor and reducing the running time by a logarithmic factor. We also present a variation...
Virial expansion coefficients in the harmonic approximation
DEFF Research Database (Denmark)
R. Armstrong, J.; Zinner, Nikolaj Thomas; V. Fedorov, D.
2012-01-01
The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated...
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Intrinsic Diophantine approximation on general polynomial surfaces
DEFF Research Database (Denmark)
Tiljeset, Morten Hein
2017-01-01
We study the Hausdorff measure and dimension of the set of intrinsically simultaneously -approximable points on a curve, surface, etc, given as a graph of integer polynomials. We obtain complete answers to these questions for algebraically “nice” manifolds. This generalizes earlier work done...
Turbo Equalization Using Partial Gaussian Approximation
DEFF Research Database (Denmark)
Zhang, Chuanzong; Wang, Zhongyong; Manchón, Carles Navarro
2016-01-01
returned by the equalizer by using a partial Gaussian approximation (PGA). We exploit the specific structure of the ISI channel model to compute the latter messages from the beliefs obtained using a Kalman smoother/equalizer. Doing so leads to a significant complexity reduction compared to the initial PGA...
Subset Selection by Local Convex Approximation
DEFF Research Database (Denmark)
Øjelund, Henrik; Sadegh, Payman; Madsen, Henrik
1999-01-01
least squares criterion. We propose an optimization technique for the posed probelm based on a modified version of the Newton-Raphson iterations, combined with a backward elimination type algorithm. THe Newton-Raphson modification concerns iterative approximations to the non-convex cost function...
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal...
Counting independent sets using the Bethe approximation
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Laboratory; Chandrasekaran, V [MIT; Gamarmik, D [MIT; Shah, D [MIT; Sin, J [MIT
2009-01-01
The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques.
Hybrid diffusion approximation in highly absorbing media and its effects of source approximation
Institute of Scientific and Technical Information of China (English)
Huijuan Tian; Ying Liu; Lijun Wang; Yuhui Zhang; Lifeng Xiao
2009-01-01
A modified diffusion approximation model called the hybrid diffusion approximation that can be used for highly absorbing media is investigated.The analytic solution of the hybrid diffusion approximation for reflectance in two-source approximation and steady-state case with extrapolated boundary is obtained.The effects of source approximation on the analytic solution are investigated,and it is validated that two-source approximation in highly absorbing media to describe the optical properties of biological tissue is necessary.Monte Carlo simulation of recovering optical parameters from reflectant data is done with the use of this model.The errors of recovering μa and μ's are smaller than 15% for the reduced albedo between 0.77 and 0.5 with the source-detector separation of 0.4-3 ram.
Polynomial approximation and cubature at approximate Fekete and Leja points of the cylinder
De Marchi, Stefano
2011-01-01
The paper deals with polynomial interpolation, least-square approximation and cubature of functions defined on the rectangular cylinder, $K=D\\times [-1,1]$, with $D$ the unit disk. The nodes used for these processes are the {\\it Approximate Fekete Points} (AFP) and the {\\it Discrete Leja Points} (DLP) extracted from suitable {\\it Weakly Admissible Meshes} (WAMs) of the cylinder. From the analysis of the growth of the Lebesgue constants, approximation and cubature errors, we show that the AFP and the DLP extracted from WAM are good points for polynomial approximation and numerical integration of functions defined on the cylinder.
Traveltime approximations for inhomogeneous HTI media
Alkhalifah, Tariq Ali
2011-01-01
Traveltimes information is convenient for parameter estimation especially if the medium is described by an anisotropic set of parameters. This is especially true if we could relate traveltimes analytically to these medium parameters, which is generally hard to do in inhomogeneous media. As a result, I develop traveltimes approximations for horizontaly transversely isotropic (HTI) media as simplified and even linear functions of the anisotropic parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to η and the azimuthal symmetry direction (usually used to describe the fracture direction) from a generally inhomogeneous elliptically anisotropic background medium. The resulting approximations can provide accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations out there. These equations will allow us to readily extend the inhomogenous background elliptical anisotropic model to an HTI with a variable, but smoothly varying, η and horizontal symmetry direction values. © 2011 Society of Exploration Geophysicists.
Approximate inverse preconditioners for general sparse matrices
Energy Technology Data Exchange (ETDEWEB)
Chow, E.; Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)
1994-12-31
Preconditioned Krylov subspace methods are often very efficient in solving sparse linear matrices that arise from the discretization of elliptic partial differential equations. However, for general sparse indifinite matrices, the usual ILU preconditioners fail, often because of the fact that the resulting factors L and U give rise to unstable forward and backward sweeps. In such cases, alternative preconditioners based on approximate inverses may be attractive. We are currently developing a number of such preconditioners based on iterating on each column to get the approximate inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., we must use sparse-matrix by sparse-vector type operatoins. We will discuss a few options and compare their performance on standard problems from the Harwell-Boeing collection.
Approximate Lesion Localization in Dermoscopy Images
Celebi, M Emre; Schaefer, Gerald; Stoecker, William V; 10.1111/j.1600-0846.2009.00357.x
2010-01-01
Background: Dermoscopy is one of the major imaging modalities used in the diagnosis of melanoma and other pigmented skin lesions. Due to the difficulty and subjectivity of human interpretation, automated analysis of dermoscopy images has become an important research area. Border detection is often the first step in this analysis. Methods: In this article, we present an approximate lesion localization method that serves as a preprocessing step for detecting borders in dermoscopy images. In this method, first the black frame around the image is removed using an iterative algorithm. The approximate location of the lesion is then determined using an ensemble of thresholding algorithms. Results: The method is tested on a set of 428 dermoscopy images. The localization error is quantified by a metric that uses dermatologist determined borders as the ground truth. Conclusion: The results demonstrate that the method presented here achieves both fast and accurate localization of lesions in dermoscopy images.
Performance of a Distributed Stochastic Approximation Algorithm
Bianchi, Pascal; Hachem, Walid
2012-01-01
In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each node in a network updates a local estimate using a stochastic approximation algorithm with decreasing step size, and a gossip step, where a node computes a local weighted average between its estimates and those of its neighbors. Convergence of the estimates toward a consensus is established under weak assumptions. The approach relies on two main ingredients: the existence of a Lyapunov function for the mean field in the agreement subspace, and a contraction property of the random matrices of weights in the subspace orthogonal to the agreement subspace. A second order analysis of the algorithm is also performed under the form of a Central Limit Theorem. The Polyak-averaged version of the algorithm is also considered.
Approximate gauge symemtry of composite vector bosons
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Mahiko
2010-06-01
It can be shown in a solvable field theory model that the couplings of the composite vector mesons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in more an intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.
Quasi-chemical approximation for polyatomic mixtures
Dávila, M V; Matoz-Fernandez, D A; Ramirez-Pastor, A J
2016-01-01
The statistical thermodynamics of binary mixtures of polyatomic species was developed on a generalization in the spirit of the lattice-gas model and the quasi-chemical approximation (QCA). The new theoretical framework is obtained by combining: (i) the exact analytical expression for the partition function of non-interacting mixtures of linear $k$-mers and $l$-mers (species occupying $k$ sites and $l$ sites, respectively) adsorbed in one dimension, and its extension to higher dimensions; and (ii) a generalization of the classical QCA for multicomponent adsorbates and multisite-occupancy adsorption. The process is analyzed through the partial adsorption isotherms corresponding to both species of the mixture. Comparisons with analytical data from Bragg-Williams approximation (BWA) and Monte Carlo simulations are performed in order to test the validity of the theoretical model. Even though a good fitting is obtained from BWA, it is found that QCA provides a more accurate description of the phenomenon of adsorpti...
Improved Approximations for Some Polymer Extension Models
Petrosyan, Rafayel
2016-01-01
We propose approximations for force-extension dependencies for the freely jointed chain (FJC) and worm-like chain (WLC) models as well as for extension-force dependence for the WLC model. Proposed expressions show less than 1% relative error in the useful range of the corresponding variables. These results can be applied for fitting force-extension curves obtained in molecular force spectroscopy experiments. Particularly they can be useful for cases where one has geometries of springs in series and/or in parallel where particular combination of expressions should be used for fitting the data. All approximations have been obtained following the same procedure of determining the asymptotes and then reducing the relative error of that expression by adding an appropriate term obtained from fitting its absolute error.
Regularized Laplacian Estimation and Fast Eigenvector Approximation
Perry, Patrick O
2011-01-01
Recently, Mahoney and Orecchia demonstrated that popular diffusion-based procedures to compute a quick \\emph{approximation} to the first nontrivial eigenvector of a data graph Laplacian \\emph{exactly} solve certain regularized Semi-Definite Programs (SDPs). In this paper, we extend that result by providing a statistical interpretation of their approximation procedure. Our interpretation will be analogous to the manner in which $\\ell_2$-regularized or $\\ell_1$-regularized $\\ell_2$-regression (often called Ridge regression and Lasso regression, respectively) can be interpreted in terms of a Gaussian prior or a Laplace prior, respectively, on the coefficient vector of the regression problem. Our framework will imply that the solutions to the Mahoney-Orecchia regularized SDP can be interpreted as regularized estimates of the pseudoinverse of the graph Laplacian. Conversely, it will imply that the solution to this regularized estimation problem can be computed very quickly by running, e.g., the fast diffusion-base...
On approximative solutions of multistopping problems
Faller, Andreas; 10.1214/10-AAP747
2012-01-01
In this paper, we consider multistopping problems for finite discrete time sequences $X_1,...,X_n$. $m$-stops are allowed and the aim is to maximize the expected value of the best of these $m$ stops. The random variables are neither assumed to be independent not to be identically distributed. The basic assumption is convergence of a related imbedded point process to a continuous time Poisson process in the plane, which serves as a limiting model for the stopping problem. The optimal $m$-stopping curves for this limiting model are determined by differential equations of first order. A general approximation result is established which ensures convergence of the finite discrete time $m$-stopping problem to that in the limit model. This allows the construction of approximative solutions of the discrete time $m$-stopping problem. In detail, the case of i.i.d. sequences with discount and observation costs is discussed and explicit results are obtained.
Numerical and approximate solutions for plume rise
Krishnamurthy, Ramesh; Gordon Hall, J.
Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585-590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).
Approximated solutions to Born-Infeld dynamics
Energy Technology Data Exchange (ETDEWEB)
Ferraro, Rafael [Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA),Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Nigro, Mauro [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina)
2016-02-01
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.
SOME CONVERSE RESULTS ON ONESIDED APPROXIMATION: JUSTIFICATIONS
Institute of Scientific and Technical Information of China (English)
Wang Jianli; Zhou Songping
2003-01-01
The present paper deals with best onesided approximation rate in Lp spaces ～En (f)Lp of f ∈ C2π. Although it is clear that the estimate ～En(f)Lp≤C ‖f‖ Lp cannot be correct for all f ∈ Lp2π in case p＜∞, the question whether ～En (f)Lp ≤Cω (f, n-1 )Lp or ～En(f)Lp ≤CEn(f)Lp holds for f ∈ C2π remains totally untouched.Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.
An Origami Approximation to the Cosmic Web
Neyrinck, Mark C
2014-01-01
The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in 'polygonal' or 'polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls ...
Improved Approximation for Orienting Mixed Graphs
Gamzu, Iftah
2012-01-01
An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs. The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that admit a directed source-target path. This problem has recently arisen in the study of biological networks, and it also has applications in communication networks. In this paper, we identify an interesting local-to-global orientation property. This property enables us to modify the best known algorithms for maximum mixed graph orientation and some of its special structured instances, due to Elberfeld et al. (CPM '11), and obtain improved approximation ratios. We further proceed by developing an algorithm that achieves an even better approximation guarantee for the general setting of the problem. Finally, we study several well-motivated variants of this orientation problem.
Flow past a porous approximate spherical shell
Srinivasacharya, D.
2007-07-01
In this paper, the creeping flow of an incompressible viscous liquid past a porous approximate spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier Stokes equation. The flow within the porous annulus region of the shell is governed by Darcy’s Law. The boundary conditions used at the interface are continuity of the normal velocity, continuity of the pressure and Beavers and Joseph slip condition. An exact solution for the problem is obtained. An expression for the drag on the porous approximate spherical shell is obtained. The drag experienced by the shell is evaluated numerically for several values of the parameters governing the flow.
Nonlinear analysis approximation theory, optimization and applications
2014-01-01
Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
Rough Sets in Approximate Solution Space
Institute of Scientific and Technical Information of China (English)
Hui Sun; Wei Tian; Qing Liu
2006-01-01
As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and in complete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set. A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.
Second derivatives for approximate spin projection methods.
Thompson, Lee M; Hratchian, Hrant P
2015-02-07
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.
Analytical Ballistic Trajectories with Approximately Linear Drag
Directory of Open Access Journals (Sweden)
Giliam J. P. de Carpentier
2014-01-01
Full Text Available This paper introduces a practical analytical approximation of projectile trajectories in 2D and 3D roughly based on a linear drag model and explores a variety of different planning algorithms for these trajectories. Although the trajectories are only approximate, they still capture many of the characteristics of a real projectile in free fall under the influence of an invariant wind, gravitational pull, and terminal velocity, while the required math for these trajectories and planners is still simple enough to efficiently run on almost all modern hardware devices. Together, these properties make the proposed approach particularly useful for real-time applications where accuracy and performance need to be carefully balanced, such as in computer games.
Pade approximants of random Stieltjes series
Marklof, Jens; Wolowski, Lech
2007-01-01
We consider the random continued fraction S(t) := 1/(s_1 + t/(s_2 + t/(s_3 + >...))) where the s_n are independent random variables with the same gamma distribution. For every realisation of the sequence, S(t) defines a Stieltjes function. We study the convergence of the finite truncations of the continued fraction or, equivalently, of the diagonal Pade approximants of the function S(t). By using the Dyson--Schmidt method for an equivalent one-dimensional disordered system, and the results of Marklof et al. (2005), we obtain explicit formulae (in terms of modified Bessel functions) for the almost-sure rate of convergence of these approximants, and for the almost-sure distribution of their poles.
Nonlinear Stochastic PDEs: Analysis and Approximations
2016-05-23
Distribution free Skorokhod-Malliavian Calculus , Stochastic And Partial Differential Equations: Analysis and Computations, (06 2016): 319. doi : Z. Zhang... doi : X. Wang, Boris Rozovskii. The Wick-Malliavin Approximation on Elliptic Problems with Long-Normal Random Coefficients, SIAM J Scientific...Computing, (10 2013): 2370. doi : Z. Zhang, M.V. Trrtykov, B. Rozovskii, G.E. Karniadakis. A Recursive Sparse Grid Collocation Methd for Differential
Finite State Transducers Approximating Hidden Markov Models
Kempe, A
1999-01-01
This paper describes the conversion of a Hidden Markov Model into a sequential transducer that closely approximates the behavior of the stochastic model. This transformation is especially advantageous for part-of-speech tagging because the resulting transducer can be composed with other transducers that encode correction rules for the most frequent tagging errors. The speed of tagging is also improved. The described methods have been implemented and successfully tested on six languages.
On approximation of functions by product operators
Directory of Open Access Journals (Sweden)
Hare Krishna Nigam
2013-12-01
Full Text Available In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α,r, 1≤ r <∞ and the weighted class W(Lr,ξ(t, 1≤ r <∞ by (C,2(E,1 product operators have been obtained. The results obtained in the present paper generalize various known results on single operators.
Variational Bayesian Approximation methods for inverse problems
Mohammad-Djafari, Ali
2012-09-01
Variational Bayesian Approximation (VBA) methods are recent tools for effective Bayesian computations. In this paper, these tools are used for inverse problems where the prior models include hidden variables and where where the estimation of the hyper parameters has also to be addressed. In particular two specific prior models (Student-t and mixture of Gaussian models) are considered and details of the algorithms are given.
Neutrino Mass Matrix with Approximate Flavor Symmetry
Riazuddin, M
2003-01-01
Phenomenological implications of neutrino oscillations implied by recent experimental data on pattern of neutrino mass matrix are disscussed. It is shown that it is possible to have a neutrino mass matrix which shows approximate flavor symmetry; the neutrino mass differences arise from flavor violation in off-diagonal Yukawa couplings. Two modest extensions of the standard model, which can embed the resulting neutrino mass matix have also been discussed.
Fast approximate convex decomposition using relative concavity
Ghosh, Mukulika
2013-02-01
Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-07
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-05
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Approximation of pressure perturbations by FEM
Bichir, Cătălin - Liviu
2011-01-01
In the mathematical problem of linear hydrodynamic stability for shear flows against Tollmien-Schlichting perturbations, the continuity equation for the perturbation of the velocity is replaced by a Poisson equation for the pressure perturbation. The resulting eigenvalue problem, an alternative form for the two - point eigenvalue problem for the Orr - Sommerfeld equation, is formulated in a variational form and this one is approximated by finite element method (FEM). Possible applications to concrete cases are revealed.
Onsager principle as a tool for approximation
Institute of Scientific and Technical Information of China (English)
Masao Doi
2015-01-01
Onsager principle is the variational principle proposed by Onsager in his celebrated paper on the reciprocal relation. The principle has been shown to be useful in deriving many evolution equations in soft matter physics. Here the principle is shown to be useful in solving such equations approximately. Two examples are discussed: the diffusion dynamics and gel dynamics. Both examples show that the present method is novel and gives new results which capture the essential dynamics in the system.
APPROXIMATE OUTPUT REGULATION FOR AFFINE NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Yali DONG; Daizhan CHENG; Huashu QIN
2003-01-01
Output regulation for affine nonlinear systems driven by an exogenous signal is investigated in this paper. In the absence of the standard exosystem hypothesis, we assume availability of the instantaneous values of the exogenous signal and its first time-derivative for use in the control law.For affine nonlinear systems, the necessary and sufficient conditions of the solvability of approximate output regulation problem are obtained. The precise form of the control law is presented under some suitable assumptions.
Space-Time Approximation with Sparse Grids
Energy Technology Data Exchange (ETDEWEB)
Griebel, M; Oeltz, D; Vassilevski, P S
2005-04-14
In this article we introduce approximation spaces for parabolic problems which are based on the tensor product construction of a multiscale basis in space and a multiscale basis in time. Proper truncation then leads to so-called space-time sparse grid spaces. For a uniform discretization of the spatial space of dimension d with O(N{sup d}) degrees of freedom, these spaces involve for d > 1 also only O(N{sup d}) degrees of freedom for the discretization of the whole space-time problem. But they provide the same approximation rate as classical space-time Finite Element spaces which need O(N{sup d+1}) degrees of freedoms. This makes these approximation spaces well suited for conventional parabolic and for time-dependent optimization problems. We analyze the approximation properties and the dimension of these sparse grid space-time spaces for general stable multiscale bases. We then restrict ourselves to an interpolatory multiscale basis, i.e. a hierarchical basis. Here, to be able to handle also complicated spatial domains {Omega}, we construct the hierarchical basis from a given spatial Finite Element basis as follows: First we determine coarse grid points recursively over the levels by the coarsening step of the algebraic multigrid method. Then, we derive interpolatory prolongation operators between the respective coarse and fine grid points by a least squares approach. This way we obtain an algebraic hierarchical basis for the spatial domain which we then use in our space-time sparse grid approach. We give numerical results on the convergence rate of the interpolation error of these spaces for various space-time problems with two spatial dimensions. Also implementational issues, data structures and questions of adaptivity are addressed to some extent.
Local characterisation of approximately finite operator algebras
Haworth, P. A.
2000-01-01
We show that the family of nest algebras with $r$ non-zero nest projections is stable, in the sense that an approximate containment of one such algebra within another is close to an exact containment. We use this result to give a local characterisation of limits formed from this family. We then consider quite general regular limit algebras and characterise these algebras using a local condition which reflects the assumed regularity of the system.
APPROXIMATION MULTIDIMENSION FUCTION WITH FUNCTIONAL NETWORK
Institute of Scientific and Technical Information of China (English)
Li Weibin; Liu Fang; Jiao Licheng; Zhang Shuling; Li Zongling
2006-01-01
The functional network was introduced by E.Catillo, which extended the neural network. Not only can it solve the problems solved, but also it can formulate the ones that cannot be solved by traditional network.This paper applies functional network to approximate the multidimension function under the ridgelet theory.The method performs more stable and faster than the traditional neural network. The numerical examples demonstrate the performance.
Development of New Density Functional Approximations
Su, Neil Qiang; Xu, Xin
2017-05-01
Kohn-Sham density functional theory has become the leading electronic structure method for atoms, molecules, and extended systems. It is in principle exact, but any practical application must rely on density functional approximations (DFAs) for the exchange-correlation energy. Here we emphasize four aspects of the subject: (a) philosophies and strategies for developing DFAs; (b) classification of DFAs; (c) major sources of error in existing DFAs; and (d) some recent developments and future directions.
Solving Math Problems Approximately: A Developmental Perspective.
Directory of Open Access Journals (Sweden)
Dana Ganor-Stern
Full Text Available Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults' ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger than the exact answer and when it was far (vs. close from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner.
Additive Approximation Algorithms for Modularity Maximization
Kawase, Yasushi; Matsui, Tomomi; Miyauchi, Atsushi
2016-01-01
The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004). Community detection in graphs is now often conducted through modularity maximization: given an undirected graph $G=(V,E)$, we are asked to find a partition $\\mathcal{C}$ of $V$ that maximizes the modularity. Although numerous algorithms have been developed to date, most of them have no theoretical approximation guarantee. Recently, to overcome this issue, the design of modularity max...
Approximate Revenue Maximization in Interdependent Value Settings
Chawla, Shuchi; Fu, Hu; Karlin, Anna
2014-01-01
We study revenue maximization in settings where agents' values are interdependent: each agent receives a signal drawn from a correlated distribution and agents' values are functions of all of the signals. We introduce a variant of the generalized VCG auction with reserve prices and random admission, and show that this auction gives a constant approximation to the optimal expected revenue in matroid environments. Our results do not require any assumptions on the signal distributions, however, ...
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
Ranking Support Vector Machine with Kernel Approximation.
Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi
2017-01-01
Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.
Approximation Algorithms for Directed Width Parameters
Kintali, Shiva; Kumar, Akash
2011-01-01
Treewidth of an undirected graph measures how close the graph is to being a tree. Several problems that are NP-hard on general graphs are solvable in polynomial time on graphs with bounded treewidth. Motivated by the success of treewidth, several directed analogues of treewidth have been introduced to measure the similarity of a directed graph to a directed acyclic graph (DAG). Directed treewidth, D-width, DAG-width, Kelly-width and directed pathwidth are some such parameters. In this paper, we present the first approximation algorithms for all these five directed width parameters. For directed treewidth and D-width we achieve an approximation factor of O(sqrt{logn}). For DAG-width, Kelly-width and directed pathwidth we achieve an O({\\log}^{3/2}{n}) approximation factor. Our algorithms are constructive, i.e., they construct the decompositions associated with these parameters. The width of these decompositions are within the above mentioned factor of the corresponding optimal width.
Conference on Abstract Spaces and Approximation
Szökefalvi-Nagy, B; Abstrakte Räume und Approximation; Abstract spaces and approximation
1969-01-01
The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs littl...
Symmetry and approximability of submodular maximization problems
Vondrak, Jan
2011-01-01
A number of recent results on optimization problems involving submodular functions have made use of the multilinear relaxation of the problem. These results hold typically in the value oracle model, where the objective function is accessible via a black box returning f(S) for a given S. We present a general approach to deriving inapproximability results in the value oracle model, based on the notion of symmetry gap. Our main result is that for any fixed instance that exhibits a certain symmetry gap in its multilinear relaxation, there is a naturally related class of instances for which a better approximation factor than the symmetry gap would require exponentially many oracle queries. This unifies several known hardness results for submodular maximization, and implies several new ones. In particular, we prove that there is no constant-factor approximation for the problem of maximizing a non-negative submodular function over the bases of a matroid. We also provide a closely matching approximation algorithm for...
CMB-lensing beyond the Born approximation
Marozzi, Giovanni; Fanizza, Giuseppe; Di Dio, Enea; Durrer, Ruth
2016-09-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles l lesssim 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.
Green-Ampt approximations: A comprehensive analysis
Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K.
2016-04-01
Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems.
The Complexity of Approximately Counting Stable Matchings
Chebolu, Prasad; Martin, Russell
2010-01-01
We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances between "preference points" and "attribute points". Irving and Leather proved that counting the number of stable matchings in the general case is $#P$-complete. Counting the number of stable matchings is reducible to counting the number of downsets in a (related) partial order and is interreducible, in an approximation-preserving sense, to a class of problems that includes counting the number of independent sets in a bipartite graph ($#BIS$). It is conjectured that no FPRAS exists for this class of problems. We show this approximation-preserving interreducibilty remains even in the restricted $k$-attribute setting when $k \\geq 3$ (dot products) or $k \\geq 2$ (Euclidean distances). Finally, we show it is easy to count the number of stable matchings in the 1-attribute dot-product ...
An Origami Approximation to the Cosmic Web
Neyrinck, Mark C.
2016-10-01
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 to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.
Generalized Quasilinear Approximation: Application to Zonal Jets
Marston, J. B.; Chini, G. P.; Tobias, S. M.
2016-05-01
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems.
Cylindrical Helix Spline Approximation of Spatial Curves
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, we present a new method for approximating spatial curves with a G1 cylindrical helix spline within a prescribed tolerance. We deduce the general formulation of a cylindrical helix,which has 11 freedoms. This means that it needs 11 restrictions to determine a cylindrical helix. Given a spatial parametric curve segment, including the start point and the end point of this segment, the tangent and the principal normal of the start point, we can always find a cylindrical segment to interpolate the given direction and position vectors. In order to approximate the known parametric curve within the prescribed tolerance, we adopt the trial method step by step. First, we must ensure the helix segment to interpolate the given two end points and match the principal normal and tangent of the start point, and then, we can keep the deviation between the cylindrical helix segment and the known curve segment within the prescribed tolerance everywhere. After the first segment had been formed, we can construct the next segment. Circularly, we can construct the G1 cylindrical helix spline to approximate the whole spatial parametric curve within the prescribed tolerance. Several examples are also given to show the efficiency of this method.
Approximating Low-Dimensional Coverage Problems
Badanidiyuru, Ashwinkumar; Lee, Hooyeon
2011-01-01
We study the complexity of the maximum coverage problem, restricted to set systems of bounded VC-dimension. Our main result is a fixed-parameter tractable approximation scheme: an algorithm that outputs a $(1-\\eps)$-approximation to the maximum-cardinality union of $k$ sets, in running time $O(f(\\eps,k,d)\\cdot poly(n))$ where $n$ is the problem size, $d$ is the VC-dimension of the set system, and $f(\\eps,k,d)$ is exponential in $(kd/\\eps)^c$ for some constant $c$. We complement this positive result by showing that the function $f(\\eps,k,d)$ in the running-time bound cannot be replaced by a function depending only on $(\\eps,d)$ or on $(k,d)$, under standard complexity assumptions. We also present an improved upper bound on the approximation ratio of the greedy algorithm in special cases of the problem, including when the sets have bounded cardinality and when they are two-dimensional halfspaces. Complementing these positive results, we show that when the sets are four-dimensional halfspaces neither the greedy ...
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.
2011-05-12
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
CMB-lensing beyond the Born approximation
Marozzi, Giovanni; Di Dio, Enea; Durrer, Ruth
2016-01-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles $\\ell\\lesssim 2500$, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum...
Approximate Equalities on Rough Intuitionistic Fuzzy Sets and an Analysis of Approximate Equalities
Directory of Open Access Journals (Sweden)
B. K. Tripathy
2012-03-01
Full Text Available In order to involve user knowledge in determining equality of sets, which may not be equal in the mathematical sense, three types of approximate (rough equalities were introduced by Novotny and Pawlak ([8, 9, 10]. These notions were generalized by Tripathy, Mitra and Ojha ([13], who introduced the concepts of approximate (rough equivalences of sets. Rough equivalences capture equality of sets at a higher level than rough equalities. More properties of these concepts were established in [14]. Combining the conditions for the two types of approximate equalities, two more approximate equalities were introduced by Tripathy [12] and a comparative analysis of their relative efficiency was provided. In [15], the four types of approximate equalities were extended by considering rough fuzzy sets instead of only rough sets. In fact the concepts of leveled approximate equalities were introduced and properties were studied. In this paper we proceed further by introducing and studying the approximate equalities based on rough intuitionistic fuzzy sets instead of rough fuzzy sets. That is we introduce the concepts of approximate (rough equalities of intuitionistic fuzzy sets and study their properties. We provide some real life examples to show the applications of rough equalities of fuzzy sets and rough equalities of intuitionistic fuzzy sets.
Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin
2016-01-01
What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics.
On the Use of Approximations in Statistical Physics
Hoffmann, C
2003-01-01
Two approximations are frequently used in statistical physics: the first one, which we shall name the mean values approximation, is generally (and improperly) named as "maximum term approximation". The second is the "Stirling approximation". In this paper we demonstrate that the error introduced by the first approximation is exactly compensated by the second approximation in the calculation of mean values of multinomial distributions.
Photoelectron spectroscopy and the dipole approximation
Energy Technology Data Exchange (ETDEWEB)
Hemmers, O.; Hansen, D.L.; Wang, H. [Univ. of Nevada, Las Vegas, NV (United States)] [and others
1997-04-01
Photoelectron spectroscopy is a powerful technique because it directly probes, via the measurement of photoelectron kinetic energies, orbital and band structure in valence and core levels in a wide variety of samples. The technique becomes even more powerful when it is performed in an angle-resolved mode, where photoelectrons are distinguished not only by their kinetic energy, but by their direction of emission as well. Determining the probability of electron ejection as a function of angle probes the different quantum-mechanical channels available to a photoemission process, because it is sensitive to phase differences among the channels. As a result, angle-resolved photoemission has been used successfully for many years to provide stringent tests of the understanding of basic physical processes underlying gas-phase and solid-state interactions with radiation. One mainstay in the application of angle-resolved photoelectron spectroscopy is the well-known electric-dipole approximation for photon interactions. In this simplification, all higher-order terms, such as those due to electric-quadrupole and magnetic-dipole interactions, are neglected. As the photon energy increases, however, effects beyond the dipole approximation become important. To best determine the range of validity of the dipole approximation, photoemission measurements on a simple atomic system, neon, where extra-atomic effects cannot play a role, were performed at BL 8.0. The measurements show that deviations from {open_quotes}dipole{close_quotes} expectations in angle-resolved valence photoemission are observable for photon energies down to at least 0.25 keV, and are quite significant at energies around 1 keV. From these results, it is clear that non-dipole angular-distribution effects may need to be considered in any application of angle-resolved photoelectron spectroscopy that uses x-ray photons of energies as low as a few hundred eV.
Approximations and Solution Estimates in Optimization
2016-04-06
this paper, we lay out a broad framework for quantifying approximations by viewing finite- and infinite-dimensional constrained minimization prob- lems...Lipschitz-stability result for near-optimal solutions with a Lipschitz modulus of 1. We also construct a class of “ elementary ” functions called epi...if C nonempty and D empty, and e(C,D) = 0 otherwise. Roughly speaking , d̂lρ(f, g) is the “padding” of epi g needed for it to contain epi f ∩ Sρ and
Exponential Polynomial Approximation with Unrestricted Upper Density
Institute of Scientific and Technical Information of China (English)
Xiang Dong YANG
2011-01-01
We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in Lp/α, where Lp/α is the weighted Banach space of complex continuous functions f defined on the real axis (R)satisfying (∫+∞/-∞|f(t)|pe-α(t)dt)1/p, 1 < p < ∞, and α(t) is a nonnegative continuous function defined on the real axis (R). In this paper, the upper density of the sequence which forms the exponential polynomials is not required to be finite. In the study of weighted polynomial approximation, consideration of the case is new.
Error Minimization of Polynomial Approximation of Delta
Indian Academy of Sciences (India)
Islam Sana; Sadiq Muhammad; Qureshi Muhammad Shahid
2008-09-01
The difference between Universal time (UT) and Dynamical time (TD), known as Delta ( ) is tabulated for the first day of each year in the Astronomical Almanac. During the last four centuries it is found that there are large differences between its values for two consecutive years. Polynomial approximations have been developed to obtain the values of for any time of a year for the period AD 1620 to AD 2000 (Meeu 2000) as no dynamical theories describe the variations in . In this work, a new set of polynomials for is obtained for the period AD 1620 to AD 2007 that is found to produce better results compared to previous attempts.
Dynamic system evolution and markov chain approximation
Directory of Open Access Journals (Sweden)
Roderick V. Nicholas Melnik
1998-01-01
Full Text Available In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of mathematical models is treated as a decision making process with limited available information.The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a discrete space–time of events. A stable approximation of the chain has been derived and the limiting cases are discussed. An intrinsic interconnection of constructive, sequential, and evolutionary approaches in related optimization problems provides new challenges for future work.
The Numerical Approximation of Functional Differential Equations
Venturi, Daniele
2016-01-01
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equations), quantum field theory (Schwinger-Dyson equations) and statistical physics (equations for generating functionals and effective action methods). However, no effective numerical method has yet been developed to compute their solution. The purpose of this manuscript is to fill this gap, and provide a new perspective on the problem of numerical approximation of nonlinear functionals and functional differential equations. The proposed methods will be described and demonstrated in various examples.
Topics in multivariate approximation and interpolation
Jetter, Kurt
2005-01-01
This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for gr
Approximation algorithms for some vehicle routing problems
Bazgan, Cristina; Hassin, Refael; Monnot, Jérôme
2005-01-01
We study vehicle routing problems with constraints on the distance traveled by each vehicle or on the number of vehicles. The objective is either to minimize the total distance traveled by vehicles or to minimize the number of vehicles used. We design constant differential approximation algorithms for kVRP. Note that, using the differential bound for METRIC 3VRP, we obtain the randomized standard ratio . This is an improvement of the best-known bound of 2 given by Haimovich et al. (Vehicle Ro...
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A V
2015-01-01
The eikonal approximation for moderately small scattering amplitudes is considered. With the purpose of using for their numerical estimations, the formulas are derived which contain no Bessel functions, and, hence, no rapidly oscillating integrands. To obtain these formulas, the improper integrals of the first kind which contain products of the Bessel functions J_0(z) are studied. The expression with four functions J_0(z) is generalized. The expressions for the integrals with the product of five and six Bessel functions J_0(z) are also found. The known formula for the improper integral with two functions J_nu(z) is generalized for non-integer nu.
Approximate Distance Oracles with Improved Query Time
Wulff-Nilsen, Christian
2012-01-01
Given an undirected graph $G$ with $m$ edges, $n$ vertices, and non-negative edge weights, and given an integer $k\\geq 2$, we show that a $(2k-1)$-approximate distance oracle for $G$ of size $O(kn^{1 + 1/k})$ and with $O(\\log k)$ query time can be constructed in $O(\\min\\{kmn^{1/k},\\sqrt km + kn^{1 + c/\\sqrt k}\\})$ time for some constant $c$. This improves the $O(k)$ query time of Thorup and Zwick. For any $0 0$ and $k = O(\\log n/\\log\\log n)$.
Compressive Imaging via Approximate Message Passing
2015-09-04
20] uses an adaptive Wiener filter [21] for 2D denoising. Another option is to use a more sophisticated image 2D denoiser such as BM3D [22] within AMP... filtering ,” IEEE Trans. Image Process ., vol. 16, no. 8, pp. 2080–2095, Aug. 2007. [23] J. Tan, Y. Ma, H. Rueda, D. Baron, and G. Arce, “Application of...JOURNAL OF SELECTED TOPICS IN in Signal Processing , (06 2015): 1. doi: Jin Tan, Yanting Ma, Dror Baron. Compressive Imaging via Approximate MessagePassing
Approximating W projection as a separable kernel
Merry, Bruce
2015-01-01
W projection is a commonly-used approach to allow interferometric imaging to be accelerated by Fast Fourier Transforms (FFTs), but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show that they can be closely approximated by separable kernels. The error scales with the fourth power of the field of view, and so is small enough to be ignored at mid to high frequencies. We also show that hybrid imaging algorithms combining W projection with ...
Shape theory categorical methods of approximation
Cordier, J M
2008-01-01
This in-depth treatment uses shape theory as a ""case study"" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and
Semiclassical approximations to quantum time correlation functions
Egorov, S. A.; Skinner, J. L.
1998-09-01
Over the last 40 years several ad hoc semiclassical approaches have been developed in order to obtain approximate quantum time correlation functions, using as input only the corresponding classical time correlation functions. The accuracy of these approaches has been tested for several exactly solvable gas-phase models. In this paper we test the accuracy of these approaches by comparing to an exactly solvable many-body condensed-phase model. We show that in the frequency domain the Egelstaff approach is the most accurate, especially at high frequencies, while in the time domain one of the other approaches is more accurate.
Roos, Bero
2012-01-01
Bobkov (2005) investigated an approximate de Finetti representation for probability measures on product measurable spaces, which are symmetric under permutations of coordinates. One of the main results of that paper was an explicit approximation bound for permanents of complex rectangular matrices, which was shown by a complicated induction argument. In this paper, we indicate how to avoid the induction argument using an (asymptotic) expansion. Our approach makes it possible to give new explicit higher order approximation bounds for such permanents and in turn for the probability measures mentioned above.
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1998-01-01
The simultaneous perturbation stochastic approximation (SPSA) algorithm has attracted considerable attention for challenging optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient...... simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1997-01-01
The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient...... simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...
Chiral baryon in the coherent pair approximation
Aly, T S T
1999-01-01
We revisit the work of K. Goeke, M. Harvey, F. Grümmer, and J. N. Urbano (Phys. Rev. {\\bf D37}, 754 (1988)) who considered a chiral model for the nucleon based on the linear sigma model with scalar-isoscalar scalar-isovector mesons coupled to quarks and solved using the coherent-pair approximation. In this way the quantum pion field can be treated in a non-perturbative fashion. In this work we review this model and the coherent pair approximation correcting several errors in the earlier work. We minimize the expectation value of the chiral hamiltonian in the ansatz coherent-pair ground state configuration and solve the resulting equations for nucleon quantum numbers. We calculate the canonical set of nucleon observables and compare with the Hedgehog model and experiment. Using the corrected equations yield slightly different values for nucleon observables but do not correct the large virial deviation in the $\\pi$-nucleon coupling. Our results therefore do not significantly alter the conclusions of Goeke, et ...
Function approximation using adaptive and overlapping intervals
Energy Technology Data Exchange (ETDEWEB)
Patil, R.B.
1995-05-01
A problem common to many disciplines is to approximate a function given only the values of the function at various points in input variable space. A method is proposed for approximating a function of several to one variable. The model takes the form of weighted averaging of overlapping basis functions defined over intervals. The number of such basis functions and their parameters (widths and centers) are automatically determined using given training data and a learning algorithm. The proposed algorithm can be seen as placing a nonuniform multidimensional grid in the input domain with overlapping cells. The non-uniformity and overlap of the cells is achieved by a learning algorithm to optimize a given objective function. This approach is motivated by the fuzzy modeling approach and a learning algorithms used for clustering and classification in pattern recognition. The basics of why and how the approach works are given. Few examples of nonlinear regression and classification are modeled. The relationship between the proposed technique, radial basis neural networks, kernel regression, probabilistic neural networks, and fuzzy modeling is explained. Finally advantages and disadvantages are discussed.
APPROXIMATING INNOVATION POTENTIAL WITH NEUROFUZZY ROBUST MODEL
Directory of Open Access Journals (Sweden)
Kasa, Richard
2015-01-01
Full Text Available In a remarkably short time, economic globalisation has changed the world’s economic order, bringing new challenges and opportunities to SMEs. These processes pushed the need to measure innovation capability, which has become a crucial issue for today’s economic and political decision makers. Companies cannot compete in this new environment unless they become more innovative and respond more effectively to consumers’ needs and preferences – as mentioned in the EU’s innovation strategy. Decision makers cannot make accurate and efficient decisions without knowing the capability for innovation of companies in a sector or a region. This need is forcing economists to develop an integrated, unified and complete method of measuring, approximating and even forecasting the innovation performance not only on a macro but also a micro level. In this recent article a critical analysis of the literature on innovation potential approximation and prediction is given, showing their weaknesses and a possible alternative that eliminates the limitations and disadvantages of classical measuring and predictive methods.
Perturbation of Operators and Approximation of Spectrum
Indian Academy of Sciences (India)
K Kumar; M N N Namboodiri; S Serra-Capizzano
2014-05-01
Let $A(x)$ be a norm continuous family of bounded self-adjoint operators on a separable Hilbert space $\\mathbb{H}$ and let $A(x)_n$ be the orthogonal compressions of $A(x)$ to the span of first elements of an orthonormal basis of $\\mathbb{H}$. The problem considered here is to approximate the spectrum of $A(x)$ using the sequence of eigenvalues of $A(x)_n$. We show that the bounds of the essential spectrum and the discrete spectral values outside the bounds of essential spectrum of $A(x)$ can be approximated uniformly on all compact subsets by the sequence of eigenvalue functions of $A(x)_n$. The known results, for a bounded self-adjoint operator, are translated into the case of a norm continuous family of operators. Also an attempt is made to predict the existence of spectral gaps that may occur between the bounds of essential spectrum of $A(0)=A$ and study the effect of norm continuous perturbation of operators in the prediction of spectral gaps. As an example, gap issues of some block Toeplitz–Laurent operators are discussed. The pure linear algebraic approach is the main advantage of the results here.
On some applications of diophantine approximations
Chudnovsky, G. V.
1984-01-01
Siegel's results [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1] on the transcendence and algebraic independence of values of E-functions are refined to obtain the best possible bound for the measures of irrationality and linear independence of values of arbitrary E-functions at rational points. Our results show that values of E-functions at rational points have measures of diophantine approximations typical to “almost all” numbers. In particular, any such number has the “2 + ε” exponent of irrationality: ǀΘ - p/qǀ > ǀqǀ-2-ε for relatively prime rational integers p,q, with q ≥ q0 (Θ, ε). These results answer some problems posed by Lang. The methods used here are based on the introduction of graded Padé approximations to systems of functions satisfying linear differential equations with rational function coefficients. The constructions and proofs of this paper were used in the functional (nonarithmetic case) in a previous paper [Chudnovsky, D. V. & Chudnovsky, G. V. (1983) Proc. Natl. Acad. Sci. USA 80, 5158-5162]. PMID:16593441
Analytic approximate radiation effects due to Bremsstrahlung
Energy Technology Data Exchange (ETDEWEB)
Ben-Zvi I.
2012-02-01
The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R&D Energy Recovery Linac.
Exact and Approximate Sizes of Convex Datacubes
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.
On Approximating String Selection Problems with Outliers
Boucher, Christina; Levy, Avivit; Pritchard, David; Weimann, Oren
2012-01-01
Many problems in bioinformatics are about finding strings that approximately represent a collection of given strings. We look at more general problems where some input strings can be classified as outliers. The Close to Most Strings problem is, given a set S of same-length strings, and a parameter d, find a string x that maximizes the number of "non-outliers" within Hamming distance d of x. We prove this problem has no PTAS unless ZPP=NP, correcting a decade-old mistake. The Most Strings with Few Bad Columns problem is to find a maximum-size subset of input strings so that the number of non-identical positions is at most k; we show it has no PTAS unless P=NP. We also observe Closest to k Strings has no EPTAS unless W[1]=FPT. In sum, outliers help model problems associated with using biological data, but we show the problem of finding an approximate solution is computationally difficult.
Optimal Approximation of Quadratic Interval Functions
Koshelev, Misha; Taillibert, Patrick
1997-01-01
Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.
Approximation of Failure Probability Using Conditional Sampling
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.
Refining Approximating Betweenness Centrality Based on Samplings
Ji, Shiyu
2016-01-01
Betweenness Centrality (BC) is an important measure used widely in complex network analysis, such as social network, web page search, etc. Computing the exact BC values is highly time consuming. Currently the fastest exact BC determining algorithm is given by Brandes, taking $O(nm)$ time for unweighted graphs and $O(nm+n^2\\log n)$ time for weighted graphs, where $n$ is the number of vertices and $m$ is the number of edges in the graph. Due to the extreme difficulty of reducing the time complexity of exact BC determining problem, many researchers have considered the possibility of any satisfactory BC approximation algorithms, especially those based on samplings. Bader et al. give the currently best BC approximation algorithm, with a high probability to successfully estimate the BC of one vertex within a factor of $1/\\varepsilon$ using $\\varepsilon t$ samples, where $t$ is the ratio between $n^2$ and the BC value of the vertex. However, some of the algorithmic parameters in Bader's work are not yet tightly boun...
Approximate Sensory Data Collection: A Survey
Cheng, Siyao; Cai, Zhipeng; Li, Jianzhong
2017-01-01
With the rapid development of the Internet of Things (IoTs), wireless sensor networks (WSNs) and related techniques, the amount of sensory data manifests an explosive growth. In some applications of IoTs and WSNs, the size of sensory data has already exceeded several petabytes annually, which brings too many troubles and challenges for the data collection, which is a primary operation in IoTs and WSNs. Since the exact data collection is not affordable for many WSN and IoT systems due to the limitations on bandwidth and energy, many approximate data collection algorithms have been proposed in the last decade. This survey reviews the state of the art of approximate data collection algorithms. We classify them into three categories: the model-based ones, the compressive sensing based ones, and the query-driven ones. For each category of algorithms, the advantages and disadvantages are elaborated, some challenges and unsolved problems are pointed out, and the research prospects are forecasted. PMID:28287440
Approximation diophantienne et approximants de Hermite-Pad\\'e de type I de fonctions exponentielles
Khémira, Samy
2010-01-01
En utilisant des approximants de Hermite-Pad\\'e de fonctions exponentielles, ainsi que des d\\'eterminants d'interpolation de Laurent, nous minorons la distance entre un nombre alg\\'ebrique et l'exponentielle d'un nombre alg\\'ebrique non nul. ----- We use Hermite-Pad\\'e approximants of exponential functions along with Laurent's interpolation determinants to obtain lower bounds for the distance between an algebraic number and the exponential of another non-zero algebraic number.
Fast approximate quadratic programming for graph matching.
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Joshua T Vogelstein
Full Text Available 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.
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.
The Electroweak Sudakov approximation in SHERPA
Thompson, Jennifer M
2016-01-01
As experimental particle physics becomes more and more precise, it is becoming increasingly important for Monte Carlo simulations to improve the precision of their predictions. In terms of the hard matrix element, this means calculating to a higher order in perturbation theory. To be consistent this requires both NNLO QCD corrections and NLO EW corrections to be included. There are also interference effects between these processes that are not simple to handle consistently. For a broad description of the behaviour of NLO EW corrections at high energies, the Sudakov logarithmic approach provides a good approximation, and is much less computationally expensive than the full calculation. The implementation of EW Sudakov logarithms within the SHERPA program are outlined here along with some initial results. As well as this, an overview of the status of full NLO EW computations with SHERPA is presented.
Approximation diffuse Hermite et ses applications
2000-01-01
De nombreuses techniques de résolution d'équations aux dérivées partielles sans maillage ont été développées dans la dernière décennie, proposant une alternative attrayante lorsque les éléments finis atteignent leurs limites. Notre travail se concentre sur l'étude de l'approximation diffuse, de ses applications au lissage et a la résolution des équations différentielles : les éléments diffus. Cependant, les solutions proposées s'appliquent aussi à d'autres méthodes et de nombreux résultats nu...
High order compact schemes for gradient approximation
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we propose three gradient recovery schemes of higher order for the linear interpolation. The first one is a weighted averaging method based on the gradients of the linear interpolation on the uniform mesh, the second is a geometric averaging method constructed from the gradients of two cubic interpolation on macro element, and the last one is a local least square method on the nodal patch with cubic polynomials. We prove that these schemes can approximate the gradient of the exact solution on the symmetry points with fourth order. In particular, for the uniform mesh, we show that these three schemes are the same on the considered points. The last scheme is more robust in general meshes. Consequently, we obtain the superconvergence results of the recovered gradient by using the aforementioned results and the supercloseness between the finite element solution and the linear interpolation of the exact solution. Finally, we provide several numerical experiments to illustrate the theoretical results.
Adaptive Control with Approximated Policy Search Approach
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Agus Naba
2010-05-01
Full Text Available Most of existing adaptive control schemes are designed to minimize error between plant state and goal state despite the fact that executing actions that are predicted to result in smaller errors only can mislead to non-goal states. We develop an adaptive control scheme that involves manipulating a controller of a general type to improve its performance as measured by an evaluation function. The developed method is closely related to a theory of Reinforcement Learning (RL but imposes a practical assumption made for faster learning. We assume that a value function of RL can be approximated by a function of Euclidean distance from a goal state and an action executed at the state. And, we propose to use it for the gradient search as an evaluation function. Simulation results provided through application of the proposed scheme to a pole-balancing problem using a linear state feedback controller and fuzzy controller verify the scheme’s efficacy.
Unitary Approximations in Fault Detection Filter Design
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Dušan Krokavec
2016-01-01
Full Text Available The paper is concerned with the fault detection filter design requirements that relax the existing conditions reported in the previous literature by adapting the unitary system principle in approximation of fault detection filter transfer function matrix for continuous-time linear MIMO systems. Conditions for the existence of a unitary construction are presented under which the fault detection filter with a unitary transfer function can be designed to provide high residual signals sensitivity with respect to faults. Otherwise, reflecting the emplacement of singular values in unitary construction principle, an associated structure of linear matrix inequalities with built-in constraints is outlined to design the fault detection filter only with a Hurwitz transfer function. All proposed design conditions are verified by the numerical illustrative examples.
Exact and Approximate Probabilistic Symbolic Execution
Luckow, Kasper; Pasareanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem
2014-01-01
Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.
Gutzwiller approximation in strongly correlated electron systems
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
Nanostructures: Scattering beyond the Born approximation
Grigoriev, S. V.; Syromyatnikov, A. V.; Chumakov, A. P.; Grigoryeva, N. A.; Napolskii, K. S.; Roslyakov, I. V.; Eliseev, A. A.; Petukhov, A. V.; Eckerlebe, H.
2010-03-01
The neutron scattering on a two-dimensional ordered nanostructure with the third nonperiodic dimension can go beyond the Born approximation. In our model supported by the exact theoretical solution a well-correlated hexagonal porous structure of anodic aluminum oxide films acts as a peculiar two-dimensional grating for the coherent neutron wave. The thickness of the film L (length of pores) plays important role in the transition from the weak to the strong scattering regimes. It is shown that the coherency of the standard small-angle neutron scattering setups suits to the geometry of the studied objects and often affects the intensity of scattering. The proposed theoretical solution can be applied in the small-angle neutron diffraction experiments with flux lines in superconductors, periodic arrays of magnetic or superconducting nanowires, as well as in small-angle diffraction experiments on synchrotron radiation.
Estimating Mutual Information by Local Gaussian Approximation
Gao, Shuyang; Galstyan, Aram
2015-01-01
Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly dependent variables and have sample complexity that scales exponentially with the true MI. This undesired behavior was attributed to the reliance of those estimators on local uniformity of the underlying (and unknown) probability density function. Here we present a novel semi-parametric estimator of mutual information, where at each sample point, densities are {\\em locally} approximated by a Gaussians distribution. We demonstrate that the estimator is asymptotically unbiased. We also show that the proposed estimator has a superior performance compared to several baselines, and is able to accurately measure relationship strengths over many orders of magnitude.
Squashed entanglement and approximate private states
Wilde, Mark M.
2016-09-01
The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This paper simplifies proofs that the squashed entanglement is an upper bound on distillable key for finite-dimensional quantum systems and solidifies such proofs for infinite-dimensional quantum systems. More specifically, this paper establishes that the logarithm of the dimension of the key system (call it log 2K ) in an ɛ -approximate private state is bounded from above by the squashed entanglement of that state plus a term that depends only ɛ and log 2K . Importantly, the extra term does not depend on the dimension of the shield systems of the private state. The result holds for the bipartite squashed entanglement, and an extension of this result is established for two different flavors of the multipartite squashed entanglement.
An approximate version of Sidorenko's conjecture
Conlon, David; Sudakov, Benny
2010-01-01
A beautiful conjecture of Erd\\H{o}s-Simonovits and Sidorenko states that if H is a bipartite graph, then the random graph with edge density p has in expectation asymptotically the minimum number of copies of H over all graphs of the same order and edge density. This conjecture also has an equivalent analytic form and has connections to a broad range of topics, such as matrix theory, Markov chains, graph limits, and quasirandomness. Here we prove the conjecture if H has a vertex complete to the other part, and deduce an approximate version of the conjecture for all H. Furthermore, for a large class of bipartite graphs, we prove a stronger stability result which answers a question of Chung, Graham, and Wilson on quasirandomness for these graphs.
Approximate particle spectra in the pyramid scheme
Banks, Tom; Torres, T. J.
2012-12-01
We construct a minimal model inspired by the general class of pyramid schemes [T. Banks and J.-F. Fortin, J. High Energy Phys. 07 (2009) 046JHEPFG1029-8479], which is consistent with both supersymmetry breaking and electroweak symmetry breaking. In order to do computations, we make unjustified approximations to the low energy Kähler potential. The phenomenological viability of the resultant mass spectrum is then examined and compared with current collider limits. We show that for certain regimes of parameters, the model, and thus generically the pyramid scheme, can accommodate the current collider mass constraints on physics beyond the standard model with a tree-level light Higgs mass near 125 GeV. However, in this regime the model exhibits a little hierarchy problem, and one must permit fine-tunings that are of order 5%.
Goldstone modes in the random phase approximation
Neergård, Kai
2016-01-01
I show that the kernel of the random phase approximation (RPA) matrix based on a stable Hartree, Hartree-Fock, Hartree-Bogolyubov or Hartree-Fock-Bogolyubov mean field solution is decomposed into a subspace with a basis whose vectors are associated, in the equivalent formalism of a classical Hamiltonian linear in canonic coordinates, with conjugate momenta of cyclic coordinates (Goldstone modes) and a subspace with a basis whose vectors are associated with pairs of conjugate canonic coordinates that do not enter the Hamiltonian at all. In a subspace complementary to the one spanned by all these coordinates including the conjugate coordinates of the Goldstone momenta, the RPA matrix behaves as in the case of a zerodimensional kernel. This result was derived very recently by Nakada as a corollary to a general analysis of RPA matrices based on both stable and unstable mean field solutions. The present proof does not rest on Nakada's general results.
Uncertainty relations and approximate quantum error correction
Renes, Joseph M.
2016-09-01
The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the outcome. Two variants are possible: either Alice tells Bob which observable she measured, or he has to furnish guesses for both cases. Here I derive uncertainty relations for both, formulated directly in terms of Bob's guessing probabilities. For the former these relate to the entanglement that can be recovered by action on Bob's system alone. This gives an explicit quantum circuit for approximate quantum error correction using the guessing measurements for "amplitude" and "phase" information, implicitly used in the recent construction of efficient quantum polar codes. I also find a relation on the guessing probabilities for the latter game, which has application to wave-particle duality relations.
Wave system and its approximate similarity solutions
Institute of Scientific and Technical Information of China (English)
Liu Ping; Fu Pei-Kai
2011-01-01
Recently,a new (2+1)-dimensional shallow water wave system,the (2+1)-dimensional displacement shallow water wave system (2DDSWWS),was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS,which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis,we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS (M2DDSWWS) is studied and four similarity solutions are obtained. For the perfect fluids,the coefficient of kinematic viscosity is zero,then the M2DDSWWS will degenerate to the 2DDSWWS.
An Approximate Model of Microchannel Cooling
Institute of Scientific and Technical Information of China (English)
ShipingYu; MingdaoXin
1994-01-01
Forced convective heat transfer in micro-rectangular channels can be described by a group of two-dimensional differential equations.These equations take the conduction in microchannel wall along the direction of flow of coolants into account,which are more generalized than those which neglect the conduction.For the same reason,they are suitable particularly for gases-cooled microchannels.With only numerical solution to the equations till today,an approximate analytic solution is derived here,From this solution,a rather simple formula can be introduced further,by which the differences between considering the conduction and neglecting it are easily found.In addition,the reasonableness of the classical fin method is also discussed.An experimental example of air-cooled microchannels is illustrated.
Approximately isometric lifting in quasidiagonal extensions
Institute of Scientific and Technical Information of China (English)
FANG XiaoChun; ZHAO YiLe
2009-01-01
Let O→I→A→A/I→O be a short exact sequence of C*-algebras with A unital.Suppose that the extension O→I→A→A/I→O is quasidiagonal,then it is shown that any positive element (projection,partial isometry,unitary element,respectively) in A/I has a lifting with the same form which commutes with some quasicentral approximate unit of I consisting of projections.Furthermore,it is shown that for any given positive number e,two positive elements (projections,As an application,it is shown that for any positive numbers e and (u) in U(A/I)0,there exists u in U(A)0which is a lifting of (u) such that cel(u) ＜ cel(u) +e.
Entropy Approximation in Lossy Source Coding Problem
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Marek Śmieja
2015-05-01
Full Text Available In this paper, we investigate a lossy source coding problem, where an upper limit on the permitted distortion is defined for every dataset element. It can be seen as an alternative approach to rate distortion theory where a bound on the allowed average error is specified. In order to find the entropy, which gives a statistical length of source code compatible with a fixed distortion bound, a corresponding optimization problem has to be solved. First, we show how to simplify this general optimization by reducing the number of coding partitions, which are irrelevant for the entropy calculation. In our main result, we present a fast and feasible for implementation greedy algorithm, which allows one to approximate the entropy within an additive error term of log2 e. The proof is based on the minimum entropy set cover problem, for which a similar bound was obtained.
Spectral clustering based on local linear approximations
Arias-Castro, Ery; Lerman, Gilad
2010-01-01
In the context of clustering, we assume a generative model where each cluster is the result of sampling points in the neighborhood of an embedded smooth surface, possibly contaminated with outliers. We consider a prototype for a higher-order spectral clustering method based on the residual from a local linear approximation. In an asymptotic setting where the number of points becomes large, we obtain theoretical guaranties for this algorithm and show that, both in terms of separation and robustness to outliers, it outperforms the standard spectral clustering algorithm based on pairwise distances of Ng, Jordan and Weiss (NIPS, 2001). Under some conditions on the dimension of, and the incidence angle at, an intersection, the algorithm is able to recover the intersecting clusters. The optimal choice for some of the tuning parameters depends on the dimension and thickness of the clusters. We provide estimators that come close enough for our purposes. We discuss the cases of clusters of mixed dimensions and of clus...
Approximate Methods for State-Space Models
Koyama, Shinsuke; Shalizi, Cosma Rohilla; Kass, Robert E; 10.1198/jasa.2009.tm08326
2010-01-01
State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace's method, an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution. This {\\em Laplace-Gaussian filter} (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulat...
Approximate Bayesian computation with functional statistics.
Soubeyrand, Samuel; Carpentier, Florence; Guiton, François; Klein, Etienne K
2013-03-26
Functional statistics are commonly used to characterize spatial patterns in general and spatial genetic structures in population genetics in particular. Such functional statistics also enable the estimation of parameters of spatially explicit (and genetic) models. Recently, Approximate Bayesian Computation (ABC) has been proposed to estimate model parameters from functional statistics. However, applying ABC with functional statistics may be cumbersome because of the high dimension of the set of statistics and the dependences among them. To tackle this difficulty, we propose an ABC procedure which relies on an optimized weighted distance between observed and simulated functional statistics. We applied this procedure to a simple step model, a spatial point process characterized by its pair correlation function and a pollen dispersal model characterized by genetic differentiation as a function of distance. These applications showed how the optimized weighted distance improved estimation accuracy. In the discussion, we consider the application of the proposed ABC procedure to functional statistics characterizing non-spatial processes.
Intelligent comparisons II inequalities and approximations
Anastassiou, George A
2017-01-01
This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.
Zeroth WKB Approximation in Quantum Mechanics
Sergeenko, M N
2002-01-01
Solution of the Schr\\"odinger's equation in the zero order WKB approximation is analyzed. We observe and investigate several remarkable features of the WKB$_0$ method. Solution in the whole region is built with the help of simple connection formulas we derive from basic requirements of continuity and finiteness for the wave function in quantum mechanics. We show that, for conservative quantum systems, not only total energy, but also momentum is the constant of motion. We derive the quantization conditions for two and more turning point problems. Exact energy eigenvalues for solvable and some ``insoluble'' potentials are obtained. The eigenfunctions have the form of a standing wave, $A_n\\cos(k_nx+\\delta_n)$, and are the asymptote of the exact solution.
Approximate truncation robust computed tomography—ATRACT
Dennerlein, Frank; Maier, Andreas
2013-09-01
We present an approximate truncation robust algorithm to compute tomographic images (ATRACT). This algorithm targets at reconstructing volumetric images from cone-beam projections in scenarios where these projections are highly truncated in each dimension. It thus facilitates reconstructions of small subvolumes of interest, without involving prior knowledge about the object. Our method is readily applicable to medical C-arm imaging, where it may contribute to new clinical workflows together with a considerable reduction of x-ray dose. We give a detailed derivation of ATRACT that starts from the conventional Feldkamp filtered-backprojection algorithm and that involves, as one component, a novel original formula for the inversion of the two-dimensional Radon transform. Discretization and numerical implementation are discussed and reconstruction results from both, simulated projections and first clinical data sets are presented.
Nuclear structure aspects in A approximately 90
Energy Technology Data Exchange (ETDEWEB)
Bucurescu, D.; Constantinescu, G.; Cutoiu, D.; Ivascu, M.; Zamfir, N.V.; Avrigeanu, M.
1981-01-01
A systematic review of the experimental studies on some neutron deficient nuclei in the A approximately 90 region performed at the Bucharest FN tandem is presented. After a brief account of the measurements, several transitionality aspects are evidenced, like a change of structure in the odd Sr isotopes from N = 48 to N = 46 and the occurence of decoupled g 9/2 bands. The description of these characteristics is discussed in connection with the triaxial rotor, with the VMI model, as well as the cluster-vibration and the interacting boson-fermion model. A systematics of the B(E2) values for the 8/sub 1//sup +/ state in the N = 46 isotones is also presented. 12 references.
Approximating acyclicity parameters of sparse hypergraphs
Fomin, Fedor V; Thilikos, Dimitrios M
2008-01-01
The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx, who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending tractability of many problems in database theory and artificial intelligence. In this paper, we study the approximability of (generalized, fractional) hyper treewidth of sparse hypergraphs where the criterion of sparsity reflects the sparsity of their incidence graphs. Our first step is to prove that the (generalized, fractional) hypertree width of a hypergraph H is constant-factor sandwiched by the treewidth of its incidence graph, when the incidence graph belongs to some apex-minor-free graph class. This determines the combinatorial borderline above which the notion of (generalized, fractional) hypertree width becomes essentially more general than treewidth...
Approximation Algorithms for Secondary Spectrum Auctions
Hoefer, Martin; Vöcking, Berthold
2010-01-01
We study combinatorial auctions for the secondary spectrum market. In this market, short-term licenses shall be given to wireless nodes for communication in their local neighborhood. In contrast to the primary market, channels can be assigned to multiple bidders, provided that the corresponding devices are well separated such that the interference is sufficiently low. Interference conflicts are described in terms of a conflict graph in which the nodes represent the bidders and the edges represent conflicts such that the feasible allocations for a channel correspond to the independent sets in the conflict graph. In this paper, we suggest a novel LP formulation for combinatorial auctions with conflict graph using a non-standard graph parameter, the so-called inductive independence number. Taking into account this parameter enables us to bypass the well-known lower bound of \\Omega(n^{1-\\epsilon}) on the approximability of independent set in general graphs with n nodes (bidders). We achieve significantly better a...
Approximation algorithm for multiprocessor parallel job scheduling
Institute of Scientific and Technical Information of China (English)
陈松乔; 黄金贵; 陈建二
2002-01-01
Pk|fix|Cmax problem is a new scheduling problem based on the multiprocessor parallel job, and it is proved to be NP-hard problem when k≥3. This paper focuses on the case of k=3. Some new observations and new techniques for P3|fix|Cmax problem are offered. The concept of semi-normal schedulings is introduced, and a very simple linear time algorithm Semi-normal Algorithm for constructing semi-normal schedulings is developed. With the method of the classical Graham List Scheduling, a thorough analysis of the optimal scheduling on a special instance is provided, which shows that the algorithm is an approximation algorithm of ratio of 9/8 for any instance of P3|fix|Cmax problem, and improves the previous best ratio of 7/6 by M.X.Goemans.
Formation Tracking Based on Approximate Velocities
Directory of Open Access Journals (Sweden)
Eduardo Gamaliel Hernandez-Martinez
2015-12-01
Full Text Available This paper analyses the formation tracking of groups of mobile robots moving on the plane. A leader robot is chosen to follow a prescribed trajectory whilst the rest, considered as followers, are formed in an open-chain configuration. Two formation-tracking control laws using approximate velocities are proposed, in which some velocities must be communicated between robots in order to ensure the simultaneous preservation of the formation and the following of the group path. The main result is analysis of the convergence of the two proposed control laws. The restriction of inaccurate information occurs in decentralized multi-robot platforms, in which the mobile agents are only able to measure positions and the velocities’ functions are estimated using online numerical methods. A numerical simulation of both controllers in the case of omnidirectional robots is shown. For the case of the unicycle-type robots, real-time experiments of both controllers were implemented and tested.
Comparing numerical and analytic approximate gravitational waveforms
Afshari, Nousha; Lovelace, Geoffrey; SXS Collaboration
2016-03-01
A direct observation of gravitational waves will test Einstein's theory of general relativity under the most extreme conditions. The Laser Interferometer Gravitational-Wave Observatory, or LIGO, began searching for gravitational waves in September 2015 with three times the sensitivity of initial LIGO. To help Advanced LIGO detect as many gravitational waves as possible, a major research effort is underway to accurately predict the expected waves. In this poster, I will explore how the gravitational waveform produced by a long binary-black-hole inspiral, merger, and ringdown is affected by how fast the larger black hole spins. In particular, I will present results from simulations of merging black holes, completed using the Spectral Einstein Code (black-holes.org/SpEC.html), including some new, long simulations designed to mimic black hole-neutron star mergers. I will present comparisons of the numerical waveforms with analytic approximations.
Approximation by max-product type operators
Bede, Barnabás; Gal, Sorin G
2016-01-01
This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly,...
Discrete Spectrum Reconstruction Using Integral Approximation Algorithm.
Sizikov, Valery; Sidorov, Denis
2017-07-01
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of linear-nonlinear equations (SLNE) with respect to intensities and frequencies of the discrete spectral lines. The SLNE is linear with respect to lines' intensities and nonlinear with respect to the lines' frequencies. The integral approximation algorithm is proposed for the solution of this SLNE. The algorithm combines solution of linear integral equations with solution of a system of linear algebraic equations and avoids nonlinear equations. Numerical examples of the application of the technique, both to synthetic and experimental spectra, demonstrate the efficacy of the proposed approach in enabling an effective enhancement of the spectrometer's resolution.
Statistical model semiquantitatively approximates arabinoxylooligosaccharides' structural diversity
DEFF Research Database (Denmark)
Dotsenko, Gleb; Nielsen, Michael Krogsgaard; Lange, Lene
2016-01-01
A statistical model describing the random distribution of substituted xylopyranosyl residues in arabinoxylooligosaccharides is suggested and compared with existing experimental data. Structural diversity of arabinoxylooligosaccharides of various length, originating from different arabinoxylans...... (wheat flour arabinoxylan (arabinose/xylose, A/X = 0.47); grass arabinoxylan (A/X = 0.24); wheat straw arabinoxylan (A/X = 0.15); and hydrothermally pretreated wheat straw arabinoxylan (A/X = 0.05)), is semiquantitatively approximated using the proposed model. The suggested approach can be applied...... not only for prediction and quantification of arabinoxylooligosaccharides' structural diversity, but also for estimate of yield and selection of the optimal source of arabinoxylan for production of arabinoxylooligosaccharides with desired structural features....
Approximation Preserving Reductions among Item Pricing Problems
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.
Robust Generalized Low Rank Approximations of Matrices.
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Jiarong Shi
Full Text Available In recent years, the intrinsic low rank structure of some datasets has been extensively exploited to reduce dimensionality, remove noise and complete the missing entries. As a well-known technique for dimensionality reduction and data compression, Generalized Low Rank Approximations of Matrices (GLRAM claims its superiority on computation time and compression ratio over the SVD. However, GLRAM is very sensitive to sparse large noise or outliers and its robust version does not have been explored or solved yet. To address this problem, this paper proposes a robust method for GLRAM, named Robust GLRAM (RGLRAM. We first formulate RGLRAM as an l1-norm optimization problem which minimizes the l1-norm of the approximation errors. Secondly, we apply the technique of Augmented Lagrange Multipliers (ALM to solve this l1-norm minimization problem and derive a corresponding iterative scheme. Then the weak convergence of the proposed algorithm is discussed under mild conditions. Next, we investigate a special case of RGLRAM and extend RGLRAM to a general tensor case. Finally, the extensive experiments on synthetic data show that it is possible for RGLRAM to exactly recover both the low rank and the sparse components while it may be difficult for previous state-of-the-art algorithms. We also discuss three issues on RGLRAM: the sensitivity to initialization, the generalization ability and the relationship between the running time and the size/number of matrices. Moreover, the experimental results on images of faces with large corruptions illustrate that RGLRAM obtains the best denoising and compression performance than other methods.