Statistics of a neuron model driven by asymmetric colored noise.

PubMed

Müller-Hansen, Finn; Droste, Felix; Lindner, Benjamin

2015-02-01

Irregular firing of neurons can be modeled as a stochastic process. Here we study the perfect integrate-and-fire neuron driven by dichotomous noise, a Markovian process that jumps between two states (i.e., possesses a non-Gaussian statistics) and exhibits nonvanishing temporal correlations (i.e., represents a colored noise). Specifically, we consider asymmetric dichotomous noise with two different transition rates. Using a first-passage-time formulation, we derive exact expressions for the probability density and the serial correlation coefficient of the interspike interval (time interval between two subsequent neural action potentials) and the power spectrum of the spike train. Furthermore, we extend the model by including additional Gaussian white noise, and we give approximations for the interspike interval (ISI) statistics in this case. Numerical simulations are used to validate the exact analytical results for pure dichotomous noise, and to test the approximations of the ISI statistics when Gaussian white noise is included. The results may help to understand how correlations and asymmetry of noise and signals in nerve cells shape neuronal firing statistics.

Gaussian Decomposition of Laser Altimeter Waveforms

NASA Technical Reports Server (NTRS)

Hofton, Michelle A.; Minster, J. Bernard; Blair, J. Bryan

1999-01-01

We develop a method to decompose a laser altimeter return waveform into its Gaussian components assuming that the position of each Gaussian within the waveform can be used to calculate the mean elevation of a specific reflecting surface within the laser footprint. We estimate the number of Gaussian components from the number of inflection points of a smoothed copy of the laser waveform, and obtain initial estimates of the Gaussian half-widths and positions from the positions of its consecutive inflection points. Initial amplitude estimates are obtained using a non-negative least-squares method. To reduce the likelihood of fitting the background noise within the waveform and to minimize the number of Gaussians needed in the approximation, we rank the "importance" of each Gaussian in the decomposition using its initial half-width and amplitude estimates. The initial parameter estimates of all Gaussians ranked "important" are optimized using the Levenburg-Marquardt method. If the sum of the Gaussians does not approximate the return waveform to a prescribed accuracy, then additional Gaussians are included in the optimization procedure. The Gaussian decomposition method is demonstrated on data collected by the airborne Laser Vegetation Imaging Sensor (LVIS) in October 1997 over the Sequoia National Forest, California.

Large-scale velocities and primordial non-Gaussianity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmidt, Fabian

2010-09-15

We study the peculiar velocities of density peaks in the presence of primordial non-Gaussianity. Rare, high-density peaks in the initial density field can be identified with tracers such as galaxies and clusters in the evolved matter distribution. The distribution of relative velocities of peaks is derived in the large-scale limit using two different approaches based on a local biasing scheme. Both approaches agree, and show that halos still stream with the dark matter locally as well as statistically, i.e. they do not acquire a velocity bias. Nonetheless, even a moderate degree of (not necessarily local) non-Gaussianity induces a significant skewnessmore » ({approx}0.1-0.2) in the relative velocity distribution, making it a potentially interesting probe of non-Gaussianity on intermediate to large scales. We also study two-point correlations in redshift space. The well-known Kaiser formula is still a good approximation on large scales, if the Gaussian halo bias is replaced with its (scale-dependent) non-Gaussian generalization. However, there are additional terms not encompassed by this simple formula which become relevant on smaller scales (k > or approx. 0.01h/Mpc). Depending on the allowed level of non-Gaussianity, these could be of relevance for future large spectroscopic surveys.« less

Comparing fixed and variable-width Gaussian networks.

PubMed

Kůrková, Věra; Kainen, Paul C

2014-09-01

The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is proven that if two Gaussian RBF networks have the same input-output functions, then they must have the same numbers of units with the same centers and widths. Further, it is shown that while sets of input-output functions of Gaussian kernel networks with two different widths are disjoint, each such set is large enough to be a universal approximator. Embedding of RKHSs induced by "flatter" Gaussians into RKHSs induced by "sharper" Gaussians is described and growth of the ratios of norms on these spaces with increasing input dimension is estimated. Finally, large sets of argminima of error functionals in sets of input-output functions of Gaussian RBFs are described. Copyright © 2014 Elsevier Ltd. All rights reserved.

The exact thermal rotational spectrum of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

The exact thermal rotational spectrum of a two-dimensional rigid rotor is obtained using Gaussian wave packet dynamics. The spectrum is obtained by propagating, without approximation, infinite sets of Gaussian wave packets. These sets are constructed so that collectively they have the correct periodicity, and indeed, are coherent states appropriate to this problem. Also, simple, almost classical, approximations to full wave packet dynamics are shown to give results which are either exact or very nearly exact. Advantages of the use of Gaussian wave packet dynamics over conventional linear response theory are discussed.

Non-Gaussian microwave background fluctuations from nonlinear gravitational effects

NASA Technical Reports Server (NTRS)

Salopek, D. S.; Kunstatter, G. (Editor)

1991-01-01

Whether the statistics of primordial fluctuations for structure formation are Gaussian or otherwise may be determined if the Cosmic Background Explorer (COBE) Satellite makes a detection of the cosmic microwave-background temperature anisotropy delta T(sub CMB)/T(sub CMB). Non-Gaussian fluctuations may be generated in the chaotic inflationary model if two scalar fields interact nonlinearly with gravity. Theoretical contour maps are calculated for the resulting Sachs-Wolfe temperature fluctuations at large angular scales (greater than 3 degrees). In the long-wavelength approximation, one can confidently determine the nonlinear evolution of quantum noise with gravity during the inflationary epoch because: (1) different spatial points are no longer in causal contact; and (2) quantum gravity corrections are typically small-- it is sufficient to model the system using classical random fields. If the potential for two scalar fields V(phi sub 1, phi sub 2) possesses a sharp feature, then non-Gaussian fluctuations may arise. An explicit model is given where cold spots in delta T(sub CMB)/T(sub CMB) maps are suppressed as compared to the Gaussian case. The fluctuations are essentially scale-invariant.

A Gaussian framework for modeling effects of frequency-dependent attenuation, frequency-dependent scattering, and gating.

PubMed

Wear, Keith A

2002-11-01

For a wide range of applications in medical ultrasound, power spectra of received signals are approximately Gaussian. It has been established previously that an ultrasound beam with a Gaussian spectrum propagating through a medium with linear attenuation remains Gaussian. In this paper, Gaussian transformations are derived to model the effects of scattering (according to a power law, as is commonly applicable in soft tissues, especially over limited frequency ranges) and gating (with a Hamming window, a commonly used gate function). These approximations are shown to be quite accurate even for relatively broad band systems with fractional bandwidths approaching 100%. The theory is validated by experiments in phantoms consisting of glass particles suspended in agar.

Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verde, Licia; Jimenez, Raul; Alvarez-Gaume, Luis

2013-06-01

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non-Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to more than 7σ for f{sub NL} values (both true and sampled) not ruledmore » out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.« less

TOPICAL REVIEW: Quasielastic He atom scattering from surfaces: a stochastic description of the dynamics of interacting adsorbates

NASA Astrophysics Data System (ADS)

Martínez-Casado, R.; Vega, J. L.; Sanz, A. S.; Miret-Artés, S.

2007-08-01

The study of diffusion and low-frequency vibrational motions of particles on metal surfaces is of paramount importance; it provides valuable information on the nature of the adsorbate-substrate and substrate-substrate interactions. In particular, the experimental broadening observed in the diffusive peak with increasing coverage is usually interpreted in terms of a dipole-dipole-like interaction among adsorbates via extensive molecular dynamics calculations within the Langevin framework. Here we present an alternative way to interpret this broadening by means of a purely stochastic description, namely the interacting single-adsorbate approximation, where two noise sources are considered: (1) a Gaussian white noise accounting for the surface friction and temperature, and (2) a white shot noise replacing the interaction potential between adsorbates. Standard Langevin numerical simulations for flat and corrugated surfaces (with a separable potential) illustrate the dynamics of Na atoms on a Cu(100) surface which fit fairly well to the analytical expressions issued from simple models (free particle and anharmonic oscillator) when the Gaussian approximation is assumed. A similar broadening is also expected for the frustrated translational mode peaks.

Hessian eigenvalue distribution in a random Gaussian landscape

NASA Astrophysics Data System (ADS)

Yamada, Masaki; Vilenkin, Alexander

2018-03-01

The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential minima. In particular, the stability of vacua and the dynamics of slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues. The Hessian eigenvalue distribution has been studied earlier, using the saddle point approximation, in the leading order of 1/ N expansion, where N is the dimensionality of the landscape. This approximation, however, is insufficient for the small eigenvalue end of the spectrum, where sub-leading terms play a significant role. We extend the saddle point method to account for the sub-leading contributions. We also develop a new approach, where the eigenvalue distribution is found as an equilibrium distribution at the endpoint of a stochastic process (Dyson Brownian motion). The results of the two approaches are consistent in cases where both methods are applicable. We discuss the implications of our results for vacuum stability and slow-roll inflation in the landscape.

Optimal approximation of harmonic growth clusters by orthogonal polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Teodorescu, Razvan

2008-01-01

Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoreticaI model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of Hele-Shaw flows), to the granular dynamics of hard spheres, and even diffusion-limited aggregation. Although a complete solution for the continuum case exists, efficient approximations of the boundary evolution are very useful due to their practical applications. In this article, the approximation scheme based on orthogonal polynomials with a deformed Gaussian kernel is discussed, as well as relations to potential theory.

Evaluation of stochastic differential equation approximation of ion channel gating models.

PubMed

Bruce, Ian C

2009-04-01

Fox and Lu derived an algorithm based on stochastic differential equations for approximating the kinetics of ion channel gating that is simpler and faster than "exact" algorithms for simulating Markov process models of channel gating. However, the approximation may not be sufficiently accurate to predict statistics of action potential generation in some cases. The objective of this study was to develop a framework for analyzing the inaccuracies and determining their origin. Simulations of a patch of membrane with voltage-gated sodium and potassium channels were performed using an exact algorithm for the kinetics of channel gating and the approximate algorithm of Fox & Lu. The Fox & Lu algorithm assumes that channel gating particle dynamics have a stochastic term that is uncorrelated, zero-mean Gaussian noise, whereas the results of this study demonstrate that in many cases the stochastic term in the Fox & Lu algorithm should be correlated and non-Gaussian noise with a non-zero mean. The results indicate that: (i) the source of the inaccuracy is that the Fox & Lu algorithm does not adequately describe the combined behavior of the multiple activation particles in each sodium and potassium channel, and (ii) the accuracy does not improve with increasing numbers of channels.

Non-Gaussian Analysis of Turbulent Boundary Layer Fluctuating Pressure on Aircraft Skin Panels

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Steinwolf, Alexander

2005-01-01

The purpose of the study is to investigate the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the outer sidewall of a supersonic transport aircraft and to approximate these PDFs by analytical models. Experimental flight results show that the fluctuating pressure PDFs differ from the Gaussian distribution even for standard smooth surface conditions. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations in front of forward-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. There is a certain spatial pattern of the skewness and kurtosis behavior depending on the distance upstream from the step. All characteristics related to non-Gaussian behavior are highly dependent upon the distance from the step and the step height, less dependent on aircraft speed, and not dependent on the fuselage location. A Hermite polynomial transform model and a piecewise-Gaussian model fit the flight data well both for the smooth and stepped conditions. The piecewise-Gaussian approximation can be additionally regarded for convenience in usage after the model is constructed.

Fractional Fourier transform of truncated elliptical Gaussian beams.

PubMed

Du, Xinyue; Zhao, Daomu

2006-12-20

Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical expression for an elliptical Gaussian beam (EGB) truncated by an elliptical aperture and passing through a fractional Fourier transform system is derived by use of vector integration. The approximate analytical results provide more convenience for studying the propagation and transformation of truncated EGBs than the usual way by using the integral formula directly, and the efficiency of numerical calculation is significantly improved.

Efficiency of the human observer for detecting a Gaussian signal at a known location in non-Gaussian distributed lumpy backgrounds.

PubMed

Park, Subok; Gallas, Bradon D; Badano, Aldo; Petrick, Nicholas A; Myers, Kyle J

2007-04-01

A previous study [J. Opt. Soc. Am. A22, 3 (2005)] has shown that human efficiency for detecting a Gaussian signal at a known location in non-Gaussian distributed lumpy backgrounds is approximately 4%. This human efficiency is much less than the reported 40% efficiency that has been documented for Gaussian-distributed lumpy backgrounds [J. Opt. Soc. Am. A16, 694 (1999) and J. Opt. Soc. Am. A18, 473 (2001)]. We conducted a psychophysical study with a number of changes, specifically in display-device calibration and data scaling, from the design of the aforementioned study. Human efficiency relative to the ideal observer was found again to be approximately 5%. Our variance analysis indicates that neither scaling nor display made a statistically significant difference in human performance for the task. We conclude that the non-Gaussian distributed lumpy background is a major factor in our low human-efficiency results.

Image denoising in mixed Poisson-Gaussian noise.

PubMed

Luisier, Florian; Blu, Thierry; Unser, Michael

2011-03-01

We propose a general methodology (PURE-LET) to design and optimize a wide class of transform-domain thresholding algorithms for denoising images corrupted by mixed Poisson-Gaussian noise. We express the denoising process as a linear expansion of thresholds (LET) that we optimize by relying on a purely data-adaptive unbiased estimate of the mean-squared error (MSE), derived in a non-Bayesian framework (PURE: Poisson-Gaussian unbiased risk estimate). We provide a practical approximation of this theoretical MSE estimate for the tractable optimization of arbitrary transform-domain thresholding. We then propose a pointwise estimator for undecimated filterbank transforms, which consists of subband-adaptive thresholding functions with signal-dependent thresholds that are globally optimized in the image domain. We finally demonstrate the potential of the proposed approach through extensive comparisons with state-of-the-art techniques that are specifically tailored to the estimation of Poisson intensities. We also present denoising results obtained on real images of low-count fluorescence microscopy.

Coupled wave-packets for non-adiabatic molecular dynamics: a generalization of Gaussian wave-packet dynamics to multiple potential energy surfaces

DOE PAGES

White, Alexander James; Tretiak, Sergei; Mozyrsky, Dima V.

2016-04-25

Accurate simulation of the non-adiabatic dynamics of molecules in excited electronic states is key to understanding molecular photo-physical processes. Here we present a novel method, based on a semiclassical approximation, that is as efficient as the commonly used mean field Ehrenfest or ad hoc surface hopping methods and properly accounts for interference and decoherence effects. This novel method is an extension of Heller's thawed Gaussian wave-packet dynamics that includes coupling between potential energy surfaces. By studying several standard test problems we demonstrate that the accuracy of the method can be systematically improved while maintaining high efficiency. The method is suitablemore » for investigating the role of quantum coherence in the non-adiabatic dynamics of many-atom molecules.« less

Dynamic splitting of Gaussian pencil beams in heterogeneity-correction algorithms for radiotherapy with heavy charged particles.

PubMed

Kanematsu, Nobuyuki; Komori, Masataka; Yonai, Shunsuke; Ishizaki, Azusa

2009-04-07

The pencil-beam algorithm is valid only when elementary Gaussian beams are small enough compared to the lateral heterogeneity of a medium, which is not always true in actual radiotherapy with protons and ions. This work addresses a solution for the problem. We found approximate self-similarity of Gaussian distributions, with which Gaussian beams can split into narrower and deflecting daughter beams when their sizes have overreached lateral heterogeneity in the beam-transport calculation. The effectiveness was assessed in a carbon-ion beam experiment in the presence of steep range compensation, where the splitting calculation reproduced a detour effect amounting to about 10% in dose or as large as the lateral particle disequilibrium effect. The efficiency was analyzed in calculations for carbon-ion and proton radiations with a heterogeneous phantom model, where the beam splitting increased computing times by factors of 4.7 and 3.2. The present method generally improves the accuracy of the pencil-beam algorithm without severe inefficiency. It will therefore be useful for treatment planning and potentially other demanding applications.

Information transmission in bosonic memory channels using Gaussian matrix-product states as near-optimal symbols

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schäfer, Joachim; Karpov, Evgueni; Cerf, Nicolas J.

2014-12-04

We seek for a realistic implementation of multimode Gaussian entangled states that can realize the optimal encoding for quantum bosonic Gaussian channels with memory. For a Gaussian channel with classical additive Markovian correlated noise and a lossy channel with non-Markovian correlated noise, we demonstrate the usefulness using Gaussian matrix-product states (GMPS). These states can be generated sequentially, and may, in principle, approximate well any Gaussian state. We show that we can achieve up to 99.9% of the classical Gaussian capacity with GMPS requiring squeezing parameters that are reachable with current technology. This may offer a way towards an experimental realization.

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle.

PubMed

Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu

2006-07-10

The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.

Capacity of PPM on Gaussian and Webb Channels

NASA Technical Reports Server (NTRS)

Divsalar, D.; Dolinar, S.; Pollara, F.; Hamkins, J.

2000-01-01

This paper computes and compares the capacities of M-ary PPM on various idealized channels that approximate the optical communication channel: (1) the standard additive white Gaussian noise (AWGN) channel;(2) a more general AWGN channel (AWGN2) allowing different variances in signal and noise slots;(3) a Webb-distributed channel (Webb2);(4) a Webb+Gaussian channel, modeling Gaussian thermal noise added to Webb-distributed channel outputs.

The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description

NASA Astrophysics Data System (ADS)

Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

2014-03-01

We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ɛ(r) is close to one everywhere inside the protein. The Gaussian widths σi of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σi. A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua.

Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description.

PubMed

Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

2014-03-14

We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ(i) of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ(i). A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua.

Accretion rates of protoplanets 2: Gaussian distribution of planestesimal velocities

NASA Technical Reports Server (NTRS)

Greenzweig, Yuval; Lissauer, Jack J.

1991-01-01

The growth rate of a protoplanet embedded in a uniform surface density disk of planetesimals having a triaxial Gaussian velocity distribution was calculated. The longitudes of the aspses and nodes of the planetesimals are uniformly distributed, and the protoplanet is on a circular orbit. The accretion rate in the two body approximation is enhanced by a factor of approximately 3, compared to the case where all planetesimals have eccentricity and inclination equal to the root mean square (RMS) values of those variables in the Gaussian distribution disk. Numerical three body integrations show comparable enhancements, except when the RMS initial planetesimal eccentricities are extremely small. This enhancement in accretion rate should be incorporated by all models, analytical or numerical, which assume a single random velocity for all planetesimals, in lieu of a Gaussian distribution.

Exact Distributions of Intraclass Correlation and Cronbach's Alpha with Gaussian Data and General Covariance

ERIC Educational Resources Information Center

Kistner, Emily O.; Muller, Keith E.

2004-01-01

Intraclass correlation and Cronbach's alpha are widely used to describe reliability of tests and measurements. Even with Gaussian data, exact distributions are known only for compound symmetric covariance (equal variances and equal correlations). Recently, large sample Gaussian approximations were derived for the distribution functions. New exact…

NGMIX: Gaussian mixture models for 2D images

NASA Astrophysics Data System (ADS)

Sheldon, Erin

2015-08-01

NGMIX implements Gaussian mixture models for 2D images. Both the PSF profile and the galaxy are modeled using mixtures of Gaussians. Convolutions are thus performed analytically, resulting in fast model generation as compared to methods that perform the convolution in Fourier space. For the galaxy model, NGMIX supports exponential disks and de Vaucouleurs and Sérsic profiles; these are implemented approximately as a sum of Gaussians using the fits from Hogg & Lang (2013). Additionally, any number of Gaussians can be fit, either completely free or constrained to be cocentric and co-elliptical.

Variational nonadiabatic dynamics in the moving crude adiabatic representation: Further merging of nuclear dynamics and electronic structure

NASA Astrophysics Data System (ADS)

Joubert-Doriol, Loïc; Izmaylov, Artur F.

2018-03-01

A new methodology of simulating nonadiabatic dynamics using frozen-width Gaussian wavepackets within the moving crude adiabatic representation with the on-the-fly evaluation of electronic structure is presented. The main feature of the new approach is the elimination of any global or local model representation of electronic potential energy surfaces; instead, the electron-nuclear interaction is treated explicitly using the Gaussian integration. As a result, the new scheme does not introduce any uncontrolled approximations. The employed variational principle ensures the energy conservation and leaves the number of electronic and nuclear basis functions as the only parameter determining the accuracy. To assess performance of the approach, a model with two electronic and two nuclear spacial degrees of freedom containing conical intersections between potential energy surfaces has been considered. Dynamical features associated with nonadiabatic transitions and nontrivial geometric (or Berry) phases were successfully reproduced within a limited basis expansion.

The effect of halo nuclear density on reaction cross-section for light ion collision

NASA Astrophysics Data System (ADS)

Hassan, M. A. M.; Nour El-Din, M. S. M.; Ellithi, A.; Ismail, E.; Hosny, H.

2015-08-01

In the framework of the optical limit approximation (OLA), the reaction cross-section for halo nucleus — stable nucleus collision at intermediate energy, has been studied. The projectile nuclei are taken to be one-neutron halo (1NHP) and two-neutron halo (2NHP). The calculations are carried out for Gaussian-Gaussian (GG), Gaussian-Oscillator (GO), and Gaussian-2S (G2S) densities for each considered projectile. As a target, the stable nuclei in the range 4-28 of the mass number are used. An analytic expression of the phase shift function has been derived. The zero range approximation is considered in the calculations. Also, the in-medium effect is studied. The obtained results are analyzed and compared with the geometrical reaction cross-section and the available experimental data.

Speech Enhancement, Gain, and Noise Spectrum Adaptation Using Approximate Bayesian Estimation

PubMed Central

Hao, Jiucang; Attias, Hagai; Nagarajan, Srikantan; Lee, Te-Won; Sejnowski, Terrence J.

2010-01-01

This paper presents a new approximate Bayesian estimator for enhancing a noisy speech signal. The speech model is assumed to be a Gaussian mixture model (GMM) in the log-spectral domain. This is in contrast to most current models in frequency domain. Exact signal estimation is a computationally intractable problem. We derive three approximations to enhance the efficiency of signal estimation. The Gaussian approximation transforms the log-spectral domain GMM into the frequency domain using minimal Kullback–Leiber (KL)-divergency criterion. The frequency domain Laplace method computes the maximum a posteriori (MAP) estimator for the spectral amplitude. Correspondingly, the log-spectral domain Laplace method computes the MAP estimator for the log-spectral amplitude. Further, the gain and noise spectrum adaptation are implemented using the expectation–maximization (EM) algorithm within the GMM under Gaussian approximation. The proposed algorithms are evaluated by applying them to enhance the speeches corrupted by the speech-shaped noise (SSN). The experimental results demonstrate that the proposed algorithms offer improved signal-to-noise ratio, lower word recognition error rate, and less spectral distortion. PMID:20428253

Cramer-Rao Bound for Gaussian Random Processes and Applications to Radar Processing of Atmospheric Signals

NASA Technical Reports Server (NTRS)

Frehlich, Rod

1993-01-01

Calculations of the exact Cramer-Rao Bound (CRB) for unbiased estimates of the mean frequency, signal power, and spectral width of Doppler radar/lidar signals (a Gaussian random process) are presented. Approximate CRB's are derived using the Discrete Fourier Transform (DFT). These approximate results are equal to the exact CRB when the DFT coefficients are mutually uncorrelated. Previous high SNR limits for CRB's are shown to be inaccurate because the discrete summations cannot be approximated with integration. The performance of an approximate maximum likelihood estimator for mean frequency approaches the exact CRB for moderate signal to noise ratio and moderate spectral width.

Extremality of Gaussian quantum states.

PubMed

Wolf, Michael M; Giedke, Geza; Cirac, J Ignacio

2006-03-03

We investigate Gaussian quantum states in view of their exceptional role within the space of all continuous variables states. A general method for deriving extremality results is provided and applied to entanglement measures, secret key distillation and the classical capacity of bosonic quantum channels. We prove that for every given covariance matrix the distillable secret key rate and the entanglement, if measured appropriately, are minimized by Gaussian states. This result leads to a clearer picture of the validity of frequently made Gaussian approximations. Moreover, it implies that Gaussian encodings are optimal for the transmission of classical information through bosonic channels, if the capacity is additive.

Gaussian beam and physical optics iteration technique for wideband beam waveguide feed design

NASA Technical Reports Server (NTRS)

Veruttipong, W.; Chen, J. C.; Bathker, D. A.

1991-01-01

The Gaussian beam technique has become increasingly popular for wideband beam waveguide (BWG) design. However, it is observed that the Gaussian solution is less accurate for smaller mirrors (approximately less than 30 lambda in diameter). Therefore, a high-performance wideband BWG design cannot be achieved by using the Gaussian beam technique alone. This article demonstrates a new design approach by iterating Gaussian beam and BWG parameters simultaneously at various frequencies to obtain a wideband BWG. The result is further improved by comparing it with physical optics results and repeating the iteration.

Effects of biases in domain wall network evolution. II. Quantitative analysis

NASA Astrophysics Data System (ADS)

Correia, J. R. C. C. C.; Leite, I. S. C. R.; Martins, C. J. A. P.

2018-04-01

Domain walls form at phase transitions which break discrete symmetries. In a cosmological context, they often overclose the Universe (contrary to observational evidence), although one may prevent this by introducing biases or forcing anisotropic evolution of the walls. In a previous work [Correia et al., Phys. Rev. D 90, 023521 (2014), 10.1103/PhysRevD.90.023521], we numerically studied the evolution of various types of biased domain wall networks in the early Universe, confirming that anisotropic networks ultimately reach scaling while those with a biased potential or biased initial conditions decay. We also found that the analytic decay law obtained by Hindmarsh was in good agreement with simulations of biased potentials, but not of biased initial conditions, and suggested that the difference was related to the Gaussian approximation underlying the analytic law. Here, we extend our previous work in several ways. For the cases of biased potential and biased initial conditions, we study in detail the field distributions in the simulations, confirming that the validity (or not) of the Gaussian approximation is the key difference between the two cases. For anisotropic walls, we carry out a more extensive set of numerical simulations and compare them to the canonical velocity-dependent one-scale model for domain walls, finding that the model accurately predicts the linear scaling regime after isotropization. Overall, our analysis provides a quantitative description of the cosmological evolution of these networks.

Achieving DFT accuracy with a machine-learning interatomic potential: Thermomechanics and defects in bcc ferromagnetic iron

NASA Astrophysics Data System (ADS)

Dragoni, Daniele; Daff, Thomas D.; Csányi, Gábor; Marzari, Nicola

2018-01-01

We show that the Gaussian Approximation Potential (GAP) machine-learning framework can describe complex magnetic potential energy surfaces, taking ferromagnetic iron as a paradigmatic challenging case. The training database includes total energies, forces, and stresses obtained from density-functional theory in the generalized-gradient approximation, and comprises approximately 150,000 local atomic environments, ranging from pristine and defected bulk configurations to surfaces and generalized stacking faults with different crystallographic orientations. We find the structural, vibrational, and thermodynamic properties of the GAP model to be in excellent agreement with those obtained directly from first-principles electronic-structure calculations. There is good transferability to quantities, such as Peierls energy barriers, which are determined to a large extent by atomic configurations that were not part of the training set. We observe the benefit and the need of using highly converged electronic-structure calculations to sample a target potential energy surface. The end result is a systematically improvable potential that can achieve the same accuracy of density-functional theory calculations, but at a fraction of the computational cost.

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

PubMed

García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G

2017-08-01

The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

PubMed

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-08-01

Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

Cosmic microwave background bispectrum from primordial magnetic fields on large angular scales.

PubMed

Seshadri, T R; Subramanian, Kandaswamy

2009-08-21

Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher-order effect. We propose a novel probe of stochastic primordial magnetic fields that exploits the characteristic CMB non-Gaussianity that they induce. We compute the CMB bispectrum (b(l1l2l3)) induced by such fields on large angular scales. We find a typical value of l1(l1 + 1)l3(l3 + 1)b(l1l2l3) approximately 10(-22), for magnetic fields of strength B0 approximately 3 nG and with a nearly scale invariant magnetic spectrum. Observational limits on the bispectrum allow us to set upper limits on B0 approximately 35 nG.

Dose impact in radiographic lung injury following lung SBRT: Statistical analysis and geometric interpretation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Victoria; Kishan, Amar U.; Cao, Minsong

2014-03-15

Purpose: To demonstrate a new method of evaluating dose response of treatment-induced lung radiographic injury post-SBRT (stereotactic body radiotherapy) treatment and the discovery of bimodal dose behavior within clinically identified injury volumes. Methods: Follow-up CT scans at 3, 6, and 12 months were acquired from 24 patients treated with SBRT for stage-1 primary lung cancers or oligometastic lesions. Injury regions in these scans were propagated to the planning CT coordinates by performing deformable registration of the follow-ups to the planning CTs. A bimodal behavior was repeatedly observed from the probability distribution for dose values within the deformed injury regions. Basedmore » on a mixture-Gaussian assumption, an Expectation-Maximization (EM) algorithm was used to obtain characteristic parameters for such distribution. Geometric analysis was performed to interpret such parameters and infer the critical dose level that is potentially inductive of post-SBRT lung injury. Results: The Gaussian mixture obtained from the EM algorithm closely approximates the empirical dose histogram within the injury volume with good consistency. The average Kullback-Leibler divergence values between the empirical differential dose volume histogram and the EM-obtained Gaussian mixture distribution were calculated to be 0.069, 0.063, and 0.092 for the 3, 6, and 12 month follow-up groups, respectively. The lower Gaussian component was located at approximately 70% prescription dose (35 Gy) for all three follow-up time points. The higher Gaussian component, contributed by the dose received by planning target volume, was located at around 107% of the prescription dose. Geometrical analysis suggests the mean of the lower Gaussian component, located at 35 Gy, as a possible indicator for a critical dose that induces lung injury after SBRT. Conclusions: An innovative and improved method for analyzing the correspondence between lung radiographic injury and SBRT treatment dose has been demonstrated. Bimodal behavior was observed in the dose distribution of lung injury after SBRT. Novel statistical and geometrical analysis has shown that the systematically quantified low-dose peak at approximately 35 Gy, or 70% prescription dose, is a good indication of a critical dose for injury. The determined critical dose of 35 Gy resembles the critical dose volume limit of 30 Gy for ipsilateral bronchus in RTOG 0618 and results from previous studies. The authors seek to further extend this improved analysis method to a larger cohort to better understand the interpatient variation in radiographic lung injury dose response post-SBRT.« less

The Nature of the Nodes, Weights and Degree of Precision in Gaussian Quadrature Rules

ERIC Educational Resources Information Center

Prentice, J. S. C.

2011-01-01

We present a comprehensive proof of the theorem that relates the weights and nodes of a Gaussian quadrature rule to its degree of precision. This level of detail is often absent in modern texts on numerical analysis. We show that the degree of precision is maximal, and that the approximation error in Gaussian quadrature is minimal, in a…

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-04-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-07-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modelling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modelling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a pre-conditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Inference with minimal Gibbs free energy in information field theory.

PubMed

Ensslin, Torsten A; Weig, Cornelius

2010-11-01

Non-linear and non-gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the gaussian approximation to the full posterior probability, which has maximal cross information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a gaussian signal with unknown spectrum, and (iii) inference of a poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-gaussian posterior.

Isocurvature constraints and anharmonic effects on QCD axion dark matter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kobayashi, Takeshi; Kurematsu, Ryosuke; Takahashi, Fuminobu, E-mail: takeshi@cita.utoronto.ca, E-mail: rkurematsu@tuhep.phys.tohoku.ac.jp, E-mail: fumi@tuhep.phys.tohoku.ac.jp

2013-09-01

We revisit the isocurvature density perturbations induced by quantum fluctuations of the axion field by extending a recently developed analytic method and approximations to a time-dependent scalar potential, which enables us to follow the evolution of the axion until it starts to oscillate. We find that, as the initial misalignment angle approaches the hilltop of the potential, the isocurvature perturbations become significantly enhanced, while the non-Gaussianity parameter increases slowly but surely. As a result, the isocurvature constraint on the inflation scale is tightened as H{sub inf}∼

Automatic selection of atomic fingerprints and reference configurations for machine-learning potentials

NASA Astrophysics Data System (ADS)

Imbalzano, Giulio; Anelli, Andrea; Giofré, Daniele; Klees, Sinja; Behler, Jörg; Ceriotti, Michele

2018-06-01

Machine learning of atomic-scale properties is revolutionizing molecular modeling, making it possible to evaluate inter-atomic potentials with first-principles accuracy, at a fraction of the costs. The accuracy, speed, and reliability of machine learning potentials, however, depend strongly on the way atomic configurations are represented, i.e., the choice of descriptors used as input for the machine learning method. The raw Cartesian coordinates are typically transformed in "fingerprints," or "symmetry functions," that are designed to encode, in addition to the structure, important properties of the potential energy surface like its invariances with respect to rotation, translation, and permutation of like atoms. Here we discuss automatic protocols to select a number of fingerprints out of a large pool of candidates, based on the correlations that are intrinsic to the training data. This procedure can greatly simplify the construction of neural network potentials that strike the best balance between accuracy and computational efficiency and has the potential to accelerate by orders of magnitude the evaluation of Gaussian approximation potentials based on the smooth overlap of atomic positions kernel. We present applications to the construction of neural network potentials for water and for an Al-Mg-Si alloy and to the prediction of the formation energies of small organic molecules using Gaussian process regression.

The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garza, Jorge; Nichols, Jeffrey A.; Dixon, David A.

2000-05-08

The Krieger, Li, and Iafrate approximation to the optimized effective potential including the self-interaction correction for density functional theory has been implemented in a molecular code, NWChem, that uses Gaussian functions to represent the Kohn and Sham spin-orbitals. The differences between the implementation of the self-interaction correction in codes where planewaves are used with an optimized effective potential are discussed. The importance of the localization of the spin-orbitals to maximize the exchange-correlation of the self-interaction correction is discussed. We carried out exchange-only calculations to compare the results obtained with these approximations, and those obtained with the local spin density approximation,more » the generalized gradient approximation and Hartree-Fock theory. Interesting results for the energy difference (GAP) between the highest occupied molecular orbital, HOMO, and the lowest unoccupied molecular orbital, LUMO, (spin-orbital energies of closed shell atoms and molecules) using the optimized effective potential and the self-interaction correction have been obtained. The effect of the diffuse character of the basis set on the HOMO and LUMO eigenvalues at the various levels is discussed. Total energies obtained with the optimized effective potential and the self-interaction correction show that the exchange energy with these approximations is overestimated and this will be an important topic for future work. (c) 2000 American Institute of Physics.« less

Series approximation to probability densities

NASA Astrophysics Data System (ADS)

Cohen, L.

2018-04-01

One of the historical and fundamental uses of the Edgeworth and Gram-Charlier series is to "correct" a Gaussian density when it is determined that the probability density under consideration has moments that do not correspond to the Gaussian [5, 6]. There is a fundamental difficulty with these methods in that if the series are truncated, then the resulting approximate density is not manifestly positive. The aim of this paper is to attempt to expand a probability density so that if it is truncated it will still be manifestly positive.

Mean Field Variational Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

Vrettas, M.; Cornford, D.; Opper, M.

2012-04-01

Current data assimilation schemes propose a range of approximate solutions to the classical data assimilation problem, particularly state estimation. Broadly there are three main active research areas: ensemble Kalman filter methods which rely on statistical linearization of the model evolution equations, particle filters which provide a discrete point representation of the posterior filtering or smoothing distribution and 4DVAR methods which seek the most likely posterior smoothing solution. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the most probably posterior distribution over the states, within the family of non-stationary Gaussian processes. Our original work on variational Bayesian approaches to data assimilation sought the best approximating time varying Gaussian process to the posterior smoothing distribution for stochastic dynamical systems. This approach was based on minimising the Kullback-Leibler divergence between the true posterior over paths, and our Gaussian process approximation. So long as the observation density was sufficiently high to bring the posterior smoothing density close to Gaussian the algorithm proved very effective, on lower dimensional systems. However for higher dimensional systems, the algorithm was computationally very demanding. We have been developing a mean field version of the algorithm which treats the state variables at a given time as being independent in the posterior approximation, but still accounts for their relationships between each other in the mean solution arising from the original dynamical system. In this work we present the new mean field variational Bayesian approach, illustrating its performance on a range of classical data assimilation problems. We discuss the potential and limitations of the new approach. We emphasise that the variational Bayesian approach we adopt, in contrast to other variational approaches, provides a bound on the marginal likelihood of the observations given parameters in the model which also allows inference of parameters such as observation errors, and parameters in the model and model error representation, particularly if this is written as a deterministic form with small additive noise. We stress that our approach can address very long time window and weak constraint settings. However like traditional variational approaches our Bayesian variational method has the benefit of being posed as an optimisation problem. We finish with a sketch of the future directions for our approach.

Improved Linear Algebra Methods for Redshift Computation from Limited Spectrum Data - II

NASA Technical Reports Server (NTRS)

Foster, Leslie; Waagen, Alex; Aijaz, Nabella; Hurley, Michael; Luis, Apolo; Rinsky, Joel; Satyavolu, Chandrika; Gazis, Paul; Srivastava, Ashok; Way, Michael

2008-01-01

Given photometric broadband measurements of a galaxy, Gaussian processes may be used with a training set to solve the regression problem of approximating the redshift of this galaxy. However, in practice solving the traditional Gaussian processes equation is too slow and requires too much memory. We employed several methods to avoid this difficulty using algebraic manipulation and low-rank approximation, and were able to quickly approximate the redshifts in our testing data within 17 percent of the known true values using limited computational resources. The accuracy of one method, the V Formulation, is comparable to the accuracy of the best methods currently used for this problem.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Modak, Viraj P., E-mail: virajmodak@gmail.com; Wyslouzil, Barbara E., E-mail: wyslouzil.1@osu.edu; Department of Chemistry and Biochemistry, Ohio State University, Columbus, Ohio 43210

The crystal-vapor surface free energy γ is an important physical parameter governing physical processes, such as wetting and adhesion. We explore exact and approximate routes to calculate γ based on cleaving an intact crystal into non-interacting sub-systems with crystal-vapor interfaces. We do this by turning off the interactions, ΔV, between the sub-systems. Using the soft-core scheme for turning off ΔV, we find that the free energy varies smoothly with the coupling parameter λ, and a single thermodynamic integration yields the exact γ. We generate another exact method, and a cumulant expansion for γ by expressing the surface free energy inmore » terms of an average of e{sup −βΔV} in the intact crystal. The second cumulant, or Gaussian approximation for γ is surprisingly accurate in most situations, even though we find that the underlying probability distribution for ΔV is clearly not Gaussian. We account for this fact by developing a non-Gaussian theory for γ and find that the difference between the non-Gaussian and Gaussian expressions for γ consist of terms that are negligible in many situations. Exact and approximate methods are applied to the (111) surface of a Lennard-Jones crystal and are also tested for more complex molecular solids, the surface of octane and nonadecane. Alkane surfaces were chosen for study because their crystal-vapor surface free energy has been of particular interest for understanding surface freezing in these systems.« less

Probability density and exceedance rate functions of locally Gaussian turbulence

NASA Technical Reports Server (NTRS)

Mark, W. D.

1989-01-01

A locally Gaussian model of turbulence velocities is postulated which consists of the superposition of a slowly varying strictly Gaussian component representing slow temporal changes in the mean wind speed and a more rapidly varying locally Gaussian turbulence component possessing a temporally fluctuating local variance. Series expansions of the probability density and exceedance rate functions of the turbulence velocity model, based on Taylor's series, are derived. Comparisons of the resulting two-term approximations with measured probability density and exceedance rate functions of atmospheric turbulence velocity records show encouraging agreement, thereby confirming the consistency of the measured records with the locally Gaussian model. Explicit formulas are derived for computing all required expansion coefficients from measured turbulence records.

Evolution of CMB spectral distortion anisotropies and tests of primordial non-Gaussianity

NASA Astrophysics Data System (ADS)

Chluba, Jens; Dimastrogiovanni, Emanuela; Amin, Mustafa A.; Kamionkowski, Marc

2017-04-01

Anisotropies in distortions to the frequency spectrum of the cosmic microwave background (CMB) can be created through spatially varying heating processes in the early Universe. For instance, the dissipation of small-scale acoustic modes does create distortion anisotropies, in particular for non-Gaussian primordial perturbations. In this work, we derive approximations that allow describing the associated distortion field. We provide a systematic formulation of the problem using Fourier-space window functions, clarifying and generalizing previous approximations. Our expressions highlight the fact that the amplitudes of the spectral-distortion fluctuations induced by non-Gaussianity depend also on the homogeneous value of those distortions. Absolute measurements are thus required to obtain model-independent distortion constraints on primordial non-Gaussianity. We also include a simple description for the evolution of distortions through photon diffusion, showing that these corrections can usually be neglected. Our formulation provides a systematic framework for computing higher order correlation functions of distortions with CMB temperature anisotropies and can be extended to describe correlations with polarization anisotropies.

Deterministic Mean-Field Ensemble Kalman Filtering

DOE PAGES

Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

2016-05-03

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d

Deterministic Mean-Field Ensemble Kalman Filtering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

DOE PAGES

White, Alec F.; Head-Gordon, Martin; McCurdy, C. William

2017-01-30

The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. Here, we critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2Π g shape resonance of N 2 - whichmore » has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We then conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.« less

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Alec F.; Head-Gordon, Martin; McCurdy, C. William

The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. Here, we critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2Π g shape resonance of N 2 - whichmore » has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We then conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.« less

Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis.

PubMed

Wilhelm, Jan; Seewald, Patrick; Del Ben, Mauro; Hutter, Jürg

2016-12-13

We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring [Formula: see text] operations and [Formula: see text] memory. The method is based on the resolution of the identity (RI) with the overlap metric, a reformulation of RI-RPA in the Gaussian basis, imaginary time, and imaginary frequency integration techniques, and the use of sparse linear algebra. Additional memory reduction without extra computations can be achieved by an iterative scheme that overcomes the memory bottleneck of canonical RPA implementations. We report a massively parallel implementation that is the key for the application to large systems. Finally, cubic-scaling RPA is applied to a thousand water molecules using a correlation-consistent triple-ζ quality basis.

Diffusion of Super-Gaussian Profiles

ERIC Educational Resources Information Center

Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.

2007-01-01

The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…

Particle rejuvenation of Rao-Blackwellized sequential Monte Carlo smoothers for conditionally linear and Gaussian models

NASA Astrophysics Data System (ADS)

Nguyen, Ngoc Minh; Corff, Sylvain Le; Moulines, Éric

2017-12-01

This paper focuses on sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use Rao-Blackwellization: particle approximation is used to sample sequences of hidden regimes while the Gaussian states are explicitly integrated conditional on the sequence of regimes and observations, using variants of the Kalman filter/smoother. The first successful attempt to use Rao-Blackwellization for smoothing extends the Bryson-Frazier smoother for Gaussian linear state space models using the generalized two-filter formula together with Kalman filters/smoothers. More recently, a forward-backward decomposition of smoothing distributions mimicking the Rauch-Tung-Striebel smoother for the regimes combined with backward Kalman updates has been introduced. This paper investigates the benefit of introducing additional rejuvenation steps in all these algorithms to sample at each time instant new regimes conditional on the forward and backward particles. This defines particle-based approximations of the smoothing distributions whose support is not restricted to the set of particles sampled in the forward or backward filter. These procedures are applied to commodity markets which are described using a two-factor model based on the spot price and a convenience yield for crude oil data.

Non-Gaussianity and Excursion Set Theory: Halo Bias

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adshead, Peter; Baxter, Eric J.; Dodelson, Scott

2012-09-01

We study the impact of primordial non-Gaussianity generated during inflation on the bias of halos using excursion set theory. We recapture the familiar result that the bias scales asmore » $$k^{-2}$$ on large scales for local type non-Gaussianity but explicitly identify the approximations that go into this conclusion and the corrections to it. We solve the more complicated problem of non-spherical halos, for which the collapse threshold is scale dependent.« less

Minimum relative entropy distributions with a large mean are Gaussian

NASA Astrophysics Data System (ADS)

Smerlak, Matteo

2016-12-01

Entropy optimization principles are versatile tools with wide-ranging applications from statistical physics to engineering to ecology. Here we consider the following constrained problem: Given a prior probability distribution q , find the posterior distribution p minimizing the relative entropy (also known as the Kullback-Leibler divergence) with respect to q under the constraint that mean (p ) is fixed and large. We show that solutions to this problem are approximately Gaussian. We discuss two applications of this result. In the context of dissipative dynamics, the equilibrium distribution of a Brownian particle confined in a strong external field is independent of the shape of the confining potential. We also derive an H -type theorem for evolutionary dynamics: The entropy of the (standardized) distribution of fitness of a population evolving under natural selection is eventually increasing in time.

Mean First Passage Time and Stochastic Resonance in a Transcriptional Regulatory System with Non-Gaussian Noise

NASA Astrophysics Data System (ADS)

Kang, Yan-Mei; Chen, Xi; Lin, Xu-Dong; Tan, Ning

The mean first passage time (MFPT) in a phenomenological gene transcriptional regulatory model with non-Gaussian noise is analytically investigated based on the singular perturbation technique. The effect of the non-Gaussian noise on the phenomenon of stochastic resonance (SR) is then disclosed based on a new combination of adiabatic elimination and linear response approximation. Compared with the results in the Gaussian noise case, it is found that bounded non-Gaussian noise inhibits the transition between different concentrations of protein, while heavy-tailed non-Gaussian noise accelerates the transition. It is also found that the optimal noise intensity for SR in the heavy-tailed noise case is smaller, while the optimal noise intensity in the bounded noise case is larger. These observations can be explained by the heavy-tailed noise easing random transitions.

Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

NASA Astrophysics Data System (ADS)

Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

2016-09-01

The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

Flat-top beam for laser-stimulated pain

NASA Astrophysics Data System (ADS)

McCaughey, Ryan; Nadeau, Valerie; Dickinson, Mark

2005-04-01

One of the main problems during laser stimulation in human pain research is the risk of tissue damage caused by excessive heating of the skin. This risk has been reduced by using a laser beam with a flattop (or superGaussian) intensity profile, instead of the conventional Gaussian beam. A finite difference approximation to the heat conduction equation has been applied to model the temperature distribution in skin as a result of irradiation by flattop and Gaussian profile CO2 laser beams. The model predicts that a 15 mm diameter, 15 W, 100 ms CO2 laser pulse with an order 6 superGaussian profile produces a maximum temperature 6 oC less than a Gaussian beam with the same energy density. A superGaussian profile was created by passing a Gaussian beam through a pair of zinc selenide aspheric lenses which refract the more intense central region of the beam towards the less intense periphery. The profiles of the lenses were determined by geometrical optics. In human pain trials the superGaussian beam required more power than the Gaussian beam to reach sensory and pain thresholds.

Super-resolving random-Gaussian apodized photon sieve.

PubMed

Sabatyan, Arash; Roshaninejad, Parisa

2012-09-10

A novel apodized photon sieve is presented in which random dense Gaussian distribution is implemented to modulate the pinhole density in each zone. The random distribution in dense Gaussian distribution causes intrazone discontinuities. Also, the dense Gaussian distribution generates a substantial number of pinholes in order to form a large degree of overlap between the holes in a few innermost zones of the photon sieve; thereby, clear zones are formed. The role of the discontinuities on the focusing properties of the photon sieve is examined as well. Analysis shows that secondary maxima have evidently been suppressed, transmission has increased enormously, and the central maxima width is approximately unchanged in comparison to the dense Gaussian distribution. Theoretical results have been completely verified by experiment.

Nonexistence of exact solutions agreeing with the Gaussian beam on the beam axis or in the focal plane

NASA Astrophysics Data System (ADS)

Lekner, John; Andrejic, Petar

2018-01-01

Solutions of the Helmholtz equation which describe electromagnetic beams (and also acoustic or particle beams) are discussed. We show that an exact solution which reproduces the Gaussian beam waveform on the beam axis does not exist. This is surprising, since the Gaussian beam is a solution of the paraxial equation, and thus supposedly accurate on and near the beam axis. Likewise, a solution of the Helmholtz equation which exactly reproduces the Gaussian beam in the focal plane does not exist. We show that the last statement also holds for Bessel-Gauss beams. However, solutions of the Helmholtz equation (one of which is discussed in detail) can approximate the Gaussian waveform within the central focal region.

Partial-Wave Representations of Laser Beams for Use in Light-Scattering Calculations

NASA Technical Reports Server (NTRS)

Gouesbet, Gerard; Lock, James A.; Grehan, Gerard

1995-01-01

In the framework of generalized Lorenz-Mie theory, laser beams are described by sets of beam-shape coefficients. The modified localized approximation to evaluate these coefficients for a focused Gaussian beam is presented. A new description of Gaussian beams, called standard beams, is introduced. A comparison is made between the values of the beam-shape coefficients in the framework of the localized approximation and the beam-shape coefficients of standard beams. This comparison leads to new insights concerning the electromagnetic description of laser beams. The relevance of our discussion is enhanced by a demonstration that the localized approximation provides a very satisfactory description of top-hat beams as well.

Propagation of a laser beam in a plasma

NASA Technical Reports Server (NTRS)

Chapman, J. M.; Kevorkian, J.; Steinhauer, L. C.; Vagners, J.

1975-01-01

This paper shows that for a nonabsorbing medium with a prescribed index of refraction, the effects of beam stability, line focusing, and beam distortion can be predicted from simple ray optics. When the paraxial approximation is used, diffraction effects are examined for Gaussian, Lorentzian, and square beams. Most importantly, it is shown that for a Gaussian beam, diffraction effects can be included simply by adding imaginary solutions to the paraxial ray equations. Also presented are several procedures to extend the paraxial approximation so that the solution will have a domain of validity of greater extent.

Gaussian-Beam/Physical-Optics Design Of Beam Waveguide

NASA Technical Reports Server (NTRS)

Veruttipong, Watt; Chen, Jacqueline C.; Bathker, Dan A.

1993-01-01

In iterative method of designing wideband beam-waveguide feed for paraboloidal-reflector antenna, Gaussian-beam approximation alternated with more nearly exact physical-optics analysis of diffraction. Includes curved and straight reflectors guiding radiation from feed horn to subreflector. For iterative design calculations, curved mirrors mathematically modeled as thin lenses. Each distance Li is combined length of two straight-line segments intersecting at one of flat mirrors. Method useful for designing beam-waveguide reflectors or mirrors required to have diameters approximately less than 30 wavelengths at one or more intended operating frequencies.

Real-time dynamics of matrix quantum mechanics beyond the classical approximation

NASA Astrophysics Data System (ADS)

Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas

2018-03-01

We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weinstein, Marvin; /SLAC

It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for themore » behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will turn to tunneling problems and show that the instanton can also be though of in the same way. I will do this for the classic problem of a double well potential in the extreme limit when the splitting between the two lowest levels is extremely small and the tunneling rate from one well to another is also very small.« less

Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system.

PubMed

Sun, Dong; Zhao, Daomu

2005-08-01

By introducing the hard-aperture function into a finite sum of complex Gaussian functions, the approximate analytical expressions of the Wigner distribution function for Hermite-cosine-Gaussian beams passing through an apertured paraxial ABCD optical system are obtained. The analytical results are compared with the numerically integrated ones, and the absolute errors are also given. It is shown that the analytical results are proper and that the calculation speed for them is much faster than for the numerical results.

Symplectic semiclassical wave packet dynamics II: non-Gaussian states

NASA Astrophysics Data System (ADS)

Ohsawa, Tomoki

2018-05-01

We generalize our earlier work on the symplectic/Hamiltonian formulation of the dynamics of the Gaussian wave packet to non-Gaussian semiclassical wave packets. We find the symplectic forms and asymptotic expansions of the Hamiltonians associated with these semiclassical wave packets, and obtain Hamiltonian systems governing their dynamics. Numerical experiments demonstrate that the dynamics give a very good approximation to the short-time dynamics of the expectation values computed by a method based on Egorov’s theorem or the initial value representation.

Accretion rates of protoplanets. II - Gaussian distributions of planetesimal velocities

NASA Technical Reports Server (NTRS)

Greenzweig, Yuval; Lissauer, Jack J.

1992-01-01

In the present growth-rate calculations for a protoplanet that is embedded in a disk of planetesimals with triaxial Gaussian velocity dispersion and uniform surface density, the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is found to be enhanced by a factor of about 3 relative to the case where all planetesimals' eccentricities and inclinations are equal to the rms values of those disk variables having locally Gaussian velocity dispersion. This accretion-rate enhancement should be incorporated by all models that assume a single random velocity for all planetesimals in lieu of a Gaussian distribution.

Correction Factor for Gaussian Deconvolution of Optically Thick Linewidths in Homogeneous Sources

NASA Technical Reports Server (NTRS)

Kastner, S. O.; Bhatia, A. K.

1999-01-01

Profiles of optically thick, non-Gaussian emission line profiles convoluted with Gaussian instrumental profiles are constructed, and are deconvoluted on the usual Gaussian basis to examine the departure from accuracy thereby caused in "measured" linewidths. It is found that "measured" linewidths underestimate the true linewidths of optically thick lines, by a factor which depends on the resolution factor r congruent to Doppler width/instrumental width and on the optical thickness tau(sub 0). An approximating expression is obtained for this factor, applicable in the range of at least 0 <= tau(sub 0) <= 10, which can provide estimates of the true linewidth and optical thickness.

Pseudo-steady-state non-Gaussian Einstein-Podolsky-Rosen steering of massive particles in pumped and damped Bose-Hubbard dimers

NASA Astrophysics Data System (ADS)

Olsen, M. K.

2017-02-01

We propose and analyze a pumped and damped Bose-Hubbard dimer as a source of continuous-variable Einstein-Podolsky-Rosen (EPR) steering with non-Gaussian statistics. We use and compare the results of the approximate truncated Wigner and the exact positive-P representation to calculate and compare the predictions for intensities, second-order quantum correlations, and third- and fourth-order cumulants. We find agreement for intensities and the products of inferred quadrature variances, which indicate that states demonstrating the EPR paradox are present. We find clear signals of non-Gaussianity in the quantum states of the modes from both the approximate and exact techniques, with quantitative differences in their predictions. Our proposed experimental configuration is extrapolated from current experimental techniques and adds another apparatus to the current toolbox of quantum atom optics.

Implementing of lognormal humidity and cloud-related control variables for the NCEP GSI hybrid EnVAR Assimilation scheme.

NASA Astrophysics Data System (ADS)

Fletcher, S. J.; Kleist, D.; Ide, K.

2017-12-01

As the resolution of operational global numerical weather prediction system approach the meso-scale, then the assumption of Gaussianity for the errors at these scales may not valid. However, it is also true that synoptic variables that are positive definite in behavior, for example humidity, cannot be optimally analyzed with a Gaussian error structure, where the increment could force the full field to go negative. In this presentation we present the initial work of implementing a mixed Gaussian-lognormal approximation for the temperature and moisture variable in both the ensemble and variational component of the NCEP GSI hybrid EnVAR. We shall also lay the foundation for the implementation of the lognormal approximation to cloud related control variables to allow for a possible more consistent assimilation of cloudy radiances.

Noise effects in nonlinear biochemical signaling

NASA Astrophysics Data System (ADS)

Bostani, Neda; Kessler, David A.; Shnerb, Nadav M.; Rappel, Wouter-Jan; Levine, Herbert

2012-01-01

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it is a priori obvious that this approximation can violate physical constraints, such as the positivity of chemical concentrations. Here, we show that even when such nonphysical fluctuations are rare, an exact solution of the Gaussian model shows that the model can yield unphysical results. This is done in the context of a simple incoherent-feedforward model which exhibits perfect adaptation in the deterministic limit. We show how one can use the natural separation of time scales in this model to yield an approximate model, that is analytically solvable, including its dynamical response to an environmental change. Alternatively, one can employ a cutoff procedure to regularize the Gaussian result.

Gaussian Finite Element Method for Description of Underwater Sound Diffraction

NASA Astrophysics Data System (ADS)

Huang, Dehua

A new method for solving diffraction problems is presented in this dissertation. It is based on the use of Gaussian diffraction theory. The Rayleigh integral is used to prove the core of Gaussian theory: the diffraction field of a Gaussian is described by a Gaussian function. The parabolic approximation used by previous authors is not necessary to this proof. Comparison of the Gaussian beam expansion and Fourier series expansion reveals that the Gaussian expansion is a more general and more powerful technique. The method combines the Gaussian beam superposition technique (Wen and Breazeale, J. Acoust. Soc. Am. 83, 1752-1756 (1988)) and the Finite element solution to the parabolic equation (Huang, J. Acoust. Soc. Am. 84, 1405-1413 (1988)). Computer modeling shows that the new method is capable of solving for the sound field even in an inhomogeneous medium, whether the source is a Gaussian source or a distributed source. It can be used for horizontally layered interfaces or irregular interfaces. Calculated results are compared with experimental results by use of a recently designed and improved Gaussian transducer in a laboratory water tank. In addition, the power of the Gaussian Finite element method is demonstrated by comparing numerical results with experimental results from use of a piston transducer in a water tank.

Some error bounds for K-iterated Gaussian recursive filters

NASA Astrophysics Data System (ADS)

Cuomo, Salvatore; Galletti, Ardelio; Giunta, Giulio; Marcellino, Livia

2016-10-01

Recursive filters (RFs) have achieved a central role in several research fields over the last few years. For example, they are used in image processing, in data assimilation and in electrocardiogram denoising. More in particular, among RFs, the Gaussian RFs are an efficient computational tool for approximating Gaussian-based convolutions and are suitable for digital image processing and applications of the scale-space theory. As is a common knowledge, the Gaussian RFs, applied to signals with support in a finite domain, generate distortions and artifacts, mostly localized at the boundaries. Heuristic and theoretical improvements have been proposed in literature to deal with this issue (namely boundary conditions). They include the case in which a Gaussian RF is applied more than once, i.e. the so called K-iterated Gaussian RFs. In this paper, starting from a summary of the comprehensive mathematical background, we consider the case of the K-iterated first-order Gaussian RF and provide the study of its numerical stability and some component-wise theoretical error bounds.

Anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field: two-loop approximation.

PubMed

Adzhemyan, L Ts; Antonov, N V; Honkonen, J; Kim, T L

2005-01-01

The field theoretic renormalization group and operator-product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the Navier-Stokes equation, subject to an external random stirring force with the correlation function proportional to delta(t- t')k(4-d-2epsilon). It is shown that the scalar field is intermittent already for small epsilon, its structure functions display anomalous scaling behavior, and the corresponding exponents can be systematically calculated as series in epsilon. The practical calculation is accomplished to order epsilon2 (two-loop approximation), including anisotropic sectors. As for the well-known Kraichnan rapid-change model, the anomalous scaling results from the existence in the model of composite fields (operators) with negative scaling dimensions, identified with the anomalous exponents. Thus the mechanism of the origin of anomalous scaling appears similar for the Gaussian model with zero correlation time and the non-Gaussian model with finite correlation time. It should be emphasized that, in contrast to Gaussian velocity ensembles with finite correlation time, the model and the perturbation theory discussed here are manifestly Galilean covariant. The relevance of these results for real passive advection and comparison with the Gaussian models and experiments are briefly discussed.

EXACT DISTRIBUTIONS OF INTRACLASS CORRELATION AND CRONBACH'S ALPHA WITH GAUSSIAN DATA AND GENERAL COVARIANCE.

PubMed

Kistner, Emily O; Muller, Keith E

2004-09-01

Intraclass correlation and Cronbach's alpha are widely used to describe reliability of tests and measurements. Even with Gaussian data, exact distributions are known only for compound symmetric covariance (equal variances and equal correlations). Recently, large sample Gaussian approximations were derived for the distribution functions. New exact results allow calculating the exact distribution function and other properties of intraclass correlation and Cronbach's alpha, for Gaussian data with any covariance pattern, not just compound symmetry. Probabilities are computed in terms of the distribution function of a weighted sum of independent chi-square random variables. New F approximations for the distribution functions of intraclass correlation and Cronbach's alpha are much simpler and faster to compute than the exact forms. Assuming the covariance matrix is known, the approximations typically provide sufficient accuracy, even with as few as ten observations. Either the exact or approximate distributions may be used to create confidence intervals around an estimate of reliability. Monte Carlo simulations led to a number of conclusions. Correctly assuming that the covariance matrix is compound symmetric leads to accurate confidence intervals, as was expected from previously known results. However, assuming and estimating a general covariance matrix produces somewhat optimistically narrow confidence intervals with 10 observations. Increasing sample size to 100 gives essentially unbiased coverage. Incorrectly assuming compound symmetry leads to pessimistically large confidence intervals, with pessimism increasing with sample size. In contrast, incorrectly assuming general covariance introduces only a modest optimistic bias in small samples. Hence the new methods seem preferable for creating confidence intervals, except when compound symmetry definitely holds.

Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance.

PubMed

Richardson, Magnus J E; Gerstner, Wulfram

2005-04-01

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units

NASA Astrophysics Data System (ADS)

Franović, Igor; Todorović, Kristina; Vasović, Nebojša; Burić, Nikola

2014-02-01

We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the Gaussian and the quasi-independence approximation, as well as the fashion in which their validity is verified, are adapted to reflect the essential properties of the underlying system. It is demonstrated that the failure of the mean-field model associated with the breakdown of the quasi-independence approximation can be predicted by the noise-induced bistability in the dynamics of the mean-field system. As for the Gaussian approximation, its violation is related to the increase of noise intensity, but the actual condition for failure can be cast in qualitative, rather than quantitative terms. We also discuss how the fulfillment of the mean-field approximations affects the statistics of the first return times for the local and global variables, further exploring the link between the fulfillment of the quasi-independence approximation and certain forms of synchronization between the individual units.

A Gaussian-based rank approximation for subspace clustering

NASA Astrophysics Data System (ADS)

Xu, Fei; Peng, Chong; Hu, Yunhong; He, Guoping

2018-04-01

Low-rank representation (LRR) has been shown successful in seeking low-rank structures of data relationships in a union of subspaces. Generally, LRR and LRR-based variants need to solve the nuclear norm-based minimization problems. Beyond the success of such methods, it has been widely noted that the nuclear norm may not be a good rank approximation because it simply adds all singular values of a matrix together and thus large singular values may dominant the weight. This results in far from satisfactory rank approximation and may degrade the performance of lowrank models based on the nuclear norm. In this paper, we propose a novel nonconvex rank approximation based on the Gaussian distribution function, which has demanding properties to be a better rank approximation than the nuclear norm. Then a low-rank model is proposed based on the new rank approximation with application to motion segmentation. Experimental results have shown significant improvements and verified the effectiveness of our method.

Kernel K-Means Sampling for Nyström Approximation.

PubMed

He, Li; Zhang, Hong

2018-05-01

A fundamental problem in Nyström-based kernel matrix approximation is the sampling method by which training set is built. In this paper, we suggest to use kernel -means sampling, which is shown in our works to minimize the upper bound of a matrix approximation error. We first propose a unified kernel matrix approximation framework, which is able to describe most existing Nyström approximations under many popular kernels, including Gaussian kernel and polynomial kernel. We then show that, the matrix approximation error upper bound, in terms of the Frobenius norm, is equal to the -means error of data points in kernel space plus a constant. Thus, the -means centers of data in kernel space, or the kernel -means centers, are the optimal representative points with respect to the Frobenius norm error upper bound. Experimental results, with both Gaussian kernel and polynomial kernel, on real-world data sets and image segmentation tasks show the superiority of the proposed method over the state-of-the-art methods.

A path integral approach to the Hodgkin-Huxley model

NASA Astrophysics Data System (ADS)

Baravalle, Roman; Rosso, Osvaldo A.; Montani, Fernando

2017-11-01

To understand how single neurons process sensory information, it is necessary to develop suitable stochastic models to describe the response variability of the recorded spike trains. Spikes in a given neuron are produced by the synergistic action of sodium and potassium of the voltage-dependent channels that open or close the gates. Hodgkin and Huxley (HH) equations describe the ionic mechanisms underlying the initiation and propagation of action potentials, through a set of nonlinear ordinary differential equations that approximate the electrical characteristics of the excitable cell. Path integral provides an adequate approach to compute quantities such as transition probabilities, and any stochastic system can be expressed in terms of this methodology. We use the technique of path integrals to determine the analytical solution driven by a non-Gaussian colored noise when considering the HH equations as a stochastic system. The different neuronal dynamics are investigated by estimating the path integral solutions driven by a non-Gaussian colored noise q. More specifically we take into account the correlational structures of the complex neuronal signals not just by estimating the transition probability associated to the Gaussian approach of the stochastic HH equations, but instead considering much more subtle processes accounting for the non-Gaussian noise that could be induced by the surrounding neural network and by feedforward correlations. This allows us to investigate the underlying dynamics of the neural system when different scenarios of noise correlations are considered.

Probabilistic inference using linear Gaussian importance sampling for hybrid Bayesian networks

NASA Astrophysics Data System (ADS)

Sun, Wei; Chang, K. C.

2005-05-01

Probabilistic inference for Bayesian networks is in general NP-hard using either exact algorithms or approximate methods. However, for very complex networks, only the approximate methods such as stochastic sampling could be used to provide a solution given any time constraint. There are several simulation methods currently available. They include logic sampling (the first proposed stochastic method for Bayesian networks, the likelihood weighting algorithm) the most commonly used simulation method because of its simplicity and efficiency, the Markov blanket scoring method, and the importance sampling algorithm. In this paper, we first briefly review and compare these available simulation methods, then we propose an improved importance sampling algorithm called linear Gaussian importance sampling algorithm for general hybrid model (LGIS). LGIS is aimed for hybrid Bayesian networks consisting of both discrete and continuous random variables with arbitrary distributions. It uses linear function and Gaussian additive noise to approximate the true conditional probability distribution for continuous variable given both its parents and evidence in a Bayesian network. One of the most important features of the newly developed method is that it can adaptively learn the optimal important function from the previous samples. We test the inference performance of LGIS using a 16-node linear Gaussian model and a 6-node general hybrid model. The performance comparison with other well-known methods such as Junction tree (JT) and likelihood weighting (LW) shows that LGIS-GHM is very promising.

A coaxially focused multi-mode beam for optical coherence tomography imaging with extended depth of focus (Conference Presentation)

NASA Astrophysics Data System (ADS)

Yin, Biwei; Liang, Chia-Pin; Vuong, Barry; Tearney, Guillermo J.

2017-02-01

Conventional OCT images, obtained using a focused Gaussian beam have a lateral resolution of approximately 30 μm and a depth of focus (DOF) of 2-3 mm, defined as the confocal parameter (twice of Gaussian beam Rayleigh range). Improvement of lateral resolution without sacrificing imaging range requires techniques that can extend the DOF. Previously, we described a self-imaging wavefront division optical system that provided an estimated one order of magnitude DOF extension. In this study, we further investigate the properties of the coaxially focused multi-mode (CAFM) beam created by this self-imaging wavefront division optical system and demonstrate its feasibility for real-time biological tissue imaging. Gaussian beam and CAFM beam fiber optic probes with similar numerical apertures (objective NA≈0.5) were fabricated, providing lateral resolutions of approximately 2 μm. Rigorous lateral resolution characterization over depth was performed for both probes. The CAFM beam probe was found to be able to provide a DOF that was approximately one order of magnitude greater than that of Gaussian beam probe. By incorporating the CAFM beam fiber optic probe into a μOCT system with 1.5 μm axial resolution, we were able to acquire cross-sectional images of swine small intestine ex vivo, enabling the visualization of subcellular structures, providing high quality OCT images over more than a 300 μm depth range.

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

NASA Technical Reports Server (NTRS)

Mashiku, Alinda; Garrison, James L.; Carpenter, J. Russell

2012-01-01

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Description of high-power laser radiation in the paraxial approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Milant'ev, V P; Karnilovich, S P; Shaar, Ya N

2015-11-30

We consider the feasibility of an adequate description of a laser pulse of arbitrary shape within the framework of the paraxial approximation. In this approximation, using a parabolic equation and an expansion in the small parameter, expressions are obtained for the field of a sufficiently intense laser radiation given in the form of axially symmetric Hermite – Gaussian beams of arbitrary mode and arbitrary polarisation. It is shown that in the case of sufficiently short pulses, corrections to the transverse components of the laser field are the first-order rather than the secondorder quantities in the expansion in the small parameter.more » The peculiarities of the description of higher-mode Hermite – Gaussian beams are outlined. (light wave transformation)« less

A Distant, X-Ray Luminous Cluster of Galaxies at Redshift 0.83

NASA Technical Reports Server (NTRS)

Donahue, Megan

1999-01-01

We have observed the most distant (= 0.829) cluster of galaxies in the Einstein Extended Medium Sensitivity Survey (EMSS), with the ASCA and ROSAT satellites. We find an X-ray temperature of 12.3(sup 3.1, sub 2.2) keV for this cluster, and the ROSAT map reveals significant substructure. The high temperature of MS1054-0321 is consistent with both its approximate velocity dispersion, based on the redshifts of 12 cluster members we have obtained at the Keck and the Canada-France-Hawaii telescopes, and with its weak lensing signature. The X-ray temperature of this cluster implies a virial mass approximately 7.4 x 10(exp 14) /h solar mass, if the mean matter density in the universe equals the critical value (OMEGA(sub 0) = 1), or larger if OMEGA(sub 0) < 1. Finding such a hot, massive cluster in the EMSS is extremely improbable if clusters grew from Gaussian perturbations in an OMEGA(sub 0) = 1 universe. Combining the assumptions that OMEGA(sub 0) = 1 and that the initial perturbations were Gaussian with the observed X-ray temperature function at low redshift, we show that this probability of this cluster occurring in the volume sampled by the EMSS is less than a few times 10(exp -5). Nor is MS1054-0321 the only hot cluster at high redshift; the only two other z > 0.5 EMSS clusters already observed with ASCA also have temperatures exceeding 8 keV. Assuming again that the initial perturbations were Gaussian and OMEGA(sub 0) = 1, we find that each one is improbable at the < 10(exp -2) level. These observations, along with the fact that these luminosities and temperatures of the high-z clusters all agree with the low-z L(sub x) - T(sub x) relation, argue strongly that OMEGA(sub 0) < 1. Otherwise, the initial perturbations must be non-Gaussian, if these clusters' temperatures do indeed reflect their gravitational potentials.

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

NASA Technical Reports Server (NTRS)

Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet

2015-01-01

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

Near-field spectral shift of a zero-order Bessel beam scattered from a spherical particle

NASA Astrophysics Data System (ADS)

Chen, Feinan; Li, Jia; Belafhal, Abdelmajid; Chafiq, Abdelghani; Sun, Xiaobing

2018-06-01

Within the accuracy of the first-order Born approximation, expressions are derived for the near-zone spectrum of a zero-order Bessel beam scattered from a spherical particle whose correlation function satisfies a Gaussian distribution. The dependence of the spectral shift and spectral switch of the scattered field on the effective size of the scattering potential (ESSP) are determined by numerical simulations. It is shown that the spectral shift of the scattered field does not occur along the longitudinal propagation direction. Furthermore, when the medium’s ESSP is comparable with the central wavelength of the beam, the spectrum of the scattered field loses the Gaussian distribution and exhibits a blue shift as the reference point sufficiently far away from central origin. These results may have prospective applications in guiding tiny particles when the near-zone spectrums of scattered beams are captured and analyzed.

Generation of a hollow dark spherical spot by 4pi focusing of a radially polarized Laguerre-Gaussian beam.

PubMed

Bokor, Nándor; Davidson, Nir

2006-01-15

The properties of the focal spot for 4pi focusing with radially polarized first-order Laguerre-Gaussian beams are calculated. It is shown that a focal spot that has an extremely sharp dark region at the center and an almost-perfect spherical symmetry can be achieved. When such a hollow dark spherical spot is used in 4pi fluorescence depletion microscopy, an axial FWHM spot size of approximately 39 nm and a transverse FWHM spot size of approximately 64 nm can be achieved simultaneously in a practical system.

On the exploration of effect of critical beam power on the propagation of Gaussian laser beam in collisionless magnetized plasma

NASA Astrophysics Data System (ADS)

Urunkar, T. U.; Valkunde, A. T.; Vhanmore, B. D.; Gavade, K. M.; Patil, S. D.; Takale, M. V.

2018-05-01

It is quite known that critical power of the laser plays vital role in the propagation of Gaussian laser beam in collisionless plasma. The nonlinearity in dielectric constant considered herein is due to the ponderomotive force. In the present analysis, the interval of critical beam power has been explored to sustain the competition between diffraction and self-focusing of Gaussian laser beam during propagation in collisionless magnetized plasma. Differential equation for beam-width parameter has been established by using WKB and paraxial approximations under parabolic equation approach. The effect of critical power on the propagation of Gaussian laser beam has been presented graphically and discussed.

Quadriphase DS-CDMA wireless communication systems employing the generalized detector

NASA Astrophysics Data System (ADS)

Tuzlukov, Vyacheslav

2012-05-01

Probability of bit-error Per performance of asynchronous direct-sequence code-division multiple-access (DS-CDMA) wireless communication systems employing the generalized detector (GD) constructed based on the generalized approach to signal processing in noise is analyzed. The effects of pulse shaping, quadriphase or direct sequence quadriphase shift keying (DS-QPSK) spreading, aperiodic spreading sequences are considered in DS-CDMA based on GD and compared with the coherent Neyman-Pearson receiver. An exact Per expression and several approximations: one using the characterristic function method, a simplified expression for the improved Gaussian approximation (IGA) and the simplified improved Gaussian approximation are derived. Under conditions typically satisfied in practice and even with a small number of interferers, the standard Gaussian approximation (SGA) for the multiple-access interference component of the GD statistic and Per performance is shown to be accurate. Moreover, the IGA is shown to reduce to the SGA for pulses with zero excess bandwidth. Second, the GD Per performance of quadriphase DS-CDMA is shown to be superior to that of bi-phase DS-CDMA. Numerical examples by Monte Carlo simulation are presented to illustrate the GD Per performance for square-root raised-cosine pulses and spreading factors of moderate to large values. Also, a superiority of GD employment in CDMA systems over the Neyman-Pearson receiver is demonstrated

Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kawasaki, Masahiro; Yamada, Masaki; ICRR, University of Tokyo, Kashiwa, 277-8582

2014-02-03

I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper,more » we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles.« less

Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kawasaki, Masahiro; Yamada, Masaki, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: yamadam@icrr.u-tokyo.ac.jp

2014-02-01

I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper,more » we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles.« less

A new test statistic for climate models that includes field and spatial dependencies using Gaussian Markov random fields

DOE PAGES

Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel

2016-07-20

A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of fieldmore » and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.« less

Efficient evaluation of the Coulomb force in the Gaussian and finite-element Coulomb method.

PubMed

Kurashige, Yuki; Nakajima, Takahito; Sato, Takeshi; Hirao, Kimihiko

2010-06-28

We propose an efficient method for evaluating the Coulomb force in the Gaussian and finite-element Coulomb (GFC) method, which is a linear-scaling approach for evaluating the Coulomb matrix and energy in large molecular systems. The efficient evaluation of the analytical gradient in the GFC is not straightforward as well as the evaluation of the energy because the SCF procedure with the Coulomb matrix does not give a variational solution for the Coulomb energy. Thus, an efficient approximate method is alternatively proposed, in which the Coulomb potential is expanded in the Gaussian and finite-element auxiliary functions as done in the GFC. To minimize the error in the gradient not just in the energy, the derived functions of the original auxiliary functions of the GFC are used additionally for the evaluation of the Coulomb gradient. In fact, the use of the derived functions significantly improves the accuracy of this approach. Although these additional auxiliary functions enlarge the size of the discretized Poisson equation and thereby increase the computational cost, it maintains the near linear scaling as the GFC and does not affects the overall efficiency of the GFC approach.

A new test statistic for climate models that includes field and spatial dependencies using Gaussian Markov random fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel

A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of fieldmore » and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.« less

Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation

NASA Technical Reports Server (NTRS)

Mcreynolds, S. R.

1975-01-01

A simplified technique is proposed for calculating multidimensional Hermite-Gaussian quadratures that involves taking the square root of a matrix by the Cholesky algorithm rather than computation of the eigenvectors of the matrix. Ways of reducing the dimension, number, and order of the quadratures are set forth. If the function f(x) under the integral sign is not well approximated by a low-order algebraic expression, the order of the quadrature may be reduced by factoring f(x) into an expression that is nearly algebraic and one that is Gaussian.

Approximations to camera sensor noise

NASA Astrophysics Data System (ADS)

Jin, Xiaodan; Hirakawa, Keigo

2013-02-01

Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

Using the thermal Gaussian approximation for the Boltzmann operator in semiclassical initial value time correlation functions.

PubMed

Liu, Jian; Miller, William H

2006-12-14

The thermal Gaussian approximation (TGA) recently developed by Frantsuzov et al. [Chem. Phys. Lett. 381, 117 (2003)] has been demonstrated to be a practical way for approximating the Boltzmann operator exp(-betaH) for multidimensional systems. In this paper the TGA is combined with semiclassical (SC) initial value representations (IVRs) for thermal time correlation functions. Specifically, it is used with the linearized SC-IVR (LSC-IVR, equivalent to the classical Wigner model), and the "forward-backward semiclassical dynamics" approximation developed by Shao and Makri [J. Phys. Chem. A 103, 7753 (1999); 103, 9749 (1999)]. Use of the TGA with both of these approximate SC-IVRs allows the oscillatory part of the IVR to be integrated out explicitly, providing an extremely simple result that is readily applicable to large molecular systems. Calculation of the force-force autocorrelation for a strongly anharmonic oscillator demonstrates its accuracy, and calculation of the velocity autocorrelation function (and thus the diffusion coefficient) of liquid neon demonstrates its applicability.

Speech Enhancement Using Gaussian Scale Mixture Models

PubMed Central

Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J.

2011-01-01

This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress. PMID:21359139

Non-Gaussian quantum states generation and robust quantum non-Gaussianity via squeezing field

NASA Astrophysics Data System (ADS)

Tang, Xu-Bing; Gao, Fang; Wang, Yao-Xiong; Kuang, Sen; Shuang, Feng

2015-03-01

Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaussian operations (namely subtracting and adding a single photon), we propose a scheme to generate non-Gaussian quantum states named single-photon-added and -subtracted coherent (SPASC) superposition states by implementing Bell measurements, and then investigate the corresponding nonclassical features. By squeezed the input field, we demonstrate that robustness of non-Gaussianity can be improved. Controllable phase space distribution offers the possibility to approximately generate a displaced coherent superposition states (DCSS). The fidelity can reach up to F ≥ 0.98 and F ≥ 0.90 for size of amplitude z = 1.53 and 2.36, respectively. Project supported by the National Natural Science Foundation of China (Grant Nos. 61203061 and 61074052), the Outstanding Young Talent Foundation of Anhui Province, China (Grant No. 2012SQRL040), and the Natural Science Foundation of Anhui Province, China (Grant No. KJ2012Z035).

GAUSSIAN BEAM LASER RESONATOR PROGRAM

NASA Technical Reports Server (NTRS)

Cross, P. L.

1994-01-01

In designing a laser cavity, the laser engineer is frequently concerned with more than the stability of the resonator. Other considerations include the size of the beam at various optical surfaces within the resonator or the performance of intracavity line-narrowing or other optical elements. Laser resonators obey the laws of Gaussian beam propagation, not geometric optics. The Gaussian Beam Laser Resonator Program models laser resonators using Gaussian ray trace techniques. It can be used to determine the propagation of radiation through laser resonators. The algorithm used in the Gaussian Beam Resonator program has three major components. First, the ray transfer matrix for the laser resonator must be calculated. Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed. Finally the propagation of the beam through the optical elements is computed. The optical elements can be modeled as parallel plates, lenses, mirrors, dummy surfaces, or Gradient Index (GRIN) lenses. A Gradient Index lens is a good approximation of a laser rod operating under a thermal load. The optical system may contain up to 50 elements. In addition to the internal beam elements the optical system may contain elements external to the resonator. The Gaussian Beam Resonator program was written in Microsoft FORTRAN (Version 4.01). It was developed for the IBM PS/2 80-071 microcomputer and has been implemented on an IBM PC compatible under MS DOS 3.21. The program was developed in 1988 and requires approximately 95K bytes to operate.

Low-complexity approximations to maximum likelihood MPSK modulation classification

NASA Technical Reports Server (NTRS)

Hamkins, Jon

2004-01-01

We present a new approximation to the maximum likelihood classifier to discriminate between M-ary and M'-ary phase-shift-keying transmitted on an additive white Gaussian noise (AWGN) channel and received noncoherentl, partially coherently, or coherently.

Non-Gaussianities in a two-field generalization of natural inflation

NASA Astrophysics Data System (ADS)

Riquelme M., Simon

2018-04-01

We describe a two-field model that generalizes natural inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spontaneously broken, and the radial mode is dynamical. We analyze how the dynamics fundamentally depends on the mass of the radial mode and calculate/estimate the non-Gaussianities arising from such a scenario.

Sensitivity of the halo nuclei-12C elastic scattering at incident nucleon energy 800 MeV to the halo density distribution

NASA Astrophysics Data System (ADS)

Hassan, M. A. M.; Nour El-Din, M. S. M.; Ellithi, A.; Hosny, H.; Salama, T. N. E.

2017-10-01

In the framework of Glauber optical limit approximation where Coulomb effect is taken into account, the elastic scattering differential cross section for halo nuclei with {}^{12}{C} at 800 MeV/N has been calculated. Its sensitivity to the halo densities and the root mean square of the core and halo is the main goal of the current study. The projectile nuclei are taken to be one-neutron and two-neutron halo. The calculations are carried out for Gaussian-Gaussian, Gaussian-Oscillator and Gaussian-2 s phenomenological densities for each considered projectile in the mass number range 6-29. Also included a comparison between the obtained results of phenomenological densities and the results within the microscopic densities LSSM of {}6{He} and {}^{11}{Li} and microscopic densities GCM of {}^{11}{Be} where the density of the target nucleus {}^{12}{C} obtained from electron-{}^{12}{C} scattering is used. The zero range approximation is considered in the calculations. We found that the sensitivity of elastic scattering differential cross section to the halo density is clear if the nucleus appears as two clear different clusters, core and halo.

Improved Discrete Approximation of Laplacian of Gaussian

NASA Technical Reports Server (NTRS)

Shuler, Robert L., Jr.

2004-01-01

An improved method of computing a discrete approximation of the Laplacian of a Gaussian convolution of an image has been devised. The primary advantage of the method is that without substantially degrading the accuracy of the end result, it reduces the amount of information that must be processed and thus reduces the amount of circuitry needed to perform the Laplacian-of- Gaussian (LOG) operation. Some background information is necessary to place the method in context. The method is intended for application to the LOG part of a process of real-time digital filtering of digitized video data that represent brightnesses in pixels in a square array. The particular filtering process of interest is one that converts pixel brightnesses to binary form, thereby reducing the amount of information that must be performed in subsequent correlation processing (e.g., correlations between images in a stereoscopic pair for determining distances or correlations between successive frames of the same image for detecting motions). The Laplacian is often included in the filtering process because it emphasizes edges and textures, while the Gaussian is often included because it smooths out noise that might not be consistent between left and right images or between successive frames of the same image.

Gaussian Process Interpolation for Uncertainty Estimation in Image Registration

PubMed Central

Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William

2014-01-01

Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127

Generating functionals and Gaussian approximations for interruptible delay reactions

NASA Astrophysics Data System (ADS)

Brett, Tobias; Galla, Tobias

2015-10-01

We develop a generating functional description of the dynamics of non-Markovian individual-based systems in which delay reactions can be terminated before completion. This generalizes previous work in which a path-integral approach was applied to dynamics in which delay reactions complete with certainty. We construct a more widely applicable theory, and from it we derive Gaussian approximations of the dynamics, valid in the limit of large, but finite, population sizes. As an application of our theory we study predator-prey models with delay dynamics due to gestation or lag periods to reach the reproductive age. In particular, we focus on the effects of delay on noise-induced cycles.

Cos-Gaussian modal field of a terahertz rectangular metal waveguide filled with multiple slices of dielectric

NASA Astrophysics Data System (ADS)

Wang, Kai; Cao, Qing; Zhang, Huifang; Shen, Pengcheng; Xing, Lujing

2018-06-01

Based on the TE01 mode of a rectangular metal waveguide and the Gaussian mode of a fiber, we propose the cos-Gaussian mode of a terahertz rectangular metal waveguide filled with multiple slices of dielectric. First, we consider a rectangular metal waveguide filled with an ideal graded-index dielectric along one direction. Furthermore, we replace the graded-index dielectric with multiple slices of dielectric according to the effective medium theory. The modal field, the effective index, and the coupling efficiency of this waveguide are investigated. It is found that the approximately linearly polarized electric field is Gaussian along one dimensionality and cosine along the other one. In addition, the low loss and high coupling efficiency with a Gaussian beam can be acquired at 0.9 THz. By optimization, the coupling efficiency could reach 88.5%.

Non-Gaussian statistics of extreme events in stimulated Raman scattering: The role of coherent memory and source noise

NASA Astrophysics Data System (ADS)

Monfared, Yashar E.; Ponomarenko, Sergey A.

2017-10-01

We explore theoretically and numerically extreme event excitation in stimulated Raman scattering in gases. We consider gas-filled hollow-core photonic crystal fibers as a particular system realization. We show that moderate amplitude pump fluctuations obeying Gaussian statistics lead to the emergence of heavy-tailed non-Gaussian statistics as coherent seed Stokes pulses are amplified on propagation along the fiber. We reveal the crucial role that coherent memory effects play in causing non-Gaussian statistics of the system. We discover that extreme events can occur even at the initial stage of stimulated Raman scattering when one can neglect energy depletion of an intense, strongly fluctuating Gaussian pump source. Our analytical results in the undepleted pump approximation explicitly illustrate power-law probability density generation as the input pump noise is transferred to the output Stokes pulses.

Do Solvated Electrons (e(aq)⁻) Reduce DNA Bases? A Gaussian 4 and Density Functional Theory-Molecular Dynamics Study.

PubMed

Kumar, Anil; Adhikary, Amitava; Shamoun, Lance; Sevilla, Michael D

2016-03-10

The solvated electron (e(aq)⁻) is a primary intermediate after an ionization event that produces reductive DNA damage. Accurate standard redox potentials (E(o)) of nucleobases and of e(aq)⁻ determine the extent of reaction of e(aq)⁻ with nucleobases. In this work, E(o) values of e(aq)⁻ and of nucleobases have been calculated employing the accurate ab initio Gaussian 4 theory including the polarizable continuum model (PCM). The Gaussian 4-calculated E(o) of e(aq)⁻ (-2.86 V) is in excellent agreement with the experimental one (-2.87 V). The Gaussian 4-calculated E(o) of nucleobases in dimethylformamide (DMF) lie in the range (-2.36 V to -2.86 V); they are in reasonable agreement with the experimental E(o) in DMF and have a mean unsigned error (MUE) = 0.22 V. However, inclusion of specific water molecules reduces this error significantly (MUE = 0.07). With the use of a model of e(aq)⁻ nucleobase complex with six water molecules, the reaction of e(aq)⁻ with the adjacent nucleobase is investigated using approximate ab initio molecular dynamics (MD) simulations including PCM. Our MD simulations show that e(aq)⁻ transfers to uracil, thymine, cytosine, and adenine, within 10 to 120 fs and e(aq)⁻ reacts with guanine only when a water molecule forms a hydrogen bond to O6 of guanine which stabilizes the anion radical.

Shear and compression buckling analysis for anisotropic panels with centrally located elliptical cutouts

NASA Technical Reports Server (NTRS)

Britt, V. O.

1993-01-01

An approximate analysis for buckling of biaxial- and shear-loaded anisotropic panels with centrally located elliptical cutouts is presented in the present paper. The analysis is composed of two parts, a prebuckling analysis and a buckling analysis. The prebuckling solution is determined using Lekhnitskii's complex variable equations of plane elastostatics combined with a Laurent series approximation and a boundary collocation method. The buckling solution is obtained using the principle of minimum potential energy. A by-product of the minimum potential energy equation is an integral equation which is solved using Gaussian quadrature. Comparisons with documented experimental results and finite element analyses indicate that the approximate analysis accurately predicts the buckling loads of square biaxial- and shear-loaded panels having elliptical cutouts with major axes up to sixty percent of the panel width. Results of a parametric study are presented for shear- and compression-loaded rectangular anisotropic panels with elliptical cutouts. The effects of panel aspect ratio, cutout shape, cutout size, cutout orientation, laminate anisotropy, and combined loading on the buckling load are examined.

Data-Driven Learning of Total and Local Energies in Elemental Boron

NASA Astrophysics Data System (ADS)

Deringer, Volker L.; Pickard, Chris J.; Csányi, Gábor

2018-04-01

The allotropes of boron continue to challenge structural elucidation and solid-state theory. Here we use machine learning combined with random structure searching (RSS) algorithms to systematically construct an interatomic potential for boron. Starting from ensembles of randomized atomic configurations, we use alternating single-point quantum-mechanical energy and force computations, Gaussian approximation potential (GAP) fitting, and GAP-driven RSS to iteratively generate a representation of the element's potential-energy surface. Beyond the total energies of the very different boron allotropes, our model readily provides atom-resolved, local energies and thus deepened insight into the frustrated β -rhombohedral boron structure. Our results open the door for the efficient and automated generation of GAPs, and other machine-learning-based interatomic potentials, and suggest their usefulness as a tool for materials discovery.

Data-Driven Learning of Total and Local Energies in Elemental Boron.

PubMed

Deringer, Volker L; Pickard, Chris J; Csányi, Gábor

2018-04-13

The allotropes of boron continue to challenge structural elucidation and solid-state theory. Here we use machine learning combined with random structure searching (RSS) algorithms to systematically construct an interatomic potential for boron. Starting from ensembles of randomized atomic configurations, we use alternating single-point quantum-mechanical energy and force computations, Gaussian approximation potential (GAP) fitting, and GAP-driven RSS to iteratively generate a representation of the element's potential-energy surface. Beyond the total energies of the very different boron allotropes, our model readily provides atom-resolved, local energies and thus deepened insight into the frustrated β-rhombohedral boron structure. Our results open the door for the efficient and automated generation of GAPs, and other machine-learning-based interatomic potentials, and suggest their usefulness as a tool for materials discovery.

A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation.

PubMed

Huang, Yong; Tao, Gang

2014-09-01

The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.

A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Yong, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn; Tao, Gang, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn

2014-09-01

The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.

Neural pulse frequency modulation of an exponentially correlated Gaussian process

NASA Technical Reports Server (NTRS)

Hutchinson, C. E.; Chon, Y.-T.

1976-01-01

The effect of NPFM (Neural Pulse Frequency Modulation) on a stationary Gaussian input, namely an exponentially correlated Gaussian input, is investigated with special emphasis on the determination of the average number of pulses in unit time, known also as the average frequency of pulse occurrence. For some classes of stationary input processes where the formulation of the appropriate multidimensional Markov diffusion model of the input-plus-NPFM system is possible, the average impulse frequency may be obtained by a generalization of the approach adopted. The results are approximate and numerical, but are in close agreement with Monte Carlo computer simulation results.

On beam models and their paraxial approximation

NASA Astrophysics Data System (ADS)

Waters, W. J.; King, B.

2018-01-01

We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Our vector-potential approach is particularly relevant to calculation of quantum electrodynamical processes in weak laser pulse backgrounds.

Increasing the efficiency and accuracy of time-resolved electronic spectra calculations with on-the-fly ab initio quantum dynamics methods

NASA Astrophysics Data System (ADS)

Vanicek, Jiri

2014-03-01

Rigorous quantum-mechanical calculations of coherent ultrafast electronic spectra remain difficult. I will present several approaches developed in our group that increase the efficiency and accuracy of such calculations: First, we justified the feasibility of evaluating time-resolved spectra of large systems by proving that the number of trajectories needed for convergence of the semiclassical dephasing representation/phase averaging is independent of dimensionality. Recently, we further accelerated this approximation with a cellular scheme employing inverse Weierstrass transform and optimal scaling of the cell size. The accuracy of potential energy surfaces was increased by combining the dephasing representation with accurate on-the-fly ab initio electronic structure calculations, including nonadiabatic and spin-orbit couplings. Finally, the inherent semiclassical approximation was removed in the exact quantum Gaussian dephasing representation, in which semiclassical trajectories are replaced by communicating frozen Gaussian basis functions evolving classically with an average Hamiltonian. Among other examples I will present an on-the-fly ab initio semiclassical dynamics calculation of the dispersed time-resolved stimulated emission spectrum of the 54-dimensional azulene. This research was supported by EPFL and by the Swiss National Science Foundation NCCR MUST (Molecular Ultrafast Science and Technology) and Grant No. 200021124936/1.

Pleiotropic Stabilizing Selection Limits the Number of Polymorphic Loci to at Most the Number of Characters

PubMed Central

Hastings, A.; Hom, C. L.

1989-01-01

We demonstrate that, in a model incorporating weak Gaussian stabilizing selection on n additively determined characters, at most n loci are polymorphic at a stable equilibrium. The number of characters is defined to be the number of independent components in the Gaussian selection scheme. We also assume linkage equilibrium, and that either the number of loci is large enough that the phenotypic distribution in the population can be approximated as multivariate Gaussian or that selection is weak enough that the mean fitness of the population can be approximated using only the mean and the variance of the characters in the population. Our results appear to rule out antagonistic pleiotropy without epistasis as a major force in maintaining additive genetic variation in a uniform environment. However, they are consistent with the maintenance of variability by genotype-environment interaction if a trait in different environments corresponds to different characters and the number of different environments exceeds the number of polymorphic loci that affect the trait. PMID:2767424

Improved key-rate bounds for practical decoy-state quantum-key-distribution systems

NASA Astrophysics Data System (ADS)

Zhang, Zhen; Zhao, Qi; Razavi, Mohsen; Ma, Xiongfeng

2017-01-01

The decoy-state scheme is the most widely implemented quantum-key-distribution protocol in practice. In order to account for the finite-size key effects on the achievable secret key generation rate, a rigorous statistical fluctuation analysis is required. Originally, a heuristic Gaussian-approximation technique was used for this purpose, which, despite its analytical convenience, was not sufficiently rigorous. The fluctuation analysis has recently been made rigorous by using the Chernoff bound. There is a considerable gap, however, between the key-rate bounds obtained from these techniques and that obtained from the Gaussian assumption. Here we develop a tighter bound for the decoy-state method, which yields a smaller failure probability. This improvement results in a higher key rate and increases the maximum distance over which secure key exchange is possible. By optimizing the system parameters, our simulation results show that our method almost closes the gap between the two previously proposed techniques and achieves a performance similar to that of conventional Gaussian approximations.

Cosmological perturbation theory and the spherical collapse model - II. Non-Gaussian initial conditions

NASA Astrophysics Data System (ADS)

Gaztanaga, Enrique; Fosalba, Pablo

1998-12-01

In Paper I of this series, we introduced the spherical collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants xi_J of density fluctuations in cosmological perturbation theory (PT). Within this approximation, the dynamics is decoupled from the statistics of the initial conditions, so we are able to present here the cumulants for generic non-Gaussian initial conditions, which can be estimated to arbitrary order including the smoothing effects. The SC model turns out to recover the exact leading-order non-linear contributions up to terms involving non-local integrals of the J-point functions. We argue that for the hierarchical ratios S_J, these non-local terms are subdominant and tend to compensate each other. The resulting predictions show a non-trivial time evolution that can be used to discriminate between models of structure formation. We compare these analytic results with non-Gaussian N-body simulations, which turn out to be in very good agreement up to scales where sigma<~1.

Topology of large-scale structure in seeded hot dark matter models

NASA Technical Reports Server (NTRS)

Beaky, Matthew M.; Scherrer, Robert J.; Villumsen, Jens V.

1992-01-01

The topology of the isodensity surfaces in seeded hot dark matter models, in which static seed masses provide the density perturbations in a universe dominated by massive neutrinos is examined. When smoothed with a Gaussian window, the linear initial conditions in these models show no trace of non-Gaussian behavior for r0 equal to or greater than 5 Mpc (h = 1/2), except for very low seed densities, which show a shift toward isolated peaks. An approximate analytic expression is given for the genus curve expected in linear density fields from randomly distributed seed masses. The evolved models have a Gaussian topology for r0 = 10 Mpc, but show a shift toward a cellular topology with r0 = 5 Mpc; Gaussian models with an identical power spectrum show the same behavior.

Renyi entropy measures of heart rate Gaussianity.

PubMed

Lake, Douglas E

2006-01-01

Sample entropy and approximate entropy are measures that have been successfully utilized to study the deterministic dynamics of heart rate (HR). A complementary stochastic point of view and a heuristic argument using the Central Limit Theorem suggests that the Gaussianity of HR is a complementary measure of the physiological complexity of the underlying signal transduction processes. Renyi entropy (or q-entropy) is a widely used measure of Gaussianity in many applications. Particularly important members of this family are differential (or Shannon) entropy (q = 1) and quadratic entropy (q = 2). We introduce the concepts of differential and conditional Renyi entropy rate and, in conjunction with Burg's theorem, develop a measure of the Gaussianity of a linear random process. Robust algorithms for estimating these quantities are presented along with estimates of their standard errors.

NON-GAUSSIANITIES IN THE LOCAL CURVATURE OF THE FIVE-YEAR WMAP DATA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rudjord, Oeystein; Groeneboom, Nicolaas E.; Hansen, Frode K.

Using the five-year WMAP data, we re-investigate claims of non-Gaussianities and asymmetries detected in local curvature statistics of the one-year WMAP data. In Hansen et al., it was found that the northern ecliptic hemisphere was non-Gaussian at the {approx}1% level testing the densities of hill, lake, and saddle points based on the second derivatives of the cosmic microwave background temperature map. The five-year WMAP data have a much lower noise level and better control of systematics. Using these, we find that the anomalies are still present at a consistent level. Also the direction of maximum non-Gaussianity remains. Due to limitedmore » availability of computer resources, Hansen et al. were unable to calculate the full covariance matrix for the {chi}{sup 2}-test used. Here, we apply the full covariance matrix instead of the diagonal approximation and find that the non-Gaussianities disappear and there is no preferred non-Gaussian direction. We compare with simulations of weak lensing to see if this may cause the observed non-Gaussianity when using a diagonal covariance matrix. We conclude that weak lensing does not produce non-Gaussianity in the local curvature statistics at the scales investigated in this paper. The cause of the non-Gaussian detection in the case of a diagonal matrix remains unclear.« less

Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.

PubMed

Lukin, Igor P

2016-04-20

The orbital angular momentum of vortex Bessel-Gaussian beams propagating in turbulent atmosphere is studied theoretically. The field of an optical beam is determined through the solution of the paraxial wave equation for a randomly inhomogeneous medium with fluctuations of the refraction index of the turbulent atmosphere. Peculiarities in the behavior of the total power of the vortex Bessel-Gaussian beam at the receiver (or transmitter) are examined. The dependence of the total power of the vortex Bessel-Gaussian beam on optical beam parameters, namely, the transverse wave number of optical radiation, amplitude factor radius, and, especially, topological charge of the optical beam, is analyzed in detail. It turns out that the mean value of the orbital angular momentum of the vortex Bessel-Gaussian beam remains constant during propagation in the turbulent atmosphere. It is shown that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam propagating in turbulent atmosphere calculated with the "mean-intensity" approximation is equal to zero identically. Thus, it is possible to declare confidently that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam in turbulent atmosphere is not very large.

The Gaussian CL s method for searches of new physics

DOE PAGES

Qian, X.; Tan, A.; Ling, J. J.; ...

2016-04-23

Here we describe a method based on the CL s approach to present results in searches of new physics, under the condition that the relevant parameter space is continuous. Our method relies on a class of test statistics developed for non-nested hypotheses testing problems, denoted by ΔT, which has a Gaussian approximation to its parent distribution when the sample size is large. This leads to a simple procedure of forming exclusion sets for the parameters of interest, which we call the Gaussian CL s method. Our work provides a self-contained mathematical proof for the Gaussian CL s method, that explicitlymore » outlines the required conditions. These conditions are milder than that required by the Wilks' theorem to set confidence intervals (CIs). We illustrate the Gaussian CL s method in an example of searching for a sterile neutrino, where the CL s approach was rarely used before. We also compare data analysis results produced by the Gaussian CL s method and various CI methods to showcase their differences.« less

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

NASA Astrophysics Data System (ADS)

Regnier, D.; Verrière, M.; Dubray, N.; Schunck, N.

2016-03-01

We describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in N-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank-Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.

Light Scattering by Gaussian Particles: A Solution with Finite-Difference Time Domain Technique

NASA Technical Reports Server (NTRS)

Sun, W.; Nousiainen, T.; Fu, Q.; Loeb, N. G.; Videen, G.; Muinonen, K.

2003-01-01

The understanding of single-scattering properties of complex ice crystals has significance in atmospheric radiative transfer and remote-sensing applications. In this work, light scattering by irregularly shaped Gaussian ice crystals is studied with the finite-difference time-domain (FDTD) technique. For given sample particle shapes and size parameters in the resonance region, the scattering phase matrices and asymmetry factors are calculated. It is found that the deformation of the particle surface can significantly smooth the scattering phase functions and slightly reduce the asymmetry factors. The polarization properties of irregular ice crystals are also significantly different from those of spherical cloud particles. These FDTD results could provide a reference for approximate light-scattering models developed for irregular particle shapes and can have potential applications in developing a much simpler practical light scattering model for ice clouds angular-distribution models and for remote sensing of ice clouds and aerosols using polarized light. (copyright) 2003 Elsevier Science Ltd. All rights reserved.

Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams.

PubMed

Dennis, Mark R; Ring, James D

2013-09-01

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wave packets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator that interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation.

Time-Harmonic Gaussian Beams: Exact Solutions of the Helmhotz Equation in Free Space

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2017-12-01

An exact solution of the Helmholtz equation u xx + u yy + u zz + k 2 u = 0 is presented, which describes propagation of monochromatic waves in the free space. The solution has the form of a superposition of plane waves with a specific weight function dependent on a certain free parameter a. If ka→∞, the solution is localized in the Gaussian manner in a vicinity of a certain straight line and asymptotically coincides with the famous approximate solution known as the fundamental mode of a paraxial Gaussian beam. The asymptotics of the aforementioned exact solution does not include a backward wave.

Gaussian theory for spatially distributed self-propelled particles

NASA Astrophysics Data System (ADS)

Seyed-Allaei, Hamid; Schimansky-Geier, Lutz; Ejtehadi, Mohammad Reza

2016-12-01

Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model, we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatiotemporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.

An adaptive Gaussian process-based method for efficient Bayesian experimental design in groundwater contaminant source identification problems: ADAPTIVE GAUSSIAN PROCESS-BASED INVERSION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Jiangjiang; Li, Weixuan; Zeng, Lingzao

Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU-demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimations of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two-stage manner. Since the two-stage MCMC requires extra original model evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate approximation of the original model can be adaptively constructed with low computational cost. Based on this idea, we propose amore » Gaussian process (GP) surrogate-based Bayesian experimental design and parameter estimation approach for groundwater contaminant source identification problems. A major advantage of the GP surrogate is that it provides a convenient estimation of the approximation error, which can be incorporated in the Bayesian formula to avoid over-confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed-up compared to our previous work using two-stage MCMC.« less

The propagation of ion-acoustic waves carrying orbital angular momentum in the electron-positron-ion plasmas

NASA Astrophysics Data System (ADS)

Mehdian, H.; Nobahar, D.; Hajisharifi, K.

2018-02-01

Ion-acoustic (IA) waves carrying orbital angular momentum (OAM) are investigated in an unmagnetized, uniform, and collisionless electron-positron-ion (e-p-i) plasma system. Employing the hydrodynamic theory, the paraxial equation in term of ion perturbed number density is derived and discussed about its Laguerre-Gaussian (LG) beam solutions. Obtaining an approximate solution for the electrostatic potential, the IA wave characteristics including helical electric field structure, energy density, and OAM density are theoretically studied. Based on the numerical analysis, the effects of positron concentration, radial and angular mode number as well as beam waist on the obtained potential profile are investigated. It is shown that the depth (height) and width of the LG potential profile wells (barriers) are considerably modify by the variation of positron concentration.

Transfer potentials shape and equilibrate monetary systems

NASA Astrophysics Data System (ADS)

Fischer, Robert; Braun, Dieter

2003-04-01

We analyze a monetary system of random money transfer on the basis of double entry bookkeeping. Without boundary conditions, we do not reach a price equilibrium and violate text-book formulas of economist's quantity theory ( MV= PQ). To match the resulting quantity of money with the model assumption of a constant price, we have to impose boundary conditions. They either restrict specific transfers globally or impose transfers locally. Both connect through a general framework of transfer potentials. We show that either restricted or imposed transfers can shape Gaussian, tent-shape exponential, Boltzmann-exponential, pareto or periodic equilibrium distributions. We derive the master equation and find its general time-dependent approximate solution. An equivalent of quantity theory for random money transfer under the boundary conditions of transfer potentials is given.

A Separable Insertion Method to Calculate Atomic and Molecular Resonances on a FE-DVR Grid using Exterior Complex Scaling

NASA Astrophysics Data System (ADS)

Abeln, Brant Anthony

The study of metastable electronic resonances, anion or neutral states of finite lifetime, in molecules is an important area of research where currently no theoretical technique is generally applicable. The role of theory is to calculate both the position and width, which is proportional to the inverse of the lifetime, of these resonances and how they vary with respect to nuclear geometry in order to generate potential energy surfaces. These surfaces are the basis of time-dependent models of the molecular dynamics where the system moves towards vibrational excitation or fragmentation. Three fundamental electronic processes that can be modeled this way are dissociative electronic attachment, vibrational excitation through electronic impact and autoionization. Currently, experimental investigation into these processes is being preformed on polyatomic molecules while theoreticians continue their fifty-year-old search for robust methods to calculate them. The separable insertion method, investigated in this thesis, seeks to tackle the problem of calculating metastable resonances by using existing quantum chemistry tools along with a grid-based method employing exterior complex scaling (ECS). Modern quantum chemistry methods are extremely efficient at calculating ground and (bound) excited electronic states of atoms and molecules by utilizing Gaussian basis functions. These functions provide both a numerically fast and analytic solution to the necessary two-electron, six-dimensional integrals required in structure calculations. However, these computer programs, based on analytic Gaussian basis sets, cannot construct solutions that are not square-integrable, such as resonance wavefunctions. ECS, on the other hand, can formally calculate resonance solutions by rotating the asymptotic electronic coordinates into the complex plane. The complex Siegert energies for resonances, Eres = ER - iGamma/2 where ER is the real-valued position of the resonance and Gamma is the width of the resonance, can be found directly as an isolated pole in the complex energy plane. Unlike the straight complex scaling, ECS on the electronic coordinates overcomes the non-analytic behavior of the nuclear attraction potential, as a function of complex [special characters omitted] where the sum is over each nucleus in a molecular system. Discouragingly, the Gaussian basis functions, which are computationally well-suited for bound electronic structure, fail at forming an effective basis set for ECS due to the derivative discontinuity generated by the complex coordinate rotation and the piecewise defined contour. This thesis seeks to explore methods for implementing ECS indirectly without losing the numerical simplicity and power of Gaussian basis sets. The separable insertion method takes advantage of existing software by constructing a N2-term separable potential of the target system using Gaussian functions to be inserted into a finite-element discrete variable representation (FE-DVR) grid that implements ECS. This work reports an exhaustive investigation into this approach for calculating resonances. This thesis shows that this technique is successful at describing an anion shape resonance of a closed-shell atom or molecule in the static-exchange approximation. This method is applied to the 2P Be-, 2pig N2- and 2pi u CO2- shape resonances to calculate their complex Seigert energies. Additionally, many details on the exact construction of the separable potential and of the expansion basis are explored. The future work considers methods for faster convergence of the resonance energy, moving beyond the static-exchange approximation and applying this technique to polyatomic systems of interest.

Dispersion in Rectangular Networks: Effective Diffusivity and Large-Deviation Rate Function

NASA Astrophysics Data System (ADS)

Tzella, Alexandra; Vanneste, Jacques

2016-09-01

The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply, and urban pollution. Motivated by this, we develop a large-deviation theory that predicts the evolution of the concentration of a scalar released in a rectangular network in the limit of large time t ≫1 . This theory provides an approximation for the concentration that remains valid for large distances from the center of mass, specifically for distances up to O (t ) and thus much beyond the O (t1 /2) range where a standard Gaussian approximation holds. A byproduct of the approach is a closed-form expression for the effective diffusivity tensor that governs this Gaussian approximation. Monte Carlo simulations of Brownian particles confirm the large-deviation results and demonstrate their effectiveness in describing the scalar distribution when t is only moderately large.

Extinction time of a stochastic predator-prey model by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao

2018-03-01

The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.

Evaluation and validity of a LORETA normative EEG database.

PubMed

Thatcher, R W; North, D; Biver, C

2005-04-01

To evaluate the reliability and validity of a Z-score normative EEG database for Low Resolution Electromagnetic Tomography (LORETA), EEG digital samples (2 second intervals sampled 128 Hz, 1 to 2 minutes eyes closed) were acquired from 106 normal subjects, and the cross-spectrum was computed and multiplied by the Key Institute's LORETA 2,394 gray matter pixel T Matrix. After a log10 transform or a Box-Cox transform the mean and standard deviation of the *.lor files were computed for each of the 2394 gray matter pixels, from 1 to 30 Hz, for each of the subjects. Tests of Gaussianity were computed in order to best approximate a normal distribution for each frequency and gray matter pixel. The relative sensitivity of a Z-score database was computed by measuring the approximation to a Gaussian distribution. The validity of the LORETA normative database was evaluated by the degree to which confirmed brain pathologies were localized using the LORETA normative database. Log10 and Box-Cox transforms approximated Gaussian distribution in the range of 95.64% to 99.75% accuracy. The percentage of normative Z-score values at 2 standard deviations ranged from 1.21% to 3.54%, and the percentage of Z-scores at 3 standard deviations ranged from 0% to 0.83%. Left temporal lobe epilepsy, right sensory motor hematoma and a right hemisphere stroke exhibited maximum Z-score deviations in the same locations as the pathologies. We conclude: (1) Adequate approximation to a Gaussian distribution can be achieved using LORETA by using a log10 transform or a Box-Cox transform and parametric statistics, (2) a Z-Score normative database is valid with adequate sensitivity when using LORETA, and (3) the Z-score LORETA normative database also consistently localized known pathologies to the expected Brodmann areas as an hypothesis test based on the surface EEG before computing LORETA.

Scalar Dissipation Modeling for Passive and Active Scalars: a priori Study Using Direct Numerical Simulation

NASA Technical Reports Server (NTRS)

Selle, L. C.; Bellan, Josette

2006-01-01

Transitional databases from Direct Numerical Simulation (DNS) of three-dimensional mixing layers for single-phase flows and two-phase flows with evaporation are analyzed and used to examine the typical hypothesis that the scalar dissipation Probability Distribution Function (PDF) may be modeled as a Gaussian. The databases encompass a single-component fuel and four multicomponent fuels, two initial Reynolds numbers (Re), two mass loadings for two-phase flows and two free-stream gas temperatures. Using the DNS calculated moments of the scalar-dissipation PDF, it is shown, consistent with existing experimental information on single-phase flows, that the Gaussian is a modest approximation of the DNS-extracted PDF, particularly poor in the range of the high scalar-dissipation values, which are significant for turbulent reaction rate modeling in non-premixed flows using flamelet models. With the same DNS calculated moments of the scalar-dissipation PDF and making a change of variables, a model of this PDF is proposed in the form of the (beta)-PDF which is shown to approximate much better the DNS-extracted PDF, particularly in the regime of the high scalar-dissipation values. Several types of statistical measures are calculated over the ensemble of the fourteen databases. For each statistical measure, the proposed (beta)-PDF model is shown to be much superior to the Gaussian in approximating the DNS-extracted PDF. Additionally, the agreement between the DNS-extracted PDF and the (beta)-PDF even improves when the comparison is performed for higher initial Re layers, whereas the comparison with the Gaussian is independent of the initial Re values. For two-phase flows, the comparison between the DNS-extracted PDF and the (beta)-PDF also improves with increasing free-stream gas temperature and mass loading. The higher fidelity approximation of the DNS-extracted PDF by the (beta)-PDF with increasing Re, gas temperature and mass loading bodes well for turbulent reaction rate modeling.

On the distribution of a product of N Gaussian random variables

NASA Astrophysics Data System (ADS)

Stojanac, Željka; Suess, Daniel; Kliesch, Martin

2017-08-01

The product of Gaussian random variables appears naturally in many applications in probability theory and statistics. It has been known that the distribution of a product of N such variables can be expressed in terms of a Meijer G-function. Here, we compute a similar representation for the corresponding cumulative distribution function (CDF) and provide a power-log series expansion of the CDF based on the theory of the more general Fox H-functions. Numerical computations show that for small values of the argument the CDF of products of Gaussians is well approximated by the lowest orders of this expansion. Analogous results are also shown for the absolute value as well as the square of such products of N Gaussian random variables. For the latter two settings, we also compute the moment generating functions in terms of Meijer G-functions.

Effect of exponential density transition on self-focusing of q-Gaussian laser beam in collisionless plasma

NASA Astrophysics Data System (ADS)

Valkunde, Amol T.; Vhanmore, Bandopant D.; Urunkar, Trupti U.; Gavade, Kusum M.; Patil, Sandip D.; Takale, Mansing V.

2018-05-01

In this work, nonlinear aspects of a high intensity q-Gaussian laser beam propagating in collisionless plasma having upward density ramp of exponential profiles is studied. We have employed the nonlinearity in dielectric function of plasma by considering ponderomotive nonlinearity. The differential equation governing the dimensionless beam width parameter is achieved by using Wentzel-Kramers-Brillouin (WKB) and paraxial approximations and solved it numerically by using Runge-Kutta fourth order method. Effect of exponential density ramp profile on self-focusing of q-Gaussian laser beam for various values of q is systematically carried out and compared with results Gaussian laser beam propagating in collisionless plasma having uniform density. It is found that exponential plasma density ramp causes the laser beam to become more focused and gives reasonably interesting results.

Novel density functional methodology for the computation of accurate electronic and thermodynamic properties of molecular systems and improved long-range behavior

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kafafi, S.A.

1998-12-10

A novel general purpose density functional methodology for the computation of accurate electronic and thermodynamic properties of molecules and improved long-range behavior is reported. Assuming the separability of the exchange (E{sub x}) and correlation (E{sub c}) contributions to the total exchange-correlation energy functional (E{sub xc}), the E{sub x} term consists of a hybrid mixture of 37.5% Hartree-Fock exchange and the appropriate local spin density exchange using the adiabatic connection formula. He demonstrated that E{sub x} and its corresponding potential V{sub x} [=dE{sub x}/d{rho}(r)] have the proper asymptotic limits at r = 0 and r {r_arrow} {infinity}, E{sub c} consists ofmore » the Vosko, Wilk, and Nusair formula for the free-electron gas correlation energy and a generalized gradient approximation term with one adjustable parameter. V{sub c} [=dE{sub c}/d{rho}(r)] was shown to obey the r {r_arrow} {infinity} limit of the corresponding potential derived from exact atomic exchange-correlation computations; namely, V{sub c} is proportional to r{sup {minus}4}. Most importantly, he demonstrated that, at r values where dispersion forces are operating, V{sub c} is proportional to 1/r{sup n} (n = 4, 6, 8, {hor_ellipsis}). The reported method was denoted by K2-BVWN because it used two adjustable parameters in its formulation. The K2-BVWN scheme scales as N{sup 3}, where N is the number of basis functions, compared to {approximately}N{sup 7} for Gaussian-2 (G2) ab initio theory and related methods, {approximately}N{sup 5} for Barone`s mPW1,3PW, and {approximately}N{sup 4} for Becke`s three-parameter density functional approaches. The G2 data set complemented by the reported molecular systems investigated in this work was recommended as a critical test for evaluating novel ab initio and density functional methodologies. The K2-BVWN method has been implemented in the Gaussian series of programs.« less

Approximate bandpass and frequency response models of the difference of Gaussian filter

NASA Astrophysics Data System (ADS)

Birch, Philip; Mitra, Bhargav; Bangalore, Nagachetan M.; Rehman, Saad; Young, Rupert; Chatwin, Chris

2010-12-01

The Difference of Gaussian (DOG) filter is widely used in optics and image processing as, among other things, an edge detection and correlation filter. It has important biological applications and appears to be part of the mammalian vision system. In this paper we analyse the filter and provide details of the full width half maximum, bandwidth and frequency response in order to aid the full characterisation of its performance.

Non-Gaussian noise-weakened stability in a foraging colony system with time delay

NASA Astrophysics Data System (ADS)

Dong, Xiaohui; Zeng, Chunhua; Yang, Fengzao; Guan, Lin; Xie, Qingshuang; Duan, Weilong

2018-02-01

In this paper, the dynamical properties in a foraging colony system with time delay and non-Gaussian noise were investigated. Using delay Fokker-Planck approach, the stationary probability distribution (SPD), the associated relaxation time (ART) and normalization correlation function (NCF) are obtained, respectively. The results show that: (i) the time delay and non-Gaussian noise can induce transition from a single peak to double peaks in the SPD, i.e., a type of bistability occurring in a foraging colony system where time delay and non-Gaussian noise not only cause transitions between stable states, but also construct the states themselves. Numerical simulations are presented and are in good agreement with the approximate theoretical results; (ii) there exists a maximum in the ART as a function of the noise intensity, this maximum for ART is identified as the characteristic of the non-Gaussian noise-weakened stability of the foraging colonies in the steady state; (iii) the ART as a function of the noise correlation time exhibits a maximum and a minimum, where the minimum for ART is identified as the signature of the non-Gaussian noise-enhanced stability of the foraging colonies; and (iv) the time delay can enhance the stability of the foraging colonies in the steady state, while the departure from Gaussian noise can weaken it, namely, the time delay and departure from Gaussian noise play opposite roles in ART or NCF.

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

DOE PAGES

Regnier, D.; Verriere, M.; Dubray, N.; ...

2015-11-30

In this study, we describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in NN-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank–Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle amore » realistic calculation of fission dynamics.« less

Generation of dark hollow beams by using a fractional radial Hilbert transform system

NASA Astrophysics Data System (ADS)

Xie, Qiansen; Zhao, Daomu

2007-07-01

The radial Hilbert transform has been extend to the fractional field, which could be called the fractional radial Hilbert transform (FRHT). Using edge-enhancement characteristics of this transform, we convert a Gaussian light beam into a variety of dark hollow beams (DHBs). Based on the fact that a hard-edged aperture can be expanded approximately as a finite sum of complex Gaussian functions, the analytical expression of a Gaussian beam passing through a FRHT system has been derived. As a numerical example, the properties of the DHBs with different fractional orders are illustrated graphically. The calculation results obtained by use of the analytical method and the integral method are also compared.

Analysis of low altitude atmospheric turbulence data measured in flight

NASA Technical Reports Server (NTRS)

Ganzer, V. M.; Joppa, R. G.; Vanderwees, G.

1977-01-01

All three components of turbulence were measured simultaneously in flight at each wing tip of a Beech D-18 aircraft. The flights were conducted at low altitude, 30.5 - 61.0 meters (100-200 ft.), over water in the presence of wind driven turbulence. Statistical properties of flight measured turbulence were compared with Gaussian and non-Gaussian turbulence models. Spatial characteristics of the turbulence were analyzed using the data from flight perpendicular and parallel to the wind. The probability density distributions of the vertical gusts show distinctly non-Gaussian characteristics. The distributions of the longitudinal and lateral gusts are generally Gaussian. The power spectra compare in the inertial subrange at some points better with the Dryden spectrum, while at other points the von Karman spectrum is a better approximation. In the low frequency range the data show peaks or dips in the power spectral density. The cross between vertical gusts in the direction of the mean wind were compared with a matched non-Gaussian model. The real component of the cross spectrum is in general close to the non-Gaussian model. The imaginary component, however, indicated a larger phase shift between these two gust components than was found in previous research.

CMB-lensing beyond the Born approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marozzi, Giovanni; Fanizza, Giuseppe; 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 ∼< 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-Gaussianmore » 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.« less

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Generation of dark hollow beam by focusing a sine-Gaussian beam using a cylindrical lens and a focusing lens

NASA Astrophysics Data System (ADS)

Tang, Huiqin; Zhu, Kaicheng

2013-12-01

Based on the generalized Huygens-Fresnel diffraction integral, a closed-form propagation equation related to sine-Gaussian beams through a cylindrical lens and a focusing lens is derived and illustrated with numerical methods. It is found that a sine-Gaussian beam through such a system may be converted into a dark hollow beam (DHB) with topological charge index one and its bright enclosure is approximately an elongated ellipse with very high ellipticity. Moreover, the parameter values at which the DHBs have perfect intensity patterns are designed. The optimal relative orientation between the dislocation line of the input sine-Gaussian beam and the axial orientation of the cylindrical lens is specified. And the ellipticity of the elliptical DHBs is mainly defined by the focal length of the cylindrical lens and the Fresnel number of the optical system.

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

A note on: "A Gaussian-product stochastic Gent-McWilliams parameterization"

NASA Astrophysics Data System (ADS)

Jansen, Malte F.

2017-02-01

This note builds on a recent article by Grooms (2016), which introduces a new stochastic parameterization for eddy buoyancy fluxes. The closure proposed by Grooms accounts for the fact that eddy fluxes arise as the product of two approximately Gaussian variables, which in turn leads to a distinctly non-Gaussian distribution. The directionality of the stochastic eddy fluxes, however, remains somewhat ad-hoc and depends on the reference frame of the chosen coordinate system. This note presents a modification of the approach proposed by Grooms, which eliminates this shortcoming. Eddy fluxes are computed based on a stochastic mixing length model, which leads to a frame invariant formulation. As in the original closure proposed by Grooms, eddy fluxes are proportional to the product of two Gaussian variables, and the parameterization reduces to the Gent and McWilliams parameterization for the mean buyoancy fluxes.

Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam

NASA Astrophysics Data System (ADS)

Romero, J.; Giovannini, D.; McLaren, M. G.; Galvez, E. J.; Forbes, A.; Padgett, M. J.

2012-08-01

We report orbital angular momentum (OAM) and angle correlations between signal and idler photons observed when the nonlinear crystal used in spontaneous parametric down-conversion is illuminated by a non-fundamental Gaussian pump beam. We introduce a π-phase step to the transverse profile of the pump, before it impinges on the crystal to create a phase-flipped Gaussian mode, which is a close approximation to an HG10 Hermite-Gaussian-like beam. The correlations in OAM and angular position are then measured holographically using two separate spatial light modulators in the signal and idler arms. We show the transfer of the OAM spectrum of the pump to the down-converted fields, manifested as a redistribution in the OAM correlations consistent with OAM conservation. This corresponds to a modulation of the angular position correlations consistent with the Fourier relationship between the OAM and angle.

Novel transform for image description and compression with implementation by neural architectures

NASA Astrophysics Data System (ADS)

Ben-Arie, Jezekiel; Rao, Raghunath K.

1991-10-01

A general method for signal representation using nonorthogonal basis functions that are composed of Gaussians are described. The Gaussians can be combined into groups with predetermined configuration that can approximate any desired basis function. The same configuration at different scales forms a set of self-similar wavelets. The general scheme is demonstrated by representing a natural signal employing an arbitrary basis function. The basic methodology is demonstrated by two novel schemes for efficient representation of 1-D and 2- D signals using Gaussian basis functions (BFs). Special methods are required here since the Gaussian functions are nonorthogonal. The first method employs a paradigm of maximum energy reduction interlaced with the A* heuristic search. The second method uses an adaptive lattice system to find the minimum-squared error of the BFs onto the signal, and a lateral-vertical suppression network to select the most efficient representation in terms of data compression.

GAUSSIAN 76: An ab initio Molecular Orbital Program

DOE R&D Accomplishments Database

Binkley, J. S.; Whiteside, R.; Hariharan, P. C.; Seeger, R.; Hehre, W. J.; Lathan, W. A.; Newton, M. D.; Ditchfield, R.; Pople, J. A.

1978-01-01

Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type Gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally for easy use. Closed shell (RHF) or unrestricted open shell (UHF) wave functions can be obtained. Facilities are provided for geometry optimization to potential minima and for limited potential surface scans.

Gaussian closure technique applied to the hysteretic Bouc model with non-zero mean white noise excitation

NASA Astrophysics Data System (ADS)

Waubke, Holger; Kasess, Christian H.

2016-11-01

Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

Ergodicity of the Stochastic Nosé-Hoover Heat Bath

NASA Astrophysics Data System (ADS)

Wei Chung Lo,; Baowen Li,

2010-07-01

We numerically study the ergodicity of the stochastic Nosé-Hoover heat bath whose formalism is based on the Markovian approximation for the Nosé-Hoover equation [J. Phys. Soc. Jpn. 77 (2008) 103001]. The approximation leads to a Langevin-like equation driven by a fluctuating dissipative force and multiplicative Gaussian white noise. The steady state solution of the associated Fokker-Planck equation is the canonical distribution. We investigate the dynamics of this method for the case of (i) free particle, (ii) nonlinear oscillators and (iii) lattice chains. We derive the Fokker-Planck equation for the free particle and present approximate analytical solution for the stationary distribution in the context of the Markovian approximation. Numerical simulation results for nonlinear oscillators show that this method results in a Gaussian distribution for the particles velocity. We also employ the method as heat baths to study nonequilibrium heat flow in one-dimensional Fermi-Pasta-Ulam (FPU-β) and Frenkel-Kontorova (FK) lattices. The establishment of well-defined temperature profiles are observed only when the lattice size is large. Our results provide numerical justification for such Markovian approximation for classical single- and many-body systems.

Gaussian white noise as a resource for work extraction.

PubMed

Dechant, Andreas; Baule, Adrian; Sasa, Shin-Ichi

2017-03-01

We show that uncorrelated Gaussian noise can drive a system out of equilibrium and can serve as a resource from which work can be extracted. We consider an overdamped particle in a periodic potential with an internal degree of freedom and a state-dependent friction, coupled to an equilibrium bath. Applying additional Gaussian white noise drives the system into a nonequilibrium steady state and causes a finite current if the potential is spatially asymmetric. The model thus operates as a Brownian ratchet, whose current we calculate explicitly in three complementary limits. Since the particle current is driven solely by additive Gaussian white noise, this shows that the latter can potentially perform work against an external load. By comparing the extracted power to the energy injection due to the noise, we discuss the efficiency of such a ratchet.

Acoustical tweezers using single spherically focused piston, X-cut, and Gaussian beams.

PubMed

Mitri, Farid G

2015-10-01

Partial-wave series expansions (PWSEs) satisfying the Helmholtz equation in spherical coordinates are derived for circular spherically focused piston (i.e., apodized by a uniform velocity amplitude normal to its surface), X-cut (i.e., apodized by a velocity amplitude parallel to the axis of wave propagation), and Gaussian (i.e., apodized by a Gaussian distribution of the velocity amplitude) beams. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSEs assuming weakly focused beams (with focusing angle α ⩽ 20°) in the Fresnel-Kirchhoff (parabolic) approximation. In contrast with previous analytical models, the derived expressions allow computing the scattering and acoustic radiation force from a sphere of radius a without restriction to either the Rayleigh (a ≪ λ, where λ is the wavelength of the incident radiation) or the ray acoustics (a ≫λ) regimes. The analytical formulations are valid for wavelengths largely exceeding the radius of the focused acoustic radiator, when the viscosity of the surrounding fluid can be neglected, and when the sphere is translated along the axis of wave propagation. Computational results illustrate the analysis with particular emphasis on the sphere's elastic properties and the axial distance to the center of the concave surface, with close connection of the emergence of negative trapping forces. Potential applications are in single-beam acoustical tweezers, acoustic levitation, and particle manipulation.

Revisiting non-Gaussianity from non-attractor inflation models

NASA Astrophysics Data System (ADS)

Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei

2018-05-01

Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition—such as in the case of smooth transition or some sharp transition scenarios—the Script O(1) local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.

Going beyond the Kaiser redshift-space distortion formula: A full general relativistic account of the effects and their detectability in galaxy clustering

NASA Astrophysics Data System (ADS)

Yoo, Jaiyul; Hamaus, Nico; Seljak, Uroš; Zaldarriaga, Matias

2012-09-01

Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing to velocity effect. We perform a Fisher matrix analysis of detectability of these terms and show that in a single tracer survey they are completely undetectable. To detect these terms one must resort to the recently developed methods to reduce sampling variance and shot noise. We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M≥1012h-1M⊙ (this can increase to 10-σ or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect primordial non-Gaussianity is little compromised.

Generation of low-divergence laser beams

DOEpatents

Kronberg, James W.

1993-01-01

Apparatus for transforming a conventional beam of coherent light, having a Gaussian energy distribution and relatively high divergence, into a beam in which the energy distribution approximates a single, non-zero-order Bessel function and which therefore has much lower divergence. The apparatus comprises a zone plate having transmitting and reflecting zones defined by the pattern of light interference produced by the combination of a beam of coherent light with a Gaussian energy distribution and one having such a Bessel distribution. The interference pattern between the two beams is a concentric array of multiple annuli, and is preferably recorded as a hologram. The hologram is then used to form the transmitting and reflecting zones by photo-etching portions of a reflecting layer deposited on a plate made of a transmitting material. A Bessel beam, containing approximately 50% of the energy of the incident beam, is produced by passing a Gaussian beam through such a Bessel zone plate. The reflected beam, also containing approximately 50% of the incident beam energy and having a Bessel energy distribution, can be redirected in the same direction and parallel to the transmitted beam. Alternatively, a filter similar to the Bessel zone plate can be placed within the resonator cavity of a conventional laser system having a front mirror and a rear mirror, preferably axially aligned with the mirrors and just inside the front mirror to generate Bessel energy distribution light beams at the laser source.

Testing the mutual information expansion of entropy with multivariate Gaussian distributions.

PubMed

Goethe, Martin; Fita, Ignacio; Rubi, J Miguel

2017-12-14

The mutual information expansion (MIE) represents an approximation of the configurational entropy in terms of low-dimensional integrals. It is frequently employed to compute entropies from simulation data of large systems, such as macromolecules, for which brute-force evaluation of the full configurational integral is intractable. Here, we test the validity of MIE for systems consisting of more than m = 100 degrees of freedom (dofs). The dofs are distributed according to multivariate Gaussian distributions which were generated from protein structures using a variant of the anisotropic network model. For the Gaussian distributions, we have semi-analytical access to the configurational entropy as well as to all contributions of MIE. This allows us to accurately assess the validity of MIE for different situations. We find that MIE diverges for systems containing long-range correlations which means that the error of consecutive MIE approximations grows with the truncation order n for all tractable n ≪ m. This fact implies severe limitations on the applicability of MIE, which are discussed in the article. For systems with correlations that decay exponentially with distance, MIE represents an asymptotic expansion of entropy, where the first successive MIE approximations approach the exact entropy, while MIE also diverges for larger orders. In this case, MIE serves as a useful entropy expansion when truncated up to a specific truncation order which depends on the correlation length of the system.

Theory of polyelectrolytes in solvents.

PubMed

Chitanvis, Shirish M

2003-12-01

Using a continuum description, we account for fluctuations in the ionic solvent surrounding a Gaussian, charged chain and derive an effective short-ranged potential between the charges on the chain. This potential is repulsive at short separations and attractive at longer distances. The chemical potential can be derived from this potential. When the chemical potential is positive, it leads to a meltlike state. For a vanishingly low concentration of segments, this state exhibits scaling behavior for long chains. The Flory exponent characterizing the radius of gyration for long chains is calculated to be approximately 0.63, close to the classical value obtained for second order phase transitions. For short chains, the radius of gyration varies linearly with N, the chain length, and is sensitive to the parameters in the interaction potential. The linear dependence on the chain length N indicates a stiff behavior. The chemical potential associated with this interaction changes sign, when the screening length in the ionic solvent exceeds a critical value. This leads to condensation when the chemical potential is negative. In this state, it is shown using the mean-field approximation that spherical and toroidal condensed shapes can be obtained. The thickness of the toroidal polyelectrolyte is studied as a function of the parameters of the model, such as the ionic screening length. The predictions of this theory should be amenable to experimental verification.

Additivity of nonsimultaneous masking for short Gaussian-shaped sinusoids.

PubMed

Laback, Bernhard; Balazs, Peter; Necciari, Thibaud; Savel, Sophie; Ystad, Solvi; Meunier, Sabine; Kronland-Martinet, Richard

2011-02-01

The additivity of nonsimultaneous masking was studied using Gaussian-shaped tone pulses (referred to as Gaussians) as masker and target stimuli. Combinations of up to four temporally separated Gaussian maskers with an equivalent rectangular bandwidth of 600 Hz and an equivalent rectangular duration of 1.7 ms were tested. Each masker was level-adjusted to produce approximately 8 dB of masking. Excess masking (exceeding linear additivity) was generally stronger than reported in the literature for longer maskers and comparable target levels. A model incorporating a compressive input/output function, followed by a linear summation stage, underestimated excess masking when using an input/output function derived from literature data for longer maskers and comparable target levels. The data could be predicted with a more compressive input/output function. Stronger compression may be explained by assuming that the Gaussian stimuli were too short to evoke the medial olivocochlear reflex (MOCR), whereas for longer maskers tested previously the MOCR caused reduced compression. Overall, the interpretation of the data suggests strong basilar membrane compression for very short stimuli.

Unpolarized infrared emissivity with shadow from anisotropic rough sea surfaces with non-Gaussian statistics.

PubMed

Bourlier, Christophe

2005-07-10

The emissivity of two-dimensional anisotropic rough sea surfaces with non-Gaussian statistics is investigated. The emissivity derivation is of importance for retrieval of the sea-surface temperature or equivalent temperature of a rough sea surface by infrared thermal imaging. The well-known Cox-Munk slope probability-density function, considered non-Gaussian, is used for the emissivity derivation, in which the skewness and the kurtosis (related to the third- and fourth-order statistics, respectively) are included. The shadowing effect, which is significant for grazing angles, is also taken into account. The geometric optics approximation is assumed to be valid, which means that the rough surface is modeled as a collection of facets reflecting locally the light in the specular direction. In addition, multiple reflections are ignored. Numerical results of the emissivity are presented for Gaussian and non-Gaussian statistics, for moderate wind speeds, for near-infrared wavelengths, for emission angles ranging from 0 degrees (nadir) to 90 degrees (horizon), and according to the wind direction. In addition, the emissivity is compared with both measurements and a Monte Carlo ray-tracing method.

Accounting for Non-Gaussian Sources of Spatial Correlation in Parametric Functional Magnetic Resonance Imaging Paradigms I: Revisiting Cluster-Based Inferences.

PubMed

Gopinath, Kaundinya; Krishnamurthy, Venkatagiri; Sathian, K

2018-02-01

In a recent study, Eklund et al. employed resting-state functional magnetic resonance imaging data as a surrogate for null functional magnetic resonance imaging (fMRI) datasets and posited that cluster-wise family-wise error (FWE) rate-corrected inferences made by using parametric statistical methods in fMRI studies over the past two decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; this was principally because the spatial autocorrelation functions (sACF) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggested otherwise. Here, we show that accounting for non-Gaussian signal components such as those arising from resting-state neural activity as well as physiological responses and motion artifacts in the null fMRI datasets yields first- and second-level general linear model analysis residuals with nearly uniform and Gaussian sACF. Further comparison with nonparametric permutation tests indicates that cluster-based FWE corrected inferences made with Gaussian spatial noise approximations are valid.

CFHTLenS: a Gaussian likelihood is a sufficient approximation for a cosmological analysis of third-order cosmic shear statistics

NASA Astrophysics Data System (ADS)

Simon, P.; Semboloni, E.; van Waerbeke, L.; Hoekstra, H.; Erben, T.; Fu, L.; Harnois-Déraps, J.; Heymans, C.; Hildebrandt, H.; Kilbinger, M.; Kitching, T. D.; Miller, L.; Schrabback, T.

2015-05-01

We study the correlations of the shear signal between triplets of sources in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) to probe cosmological parameters via the matter bispectrum. In contrast to previous studies, we adopt a non-Gaussian model of the data likelihood which is supported by our simulations of the survey. We find that for state-of-the-art surveys, similar to CFHTLenS, a Gaussian likelihood analysis is a reasonable approximation, albeit small differences in the parameter constraints are already visible. For future surveys we expect that a Gaussian model becomes inaccurate. Our algorithm for a refined non-Gaussian analysis and data compression is then of great utility especially because it is not much more elaborate if simulated data are available. Applying this algorithm to the third-order correlations of shear alone in a blind analysis, we find a good agreement with the standard cosmological model: Σ _8=σ _8(Ω _m/0.27)^{0.64}=0.79^{+0.08}_{-0.11} for a flat Λ cold dark matter cosmology with h = 0.7 ± 0.04 (68 per cent credible interval). Nevertheless our models provide only moderately good fits as indicated by χ2/dof = 2.9, including a 20 per cent rms uncertainty in the predicted signal amplitude. The models cannot explain a signal drop on scales around 15 arcmin, which may be caused by systematics. It is unclear whether the discrepancy can be fully explained by residual point spread function systematics of which we find evidence at least on scales of a few arcmin. Therefore we need a better understanding of higher order correlations of cosmic shear and their systematics to confidently apply them as cosmological probes.

Non-model-based damage identification of plates using principal, mean and Gaussian curvature mode shapes

DOE PAGES

Xu, Yongfeng F.; Zhu, Weidong D.; Smith, Scott A.

2017-07-01

Mode shapes (MSs) have been extensively used to identify structural damage. This paper presents a new non-model-based method that uses principal, mean and Gaussian curvature MSs (CMSs) to identify damage in plates; the method is applicable and robust to MSs associated with low and high elastic modes on dense and coarse measurement grids. A multi-scale discrete differential-geometry scheme is proposed to calculate principal, mean and Gaussian CMSs associated with a MS of a plate, which can alleviate adverse effects of measurement noise on calculating the CMSs. Principal, mean and Gaussian CMSs of a damaged plate and those of an undamagedmore » one are used to yield four curvature damage indices (CDIs), including Maximum-CDIs, Minimum-CDIs, Mean-CDIs and Gaussian-CDIs. Damage can be identified near regions with consistently higher values of the CDIs. It is shown that a MS of an undamaged plate can be well approximated using a polynomial with a properly determined order that fits a MS of a damaged one, provided that the undamaged plate has a smooth geometry and is made of material that has no stiffness and mass discontinuities. New fitting and convergence indices are proposed to quantify the level of approximation of a MS from a polynomial fit to that of a damaged plate and to determine the proper order of the polynomial fit, respectively. A MS of an aluminum plate with damage in the form of a machined thickness reduction area was measured to experimentally investigate the effectiveness of the proposed CDIs in damage identification; the damage on the plate was successfully identified.« less

Non-model-based damage identification of plates using principal, mean and Gaussian curvature mode shapes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Yongfeng F.; Zhu, Weidong D.; Smith, Scott A.

Mode shapes (MSs) have been extensively used to identify structural damage. This paper presents a new non-model-based method that uses principal, mean and Gaussian curvature MSs (CMSs) to identify damage in plates; the method is applicable and robust to MSs associated with low and high elastic modes on dense and coarse measurement grids. A multi-scale discrete differential-geometry scheme is proposed to calculate principal, mean and Gaussian CMSs associated with a MS of a plate, which can alleviate adverse effects of measurement noise on calculating the CMSs. Principal, mean and Gaussian CMSs of a damaged plate and those of an undamagedmore » one are used to yield four curvature damage indices (CDIs), including Maximum-CDIs, Minimum-CDIs, Mean-CDIs and Gaussian-CDIs. Damage can be identified near regions with consistently higher values of the CDIs. It is shown that a MS of an undamaged plate can be well approximated using a polynomial with a properly determined order that fits a MS of a damaged one, provided that the undamaged plate has a smooth geometry and is made of material that has no stiffness and mass discontinuities. New fitting and convergence indices are proposed to quantify the level of approximation of a MS from a polynomial fit to that of a damaged plate and to determine the proper order of the polynomial fit, respectively. A MS of an aluminum plate with damage in the form of a machined thickness reduction area was measured to experimentally investigate the effectiveness of the proposed CDIs in damage identification; the damage on the plate was successfully identified.« less

FIBER AND INTEGRATED OPTICS: Use of the offset method in an analysis of a non-Gaussian field distribution in single-mode fiber waveguides

NASA Astrophysics Data System (ADS)

Belov, A. V.; Kurkov, Andrei S.; Chikolini, A. V.

1990-08-01

An offset method is modified to allow an analysis of the distribution of fields in a single-mode fiber waveguide without recourse to the Gaussian approximation. A new approximation for the field is obtained for fiber waveguides with a step refractive index profile and a special analysis employing the Hankel transformation is applied to waveguides with a distributed refractive index. The field distributions determined by this method are compared with the corresponding distributions calculated from the refractive index of a preform from which the fibers are drawn. It is shown that these new approaches can be used to determine the dimensions of a mode spot defined in different ways and to forecast the dispersion characteristics of single-mode fiber waveguides.

Receiver design for SPAD-based VLC systems under Poisson-Gaussian mixed noise model.

PubMed

Mao, Tianqi; Wang, Zhaocheng; Wang, Qi

2017-01-23

Single-photon avalanche diode (SPAD) is a promising photosensor because of its high sensitivity to optical signals in weak illuminance environment. Recently, it has drawn much attention from researchers in visible light communications (VLC). However, existing literature only deals with the simplified channel model, which only considers the effects of Poisson noise introduced by SPAD, but neglects other noise sources. Specifically, when an analog SPAD detector is applied, there exists Gaussian thermal noise generated by the transimpedance amplifier (TIA) and the digital-to-analog converter (D/A). Therefore, in this paper, we propose an SPAD-based VLC system with pulse-amplitude-modulation (PAM) under Poisson-Gaussian mixed noise model, where Gaussian-distributed thermal noise at the receiver is also investigated. The closed-form conditional likelihood of received signals is derived using the Laplace transform and the saddle-point approximation method, and the corresponding quasi-maximum-likelihood (quasi-ML) detector is proposed. Furthermore, the Poisson-Gaussian-distributed signals are converted to Gaussian variables with the aid of the generalized Anscombe transform (GAT), leading to an equivalent additive white Gaussian noise (AWGN) channel, and a hard-decision-based detector is invoked. Simulation results demonstrate that, the proposed GAT-based detector can reduce the computational complexity with marginal performance loss compared with the proposed quasi-ML detector, and both detectors are capable of accurately demodulating the SPAD-based PAM signals.

Dynamical analysis of contrastive divergence learning: Restricted Boltzmann machines with Gaussian visible units.

PubMed

Karakida, Ryo; Okada, Masato; Amari, Shun-Ichi

2016-07-01

The restricted Boltzmann machine (RBM) is an essential constituent of deep learning, but it is hard to train by using maximum likelihood (ML) learning, which minimizes the Kullback-Leibler (KL) divergence. Instead, contrastive divergence (CD) learning has been developed as an approximation of ML learning and widely used in practice. To clarify the performance of CD learning, in this paper, we analytically derive the fixed points where ML and CDn learning rules converge in two types of RBMs: one with Gaussian visible and Gaussian hidden units and the other with Gaussian visible and Bernoulli hidden units. In addition, we analyze the stability of the fixed points. As a result, we find that the stable points of CDn learning rule coincide with those of ML learning rule in a Gaussian-Gaussian RBM. We also reveal that larger principal components of the input data are extracted at the stable points. Moreover, in a Gaussian-Bernoulli RBM, we find that both ML and CDn learning can extract independent components at one of stable points. Our analysis demonstrates that the same feature components as those extracted by ML learning are extracted simply by performing CD1 learning. Expanding this study should elucidate the specific solutions obtained by CD learning in other types of RBMs or in deep networks. Copyright © 2016 Elsevier Ltd. All rights reserved.

Time-spatial drift of decelerating electromagnetic pulses.

PubMed

Nerukh, Alexander G; Nerukh, Dmitry A

2013-07-15

A time dependent electromagnetic pulse generated by a current running laterally to the direction of the pulse propagation is considered in paraxial approximation. It is shown that the pulse envelope moves in the time-spatial coordinates on the surface of a parabolic cylinder for the Airy pulse and a hyperbolic cylinder for the Gaussian. These pulses propagate in time with deceleration along the dominant propagation direction and drift uniformly in the lateral direction. The Airy pulse stops at infinity while the asymptotic velocity of the Gaussian is nonzero.

Phase behavior of a fluid with a double Gaussian potential displaying waterlike features

NASA Astrophysics Data System (ADS)

Speranza, Cristina; Prestipino, Santi; Malescio, Gianpietro; Giaquinta, Paolo V.

2014-07-01

Pair potentials that are bounded at the origin provide an accurate description of the effective interaction for many systems of dissolved soft macromolecules (e.g., flexible dendrimers). Using numerical free-energy calculations, we reconstruct the equilibrium phase diagram of a system of particles interacting through a potential that brings together a Gaussian repulsion with a much weaker Gaussian attraction, close to the thermodynamic stability threshold. Compared to the purely repulsive model, only the reentrant branch of the melting line survives, since for lower densities solidification is overridden by liquid-vapor separation. As a result, the phase diagram of the system recalls that of water up to moderate (i.e., a few tens of MPa) pressures. Upon superimposing a suitable hard core on the double-Gaussian potential, a further transition to a more compact solid phase is induced at high pressure, which might be regarded as the analog of the ice I-to-ice III transition in water.

Relativistic wide-angle galaxy bispectrum on the light cone

NASA Astrophysics Data System (ADS)

Bertacca, Daniele; Raccanelli, Alvise; Bartolo, Nicola; Liguori, Michele; Matarrese, Sabino; Verde, Licia

2018-01-01

Given the important role that the galaxy bispectrum has recently acquired in cosmology and the scale and precision of forthcoming galaxy clustering observations, it is timely to derive the full expression of the large-scale bispectrum going beyond approximated treatments which neglect integrated terms or higher-order bias terms or use the Limber approximation. On cosmological scales, relativistic effects that arise from observing the past light cone alter the observed galaxy number counts, therefore leaving their imprints on N-point correlators at all orders. In this paper we compute for the first time the bispectrum including all general relativistic, local and integrated, effects at second order, the tracers' bias at second order, geometric effects as well as the primordial non-Gaussianity contribution. This is timely considering that future surveys will probe scales comparable to the horizon where approximations widely used currently may not hold; neglecting these effects may introduce biases in estimation of cosmological parameters as well as primordial non-Gaussianity.

Gaussian process regression for sensor networks under localization uncertainty

USGS Publications Warehouse

Jadaliha, M.; Xu, Yunfei; Choi, Jongeun; Johnson, N.S.; Li, Weiming

2013-01-01

In this paper, we formulate Gaussian process regression with observations under the localization uncertainty due to the resource-constrained sensor networks. In our formulation, effects of observations, measurement noise, localization uncertainty, and prior distributions are all correctly incorporated in the posterior predictive statistics. The analytically intractable posterior predictive statistics are proposed to be approximated by two techniques, viz., Monte Carlo sampling and Laplace's method. Such approximation techniques have been carefully tailored to our problems and their approximation error and complexity are analyzed. Simulation study demonstrates that the proposed approaches perform much better than approaches without considering the localization uncertainty properly. Finally, we have applied the proposed approaches on the experimentally collected real data from a dye concentration field over a section of a river and a temperature field of an outdoor swimming pool to provide proof of concept tests and evaluate the proposed schemes in real situations. In both simulation and experimental results, the proposed methods outperform the quick-and-dirty solutions often used in practice.

Photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams

NASA Astrophysics Data System (ADS)

Karbstein, Felix; Mosman, Elena A.

2017-12-01

In this article, we provide analytical expressions for the photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams. Our results are based on a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics. Hence, by construction they are limited to slowly varying electromagnetic fields, varying on spatial and temporal scales significantly larger than the Compton wavelength/time of the electron. The latter criterion is fulfilled by all laser beams currently available in the laboratory. Our findings will, e.g., be relevant for the study of vacuum birefringence experienced by probe photons brought into collision with a high-intensity laser pulse which can be represented as a superposition of either Hermite- or Laguerre-Gaussian modes.

Calculation of the force acting on a micro-sized particle with optical vortex array laser beam tweezers

NASA Astrophysics Data System (ADS)

Kuo, Chun-Fu; Chu, Shu-Chun

2013-03-01

Optical vortices possess several special properties, including carrying optical angular momentum (OAM) and exhibiting zero intensity. Vortex array laser beams have attracts many interests due to its special mesh field distributions, which show great potential in the application of multiple optical traps and dark optical traps. Previously study developed an Ince-Gaussian Mode (IGM)-based vortex array laser beam1. This study develops a simulation model based on the discrete dipole approximation (DDA) method for calculating the resultant force acting on a micro-sized spherical dielectric particle that situated at the beam waist of the IGM-based vortex array laser beams1.

Direct test of the Gaussian auxiliary field ansatz in nonconserved order parameter phase ordering dynamics

NASA Astrophysics Data System (ADS)

Yeung, Chuck

2018-06-01

The assumption that the local order parameter is related to an underlying spatially smooth auxiliary field, u (r ⃗,t ) , is a common feature in theoretical approaches to non-conserved order parameter phase separation dynamics. In particular, the ansatz that u (r ⃗,t ) is a Gaussian random field leads to predictions for the decay of the autocorrelation function which are consistent with observations, but distinct from predictions using alternative theoretical approaches. In this paper, the auxiliary field is obtained directly from simulations of the time-dependent Ginzburg-Landau equation in two and three dimensions. The results show that u (r ⃗,t ) is equivalent to the distance to the nearest interface. In two dimensions, the probability distribution, P (u ) , is well approximated as Gaussian except for small values of u /L (t ) , where L (t ) is the characteristic length-scale of the patterns. The behavior of P (u ) in three dimensions is more complicated; the non-Gaussian region for small u /L (t ) is much larger than that in two dimensions but the tails of P (u ) begin to approach a Gaussian form at intermediate times. However, at later times, the tails of the probability distribution appear to decay faster than a Gaussian distribution.

A Method for Approximating the Bivariate Normal Correlation Coefficient.

ERIC Educational Resources Information Center

Kirk, David B.

Improvements of the Gaussian quadrature in conjunction with the Newton-Raphson iteration technique (TM 000 789) are discussed as effective methods of calculating the bivariate normal correlation coefficient. (CK)

Born Oppenheimer potential energy for interaction of antihydrogen with molecular hydrogen

NASA Astrophysics Data System (ADS)

Strasburger, Krzysztof

2005-09-01

Inelastic collisions with hydrogen molecules are claimed to be an important channel of antihydrogen (\\overlineH) losses (Armour and Zeman 1999 Int. J. Quantum Chem. 74 645). In the present work, interaction energies for the H_{2}\\--\\overlineH system in the ground state have been calculated within the Born-Oppenheimer approximation. The leptonic problem was solved variationally with the basis of explicitly correlated Gaussian functions. The geometry of H2 was fixed at equilibrium geometry and the \\overlineH atom approached the molecule from two directions—along or perpendicularly to the bond axis. Purely attractive potential energy curve has been obtained for the first nuclear configuration, while a local maximum (lower than the energy at infinite separation) has been found for the second one.

The HVT technique and the 'uncertainty' relation for central potentials

NASA Astrophysics Data System (ADS)

Grypeos, M. E.; Koutroulos, C. G.; Oyewumi, K. J.; Petridou, Th

2004-08-01

The quantum mechanical hypervirial theorems (HVT) technique is used to treat the so-called 'uncertainty' relation for quite a general class of central potential wells, including the (reduced) Poeschl-Teller and the Gaussian one. It is shown that this technique is quite suitable in deriving an approximate analytic expression in the form of a truncated power series expansion for the dimensionless product Pnl equiv langr2rangnllangp2rangnl/planck2, for every (deeply) bound state of a particle moving non-relativistically in the well, provided that a (dimensionless) parameter s is sufficiently small. Attention is also paid to a number of cases, among the limited existing ones, in which exact analytic or semi-analytic expressions for Pnl can be derived. Finally, numerical results are given and discussed.

On the line-shape analysis of Compton profiles and its application to neutron scattering

NASA Astrophysics Data System (ADS)

Romanelli, G.; Krzystyniak, M.

2016-05-01

Analytical properties of Compton profiles are used in order to simplify the analysis of neutron Compton scattering experiments. In particular, the possibility to fit the difference of Compton profiles is discussed as a way to greatly decrease the level of complexity of the data treatment, making the analysis easier, faster and more robust. In the context of the novel method proposed, two mathematical models describing the shapes of differenced Compton profiles are discussed: the simple Gaussian approximation for harmonic and isotropic local potential, and an analytical Gauss-Hermite expansion for an anharmonic or anisotropic potential. The method is applied to data collected by VESUVIO spectrometer at ISIS neutron and muon pulsed source (UK) on Copper and Aluminium samples at ambient and low temperatures.

Effects of hydrogen-like impurity and electromagnetic field on quantum transition of an electron in a Gaussian potential with QD thickness

NASA Astrophysics Data System (ADS)

Xin, Wei; Zhao, Yu-Wei; Sudu; Eerdunchaolu

2018-05-01

Considering Hydrogen-like impurity and the thickness effect, the eigenvalues and eigenfunctions of the electronic ground and first exited states in a quantum dot (QD) are derived by using the Lee-Low-Pins-Pekar variational method with the harmonic and Gaussian potentials as the transverse and longitudinal confinement potentials, respectively. A two-level system is constructed on the basis of those two states, and the electronic quantum transition affected by an electromagnetic field is discussed in terms of the two-level system theory. The results indicate the Gaussian potential reflects the real confinement potential more accurately than the parabolic one; the influence of the thickness of the QD on the electronic transition probability is interesting and significant, and cannot be ignored; the electronic transition probability Γ is influenced significantly by some physical quantities, such as the strength of the electron-phonon coupling α, the electric-field strength F, the magnetic-field cyclotron frequency ωc , the barrier height V0 and confinement range L of the asymmetric Gaussian potential, suggesting the transport and optical properties of the QD can be manipulated further though those physical quantities.

Implementation of Two-Component Time-Dependent Density Functional Theory in TURBOMOLE.

PubMed

Kühn, Michael; Weigend, Florian

2013-12-10

We report the efficient implementation of a two-component time-dependent density functional theory proposed by Wang et al. (Wang, F.; Ziegler, T.; van Lenthe, E.; van Gisbergen, S.; Baerends, E. J. J. Chem. Phys. 2005, 122, 204103) that accounts for spin-orbit effects on excitations of closed-shell systems by employing a noncollinear exchange-correlation kernel. In contrast to the aforementioned implementation, our method is based on two-component effective core potentials as well as Gaussian-type basis functions. It is implemented in the TURBOMOLE program suite for functionals of the local density approximation and the generalized gradient approximation. Accuracy is assessed by comparison of two-component vertical excitation energies of heavy atoms and ions (Cd, Hg, Au(+)) and small molecules (I2, TlH) to other two- and four-component approaches. Efficiency is demonstrated by calculating the electronic spectrum of Au20.

Fast and Accurate Multivariate Gaussian Modeling of Protein Families: Predicting Residue Contacts and Protein-Interaction Partners

PubMed Central

Feinauer, Christoph; Procaccini, Andrea; Zecchina, Riccardo; Weigt, Martin; Pagnani, Andrea

2014-01-01

In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our method aims at extracting such constraints from rapidly accumulating sequence data, and thereby at inferring protein structure and function from sequence information alone. Recently, global statistical inference methods (e.g. direct-coupling analysis, sparse inverse covariance estimation) have achieved a breakthrough towards this aim, and their predictions have been successfully implemented into tertiary and quaternary protein structure prediction methods. However, due to the discrete nature of the underlying variable (amino-acids), exact inference requires exponential time in the protein length, and efficient approximations are needed for practical applicability. Here we propose a very efficient multivariate Gaussian modeling approach as a variant of direct-coupling analysis: the discrete amino-acid variables are replaced by continuous Gaussian random variables. The resulting statistical inference problem is efficiently and exactly solvable. We show that the quality of inference is comparable or superior to the one achieved by mean-field approximations to inference with discrete variables, as done by direct-coupling analysis. This is true for (i) the prediction of residue-residue contacts in proteins, and (ii) the identification of protein-protein interaction partner in bacterial signal transduction. An implementation of our multivariate Gaussian approach is available at the website http://areeweb.polito.it/ricerca/cmp/code. PMID:24663061

EVOLUTION OF THE MAGNETIC FIELD LINE DIFFUSION COEFFICIENT AND NON-GAUSSIAN STATISTICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Snodin, A. P.; Ruffolo, D.; Matthaeus, W. H.

The magnetic field line random walk (FLRW) plays an important role in the transport of energy and particles in turbulent plasmas. For magnetic fluctuations that are transverse or almost transverse to a large-scale mean magnetic field, theories describing the FLRW usually predict asymptotic diffusion of magnetic field lines perpendicular to the mean field. Such theories often depend on the assumption that one can relate the Lagrangian and Eulerian statistics of the magnetic field via Corrsin’s hypothesis, and additionally take the distribution of magnetic field line displacements to be Gaussian. Here we take an ordinary differential equation (ODE) model with thesemore » underlying assumptions and test how well it describes the evolution of the magnetic field line diffusion coefficient in 2D+slab magnetic turbulence, by comparisons to computer simulations that do not involve such assumptions. In addition, we directly test the accuracy of the Corrsin approximation to the Lagrangian correlation. Over much of the studied parameter space we find that the ODE model is in fairly good agreement with computer simulations, in terms of both the evolution and asymptotic values of the diffusion coefficient. When there is poor agreement, we show that this can be largely attributed to the failure of Corrsin’s hypothesis rather than the assumption of Gaussian statistics of field line displacements. The degree of non-Gaussianity, which we measure in terms of the kurtosis, appears to be an indicator of how well Corrsin’s approximation works.« less

Quantum Brownian motion with inhomogeneous damping and diffusion

NASA Astrophysics Data System (ADS)

Massignan, Pietro; Lampo, Aniello; Wehr, Jan; Lewenstein, Maciej

2015-03-01

We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear function of the position of the particle. Physically, this corresponds to a configuration in which damping and diffusion are spatially inhomogeneous. We derive systematically the quantum master equation for the Brownian particle in the Born-Markov approximation and we discuss the appearance of additional terms, for various polynomials forms of the coupling. We discuss the cases of linear and quadratic coupling in great detail and we derive, using Wigner function techniques, the stationary solutions of the master equation for a Brownian particle in a harmonic trapping potential. We predict quite generally Gaussian stationary states, and we compute the aspect ratio and the spread of the distributions. In particular, we find that these solutions may be squeezed (superlocalized) with respect to the position of the Brownian particle. We analyze various restrictions to the validity of our theory posed by non-Markovian effects and by the Heisenberg principle. We further study the dynamical stability of the system, by applying a Gaussian approximation to the time-dependent Wigner function, and we compute the decoherence rates of coherent quantum superpositions in position space. Finally, we propose a possible experimental realization of the physics discussed here, by considering an impurity particle embedded in a degenerate quantum gas.

Steady and Oscillatory, Subsonic and Supersonic, Aerodynamic Pressure and Generalized Forces for Complex Aircraft Configurations and Applications to Flutter. M.S. Thesis

NASA Technical Reports Server (NTRS)

Chen, L. T.

1975-01-01

A general method for analyzing aerodynamic flows around complex configurations is presented. By applying the Green function method, a linear integral equation relating the unknown, small perturbation potential on the surface of the body, to the known downwash is obtained. The surfaces of the aircraft, wake and diaphragm (if necessary) are divided into small quadrilateral elements which are approximated with hyperboloidal surfaces. The potential and its normal derivative are assumed to be constant within each element. This yields a set of linear algebraic equations and the coefficients are evaluated analytically. By using Gaussian elimination method, equations are solved for the potentials at the centroids of elements. The pressure coefficient is evaluated by the finite different method; the lift and moment coefficients are evaluated by numerical integration. Numerical results are presented, and applications to flutter are also included.

Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations

DOE PAGES

Del-Castillo-Negrete, Diego B.; Moradi, Sara; Anderson, Johan

2016-09-01

Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of -stable Levy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Levy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Levy fluctuations. The absolute value ofmore » the power law decay exponents are linearly proportional to the Levy index. Furthermore, the observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Levy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.« less

Ionospheric scintillation by a random phase screen Spectral approach

NASA Technical Reports Server (NTRS)

Rufenach, C. L.

1975-01-01

The theory developed by Briggs and Parkin, given in terms of an anisotropic gaussian correlation function, is extended to a spectral description specified as a continuous function of spatial wavenumber with an intrinsic outer scale as would be expected from a turbulent medium. Two spectral forms were selected for comparison: (1) a power-law variation in wavenumber with a constant three-dimensional index equal to 4, and (2) Gaussian spectral variation. The results are applied to the F-region ionosphere with an outer-scale wavenumber of 2 per km (approximately equal to the Fresnel wavenumber) for the power-law variation, and 0.2 per km for the Gaussian spectral variation. The power-law form with a small outer-scale wavenumber is consistent with recent F-region in-situ measurements, whereas the gaussian form is mathematically convenient and, hence, mostly used in the previous developments before the recent in-situ measurements. Some comparison with microwave scintillation in equatorial areas is made.

Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations

NASA Astrophysics Data System (ADS)

Moradi, Sara; del-Castillo-Negrete, Diego; Anderson, Johan

2016-09-01

Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of α-stable Lévy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Lévy fluctuations. The absolute value of the power law decay exponents is linearly proportional to the Lévy index α. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Lévy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.

Prediction of sound transmission loss through multilayered panels by using Gaussian distribution of directional incident energy

PubMed

Kang; Ih; Kim; Kim

2000-03-01

In this study, a new prediction method is suggested for sound transmission loss (STL) of multilayered panels of infinite extent. Conventional methods such as random or field incidence approach often given significant discrepancies in predicting STL of multilayered panels when compared with the experiments. In this paper, appropriate directional distributions of incident energy to predict the STL of multilayered panels are proposed. In order to find a weighting function to represent the directional distribution of incident energy on the wall in a reverberation chamber, numerical simulations by using a ray-tracing technique are carried out. Simulation results reveal that the directional distribution can be approximately expressed by the Gaussian distribution function in terms of the angle of incidence. The Gaussian function is applied to predict the STL of various multilayered panel configurations as well as single panels. The compared results between the measurement and the prediction show good agreements, which validate the proposed Gaussian function approach.

A method for predicting DCT-based denoising efficiency for grayscale images corrupted by AWGN and additive spatially correlated noise

NASA Astrophysics Data System (ADS)

Rubel, Aleksey S.; Lukin, Vladimir V.; Egiazarian, Karen O.

2015-03-01

Results of denoising based on discrete cosine transform for a wide class of images corrupted by additive noise are obtained. Three types of noise are analyzed: additive white Gaussian noise and additive spatially correlated Gaussian noise with middle and high correlation levels. TID2013 image database and some additional images are taken as test images. Conventional DCT filter and BM3D are used as denoising techniques. Denoising efficiency is described by PSNR and PSNR-HVS-M metrics. Within hard-thresholding denoising mechanism, DCT-spectrum coefficient statistics are used to characterize images and, subsequently, denoising efficiency for them. Results of denoising efficiency are fitted for such statistics and efficient approximations are obtained. It is shown that the obtained approximations provide high accuracy of prediction of denoising efficiency.

A State-Space Approach to Optimal Level-Crossing Prediction for Linear Gaussian Processes

NASA Technical Reports Server (NTRS)

Martin, Rodney Alexander

2009-01-01

In many complex engineered systems, the ability to give an alarm prior to impending critical events is of great importance. These critical events may have varying degrees of severity, and in fact they may occur during normal system operation. In this article, we investigate approximations to theoretically optimal methods of designing alarm systems for the prediction of level-crossings by a zero-mean stationary linear dynamic system driven by Gaussian noise. An optimal alarm system is designed to elicit the fewest false alarms for a fixed detection probability. This work introduces the use of Kalman filtering in tandem with the optimal level-crossing problem. It is shown that there is a negligible loss in overall accuracy when using approximations to the theoretically optimal predictor, at the advantage of greatly reduced computational complexity. I

Generation of low-divergence laser beams

DOEpatents

Kronberg, J.W.

1993-09-14

Apparatus for transforming a conventional beam of coherent light, having a Gaussian energy distribution and relatively high divergence, into a beam in which the energy distribution approximates a single, non-zero-order Bessel function and which therefore has much lower divergence. The apparatus comprises a zone plate having transmitting and reflecting zones defined by the pattern of light interference produced by the combination of a beam of coherent light with a Gaussian energy distribution and one having such a Bessel distribution. The interference pattern between the two beams is a concentric array of multiple annuli, and is preferably recorded as a hologram. The hologram is then used to form the transmitting and reflecting zones by photo-etching portions of a reflecting layer deposited on a plate made of a transmitting material. A Bessel beam, containing approximately 50% of the energy of the incident beam, is produced by passing a Gaussian beam through such a Bessel zone plate. The reflected beam, also containing approximately 50% of the incident beam energy and having a Bessel energy distribution, can be redirected in the same direction and parallel to the transmitted beam. Alternatively, a filter similar to the Bessel zone plate can be placed within the resonator cavity of a conventional laser system having a front mirror and a rear mirror, preferably axially aligned with the mirrors and just inside the front mirror to generate Bessel energy distribution light beams at the laser source. 11 figures.

The robustness of truncated Airy beam in PT Gaussian potentials media

NASA Astrophysics Data System (ADS)

Wang, Xianni; Fu, Xiquan; Huang, Xianwei; Yang, Yijun; Bai, Yanfeng

2018-03-01

The robustness of truncated Airy beam in parity-time (PT) symmetric Gaussian potentials media is numerically investigated. A high-peak power beam sheds from the Airy beam due to the media modulation while the Airy wavefront still retain its self-bending and non-diffraction characteristics under the influence of modulation parameters. Increasing the modulation factor results in the smaller value of maximum power of the center beam, and the opposite trend occurs with the increment of the modulation depth. However, the parabolic trajectory of the Airy wavefront does not be influenced. By utilizing the unique features, the Airy beam can be used as a long distance transmission source under the PT symmetric Gaussian potentials medium.

Mean-force-field and mean-spherical approximations for the electric microfield distribution at a charged point in the charged-hard-particles fluid

NASA Astrophysics Data System (ADS)

Rosenfeld, Yaakov

1989-01-01

The linearized mean-force-field approximation, leading to a Gaussian distribution, provides an exact formal solution to the mean-spherical integral equation model for the electric microfield distribution at a charged point in the general charged-hard-particles fluid. Lado's explicit solution for plasmas immediately follows this general observation.

Use of the Box-Cox Transformation in Detecting Changepoints in Daily Precipitation Data Series

NASA Astrophysics Data System (ADS)

Wang, X. L.; Chen, H.; Wu, Y.; Pu, Q.

2009-04-01

This study integrates a Box-Cox power transformation procedure into two statistical tests for detecting changepoints in Gaussian data series, to make the changepoint detection methods applicable to non-Gaussian data series, such as daily precipitation amounts. The detection power aspects of transformed methods in a common trend two-phase regression setting are assessed by Monte Carlo simulations for data of a log-normal or Gamma distribution. The results show that the transformed methods have increased the power of detection, in comparison with the corresponding original (untransformed) methods. The transformed data much better approximate to a Gaussian distribution. As an example of application, the new methods are applied to a series of daily precipitation amounts recorded at a station in Canada, showing satisfactory detection power.

Novel palmprint representations for palmprint recognition

NASA Astrophysics Data System (ADS)

Li, Hengjian; Dong, Jiwen; Li, Jinping; Wang, Lei

2015-02-01

In this paper, we propose a novel palmprint recognition algorithm. Firstly, the palmprint images are represented by the anisotropic filter. The filters are built on Gaussian functions along one direction, and on second derivative of Gaussian functions in the orthogonal direction. Also, this choice is motivated by the optimal joint spatial and frequency localization of the Gaussian kernel. Therefore,they can better approximate the edge or line of palmprint images. A palmprint image is processed with a bank of anisotropic filters at different scales and rotations for robust palmprint features extraction. Once these features are extracted, subspace analysis is then applied to the feature vectors for dimension reduction as well as class separability. Experimental results on a public palmprint database show that the accuracy could be improved by the proposed novel representations, compared with Gabor.

Parameterization of cloud lidar backscattering profiles by means of asymmetrical Gaussians

NASA Astrophysics Data System (ADS)

del Guasta, Massimo; Morandi, Marco; Stefanutti, Leopoldo

1995-06-01

A fitting procedure for cloud lidar data processing is shown that is based on the computation of the first three moments of the vertical-backscattering (or -extinction) profile. Single-peak clouds or single cloud layers are approximated to asymmetrical Gaussians. The algorithm is particularly stable with respect to noise and processing errors, and it is much faster than the equivalent least-squares approach. Multilayer clouds can easily be treated as a sum of single asymmetrical Gaussian peaks. The method is suitable for cloud-shape parametrization in noisy lidar signatures (like those expected from satellite lidars). It also permits an improvement of cloud radiative-property computations that are based on huge lidar data sets for which storage and careful examination of single lidar profiles can't be carried out.

Numerical modeling of Gaussian beam propagation and diffraction in inhomogeneous media based on the complex eikonal equation

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Hui

2018-05-01

Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss-Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.

A Gaussian beam method for ultrasonic non-destructive evaluation modeling

NASA Astrophysics Data System (ADS)

Jacquet, O.; Leymarie, N.; Cassereau, D.

2018-05-01

The propagation of high-frequency ultrasonic body waves can be efficiently estimated with a semi-analytic Dynamic Ray Tracing approach using paraxial approximation. Although this asymptotic field estimation avoids the computational cost of numerical methods, it may encounter several limitations in reproducing identified highly interferential features. Nevertheless, some can be managed by allowing paraxial quantities to be complex-valued. This gives rise to localized solutions, known as paraxial Gaussian beams. Whereas their propagation and transmission/reflection laws are well-defined, the fact remains that the adopted complexification introduces additional initial conditions. While their choice is usually performed according to strategies specifically tailored to limited applications, a Gabor frame method has been implemented to indiscriminately initialize a reasonable number of paraxial Gaussian beams. Since this method can be applied for an usefully wide range of ultrasonic transducers, the typical case of the time-harmonic piston radiator is investigated. Compared to the commonly used Multi-Gaussian Beam model [1], a better agreement is obtained throughout the radiated field between the results of numerical integration (or analytical on-axis solution) and the resulting Gaussian beam superposition. Sparsity of the proposed solution is also discussed.

Spin angular momentum transfer from TEM00 focused Gaussian beams to negative refractive index spherical particles

PubMed Central

Ambrosio, Leonardo A.; Hernández-Figueroa, Hugo E.

2011-01-01

We investigate optical torques over absorbent negative refractive index spherical scatterers under the influence of linear and circularly polarized TEM00 focused Gaussian beams, in the framework of the generalized Lorenz-Mie theory with the integral localized approximation. The fundamental differences between optical torques due to spin angular momentum transfer in positive and negative refractive index optical trapping are outlined, revealing the effect of the Mie scattering coefficients in one of the most fundamental properties in optical trapping systems. PMID:21833372

Observation of enhanced thermal lensing due to near-Gaussian pump energy deposition in a laser-diode side-pumped Nd:YAG laser

NASA Technical Reports Server (NTRS)

Welford, David; Rines, David M.; Dinerman, Bradley J.; Martinsen, Robert

1992-01-01

The authors report operation of a laser-diode side-pumped Nd:YAG laser with a novel pumping geometry that ensures efficient conversion of pump energy into the TEM00 mode. Significant enhancement of thermally induced lensing due to the near-Gaussian energy deposition profile of the pump radiation was observed. An induced lens of approximately 3.2-m focal length was measured at average incident pump powers of only 3.2 W (corresponding to a 0.6 W heat load).

Shear Melting of a Colloidal Glass

NASA Astrophysics Data System (ADS)

Eisenmann, Christoph; Kim, Chanjoong; Mattsson, Johan; Weitz, David A.

2010-01-01

We use confocal microscopy to explore shear melting of colloidal glasses, which occurs at strains of ˜0.08, coinciding with a strongly non-Gaussian step size distribution. For larger strains, the particle mean square displacement increases linearly with strain and the step size distribution becomes Gaussian. The effective diffusion coefficient varies approximately linearly with shear rate, consistent with a modified Stokes-Einstein relationship in which thermal energy is replaced by shear energy and the length scale is set by the size of cooperatively moving regions consisting of ˜3 particles.

Ewald Summation Approach to Potential Models of Aqueous Electrolytes Involving Gaussian Charges and Induced Dipoles: Formal and Simulation Results

DOE PAGES

Chialvo, Ariel A.; Vlcek, Lukas

2014-11-01

We present a detailed derivation of the complete set of expressions required for the implementation of an Ewald summation approach to handle the long-range electrostatic interactions of polar and ionic model systems involving Gaussian charges and induced dipole moments with a particular application to the isobaricisothermal molecular dynamics simulation of our Gaussian Charge Polarizable (GCP) water model and its extension to aqueous electrolytes solutions. The set comprises the individual components of the potential energy, electrostatic potential, electrostatic field and gradient, the electrostatic force and the corresponding virial. Moreover, we show how the derived expressions converge to known point-based electrostatic counterpartsmore » when the parameters, defining the Gaussian charge and induced-dipole distributions, are extrapolated to their limiting point values. Finally, we illustrate the Ewald implementation against the current reaction field approach by isothermal-isobaric molecular dynamics of ambient GCP water for which we compared the outcomes of the thermodynamic, microstructural, and polarization behavior.« less

Quadratures with multiple nodes, power orthogonality, and moment-preserving spline approximation

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.

2001-01-01

Quadrature formulas with multiple nodes, power orthogonality, and some applications of such quadratures to moment-preserving approximation by defective splines are considered. An account on power orthogonality (s- and [sigma]-orthogonal polynomials) and generalized Gaussian quadratures with multiple nodes, including stable algorithms for numerical construction of the corresponding polynomials and Cotes numbers, are given. In particular, the important case of Chebyshev weight is analyzed. Finally, some applications in moment-preserving approximation of functions by defective splines are discussed.

Theory and generation of conditional, scalable sub-Gaussian random fields

NASA Astrophysics Data System (ADS)

Panzeri, M.; Riva, M.; Guadagnini, A.; Neuman, S. P.

2016-03-01

Many earth and environmental (as well as a host of other) variables, Y, and their spatial (or temporal) increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture key aspects of such non-Gaussian scaling by treating Y and/or ΔY as sub-Gaussian random fields (or processes). This however left unaddressed the empirical finding that whereas sample frequency distributions of Y tend to display relatively mild non-Gaussian peaks and tails, those of ΔY often reveal peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we proposed a generalized sub-Gaussian model (GSG) which resolves this apparent inconsistency between the statistical scaling behaviors of observed variables and their increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. Most importantly, we demonstrated the feasibility of estimating all parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments, ΔY. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random fields, introduce two approximate versions of this algorithm to reduce CPU time, and explore them on one and two-dimensional synthetic test cases.

The Gaussian-Lorentzian Sum, Product, and Convolution (Voigt) functions in the context of peak fitting X-ray photoelectron spectroscopy (XPS) narrow scans

NASA Astrophysics Data System (ADS)

Jain, Varun; Biesinger, Mark C.; Linford, Matthew R.

2018-07-01

X-ray photoelectron spectroscopy (XPS) is arguably the most important vacuum technique for surface chemical analysis, and peak fitting is an indispensable part of XPS data analysis. Functions that have been widely explored and used in XPS peak fitting include the Gaussian, Lorentzian, Gaussian-Lorentzian sum (GLS), Gaussian-Lorentzian product (GLP), and Voigt functions, where the Voigt function is a convolution of a Gaussian and a Lorentzian function. In this article we discuss these functions from a graphical perspective. Arguments based on convolution and the Central Limit Theorem are made to justify the use of functions that are intermediate between pure Gaussians and pure Lorentzians in XPS peak fitting. Mathematical forms for the GLS and GLP functions are presented with a mixing parameter m. Plots are shown for GLS and GLP functions with mixing parameters ranging from 0 to 1. There are fundamental differences between the GLS and GLP functions. The GLS function better follows the 'wings' of the Lorentzian, while these 'wings' are suppressed in the GLP. That is, these two functions are not interchangeable. The GLS and GLP functions are compared to the Voigt function, where the GLS is shown to be a decent approximation of it. Practically, both the GLS and the GLP functions can be useful for XPS peak fitting. Examples of the uses of these functions are provided herein.

Gaussianization for fast and accurate inference from cosmological data

NASA Astrophysics Data System (ADS)

Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.

2016-06-01

We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box-Cox transformations and generalizations thereof. This permits an analytical reconstruction of the posterior from a point sample, like a Markov chain, and simplifies the subsequent joint analysis with other experiments. This way, a multivariate posterior density can be reported efficiently, by compressing the information contained in Markov Chain Monte Carlo samples. Further, the model evidence integral (I.e. the marginal likelihood) can be computed analytically. This method is analogous to the search for normal parameters in the cosmic microwave background, but is more general. The search for the optimally Gaussianizing transformation is performed computationally through a maximum-likelihood formalism; its quality can be judged by how well the credible regions of the posterior are reproduced. We demonstrate that our method outperforms kernel density estimates in this objective. Further, we select marginal posterior samples from Planck data with several distinct strongly non-Gaussian features, and verify the reproduction of the marginal contours. To demonstrate evidence computation, we Gaussianize the joint distribution of data from weak lensing and baryon acoustic oscillations, for different cosmological models, and find a preference for flat Λcold dark matter. Comparing to values computed with the Savage-Dickey density ratio, and Population Monte Carlo, we find good agreement of our method within the spread of the other two.

Beam shape coefficients calculation for an elliptical Gaussian beam with 1-dimensional quadrature and localized approximation methods

NASA Astrophysics Data System (ADS)

Wang, Wei; Shen, Jianqi

2018-06-01

The use of a shaped beam for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively. Numerical techniques for evaluating the BSCs of a shaped beam, such as the quadrature, the localized approximation (LA), the integral localized approximation (ILA) methods, have been developed within the framework of generalized Lorenz-Mie theory (GLMT). The quadrature methods usually employ the 2-/3-dimensional integrations. In this work, the expressions of the BSCs for an elliptical Gaussian beam (EGB) are simplified into the 1-dimensional integral so as to speed up the numerical computation. Numerical results of BSCs are used to reconstruct the beam field and the fidelity of the reconstructed field to the given beam field is estimated. It is demonstrated that the proposed method is much faster than the 2-dimensional integrations and it can acquire more accurate results than the LA method. Limitations of the quadrature method and also the LA method in the numerical calculation are analyzed in detail.

A new probability distribution model of turbulent irradiance based on Born perturbation theory

NASA Astrophysics Data System (ADS)

Wang, Hongxing; Liu, Min; Hu, Hao; Wang, Qian; Liu, Xiguo

2010-10-01

The subject of the PDF (Probability Density Function) of the irradiance fluctuations in a turbulent atmosphere is still unsettled. Theory reliably describes the behavior in the weak turbulence regime, but theoretical description in the strong and whole turbulence regimes are still controversial. Based on Born perturbation theory, the physical manifestations and correlations of three typical PDF models (Rice-Nakagami, exponential-Bessel and negative-exponential distribution) were theoretically analyzed. It is shown that these models can be derived by separately making circular-Gaussian, strong-turbulence and strong-turbulence-circular-Gaussian approximations in Born perturbation theory, which denies the viewpoint that the Rice-Nakagami model is only applicable in the extremely weak turbulence regime and provides theoretical arguments for choosing rational models in practical applications. In addition, a common shortcoming of the three models is that they are all approximations. A new model, called the Maclaurin-spread distribution, is proposed without any approximation except for assuming the correlation coefficient to be zero. So, it is considered that the new model can exactly reflect the Born perturbation theory. Simulated results prove the accuracy of this new model.

The determination of modified barrier heights in Ti/GaN nano-Schottky diodes at high temperature.

PubMed

Lee, Seung-Yong; Kim, Tae-Hong; Chol, Nam-Kyu; Seong, Han-Kyu; Choi, Heon-Jin; Ahn, Byung-Guk; Lee, Sang-Kwon

2008-10-01

We have investigated the size-effect of the nano-Schottky diodes on the electrical transport properties and the temperature-dependent current transport mechanism in a metal-semiconductor nanowire junction (a Ti/GaN nano-Schottky diode) using current-voltage characterization in the range of 300-423 K. We found that the modified mean Schottky barrier height (SBH) was approximately 0.7 eV with a standard deviation of approximately 0.14 V using a Gaussian distribution model of the barrier heights. The slightly high value of the modified mean SBH (approximately 0.11 eV) compared to the results from the thin-film based Ti/GaN Schottky diodes could be due to an additional oxide layer at the interface between the Ti and GaN nanowires. Moreover, we found that the abnormal behavior of the barrier heights and the ideality factors in a Ti/GaN nano-Schottky diode at a temperature below 423 K could be explained by a combination of the enhancement of the tunneling current and a model with a Gaussian distribution of the barrier heights.

LD-SPatt: large deviations statistics for patterns on Markov chains.

PubMed

Nuel, G

2004-01-01

Statistics on Markov chains are widely used for the study of patterns in biological sequences. Statistics on these models can be done through several approaches. Central limit theorem (CLT) producing Gaussian approximations are one of the most popular ones. Unfortunately, in order to find a pattern of interest, these methods have to deal with tail distribution events where CLT is especially bad. In this paper, we propose a new approach based on the large deviations theory to assess pattern statistics. We first recall theoretical results for empiric mean (level 1) as well as empiric distribution (level 2) large deviations on Markov chains. Then, we present the applications of these results focusing on numerical issues. LD-SPatt is the name of GPL software implementing these algorithms. We compare this approach to several existing ones in terms of complexity and reliability and show that the large deviations are more reliable than the Gaussian approximations in absolute values as well as in terms of ranking and are at least as reliable as compound Poisson approximations. We then finally discuss some further possible improvements and applications of this new method.

Modular design and implementation of field-programmable-gate-array-based Gaussian noise generator

NASA Astrophysics Data System (ADS)

Li, Yuan-Ping; Lee, Ta-Sung; Hwang, Jeng-Kuang

2016-05-01

The modular design of a Gaussian noise generator (GNG) based on field-programmable gate array (FPGA) technology was studied. A new range reduction architecture was included in a series of elementary function evaluation modules and was integrated into the GNG system. The approximation and quantisation errors for the square root module with a first polynomial approximation were high; therefore, we used the central limit theorem (CLT) to improve the noise quality. This resulted in an output rate of one sample per clock cycle. We subsequently applied Newton's method for the square root module, thus eliminating the need for the use of the CLT because applying the CLT resulted in an output rate of two samples per clock cycle (>200 million samples per second). Two statistical tests confirmed that our GNG is of high quality. Furthermore, the range reduction, which is used to solve a limited interval of the function approximation algorithms of the System Generator platform using Xilinx FPGAs, appeared to have a higher numerical accuracy, was operated at >350 MHz, and can be suitably applied for any function evaluation.

Non-Gaussian analysis of diffusion weighted imaging in head and neck at 3T: a pilot study in patients with nasopharyngeal carcinoma.

PubMed

Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S P; Bhatia, Kunwar S; Wang, Yi-Xiang J; Ahuja, Anil T; King, Ann D

2014-01-01

To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm(2). DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization.

Modelling the excitation field of an optical resonator

NASA Astrophysics Data System (ADS)

Romanini, Daniele

2014-06-01

Assuming the paraxial approximation, we derive efficient recursive expressions for the projection coefficients of a Gaussian beam over the Gauss--Hermite transverse electro-magnetic (TEM) modes of an optical cavity. While previous studies considered cavities with cylindrical symmetry, our derivation accounts for "simple" astigmatism and ellipticity, which allows to deal with more realistic optical systems. The resulting expansion of the Gaussian beam over the cavity TEM modes provides accurate simulation of the excitation field distribution inside the cavity, in transmission, and in reflection. In particular, this requires including counter-propagating TEM modes, usually neglected in textbooks. As an illustrative application to a complex case, we simulate reentrant cavity configurations where Herriott spots are obtained at cavity output. We show that the case of an astigmatic cavity is also easily modelled. To our knowledge, such relevant applications are usually treated under the simplified geometrical optics approximation, or using heavier numerical methods.

Semiparametric Identification of Human Arm Dynamics for Flexible Control of a Functional Electrical Stimulation Neuroprosthesis

PubMed Central

Schearer, Eric M.; Liao, Yu-Wei; Perreault, Eric J.; Tresch, Matthew C.; Memberg, William D.; Kirsch, Robert F.; Lynch, Kevin M.

2016-01-01

We present a method to identify the dynamics of a human arm controlled by an implanted functional electrical stimulation neuroprosthesis. The method uses Gaussian process regression to predict shoulder and elbow torques given the shoulder and elbow joint positions and velocities and the electrical stimulation inputs to muscles. We compare the accuracy of torque predictions of nonparametric, semiparametric, and parametric model types. The most accurate of the three model types is a semiparametric Gaussian process model that combines the flexibility of a black box function approximator with the generalization power of a parameterized model. The semiparametric model predicted torques during stimulation of multiple muscles with errors less than 20% of the total muscle torque and passive torque needed to drive the arm. The identified model allows us to define an arbitrary reaching trajectory and approximately determine the muscle stimulations required to drive the arm along that trajectory. PMID:26955041

THE DISTRIBUTION OF COOK’S D STATISTIC

PubMed Central

Muller, Keith E.; Mok, Mario Chen

2013-01-01

Cook (1977) proposed a diagnostic to quantify the impact of deleting an observation on the estimated regression coefficients of a General Linear Univariate Model (GLUM). Simulations of models with Gaussian response and predictors demonstrate that his suggestion of comparing the diagnostic to the median of the F for overall regression captures an erratically varying proportion of the values. We describe the exact distribution of Cook’s statistic for a GLUM with Gaussian predictors and response. We also present computational forms, simple approximations, and asymptotic results. A simulation supports the accuracy of the results. The methods allow accurate evaluation of a single value or the maximum value from a regression analysis. The approximations work well for a single value, but less well for the maximum. In contrast, the cut-point suggested by Cook provides widely varying tail probabilities. As with all diagnostics, the data analyst must use scientific judgment in deciding how to treat highlighted observations. PMID:24363487

Detailed noise statistics for an optically preamplified direct detection receiver

NASA Astrophysics Data System (ADS)

Danielsen, Soeren Lykke; Mikkelsen, Benny; Durhuus, Terji; Joergensen, Carsten; Stubkjaer, Kristian E.

We describe the exact statistics of an optically preamplified direct detection receiver by means of the moment generating function. The theory allows an arbitrary shaped electrical filter in the receiver circuit. The moment generating function (MGF) allows for a precise calculation of the error rate by using the inverse Fast Fourier transform (FFT). The exact results are compared with the usual Gaussian approximation (GA), the saddlepoint approximation (SAP) and the modified Chernoff bound (MCB). This comparison shows that the noise is not Gaussian distributed for all values of the optical amplifier gain. In the region from 20-30 dB gain, calculations shows that the GA underestimates the receiver sensitivity while the SAP is very close to the results of our exact model. Using the MGF derived in the article we then find the optimal bandwidth of the electrical filter in the receiver circuit and calculate the sensitivity degradation due to inter symbol interference (ISI).

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

A Gaussian Wave Packet Propagation Approach to Vibrationally Resolved Optical Spectra at Non-Zero Temperatures.

PubMed

Reddy, Ch Sridhar; Prasad, M Durga

2016-04-28

An effective time dependent approach based on a method that is similar to the Gaussian wave packet propagation (GWP) technique of Heller is developed for the computation of vibrationally resolved electronic spectra at finite temperatures in the harmonic, Franck-Condon/Hertzberg-Teller approximations. Since the vibrational thermal density matrix of the ground electronic surface and the time evolution operator on that surface commute, it is possible to write the spectrum generating correlation function as a trace of the time evolved doorway state. In the stated approximations, the doorway state is a superposition of the harmonic oscillator zero and one quantum eigenfunctions and thus can be propagated by the GWP. The algorithm has an O(N(3)) dependence on the number of vibrational modes. An application to pyrene absorption spectrum at two temperatures is presented as a proof of the concept.

Ridge Minimization of Ablated Morphologies on ITO Thin Films Using Squared Quasi-Flat Top Beam

PubMed Central

Jeon, Jin-Woo; Choi, Wonsuk; Shin, Young-Gwan; Ji, Suk-Young

2018-01-01

In this study, we explore the improvements in pattern quality that was obtained with a femtosecond laser with quasi-flat top beam profiles at the ablated edge of indium tin oxide (ITO) thin films for the patterning of optoelectronic devices. To ablate the ITO thin films, a femtosecond laser is used that has a wavelength and pulse duration of 1030 nm and 190 fs, respectively. The squared quasi-flat top beam is obtained from a circular Gaussian beam using slits with varying x-y axes. Then, the patterned ITO thin films are measured using both scanning electron and atomic force microscopes. In the case of the Gaussian beam, the ridge height and width are approximately 39 nm and 1.1 μm, respectively, whereas, when the quasi-flat top beam is used, the ridge height and width are approximately 7 nm and 0.25 μm, respectively. PMID:29601515

Almost sure convergence in quantum spin glasses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buzinski, David, E-mail: dab197@case.edu; Meckes, Elizabeth, E-mail: elizabeth.meckes@case.edu

2015-12-15

Recently, Keating, Linden, and Wells [Markov Processes Relat. Fields 21(3), 537-555 (2015)] showed that the density of states measure of a nearest-neighbor quantum spin glass model is approximately Gaussian when the number of particles is large. The density of states measure is the ensemble average of the empirical spectral measure of a random matrix; in this paper, we use concentration of measure and entropy techniques together with the result of Keating, Linden, and Wells to show that in fact the empirical spectral measure of such a random matrix is almost surely approximately Gaussian itself with no ensemble averaging. We alsomore » extend this result to a spherical quantum spin glass model and to the more general coupling geometries investigated by Erdős and Schröder [Math. Phys., Anal. Geom. 17(3-4), 441–464 (2014)].« less

Free energy calculations, enhanced by a Gaussian ansatz, for the "chemical work" distribution.

PubMed

Boulougouris, Georgios C

2014-05-15

The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the "chemical work" of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the "irreversible" work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible "chemical work" minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the "chemical work," accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the "chemical work." For a more general free energy perturbation scheme that the Gaussian ansatz may not be valid, the free energy calculation can be expressed in terms of the moment generating function of the "chemical work" distribution. Copyright © 2014 Wiley Periodicals, Inc.

Digital processing of satellite imagery application to jungle areas of Peru

NASA Technical Reports Server (NTRS)

Pomalaza, J. C. (Principal Investigator); Pomalaza, C. A.; Espinoza, J.

1976-01-01

The author has identified the following significant results. The use of clustering methods permits the development of relatively fast classification algorithms that could be implemented in an inexpensive computer system with limited amount of memory. Analysis of CCTs using these techniques can provide a great deal of detail permitting the use of the maximum resolution of LANDSAT imagery. Potential cases were detected in which the use of other techniques for classification using a Gaussian approximation for the distribution functions can be used with advantage. For jungle areas, channels 5 and 7 can provide enough information to delineate drainage patterns, swamp and wet areas, and make a reasonable broad classification of forest types.

Propagation properties of hollow sinh-Gaussian beams through fractional Fourier transform optical systems

NASA Astrophysics Data System (ADS)

Tang, Bin; Jiang, ShengBao; Jiang, Chun; Zhu, Haibin

2014-07-01

A hollow sinh-Gaussian beam (HsG) is an appropriate model to describe the dark-hollow beam. Based on Collins integral formula and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of a HsG beam passing through fractional Fourier transform (FRFT) optical systems with and without apertures have been studied in detail by some typical numerical examples. The results obtained using the approximate analytical formula are in good agreement with those obtained using numerical integral calculation. Further, the studies indicate that the normalized intensity distribution of the HsG beam in FRFT plane is closely related with not only the fractional order but also the beam order and the truncation parameter. The FRFT optical systems provide a convenient way for laser beam shaping.

Progress in integrated-circuit horn antennas for receiver applications. Part 1: Antenna design

NASA Technical Reports Server (NTRS)

Eleftheriades, George V.; Ali-Ahmad, Walid Y.; Rebeiz, Gabriel M.

1992-01-01

The purpose of this work is to present a systematic method for the design of multimode quasi-integrated horn antennas. The design methodology is based on the Gaussian beam approach and the structures are optimized for achieving maximum fundamental Gaussian coupling efficiency. For this purpose, a hybrid technique is employed in which the integrated part of the antennas is treated using full-wave analysis, whereas the machined part is treated using an approximate method. This results in a simple and efficient design process. The developed design procedure has been applied for the design of a 20, a 23, and a 25 dB quasi-integrated horn antennas, all with a Gaussian coupling efficiency exceeding 97 percent. The designed antennas have been tested and characterized using both full-wave analysis and 90 GHz/370 GHz measurements.

A sharp interpolation between the Hölder and Gaussian Young inequalities

NASA Astrophysics Data System (ADS)

da Pelo, Paolo; Lanconelli, Alberto; Stan, Aurel I.

2016-03-01

We prove a very general sharp inequality of the Hölder-Young-type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative products for functions which interpolates between the pointwise and Wick products; this family arises naturally in the context of stochastic differential equations, through Wong-Zakai-type approximation theorems, and plays a key role in some generalizations of the Beckner-type Poincaré inequality. We then obtain a crucial integral representation for that family of products which is employed, together with a generalization of the classic Young inequality due to Lieb, to prove our main theorem. We stress that our main inequality contains as particular cases the Hölder inequality and Nelson’s hyper-contractive estimate, thus providing a unified framework for two fundamental results of the Gaussian analysis.

Computationally efficient algorithm for Gaussian Process regression in case of structured samples

NASA Astrophysics Data System (ADS)

Belyaev, M.; Burnaev, E.; Kapushev, Y.

2016-04-01

Surrogate modeling is widely used in many engineering problems. Data sets often have Cartesian product structure (for instance factorial design of experiments with missing points). In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation-Gaussian Process regression-can be hardly applied due to its computational complexity. In this paper a computationally efficient approach for constructing Gaussian Process regression in case of data sets with Cartesian product structure is presented. Efficiency is achieved by using a special structure of the data set and operations with tensors. Proposed algorithm has low computational as well as memory complexity compared to existing algorithms. In this work we also introduce a regularization procedure allowing to take into account anisotropy of the data set and avoid degeneracy of regression model.

Efficient evaluation of Coulomb integrals in a mixed Gaussian and plane-wave basis using the density fitting and Cholesky decomposition.

PubMed

Čársky, Petr; Čurík, Roman; Varga, Štefan

2012-03-21

The objective of this paper is to show that the density fitting (resolution of the identity approximation) can also be applied to Coulomb integrals of the type (k(1)(1)k(2)(1)|g(1)(2)g(2)(2)), where k and g symbols refer to plane-wave functions and gaussians, respectively. We have shown how to achieve the accuracy of these integrals that is needed in wave-function MO and density functional theory-type calculations using mixed Gaussian and plane-wave basis sets. The crucial issues for achieving such a high accuracy are application of constraints for conservation of the number electrons and components of the dipole moment, optimization of the auxiliary basis set, and elimination of round-off errors in the matrix inversion. © 2012 American Institute of Physics

Quantifying non-Markovianity of continuous-variable Gaussian dynamical maps

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasile, Ruggero; Maniscalco, Sabrina; Paris, Matteo G. A.

2011-11-15

We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer et al.[Phys. Rev. Lett. 103, 210401 (2009);], that is, by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow ofmore » information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit.« less

Characterization of Adrenal Adenoma by Gaussian Model-Based Algorithm.

PubMed

Hsu, Larson D; Wang, Carolyn L; Clark, Toshimasa J

2016-01-01

We confirmed that computed tomography (CT) attenuation values of pixels in an adrenal nodule approximate a Gaussian distribution. Building on this and the previously described histogram analysis method, we created an algorithm that uses mean and standard deviation to estimate the percentage of negative attenuation pixels in an adrenal nodule, thereby allowing differentiation of adenomas and nonadenomas. The institutional review board approved both components of this study in which we developed and then validated our criteria. In the first, we retrospectively assessed CT attenuation values of adrenal nodules for normality using a 2-sample Kolmogorov-Smirnov test. In the second, we evaluated a separate cohort of patients with adrenal nodules using both the conventional 10HU unit mean attenuation method and our Gaussian model-based algorithm. We compared the sensitivities of the 2 methods using McNemar's test. A total of 183 of 185 observations (98.9%) demonstrated a Gaussian distribution in adrenal nodule pixel attenuation values. The sensitivity and specificity of our Gaussian model-based algorithm for identifying adrenal adenoma were 86.1% and 83.3%, respectively. The sensitivity and specificity of the mean attenuation method were 53.2% and 94.4%, respectively. The sensitivities of the 2 methods were significantly different (P value < 0.001). In conclusion, the CT attenuation values within an adrenal nodule follow a Gaussian distribution. Our Gaussian model-based algorithm can characterize adrenal adenomas with higher sensitivity than the conventional mean attenuation method. The use of our algorithm, which does not require additional postprocessing, may increase workflow efficiency and reduce unnecessary workup of benign nodules. Copyright © 2016 Elsevier Inc. All rights reserved.

Theory of the fundamental vibration-rotation-translation spectrum of H2 in a C60 lattice

NASA Astrophysics Data System (ADS)

Herman, Roger M.; Lewis, John Courtenay

2006-04-01

Calculations are presented for the fundamental vibration-rotation spectrum of H2 in fcc C60 (fullerite) lattices. The principal features are identified as lattice-shifted “vibration-rotation-translation” state absorption transitions. The level spacings of the H2 modes are calculated numerically for the potential function resulting from the summation of the individual C-H2 potentials for all C atoms in the six nearest neighbor C60 molecules. The potential is approximately separable in Cartesian coordinates, giving a very good approximation to exactly calculated translational energies for the lower levels. The positions and relative strengths of the individual transitions are calculated from the eigenfunctions for this separable potential. The line shapes are assumed to be Lorentzian, and the widths are chosen so as to give good fits to the DRIFT spectrum of FitzGerald [Phys. Rev. B 65, 140302(R) (2002)]. A theory of the C-H2 induced dipole moment is developed with which to calculate intensities. In order to fit the observed DRIFTS transition frequencies it is found necessary to take the overlap part of the C-H2 potential to be about 13% longer in range than the C-H2 potential in graphene. Furthermore, differences in the theoretical spectra obtained with a near-optimal exp-6 potential and near-optimal Lennard-Jones 12-6 potential are clearly evident, with the exp-6 potential giving a better fit to observation than the Lennard-Jones potential. Similarly, Lorentzian line shapes assumed for the individual transitions yield better agreement with observation than Gaussian line shapes.

Gaussian basis functions for highly oscillatory scattering wavefunctions

NASA Astrophysics Data System (ADS)

Mant, B. P.; Law, M. M.

2018-04-01

We have applied a basis set of distributed Gaussian functions within the S-matrix version of the Kohn variational method to scattering problems involving deep potential energy wells. The Gaussian positions and widths are tailored to the potential using the procedure of Bačić and Light (1986 J. Chem. Phys. 85 4594) which has previously been applied to bound-state problems. The placement procedure is shown to be very efficient and gives scattering wavefunctions and observables in agreement with direct numerical solutions. We demonstrate the basis function placement method with applications to hydrogen atom–hydrogen atom scattering and antihydrogen atom–hydrogen atom scattering.

Regularized wave equation migration for imaging and data reconstruction

NASA Astrophysics Data System (ADS)

Kaplan, Sam T.

The reflection seismic experiment results in a measurement (reflection seismic data) of the seismic wavefield. The linear Born approximation to the seismic wavefield leads to a forward modelling operator that we use to approximate reflection seismic data in terms of a scattering potential. We consider approximations to the scattering potential using two methods: the adjoint of the forward modelling operator (migration), and regularized numerical inversion using the forward and adjoint operators. We implement two parameterizations of the forward modelling and migration operators: source-receiver and shot-profile. For both parameterizations, we find requisite Green's function using the split-step approximation. We first develop the forward modelling operator, and then find the adjoint (migration) operator by recognizing a Fredholm integral equation of the first kind. The resulting numerical system is generally under-determined, requiring prior information to find a solution. In source-receiver migration, the parameterization of the scattering potential is understood using the migration imaging condition, and this encourages us to apply sparse prior models to the scattering potential. To that end, we use both a Cauchy prior and a mixed Cauchy-Gaussian prior, finding better resolved estimates of the scattering potential than are given by the adjoint. In shot-profile migration, the parameterization of the scattering potential has its redundancy in multiple active energy sources (i.e. shots). We find that a smallest model regularized inverse representation of the scattering potential gives a more resolved picture of the earth, as compared to the simpler adjoint representation. The shot-profile parameterization allows us to introduce a joint inversion to further improve the estimate of the scattering potential. Moreover, it allows us to introduce a novel data reconstruction algorithm so that limited data can be interpolated/extrapolated. The linearized operators are expensive, encouraging their parallel implementation. For the source-receiver parameterization of the scattering potential this parallelization is non-trivial. Seismic data is typically corrupted by various types of noise. Sparse coding can be used to suppress noise prior to migration. It is a method that stems from information theory and that we apply to noise suppression in seismic data.

Probabilistic analysis and fatigue damage assessment of offshore mooring system due to non-Gaussian bimodal tension processes

NASA Astrophysics Data System (ADS)

Chang, Anteng; Li, Huajun; Wang, Shuqing; Du, Junfeng

2017-08-01

Both wave-frequency (WF) and low-frequency (LF) components of mooring tension are in principle non-Gaussian due to nonlinearities in the dynamic system. This paper conducts a comprehensive investigation of applicable probability density functions (PDFs) of mooring tension amplitudes used to assess mooring-line fatigue damage via the spectral method. Short-term statistical characteristics of mooring-line tension responses are firstly investigated, in which the discrepancy arising from Gaussian approximation is revealed by comparing kurtosis and skewness coefficients. Several distribution functions based on present analytical spectral methods are selected to express the statistical distribution of the mooring-line tension amplitudes. Results indicate that the Gamma-type distribution and a linear combination of Dirlik and Tovo-Benasciutti formulas are suitable for separate WF and LF mooring tension components. A novel parametric method based on nonlinear transformations and stochastic optimization is then proposed to increase the effectiveness of mooring-line fatigue assessment due to non-Gaussian bimodal tension responses. Using time domain simulation as a benchmark, its accuracy is further validated using a numerical case study of a moored semi-submersible platform.

Edge detection - Image-plane versus digital processing

NASA Technical Reports Server (NTRS)

Huck, Friedrich O.; Fales, Carl L.; Park, Stephen K.; Triplett, Judith A.

1987-01-01

To optimize edge detection with the familiar Laplacian-of-Gaussian operator, it has become common to implement this operator with a large digital convolution mask followed by some interpolation of the processed data to determine the zero crossings that locate edges. It is generally recognized that this large mask causes substantial blurring of fine detail. It is shown that the spatial detail can be improved by a factor of about four with either the Wiener-Laplacian-of-Gaussian filter or an image-plane processor. The Wiener-Laplacian-of-Gaussian filter minimizes the image-gathering degradations if the scene statistics are at least approximately known and also serves as an interpolator to determine the desired zero crossings directly. The image-plane processor forms the Laplacian-of-Gaussian response by properly combining the optical design of the image-gathering system with a minimal three-by-three lateral-inhibitory processing mask. This approach, which is suggested by Marr's model of early processing in human vision, also reduces data processing by about two orders of magnitude and data transmission by up to an order of magnitude.

Multi-Target Tracking Using an Improved Gaussian Mixture CPHD Filter.

PubMed

Si, Weijian; Wang, Liwei; Qu, Zhiyu

2016-11-23

The cardinalized probability hypothesis density (CPHD) filter is an alternative approximation to the full multi-target Bayesian filter for tracking multiple targets. However, although the joint propagation of the posterior intensity and cardinality distribution in its recursion allows more reliable estimates of the target number than the PHD filter, the CPHD filter suffers from the spooky effect where there exists arbitrary PHD mass shifting in the presence of missed detections. To address this issue in the Gaussian mixture (GM) implementation of the CPHD filter, this paper presents an improved GM-CPHD filter, which incorporates a weight redistribution scheme into the filtering process to modify the updated weights of the Gaussian components when missed detections occur. In addition, an efficient gating strategy that can adaptively adjust the gate sizes according to the number of missed detections of each Gaussian component is also presented to further improve the computational efficiency of the proposed filter. Simulation results demonstrate that the proposed method offers favorable performance in terms of both estimation accuracy and robustness to clutter and detection uncertainty over the existing methods.

Accuracy of maximum likelihood and least-squares estimates in the lidar slope method with noisy data.

PubMed

Eberhard, Wynn L

2017-04-01

The maximum likelihood estimator (MLE) is derived for retrieving the extinction coefficient and zero-range intercept in the lidar slope method in the presence of random and independent Gaussian noise. Least-squares fitting, weighted by the inverse of the noise variance, is equivalent to the MLE. Monte Carlo simulations demonstrate that two traditional least-squares fitting schemes, which use different weights, are less accurate. Alternative fitting schemes that have some positive attributes are introduced and evaluated. The principal factors governing accuracy of all these schemes are elucidated. Applying these schemes to data with Poisson rather than Gaussian noise alters accuracy little, even when the signal-to-noise ratio is low. Methods to estimate optimum weighting factors in actual data are presented. Even when the weighting estimates are coarse, retrieval accuracy declines only modestly. Mathematical tools are described for predicting retrieval accuracy. Least-squares fitting with inverse variance weighting has optimum accuracy for retrieval of parameters from single-wavelength lidar measurements when noise, errors, and uncertainties are Gaussian distributed, or close to optimum when only approximately Gaussian.

FROM FINANCE TO COSMOLOGY: THE COPULA OF LARGE-SCALE STRUCTURE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scherrer, Robert J.; Berlind, Andreas A.; Mao, Qingqing

2010-01-01

Any multivariate distribution can be uniquely decomposed into marginal (one-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an important new methodology for analyzing the density field in large-scale structure. We derive the empirical two-point copula for the evolved dark matter density field. We find that this empirical copula is well approximated by a Gaussian copula. We consider the possibility that the full n-point copula is also Gaussian and describe some of the consequences of this hypothesis. Future directions for investigation are discussed.

Effect of turbulent atmosphere on the on-axis average intensity of Pearcey-Gaussian beam

NASA Astrophysics Data System (ADS)

F, Boufalah; L, Dalil-Essakali; H, Nebdi; A, Belafhal

2016-06-01

The propagation characteristics of the Pearcey-Gaussian (PG) beam in turbulent atmosphere are investigated in this paper. The Pearcey beam is a new kind of paraxial beam, based on the Pearcey function of catastrophe theory, which describes diffraction about a cusp caustic. By using the extended Huygens-Fresnel integral formula in the paraxial approximation and the Rytov theory, an analytical expression of axial intensity for the considered beam family is derived. Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors, including incident beam parameters and turbulence strengths.

Stochastic transfer of polarized radiation in finite cloudy atmospheric media with reflective boundaries

NASA Astrophysics Data System (ADS)

Sallah, M.

2014-03-01

The problem of monoenergetic radiative transfer in a finite planar stochastic atmospheric medium with polarized (vector) Rayleigh scattering is proposed. The solution is presented for an arbitrary absorption and scattering cross sections. The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as reflectivity and transmissivity, for an arbitrary correlation function. A modified Gaussian probability distribution function is also used to average the solution in order to exclude the probable negative values of the optical variable. Pomraning-Eddington approximation is used, at first, to obtain the deterministic analytical solution for both the total intensity and the difference function used to describe the polarized radiation. The problem is treated with specular reflecting boundaries and angular-dependent externally incident flux upon the medium from one side and with no flux from the other side. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the average reflectivity and average transmissivity are obtained for both Gaussian and modified Gaussian probability density functions at the different degrees of polarization.

Novel theory for propagation of tilted Gaussian beam through aligned optical system

NASA Astrophysics Data System (ADS)

Xia, Lei; Gao, Yunguo; Han, Xudong

2017-03-01

A novel theory for tilted beam propagation is established in this paper. By setting the propagation direction of the tilted beam as the new optical axis, we establish a virtual optical system that is aligned with the new optical axis. Within the first order approximation of the tilt and off-axis, the propagation of the tilted beam is studied in the virtual system instead of the actual system. To achieve more accurate optical field distributions of tilted Gaussian beams, a complete diffraction integral for a misaligned optical system is derived by using the matrix theory with angular momentums. The theory demonstrates that a tilted TEM00 Gaussian beam passing through an aligned optical element transforms into a decentered Gaussian beam along the propagation direction. The deviations between the peak intensity axis of the decentered Gaussian beam and the new optical axis have linear relationships with the misalignments in the virtual system. ZEMAX simulation of a tilted beam through a thick lens exposed to air shows that the errors between the simulation results and theoretical calculations of the position deviations are less than 2‰ when the misalignments εx, εy, εx', εy' are in the range of [-0.5, 0.5] mm and [-0.5, 0.5]°.

Occupancy mapping and surface reconstruction using local Gaussian processes with Kinect sensors.

PubMed

Kim, Soohwan; Kim, Jonghyuk

2013-10-01

Although RGB-D sensors have been successfully applied to visual SLAM and surface reconstruction, most of the applications aim at visualization. In this paper, we propose a noble method of building continuous occupancy maps and reconstructing surfaces in a single framework for both navigation and visualization. Particularly, we apply a Bayesian nonparametric approach, Gaussian process classification, to occupancy mapping. However, it suffers from high-computational complexity of O(n(3))+O(n(2)m), where n and m are the numbers of training and test data, respectively, limiting its use for large-scale mapping with huge training data, which is common with high-resolution RGB-D sensors. Therefore, we partition both training and test data with a coarse-to-fine clustering method and apply Gaussian processes to each local clusters. In addition, we consider Gaussian processes as implicit functions, and thus extract iso-surfaces from the scalar fields, continuous occupancy maps, using marching cubes. By doing that, we are able to build two types of map representations within a single framework of Gaussian processes. Experimental results with 2-D simulated data show that the accuracy of our approximated method is comparable to previous work, while the computational time is dramatically reduced. We also demonstrate our method with 3-D real data to show its feasibility in large-scale environments.

Non-Gaussian Analysis of Diffusion Weighted Imaging in Head and Neck at 3T: A Pilot Study in Patients with Nasopharyngeal Carcinoma

PubMed Central

Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S. P.; Bhatia, Kunwar S.; Wang, Yi-Xiang J.; Ahuja, Anil T.; King, Ann D.

2014-01-01

Purpose To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). Materials and Methods After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm2. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Results Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Conclusion Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization. PMID:24466318

Variational mixed quantum/semiclassical simulation of dihalogen guest and rare-gas solid host dynamics

NASA Astrophysics Data System (ADS)

Cheng, Xiaolu; Cina, Jeffrey A.

2014-07-01

A variational mixed quantum-semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested, and used to simulate the temporal evolution of nonstationary states of the internal molecular and surrounding medium degrees of freedom. In this theory, termed the Fixed Vibrational Basis/Gaussian Bath (FVB/GB) method, the system is treated fully quantum mechanically while Gaussian wave packets are used for the bath degrees of freedom. An approximate time-dependent wave function of the entire model is obtained instead of just a reduced system density matrix, so the theory enables the analysis of the entangled system and bath dynamics that ensues following initial displacement of the internal-molecular (system) coordinate from its equilibrium position. The norm- and energy-conserving properties of the propagation of our trial wave function are natural consequences of the Dirac-Frenkel-McLachlan variational principle. The variational approach also stabilizes the time evolution in comparison to the same ansatz propagated under a previously employed locally quadratic approximation to the bath potential and system-bath interaction terms in the bath-parameter equations of motion. Dynamics calculations are carried out for molecular iodine in a 2D krypton lattice that reveal both the time-course of vibrational decoherence and the details of host-atom motion accompanying energy dissipation and dephasing. This work sets the stage for the comprehensive simulation of ultrafast time-resolved optical experiments on small molecules in low-temperature solids.

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States

NASA Astrophysics Data System (ADS)

Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas

2017-11-01

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States.

PubMed

Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas

2017-11-03

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

Hamiltonian chaos acts like a finite energy reservoir: accuracy of the Fokker-Planck approximation.

PubMed

Riegert, Anja; Baba, Nilüfer; Gelfert, Katrin; Just, Wolfram; Kantz, Holger

2005-02-11

The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic approximation on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.

Second harmonic sound field after insertion of a biological tissue sample

NASA Astrophysics Data System (ADS)

Zhang, Dong; Gong, Xiu-Fen; Zhang, Bo

2002-01-01

Second harmonic sound field after inserting a biological tissue sample is investigated by theory and experiment. The sample is inserted perpendicular to the sound axis, whose acoustical properties are different from those of surrounding medium (distilled water). By using the superposition of Gaussian beams and the KZK equation in quasilinear and parabolic approximations, the second harmonic field after insertion of the sample can be derived analytically and expressed as a linear combination of self- and cross-interaction of the Gaussian beams. Egg white, egg yolk, porcine liver, and porcine fat are used as the samples and inserted in the sound field radiated from a 2 MHz uniformly excited focusing source. Axial normalized sound pressure curves of the second harmonic wave before and after inserting the sample are measured and compared with the theoretical results calculated with 10 items of Gaussian beam functions.

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

PubMed Central

Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.

2017-01-01

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537

Two-time correlation function of an open quantum system in contact with a Gaussian reservoir

NASA Astrophysics Data System (ADS)

Ban, Masashi; Kitajima, Sachiko; Shibata, Fumiaki

2018-05-01

An exact formula of a two-time correlation function is derived for an open quantum system which interacts with a Gaussian thermal reservoir. It is provided in terms of functional derivative with respect to fictitious fields. A perturbative expansion and its diagrammatic representation are developed, where the small expansion parameter is related to a correlation time of the Gaussian thermal reservoir. The two-time correlation function of the lowest order is equivalent to that calculated by means of the quantum regression theorem. The result clearly shows that the violation of the quantum regression theorem is caused by a finiteness of the reservoir correlation time. By making use of an exactly solvable model consisting of a two-level system and a set of harmonic oscillators, it is shown that the two-time correlation function up to the first order is a good approximation to the exact one.

Gaussian impurity moving through a Bose-Einstein superfluid

NASA Astrophysics Data System (ADS)

Pinsker, Florian

2017-09-01

In this paper a finite Gaussian impurity moving through an equilibrium Bose-Einstein condensate at T = 0 is studied. The problem can be described by a Gross-Pitaevskii equation, which is solved perturbatively. The analysis is done for systems of 2 and 3 spatial dimensions. The Bogoliubov equation solutions for the condensate perturbed by a finite impurity are calculated in the co-moving frame. From these solutions the total energy of the perturbed system is determined as a function of the width and the amplitude of the moving Gaussian impurity and its velocity. In addition we derive the drag force the finite sized impurity approximately experiences as it moves through the superfluid, which proves the existence of a superfluid phase for finite extensions of the impurities below the speed of sound. Finally we find that the force increases with velocity until an inflection point from which it decreases again in 2 and 3d.

Approximating high angular resolution apparent diffusion coefficient profiles using spherical harmonics under BiGaussian assumption

NASA Astrophysics Data System (ADS)

Cao, Ning; Liang, Xuwei; Zhuang, Qi; Zhang, Jun

2009-02-01

Magnetic Resonance Imaging (MRI) techniques have achieved much importance in providing visual and quantitative information of human body. Diffusion MRI is the only non-invasive tool to obtain information of the neural fiber networks of the human brain. The traditional Diffusion Tensor Imaging (DTI) is only capable of characterizing Gaussian diffusion. High Angular Resolution Diffusion Imaging (HARDI) extends its ability to model more complex diffusion processes. Spherical harmonic series truncated to a certain degree is used in recent studies to describe the measured non-Gaussian Apparent Diffusion Coefficient (ADC) profile. In this study, we use the sampling theorem on band-limited spherical harmonics to choose a suitable degree to truncate the spherical harmonic series in the sense of Signal-to-Noise Ratio (SNR), and use Monte Carlo integration to compute the spherical harmonic transform of human brain data obtained from icosahedral schema.

Small target detection based on difference accumulation and Gaussian curvature under complex conditions

NASA Astrophysics Data System (ADS)

Zhang, He; Niu, Yanxiong; Zhang, Hao

2017-12-01

Small target detection is a significant subject in infrared search and track and other photoelectric imaging systems. The small target is imaged under complex conditions, which contains clouds, horizon and bright part. In this paper, a novel small target detection method is proposed based on difference accumulation, clustering and Gaussian curvature. Difference accumulation varies from regions. Therefore, after obtaining difference accumulations, clustering is applied to determine whether the pixel belongs to the heterogeneous region, and eliminate heterogeneous region. Then Gaussian curvature is used to separate target from the homogeneous region. Experiments are conducted for verification, along with comparisons to several other methods. The experimental results demonstrate that our method has an advantage of 1-2 orders of magnitude on SCRG and BSF than others. Given that the false alarm rate is 1, the detection probability can be approximately 0.9 by using proposed method.

Interpretation of Extinction in Gaussian-Beam Scattering

NASA Technical Reports Server (NTRS)

Lock, James A.

1995-01-01

The extinction efficiency for the interaction of a plane wave with a large nonabsorbing spherical particle is approximately 2.0. When a Gaussian beam of half-width w(sub 0) is incident upon a spherical particle of radius a with w(sub 0)/a less than 1, the extinction efficiency attains unexpectedly high or low values, contrary to intuitive expectations. The reason for this is associated with the so-called compensating term in the scattered field, which cancels the field of the Gaussian beam behind the particle, thereby producing the particle's shadow. I introduce a decomposition of the total exterior field into incoming and outgoing portions that are free of compensating terms. It is then shown that a suitably defined interaction efficiency has the intuitively expected asymptotic values of 2.0 for w(sub 0)/a much greater than 1 and 1.0 for w(sub 0)/a much less than 1.

Geometrical Description of fractional quantum Hall quasiparticles

NASA Astrophysics Data System (ADS)

Park, Yeje; Yang, Bo; Haldane, F. D. M.

2012-02-01

We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized ``guiding-center spin'' times the Gaussian curvature of a ``guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as ``punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation.

Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iacob, Felix, E-mail: felix@physics.uvt.ro; Lute, Marina, E-mail: marina.lute@upt.ro

2015-12-15

We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.

This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms--theory and practice.

PubMed

Harmany, Zachary T; Marcia, Roummel F; Willett, Rebecca M

2012-03-01

Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

Comparison of dynamical approximation schemes for non-linear gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present.

An unconventional adaptation of a classical Gaussian plume dispersion scheme for the fast assessment of external irradiation from a radioactive cloud

NASA Astrophysics Data System (ADS)

Pecha, Petr; Pechova, Emilie

2014-06-01

This article focuses on derivation of an effective algorithm for the fast estimation of cloudshine doses/dose rates induced by a large mixture of radionuclides discharged into the atmosphere. A certain special modification of the classical Gaussian plume approach is proposed for approximation of the near-field dispersion problem. Specifically, the accidental radioactivity release is subdivided into consecutive one-hour Gaussian segments, each driven by a short-term meteorological forecast for the respective hours. Determination of the physical quantity of photon fluence rate from an ambient cloud irradiation is coupled to a special decomposition of the Gaussian plume shape into the equivalent virtual elliptic disks. It facilitates solution of the formerly used time-consuming 3-D integration and provides advantages with regard to acceleration of the computational process on a local scale. An optimal choice of integration limit is adopted on the basis of the mean free path of γ-photons in the air. An efficient approach is introduced for treatment of a wide range of energetic spectrum of the emitted photons when the usual multi-nuclide approach is replaced by a new multi-group scheme. The algorithm is capable of generating the radiological responses in a large net of spatial nodes. It predetermines the proposed procedure such as a proper tool for online data assimilation analysis in the near-field areas. A specific technique for numerical integration is verified on the basis of comparison with a partial analytical solution. Convergence of the finite cloud approximation to the tabulated semi-infinite cloud values for dose conversion factors was validated.

Phenomenological Study of Interaction between Solar Acoustic Waves and Sunspots from Measured Scattered Wavefunctions

NASA Astrophysics Data System (ADS)

Yang, Ming-Hsu; Chou, Dean-Yi; Zhao, Hui; Liang, Zhi-Chao

2012-08-01

The solar acoustic waves around a sunspot are modified because of the interaction with the sunspot. The interaction can be viewed as that the sunspot, excited by the incident wave, generates the scattered wave, and the scattered wave is added to the incident wave to form the total wave around the sunspot. We define an interaction parameter, which could be complex, describing the interaction between the acoustic waves and the sunspot. The scattered wavefunction on the surface can be expressed as a two-dimensional integral of the product of the Green's function, the wavefunction, and the two-dimensional interaction parameter over the sunspot area for the Born approximation of different orders. We assume a simple model for the two-dimensional interaction parameter distribution: its absolute value is axisymmetric with a Gaussian distribution and its phase is a constant. The measured scattered wavefunctions of various modes for NOAAs 11084 and 11092 are fitted to the theoretical scattered wavefunctions to determine the three model parameters, magnitude, Gaussian radius, and phase, for the Born approximation of different orders. The three model parameters converge to some values at high-order Born approximations. The result of the first-order Born approximation is significantly different from the convergent value in some cases. The rate of convergence depends on the sunspot size and wavelength. It converges more rapidly for the smaller sunspot and longer wavelength. The magnitude increases with mode frequency and degree for each radial order. The Gaussian radius is insensitive to frequency and degree. The spatial range of the interaction parameter is greater than that of the continuum intensity deficit, but smaller than that of the acoustic power deficit of the sunspot. The phase versus phase speed falls into a small range. This suggests that the phase could be a function phase speed. NOAAs 11084 and 11092 have a similar magnitude and phase, although the ratio of their sizes is 0.75.

Electric dipole moment of the deuteron in the standard model with NN - ΛN - ΣN coupling

NASA Astrophysics Data System (ADS)

Yamanaka, Nodoka

2017-07-01

We calculate the electric dipole moment (EDM) of the deuteron in the standard model with | ΔS | = 1 interactions by taking into account the NN - ΛN - ΣN channel coupling, which is an important nuclear level systematics. The two-body problem is solved with the Gaussian Expansion Method using the realistic Argonne v18 nuclear force and the YN potential which can reproduce the binding energies of Λ3H, Λ3He, and Λ4He. The | ΔS | = 1 interbaryon potential is modeled by the one-meson exchange process. It is found that the deuteron EDM is modified by less than 10%, and the main contribution to this deviation is due to the polarization of the hyperon-nucleon channels. The effect of the YN interaction is small, and treating ΛN and ΣN channels as free is a good approximation for the EDM of the deuteron.

An adiabatic spectroscopic investigation of the CsRb system in ground and numerous excited states

NASA Astrophysics Data System (ADS)

Souissi, Hanen; Jellali, Soulef; Maha, Chaieb; Habli, Héla; Oujia, Brahim; Gadéa, Florent Xavier

2017-10-01

Via ab-initio approximations, we investigate the electronic and structural features of the CsRb molecule. Adiabatic potential energy curves of 261,3Σ+, 181,3Π and 61,3Δ electronic states with their derived spectroscopic constants as well as vibrational levels spacing have been carried out and well explained. Our approach is founded on an Effective Core Potential (ECP) describing the valence electrons of the system. Using a large Gaussian basis set, the full valence Configuration Interaction can be applied easily on the two-effective valence electrons of the CsRb system. Furthermore, a detailed analysis of the electric dipolar properties has been made through the investigation of both permanent and transition dipole moments (PDM and TDM). It is significant that the ionic character connected with electron transfer that is linked to Cs+ Rb- state has been clearly illustrated in the adiabatic permanent dipole moment.

Inflation with a graceful exit in a random landscape

NASA Astrophysics Data System (ADS)

Pedro, F. G.; Westphal, A.

2017-03-01

We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N ≪ 10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.

Self-consistent determination of the spike-train power spectrum in a neural network with sparse connectivity.

PubMed

Dummer, Benjamin; Wieland, Stefan; Lindner, Benjamin

2014-01-01

A major source of random variability in cortical networks is the quasi-random arrival of presynaptic action potentials from many other cells. In network studies as well as in the study of the response properties of single cells embedded in a network, synaptic background input is often approximated by Poissonian spike trains. However, the output statistics of the cells is in most cases far from being Poisson. This is inconsistent with the assumption of similar spike-train statistics for pre- and postsynaptic cells in a recurrent network. Here we tackle this problem for the popular class of integrate-and-fire neurons and study a self-consistent statistics of input and output spectra of neural spike trains. Instead of actually using a large network, we use an iterative scheme, in which we simulate a single neuron over several generations. In each of these generations, the neuron is stimulated with surrogate stochastic input that has a similar statistics as the output of the previous generation. For the surrogate input, we employ two distinct approximations: (i) a superposition of renewal spike trains with the same interspike interval density as observed in the previous generation and (ii) a Gaussian current with a power spectrum proportional to that observed in the previous generation. For input parameters that correspond to balanced input in the network, both the renewal and the Gaussian iteration procedure converge quickly and yield comparable results for the self-consistent spike-train power spectrum. We compare our results to large-scale simulations of a random sparsely connected network of leaky integrate-and-fire neurons (Brunel, 2000) and show that in the asynchronous regime close to a state of balanced synaptic input from the network, our iterative schemes provide an excellent approximations to the autocorrelation of spike trains in the recurrent network.

Gaussian temporal modulation for the behavior of multi-sinc Schell-model pulses in dispersive media

NASA Astrophysics Data System (ADS)

Liu, Xiayin; Zhao, Daomu; Tian, Kehan; Pan, Weiqing; Zhang, Kouwen

2018-06-01

A new class of pulse source with correlation being modeled by the convolution operation of two legitimate temporal correlation function is proposed. Particularly, analytical formulas for the Gaussian temporally modulated multi-sinc Schell-model (MSSM) pulses generated by such pulse source propagating in dispersive media are derived. It is demonstrated that the average intensity of MSSM pulses on propagation are reshaped from flat profile or a train to a distribution with a Gaussian temporal envelope by adjusting the initial correlation width of the Gaussian pulse. The effects of the Gaussian temporal modulation on the temporal degree of coherence of the MSSM pulse are also analyzed. The results presented here show the potential of coherence modulation for pulse shaping and pulsed laser material processing.

Transfer of non-Gaussian quantum states of mechanical oscillator to light

NASA Astrophysics Data System (ADS)

Filip, Radim; Rakhubovsky, Andrey A.

2015-11-01

Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

The inner mass power spectrum of galaxies using strong gravitational lensing: beyond linear approximation

NASA Astrophysics Data System (ADS)

Chatterjee, Saikat; Koopmans, Léon V. E.

2018-02-01

In the last decade, the detection of individual massive dark matter sub-haloes has been possible using potential correction formalism in strong gravitational lens imaging. Here, we propose a statistical formalism to relate strong gravitational lens surface brightness anomalies to the lens potential fluctuations arising from dark matter distribution in the lens galaxy. We consider these fluctuations as a Gaussian random field in addition to the unperturbed smooth lens model. This is very similar to weak lensing formalism and we show that in this way we can measure the power spectrum of these perturbations to the potential. We test the method by applying it to simulated mock lenses of different geometries and by performing an MCMC analysis of the theoretical power spectra. This method can measure density fluctuations in early type galaxies on scales of 1-10 kpc at typical rms levels of a per cent, using a single lens system observed with the Hubble Space Telescope with typical signal-to-noise ratios obtained in a single orbit.

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

NASA Astrophysics Data System (ADS)

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33TC.

Bayesian approach to spectral function reconstruction for Euclidean quantum field theories.

PubMed

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33T(C).

Computational Stimulation of the Basal Ganglia Neurons with Cost Effective Delayed Gaussian Waveforms

PubMed Central

Daneshzand, Mohammad; Faezipour, Miad; Barkana, Buket D.

2017-01-01

Deep brain stimulation (DBS) has compelling results in the desynchronization of the basal ganglia neuronal activities and thus, is used in treating the motor symptoms of Parkinson's disease (PD). Accurate definition of DBS waveform parameters could avert tissue or electrode damage, increase the neuronal activity and reduce energy cost which will prolong the battery life, hence avoiding device replacement surgeries. This study considers the use of a charge balanced Gaussian waveform pattern as a method to disrupt the firing patterns of neuronal cell activity. A computational model was created to simulate ganglia cells and their interactions with thalamic neurons. From the model, we investigated the effects of modified DBS pulse shapes and proposed a delay period between the cathodic and anodic parts of the charge balanced Gaussian waveform to desynchronize the firing patterns of the GPe and GPi cells. The results of the proposed Gaussian waveform with delay outperformed that of rectangular DBS waveforms used in in-vivo experiments. The Gaussian Delay Gaussian (GDG) waveforms achieved lower number of misses in eliciting action potential while having a lower amplitude and shorter length of delay compared to numerous different pulse shapes. The amount of energy consumed in the basal ganglia network due to GDG waveforms was dropped by 22% in comparison with charge balanced Gaussian waveforms without any delay between the cathodic and anodic parts and was also 60% lower than a rectangular charged balanced pulse with a delay between the cathodic and anodic parts of the waveform. Furthermore, by defining a Synchronization Level metric, we observed that the GDG waveform was able to reduce the synchronization of GPi neurons more effectively than any other waveform. The promising results of GDG waveforms in terms of eliciting action potential, desynchronization of the basal ganglia neurons and reduction of energy consumption can potentially enhance the performance of DBS devices. PMID:28848417

Computational Stimulation of the Basal Ganglia Neurons with Cost Effective Delayed Gaussian Waveforms.

PubMed

Daneshzand, Mohammad; Faezipour, Miad; Barkana, Buket D

2017-01-01

Deep brain stimulation (DBS) has compelling results in the desynchronization of the basal ganglia neuronal activities and thus, is used in treating the motor symptoms of Parkinson's disease (PD). Accurate definition of DBS waveform parameters could avert tissue or electrode damage, increase the neuronal activity and reduce energy cost which will prolong the battery life, hence avoiding device replacement surgeries. This study considers the use of a charge balanced Gaussian waveform pattern as a method to disrupt the firing patterns of neuronal cell activity. A computational model was created to simulate ganglia cells and their interactions with thalamic neurons. From the model, we investigated the effects of modified DBS pulse shapes and proposed a delay period between the cathodic and anodic parts of the charge balanced Gaussian waveform to desynchronize the firing patterns of the GPe and GPi cells. The results of the proposed Gaussian waveform with delay outperformed that of rectangular DBS waveforms used in in-vivo experiments. The Gaussian Delay Gaussian (GDG) waveforms achieved lower number of misses in eliciting action potential while having a lower amplitude and shorter length of delay compared to numerous different pulse shapes. The amount of energy consumed in the basal ganglia network due to GDG waveforms was dropped by 22% in comparison with charge balanced Gaussian waveforms without any delay between the cathodic and anodic parts and was also 60% lower than a rectangular charged balanced pulse with a delay between the cathodic and anodic parts of the waveform. Furthermore, by defining a Synchronization Level metric, we observed that the GDG waveform was able to reduce the synchronization of GPi neurons more effectively than any other waveform. The promising results of GDG waveforms in terms of eliciting action potential, desynchronization of the basal ganglia neurons and reduction of energy consumption can potentially enhance the performance of DBS devices.

Optical assembly of microparticles into highly ordered structures using Ince-Gaussian beams

NASA Astrophysics Data System (ADS)

Woerdemann, Mike; Alpmann, Christina; Denz, Cornelia

2011-03-01

Ince-Gaussian (IG) beams are a third complete family of solutions of the paraxial Helmholtz equation. While many applications of Hermite-Gaussian and Laguerre-Gaussian beams have been demonstrated for manipulation of microparticles, the potential of the more general class of IG beams has not yet been exploited at all. We describe the unique properties of IG beams with respect to optical trapping applications, demonstrate a flexible experimental realization of arbitrary IG beams and prove the concept by creating two- and three-dimensional, highly ordered assemblies of typical microparticles. The concept is universal and can easily be integrated into existing holographic optical tweezers setups.

Application of ab initio many-body perturbation theory with Gaussian basis sets to the singlet and triplet excitations of organic molecules

NASA Astrophysics Data System (ADS)

Hamed, Samia; Rangel, Tonatiuh; Bruneval, Fabien; Neaton, Jeffrey B.

Quantitative understanding of charged and neutral excitations of organic molecules is critical in diverse areas of study that include astrophysics and the development of energy technologies that are clean and efficient. The recent use of local basis sets with ab initio many-body perturbation theory in the GW approximation and the Bethe-Saltpeter equation approach (BSE), methods traditionally applied to periodic condensed phases with a plane-wave basis, has opened the door to detailed study of such excitations for molecules, as well as accurate numerical benchmarks. Here, through a series of systematic benchmarks with a Gaussian basis, we report on the extent to which the predictive power and utility of this approach depend critically on interdependent underlying approximations and choices for molecules, including the mean-field starting point (eg optimally-tuned range separated hybrids, pure DFT functionals, and untuned hybrids), the GW scheme, and the Tamm Dancoff approximation. We demonstrate the effects of these choices in the context of Thiels' set while drawing analogies to linear-response time-dependent DFT and making comparisons to best theoretical estimates from higher-order wavefunction-based theories.

On the Validity of Certain Approximations Used in the Modeling of Nuclear EMP

DOE PAGES

Farmer, William A.; Cohen, Bruce I.; Eng, Chester D.

2016-04-01

The legacy codes developed for the modeling of EMP, multiple scattering of Compton electrons has typically been modeled by the obliquity factor. A recent publication has examined this approximation in the context of the generated Compton current [W. A. Farmer and A. Friedman, IEEE Trans. Nucl. Sc. 62, 1695 (2015)]. Here, this previous analysis is extended to include the generation of the electromagnetic fields. Obliquity factor predictions are compared with Monte-Carlo models. In using a Monte-Carlo description of scattering, two distributions of scattering angles are considered: Gaussian and a Gaussian with a single-scattering tail. Additionally, legacy codes also neglect themore » radial derivative of the backward-traveling wave for computational efficiency. The neglect of this derivative improperly treats the backward-traveling wave. Moreover, these approximations are examined in the context of a high-altitude burst, and it is shown that in comparison to more complete models, the discrepancy between field amplitudes is roughly two to three percent and between rise-times, 10%. Finally, it is concluded that the biggest factor in determining the rise time of the signal is not the dynamics of the Compton current, but is instead the conductivity.« less

Development of a machine learning potential for graphene

NASA Astrophysics Data System (ADS)

Rowe, Patrick; Csányi, Gábor; Alfè, Dario; Michaelides, Angelos

2018-02-01

We present an accurate interatomic potential for graphene, constructed using the Gaussian approximation potential (GAP) machine learning methodology. This GAP model obtains a faithful representation of a density functional theory (DFT) potential energy surface, facilitating highly accurate (approaching the accuracy of ab initio methods) molecular dynamics simulations. This is achieved at a computational cost which is orders of magnitude lower than that of comparable calculations which directly invoke electronic structure methods. We evaluate the accuracy of our machine learning model alongside that of a number of popular empirical and bond-order potentials, using both experimental and ab initio data as references. We find that whilst significant discrepancies exist between the empirical interatomic potentials and the reference data—and amongst the empirical potentials themselves—the machine learning model introduced here provides exemplary performance in all of the tested areas. The calculated properties include: graphene phonon dispersion curves at 0 K (which we predict with sub-meV accuracy), phonon spectra at finite temperature, in-plane thermal expansion up to 2500 K as compared to NPT ab initio molecular dynamics simulations and a comparison of the thermally induced dispersion of graphene Raman bands to experimental observations. We have made our potential freely available online at [http://www.libatoms.org].

Ferroelectric hydration shells around proteins: electrostatics of the protein-water interface.

PubMed

LeBard, David N; Matyushov, Dmitry V

2010-07-22

Numerical simulations of hydrated proteins show that protein hydration shells are polarized into a ferroelectric layer with large values of the average dipole moment magnitude and the dipole moment variance. The emergence of the new polarized mesophase dramatically alters the statistics of electrostatic fluctuations at the protein-water interface. The linear response relation between the average electrostatic potential and its variance breaks down, with the breadth of the electrostatic fluctuations far exceeding the expectations of the linear response theories. The dynamics of these non-Gaussian electrostatic fluctuations are dominated by a slow (approximately = 1 ns) component that freezes in at the temperature of the dynamical transition of proteins. The ferroelectric shell propagates 3-5 water diameters into the bulk.

Heavy baryons in the large N c limit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Albertus, C.; Ruiz Arriola, Enrique; Fernando, Ishara P.

It is shown that in the large N c limit heavy baryon masses can be estimated quantitatively in a 1/N c expansion using the Hartree approximation. The results are compared with available lattice calculations for different values of the ratio between the square root of the string tension and the heavy quark mass tension independent of N c. Using a potential adjusted to agree with the one obtained in lattice QCD, a variational analysis of the ground state spin averaged baryon mass is performed using Gaussian Hartree wave functions. Relativistic corrections through the quark kinetic energy are included. Lastly, themore » results provide good estimates for the first sub-leading in 1/N c corrections.« less

Heavy baryons in the large N c limit

DOE PAGES

Albertus, C.; Ruiz Arriola, Enrique; Fernando, Ishara P.; ...

2015-09-16

It is shown that in the large N c limit heavy baryon masses can be estimated quantitatively in a 1/N c expansion using the Hartree approximation. The results are compared with available lattice calculations for different values of the ratio between the square root of the string tension and the heavy quark mass tension independent of N c. Using a potential adjusted to agree with the one obtained in lattice QCD, a variational analysis of the ground state spin averaged baryon mass is performed using Gaussian Hartree wave functions. Relativistic corrections through the quark kinetic energy are included. Lastly, themore » results provide good estimates for the first sub-leading in 1/N c corrections.« less

Identification and annotation of erotic film based on content analysis

NASA Astrophysics Data System (ADS)

Wang, Donghui; Zhu, Miaoliang; Yuan, Xin; Qian, Hui

2005-02-01

The paper brings forward a new method for identifying and annotating erotic films based on content analysis. First, the film is decomposed to video and audio stream. Then, the video stream is segmented into shots and key frames are extracted from each shot. We filter the shots that include potential erotic content by finding the nude human body in key frames. A Gaussian model in YCbCr color space for detecting skin region is presented. An external polygon that covered the skin regions is used for the approximation of the human body. Last, we give the degree of the nudity by calculating the ratio of skin area to whole body area with weighted parameters. The result of the experiment shows the effectiveness of our method.

Spatio-Temporal Data Analysis at Scale Using Models Based on Gaussian Processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stein, Michael

Gaussian processes are the most commonly used statistical model for spatial and spatio-temporal processes that vary continuously. They are broadly applicable in the physical sciences and engineering and are also frequently used to approximate the output of complex computer models, deterministic or stochastic. We undertook research related to theory, computation, and applications of Gaussian processes as well as some work on estimating extremes of distributions for which a Gaussian process assumption might be inappropriate. Our theoretical contributions include the development of new classes of spatial-temporal covariance functions with desirable properties and new results showing that certain covariance models lead tomore » predictions with undesirable properties. To understand how Gaussian process models behave when applied to deterministic computer models, we derived what we believe to be the first significant results on the large sample properties of estimators of parameters of Gaussian processes when the actual process is a simple deterministic function. Finally, we investigated some theoretical issues related to maxima of observations with varying upper bounds and found that, depending on the circumstances, standard large sample results for maxima may or may not hold. Our computational innovations include methods for analyzing large spatial datasets when observations fall on a partially observed grid and methods for estimating parameters of a Gaussian process model from observations taken by a polar-orbiting satellite. In our application of Gaussian process models to deterministic computer experiments, we carried out some matrix computations that would have been infeasible using even extended precision arithmetic by focusing on special cases in which all elements of the matrices under study are rational and using exact arithmetic. The applications we studied include total column ozone as measured from a polar-orbiting satellite, sea surface temperatures over the Pacific Ocean, and annual temperature extremes at a site in New York City. In each of these applications, our theoretical and computational innovations were directly motivated by the challenges posed by analyzing these and similar types of data.« less

Frozen Gaussian approximation for 3D seismic tomography

NASA Astrophysics Data System (ADS)

Chai, Lihui; Tong, Ping; Yang, Xu

2018-05-01

Three-dimensional (3D) wave-equation-based seismic tomography is computationally challenging in large scales and high-frequency regime. In this paper, we apply the frozen Gaussian approximation (FGA) method to compute 3D sensitivity kernels and seismic tomography of high-frequency. Rather than standard ray theory used in seismic inversion (e.g. Kirchhoff migration and Gaussian beam migration), FGA is used to compute the 3D high-frequency sensitivity kernels for travel-time or full waveform inversions. Specifically, we reformulate the equations of the forward and adjoint wavefields for the purpose of convenience to apply FGA, and with this reformulation, one can efficiently compute the Green’s functions whose convolutions with source time function produce wavefields needed for the construction of 3D kernels. Moreover, a fast summation method is proposed based on local fast Fourier transform which greatly improves the speed of reconstruction as the last step of FGA algorithm. We apply FGA to both the travel-time adjoint tomography and full waveform inversion (FWI) on synthetic crosswell seismic data with dominant frequencies as high as those of real crosswell data, and confirm again that FWI requires a more sophisticated initial velocity model for the convergence than travel-time adjoint tomography. We also numerically test the accuracy of applying FGA to local earthquake tomography. This study paves the way to directly apply wave-equation-based seismic tomography methods into real data around their dominant frequencies.

A Gaussian Approximation Approach for Value of Information Analysis.

PubMed

Jalal, Hawre; Alarid-Escudero, Fernando

2018-02-01

Most decisions are associated with uncertainty. Value of information (VOI) analysis quantifies the opportunity loss associated with choosing a suboptimal intervention based on current imperfect information. VOI can inform the value of collecting additional information, resource allocation, research prioritization, and future research designs. However, in practice, VOI remains underused due to many conceptual and computational challenges associated with its application. Expected value of sample information (EVSI) is rooted in Bayesian statistical decision theory and measures the value of information from a finite sample. The past few years have witnessed a dramatic growth in computationally efficient methods to calculate EVSI, including metamodeling. However, little research has been done to simplify the experimental data collection step inherent to all EVSI computations, especially for correlated model parameters. This article proposes a general Gaussian approximation (GA) of the traditional Bayesian updating approach based on the original work by Raiffa and Schlaifer to compute EVSI. The proposed approach uses a single probabilistic sensitivity analysis (PSA) data set and involves 2 steps: 1) a linear metamodel step to compute the EVSI on the preposterior distributions and 2) a GA step to compute the preposterior distribution of the parameters of interest. The proposed approach is efficient and can be applied for a wide range of data collection designs involving multiple non-Gaussian parameters and unbalanced study designs. Our approach is particularly useful when the parameters of an economic evaluation are correlated or interact.

Generalized elimination of the global translation from explicitly correlated Gaussian functions

NASA Astrophysics Data System (ADS)

Muolo, Andrea; Mátyus, Edit; Reiher, Markus

2018-02-01

This paper presents the multi-channel generalization of the center-of-mass kinetic energy elimination approach [B. Simmen et al., Mol. Phys. 111, 2086 (2013)] when the Schrödinger equation is solved variationally with explicitly correlated Gaussian functions. The approach has immediate relevance in many-particle systems which are handled without the Born-Oppenheimer approximation and can be employed also for Dirac-type Hamiltonians. The practical realization and numerical properties of solving the Schrödinger equation in laboratory-frame Cartesian coordinates are demonstrated for the ground rovibronic state of the H2+={p+,p+,e- } ion and the H2 = {p+, p+, e-, e-} molecule.

Gaussian Processes for Prediction of Homing Pigeon Flight Trajectories

NASA Astrophysics Data System (ADS)

Mann, Richard; Freeman, Robin; Osborne, Michael; Garnett, Roman; Meade, Jessica; Armstrong, Chris; Biro, Dora; Guilford, Tim; Roberts, Stephen

2009-12-01

We construct and apply a stochastic Gaussian Process (GP) model of flight trajectory generation for pigeons trained to home from specific release sites. The model shows increasing predictive power as the birds become familiar with the sites, mirroring the animal's learning process. We show how the increasing similarity between successive flight trajectories can be used to infer, with increasing accuracy, an idealised route that captures the repeated spatial aspects of the bird's flight. We subsequently use techniques associated with reduced-rank GP approximations to objectively identify the key waypoints used by each bird to memorise its idiosyncratic habitual route between the release site and the home loft.

A Gaussian measure of quantum phase noise

NASA Technical Reports Server (NTRS)

Schleich, Wolfgang P.; Dowling, Jonathan P.

1992-01-01

We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.

Generalized elimination of the global translation from explicitly correlated Gaussian functions.

PubMed

Muolo, Andrea; Mátyus, Edit; Reiher, Markus

2018-02-28

This paper presents the multi-channel generalization of the center-of-mass kinetic energy elimination approach [B. Simmen et al., Mol. Phys. 111, 2086 (2013)] when the Schrödinger equation is solved variationally with explicitly correlated Gaussian functions. The approach has immediate relevance in many-particle systems which are handled without the Born-Oppenheimer approximation and can be employed also for Dirac-type Hamiltonians. The practical realization and numerical properties of solving the Schrödinger equation in laboratory-frame Cartesian coordinates are demonstrated for the ground rovibronic state of the H 2 + ={p + ,p + ,e - } ion and the H 2 = {p + , p + , e - , e - } molecule.

Subluminous phase velocity regions of an accurately described Gaussian laser field and laser-driven acceleration

NASA Astrophysics Data System (ADS)

Xie, Y. J.; Ho, Y. K.; Cao, N.; Shao, L.; Pang, J.; Chen, Z.; Zhang, S. Y.; Liu, J. R.

2003-11-01

By taking account of the high-order corrections to the paraxial approximation of a Gaussian beam, it has been verified that for a focused laser beam propagating in vacuum, there indeed exists a subluminous wave phase velocity region surrounding the laser beam axis. The magnitude of the phase velocity scales as Vϕm∼ c(1+ b/( kw0) 2), where Vϕm is the phase velocity of the wave, c is the speed of light in vacuum, w0 is the beam width at focus. This feature gives a reasonable explanation for the mechanism of capture and acceleration scenario.

Graphical Models for Ordinal Data

PubMed Central

Guo, Jian; Levina, Elizaveta; Michailidis, George; Zhu, Ji

2014-01-01

A graphical model for ordinal variables is considered, where it is assumed that the data are generated by discretizing the marginal distributions of a latent multivariate Gaussian distribution. The relationships between these ordinal variables are then described by the underlying Gaussian graphical model and can be inferred by estimating the corresponding concentration matrix. Direct estimation of the model is computationally expensive, but an approximate EM-like algorithm is developed to provide an accurate estimate of the parameters at a fraction of the computational cost. Numerical evidence based on simulation studies shows the strong performance of the algorithm, which is also illustrated on data sets on movie ratings and an educational survey. PMID:26120267

Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows

NASA Technical Reports Server (NTRS)

He, Guowei; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The Eulerian mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An Eulerian mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.

Parametric vs. non-parametric statistics of low resolution electromagnetic tomography (LORETA).

PubMed

Thatcher, R W; North, D; Biver, C

2005-01-01

This study compared the relative statistical sensitivity of non-parametric and parametric statistics of 3-dimensional current sources as estimated by the EEG inverse solution Low Resolution Electromagnetic Tomography (LORETA). One would expect approximately 5% false positives (classification of a normal as abnormal) at the P < .025 level of probability (two tailed test) and approximately 1% false positives at the P < .005 level. EEG digital samples (2 second intervals sampled 128 Hz, 1 to 2 minutes eyes closed) from 43 normal adult subjects were imported into the Key Institute's LORETA program. We then used the Key Institute's cross-spectrum and the Key Institute's LORETA output files (*.lor) as the 2,394 gray matter pixel representation of 3-dimensional currents at different frequencies. The mean and standard deviation *.lor files were computed for each of the 2,394 gray matter pixels for each of the 43 subjects. Tests of Gaussianity and different transforms were computed in order to best approximate a normal distribution for each frequency and gray matter pixel. The relative sensitivity of parametric vs. non-parametric statistics were compared using a "leave-one-out" cross validation method in which individual normal subjects were withdrawn and then statistically classified as being either normal or abnormal based on the remaining subjects. Log10 transforms approximated Gaussian distribution in the range of 95% to 99% accuracy. Parametric Z score tests at P < .05 cross-validation demonstrated an average misclassification rate of approximately 4.25%, and range over the 2,394 gray matter pixels was 27.66% to 0.11%. At P < .01 parametric Z score cross-validation false positives were 0.26% and ranged from 6.65% to 0% false positives. The non-parametric Key Institute's t-max statistic at P < .05 had an average misclassification error rate of 7.64% and ranged from 43.37% to 0.04% false positives. The nonparametric t-max at P < .01 had an average misclassification rate of 6.67% and ranged from 41.34% to 0% false positives of the 2,394 gray matter pixels for any cross-validated normal subject. In conclusion, adequate approximation to Gaussian distribution and high cross-validation can be achieved by the Key Institute's LORETA programs by using a log10 transform and parametric statistics, and parametric normative comparisons had lower false positive rates than the non-parametric tests.

Mean Field Approach to the Giant Wormhole Problem

NASA Astrophysics Data System (ADS)

Gamba, A.; Kolokolov, I.; Martellini, M.

We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.

Approximate message passing for nonconvex sparse regularization with stability and asymptotic analysis

NASA Astrophysics Data System (ADS)

Sakata, Ayaka; Xu, Yingying

2018-03-01

We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm considering nonconvex regularization, namely SCAD-AMP, and analytically show that the stability condition corresponds to the de Almeida-Thouless condition in spin glass literature. Through asymptotic analysis, we show the correspondence between the density evolution of SCAD-AMP and the replica symmetric (RS) solution. Numerical experiments confirm that for a sufficiently large system size, SCAD-AMP achieves the optimal performance predicted by the replica method. Through replica analysis, a phase transition between replica symmetric and replica symmetry breaking (RSB) region is found in the parameter space of SCAD. The appearance of the RS region for a nonconvex penalty is a significant advantage that indicates the region of smooth landscape of the optimization problem. Furthermore, we analytically show that the statistical representation performance of the SCAD penalty is better than that of \

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed.

PubMed

Weiss, M; Stedtler, C; Roberts, M S

1997-09-01

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximately by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as an alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models.

Gaussian functional regression for output prediction: Model assimilation and experimental design

NASA Astrophysics Data System (ADS)

Nguyen, N. C.; Peraire, J.

2016-03-01

In this paper, we introduce a Gaussian functional regression (GFR) technique that integrates multi-fidelity models with model reduction to efficiently predict the input-output relationship of a high-fidelity model. The GFR method combines the high-fidelity model with a low-fidelity model to provide an estimate of the output of the high-fidelity model in the form of a posterior distribution that can characterize uncertainty in the prediction. A reduced basis approximation is constructed upon the low-fidelity model and incorporated into the GFR method to yield an inexpensive posterior distribution of the output estimate. As this posterior distribution depends crucially on a set of training inputs at which the high-fidelity models are simulated, we develop a greedy sampling algorithm to select the training inputs. Our approach results in an output prediction model that inherits the fidelity of the high-fidelity model and has the computational complexity of the reduced basis approximation. Numerical results are presented to demonstrate the proposed approach.

Paraconductivity of pseudogapped superconductors

NASA Astrophysics Data System (ADS)

Poboiko, Igor; Feigel'man, Mikhail

2018-01-01

We calculate Aslamazov-Larkin (AL) paraconductity σAL(T ) for a model of strongly disordered superconductors (dimensions d =2 ,3 ) with a large pseudogap whose magnitude strongly exceeds transition temperature Tc. We show that, within Gaussian approximation over Cooper-pair fluctuations, paraconductivity is just twice larger that the classical AL result at the same ɛ =(T -Tc) /Tc . Upon decreasing ɛ , Gaussian approximation is violated due to local fluctuations of pairing fields that become relevant at ɛ ≤ɛ1≪1 . Characteristic scale ɛ1 is much larger than the width ɛ2 of the thermodynamical critical region, that is determined via the Ginzburg criterion, ɛ2≈ɛ1d . We argue that in the intermediate region ɛ2≤ɛ ≤ɛ1 , paraconductivity follows the same AL power law, albeit with another (yet unknown) numerical prefactor. At further decrease of the temperature, all kinds of fluctuational corrections become strong at ɛ ≤ɛ2 ; in particular, conductivity occurs to be strongly inhomogeneous in real space.

Near grazing scattering from non-Gaussian ocean surfaces

NASA Technical Reports Server (NTRS)

Kim, Yunjin; Rodriguez, Ernesto

1993-01-01

We investigate the behavior of the scattered electromagnetic waves from non-Gaussian ocean surfaces at near grazing incidence. Even though the scattering mechanisms at moderate incidence angles are relatively well understood, the same is not true for near grazing rough surface scattering. However, from the experimental ocean scattering data, it has been observed that the backscattering cross section of a horizontally polarized wave can be as large as the vertical counterpart at near grazing incidence. In addition, these returns are highly intermittent in time. There have been some suggestions that these unexpected effects may come from shadowing or feature scattering. Using numerical scattering simulations, it can be shown that the horizontal backscattering cannot be larger than the vertical one for the Gaussian surfaces. Our main objective of this study is to gain a clear understanding of scattering mechanisms underlying the near grazing ocean scattering. In order to evaluate the backscattering cross section from ocean surfaces at near grazing incidence, both the hydrodynamic modeling of ocean surfaces and an accurate near grazing scattering theory are required. For the surface modeling, we generate Gaussian surfaces from the ocean surface power spectrum which is derived using several experimental data. Then, weakly nonlinear large scale ocean surfaces are generated following Longuet-Higgins. In addition, the modulation of small waves by large waves is included using the conservation of wave action. For surface scattering, we use MOM (Method of Moments) to calculate the backscattering from scattering patches with the two scale shadowing approximation. The differences between Gaussian and non-Gaussian surface scattering at near grazing incidence are presented.

Microscopic few-body and Gaussian-shaped density distributions for the analysis of the 6He exotic nucleus with different target nuclei

NASA Astrophysics Data System (ADS)

Aygun, M.; Kucuk, Y.; Boztosun, I.; Ibraheem, Awad A.

2010-12-01

The elastic scattering angular distributions of 6He projectile on different medium and heavy mass target nuclei including 12C, 27Al, 58Ni, 64Zn, 65Cu, 197Au, 208Pb and 209Bi have been examined by using the few-body and Gaussian-shaped density distributions at various energies. The microscopic real parts of the complex nuclear optical potential have been obtained by using the double-folding model for each of the density distributions and the phenomenological imaginary potentials have been taken as the Woods-Saxon type. Comparative results of the few-body and Gaussian-shaped density distributions together with the experimental data are presented within the framework of the optical model.

Recent Results on "Approximations to Optimal Alarm Systems for Anomaly Detection"

NASA Technical Reports Server (NTRS)

Martin, Rodney Alexander

2009-01-01

An optimal alarm system and its approximations may use Kalman filtering for univariate linear dynamic systems driven by Gaussian noise to provide a layer of predictive capability. Predicted Kalman filter future process values and a fixed critical threshold can be used to construct a candidate level-crossing event over a predetermined prediction window. An optimal alarm system can be designed to elicit the fewest false alarms for a fixed detection probability in this particular scenario.

Nernst effect from fluctuating pairs in the pseudogap phase of the cuprates.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levchenko, A.; Norman, M. R.; Varlamov, A. A.

2011-01-31

The observation of a large Nernst signal in cuprates above the superconducting transition temperature has attracted much attention. A potential explanation is that it originates from superconducting fluctuations. Although the Nernst signal is indeed consistent with Gaussian fluctuations for overdoped cuprates, Gaussian theory fails to describe the temperature dependence seen for underdoped cuprates. Here, we consider the vertex correction to Gaussian theory resulting from the pseudogap. This yields a Nernst signal in good agreement with the data.

Dynamic generation of Ince-Gaussian modes with a digital micromirror device

NASA Astrophysics Data System (ADS)

Ren, Yu-Xuan; Fang, Zhao-Xiang; Gong, Lei; Huang, Kun; Chen, Yue; Lu, Rong-De

2015-04-01

Ince-Gaussian (IG) beam with elliptical profile, as a connection between Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) beams, has showed unique advantages in some applications such as quantum entanglement and optical micromanipulation. However, its dynamic generation with high switching frequency is still challenging. Here, we experimentally reported the quick generation of Ince-Gaussian beam by using a digital micro-mirror device (DMD), which has the highest switching frequency of 5.2 kHz in principle. The configurable properties of DMD allow us to observe the quasi-smooth variation from LG (with ellipticity ɛ = 0 ) to IG and HG ( ɛ = ∞ ) beam. This approach might pave a path to high-speed quantum communication in terms of IG beam. Additionally, the characterized axial plane intensity distribution exhibits a 3D mould potentially being employed for optical micromanipulation.

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Wavelets in electronic structure calculations

NASA Astrophysics Data System (ADS)

Modisette, Jason Perry

1997-09-01

Ab initio calculations of the electronic structure of bulk materials and large clusters are not possible on today's computers using current techniques. The storage and diagonalization of the Hamiltonian matrix are the limiting factors in both memory and execution time. The scaling of both quantities with problem size can be reduced by using approximate diagonalization or direct minimization of the total energy with respect to the density matrix in conjunction with a localized basis. Wavelet basis members are much more localized than conventional bases such as Gaussians or numerical atomic orbitals. This localization leads to sparse matrices of the operators that arise in SCF multi-electron calculations. We have investigated the construction of the one-electron Hamiltonian, and also the effective one- electron Hamiltonians that appear in density-functional and Hartree-Fock theories. We develop efficient methods for the generation of the kinetic energy and potential matrices, the Hartree and exchange potentials, and the local exchange-correlation potential of the LDA. Test calculations are performed on one-electron problems with a variety of potentials in one and three dimensions.

Simulating the effect of non-linear mode coupling in cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Kiessling, A.; Taylor, A. N.; Heavens, A. F.

2011-09-01

Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment and to optimize the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimization it is usually assumed that the power-spectrum covariance matrix is diagonal in Fourier space. However, in the low-redshift Universe, non-linear mode coupling will tend to correlate small-scale power, moving information from lower to higher order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naïve Gaussian Fisher matrix forecasts with a maximum likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2D and tomographic shear analysis of a Euclid-like survey. In both cases, we find that the 68 per cent confidence area of the Ωm-σ8 plane increases by a factor of 5. However, the marginal errors increase by just 20-40 per cent. We propose a new method to model the effects of non-linear shear-power mode coupling in the Fisher matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68 per cent confidence regions of the full maximum likelihood analysis in the Ωm-σ8 plane to high accuracy for both 2D and tomographic weak lensing surveys. Finally, we perform a multiparameter analysis of Ωm, σ8, h, ns, w0 and wa to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The 6D volume of the 1σ error contours for the non-linear Fisher analysis is a factor of 3 larger than for the Gaussian case, and the shape of the 68 per cent confidence volume is modified. We propose that future Fisher matrix estimates of cosmological parameter accuracies should include mode-coupling effects.

Comparison of three NDVI time-series fitting methods in crop phenology detection in Northeast China

NASA Astrophysics Data System (ADS)

Wang, Meng; Tao, Fulu

2014-03-01

Phenological changes of cropland are the pivotal basis for farm management, agricultural production, and climate change research. Over the past decades, a range of methods have been used to extract phenological events based on satellite derived continuous vegetation index time series, however, large uncertainties still exist. In this study, three smoothing methods were compared to reduce the potential uncertainty and to quantify crop green-up dates over Northeast China. The results indicated that the crop spring onset dates estimated by three methods show variance in the dates, but with similar spatial pattern. In 60% of the study area, the standard deviation (SD) of the estimated starting date from different method is less than 10 days, while 39.5% of total pixels have SDs between 10days and 30 days. Through comparative analysis against the observation phenological data, we concluded that Asymmetric Gaussians produced the most approximative results of all, followed by Double Logistic algorithm, and Savizky-Glolay algorithm performed worst. The starting dates of crops occur mostly between May and June in this region. The Savitzky-Golay has the earliest estimates, while the Asymmetric Gaussians and Double logistic fitting method show similar and later estimates, which are more consistent with the observed data.

A novel latent gaussian copula framework for modeling spatial correlation in quantized SAR imagery with applications to ATR

NASA Astrophysics Data System (ADS)

Thelen, Brian T.; Xique, Ismael J.; Burns, Joseph W.; Goley, G. Steven; Nolan, Adam R.; Benson, Jonathan W.

2017-04-01

With all of the new remote sensing modalities available, and with ever increasing capabilities and frequency of collection, there is a desire to fundamentally understand/quantify the information content in the collected image data relative to various exploitation goals, such as detection/classification. A fundamental approach for this is the framework of Bayesian decision theory, but a daunting challenge is to have significantly flexible and accurate multivariate models for the features and/or pixels that capture a wide assortment of distributions and dependen- cies. In addition, data can come in the form of both continuous and discrete representations, where the latter is often generated based on considerations of robustness to imaging conditions and occlusions/degradations. In this paper we propose a novel suite of "latent" models fundamentally based on multivariate Gaussian copula models that can be used for quantized data from SAR imagery. For this Latent Gaussian Copula (LGC) model, we derive an approximate, maximum-likelihood estimation algorithm and demonstrate very reasonable estimation performance even for the larger images with many pixels. However applying these LGC models to large dimen- sions/images within a Bayesian decision/classification theory is infeasible due to the computational/numerical issues in evaluating the true full likelihood, and we propose an alternative class of novel pseudo-likelihoood detection statistics that are computationally feasible. We show in a few simple examples that these statistics have the potential to provide very good and robust detection/classification performance. All of this framework is demonstrated on a simulated SLICY data set, and the results show the importance of modeling the dependencies, and of utilizing the pseudo-likelihood methods.

Random medium model for cusping of plane waves.

PubMed

Li, Jia; Korotkova, Olga

2017-09-01

We introduce a model for a three-dimensional (3D) Schell-type stationary medium whose degree of potential's correlation satisfies the Fractional Multi-Gaussian (FMG) function. Compared with the scattered profile produced by the Gaussian Schell-model (GSM) medium, the Fractional Multi-Gaussian Schell-model (FMGSM) medium gives rise to a sharp concave intensity apex in the scattered field. This implies that the FMGSM medium also accounts for a larger than Gaussian's power in the bucket (PIB) in the forward scattering direction, hence being a better candidate than the GSM medium for generating highly-focused (cusp-like) scattered profiles in the far zone. Compared to other mathematical models for the medium's correlation function which can produce similar cusped scattered profiles the FMG function offers unprecedented tractability being the weighted superposition of Gaussian functions. Our results provide useful applications to energy counter problems and particle manipulation by weakly scattered fields.

Dynamic generation of Ince-Gaussian modes with a digital micromirror device

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Yu-Xuan, E-mail: yxren@ustc.edu.cn; Fang, Zhao-Xiang; Chen, Yue

Ince-Gaussian (IG) beam with elliptical profile, as a connection between Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) beams, has showed unique advantages in some applications such as quantum entanglement and optical micromanipulation. However, its dynamic generation with high switching frequency is still challenging. Here, we experimentally reported the quick generation of Ince-Gaussian beam by using a digital micro-mirror device (DMD), which has the highest switching frequency of 5.2 kHz in principle. The configurable properties of DMD allow us to observe the quasi-smooth variation from LG (with ellipticity ε=0) to IG and HG (ε=∞) beam. This approach might pave a path to high-speedmore » quantum communication in terms of IG beam. Additionally, the characterized axial plane intensity distribution exhibits a 3D mould potentially being employed for optical micromanipulation.« less

Temperature dependence of photoluminescence peaks of porous silicon structures

NASA Astrophysics Data System (ADS)

Brunner, Róbert; Pinčík, Emil; Kučera, Michal; Greguš, Ján; Vojtek, Pavel; Zábudlá, Zuzana

2017-12-01

Evaluation of photoluminescence spectra of porous silicon (PS) samples prepared by electrochemical etching is presented. The samples were measured at temperatures 30, 70 and 150 K. Peak parameters (energy, intensity and width) were calculated. The PL spectrum was approximated by a set of Gaussian peaks. Their parameters were fixed using fitting a procedure in which the optimal number of peeks included into the model was estimated using the residuum of the approximation. The weak thermal dependence of the spectra indicates the strong influence of active defects.

Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fukushima, N.; Ohashi, Y.; Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama 223

2007-03-15

The superfluid density is a fundamental quantity describing the response to a rotation as well as in two-fluid collisional hydrodynamics. We present extensive calculations of the superfluid density {rho}{sub s} in the BCS-BEC crossover regime of a uniform superfluid Fermi gas at finite temperatures. We include strong-coupling or fluctuation effects on these quantities within a Gaussian approximation. We also incorporate the same fluctuation effects into the BCS single-particle excitations described by the superfluid order parameter {delta} and Fermi chemical potential {mu}, using the Nozieres-Schmitt-Rink approximation. This treatment is shown to be necessary for consistent treatment of {rho}{sub s} over themore » entire BCS-BEC crossover. We also calculate the condensate fraction N{sub c} as a function of the temperature, a quantity which is quite different from the superfluid density {rho}{sub s}. We show that the mean-field expression for the condensate fraction N{sub c} is a good approximation even in the strong-coupling BEC regime. Our numerical results show how {rho}{sub s} and N{sub c} depend on temperature, from the weak-coupling BCS region to the BEC region of tightly bound Cooper pair molecules. In a companion paper [Phys. Rev. A 74, 063626 (2006)], we derive an equivalent expression for {rho}{sub s} from the thermodynamic potential, which exhibits the role of the pairing fluctuations in a more explicit manner.« less

AIRIS Wide Area Detection System

DTIC Science & Technology

2003-07-01

herbicola, the chemical stimulant SF6, as well as the interferents kaolin clay dust, Dugway road dust, and diesel soot. In this paper we will report on...the SF6 column density of approximately 200 ppmv-m. In future work we hope to correlate this measurement with a Gaussian plume dispersion model of

Direct Observation of Ultralow Vertical Emittance using a Vertical Undulator - presentation slides

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wootton, Kent

2015-09-17

Direct emittance measurement based on vertical undulator is discussed. Emittance was evaluated from peak ratios, the smallest measured being =0.9 ±0.3 pm rad. The angular distribution of undulator radiation departs from Gaussian approximations, a fact of which diffraction-limited light sources should be aware.

Channel capacity of OAM based FSO communication systems with partially coherent Bessel-Gaussian beams in anisotropic turbulence

NASA Astrophysics Data System (ADS)

Peng, Juan; Zhang, Li; Zhang, Kecheng; Ma, Junxian

2018-07-01

Based on the Rytov approximation theory, the transmission model of an orbital angular momentum (OAM)-carrying partially coherent Bessel-Gaussian (BG) beams propagating in weak anisotropic turbulence is established. The corresponding analytical expression of channel capacity is presented. Influences of anisotropic turbulence parameters and beam parameters on channel capacity of OAM-based free-space optical (FSO) communication systems are discussed in detail. The results indicate channel capacity increases with increasing of almost all of the parameters except for transmission distance. Raising the values of some parameters such as wavelength, propagation altitude and non-Kolmogorov power spectrum index, would markedly improve the channel capacity. In addition, we evaluate the channel capacity of Laguerre-Gaussian (LG) beams and partially coherent BG beams in anisotropic turbulence. It indicates that partially coherent BG beams are better light sources candidates for mitigating the influences of anisotropic turbulence on channel capacity of OAM-based FSO communication systems.

Fast estimate of Hartley entropy in image sharpening

NASA Astrophysics Data System (ADS)

Krbcová, Zuzana; Kukal, Jaromír.; Svihlik, Jan; Fliegel, Karel

2016-09-01

Two classes of linear IIR filters: Laplacian of Gaussian (LoG) and Difference of Gaussians (DoG) are frequently used as high pass filters for contextual vision and edge detection. They are also used for image sharpening when linearly combined with the original image. Resulting sharpening filters are radially symmetric in spatial and frequency domains. Our approach is based on the radial approximation of unknown optimal filter, which is designed as a weighted sum of Gaussian filters with various radii. The novel filter is designed for MRI image enhancement where the image intensity represents anatomical structure plus additive noise. We prefer the gradient norm of Hartley entropy of whole image intensity as a measure which has to be maximized for the best sharpening. The entropy estimation procedure is as fast as FFT included in the filter but this estimate is a continuous function of enhanced image intensities. Physically motivated heuristic is used for optimum sharpening filter design by its parameter tuning. Our approach is compared with Wiener filter on MRI images.

Childhood malnutrition in Egypt using geoadditive Gaussian and latent variable models.

PubMed

Khatab, Khaled

2010-04-01

Major progress has been made over the last 30 years in reducing the prevalence of malnutrition amongst children less than 5 years of age in developing countries. However, approximately 27% of children under the age of 5 in these countries are still malnourished. This work focuses on the childhood malnutrition in one of the biggest developing countries, Egypt. This study examined the association between bio-demographic and socioeconomic determinants and the malnutrition problem in children less than 5 years of age using the 2003 Demographic and Health survey data for Egypt. In the first step, we use separate geoadditive Gaussian models with the continuous response variables stunting (height-for-age), underweight (weight-for-age), and wasting (weight-for-height) as indicators of nutritional status in our case study. In a second step, based on the results of the first step, we apply the geoadditive Gaussian latent variable model for continuous indicators in which the 3 measurements of the malnutrition status of children are assumed as indicators for the latent variable "nutritional status".

Spatiotemporal dynamics of Gaussian laser pulse in a multi ions plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jafari Milani, M. R., E-mail: mrj.milani@gmail.com

Spatiotemporal evolutions of Gaussian laser pulse propagating through a plasma with multiple charged ions are studied, taking into account the ponderomotive nonlinearity. Coupled differential equations for beam width and pulse length parameters are established and numerically solved using paraxial ray approximation. In one-dimensional geometry, effects of laser and plasma parameters such as laser intensity, plasma density, and temperature on the longitudinal pulse compression and the laser intensity distribution are analyzed for plasmas with singly and doubly charged ions. The results demonstrate that self-compression occurs in a laser intensity range with a turning point intensity in which the self-compression process hasmore » its strongest extent. The results also show that the multiply ionized ions have different effect on the pulse compression above and below turning point intensity. Finally, three-dimensional geometry is used to analyze the simultaneous evolution of both self-focusing and self-compression of Gaussian laser pulse in such plasmas.« less

Log-amplitude statistics for Beck-Cohen superstatistics

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Konno, Hidetoshi

2013-05-01

As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for χ2, inverse χ2, and log-normal superstatistical distributions. Furthermore, we show that χ2 and inverse χ2 superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the q-Gaussian distribution with q=5/3 and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the χ2 superstatistical distribution with degree 2.

Cosmic microwave background trispectrum and primordial magnetic field limits.

PubMed

Trivedi, Pranjal; Seshadri, T R; Subramanian, Kandaswamy

2012-06-08

Primordial magnetic fields will generate non-gaussian signals in the cosmic microwave background (CMB) as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. We compute a new measure of magnetic non-gaussianity, the CMB trispectrum, on large angular scales, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately a few times 10(-29) and 10(-19), respectively. Observational limits on CMB non-gaussianity from WMAP data allow us to conservatively set upper limits of a nG, and plausibly sub-nG, on the present value of the primordial cosmic magnetic field. This represents the tightest limit so far on the strength of primordial magnetic fields, on Mpc scales, and is better than limits from the CMB bispectrum and all modes in the CMB power spectrum. Thus, the CMB trispectrum is a new and more sensitive probe of primordial magnetic fields on large scales.

Recent HBT results in Au+Au and p+p collisions from PHENIX

NASA Astrophysics Data System (ADS)

PHENIX Collaboration; Glenn, Andrew; PHENIX Collaboration

2009-11-01

We present Hanbury-Brown Twiss measurements from the PHENIX experiment at RHIC for final results for charged kaon pairs from s=200 GeV Au+Au collisions and preliminary results for charged pion pairs from s=200 GeVp+p collisions. We find that for kaon pairs from Au+Au, each traditional 3D Gaussian radius shows approximately the same linear increase as a function of Npart1/3. An imaging analysis reveals a significant non-Gaussian tail for r≳10 fm. The presence of a tail for kaon pairs demonstrates that similar non-Gaussian tails observed in earlier pion measurements cannot be fully explained by decays of long-lived resonances. The preliminary analysis of pions from s=200 GeV p+p minimum biased collisions show correlations which are well suited to traditional 3D HBT radii extraction via the Bowler-Sinyukov method, and we present R, R, and R as a function of mean transverse pair mass.

The ground state magnetic moment and susceptibility of a two electron Gaussian quantum dot

NASA Astrophysics Data System (ADS)

Boda, Aalu; Chatterjee, Ashok

2018-04-01

The problem of two interacting electrons moving in a two-dimensional semiconductor quantum dot with Gaussian confinement under the influence of an external magnetic field is studied by using a method of numerical diagonalization of the Hamiltonian matrix with in the effective-mass approximation. The energy spectrum is calculated as a function of the magnetic field. We find the ground state magnetic moment and the magnetic susceptibility show zero temperature diamagnetic peaks due to exchange induced singlet-triplet oscillations. The position and the number of these peaks depend on the size of the quantum dot and also strength of the electro-electron interaction. The theory is applied to a GaAs quantum dot.

Color Histogram Diffusion for Image Enhancement

NASA Technical Reports Server (NTRS)

Kim, Taemin

2011-01-01

Various color histogram equalization (CHE) methods have been proposed to extend grayscale histogram equalization (GHE) for color images. In this paper a new method called histogram diffusion that extends the GHE method to arbitrary dimensions is proposed. Ranges in a histogram are specified as overlapping bars of uniform heights and variable widths which are proportional to their frequencies. This diagram is called the vistogram. As an alternative approach to GHE, the squared error of the vistogram from the uniform distribution is minimized. Each bar in the vistogram is approximated by a Gaussian function. Gaussian particles in the vistoram diffuse as a nonlinear autonomous system of ordinary differential equations. CHE results of color images showed that the approach is effective.

Unstable Resonator Optical Parametric Oscillator Based on Quasi-Phase-Matched RbTiOAsO(4).

PubMed

Hansson, G; Karlsson, H; Laurell, F

2001-10-20

We demonstrate improved signal and idler-beam quality of a 3-mm-aperture quasi-phase-matched RbTiOAsO(4) optical parametric oscillator through use of a confocal unstable resonator as compared with a plane-parallel resonator. Both oscillators were singly resonant, and the periodically poled RbTiOAsO(4) crystal generated a signal at 1.56 mum and an idler at 3.33 mum when pumped at 1.064 mum. We compared the beam quality produced by the 1.2-magnification confocal unstable resonator with the beam quality produced by the plane-parallel resonator by measuring the signal and the idler beam M(2) value. We also investigated the effect of pump-beam intensity distribution by comparing the result of a Gaussian and a top-hat intensity profile pump beam. We generated a signal beam of M(2) approximately 7 and an idler beam of M(2) approximately 2.5 through use of an unstable resonator and a Gaussian intensity profile pump beam. This corresponds to an increase of a factor of approximately 2 in beam quality for the signal and a factor of 3 for the idler, compared with the beam quality of the plane-parallel resonator optical parametric oscillator.

Validity of the Born approximation for beyond Gaussian weak lensing observables

DOE PAGES

Petri, Andrea; Haiman, Zoltan; May, Morgan

2017-06-06

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show thatmore » deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O(Φ 3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O(Φ 4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5σ. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.« less

Validity of the Born approximation for beyond Gaussian weak lensing observables

NASA Astrophysics Data System (ADS)

Petri, Andrea; Haiman, Zoltán; May, Morgan

2017-06-01

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N -body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O (Φ3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O (Φ4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5 σ . Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.

Discretisation Schemes for Level Sets of Planar Gaussian Fields

NASA Astrophysics Data System (ADS)

Beliaev, D.; Muirhead, S.

2018-01-01

Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic compact manifolds. Our work is motivated by questions about the geometry of such random functions, in particular relating to the structure of their nodal and level sets. We study four discretisation schemes that extract information about level sets of planar Gaussian fields. Each scheme recovers information up to a different level of precision, and each requires a maximum mesh-size in order to be valid with high probability. The first two schemes are generalisations and enhancements of similar schemes that have appeared in the literature (Beffara and Gayet in Publ Math IHES, 2017. https://doi.org/10.1007/s10240-017-0093-0; Mischaikow and Wanner in Ann Appl Probab 17:980-1018, 2007); these give complete topological information about the level sets on either a local or global scale. As an application, we improve the results in Beffara and Gayet (2017) on Russo-Seymour-Welsh estimates for the nodal set of positively-correlated planar Gaussian fields. The third and fourth schemes are, to the best of our knowledge, completely new. The third scheme is specific to the nodal set of the random plane wave, and provides global topological information about the nodal set up to `visible ambiguities'. The fourth scheme gives a way to approximate the mean number of excursion domains of planar Gaussian fields.

fNL‑gNL mixing in the matter density field at higher orders

NASA Astrophysics Data System (ADS)

Gressel, Hedda A.; Bruni, Marco

2018-06-01

In this paper we examine how primordial non-Gaussianity contributes to nonlinear perturbative orders in the expansion of the density field at large scales in the matter dominated era. General Relativity is an intrinsically nonlinear theory, establishing a nonlinear relation between the metric and the density field. Representing the metric perturbations with the curvature perturbation ζ, it is known that nonlinearity produces effective non-Gaussian terms in the nonlinear perturbations of the matter density field δ, even if the primordial ζ is Gaussian. Here we generalise these results to the case of a non-Gaussian primordial ζ. Using a standard parametrization of primordial non-Gaussianity in ζ in terms of fNL, gNL, hNL\\ldots , we show how at higher order (from third and higher) nonlinearity also produces a mixing of these contributions to the density field at large scales, e.g. both fNL and gNL contribute to the third order in δ. This is the main result of this paper. Our analysis is based on the synergy between a gradient expansion (aka long-wavelength approximation) and standard perturbation theory at higher order. In essence, mathematically the equations for the gradient expansion are equivalent to those of first order perturbation theory, thus first-order results convert into gradient expansion results and, vice versa, the gradient expansion can be used to derive results in perturbation theory at higher order and large scales.

A Gaussian theory for fluctuations in simple liquids.

PubMed

Krüger, Matthias; Dean, David S

2017-04-07

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

Single Frequency Monolithic Solid State Green Laser as a Potential Source for Vibrometry Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sotor, Jaroslaw Z.; Antonczak, Arkadiusz J.; Abramski, Krzysztof M.

2010-05-28

In this paper miniature, monolithic single frequency solid state laser operating at 532 nm is presented. Developed Nd:GdVO{sub 4}/YVO{sub 4}/KTP consist of three crystal bonded together with a UV adhesive. The single frequency operation was obtained in wide temperature range from 17 deg. C to 27 deg. C. The laser operated with output power up to 90 mW at 532 nm. The total optical efficiency (808 nm to 532 nm) was 9.5%. Power stability was at the level of +-0.8% and the long term frequency stability was approximately 3centre dot10{sup -8}. The beam has a Gaussian profile and the M2more » parameter was below 1.1.« less

A Gaussian theory for fluctuations in simple liquids

NASA Astrophysics Data System (ADS)

Krüger, Matthias; Dean, David S.

2017-04-01

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

Modal, ray, and beam techniques for analyzing the EM scattering by open-ended waveguide cavities

NASA Technical Reports Server (NTRS)

Pathak, Prabhakar H.; Burkholder, Robert J.

1989-01-01

The problem of high-frequency electromagnetic (EM) scattering by open-ended waveguide cavities with an interior termination is analyzed via three different approaches. When cavities can be adequately modeled by joining together piecewise separable waveguide sections, a hybrid combination of asymptotic high-frequency and modal techniques is employed. In the case of more arbitrarily shaped waveguide cavities for which modes cannot even be defined in the conventional sense, the geometrical optics ray approach proves to be highly useful. However, at sufficiently high frequencies, both of these approaches tend to become inefficient. Hence, a paraxial Gaussian batch technique, which retains much of the simplicity of the ray approximation but is potentially more efficient, is investigated. Typical numerical results based on the different approaches are discussed.

Fully adaptive propagation of the quantum-classical Liouville equation

NASA Astrophysics Data System (ADS)

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-01

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Fully adaptive propagation of the quantum-classical Liouville equation.

PubMed

Horenko, Illia; Weiser, Martin; Schmidt, Burkhard; Schütte, Christof

2004-05-15

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The TRAIL (trapezoidal rule for adaptive integration of Liouville dynamics) scheme [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for nonadiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac deltalike trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-type trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multidimensional problems with deterministic treatment of nonadiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Nonadiabatic effects occurring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results.

Solute Concentration at a Pumping Well in Non-Gaussian Random Aquifers under Time-Varying Operational Schedules

NASA Astrophysics Data System (ADS)

Libera, A.; de Barros, F.; Riva, M.; Guadagnini, A.

2016-12-01

Managing contaminated groundwater systems is an arduous task for multiple reasons. First, subsurface hydraulic properties are heterogeneous and the high costs associated with site characterization leads to data scarcity (therefore, model predictions are uncertain). Second, it is common for water agencies to schedule groundwater extraction through a temporal sequence of pumping rates to maximize the benefits to anthropogenic activities and minimize the environmental footprint of the withdrawal operations. The temporal variability in pumping rates and aquifer heterogeneity affect dilution rates of contaminant plumes and chemical concentration breakthrough curves (BTCs) at the well. While contaminant transport under steady-state pumping is widely studied, the manner in which a given time-varying pumping schedule affects contaminant plume behavior is tackled only marginally. At the same time, most studies focus on the impact of Gaussian random hydraulic conductivity (K) fields on transport. Here, we systematically analyze the significance of the random space function (RSF) model characterizing K in the presence of distinct pumping operations on the uncertainty of the concentration BTC at the operating well. We juxtapose Monte Carlo based numerical results associated with two models: (a) a recently proposed Generalized Sub-Gaussian model which allows capturing non-Gaussian statistical scaling features of RSFs such as hydraulic conductivity, and (b) the commonly used Gaussian field approximation. Our novel results include an appraisal of the coupled effect of (a) the model employed to depict the random spatial variability of K and (b) transient flow regime, as induced by a temporally varying pumping schedule, on the concentration BTC at the operating well. We systematically quantify the sensitivity of the uncertainty in the contaminant BTC to the RSF model adopted for K (non-Gaussian or Gaussian) in the presence of diverse well pumping schedules. Results contribute to determine conditions under which any of these two key factors prevails on the other.

Accounting for Non-Gaussian Sources of Spatial Correlation in Parametric Functional Magnetic Resonance Imaging Paradigms II: A Method to Obtain First-Level Analysis Residuals with Uniform and Gaussian Spatial Autocorrelation Function and Independent and Identically Distributed Time-Series.

PubMed

Gopinath, Kaundinya; Krishnamurthy, Venkatagiri; Lacey, Simon; Sathian, K

2018-02-01

In a recent study Eklund et al. have shown that cluster-wise family-wise error (FWE) rate-corrected inferences made in parametric statistical method-based functional magnetic resonance imaging (fMRI) studies over the past couple of decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; principally because the spatial autocorrelation functions (sACFs) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggest otherwise. Hence, the residuals from general linear model (GLM)-based fMRI activation estimates in these studies may not have possessed a homogenously Gaussian sACF. Here we propose a method based on the assumption that heterogeneity and non-Gaussianity of the sACF of the first-level GLM analysis residuals, as well as temporal autocorrelations in the first-level voxel residual time-series, are caused by unmodeled MRI signal from neuronal and physiological processes as well as motion and other artifacts, which can be approximated by appropriate decompositions of the first-level residuals with principal component analysis (PCA), and removed. We show that application of this method yields GLM residuals with significantly reduced spatial correlation, nearly Gaussian sACF and uniform spatial smoothness across the brain, thereby allowing valid cluster-based FWE-corrected inferences based on assumption of Gaussian spatial noise. We further show that application of this method renders the voxel time-series of first-level GLM residuals independent, and identically distributed across time (which is a necessary condition for appropriate voxel-level GLM inference), without having to fit ad hoc stochastic colored noise models. Furthermore, the detection power of individual subject brain activation analysis is enhanced. This method will be especially useful for case studies, which rely on first-level GLM analysis inferences.

Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.; Korte, John J.; Mauery, Timothy M.; Mistree, Farrokh

1998-01-01

In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

Biasing and the search for primordial non-Gaussianity beyond the local type

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gleyzes, Jérôme; De Putter, Roland; Doré, Olivier

Primordial non-Gaussianity encodes valuable information about the physics of inflation, including the spectrum of particles and interactions. Significant improvements in our understanding of non-Gaussanity beyond Planck require information from large-scale structure. The most promising approach to utilize this information comes from the scale-dependent bias of halos. For local non-Gaussanity, the improvements available are well studied but the potential for non-Gaussianity beyond the local type, including equilateral and quasi-single field inflation, is much less well understood. In this paper, we forecast the capabilities of large-scale structure surveys to detect general non-Gaussianity through galaxy/halo power spectra. We study how non-Gaussanity can bemore » distinguished from a general biasing model and where the information is encoded. For quasi-single field inflation, significant improvements over Planck are possible in some regions of parameter space. We also show that the multi-tracer technique can significantly improve the sensitivity for all non-Gaussianity types, providing up to an order of magnitude improvement for equilateral non-Gaussianity over the single-tracer measurement.« less

Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals.

PubMed

Golze, Dorothea; Benedikter, Niels; Iannuzzi, Marcella; Wilhelm, Jan; Hutter, Jürg

2017-01-21

An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb, and Gaussian-type operators, which occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both integrals and their derivatives. In particular, our method is increasingly efficient for large angular momenta and highly contracted basis sets.

Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals

NASA Astrophysics Data System (ADS)

Golze, Dorothea; Benedikter, Niels; Iannuzzi, Marcella; Wilhelm, Jan; Hutter, Jürg

2017-01-01

An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb, and Gaussian-type operators, which occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both integrals and their derivatives. In particular, our method is increasingly efficient for large angular momenta and highly contracted basis sets.

Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.

1998-01-01

The use of response surface models and kriging models are compared for approximating non-random, deterministic computer analyses. After discussing the traditional response surface approach for constructing polynomial models for approximation, kriging is presented as an alternative statistical-based approximation method for the design and analysis of computer experiments. Both approximation methods are applied to the multidisciplinary design and analysis of an aerospike nozzle which consists of a computational fluid dynamics model and a finite element analysis model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations. Four optimization problems are formulated and solved using both approximation models. While neither approximation technique consistently outperforms the other in this example, the kriging models using only a constant for the underlying global model and a Gaussian correlation function perform as well as the second order polynomial response surface models.

A New Closed Form Approximation for BER for Optical Wireless Systems in Weak Atmospheric Turbulence

NASA Astrophysics Data System (ADS)

Kaushik, Rahul; Khandelwal, Vineet; Jain, R. C.

2018-04-01

Weak atmospheric turbulence condition in an optical wireless communication (OWC) is captured by log-normal distribution. The analytical evaluation of average bit error rate (BER) of an OWC system under weak turbulence is intractable as it involves the statistical averaging of Gaussian Q-function over log-normal distribution. In this paper, a simple closed form approximation for BER of OWC system under weak turbulence is given. Computation of BER for various modulation schemes is carried out using proposed expression. The results obtained using proposed expression compare favorably with those obtained using Gauss-Hermite quadrature approximation and Monte Carlo Simulations.

Quantum scattering in one-dimensional systems satisfying the minimal length uncertainty relation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernardo, Reginald Christian S., E-mail: rcbernardo@nip.upd.edu.ph; Esguerra, Jose Perico H., E-mail: jesguerra@nip.upd.edu.ph

In quantum gravity theories, when the scattering energy is comparable to the Planck energy the Heisenberg uncertainty principle breaks down and is replaced by the minimal length uncertainty relation. In this paper, the consequences of the minimal length uncertainty relation on one-dimensional quantum scattering are studied using an approach involving a recently proposed second-order differential equation. An exact analytical expression for the tunneling probability through a locally-periodic rectangular potential barrier system is obtained. Results show that the existence of a non-zero minimal length uncertainty tends to shift the resonant tunneling energies to the positive direction. Scattering through a locally-periodic potentialmore » composed of double-rectangular potential barriers shows that the first band of resonant tunneling energies widens for minimal length cases when the double-rectangular potential barrier is symmetric but narrows down when the double-rectangular potential barrier is asymmetric. A numerical solution which exploits the use of Wronskians is used to calculate the transmission probabilities through the Pöschl–Teller well, Gaussian barrier, and double-Gaussian barrier. Results show that the probability of passage through the Pöschl–Teller well and Gaussian barrier is smaller in the minimal length cases compared to the non-minimal length case. For the double-Gaussian barrier, the probability of passage for energies that are more positive than the resonant tunneling energy is larger in the minimal length cases compared to the non-minimal length case. The approach is exact and applicable to many types of scattering potential.« less

Localization in one-dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-Andre models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biddle, J.; Priour, D. J. Jr.; Wang, B.

We study the quantum localization phenomena of noninteracting particles in one-dimensional lattices based on tight-binding models with various forms of hopping terms beyond the nearest neighbor, which are generalizations of the famous Aubry-Andre and noninteracting Anderson models. For the case with deterministic disordered potential induced by a secondary incommensurate lattice (i.e., the Aubry-Andre model), we identify a class of self-dual models, for which the boundary between localized and extended eigenstates are determined analytically by employing a generalized Aubry-Andre transformation. We also numerically investigate the localization properties of nondual models with next-nearest-neighbor hopping, Gaussian, and power-law decay hopping terms. We findmore » that even for these nondual models, the numerically obtained mobility edges can be well approximated by the analytically obtained condition for localization transition in the self-dual models, as long as the decay of the hopping rate with respect to distance is sufficiently fast. For the disordered potential with genuinely random character, we examine scenarios with next-nearest-neighbor hopping, exponential, Gaussian, and power-law decay hopping terms numerically. We find that the higher-order hopping terms can remove the symmetry in the localization length about the energy band center compared to the Anderson model. Furthermore, our results demonstrate that for the power-law decay case, there exists a critical exponent below which mobility edges can be found. Our theoretical results could, in principle, be directly tested in shallow atomic optical lattice systems enabling non-nearest-neighbor hopping.« less

Forecasts of non-Gaussian parameter spaces using Box-Cox transformations

NASA Astrophysics Data System (ADS)

Joachimi, B.; Taylor, A. N.

2011-09-01

Forecasts of statistical constraints on model parameters using the Fisher matrix abound in many fields of astrophysics. The Fisher matrix formalism involves the assumption of Gaussianity in parameter space and hence fails to predict complex features of posterior probability distributions. Combining the standard Fisher matrix with Box-Cox transformations, we propose a novel method that accurately predicts arbitrary posterior shapes. The Box-Cox transformations are applied to parameter space to render it approximately multivariate Gaussian, performing the Fisher matrix calculation on the transformed parameters. We demonstrate that, after the Box-Cox parameters have been determined from an initial likelihood evaluation, the method correctly predicts changes in the posterior when varying various parameters of the experimental setup and the data analysis, with marginally higher computational cost than a standard Fisher matrix calculation. We apply the Box-Cox-Fisher formalism to forecast cosmological parameter constraints by future weak gravitational lensing surveys. The characteristic non-linear degeneracy between matter density parameter and normalization of matter density fluctuations is reproduced for several cases, and the capabilities of breaking this degeneracy by weak-lensing three-point statistics is investigated. Possible applications of Box-Cox transformations of posterior distributions are discussed, including the prospects for performing statistical data analysis steps in the transformed Gaussianized parameter space.

Real-time model learning using Incremental Sparse Spectrum Gaussian Process Regression.

PubMed

Gijsberts, Arjan; Metta, Giorgio

2013-05-01

Novel applications in unstructured and non-stationary human environments require robots that learn from experience and adapt autonomously to changing conditions. Predictive models therefore not only need to be accurate, but should also be updated incrementally in real-time and require minimal human intervention. Incremental Sparse Spectrum Gaussian Process Regression is an algorithm that is targeted specifically for use in this context. Rather than developing a novel algorithm from the ground up, the method is based on the thoroughly studied Gaussian Process Regression algorithm, therefore ensuring a solid theoretical foundation. Non-linearity and a bounded update complexity are achieved simultaneously by means of a finite dimensional random feature mapping that approximates a kernel function. As a result, the computational cost for each update remains constant over time. Finally, algorithmic simplicity and support for automated hyperparameter optimization ensures convenience when employed in practice. Empirical validation on a number of synthetic and real-life learning problems confirms that the performance of Incremental Sparse Spectrum Gaussian Process Regression is superior with respect to the popular Locally Weighted Projection Regression, while computational requirements are found to be significantly lower. The method is therefore particularly suited for learning with real-time constraints or when computational resources are limited. Copyright © 2012 Elsevier Ltd. All rights reserved.

Gaussian versus flat-top spatial beam profiles for optical stimulation of the prostate nerves

NASA Astrophysics Data System (ADS)

Tozburun, Serhat; Lagoda, Gwen A.; Burnett, Arthur L.; Fried, Nathaniel M.

2010-02-01

The cavernous nerves (CN) course along the prostate surface and are responsible for erectile function. Improved identification and preservation of the CN's is critical to maintaining sexual potency after prostate cancer surgery. Noncontact optical nerve stimulation (ONS) of the CN's was recently demonstrated in a rat model, in vivo, as a potential alternative to electrical nerve stimulation (ENS) for identification of the CN's during prostate surgery. However, the therapeutic window for ONS is narrow, so optimal design of the fiber optic delivery system is critical for safe, reproducible stimulation. This study describes modeling, assembly, and testing of an ONS probe for delivering a small, collimated, flat-top laser beam for uniform CN stimulation. A direct comparison of the magnitude and response time of the intracavernosal pressure (ICP) for both Gaussian and flat-top spatial beam profiles was performed. Thulium fiber laser radiation (λ=1870 nm) was delivered through a 200-μm fiber, with distal fiber tip chemically etched to convert a Gaussian to flat-top beam profile. The laser beam was collimated to a 1-mm-diameter spot using an aspheric lens. Computer simulations of light propagation were used to optimize the probe design. The 10-Fr (3.4-mm-OD) laparoscopic probe provided a constant radiant exposure at the CN surface. The probe was tested in four rats, in vivo. ONS of the CN's was performed with a 1-mm-diameter spot, 5-ms pulse duration, and pulse rate of 20 Hz for a duration of 15-30 s. The flat-top laser beam profile consistently produced a faster and higher ICP response at a lower radiant exposure than the Gaussian beam profile due, in part, to easier alignment of the more uniform beam with nerve. The threshold for ONS was approximately 0.14 J/cm2, corresponding to a temperature increase of 6-8°C at the CN surface after a stimulation time of 15 s. With further development, ONS may be used as a diagnostic tool for identification of CN's during prostate cancer surgery.

Topological Defects and Structures in the Early Universe

NASA Astrophysics Data System (ADS)

Zhu, Yong

1997-08-01

This thesis discusses the topological defects generated in the early universe and their contributions to cosmic structure formation. First, we investigate non-Gaussian isocurvature perturbations generated by the evolution of Goldstone modes during inflation. If a global symmetry is broken before inflation, the resulting Goldstone modes are disordered during inflation in a precise and predictable way. After inflation these Goldstone modes order themselves in a self-similar way, much as Goldstone modes in field ordering scenarios based on the Kibble mechanism. For (Hi2/Mpl2)~10- 6, through their gravitational interaction these Goldstone modes generate density perturbations of approximately the right magnitude to explain the cosmic microwave background (CMB) anisotropy and seed the structure seen in the universe today. In such a model non-Gaussian perturbations result because to lowest order density perturbations are sourced by products of Gaussian fields. We explore the issue of phase dispersion and conclude that this non-Gaussian model predicts Doppler peaks in the CMB anisotropy. Topological defects generated from quantum fluctuations during inflation are studied in chapter four. We present a calculation of the power spectrum generated in a classically symmetry-breaking O(N) scalar field through inflationary quantum fluctuations, using the large-N limit. The effective potential of the theory in de Sitter space is obtained from a gap equation which is exact at large N. Quantum fluctuations restore the O(N) symmetry in de Sitter space, but for the finite values of N of interest, there is symmetry breaking and phase ordering after inflation, described by the classical nonlinear sigma model. The scalar field power spectrum is obtained as a function of the scalar field self-coupling. In the second part of the thesis, we investigate non-Abelian topological worm-holes, obtained when winding number one texture field is coupled to Einstein gravity with a conserved global charge. This topological wormhole has the same Euclidean action as axion wormholes and charged scalar wormholes. We find that free topological wormholes are spontaneously generated in the Euclidean space-time with finite density. It is then shown that wormholes with finite density might destroy any long range order in the global fields.

A Very Hot, High Redshift Cluster of Galaxies: More Trouble for Omega(0) = 1

NASA Technical Reports Server (NTRS)

Donahue, Megan; Voit, G. Mark; Gioia, Isabella; Luppino, Gerry; Hughes, John P.; Stocke, John T.

1998-01-01

We have observed the most distant (= 0.829) cluster of galaxies in the Einstein Extended Medium Sensitivity Survey (EMSS), with the ASCA and ROSAT satellites. We find an X-ray temperature of 12.3 (sup +3.1) (sub -2.2)keV for this cluster, and the ROSAT map reveals significant substructure. The high temperature of MS1054-0321 is consistent with both its approximate velocity dispersion, based on the redshifts of 12 cluster members we have obtained at the Keck and the Canada-France-Hawaii telescopes, and with its weak lensing signature. The X-ray temperature of this cluster implies a virial mass approx. 7.4 x 10 (sup 14) h (sup -1) M (circle dot), if the mean matter density in the universe equals the critical value (OMEGA (sub 0) = 1), or larger if OMEGA (sub 0) is less than 1. Finding such a hot, massive cluster in the EMSS is extremely improbable if clusters grew from Gaussian perturbations in an OMEGA (sub 0) = 1 universe. Combining the assumptions that OMEGA (sub 0) = 1 and that the initial perturbations were Gaussian with the observed X-ray temperature function at low redshift, we show that this probability of this cluster occurring in the volume sampled by the EMSS is less than a few times 10 (sup -5). Nor is MS1054-0321 the only hot cluster at high redshift; the only two other z greater than 0.5 EMSS clusters already observed with ASCA also have temperatures exceeding 8 keV. Assuming again that the initial perturbations were Gaussian and OMEGA (sub 0) = 1, we find that each one is improbable at the less than 10 (sup -2) level. These observations, along with the fact that these luminosities and temperatures of the high-z clusters all agree with the low-z L (sub X) - T (sub X) relation, argue strongly that OMEGA (sub 0) less than 1. Otherwise, the initial perturbations must be non-Gaussian, if these clusters' temperatures do indeed reflect their gravitational potentials.

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

PubMed

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence.

PubMed

Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu; Shen, Jianqi

2006-07-10

On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the Möbius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.

Self-Consistent Field Theory of Gaussian Ring Polymers

NASA Astrophysics Data System (ADS)

Kim, Jaeup; Yang, Yong-Biao; Lee, Won Bo

2012-02-01

Ring polymers, being free from chain ends, have fundamental importance in understanding the polymer statics and dynamics which are strongly influenced by the chain end effects. At a glance, their theoretical treatment may not seem particularly difficult, but the absence of chain ends and the topological constraints make the problem non-trivial, which results in limited success in the analytical or semi-analytical formulation of ring polymer theory. Here, I present a self-consistent field theory (SCFT) formalism of Gaussian (topologically unconstrained) ring polymers for the first time. The resulting static property of homogeneous and inhomogeneous ring polymers are compared with the random phase approximation (RPA) results. The critical point for ring homopolymer system is exactly the same as the linear polymer case, χN = 2, since a critical point does not depend on local structures of polymers. The critical point for ring diblock copolymer melts is χN 17.795, which is approximately 1.7 times of that of linear diblock copolymer melts, χN 10.495. The difference is due to the ring structure constraint.

Towards information-optimal simulation of partial differential equations.

PubMed

Leike, Reimar H; Enßlin, Torsten A

2018-03-01

Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an information-optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier-Galerkin methods. We discuss implications of the approximations made.

Energy levels of one-dimensional systems satisfying the minimal length uncertainty relation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernardo, Reginald Christian S., E-mail: rcbernardo@nip.upd.edu.ph; Esguerra, Jose Perico H., E-mail: jesguerra@nip.upd.edu.ph

2016-10-15

The standard approach to calculating the energy levels for quantum systems satisfying the minimal length uncertainty relation is to solve an eigenvalue problem involving a fourth- or higher-order differential equation in quasiposition space. It is shown that the problem can be reformulated so that the energy levels of these systems can be obtained by solving only a second-order quasiposition eigenvalue equation. Through this formulation the energy levels are calculated for the following potentials: particle in a box, harmonic oscillator, Pöschl–Teller well, Gaussian well, and double-Gaussian well. For the particle in a box, the second-order quasiposition eigenvalue equation is a second-ordermore » differential equation with constant coefficients. For the harmonic oscillator, Pöschl–Teller well, Gaussian well, and double-Gaussian well, a method that involves using Wronskians has been used to solve the second-order quasiposition eigenvalue equation. It is observed for all of these quantum systems that the introduction of a nonzero minimal length uncertainty induces a positive shift in the energy levels. It is shown that the calculation of energy levels in systems satisfying the minimal length uncertainty relation is not limited to a small number of problems like particle in a box and the harmonic oscillator but can be extended to a wider class of problems involving potentials such as the Pöschl–Teller and Gaussian wells.« less

Multi-field inflation with a random potential

NASA Astrophysics Data System (ADS)

Tye, S.-H. Henry; Xu, Jiajun; Zhang, Yang

2009-04-01

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian-like motion with a drift in the D-dimensional field space, allowing entropic perturbation modes to continuously and randomly feed into the adiabatic mode. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario where the stochastic scatterings are frequent but mild, the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, in which the coarse-grained motion of the inflaton is significantly slowed down by the scatterings, leads to rich phenomenologies. The power spectrum exhibits primordial fluctuations on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and have been smoothed out by binning of data points. With more data coming in the future, we expect these features can be detected or falsified. On the other hand the tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced by the large ratio of the Brownian-like motion speed over the drift speed. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, and is negligible in the weakly random scenario. However, non-Gaussianity can possibly be enhanced by resonant effects in the strongly random scenario or arise from the entropic perturbations during the onset of (p)reheating if the background inflaton trajectory exhibits particular properties. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.

Scaling of Ln(Permeability) in Sediments and Velocity Distributions in Turbulence: The Possibility of an Analogy.

NASA Astrophysics Data System (ADS)

Molz, F. J.; Kozubowski, T. J.; Miller, R. S.; Podgorski, K.

2005-12-01

The theory of non-stationary stochastic processes with stationary increments gives rise to stochastic fractals. When such fractals are used to represent measurements of (assumed stationary) physical properties, such as ln(k) increments in sediments or velocity increments "delta(v)" in turbulent flows, the resulting measurements exhibit scaling, either spatial, temporal or both. (In the present context, such scaling refers to systematic changes in the statistical properties of the increment distributions, such as variance, with the lag size over which the increments are determined.) Depending on the class of probability density functions (PDFs) that describe the increment distributions, the resulting stochastic fractals will display different properties. Until recently, the stationary increment process was represented using mainly Gaussian, Gamma or Levy PDFs. However, measurements in both sediments and fluid turbulence indicate that these PDFs are not commonly observed. Based on recent data and previous studies referenced and discussed in Meerschaert et al. (2004) and Molz et al. (2005), the measured increment PDFs display an approximate double exponential (Laplace) shape at smaller lags, and this shape evolves towards Gaussian at larger lags. A model for this behavior based on the Generalized Laplace PDF family called fractional Laplace motion, in analogy with its Gaussian counterpart - fractional Brownian motion, has been suggested (Meerschaert et al., 2004) and the necessary mathematics elaborated (Kozubowski et al., 2005). The resulting stochastic fractal is not a typical self-affine monofractal, but it does exhibit monofractal-like scaling in certain lag size ranges. To date, it has been shown that the Generalized Laplace family fits ln(k) increment distributions and reproduces the original 1941 theory of Kolmogorov when applied to Eulerian turbulent velocity increments. However, to make a physically self-consistent application to turbulence, one must adopt a Lagrangian viewpoint, and the details of this approach are still being developed. The potential analogy between turbulent delta(v) and sediment delta[ln(k)] is intriguing, and perhaps offers insight into the underlying chaotic processes that constitute turbulence and may result also in the pervasive heterogeneity observed in most natural sediments. Properties of the new Laplace fractal are presented, and potential applications to both sediments and fluid turbulence are discussed.

Self-assembled structures of Gaussian nematic particles.

PubMed

Nikoubashman, Arash; Likos, Christos N

2010-03-17

We investigate the stable crystalline configurations of a nematic liquid crystal made of soft parallel ellipsoidal particles interacting via a repulsive, anisotropic Gaussian potential. For this purpose, we use genetic algorithms (GA) in order to predict all relevant and possible solid phase candidates into which this fluid can freeze. Subsequently we present and discuss the emerging novel structures and the resulting zero-temperature phase diagram of this system. The latter features a variety of crystalline arrangements, in which the elongated Gaussian particles in general do not align with any one of the high-symmetry crystallographic directions, a compromise arising from the interplay and competition between anisotropic repulsions and crystal ordering. Only at very strong degrees of elongation does a tendency of the Gaussian nematics to align with the longest axis of the elementary unit cell emerge.

Automated discovery and construction of surface phase diagrams using machine learning

DOE PAGES

Ulissi, Zachary W.; Singh, Aayush R.; Tsai, Charlie; ...

2016-08-24

Surface phase diagrams are necessary for understanding surface chemistry in electrochemical catalysis, where a range of adsorbates and coverages exist at varying applied potentials. These diagrams are typically constructed using intuition, which risks missing complex coverages and configurations at potentials of interest. More accurate cluster expansion methods are often difficult to implement quickly for new surfaces. We adopt a machine learning approach to rectify both issues. Using a Gaussian process regression model, the free energy of all possible adsorbate coverages for surfaces is predicted for a finite number of adsorption sites. Our result demonstrates a rational, simple, and systematic approachmore » for generating accurate free-energy diagrams with reduced computational resources. Finally, the Pourbaix diagram for the IrO 2(110) surface (with nine coverages from fully hydrogenated to fully oxygenated surfaces) is reconstructed using just 20 electronic structure relaxations, compared to approximately 90 using typical search methods. Similar efficiency is demonstrated for the MoS 2 surface.« less

Naturalistic stimulation changes the dynamic response of action potential encoding in a mechanoreceptor

PubMed Central

Pfeiffer, Keram; French, Andrew S.

2015-01-01

Naturalistic signals were created from vibrations made by locusts walking on a Sansevieria plant. Both naturalistic and Gaussian noise signals were used to mechanically stimulate VS-3 slit-sense mechanoreceptor neurons of the spider, Cupiennius salei, with stimulus amplitudes adjusted to give similar firing rates for either stimulus. Intracellular microelectrodes recorded action potentials, receptor potential, and receptor current, using current clamp and voltage clamp. Frequency response analysis showed that naturalistic stimulation contained relatively more power at low frequencies, and caused increased neuronal sensitivity to higher frequencies. In contrast, varying the amplitude of Gaussian stimulation did not change neuronal dynamics. Naturalistic stimulation contained less entropy than Gaussian, but signal entropy was higher than stimulus in the resultant receptor current, indicating addition of uncorrelated noise during transduction. The presence of added noise was supported by measuring linear information capacity in the receptor current. Total entropy and information capacity in action potentials produced by either stimulus were much lower than in earlier stages, and limited to the maximum entropy of binary signals. We conclude that the dynamics of action potential encoding in VS-3 neurons are sensitive to the form of stimulation, but entropy and information capacity of action potentials are limited by firing rate. PMID:26578975

A method for selective excitation of Ince-Gaussian modes in an end-pumped solid-state laser

NASA Astrophysics Data System (ADS)

Lei, J.; Hu, A.; Wang, Y.; Chen, P.

2014-12-01

A method for selective excitation of Ince-Gaussian modes is presented. The method is based on the spatial distributions of Ince-Gaussian modes as well as the transverse mode selection theory. Significant diffraction loss is introduced in a resonator by using opaque lines at zero-intensity positions, and this loss allows to excite a specific mode; we call this method "loss control." We study the method by means of numerical simulation of a half-symmetric laser resonator. The simulated field is represented by angular spectrum of the plane waves representation, and its changes are calculated by the two-dimensional fast Fourier transform algorithm when it passes through the optical elements and propagates back and forth in the resonator. The output lasing modes of our method have an overlap of over 90 % with the target Ince-Gaussian modes. The method will be beneficial to the further study of properties and potential applications of Ince-Gaussian modes.

Analysis of the EM scattering from arbitrary open-ended waveguide cavities using axial Gaussian Beam tracking

NASA Technical Reports Server (NTRS)

Burkholder, R. J.; Pathak, P. H.

1988-01-01

The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width.

Reverse engineering gene regulatory networks from measurement with missing values.

PubMed

Ogundijo, Oyetunji E; Elmas, Abdulkadir; Wang, Xiaodong

2016-12-01

Gene expression time series data are usually in the form of high-dimensional arrays. Unfortunately, the data may sometimes contain missing values: for either the expression values of some genes at some time points or the entire expression values of a single time point or some sets of consecutive time points. This significantly affects the performance of many algorithms for gene expression analysis that take as an input, the complete matrix of gene expression measurement. For instance, previous works have shown that gene regulatory interactions can be estimated from the complete matrix of gene expression measurement. Yet, till date, few algorithms have been proposed for the inference of gene regulatory network from gene expression data with missing values. We describe a nonlinear dynamic stochastic model for the evolution of gene expression. The model captures the structural, dynamical, and the nonlinear natures of the underlying biomolecular systems. We present point-based Gaussian approximation (PBGA) filters for joint state and parameter estimation of the system with one-step or two-step missing measurements . The PBGA filters use Gaussian approximation and various quadrature rules, such as the unscented transform (UT), the third-degree cubature rule and the central difference rule for computing the related posteriors. The proposed algorithm is evaluated with satisfying results for synthetic networks, in silico networks released as a part of the DREAM project, and the real biological network, the in vivo reverse engineering and modeling assessment (IRMA) network of yeast Saccharomyces cerevisiae . PBGA filters are proposed to elucidate the underlying gene regulatory network (GRN) from time series gene expression data that contain missing values. In our state-space model, we proposed a measurement model that incorporates the effect of the missing data points into the sequential algorithm. This approach produces a better inference of the model parameters and hence, more accurate prediction of the underlying GRN compared to when using the conventional Gaussian approximation (GA) filters ignoring the missing data points.

Relativistic longitudinal self-compression of ultrashort time-domain hollow Gaussian pulses in plasma

NASA Astrophysics Data System (ADS)

Cao, Xiaochao; Fang, Feiyun; Wang, Zhaoying; Lin, Qiang

2017-10-01

We report a study on dynamical evolution of the ultrashort time-domain dark hollow Gaussian (TDHG) pulses beyond the slowly varying envelope approximation in homogenous plasma. Using the complex-source-point model, an analytical formula is proposed for describing TDHG pulses based on the oscillating electric dipoles, which is the exact solution of the Maxwell's equations. The numerical simulations show the relativistic longitudinal self-compression (RSC) due to the relativistic mass variation of moving electrons. The influences of plasma oscillation frequency and collision effect on dynamics of the TDHG pulses in plasma have been considered. Furthermore, we analyze the evolution of instantaneous energy density of the TDHG pulses on axis as well as the off axis condition.

Influence of light absorption on relativistic self-focusing of Gaussian laser beam in cold quantum plasma

NASA Astrophysics Data System (ADS)

Patil, S. D.; Valkunde, A. T.; Vhanmore, B. D.; Urunkar, T. U.; Gavade, K. M.; Takale, M. V.

2018-05-01

When inter particle distance is comparable to the de Broglies wavelength of charged particles, quantum effects in plasmas are unavoidable. We have exploited an influence of light absorption on self-focusing of Gaussian laser beam in cold quantum plasma by considering relativistic nonlinearity. Nonlinear differential equation governing beam-width parameter has been established by using parabolic equation approach under paraxial and WKB approximations. The effect of light absorption on variation of beam-width parameter with dimensionless distance of propagation is presented graphically and discussed. It is found that light absorption plays vital role in weakening the relativistic self-focusing of laser beam during propagation in cold quantum plasma and gives reasonably interesting results.

Higher-order correlations for fluctuations in the presence of fields.

PubMed

Boer, A; Dumitru, S

2002-10-01

The higher-order moments of the fluctuations for thermodynamic systems in the presence of fields are investigated in the framework of a theoretical method. The method uses a generalized statistical ensemble consistent with an adequate expression for the internal energy. The applications refer to the case of a system in a magnetoquasistatic field. In the case of linear magnetic media, one finds that, for the description of the magnetic induction fluctuations, the Gaussian approximation is satisfactory. For nonlinear media, the corresponding fluctuations are non-Gaussian, having a non-null asymmetry. Furthermore, the respective fluctuations have characteristics of leptokurtic, mesokurtic and platykurtic type, depending on the value of the magnetic field strength as compared with a scaling factor of the magnetization curve.

Two-component Gaussian core model: Strong-coupling limit, Bjerrum pairs, and gas-liquid phase transition.

PubMed

Frydel, Derek; Levin, Yan

2018-01-14

In the present work, we investigate a gas-liquid transition in a two-component Gaussian core model, where particles of the same species repel and those of different species attract. Unlike a similar transition in a one-component system with particles having attractive interactions at long separations and repulsive interactions at short separations, a transition in the two-component system is not driven solely by interactions but by a specific feature of the interactions, the correlations. This leads to extremely low critical temperature, as correlations are dominant in the strong-coupling limit. By carrying out various approximations based on standard liquid-state methods, we show that a gas-liquid transition of the two-component system poses a challenging theoretical problem.

Two-component Gaussian core model: Strong-coupling limit, Bjerrum pairs, and gas-liquid phase transition

NASA Astrophysics Data System (ADS)

Frydel, Derek; Levin, Yan

2018-01-01

In the present work, we investigate a gas-liquid transition in a two-component Gaussian core model, where particles of the same species repel and those of different species attract. Unlike a similar transition in a one-component system with particles having attractive interactions at long separations and repulsive interactions at short separations, a transition in the two-component system is not driven solely by interactions but by a specific feature of the interactions, the correlations. This leads to extremely low critical temperature, as correlations are dominant in the strong-coupling limit. By carrying out various approximations based on standard liquid-state methods, we show that a gas-liquid transition of the two-component system poses a challenging theoretical problem.

MAI statistics estimation and analysis in a DS-CDMA system

NASA Astrophysics Data System (ADS)

Alami Hassani, A.; Zouak, M.; Mrabti, M.; Abdi, F.

2018-05-01

A primary limitation of Direct Sequence Code Division Multiple Access DS-CDMA link performance and system capacity is multiple access interference (MAI). To examine the performance of CDMA systems in the presence of MAI, i.e., in a multiuser environment, several works assumed that the interference can be approximated by a Gaussian random variable. In this paper, we first develop a new and simple approach to characterize the MAI in a multiuser system. In addition to statistically quantifying the MAI power, the paper also proposes a statistical model for both variance and mean of the MAI for synchronous and asynchronous CDMA transmission. We show that the MAI probability density function (PDF) is Gaussian for the equal-received-energy case and validate it by computer simulations.

Conductance fluctuation of edge-disordered graphene nanoribbons: Crossover from diffusive transport to Anderson localization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takashima, Kengo; Yamamoto, Takahiro, E-mail: takahiro@rs.tus.ac.jp; Department of Liberal Arts

Conductance fluctuation of edge-disordered graphene nanoribbons (ED-GNRs) is examined using the non-equilibrium Green's function technique combined with the extended Hückel approximation. The mean free path λ and the localization length ξ of the ED-GNRs are determined to classify the quantum transport regimes. In the diffusive regime where the length L{sub c} of the ED-GNRs is much longer than λ and much shorter than ξ, the conductance histogram is given by a Gaussian distribution function with universal conductance fluctuation. In the localization regime where L{sub c}≫ξ, the histogram is no longer the universal Gaussian distribution but a lognormal distribution that characterizesmore » Anderson localization.« less

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-01

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-14

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Analysis of the Hessian for Inverse Scattering Problems. Part 3. Inverse Medium Scattering of Electromagnetic Waves in Three Dimensions

DTIC Science & Technology

2012-08-01

small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This in turn enables fast solution of an appropriately...implication of the compactness of the Hessian is that for small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This...probability distribution is given by the inverse of the Hessian of the negative log likelihood function. For Gaussian data noise and model error, this

Nonparaxial and paraxial focusing of azimuthal-variant vector beams.

PubMed

Gu, Bing; Cui, Yiping

2012-07-30

Based on the vectorial Rayleigh-Sommerfeld formulas under the weak nonparaxial approximation, we investigate the propagation behavior of a lowest-order Laguerre-Gaussian beam with azimuthal-variant states of polarization. We present the analytical expressions for the radial, azimuthal, and longitudinal components of the electric field with an arbitrary integer topological charge m focused by a nonaperturing thin lens. We illustrate the three-dimensional optical intensities, energy flux distributions, beam waists, and focal shifts of the focused azimuthal-variant vector beams under the nonparaxial and paraxial approximations.

An approximate generalized linear model with random effects for informative missing data.

PubMed

Follmann, D; Wu, M

1995-03-01

This paper develops a class of models to deal with missing data from longitudinal studies. We assume that separate models for the primary response and missingness (e.g., number of missed visits) are linked by a common random parameter. Such models have been developed in the econometrics (Heckman, 1979, Econometrica 47, 153-161) and biostatistics (Wu and Carroll, 1988, Biometrics 44, 175-188) literature for a Gaussian primary response. We allow the primary response, conditional on the random parameter, to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness. The resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects. An example is given to illustrate the approximate approach, and simulations are performed to critique the adequacy of the approximation for repeated binary data.

Probabilistic solutions of nonlinear oscillators excited by combined colored and white noise excitations

NASA Astrophysics Data System (ADS)

Siu-Siu, Guo; Qingxuan, Shi

2017-03-01

In this paper, single-degree-of-freedom (SDOF) systems combined to Gaussian white noise and Gaussian/non-Gaussian colored noise excitations are investigated. By expressing colored noise excitation as a second-order filtered white noise process and introducing colored noise as an additional state variable, the equation of motion for SDOF system under colored noise is then transferred artificially to multi-degree-of-freedom (MDOF) system under white noise excitations with four-coupled first-order differential equations. As a consequence, corresponding Fokker-Planck-Kolmogorov (FPK) equation governing the joint probabilistic density function (PDF) of state variables increases to 4-dimension (4-D). Solution procedure and computer programme become much more sophisticated. The exponential-polynomial closure (EPC) method, widely applied for cases of SDOF systems under white noise excitations, is developed and improved for cases of systems under colored noise excitations and for solving the complex 4-D FPK equation. On the other hand, Monte Carlo simulation (MCS) method is performed to test the approximate EPC solutions. Two examples associated with Gaussian and non-Gaussian colored noise excitations are considered. Corresponding band-limited power spectral densities (PSDs) for colored noise excitations are separately given. Numerical studies show that the developed EPC method provides relatively accurate estimates of the stationary probabilistic solutions, especially the ones in the tail regions of the PDFs. Moreover, statistical parameter of mean-up crossing rate (MCR) is taken into account, which is important for reliability and failure analysis. Hopefully, our present work could provide insights into the investigation of structures under random loadings.

Non-Gaussian structure of B-mode polarization after delensing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Namikawa, Toshiya; Nagata, Ryo, E-mail: namikawa@slac.stanford.edu, E-mail: rnagata@post.kek.jp

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less

Non-Gaussian structure of B-mode polarization after delensing

NASA Astrophysics Data System (ADS)

Namikawa, Toshiya; Nagata, Ryo

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. In this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.

Non-Gaussian structure of B-mode polarization after delensing

DOE PAGES

Namikawa, Toshiya; Nagata, Ryo

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. Furthermore, as a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less

The impact of non-Gaussianity upon cosmological forecasts

NASA Astrophysics Data System (ADS)

Repp, A.; Szapudi, I.; Carron, J.; Wolk, M.

2015-12-01

The primary science driver for 3D galaxy surveys is their potential to constrain cosmological parameters. Forecasts of these surveys' effectiveness typically assume Gaussian statistics for the underlying matter density, despite the fact that the actual distribution is decidedly non-Gaussian. To quantify the effect of this assumption, we employ an analytic expression for the power spectrum covariance matrix to calculate the Fisher information for Baryon Acoustic Oscillation (BAO)-type model surveys. We find that for typical number densities, at kmax = 0.5h Mpc-1, Gaussian assumptions significantly overestimate the information on all parameters considered, in some cases by up to an order of magnitude. However, after marginalizing over a six-parameter set, the form of the covariance matrix (dictated by N-body simulations) causes the majority of the effect to shift to the `amplitude-like' parameters, leaving the others virtually unaffected. We find that Gaussian assumptions at such wavenumbers can underestimate the dark energy parameter errors by well over 50 per cent, producing dark energy figures of merit almost three times too large. Thus, for 3D galaxy surveys probing the non-linear regime, proper consideration of non-Gaussian effects is essential.

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

NASA Astrophysics Data System (ADS)

Song, Jong-Won; Hirao, Kimihiko

2015-07-01

We previously developed an efficient screened hybrid functional called Gaussian-Perdew-Burke-Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals. We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Jong-Won; Hirao, Kimihiko, E-mail: hirao@riken.jp

2015-07-14

We previously developed an efficient screened hybrid functional called Gaussian-Perdew–Burke–Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals.more » We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.« less

Dynamical transition for a particle in a squared Gaussian potential

NASA Astrophysics Data System (ADS)

Touya, C.; Dean, D. S.

2007-02-01

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by ψ = phi2/2 where phi is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.

Analysis of multidimensional difference-of-Gaussians filters in terms of directly observable parameters.

PubMed

Cope, Davis; Blakeslee, Barbara; McCourt, Mark E

2013-05-01

The difference-of-Gaussians (DOG) filter is a widely used model for the receptive field of neurons in the retina and lateral geniculate nucleus (LGN) and is a potential model in general for responses modulated by an excitatory center with an inhibitory surrounding region. A DOG filter is defined by three standard parameters: the center and surround sigmas (which define the variance of the radially symmetric Gaussians) and the balance (which defines the linear combination of the two Gaussians). These parameters are not directly observable and are typically determined by nonlinear parameter estimation methods applied to the frequency response function. DOG filters show both low-pass (optimal response at zero frequency) and bandpass (optimal response at a nonzero frequency) behavior. This paper reformulates the DOG filter in terms of a directly observable parameter, the zero-crossing radius, and two new (but not directly observable) parameters. In the two-dimensional parameter space, the exact region corresponding to bandpass behavior is determined. A detailed description of the frequency response characteristics of the DOG filter is obtained. It is also found that the directly observable optimal frequency and optimal gain (the ratio of the response at optimal frequency to the response at zero frequency) provide an alternate coordinate system for the bandpass region. Altogether, the DOG filter and its three standard implicit parameters can be determined by three directly observable values. The two-dimensional bandpass region is a potential tool for the analysis of populations of DOG filters (for example, populations of neurons in the retina or LGN), because the clustering of points in this parameter space may indicate an underlying organizational principle. This paper concentrates on circular Gaussians, but the results generalize to multidimensional radially symmetric Gaussians and are given as an appendix.

Evaluation of a finite multipole expansion technique for the computation of electrostatic potentials of dibenzo-p-dioxins and related systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murray, J.S.; Grice, M.E.; Politzer, P.

1990-01-01

The electrostatic potential V(r) that the nuclei and electrons of a molecule create in the surrounding space is well established as a guide in the study of molecular reactivity, and particularly, of biological recognition processes. Its rigorous computation is, however, very demanding of computer time for large molecules, such as those of interest in recognition interactions. The authors have accordingly investigated the use of an approximate finite multicenter multipole expansion technique to determine its applicability for producing reliable electrostatic potentials of dibenzo-p-dioxins and related molecules, with significantly reduced amounts of computer time, at distances of interest in recognition studies. Amore » comparative analysis of the potentials of three dibenzo-q-dioxins and a substituted naphthalene molecule computed using both the multipole expansion technique and GAUSSIAN 82 at the STO-5G level has been carried out. Overall they found that regions of negative and positive V(r) at 1.75 A above the molecular plane are very well reproduced by the multipole expansion technique, with up to a twenty-fold improvement in computer time.« less

Signal Partitioning Algorithm for Highly Efficient Gaussian Mixture Modeling in Mass Spectrometry

PubMed Central

Polanski, Andrzej; Marczyk, Michal; Pietrowska, Monika; Widlak, Piotr; Polanska, Joanna

2015-01-01

Mixture - modeling of mass spectra is an approach with many potential applications including peak detection and quantification, smoothing, de-noising, feature extraction and spectral signal compression. However, existing algorithms do not allow for automated analyses of whole spectra. Therefore, despite highlighting potential advantages of mixture modeling of mass spectra of peptide/protein mixtures and some preliminary results presented in several papers, the mixture modeling approach was so far not developed to the stage enabling systematic comparisons with existing software packages for proteomic mass spectra analyses. In this paper we present an efficient algorithm for Gaussian mixture modeling of proteomic mass spectra of different types (e.g., MALDI-ToF profiling, MALDI-IMS). The main idea is automated partitioning of protein mass spectral signal into fragments. The obtained fragments are separately decomposed into Gaussian mixture models. The parameters of the mixture models of fragments are then aggregated to form the mixture model of the whole spectrum. We compare the elaborated algorithm to existing algorithms for peak detection and we demonstrate improvements of peak detection efficiency obtained by using Gaussian mixture modeling. We also show applications of the elaborated algorithm to real proteomic datasets of low and high resolution. PMID:26230717

Wavelength interrogation of fiber Bragg grating sensors based on crossed optical Gaussian filters.

PubMed

Cheng, Rui; Xia, Li; Zhou, Jiaao; Liu, Deming

2015-04-15

Conventional intensity-modulated measurements require to be operated in linear range of filter or interferometric response to ensure a linear detection. Here, we present a wavelength interrogation system for fiber Bragg grating sensors where the linear transition is achieved with crossed Gaussian transmissions. This unique filtering characteristic makes the responses of the two branch detections follow Gaussian functions with the same parameters except for a delay. The substraction of these two delayed Gaussian responses (in dB) ultimately leads to a linear behavior, which is exploited for the sensor wavelength determination. Beside its flexibility and inherently power insensitivity, the proposal also shows a potential of a much wider operational range. Interrogation of a strain-tuned grating was accomplished, with a wide sensitivity tuning range from 2.56 to 8.7 dB/nm achieved.

Stochastic inflation lattice simulations - Ultra-large scale structure of the universe

NASA Technical Reports Server (NTRS)

Salopek, D. S.

1991-01-01

Non-Gaussian fluctuations for structure formation may arise in inflation from the nonlinear interaction of long wavelength gravitational and scalar fields. Long wavelength fields have spatial gradients, a (exp -1), small compared to the Hubble radius, and they are described in terms of classical random fields that are fed by short wavelength quantum noise. Lattice Langevin calculations are given for a toy model with a scalar field interacting with an exponential potential where one can obtain exact analytic solutions of the Fokker-Planck equation. For single scalar field models that are consistent with current microwave background fluctuations, the fluctuations are Gaussian. However, for scales much larger than our observable Universe, one expects large metric fluctuations that are non-Gaussian. This example illuminates non-Gaussian models involving multiple scalar fields which are consistent with current microwave background limits.

Coherent state coding approaches the capacity of non-Gaussian bosonic channels

NASA Astrophysics Data System (ADS)

Huber, Stefan; König, Robert

2018-05-01

The additivity problem asks if the use of entanglement can boost the information-carrying capacity of a given channel beyond what is achievable by coding with simple product states only. This has recently been shown not to be the case for phase-insensitive one-mode Gaussian channels, but remains unresolved in general. Here we consider two general classes of bosonic noise channels, which include phase-insensitive Gaussian channels as special cases: these are attenuators with general, potentially non-Gaussian environment states and classical noise channels with general probabilistic noise. We show that additivity violations, if existent, are rather minor for all these channels: the maximal gain in classical capacity is bounded by a constant independent of the input energy. Our proof shows that coding by simple classical modulation of coherent states is close to optimal.

Analysis of dynamic system response to product random processes

NASA Technical Reports Server (NTRS)

Sidwell, K.

1978-01-01

The response of dynamic systems to the product of two independent Gaussian random processes is developed by use of the Fokker-Planck and associated moment equations. The development is applied to the amplitude modulated process which is used to model atmospheric turbulence in aeronautical applications. The exact solution for the system response is compared with the solution obtained by the quasi-steady approximation which omits the dynamic properties of the random amplitude modulation. The quasi-steady approximation is valid as a limiting case of the exact solution for the dynamic response of linear systems to amplitude modulated processes. In the nonlimiting case the quasi-steady approximation can be invalid for dynamic systems with low damping.

Gaussian and Airy wave packets of massive particles with orbital angular momentum

NASA Astrophysics Data System (ADS)

Karlovets, Dmitry V.

2015-01-01

While wave-packet solutions for relativistic wave equations are oftentimes thought to be approximate (paraxial), we demonstrate, by employing a null-plane- (light-cone-) variable formalism, that there is a family of such solutions that are exact. A scalar Gaussian wave packet in the transverse plane is generalized so that it acquires a well-defined z component of the orbital angular momentum (OAM), while it may not acquire a typical "doughnut" spatial profile. Such quantum states and beams, in contrast to the Bessel states, may have an azimuthal-angle-dependent probability density and finite uncertainty of the OAM, which is determined by the packet's width. We construct a well-normalized Airy wave packet, which can be interpreted as a one-particle state for a relativistic massive boson, show that its center moves along the same quasiclassical straight path, and, which is more important, spreads with time and distance exactly as a Gaussian wave packet does, in accordance with the uncertainty principle. It is explained that this fact does not contradict the well-known "nonspreading" feature of the Airy beams. While the effective OAM for such states is zero, its uncertainty (or the beam's OAM bandwidth) is found to be finite, and it depends on the packet's parameters. A link between exact solutions for the Klein-Gordon equation in the null-plane-variable formalism and the approximate ones in the usual approach is indicated; generalizations of these states for a boson in the external field of a plane electromagnetic wave are also presented.

Computer generated hologram from point cloud using graphics processor.

PubMed

Chen, Rick H-Y; Wilkinson, Timothy D

2009-12-20

Computer generated holography is an extremely demanding and complex task when it comes to providing realistic reconstructions with full parallax, occlusion, and shadowing. We present an algorithm designed for data-parallel computing on modern graphics processing units to alleviate the computational burden. We apply Gaussian interpolation to create a continuous surface representation from discrete input object points. The algorithm maintains a potential occluder list for each individual hologram plane sample to keep the number of visibility tests to a minimum. We experimented with two approximations that simplify and accelerate occlusion computation. It is observed that letting several neighboring hologram plane samples share visibility information on object points leads to significantly faster computation without causing noticeable artifacts in the reconstructed images. Computing a reduced sample set via nonuniform sampling is also found to be an effective acceleration technique.

Doubly self-consistent field theory of grafted polymers under simple shear in steady state.

PubMed

Suo, Tongchuan; Whitmore, Mark D

2014-03-21

We present a generalization of the numerical self-consistent mean-field theory of polymers to the case of grafted polymers under simple shear. The general theoretical framework is presented, and then applied to three different chain models: rods, Gaussian chains, and finitely extensible nonlinear elastic (FENE) chains. The approach is self-consistent at two levels. First, for any flow field, the polymer density profile and effective potential are calculated self-consistently in a manner similar to the usual self-consistent field theory of polymers, except that the calculation is inherently two-dimensional even for a laterally homogeneous system. Second, through the use of a modified Brinkman equation, the flow field and the polymer profile are made self-consistent with respect to each other. For all chain models, we find that reasonable levels of shear cause the chains to tilt, but it has very little effect on the overall thickness of the polymer layer, causing a small decrease for rods, and an increase of no more than a few percent for the Gaussian and FENE chains. Using the FENE model, we also probe the individual bond lengths, bond correlations, and bond angles along the chains, the effects of the shear on them, and the solvent and bonded stress profiles. We find that the approximations needed within the theory for the Brinkman equation affect the bonded stress, but none of the other quantities.

Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency

NASA Astrophysics Data System (ADS)

Papalexiou, Simon Michael

2018-05-01

Hydroclimatic processes come in all "shapes and sizes". They are characterized by different spatiotemporal correlation structures and probability distributions that can be continuous, mixed-type, discrete or even binary. Simulating such processes by reproducing precisely their marginal distribution and linear correlation structure, including features like intermittency, can greatly improve hydrological analysis and design. Traditionally, modelling schemes are case specific and typically attempt to preserve few statistical moments providing inadequate and potentially risky distribution approximations. Here, a single framework is proposed that unifies, extends, and improves a general-purpose modelling strategy, based on the assumption that any process can emerge by transforming a specific "parent" Gaussian process. A novel mathematical representation of this scheme, introducing parametric correlation transformation functions, enables straightforward estimation of the parent-Gaussian process yielding the target process after the marginal back transformation, while it provides a general description that supersedes previous specific parameterizations, offering a simple, fast and efficient simulation procedure for every stationary process at any spatiotemporal scale. This framework, also applicable for cyclostationary and multivariate modelling, is augmented with flexible parametric correlation structures that parsimoniously describe observed correlations. Real-world simulations of various hydroclimatic processes with different correlation structures and marginals, such as precipitation, river discharge, wind speed, humidity, extreme events per year, etc., as well as a multivariate example, highlight the flexibility, advantages, and complete generality of the method.

Rubber elasticity for percolation network consisting of Gaussian chains.

PubMed

Nishi, Kengo; Noguchi, Hiroshi; Sakai, Takamasa; Shibayama, Mitsuhiro

2015-11-14

A theory describing the elastic modulus for percolation networks of Gaussian chains on general lattices such as square and cubic lattices is proposed and its validity is examined with simulation and mechanical experiments on well-defined polymer networks. The theory was developed by generalizing the effective medium approximation (EMA) for Hookian spring network to Gaussian chain networks. From EMA theory, we found that the ratio of the elastic modulus at p, G to that at p = 1, G0, must be equal to G/G0 = (p - 2/f)/(1 - 2/f) if the position of sites can be determined so as to meet the force balance, where p is the degree of cross-linking reaction. However, the EMA prediction cannot be applicable near its percolation threshold because EMA is a mean field theory. Thus, we combine real-space renormalization and EMA and propose a theory called real-space renormalized EMA, i.e., REMA. The elastic modulus predicted by REMA is in excellent agreement with the results of simulations and experiments of near-ideal diamond lattice gels.

GIFTed Demons: deformable image registration with local structure-preserving regularization using supervoxels for liver applications

PubMed Central

Gleeson, Fergus V.; Brady, Michael; Schnabel, Julia A.

2018-01-01

Abstract. Deformable image registration, a key component of motion correction in medical imaging, needs to be efficient and provides plausible spatial transformations that reliably approximate biological aspects of complex human organ motion. Standard approaches, such as Demons registration, mostly use Gaussian regularization for organ motion, which, though computationally efficient, rule out their application to intrinsically more complex organ motions, such as sliding interfaces. We propose regularization of motion based on supervoxels, which provides an integrated discontinuity preserving prior for motions, such as sliding. More precisely, we replace Gaussian smoothing by fast, structure-preserving, guided filtering to provide efficient, locally adaptive regularization of the estimated displacement field. We illustrate the approach by applying it to estimate sliding motions at lung and liver interfaces on challenging four-dimensional computed tomography (CT) and dynamic contrast-enhanced magnetic resonance imaging datasets. The results show that guided filter-based regularization improves the accuracy of lung and liver motion correction as compared to Gaussian smoothing. Furthermore, our framework achieves state-of-the-art results on a publicly available CT liver dataset. PMID:29662918

GIFTed Demons: deformable image registration with local structure-preserving regularization using supervoxels for liver applications.

PubMed

Papież, Bartłomiej W; Franklin, James M; Heinrich, Mattias P; Gleeson, Fergus V; Brady, Michael; Schnabel, Julia A

2018-04-01

Deformable image registration, a key component of motion correction in medical imaging, needs to be efficient and provides plausible spatial transformations that reliably approximate biological aspects of complex human organ motion. Standard approaches, such as Demons registration, mostly use Gaussian regularization for organ motion, which, though computationally efficient, rule out their application to intrinsically more complex organ motions, such as sliding interfaces. We propose regularization of motion based on supervoxels, which provides an integrated discontinuity preserving prior for motions, such as sliding. More precisely, we replace Gaussian smoothing by fast, structure-preserving, guided filtering to provide efficient, locally adaptive regularization of the estimated displacement field. We illustrate the approach by applying it to estimate sliding motions at lung and liver interfaces on challenging four-dimensional computed tomography (CT) and dynamic contrast-enhanced magnetic resonance imaging datasets. The results show that guided filter-based regularization improves the accuracy of lung and liver motion correction as compared to Gaussian smoothing. Furthermore, our framework achieves state-of-the-art results on a publicly available CT liver dataset.

Moderately nonlinear ultrasound propagation in blood-mimicking fluid.

PubMed

Kharin, Nikolay A; Vince, D Geoffrey

2004-04-01

In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma < 1) or strong waves (Gamma > 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading.

Gaussian step-pressure loading of rigid viscoplastic plates. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Hayduk, R. J.; Durling, B. J.

1978-01-01

The response of a thin, rigid viscoplastic plate subjected to a spatially axisymmetric Gaussian step pressure impulse loading was studied analytically. A Gaussian pressure distribution in excess of the collapse load was applied to the plate, held constant for a length of time, and then suddenly removed. The plate deforms with monotonically increasing deflections until the dynamic energy is completely dissipated in plastic work. The simply supported plate of uniform thickness obeys the von Mises yield criterion and a generalized constitutive equation for rigid viscoplastic materials. For the small deflection bending response of the plate, the governing system of equations is essentially nonlinear. Transverse shear stress is neglected in the yield condition and rotary inertia in the equations of dynamic equilibrium. A proportional loading technique, known to give excellent approximations of the exact solution for the uniform load case, was used to linearize the problem and to obtain the analytical solutions in the form of eigenvalue expansions. The effects of load concentration, of an order of magnitude change in the viscosity of the plate material, and of load duration were examined while holding the total impulse constant.

Spatiotemporal Airy Ince-Gaussian wave packets in strongly nonlocal nonlinear media.

PubMed

Peng, Xi; Zhuang, Jingli; Peng, Yulian; Li, DongDong; Zhang, Liping; Chen, Xingyu; Zhao, Fang; Deng, Dongmei

2018-03-08

The self-accelerating Airy Ince-Gaussian (AiIG) and Airy helical Ince-Gaussian (AihIG) wave packets in strongly nonlocal nonlinear media (SNNM) are obtained by solving the strongly nonlocal nonlinear Schrödinger equation. For the first time, the propagation properties of three dimensional localized AiIG and AihIG breathers and solitons in the SNNM are demonstrated, these spatiotemporal wave packets maintain the self-accelerating and approximately non-dispersion properties in temporal dimension, periodically oscillating (breather state) or steady (soliton state) in spatial dimension. In particular, their numerical experiments of spatial intensity distribution, numerical simulations of spatiotemporal distribution, as well as the transverse energy flow and the angular momentum in SNNM are presented. Typical examples of the obtained solutions are based on the ratio between the input power and the critical power, the ellipticity and the strong nonlocality parameter. The comparisons of analytical solutions with numerical simulations and numerical experiments of the AiIG and AihIG optical solitons show that the numerical results agree well with the analytical solutions in the case of strong nonlocality.

Some new results on the statistics of radio wave scintillation. I - Empirical evidence for Gaussian statistics

NASA Technical Reports Server (NTRS)

Rino, C. L.; Livingston, R. C.; Whitney, H. E.

1976-01-01

This paper presents an analysis of ionospheric scintillation data which shows that the underlying statistical structure of the signal can be accurately modeled by the additive complex Gaussian perturbation predicted by the Born approximation in conjunction with an application of the central limit theorem. By making use of this fact, it is possible to estimate the in-phase, phase quadrature, and cophased scattered power by curve fitting to measured intensity histograms. By using this procedure, it is found that typically more than 80% of the scattered power is in phase quadrature with the undeviated signal component. Thus, the signal is modeled by a Gaussian, but highly non-Rician process. From simultaneous UHF and VHF data, only a weak dependence of this statistical structure on changes in the Fresnel radius is deduced. The signal variance is found to have a nonquadratic wavelength dependence. It is hypothesized that this latter effect is a subtle manifestation of locally homogeneous irregularity structures, a mathematical model proposed by Kolmogorov (1941) in his early studies of incompressible fluid turbulence.

Short-term prediction of chaotic time series by using RBF network with regression weights.

PubMed

Rojas, I; Gonzalez, J; Cañas, A; Diaz, A F; Rojas, F J; Rodriguez, M

2000-10-01

We propose a framework for constructing and training a radial basis function (RBF) neural network. The structure of the gaussian functions is modified using a pseudo-gaussian function (PG) in which two scaling parameters sigma are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater flexibility with respect to function approximation. We propose a modified PG-BF (pseudo-gaussian basis function) network in which the regression weights are used to replace the constant weights in the output layer. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit and also to detect and remove inactive units. A salient feature of the network systems is that the method used for calculating the overall output is the weighted average of the output associated with each receptive field. The superior performance of the proposed PG-BF system over the standard RBF are illustrated using the problem of short-term prediction of chaotic time series.

Screening and clustering of sparse regressions with finite non-Gaussian mixtures.

PubMed

Zhang, Jian

2017-06-01

This article proposes a method to address the problem that can arise when covariates in a regression setting are not Gaussian, which may give rise to approximately mixture-distributed errors, or when a true mixture of regressions produced the data. The method begins with non-Gaussian mixture-based marginal variable screening, followed by fitting a full but relatively smaller mixture regression model to the selected data with help of a new penalization scheme. Under certain regularity conditions, the new screening procedure is shown to possess a sure screening property even when the population is heterogeneous. We further prove that there exists an elbow point in the associated scree plot which results in a consistent estimator of the set of active covariates in the model. By simulations, we demonstrate that the new procedure can substantially improve the performance of the existing procedures in the content of variable screening and data clustering. By applying the proposed procedure to motif data analysis in molecular biology, we demonstrate that the new method holds promise in practice. © 2016, The International Biometric Society.

Rubber elasticity for percolation network consisting of Gaussian chains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nishi, Kengo, E-mail: kengo.nishi@phys.uni-goettingen.de, E-mail: sakai@tetrapod.t.u-tokyo.ac.jp, E-mail: sibayama@issp.u-tokyo.ac.jp; Noguchi, Hiroshi; Shibayama, Mitsuhiro, E-mail: kengo.nishi@phys.uni-goettingen.de, E-mail: sakai@tetrapod.t.u-tokyo.ac.jp, E-mail: sibayama@issp.u-tokyo.ac.jp

2015-11-14

A theory describing the elastic modulus for percolation networks of Gaussian chains on general lattices such as square and cubic lattices is proposed and its validity is examined with simulation and mechanical experiments on well-defined polymer networks. The theory was developed by generalizing the effective medium approximation (EMA) for Hookian spring network to Gaussian chain networks. From EMA theory, we found that the ratio of the elastic modulus at p, G to that at p = 1, G{sub 0}, must be equal to G/G{sub 0} = (p − 2/f)/(1 − 2/f) if the position of sites can be determined somore » as to meet the force balance, where p is the degree of cross-linking reaction. However, the EMA prediction cannot be applicable near its percolation threshold because EMA is a mean field theory. Thus, we combine real-space renormalization and EMA and propose a theory called real-space renormalized EMA, i.e., REMA. The elastic modulus predicted by REMA is in excellent agreement with the results of simulations and experiments of near-ideal diamond lattice gels.« less

HOW WELL ARE HYDRAULIC CONDUCTIVITY VARIATIONS APPROXIMATED BY ADDITIVE STABLE PROCESSES? (R826171)

EPA Science Inventory

Abstract

Analysis of the higher statistical moments of a hydraulic conductivity (K) and an intrinsic permeability (k) data set leads to the conclusion that the increments of the data and the logs of the data are not governed by Levy-stable or Gaussian dis...

Estimating Mutual Information by Local Gaussian Approximation

DTIC Science & Technology

2015-07-13

suggesstions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway...following conditions: lim N→∞ hi = 0 , lim N→∞ Nhi =∞, i = 1, 2, . . . , d. (9) Then the following holds: lim N→∞ E|f̂ (x)− f (x)| = 0 (10) lim N→∞ E|f̂ (x

Calculation of the detection limit in radiation measurements with systematic uncertainties

NASA Astrophysics Data System (ADS)

Kirkpatrick, J. M.; Russ, W.; Venkataraman, R.; Young, B. M.

2015-06-01

The detection limit (LD) or Minimum Detectable Activity (MDA) is an a priori evaluation of assay sensitivity intended to quantify the suitability of an instrument or measurement arrangement for the needs of a given application. Traditional approaches as pioneered by Currie rely on Gaussian approximations to yield simple, closed-form solutions, and neglect the effects of systematic uncertainties in the instrument calibration. These approximations are applicable over a wide range of applications, but are of limited use in low-count applications, when high confidence values are required, or when systematic uncertainties are significant. One proposed modification to the Currie formulation attempts account for systematic uncertainties within a Gaussian framework. We have previously shown that this approach results in an approximation formula that works best only for small values of the relative systematic uncertainty, for which the modification of Currie's method is the least necessary, and that it significantly overestimates the detection limit or gives infinite or otherwise non-physical results for larger systematic uncertainties where such a correction would be the most useful. We have developed an alternative approach for calculating detection limits based on realistic statistical modeling of the counting distributions which accurately represents statistical and systematic uncertainties. Instead of a closed form solution, numerical and iterative methods are used to evaluate the result. Accurate detection limits can be obtained by this method for the general case.

Comparison of non-Gaussian and Gaussian diffusion models of diffusion weighted imaging of rectal cancer at 3.0 T MRI.

PubMed

Zhang, Guangwen; Wang, Shuangshuang; Wen, Didi; Zhang, Jing; Wei, Xiaocheng; Ma, Wanling; Zhao, Weiwei; Wang, Mian; Wu, Guosheng; Zhang, Jinsong

2016-12-09

Water molecular diffusion in vivo tissue is much more complicated. We aimed to compare non-Gaussian diffusion models of diffusion-weighted imaging (DWI) including intra-voxel incoherent motion (IVIM), stretched-exponential model (SEM) and Gaussian diffusion model at 3.0 T MRI in patients with rectal cancer, and to determine the optimal model for investigating the water diffusion properties and characterization of rectal carcinoma. Fifty-nine consecutive patients with pathologically confirmed rectal adenocarcinoma underwent DWI with 16 b-values at a 3.0 T MRI system. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models (IVIM-mono, IVIM-bi and SEM) on primary tumor and adjacent normal rectal tissue. Parameters of standard apparent diffusion coefficient (ADC), slow- and fast-ADC, fraction of fast ADC (f), α value and distributed diffusion coefficient (DDC) were generated and compared between the tumor and normal tissues. The SEM exhibited the best fitting results of actual DWI signal in rectal cancer and the normal rectal wall (R 2  = 0.998, 0.999 respectively). The DDC achieved relatively high area under the curve (AUC = 0.980) in differentiating tumor from normal rectal wall. Non-Gaussian diffusion models could assess tissue properties more accurately than the ADC derived Gaussian diffusion model. SEM may be used as a potential optimal model for characterization of rectal cancer.

First-principles energetics of water clusters and ice: A many-body analysis

NASA Astrophysics Data System (ADS)

Gillan, M. J.; Alfè, D.; Bartók, A. P.; Csányi, G.

2013-12-01

Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.

Curvature perturbations in the early universe: Theoretical models and observational tests

NASA Astrophysics Data System (ADS)

Vallinotto, Alberto

A very general prediction of inflation is that the power spectrum of density perturbations is characterized by a spectral index ns which is scale independent and approximately equal to unity. Drawing from the potential reconstruction method and adopting the slow-roll parameter expansion technique, we derive all possible single field inflationary potentials that would lead to a scale invariant density spectral index, consistent with current observations. In the process, a new method to determine the functional form of the inflationary potential in the slow roll approximation is devised, based on the reparametrization of the field dynamics with respect to the slow roll parameter epsilon which also allowed to show that under the assumptions made the investigation proved to be exhaustive and that no other solutions are available. Next, we focus on the fact that there exist a large class of inflationary models currently ruled out because the predicted production of curvature perturbations during the slow-roll stage results exponentially suppressed. We investigate whether an alternative mechanism for the generation of curvature perturbations can be devised for such a class of models. In the process, it is shown that it is sufficient for the inflationary potential to exhibit a broken symmetry to successfully convert isocurvature perturbations, which are excited during the slow-roll stage, into curvature perturbations thanks to an inhomogeneous decay stage. This conclusion is general, requiring as a sufficient condition only the fact that the inflation potential is characterized by a broken symmetry. Finally, we show that the perturbations thus produced are generally characterized by a non-negligible degree of non-gaussianity, which then provides a clear experimental signature for experimental detection or rejection.

Slow-roll corrections in multi-field inflation: a separate universes approach

NASA Astrophysics Data System (ADS)

Karčiauskas, Mindaugas; Kohri, Kazunori; Mori, Taro; White, Jonathan

2018-05-01

In view of cosmological parameters being measured to ever higher precision, theoretical predictions must also be computed to an equally high level of precision. In this work we investigate the impact on such predictions of relaxing some of the simplifying assumptions often used in these computations. In particular, we investigate the importance of slow-roll corrections in the computation of multi-field inflation observables, such as the amplitude of the scalar spectrum Pζ, its spectral tilt ns, the tensor-to-scalar ratio r and the non-Gaussianity parameter fNL. To this end we use the separate universes approach and δ N formalism, which allows us to consider slow-roll corrections to the non-Gaussianity of the primordial curvature perturbation as well as corrections to its two-point statistics. In the context of the δ N expansion, we divide slow-roll corrections into two categories: those associated with calculating the correlation functions of the field perturbations on the initial flat hypersurface and those associated with determining the derivatives of the e-folding number with respect to the field values on the initial flat hypersurface. Using the results of Nakamura & Stewart '96, corrections of the first kind can be written in a compact form. Corrections of the second kind arise from using different levels of slow-roll approximation in solving for the super-horizon evolution, which in turn corresponds to using different levels of slow-roll approximation in the background equations of motion. We consider four different levels of approximation and apply the results to a few example models. The various approximations are also compared to exact numerical solutions.

Common inputs in subthreshold membrane potential: The role of quiescent states in neuronal activity

NASA Astrophysics Data System (ADS)

Montangie, Lisandro; Montani, Fernando

2018-06-01

Experiments in certain regions of the cerebral cortex suggest that the spiking activity of neuronal populations is regulated by common non-Gaussian inputs across neurons. We model these deviations from random-walk processes with q -Gaussian distributions into simple threshold neurons, and investigate the scaling properties in large neural populations. We show that deviations from the Gaussian statistics provide a natural framework to regulate population statistics such as sparsity, entropy, and specific heat. This type of description allows us to provide an adequate strategy to explain the information encoding in the case of low neuronal activity and its possible implications on information transmission.

Combining Mixture Components for Clustering*

PubMed Central

Baudry, Jean-Patrick; Raftery, Adrian E.; Celeux, Gilles; Lo, Kenneth; Gottardo, Raphaël

2010-01-01

Model-based clustering consists of fitting a mixture model to data and identifying each cluster with one of its components. Multivariate normal distributions are typically used. The number of clusters is usually determined from the data, often using BIC. In practice, however, individual clusters can be poorly fitted by Gaussian distributions, and in that case model-based clustering tends to represent one non-Gaussian cluster by a mixture of two or more Gaussian distributions. If the number of mixture components is interpreted as the number of clusters, this can lead to overestimation of the number of clusters. This is because BIC selects the number of mixture components needed to provide a good approximation to the density, rather than the number of clusters as such. We propose first selecting the total number of Gaussian mixture components, K, using BIC and then combining them hierarchically according to an entropy criterion. This yields a unique soft clustering for each number of clusters less than or equal to K. These clusterings can be compared on substantive grounds, and we also describe an automatic way of selecting the number of clusters via a piecewise linear regression fit to the rescaled entropy plot. We illustrate the method with simulated data and a flow cytometry dataset. Supplemental Materials are available on the journal Web site and described at the end of the paper. PMID:20953302

Three dimensional indoor positioning based on visible light with Gaussian mixture sigma-point particle filter technique

NASA Astrophysics Data System (ADS)

Gu, Wenjun; Zhang, Weizhi; Wang, Jin; Amini Kashani, M. R.; Kavehrad, Mohsen

2015-01-01

Over the past decade, location based services (LBS) have found their wide applications in indoor environments, such as large shopping malls, hospitals, warehouses, airports, etc. Current technologies provide wide choices of available solutions, which include Radio-frequency identification (RFID), Ultra wideband (UWB), wireless local area network (WLAN) and Bluetooth. With the rapid development of light-emitting-diodes (LED) technology, visible light communications (VLC) also bring a practical approach to LBS. As visible light has a better immunity against multipath effect than radio waves, higher positioning accuracy is achieved. LEDs are utilized both for illumination and positioning purpose to realize relatively lower infrastructure cost. In this paper, an indoor positioning system using VLC is proposed, with LEDs as transmitters and photo diodes as receivers. The algorithm for estimation is based on received-signalstrength (RSS) information collected from photo diodes and trilateration technique. By appropriately making use of the characteristics of receiver movements and the property of trilateration, estimation on three-dimensional (3-D) coordinates is attained. Filtering technique is applied to enable tracking capability of the algorithm, and a higher accuracy is reached compare to raw estimates. Gaussian mixture Sigma-point particle filter (GM-SPPF) is proposed for this 3-D system, which introduces the notion of Gaussian Mixture Model (GMM). The number of particles in the filter is reduced by approximating the probability distribution with Gaussian components.

Three-photon Gaussian-Gaussian-Laguerre-Gaussian excitation of a localized atom to a highly excited Rydberg state

NASA Astrophysics Data System (ADS)

Mashhadi, L.

2017-12-01

Optical vortices are currently one of the most intensively studied topics in light-matter interaction. In this work, a three-step axial Doppler- and recoil-free Gaussian-Gaussian-Laguerre-Gaussian (GGLG) excitation of a localized atom to the highly excited Rydberg state is presented. By assuming a large detuning for intermediate states, an effective quadrupole excitation related to the Laguerre-Gaussian (LG) excitation to the highly excited Rydberg state is obtained. This special excitation system radially confines the single highly excited Rydberg atom independently of the trapping system into a sharp potential landscape into the so-called ‘far-off-resonance optical dipole-quadrupole trap’ (FORDQT). The key parameters of the Rydberg excitation to the highly excited state, namely the effective Rabi frequency and the effective detuning including a position-dependent AC Stark shift, are calculated in terms of the basic parameters of the LG beam and of the polarization of the excitation lasers. It is shown that the obtained parameters can be tuned to have a precise excitation of a single atom to the desired Rydberg state as well. The features of transferring the optical orbital and spin angular momentum of the polarized LG beam to the atom via quadrupole Rydberg excitation offer a long-lived and controllable qudit quantum memory. In addition, in contrast to the Gaussian laser beam, the doughnut-shaped LG beam makes it possible to use a high intensity laser beam to increase the signal-to-noise ratio in quadrupole excitation with minimized perturbations coming from stray light broadening in the last Rydberg excitation process.

New more accurate calculations of the ground state potential energy surface of H(3) (+).

PubMed

Pavanello, Michele; Tung, Wei-Cheng; Leonarski, Filip; Adamowicz, Ludwik

2009-02-21

Explicitly correlated Gaussian functions with floating centers have been employed to recalculate the ground state potential energy surface (PES) of the H(3) (+) ion with much higher accuracy than it was done before. The nonlinear parameters of the Gaussians (i.e., the exponents and the centers) have been variationally optimized with a procedure employing the analytical gradient of the energy with respect to these parameters. The basis sets for calculating new PES points were guessed from the points already calculated. This allowed us to considerably speed up the calculations and achieve very high accuracy of the results.

Bayesian sensitivity analysis of bifurcating nonlinear models

NASA Astrophysics Data System (ADS)

Becker, W.; Worden, K.; Rowson, J.

2013-01-01

Sensitivity analysis allows one to investigate how changes in input parameters to a system affect the output. When computational expense is a concern, metamodels such as Gaussian processes can offer considerable computational savings over Monte Carlo methods, albeit at the expense of introducing a data modelling problem. In particular, Gaussian processes assume a smooth, non-bifurcating response surface. This work highlights a recent extension to Gaussian processes which uses a decision tree to partition the input space into homogeneous regions, and then fits separate Gaussian processes to each region. In this way, bifurcations can be modelled at region boundaries and different regions can have different covariance properties. To test this method, both the treed and standard methods were applied to the bifurcating response of a Duffing oscillator and a bifurcating FE model of a heart valve. It was found that the treed Gaussian process provides a practical way of performing uncertainty and sensitivity analysis on large, potentially-bifurcating models, which cannot be dealt with by using a single GP, although an open problem remains how to manage bifurcation boundaries that are not parallel to coordinate axes.

Displacements and evolution of optical vortices in edge-diffracted Laguerre-Gaussian beams

NASA Astrophysics Data System (ADS)

Bekshaev, Aleksandr; Chernykh, Aleksey; Khoroshun, Anna; Mikhaylovskaya, Lidiya

2017-05-01

Based on the Kirchhoff-Fresnel approximation, we consider the behavior of optical vortices (OV) upon propagation of diffracted Laguerre-Gaussian (LG) beams with topological charge ∣m∣ = 1, 2. Under conditions of weak diffraction perturbation (i.e. the diffraction obstacle covers only the far transverse periphery of the incident LG beam), these OVs describe almost perfect 3D spirals within the diffracted beam body, which is an impressive demonstration of the helical nature of an OV beam. The far-field OV positions within the diffracted beam cross section depend on the wavefront curvature of the incident OV beam, so that the input wavefront curvature is transformed into the output azimuthal OV rotation. The results are expected to be useful in OV metrology and OV beam diagnostics.

Nonlinear estimation theory applied to the interplanetary orbit determination problem.

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Choe, C. Y.

1972-01-01

Martingale theory and appropriate smoothing properties of Loeve (1953) have been used to develop a modified Gaussian second-order filter. The performance of the filter is evaluated through numerical simulation of a Jupiter flyby mission. The observations used in the simulation are on-board measurements of the angle between Jupiter and a fixed star taken at discrete time intervals. In the numerical study, the influence of each of the second-order terms is evaluated. Five filter algorithms are used in the simulations. Four of the filters are the modified Gaussian second-order filter and three approximations derived by neglecting one or more of the second-order terms in the equations. The fifth filter is the extended Kalman-Bucy filter which is obtained by neglecting all of the second-order terms.

Three-dimensional computation of laser cavity eigenmodes by the use of finite element analysis (FEA)

NASA Astrophysics Data System (ADS)

Altmann, Konrad; Pflaum, Christoph; Seider, David

2004-06-01

A new method for computing eigenmodes of a laser resonator by the use of finite element analysis (FEA) is presented. For this purpose, the scalar wave equation [Δ + k2]E(x,y,z) = 0 is transformed into a solvable 3D eigenvalue problem by separating out the propagation factor exp(-ikz) from the phasor amplitude E(x,y,z) of the time-harmonic electrical field. For standing wave resonators, the beam inside the cavity is represented by a two-wave ansatz. For cavities with parabolic optical elements the new approach has successfully been verified by the use of the Gaussian mode algorithm. For a DPSSL with a thermally lensing crystal inside the cavity the expected deviation between Gaussian approximation and numerical solution could be demonstrated clearly.

Decoupling of rotational and translational diffusion in supercooled colloidal fluids

PubMed Central

Edmond, Kazem V.; Elsesser, Mark T.; Hunter, Gary L.; Pine, David J.; Weeks, Eric R.

2012-01-01

We use confocal microscopy to directly observe 3D translational and rotational diffusion of tetrahedral clusters, which serve as tracers in colloidal supercooled fluids. We find that as the colloidal glass transition is approached, translational and rotational diffusion decouple from each other: Rotational diffusion remains inversely proportional to the growing viscosity whereas translational diffusion does not, decreasing by a much lesser extent. We quantify the rotational motion with two distinct methods, finding agreement between these methods, in contrast with recent simulation results. The decoupling coincides with the emergence of non-Gaussian displacement distributions for translation whereas rotational displacement distributions remain Gaussian. Ultimately, our work demonstrates that as the glass transition is approached, the sample can no longer be approximated as a continuum fluid when considering diffusion. PMID:23071311

Spin-Hall effect in the scattering of structured light from plasmonic nanowire

NASA Astrophysics Data System (ADS)

Sharma, Deepak K.; Kumar, Vijay; Vasista, Adarsh B.; Chaubey, Shailendra K.; Kumar, G. V. Pavan

2018-06-01

Spin-orbit interactions are subwavelength phenomena which can potentially lead to numerous device related applications in nanophotonics. Here, we report Spin-Hall effect in the forward scattering of Hermite-Gaussian and Gaussian beams from a plasmonic nanowire. Asymmetric scattered radiation distribution was observed for circularly polarized beams. Asymmetry in the scattered radiation distribution changes the sign when the polarization handedness inverts. We found a significant enhancement in the Spin-Hall effect for Hermite-Gaussian beam as compared to Gaussian beam for constant input power. The difference between scattered powers perpendicular to the long axis of the plasmonic nanowire was used to quantify the enhancement. In addition to it, nodal line of HG beam acts as the marker for the Spin-Hall shift. Numerical calculations corroborate experimental observations and suggest that the Spin flow component of Poynting vector associated with the circular polarization is responsible for the Spin-Hall effect and its enhancement.

Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous-variable systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adesso, Gerardo; CNR-INFM Coherentia , Naples; Grup d'Informacio Quantica, Universitat Autonoma de Barcelona, E-08193 Bellaterra

2007-08-15

Quantum mechanics imposes 'monogamy' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully 'promiscuous', i.e., simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of N-mode (N{>=}4) Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of individual qubits. Such a finding is of importance for the quantification, understanding, and potential exploitation of shared quantummore » correlations in continuous variable systems. We discuss how promiscuity gradually arises when considering simple families of discrete variable states, with increasing Hilbert space dimension towards the continuous variable limit. Such models are somehow analogous to Gaussian states with asymptotically diverging, but finite, squeezing. In this respect, we find that non-Gaussian states (which in general are more entangled than Gaussian states) exhibit also the interesting feature that their entanglement is more shareable: in the non-Gaussian multipartite arena, unlimited promiscuity can be already achieved among three entangled parties, while this is impossible for Gaussian, even infinitely squeezed states.« less

Estimate of the cosmological bispectrum from the MAXIMA-1 cosmic microwave background map.

PubMed

Santos, M G; Balbi, A; Borrill, J; Ferreira, P G; Hanany, S; Jaffe, A H; Lee, A T; Magueijo, J; Rabii, B; Richards, P L; Smoot, G F; Stompor, R; Winant, C D; Wu, J H P

2002-06-17

We use the measurement of the cosmic microwave background taken during the MAXIMA-1 flight to estimate the bispectrum of cosmological perturbations. We propose an estimator for the bispectrum that is appropriate in the flat sky approximation, apply it to the MAXIMA-1 data, and evaluate errors using bootstrap methods. We compare the estimated value with what would be expected if the sky signal were Gaussian and find that it is indeed consistent, with a chi(2) per degree of freedom of approximately unity. This measurement places constraints on models of inflation.

Stochastic Analysis for Navigation of Autonomous Platforms Using Range Finders.

DTIC Science & Technology

1987-08-01

34) where T oi2 = E[vivi] ( 35 ) and T _j2 = E[ujuj] (36) Choice of An Approximating Function In this report, we are interested in obtaining smoothed...1. Gaussian curvature: The mean curvature of a surface at (tq) is defined as: (0.5) ZsM (Sn) (45) Noting in Euler’s theorem that the sum of two

Demonstration of differential phase-shift keying demodulation at 10 Gbit/s optimal fiber Bragg grating filters.

PubMed

Gatti, Davide; Galzerano, Gianluca; Laporta, Paolo; Longhi, Stefano; Janner, Davide; Guglierame, Andrea; Belmonte, Michele

2008-07-01

Optimal demodulation of differential phase-shift keying signals at 10 Gbit/s is experimentally demonstrated using a specially designed structured fiber Bragg grating composed by Fabry-Perot coupled cavities. Bit-error-rate measurements show that, as compared with a conventional Gaussian-shaped filter, our demodulator gives approximately 2.8 dB performance improvement.

Localized light waves: Paraxial and exact solutions of the wave equation (a review)

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2007-04-01

Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “ X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.

Semiclassical initial value representation for the quantum propagator in the Heisenberg interaction representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petersen, Jakob; Pollak, Eli, E-mail: eli.pollak@weizmann.ac.il

2015-12-14

One of the challenges facing on-the-fly ab initio semiclassical time evolution is the large expense needed to converge the computation. In this paper, we suggest that a significant saving in computational effort may be achieved by employing a semiclassical initial value representation (SCIVR) of the quantum propagator based on the Heisenberg interaction representation. We formulate and test numerically a modification and simplification of the previous semiclassical interaction representation of Shao and Makri [J. Chem. Phys. 113, 3681 (2000)]. The formulation is based on the wavefunction form of the semiclassical propagation instead of the operator form, and so is simpler andmore » cheaper to implement. The semiclassical interaction representation has the advantage that the phase and prefactor vary relatively slowly as compared to the “standard” SCIVR methods. This improves its convergence properties significantly. Using a one-dimensional model system, the approximation is compared with Herman-Kluk’s frozen Gaussian and Heller’s thawed Gaussian approximations. The convergence properties of the interaction representation approach are shown to be favorable and indicate that the interaction representation is a viable way of incorporating on-the-fly force field information within a semiclassical framework.« less

A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Jinglai, E-mail: jinglaili@sjtu.edu.cn; Lin, Guang, E-mail: lin491@purdue.edu; Computational Sciences and Mathematics Division, Pacific Northwest National Laboratory, Richland, WA 99352

2015-09-01

In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by threemore » steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.« less

Basis for paraxial surface-plasmon-polariton packets

NASA Astrophysics Data System (ADS)

Martinez-Herrero, Rosario; Manjavacas, Alejandro

2016-12-01

We present a theoretical framework for the study of surface-plasmon polariton (SPP) packets propagating along a lossy metal-dielectric interface within the paraxial approximation. Using a rigorous formulation based on the plane-wave spectrum formalism, we introduce a set of modes that constitute a complete basis set for the solutions of Maxwell's equations for a metal-dielectric interface in the paraxial approximation. The use of this set of modes allows us to fully analyze the evolution of the transversal structure of SPP packets beyond the single plane-wave approximation. As a paradigmatic example, we analyze the case of a Gaussian SPP mode, for which, exploiting the analogy with paraxial optical beams, we introduce a set of parameters that characterize its propagation.

Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.

2007-01-01

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory.

PubMed

Baaquie, Belal E

2007-01-01

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

Controlling the sign problem in finite-density quantum field theory

NASA Astrophysics Data System (ADS)

Garron, Nicolas; Langfeld, Kurt

2017-07-01

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the "telegraphic" approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close—if not identical—to the full answer in the strong sign-problem regime.

The Effects of Hydrogen-Like Impurity and Temperature on State Energies and Transition Frequency of Strong-Coupling Bound Polaron in an Asymmetric Gaussian Potential Quantum Well

NASA Astrophysics Data System (ADS)

Xiao, Jing-lin

2018-02-01

In the present work, we study the ground state energy, the first excited state energy and the transition frequency (TF) between the two states of the strong-coupling impurity bound polaron in an asymmetric Gaussian potential quantum well (AGPQW) by using the variational method of the Pekar type. By employing quantum statistics theory, the temperature effect on the state energies (SEs) and the TF are also calculated with a hydrogen-like impurity at the coordinate origin of the AGPQW. According to the obtained results, we found that the SEs and the TF are increasing functions of the temperature, whereas they are decreasing ones of the Coulombic impurity potential.

First-principles calculations on anharmonic vibrational frequencies of polyethylene and polyacetylene in the Gamma approximation.

PubMed

Keçeli, Murat; Hirata, So; Yagi, Kiyoshi

2010-07-21

The frequencies of the infrared- and/or Raman-active (k=0) vibrations of polyethylene and polyacetylene are computed by taking account of the anharmonicity in the potential energy surfaces (PESs) and the resulting phonon-phonon couplings explicitly. The electronic part of the calculations is based on Gaussian-basis-set crystalline orbital theory at the Hartree-Fock and second-order Møller-Plesset (MP2) perturbation levels, providing one-, two-, and/or three-dimensional slices of the PES (namely, using the so-called n-mode coupling approximation with n=3), which are in turn expanded in the fourth-order Taylor series with respect to the normal coordinates. The vibrational part uses the vibrational self-consistent field, vibrational MP2, and vibrational truncated configuration-interaction (VCI) methods within the Gamma approximation, which amounts to including only k=0 phonons. It is shown that accounting for both electron correlation and anharmonicity is essential in achieving good agreement (the mean and maximum absolute deviations less than 50 and 90 cm(-1), respectively, for polyethylene and polyacetylene) between computed and observed frequencies. The corresponding values for the calculations including only one of such effects are in excess of 120 and 300 cm(-1), respectively. The VCI calculations also reproduce semiquantitatively the frequency separation and intensity ratio of the Fermi doublet involving the nu(2)(0) fundamental and nu(8)(pi) first overtone in polyethylene.

Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus-Yevick values of the fourth virial coefficient.

PubMed

Santos, Andrés; Manzano, Gema

2010-04-14

As is well known, approximate integral equations for liquids, such as the hypernetted chain (HNC) and Percus-Yevick (PY) theories, are in general thermodynamically inconsistent in the sense that the macroscopic properties obtained from the spatial correlation functions depend on the route followed. In particular, the values of the fourth virial coefficient B(4) predicted by the HNC and PY approximations via the virial route differ from those obtained via the compressibility route. Despite this, it is shown in this paper that the value of B(4) obtained from the virial route in the HNC theory is exactly three halves the value obtained from the compressibility route in the PY theory, irrespective of the interaction potential (whether isotropic or not), the number of components, and the dimensionality of the system. This simple relationship is confirmed in one-component systems by analytical results for the one-dimensional penetrable-square-well model and the three-dimensional penetrable-sphere model, as well as by numerical results for the one-dimensional Lennard-Jones model, the one-dimensional Gaussian core model, and the three-dimensional square-well model.

Nonlinear optical response in a zincblende GaN cylindrical quantum dot with donor impurity center

NASA Astrophysics Data System (ADS)

Hoyos, Jaime H.; Correa, J. D.; Mora-Ramos, M. E.; Duque, C. A.

2016-03-01

We calculate the nonlinear optical absorption coefficient of a cylindrical zincblende GaN-based quantum dot. For this purpose, we consider Coulomb interactions between electrons and an impurity ionized donor atom. The electron-donor-impurity spectrum and the associated quantum states are calculated using the effective mass approximation with a parabolic potential energy model describing both the radial and axial electron confinement. We also include the effects of the hydrostatic pressure and external electrostatic fields. The energy spectrum is obtained through an expansion of the eigenstates as a linear combination of Gaussian-type functions which reduces the computational effort since all the matrix elements are obtained analytically. Therefore, the numerical problem is reduced to the direct diagonalization of the Hamiltonian. The obtained energies are used in the evaluation of the dielectric susceptibility and the nonlinear optical absorption coefficient within a modified two-level approach in a rotating wave approximation. This quantity is investigated as a function of the quantum dot dimensions, the impurity position, the external electric field intensity and the hydrostatic pressure. The results of this research could be important in the design and fabrication of zincblende GaN-quantum-dot-based electro-optical devices.

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments.

PubMed

Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J

2017-01-01

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D , observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄ . When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model.

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments*

PubMed Central

Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J.

2017-01-01

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D, observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄. When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model. PMID:28989561

Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

DOE PAGES

Clerkin, L.; Kirk, D.; Manera, M.; ...

2016-08-30

It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (kappa_WL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the Counts in Cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey (DES) Science Verification data over 139 deg^2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirmmore » that the galaxy density contrast distribution is well modeled by a lognormal PDF convolved with Poisson noise at angular scales from 10-40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as kappa_WL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the kappa_WL distribution is well modeled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fit chi^2/DOF of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07 respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.« less

Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

NASA Astrophysics Data System (ADS)

Clerkin, L.; Kirk, D.; Manera, M.; Lahav, O.; Abdalla, F.; Amara, A.; Bacon, D.; Chang, C.; Gaztañaga, E.; Hawken, A.; Jain, B.; Joachimi, B.; Vikram, V.; Abbott, T.; Allam, S.; Armstrong, R.; Benoit-Lévy, A.; Bernstein, G. M.; Bernstein, R. A.; Bertin, E.; Brooks, D.; Burke, D. L.; Rosell, A. Carnero; Carrasco Kind, M.; Crocce, M.; Cunha, C. E.; D'Andrea, C. B.; da Costa, L. N.; Desai, S.; Diehl, H. T.; Dietrich, J. P.; Eifler, T. F.; Evrard, A. E.; Flaugher, B.; Fosalba, P.; Frieman, J.; Gerdes, D. W.; Gruen, D.; Gruendl, R. A.; Gutierrez, G.; Honscheid, K.; James, D. J.; Kent, S.; Kuehn, K.; Kuropatkin, N.; Lima, M.; Melchior, P.; Miquel, R.; Nord, B.; Plazas, A. A.; Romer, A. K.; Roodman, A.; Sanchez, E.; Schubnell, M.; Sevilla-Noarbe, I.; Smith, R. C.; Soares-Santos, M.; Sobreira, F.; Suchyta, E.; Swanson, M. E. C.; Tarle, G.; Walker, A. R.

2017-04-01

It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (κWL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the counts-in-cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey Science Verification data over 139 deg2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirm that the galaxy density contrast distribution is well modelled by a lognormal PDF convolved with Poisson noise at angular scales from 10 to 40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as κWL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the κWL distribution is well modelled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fitting χ2/dof of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07, respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check, we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.

A test of the adhesion approximation for gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.

1993-01-01

We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

A test of the adhesion approximation for gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Shandarin, Sergei F.; Weinberg, David H.

1994-01-01

We quantitatively compare a particle implementation of the adhesion approximation to fully nonlinear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Demonstration of temperature imaging by H₂O absorption spectroscopy using compressed sensing tomography.

PubMed

An, Xinliang; Brittelle, Mack S; Lauzier, Pascal T; Gord, James R; Roy, Sukesh; Chen, Guang-Hong; Sanders, Scott T

2015-11-01

This paper introduces temperature imaging by total-variation-based compressed sensing (CS) tomography of H2O vapor absorption spectroscopy. A controlled laboratory setup is used to generate a constant two-dimensional temperature distribution in air (a roughly Gaussian temperature profile with a central temperature of 677 K). A wavelength-tunable laser beam is directed through the known distribution; the beam is translated and rotated using motorized stages to acquire complete absorption spectra in the 1330-1365 nm range at each of 64 beam locations and 60 view angles. Temperature reconstructions are compared to independent thermocouple measurements. Although the distribution studied is approximately axisymmetric, axisymmetry is not assumed and simulations show similar performance for arbitrary temperature distributions. We study the measurement error as a function of number of beams and view angles used in reconstruction to gauge the potential for application of CS in practical test articles where optical access is limited.

Physics of Electronic Materials

NASA Astrophysics Data System (ADS)

Rammer, Jørgen

2017-03-01

1. Quantum mechanics; 2. Quantum tunneling; 3. Standard metal model; 4. Standard conductor model; 5. Electric circuit theory; 6. Quantum wells; 7. Particle in a periodic potential; 8. Bloch currents; 9. Crystalline solids; 10. Semiconductor doping; 11. Transistors; 12. Heterostructures; 13. Mesoscopic physics; 14. Arithmetic, logic and machines; Appendix A. Principles of quantum mechanics; Appendix B. Dirac's delta function; Appendix C. Fourier analysis; Appendix D. Classical mechanics; Appendix E. Wave function properties; Appendix F. Transfer matrix properties; Appendix G. Momentum; Appendix H. Confined particles; Appendix I. Spin and quantum statistics; Appendix J. Statistical mechanics; Appendix K. The Fermi-Dirac distribution; Appendix L. Thermal current fluctuations; Appendix M. Gaussian wave packets; Appendix N. Wave packet dynamics; Appendix O. Screening by symmetry method; Appendix P. Commutation and common eigenfunctions; Appendix Q. Interband coupling; Appendix R. Common crystal structures; Appendix S. Effective mass approximation; Appendix T. Integral doubling formula; Bibliography; Index.

Approximate Bayesian computation for forward modeling in cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akeret, Joël; Refregier, Alexandre; Amara, Adam

Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to themore » posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release.« less

Moments and Root-Mean-Square Error of the Bayesian MMSE Estimator of Classification Error in the Gaussian Model.

PubMed

Zollanvari, Amin; Dougherty, Edward R

2014-06-01

The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been designed. Use of prior knowledge, in the form of a prior distribution on an uncertainty class of feature-label distributions to which the true, but unknown, feature-distribution belongs, can facilitate accurate error estimation (in the mean-square sense) in circumstances where accurate completely model-free error estimation is impossible. This paper provides analytic asymptotically exact finite-sample approximations for various performance metrics of the resulting Bayesian Minimum Mean-Square-Error (MMSE) error estimator in the case of linear discriminant analysis (LDA) in the multivariate Gaussian model. These performance metrics include the first, second, and cross moments of the Bayesian MMSE error estimator with the true error of LDA, and therefore, the Root-Mean-Square (RMS) error of the estimator. We lay down the theoretical groundwork for Kolmogorov double-asymptotics in a Bayesian setting, which enables us to derive asymptotic expressions of the desired performance metrics. From these we produce analytic finite-sample approximations and demonstrate their accuracy via numerical examples. Various examples illustrate the behavior of these approximations and their use in determining the necessary sample size to achieve a desired RMS. The Supplementary Material contains derivations for some equations and added figures.

Diffracted field distributions from the HE11 mode in a hollow optical fibre for an atomic funnel

NASA Astrophysics Data System (ADS)

Ni, Yun; Liu, Nanchun; Yin, Jianping

2003-06-01

The diffracted near field distribution from an LP01 mode in a hollow optical fibre was recently calculated using a scalar model based on the weakly waveguiding approximation (Yoo et al 1999 J. Opt. B: Quantum Semiclass. Opt. 1 364). It showed a dominant Gaussian-like distribution with an increased axial intensity in the central region (not a doughnut-like distribution), so the diffracted output beam from the hollow fibre cannot be used to form an atomic funnel. Using exact solutions of the Maxwell equations based on a vector model, however, we calculate the electric field and intensity distributions of the HE11 mode in the same hollow fibre and study the diffracted near- and far-field distributions of the HE11-mode output beam under the Fresnel approximation. We analyse and compare the differences between the output beams from the HE11 and LP01 modes. Our study shows that both the near- and far-field intensity distributions of the HE11-mode output beam are doughnut-like and can be used to form a simple atomic funnel. However, it is not suitable to use the weakly waveguiding approximation to calculate the diffracted near-field distribution of the hollow fibre due to the greater refractive-index difference between the hollow region (n0 = 1) and the core (n1 = 1.45 or 1.5). Finally, the 3D intensity distribution of the HE11-mode output beam is modelled and the corresponding optical potentials for cold atoms are calculated. Some potential applications of the HE11-mode output beam in an atomic guide and funnel are briefly discussed.

Generic evolution of mixing in heterogeneous media

NASA Astrophysics Data System (ADS)

De Dreuzy, J.; Carrera, J.; Dentz, M.; Le Borgne, T.

2011-12-01

Mixing in heterogeneous media results from the competition bewteen flow fluctuations and local scale diffusion. Flow fluctuations quickly create concentration contrasts and thus heterogeneity of the concentration field, which is slowly homogenized by local scale diffusion. Mixing first deviates from Gaussian mixing, which represents the potential mixing induced by spreading before approaching it. This deviation fundamentally expresses the evolution of the interaction between spreading and local scale diffusion. We characterize it by the ratio γ of the non-Gaussian to the Gaussian mixing states. We define the Gaussian mixing state as the integrated squared concentration of the Gaussian plume that has the same longitudinal dispersion as the real plume. The non-Gaussian mixing state is the difference between the overall mixing state defined as the integrated squared concentration and the Gaussian mixing state. The main advantage of this definition is to use the full knowledge previously acquired on dispersion for characterizing mixing even when the solute concentration field is highly non Gaussian. Using high precision numerical simulations, we show that γ quickly increases, peaks and slowly decreases. γ can be derived from two scales characterizing spreading and local mixing, at least for large flux-weighted solute injection conditions into classically log-normal Gaussian correlated permeability fields. The spreading scale is directly related to the longitudinal dispersion. The local mixing scale is the largest scale over which solute concentrations can be considered locally uniform. More generally, beyond the characteristics of its maximum, γ turns out to have a highly generic scaling form. Its fast increase and slow decrease depend neither on the heterogeneity level, nor on the ratio of diffusion to advection, nor on the injection conditions. They might even not depend on the particularities of the flow fields as the same generic features also prevail for Taylor dispersion. This generic characterization of mixing can offer new ways to set up transport equations that honor not only advection and spreading (dispersion), but also mixing.

Hydrocarbon Reservoir Prediction Using Bi-Gaussian S Transform Based Time-Frequency Analysis Approach

NASA Astrophysics Data System (ADS)

Cheng, Z.; Chen, Y.; Liu, Y.; Liu, W.; Zhang, G.

2015-12-01

Among those hydrocarbon reservoir detection techniques, the time-frequency analysis based approach is one of the most widely used approaches because of its straightforward indication of low-frequency anomalies from the time-frequency maps, that is to say, the low-frequency bright spots usually indicate the potential hydrocarbon reservoirs. The time-frequency analysis based approach is easy to implement, and more importantly, is usually of high fidelity in reservoir prediction, compared with the state-of-the-art approaches, and thus is of great interest to petroleum geologists, geophysicists, and reservoir engineers. The S transform has been frequently used in obtaining the time-frequency maps because of its better performance in controlling the compromise between the time and frequency resolutions than the alternatives, such as the short-time Fourier transform, Gabor transform, and continuous wavelet transform. The window function used in the majority of previous S transform applications is the symmetric Gaussian window. However, one problem with the symmetric Gaussian window is the degradation of time resolution in the time-frequency map due to the long front taper. In our study, a bi-Gaussian S transform that substitutes the symmetric Gaussian window with an asymmetry bi-Gaussian window is proposed to analyze the multi-channel seismic data in order to predict hydrocarbon reservoirs. The bi-Gaussian window introduces asymmetry in the resultant time-frequency spectrum, with time resolution better in the front direction, as compared with the back direction. It is the first time that the bi-Gaussian S transform is used for analyzing multi-channel post-stack seismic data in order to predict hydrocarbon reservoirs since its invention in 2003. The superiority of the bi-Gaussian S transform over traditional S transform is tested on a real land seismic data example. The performance shows that the enhanced temporal resolution can help us depict more clearly the edge of the hydrocarbon reservoir, especially when the thickness of the reservoir is small (such as the thin beds).

Gaussian mixture models for detection of autism spectrum disorders (ASD) in magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Almeida, Javier; Velasco, Nelson; Alvarez, Charlens; Romero, Eduardo

2017-11-01

Autism Spectrum Disorder (ASD) is a complex neurological condition characterized by a triad of signs: stereotyped behaviors, verbal and non-verbal communication problems. The scientific community has been interested on quantifying anatomical brain alterations of this disorder. Several studies have focused on measuring brain cortical and sub-cortical volumes. This article presents a fully automatic method which finds out differences among patients diagnosed with autism and control patients. After the usual pre-processing, a template (MNI152) is registered to an evaluated brain which becomes then a set of regions. Each of these regions is the represented by the normalized histogram of intensities which is approximated by mixture of Gaussian (GMM). The gray and white matter are separated to calculate the mean and standard deviation of each Gaussian. These features are then used to train, region per region, a binary SVM classifier. The method was evaluated in an adult population aged from 18 to 35 years, from the public database Autism Brain Imaging Data Exchange (ABIDE). Highest discrimination values were found for the Right Middle Temporal Gyrus, with an Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC) the curve of 0.72.

A Variational Approach to Simultaneous Image Segmentation and Bias Correction.

PubMed

Zhang, Kaihua; Liu, Qingshan; Song, Huihui; Li, Xuelong

2015-08-01

This paper presents a novel variational approach for simultaneous estimation of bias field and segmentation of images with intensity inhomogeneity. We model intensity of inhomogeneous objects to be Gaussian distributed with different means and variances, and then introduce a sliding window to map the original image intensity onto another domain, where the intensity distribution of each object is still Gaussian but can be better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying the bias field with a piecewise constant signal within the sliding window. A maximum likelihood energy functional is then defined on each local region, which combines the bias field, the membership function of the object region, and the constant approximating the true signal from its corresponding object. The energy functional is then extended to the whole image domain by the Bayesian learning approach. An efficient iterative algorithm is proposed for energy minimization, via which the image segmentation and bias field correction are simultaneously achieved. Furthermore, the smoothness of the obtained optimal bias field is ensured by the normalized convolutions without extra cost. Experiments on real images demonstrated the superiority of the proposed algorithm to other state-of-the-art representative methods.

Strength functions, entropies, and duality in weakly to strongly interacting fermionic systems.

PubMed

Angom, D; Ghosh, S; Kota, V K B

2004-01-01

We revisit statistical wave function properties of finite systems of interacting fermions in the light of strength functions and their participation ratio and information entropy. For weakly interacting fermions in a mean-field with random two-body interactions of increasing strength lambda, the strength functions F(k) (E) are well known to change, in the regime where level fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We propose an ansatz for the function describing this transition which we use to investigate the participation ratio xi(2) and the information entropy S(info) during this crossover, thereby extending the known behavior valid in the Gaussian domain into much of the Breit-Wigner domain. Our method also allows us to derive the scaling law lambda(d) approximately 1/sqrt[m] ( m is number of fermions) for the duality point lambda= lambda(d), where F(k) (E), xi(2), and S(info) in both the weak ( lambda=0 ) and strong mixing ( lambda= infinity ) basis coincide. As an application, the ansatz function for strength functions is used in describing the Breit-Wigner to Gaussian transition seen in neutral atoms CeI to SmI with valence electrons changing from 4 to 8.

Nested polynomial trends for the improvement of Gaussian process-based predictors

NASA Astrophysics Data System (ADS)

Perrin, G.; Soize, C.; Marque-Pucheu, S.; Garnier, J.

2017-10-01

The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.

A novel multitarget model of radiation-induced cell killing based on the Gaussian distribution.

PubMed

Zhao, Lei; Mi, Dong; Sun, Yeqing

2017-05-07

The multitarget version of the traditional target theory based on the Poisson distribution is still used to describe the dose-survival curves of cells after ionizing radiation in radiobiology and radiotherapy. However, noting that the usual ionizing radiation damage is the result of two sequential stochastic processes, the probability distribution of the damage number per cell should follow a compound Poisson distribution, like e.g. Neyman's distribution of type A (N. A.). In consideration of that the Gaussian distribution can be considered as the approximation of the N. A. in the case of high flux, a multitarget model based on the Gaussian distribution is proposed to describe the cell inactivation effects in low linear energy transfer (LET) radiation with high dose-rate. Theoretical analysis and experimental data fitting indicate that the present theory is superior to the traditional multitarget model and similar to the Linear - Quadratic (LQ) model in describing the biological effects of low-LET radiation with high dose-rate, and the parameter ratio in the present model can be used as an alternative indicator to reflect the radiation damage and radiosensitivity of the cells. Copyright © 2017 Elsevier Ltd. All rights reserved.

Self-focusing and defocusing of Gaussian laser beams in collisional underdense magnetized plasmas with considering the nonlinear ohmic heating and ponderomotive force effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ettehadi Abari, Mehdi; Sedaghat, Mahsa; Shokri, Babak, E-mail: b-shokri@sbu.ac.ir

2015-10-15

The propagation characteristics of a Gaussian laser beam in collisional magnetized plasma are investigated by considering the ponderomotive and ohmic heating nonlinearities. Here, by taking into account the effect of the external magnetic field, the second order differential equation of the dimensionless beam width parameter is solved numerically. Furthermore, the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the Gaussian laser pulse is obtained, and its variation in terms of the dimensionless plasma length is analyzed at different initial normalized plasma and cyclotron frequencies. The results show thatmore » the dimensionless beam width parameter is strongly affected by the initial plasma frequency, magnetic strength, and laser pulse intensity. Furthermore, it is found that there exists a certain intensity value below which the laser pulse tends to self focus, while the beam diverges above of this value. In addition, the results confirm that, by increasing the plasma and cyclotron frequencies (plasma density and magnetic strength), the self-focusing effect can occur intensively.« less

Electron Acceleration by Beating of Two Intense Cross-Focused Hollow Gaussian Laser Beams in Plasma

NASA Astrophysics Data System (ADS)

Mahmoud, Saleh T.; Gauniyal, Rakhi; Ahmad, Nafis; Rawat, Priyanka; Purohit, Gunjan

2018-01-01

This paper presents propagation of two cross-focused intense hollow Gaussian laser beams (HGBs) in collisionless plasma and its effect on the generation of electron plasma wave (EPW) and electron acceleration process, when relativistic and ponderomotive nonlinearities are simultaneously operative. Nonlinear differential equations have been set up for beamwidth of laser beams, power of generated EPW, and energy gain by electrons using WKB and paraxial approximations. Numerical simulations have been carried out to investigate the effect of typical laser-plasma parameters on the focusing of laser beams in plasmas and further its effect on power of excited EPW and acceleration of electrons. It is observed that focusing of two laser beams in plasma increases for higher order of hollow Gaussian beams, which significantly enhanced the power of generated EPW and energy gain. The amplitude of EPW and energy gain by electrons is found to enhance with an increase in the intensity of laser beams and plasma density. This study will be useful to plasma beat wave accelerator and in other applications requiring multiple laser beams. Supported by United Arab Emirates University for Financial under Grant No. UPAR (2014)-31S164

Analysis of piezoelectric energy harvester under modulated and filtered white Gaussian noise

NASA Astrophysics Data System (ADS)

Quaranta, Giuseppe; Trentadue, Francesco; Maruccio, Claudio; Marano, Giuseppe C.

2018-05-01

This paper proposes a comprehensive method for the electromechanical probabilistic analysis of piezoelectric energy harvesters subjected to modulated and filtered white Gaussian noise (WGN) at the base. Specifically, the dynamic excitation is simulated by means of an amplitude-modulated WGN, which is filtered through the Clough-Penzien filter. The considered piezoelectric harvester is a cantilever bimorph modeled as Euler-Bernoulli beam with a concentrated mass at the free-end, and its global behavior is approximated by the fundamental vibration mode (which is tuned with the dominant frequency of the dynamic input). A resistive electrical load is considered in the circuit. Once the Lyapunov equation of the coupled electromechanical problem has been formulated, an original and efficient semi-analytical procedure is proposed to estimate mean and standard deviation of the electrical energy extracted from the piezoelectric layers.

A note about Gaussian statistics on a sphere

NASA Astrophysics Data System (ADS)

Chave, Alan D.

2015-11-01

The statistics of directional data on a sphere can be modelled either using the Fisher distribution that is conditioned on the magnitude being unity, in which case the sample space is confined to the unit sphere, or using the latitude-longitude marginal distribution derived from a trivariate Gaussian model that places no constraint on the magnitude. These two distributions are derived from first principles and compared. The Fisher distribution more closely approximates the uniform distribution on a sphere for a given small value of the concentration parameter, while the latitude-longitude marginal distribution is always slightly larger than the Fisher distribution at small off-axis angles for large values of the concentration parameter. Asymptotic analysis shows that the two distributions only become equivalent in the limit of large concentration parameter and very small off-axis angle.

Study of the intensity noise and intensity modulation in a of hybrid soliton pulsed source

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dogru, Nuran; Oziazisi, M Sadetin

2005-10-31

The relative intensity noise (RIN) and small-signal intensity modulation (IM) of a hybrid soliton pulsed source (HSPS) with a linearly chirped Gaussian apodised fibre Bragg grating (FBG) are considered in the electric-field approximation. The HSPS is described by solving the dynamic coupled-mode equations. It is shown that consideration of the carrier density noise in the HSPS in addition to the spontaneous noise is necessary to analyse accurately noise in the mode-locked HSPS. It is also shown that the resonance peak spectral splitting (RPSS) of the IM near the frequency inverse to the round-trip time of light in the external cavitymore » can be eliminated by selecting an appropriate linear chirp rate in the Gaussian apodised FBG. (laser applications and other topics in quantum electronics)« less

Rotating a curvaton brane in a warped throat

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Jun; Piao, Yun-Song; Cai, Yi-Fu, E-mail: zhangjun408@mails.gucas.ac.cn, E-mail: caiyf@ihep.ac.cn, E-mail: yspiao@gucas.ac.cn

2010-05-01

In this paper we study a curvaton model obtained by considering a probe anti-D3-brane with angular motion at the bottom of a KS throat with approximate isometries. We calculate the spectrum of curvature perturbations and the non-Gaussianities of this model. Specifically, we consider the limit of relativistic rotation of the curvaton brane which leads to a small sound speed, and thus it can be viewed as an implementation of the DBI-curvaton mechanism. We find that the primordial power spectrum is nearly scale-invariant while the non-Gaussianity of local type is sizable and that of equilateral type is usually large and negative.more » Moreover, we study both the theoretical and observational constraints on this model, and find that there exists a sizable allowed region for the phase space of this model.« less

Comparison of numerical techniques for the evaluation of the Doppler broadening functions psi(x,theta) and chi(x,theta)

NASA Technical Reports Server (NTRS)

Canright, R. B., Jr.; Semler, T. T.

1972-01-01

Several approximations to the Doppler broadening functions psi(x, theta) and chi(x, theta) are compared with respect to accuracy and speed of evaluation. A technique, due to A. M. Turning (1943), is shown to be at least as accurate as direct numerical quadrature and somewhat faster than Gaussian quadrature. FORTRAN 4 listings are included.

Development of Improved Algorithms and Multiscale Modeling Capability with SUNTANS

DTIC Science & Technology

2013-09-30

solves the Navier-Stokes equations under the Boussinesq approximation (Fringer et al.,2006). The formulation is based on the method outlined by...stratified systems . Figure 4 shows a nonhydrostatic isopycnal simulation of oscillatory flow in a continuously stratified fluid over a Gaussian sill. This...Modeling the Earth System , Boulder (invited). Sankaranarayanan, S., and Fringer, O. B., 2013, "Dynamics of barotropic low-frequency fluctuations in

On the development of efficient algorithms for three dimensional fluid flow

NASA Technical Reports Server (NTRS)

Maccormack, R. W.

1988-01-01

The difficulties of constructing efficient algorithms for three-dimensional flow are discussed. Reasonable candidates are analyzed and tested, and most are found to have obvious shortcomings. Yet, there is promise that an efficient class of algorithms exist between the severely time-step sized-limited explicit or approximately factored algorithms and the computationally intensive direct inversion of large sparse matrices by Gaussian elimination.

Detecting Compartmental non-Gaussian Diffusion with Symmetrized Double-PFG MRI

PubMed Central

Paulsen, Jeffrey L.; Özarslan, Evren; Komlosh, Michal E.; Basser, Peter J.; Song, Yi-Qiao

2015-01-01

Diffusion in tissue and porous media is known to be non-Gaussian and has been used for clinical indications of stroke and other tissue pathologies. However, when conventional NMR techniques are applied to biological tissues and other heterogeneous materials, the presence of multiple compartments (pores) with different Gaussian diffusivities will also contribute to the measurement of non-Gaussian behavior. Here we present Symmetrized Double PFG (sd-PFG), which can separate these two contributions to non-Gaussian signal decay as having distinct angular modulation frequencies. In contrast to prior angular d-PFG methods, sd-PFG can unambiguously extract kurtosis as an oscillation from samples with isotropic or uniformly oriented anisotropic pores, and can generally extract a combination of compartmental anisotropy and kurtosis. The method further fixes its sensitivity with respect to the time-dependence of the apparent diffusion coefficient. We experimentally demonstrate the measurement of the fourth moment (kurtosis) of diffusion and find it consistent with theoretical predictions. By enabling the unambiguous identification of contributions of compartmental kurtosis to the signal, sd-PFG has the potential to help identify the underlying micro-structural changes corresponding to current kurtosis based diagnostics and act as a novel source of contrast to better resolve tissue micro-structure. PMID:26434812

Measurement and dynamics of the spatial distribution of an electron localized at a metal-dielectric interface

NASA Astrophysics Data System (ADS)

Bezel, Ilya; Gaffney, Kelly J.; Garrett-Roe, Sean; Liu, Simon H.; Miller, André D.; Szymanski, Paul; Harris, Charles B.

2004-01-01

The ability of time- and angle-resolved two-photon photoemission to estimate the size distribution of electron localization in the plane of a metal-adsorbate interface is discussed. It is shown that the width of angular distribution of the photoelectric current is inversely proportional to the electron localization size within the most common approximations in the description of image potential states. The localization of the n=1 image potential state for two monolayers of butyronitrile on Ag(111) is used as an example. For the delocalized n=1 state, the shape of the signal amplitude as a function of momentum parallel to the surface changes rapidly with time, indicating efficient intraband relaxation on a 100 fs time scale. For the localized state, little change was observed. The latter is related to the constant size distribution of electron localization, which is estimated to be a Gaussian with a 15±4 Å full width at half maximum in the plane of the interface. A simple model was used to study the effect of a weak localization potential on the overall width of the angular distribution of the photoemitted electrons, which exhibited little sensitivity to the details of the potential. This substantiates the validity of the localization size estimate.

Doubly self-consistent field theory of grafted polymers under simple shear in steady state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suo, Tongchuan; Whitmore, Mark D., E-mail: mark-whitmore@umanitoba.ca

2014-03-21

We present a generalization of the numerical self-consistent mean-field theory of polymers to the case of grafted polymers under simple shear. The general theoretical framework is presented, and then applied to three different chain models: rods, Gaussian chains, and finitely extensible nonlinear elastic (FENE) chains. The approach is self-consistent at two levels. First, for any flow field, the polymer density profile and effective potential are calculated self-consistently in a manner similar to the usual self-consistent field theory of polymers, except that the calculation is inherently two-dimensional even for a laterally homogeneous system. Second, through the use of a modified Brinkmanmore » equation, the flow field and the polymer profile are made self-consistent with respect to each other. For all chain models, we find that reasonable levels of shear cause the chains to tilt, but it has very little effect on the overall thickness of the polymer layer, causing a small decrease for rods, and an increase of no more than a few percent for the Gaussian and FENE chains. Using the FENE model, we also probe the individual bond lengths, bond correlations, and bond angles along the chains, the effects of the shear on them, and the solvent and bonded stress profiles. We find that the approximations needed within the theory for the Brinkman equation affect the bonded stress, but none of the other quantities.« less

Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field

NASA Astrophysics Data System (ADS)

Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

2017-10-01

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

Generation of 2 µm Laguerre-Gaussian mode in a Tm:LuYAG solid-state laser

NASA Astrophysics Data System (ADS)

Liu, Qiyao; Ding, Manman; Zhao, Yongguang; Zhou, Wei; Shen, Deyuan

2018-04-01

In this article, we discuss the first vortex laser in the 2 µm spectral range directly generated from a Tm:LuYAG oscillator, in which a pump beam with annular intensity distribution is employed in line with Laguerre-Gaussian modes. Laser thresholds of different-order Laguerre-Gaussian modes are theoretically analyzed and discussed. Vortex lasers with orbital angular momentum of ħ and  -ħ were experimentally produced with corresponding output powers of 1.75 W and 1.64 W, respectively. This directly emitted vortex laser generated in the ~2 µm region from a compact and robust Tm:LuYAG oscillator has potential applications in the areas of molecular spectroscopy and organic material processing amongst others.

Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory

PubMed Central

Ambrosio, Leonardo A.; Hernández-Figueroa, Hugo E.

2010-01-01

Based on the generalized Lorenz-Mie theory (GLMT), this paper reveals, for the first time in the literature, the principal characteristics of the optical forces and radiation pressure cross-sections exerted on homogeneous, linear, isotropic and spherical hypothetical negative refractive index (NRI) particles under the influence of focused Gaussian beams in the Mie regime. Starting with ray optics considerations, the analysis is then extended through calculating the Mie coefficients and the beam-shape coefficients for incident focused Gaussian beams. Results reveal new and interesting trapping properties which are not observed for commonly positive refractive index particles and, in this way, new potential applications in biomedical optics can be devised. PMID:21258549