Sparse decomposition of seismic data and migration using Gaussian beams with nonzero initial curvature

NASA Astrophysics Data System (ADS)

Liu, Peng; Wang, Yanfei

2018-04-01

We study problems associated with seismic data decomposition and migration imaging. We first represent the seismic data utilizing Gaussian beam basis functions, which have nonzero curvature, and then consider the sparse decomposition technique. The sparse decomposition problem is an l0-norm constrained minimization problem. In solving the l0-norm minimization, a polynomial Radon transform is performed to achieve sparsity, and a fast gradient descent method is used to calculate the waveform functions. The waveform functions can subsequently be used for sparse Gaussian beam migration. Compared with traditional sparse Gaussian beam methods, the seismic data can be properly reconstructed employing fewer Gaussian beams with nonzero initial curvature. The migration approach described in this paper is more efficient than the traditional sparse Gaussian beam migration.

Gaussian-input Gaussian mixture model for representing density maps and atomic models.

PubMed

Kawabata, Takeshi

2018-07-01

A new Gaussian mixture model (GMM) has been developed for better representations of both atomic models and electron microscopy 3D density maps. The standard GMM algorithm employs an EM algorithm to determine the parameters. It accepted a set of 3D points with weights, corresponding to voxel or atomic centers. Although the standard algorithm worked reasonably well; however, it had three problems. First, it ignored the size (voxel width or atomic radius) of the input, and thus it could lead to a GMM with a smaller spread than the input. Second, the algorithm had a singularity problem, as it sometimes stopped the iterative procedure due to a Gaussian function with almost zero variance. Third, a map with a large number of voxels required a long computation time for conversion to a GMM. To solve these problems, we have introduced a Gaussian-input GMM algorithm, which considers the input atoms or voxels as a set of Gaussian functions. The standard EM algorithm of GMM was extended to optimize the new GMM. The new GMM has identical radius of gyration to the input, and does not suddenly stop due to the singularity problem. For fast computation, we have introduced a down-sampled Gaussian functions (DSG) by merging neighboring voxels into an anisotropic Gaussian function. It provides a GMM with thousands of Gaussian functions in a short computation time. We also have introduced a DSG-input GMM: the Gaussian-input GMM with the DSG as the input. This new algorithm is much faster than the standard algorithm. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

Testing for the Gaussian nature of cosmological density perturbations through the three-point temperature correlation function

NASA Technical Reports Server (NTRS)

Luo, Xiaochun; Schramm, David N.

1993-01-01

One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian where seeds produced by topological defects tend to be non-Gaussian. The three-point correlation function of the temperature anisotropy of the cosmic microwave background radiation (CBR) provides a sensitive test of this aspect of the primordial density field. In this paper, this function is calculated in the general context of various allowed non-Gaussian models. It is shown that the Cosmic Background Explorer and the forthcoming South Pole and balloon CBR anisotropy data may be able to provide a crucial test of the Gaussian nature of the perturbations.

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.

Naked singularities are not singular in distorted gravity

NASA Astrophysics Data System (ADS)

Garattini, Remo; Majumder, Barun

2014-07-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.

Representing Color Ensembles.

PubMed

Chetverikov, Andrey; Campana, Gianluca; Kristjánsson, Árni

2017-10-01

Colors are rarely uniform, yet little is known about how people represent color distributions. We introduce a new method for studying color ensembles based on intertrial learning in visual search. Participants looked for an oddly colored diamond among diamonds with colors taken from either uniform or Gaussian color distributions. On test trials, the targets had various distances in feature space from the mean of the preceding distractor color distribution. Targets on test trials therefore served as probes into probabilistic representations of distractor colors. Test-trial response times revealed a striking similarity between the physical distribution of colors and their internal representations. The results demonstrate that the visual system represents color ensembles in a more detailed way than previously thought, coding not only mean and variance but, most surprisingly, the actual shape (uniform or Gaussian) of the distribution of colors in the environment.

Investigating task inhibition in children versus adults: A diffusion model analysis.

PubMed

Schuch, Stefanie; Konrad, Kerstin

2017-04-01

One can take n-2 task repetition costs as a measure of inhibition on the level of task sets. When switching back to a Task A after only one intermediate trial (ABA task sequence), Task A is thought to still be inhibited, leading to performance costs relative to task sequences where switching back to Task A is preceded by at least two intermediary trials (CBA). The current study investigated differences in inhibitory ability between children and adults by comparing n-2 task repetition costs in children (9-11years of age, N=32) and young adults (21-30years of age, N=32). The mean reaction times and error rate differences between ABA and CBA sequences did not differ between the two age groups. However, diffusion model analysis revealed that different cognitive processes contribute to the inhibition effect in the two age groups: The adults, but not the children, showed a smaller drift rate in ABA than in CBA, suggesting that persisting task inhibition is associated with slower response selection in adults. In children, non-decision time was longer in ABA than in CBA, possibly reflecting longer task preparation in ABA than in CBA. In addition, Ex-Gaussian functions were fitted to the distributions of correct reaction times. In adults, the ABA-CBA difference was reflected in the exponential parameter of the distribution; in children, the ABA-CBA difference was found in the Gaussian mu parameter. Hence, Ex-Gaussian analysis, although noisier, was generally in line with diffusion model analysis. Taken together, the data suggest that the task inhibition effect found in mean performance is mediated by different cognitive processes in children versus adults. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

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

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

Smallwood, D.O.

It is recognized that some dynamic and noise environments are characterized by time histories which are not Gaussian. An example is high intensity acoustic noise. Another example is some transportation vibration. A better simulation of these environments can be generated if a zero mean non-Gaussian time history can be reproduced with a specified auto (or power) spectral density (ASD or PSD) and a specified probability density function (pdf). After the required time history is synthesized, the waveform can be used for simulation purposes. For example, modem waveform reproduction techniques can be used to reproduce the waveform on electrodynamic or electrohydraulicmore » shakers. Or the waveforms can be used in digital simulations. A method is presented for the generation of realizations of zero mean non-Gaussian random time histories with a specified ASD, and pdf. First a Gaussian time history with the specified auto (or power) spectral density (ASD) is generated. A monotonic nonlinear function relating the Gaussian waveform to the desired realization is then established based on the Cumulative Distribution Function (CDF) of the desired waveform and the known CDF of a Gaussian waveform. The established function is used to transform the Gaussian waveform to a realization of the desired waveform. Since the transformation preserves the zero-crossings and peaks of the original Gaussian waveform, and does not introduce any substantial discontinuities, the ASD is not substantially changed. Several methods are available to generate a realization of a Gaussian distributed waveform with a known ASD. The method of Smallwood and Paez (1993) is an example. However, the generation of random noise with a specified ASD but with a non-Gaussian distribution is less well known.« less

Simulation and analysis of scalable non-Gaussian statistically anisotropic random functions

NASA Astrophysics Data System (ADS)

Riva, Monica; Panzeri, Marco; Guadagnini, Alberto; Neuman, Shlomo P.

2015-12-01

Many earth and environmental (as well as other) variables, Y, and their spatial or temporal increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture some key aspects of such scaling by treating Y or ΔY as standard sub-Gaussian random functions. We were however unable to reconcile two seemingly contradictory observations, namely that whereas sample frequency distributions of Y (or its logarithm) exhibit relatively mild non-Gaussian peaks and tails, those of ΔY display peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we overcame this difficulty by developing a new generalized sub-Gaussian model which captures both behaviors in a unified and consistent manner, exploring it on synthetically generated random functions in one dimension (Riva et al., 2015). Here we extend our generalized sub-Gaussian model to multiple dimensions, present an algorithm to generate corresponding random realizations of statistically isotropic or anisotropic sub-Gaussian functions and illustrate it in two dimensions. We demonstrate the accuracy of our algorithm by comparing ensemble statistics of Y and ΔY (such as, mean, variance, variogram and probability density function) with those of Monte Carlo generated realizations. We end by exploring the feasibility of estimating all relevant parameters of our model by analyzing jointly spatial moments of Y and ΔY obtained from a single realization of Y.

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.

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.

The Harmonic Oscillator with a Gaussian Perturbation: Evaluation of the Integrals and Example Applications

ERIC Educational Resources Information Center

Earl, Boyd L.

2008-01-01

A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…

Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams

NASA Technical Reports Server (NTRS)

Steely, Sidney L.

1993-01-01

The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.

Surrogacy assessment using principal stratification with multivariate normal and Gaussian copula models.

PubMed

Taylor, Jeremy M G; Conlon, Anna S C; Elliott, Michael R

2015-08-01

The validation of intermediate markers as surrogate markers (S) for the true outcome of interest (T) in clinical trials offers the possibility for trials to be run more quickly and cheaply by using the surrogate endpoint in place of the true endpoint. Working within a principal stratification framework, we propose causal quantities to evaluate surrogacy using a Gaussian copula model for an ordinal surrogate and time-to-event final outcome. The methods are applied to data from four colorectal cancer clinical trials, where S is tumor response and T is overall survival. For the Gaussian copula model, a Bayesian estimation strategy is used and, as some parameters are not identifiable from the data, we explore the use of informative priors that are consistent with reasonable assumptions in the surrogate marker setting to aid in estimation. While there is some bias in the estimation of the surrogacy quantities of interest, the estimation procedure does reasonably well at distinguishing between poor and good surrogate markers. Some of the parameters of the proposed model are not identifiable from the data, and therefore, assumptions must be made in order to aid in their estimation. The proposed quantities can be used in combination to provide evidence about the validity of S as a surrogate marker for T. © The Author(s) 2014.

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.

Probability distribution for the Gaussian curvature of the zero level surface of a random function

NASA Astrophysics Data System (ADS)

Hannay, J. H.

2018-04-01

A rather natural construction for a smooth random surface in space is the level surface of value zero, or ‘nodal’ surface f(x,y,z)  =  0, of a (real) random function f; the interface between positive and negative regions of the function. A physically significant local attribute at a point of a curved surface is its Gaussian curvature (the product of its principal curvatures) because, when integrated over the surface it gives the Euler characteristic. Here the probability distribution for the Gaussian curvature at a random point on the nodal surface f  =  0 is calculated for a statistically homogeneous (‘stationary’) and isotropic zero mean Gaussian random function f. Capitalizing on the isotropy, a ‘fixer’ device for axes supplies the probability distribution directly as a multiple integral. Its evaluation yields an explicit algebraic function with a simple average. Indeed, this average Gaussian curvature has long been known. For a non-zero level surface instead of the nodal one, the probability distribution is not fully tractable, but is supplied as an integral expression.

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.

Conversion of the high-mode solitons in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Zhang, Xiaping

2017-01-01

The conversion of high-mode solitons propagating in Strongly Nonlocal Nonlinear Media (SNNM) in three coordinate systems, namely, the elliptic coordinate system, the rectangular coordinate system and the cylindrical coordinate system, based on the Snyder-Mitchell Model that describes the paraxial beam propagating in SNNM, is discussed. Through constituting the trial solution with modulating the Gaussian beam by Ince polynomials, the closed-solution of Gaussian beams in elliptic coordinate is accessed. The Ince-Gaussian (IG) beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian (LG) beams, which is controlled by the elliptic parameter. The conditions of conversion in the three types of solitons are given in relation to the Gouy phase invariability in stable propagation. The profiles of the IG breather at a different propagating distance are numerically obtained, and the conversions of a few IG solitons are illustrated. The difference between the IG soliton and the corresponding LG soliton is remarkable from the Poynting vector and phase plots at their profiles along the propagating axis.

X-ray beam-shaping via deformable mirrors: surface profile and point spread function computation for Gaussian beams using physical optics.

PubMed

Spiga, D

2018-01-01

X-ray mirrors with high focusing performances are commonly used in different sectors of science, such as X-ray astronomy, medical imaging and synchrotron/free-electron laser beamlines. While deformations of the mirror profile may cause degradation of the focus sharpness, a deliberate deformation of the mirror can be made to endow the focus with a desired size and distribution, via piezo actuators. The resulting profile can be characterized with suitable metrology tools and correlated with the expected optical quality via a wavefront propagation code or, sometimes, predicted using geometric optics. In the latter case and for the special class of profile deformations with monotonically increasing derivative, i.e. concave upwards, the point spread function (PSF) can even be predicted analytically. Moreover, under these assumptions, the relation can also be reversed: from the desired PSF the required profile deformation can be computed analytically, avoiding the use of trial-and-error search codes. However, the computation has been so far limited to geometric optics, which entailed some limitations: for example, mirror diffraction effects and the size of the coherent X-ray source were not considered. In this paper, the beam-shaping formalism in the framework of physical optics is reviewed, in the limit of small light wavelengths and in the case of Gaussian intensity wavefronts. Some examples of shaped profiles are also shown, aiming at turning a Gaussian intensity distribution into a top-hat one, and checks of the shaping performances computing the at-wavelength PSF by means of the WISE code are made.

Ince-Gaussian series representation of the two-dimensional fractional Fourier transform.

PubMed

Bandres, Miguel A; Gutiérrez-Vega, Julio C

2005-03-01

We introduce the Ince-Gaussian series representation of the two-dimensional fractional Fourier transform in elliptical coordinates. A physical interpretation is provided in terms of field propagation in quadratic graded-index media whose eigenmodes in elliptical coordinates are derived for the first time to our knowledge. The kernel of the new series representation is expressed in terms of Ince-Gaussian functions. The equivalence among the Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian series representations is verified by establishing the relation among the three definitions.

Elegant Ince-Gaussian beams in a quadratic-index medium

NASA Astrophysics Data System (ADS)

Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

2011-09-01

Elegant Ince—Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard Ince—Gaussian beams and they display better symmetry between the Ince-polynomials and the Gaussian function in mathematics. The transverse intensity distribution and the phase of the elegant Ince—Gaussian beams are discussed.

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

Smallwood, D.O.

In a previous paper Smallwood and Paez (1991) showed how to generate realizations of partially coherent stationary normal time histories with a specified cross-spectral density matrix. This procedure is generalized for the case of multiple inputs with a specified cross-spectral density function and a specified marginal probability density function (pdf) for each of the inputs. The specified pdfs are not required to be Gaussian. A zero memory nonlinear (ZMNL) function is developed for each input to transform a Gaussian or normal time history into a time history with a specified non-Gaussian distribution. The transformation functions have the property that amore » transformed time history will have nearly the same auto spectral density as the original time history. A vector of Gaussian time histories are then generated with the specified cross-spectral density matrix. These waveforms are then transformed into the required time history realizations using the ZMNL function.« less

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.

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.

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

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

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.

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

NASA Technical Reports Server (NTRS)

Kogut, A.; Banday, A. J.; Bennett, C. L.; Hinshaw, G.; Lubin, P. M.; Smoot, G. F.

1995-01-01

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

Rightfulness of Summation Cut-Offs in the Albedo Problem with Gaussian Fluctuations of the Density of Scatterers

NASA Astrophysics Data System (ADS)

Selim, M. M.; Bezák, V.

2003-06-01

The one-dimensional version of the radiative transfer problem (i.e. the so-called rod model) is analysed with a Gaussian random extinction function (x). Then the optical length X = 0 Ldx(x) is a Gaussian random variable. The transmission and reflection coefficients, T(X) and R(X), are taken as infinite series. When these series (and also when the series representing T 2(X), T 2(X), R(X)T(X), etc.) are averaged, term by term, according to the Gaussian statistics, the series become divergent after averaging. As it was shown in a former paper by the authors (in Acta Physica Slovaca (2003)), a rectification can be managed when a `modified' Gaussian probability density function is used, equal to zero for X > 0 and proportional to the standard Gaussian probability density for X > 0. In the present paper, the authors put forward an alternative, showing that if the m.s.r. of X is sufficiently small in comparison with & $bar X$ ; , the standard Gaussian averaging is well functional provided that the summation in the series representing the variable T m-j (X)R j (X) (m = 1,2,..., j = 1,...,m) is truncated at a well-chosen finite term. The authors exemplify their analysis by some numerical calculations.

From plane waves to local Gaussians for the simulation of correlated periodic systems

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

Booth, George H., E-mail: george.booth@kcl.ac.uk; Tsatsoulis, Theodoros; Grüneis, Andreas, E-mail: a.grueneis@fkf.mpg.de

2016-08-28

We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of themore » basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller–Plesset perturbation theory.« less

A Concept for Measuring Electron Distribution Functions Using Collective Thomson Scattering

NASA Astrophysics Data System (ADS)

Milder, A. L.; Froula, D. H.

2017-10-01

A.B. Langdon proposed that stable non-Maxwellian distribution functions are realized in coronal inertial confinement fusion plasmas via inverse bremsstrahlung heating. For Zvosc2 Zvosc2 vth2 > 1 , vth2 > 1 , the inverse bremsstrahlung heating rate is sufficiently fast to compete with electron-electron collisions. This process preferentially heats the subthermal electrons leading to super-Gaussian distribution functions. A method to identify the super-Gaussian order of the distribution functions in these plasmas using collective Thomson scattering will be proposed. By measuring the collective Thomson spectra over a range of angles the density, temperature and super-Gaussian order can be determined. This is accomplished by fitting non-Maxwellian distribution data with a super-Gaussian model; in order to match the density and electron temperature to within 10%, the super-Gaussian order must be varied. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.

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.

New deconvolution method for microscopic images based on the continuous Gaussian radial basis function interpolation model.

PubMed

Chen, Zhaoxue; Chen, Hao

2014-01-01

A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution.

Theoretical investigation of gas-surface interactions

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1990-01-01

A Dirac-Hartree-Fock code was developed for polyatomic molecules. The program uses integrals over symmetry-adapted real spherical harmonic Gaussian basis functions generated by a modification of the MOLECULE integrals program. A single Gaussian function is used for the nuclear charge distribution, to ensure proper boundary conditions at the nuclei. The Gaussian primitive functions are chosen to satisfy the kinetic balance condition. However, contracted functions which do not necessarily satisfy this condition may be used. The Fock matrix is constructed in the scalar basis and transformed to a jj-coupled 2-spinor basis before diagonalization. The program was tested against numerical results for atoms with a Gaussian nucleus and diatomic molecules with point nuclei. The energies converge on the numerical values as the basis set size is increased. Full use of molecular symmetry (restricted to D sub 2h and subgroups) is yet to be implemented.

Data from fitting Gaussian process models to various data sets using eight Gaussian process software packages.

PubMed

Erickson, Collin B; Ankenman, Bruce E; Sanchez, Susan M

2018-06-01

This data article provides the summary data from tests comparing various Gaussian process software packages. Each spreadsheet represents a single function or type of function using a particular input sample size. In each spreadsheet, a row gives the results for a particular replication using a single package. Within each spreadsheet there are the results from eight Gaussian process model-fitting packages on five replicates of the surface. There is also one spreadsheet comparing the results from two packages performing stochastic kriging. These data enable comparisons between the packages to determine which package will give users the best results.

Consistency relations for sharp inflationary non-Gaussian features

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

Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris

If cosmic inflation suffered tiny time-dependent deviations from the slow-roll regime, these would induce the existence of small scale-dependent features imprinted in the primordial spectra, with their shapes and sizes revealing information about the physics that produced them. Small sharp features could be suppressed at the level of the two-point correlation function, making them undetectable in the power spectrum, but could be amplified at the level of the three-point correlation function, offering us a window of opportunity to uncover them in the non-Gaussian bispectrum. In this article, we show that sharp features may be analyzed using only data coming frommore » the three point correlation function parametrizing primordial non-Gaussianity. More precisely, we show that if features appear in a particular non-Gaussian triangle configuration (e.g. equilateral, folded, squeezed), these must reappear in every other configuration according to a specific relation allowing us to correlate features across the non-Gaussian bispectrum. As a result, we offer a method to study scale-dependent features generated during inflation that depends only on data coming from measurements of non-Gaussianity, allowing us to omit data from the power spectrum.« less

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.

PubMed

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Age-Associated Changes in the Spectral and Statistical Parameters of Surface Electromyogram of Tibialis Anterior.

PubMed

Siddiqi, Ariba; Arjunan, Sridhar Poosapadi; Kumar, Dinesh Kant

2016-01-01

Age-related neuromuscular change of Tibialis Anterior (TA) is a leading cause of muscle strength decline among the elderly. This study has established the baseline for age-associated changes in sEMG of TA at different levels of voluntary contraction. We have investigated the use of Gaussianity and maximal power of the power spectral density (PSD) as suitable features to identify age-associated changes in the surface electromyogram (sEMG). Eighteen younger (20-30 years) and 18 older (60-85 years) cohorts completed two trials of isometric dorsiflexion at four different force levels between 10% and 50% of the maximal voluntary contraction. Gaussianity and maximal power of the PSD of sEMG were determined. Results show a significant increase in sEMG's maximal power of the PSD and Gaussianity with increase in force for both cohorts. It was also observed that older cohorts had higher maximal power of the PSD and lower Gaussianity. These age-related differences observed in the PSD and Gaussianity could be due to motor unit remodelling. This can be useful for noninvasive tracking of age-associated neuromuscular changes.

Feasibility study on the least square method for fitting non-Gaussian noise data

NASA Astrophysics Data System (ADS)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.

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.

Outlier Resistant Predictive Source Encoding for a Gaussian Stationary Nominal Source.

DTIC Science & Technology

1987-09-18

breakdown point and influence function . The proposed sequence of predictive encoders attains strictly positive breakdown point and uniformly bounded... influence function , at the expense of increased mean difference-squared distortion and differential entropy, at the Gaussian nominal source.

Explicitly-correlated Gaussian geminals in electronic structure calculations

NASA Astrophysics Data System (ADS)

Szalewicz, Krzysztof; Jeziorski, Bogumił

2010-11-01

Explicitly correlated functions have been used since 1929, but initially only for two-electron systems. In 1960, Boys and Singer showed that if the correlating factor is of Gaussian form, many-electron integrals can be computed for general molecules. The capability of explicitly correlated Gaussian (ECG) functions to accurately describe many-electron atoms and molecules was demonstrated only in the early 1980s when Monkhorst, Zabolitzky and the present authors cast the many-body perturbation theory (MBPT) and coupled cluster (CC) equations as a system of integro-differential equations and developed techniques of solving these equations with two-electron ECG functions (Gaussian-type geminals, GTG). This work brought a new accuracy standard to MBPT/CC calculations. In 1985, Kutzelnigg suggested that the linear r 12 correlating factor can also be employed if n-electron integrals, n > 2, are factorised with the resolution of identity. Later, this factor was replaced by more general functions f (r 12), most often by ? , usually represented as linear combinations of Gaussian functions which makes the resulting approach (called F12) a special case of the original GTG expansion. The current state-of-art is that, for few-electron molecules, ECGs provide more accurate results than any other basis available, but for larger systems the F12 approach is the method of choice, giving significant improvements over orbital calculations.

Coherent superposition of propagation-invariant laser beams

NASA Astrophysics Data System (ADS)

Soskind, R.; Soskind, M.; Soskind, Y. G.

2012-10-01

The coherent superposition of propagation-invariant laser beams represents an important beam-shaping technique, and results in new beam shapes which retain the unique property of propagation invariance. Propagation-invariant laser beam shapes depend on the order of the propagating beam, and include Hermite-Gaussian and Laguerre-Gaussian beams, as well as the recently introduced Ince-Gaussian beams which additionally depend on the beam ellipticity parameter. While the superposition of Hermite-Gaussian and Laguerre-Gaussian beams has been discussed in the past, the coherent superposition of Ince-Gaussian laser beams has not received significant attention in literature. In this paper, we present the formation of propagation-invariant laser beams based on the coherent superposition of Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian beams of different orders. We also show the resulting field distributions of the superimposed Ince-Gaussian laser beams as a function of the ellipticity parameter. By changing the beam ellipticity parameter, we compare the various shapes of the superimposed propagation-invariant laser beams transitioning from Laguerre-Gaussian beams at one ellipticity extreme to Hermite-Gaussian beams at the other extreme.

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.

An adaptive Hinfinity controller design for bank-to-turn missiles using ridge Gaussian neural networks.

PubMed

Lin, Chuan-Kai; Wang, Sheng-De

2004-11-01

A new autopilot design for bank-to-turn (BTT) missiles is presented. In the design of autopilot, a ridge Gaussian neural network with local learning capability and fewer tuning parameters than Gaussian neural networks is proposed to model the controlled nonlinear systems. We prove that the proposed ridge Gaussian neural network, which can be a universal approximator, equals the expansions of rotated and scaled Gaussian functions. Although ridge Gaussian neural networks can approximate the nonlinear and complex systems accurately, the small approximation errors may affect the tracking performance significantly. Therefore, by employing the Hinfinity control theory, it is easy to attenuate the effects of the approximation errors of the ridge Gaussian neural networks to a prescribed level. Computer simulation results confirm the effectiveness of the proposed ridge Gaussian neural networks-based autopilot with Hinfinity stabilization.

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.

Estimation of a monotone percentile residual life function under random censorship.

PubMed

Franco-Pereira, Alba M; de Uña-Álvarez, Jacobo

2013-01-01

In this paper, we introduce a new estimator of a percentile residual life function with censored data under a monotonicity constraint. Specifically, it is assumed that the percentile residual life is a decreasing function. This assumption is useful when estimating the percentile residual life of units, which degenerate with age. We establish a law of the iterated logarithm for the proposed estimator, and its n-equivalence to the unrestricted estimator. The asymptotic normal distribution of the estimator and its strong approximation to a Gaussian process are also established. We investigate the finite sample performance of the monotone estimator in an extensive simulation study. Finally, data from a clinical trial in primary biliary cirrhosis of the liver are analyzed with the proposed methods. One of the conclusions of our work is that the restricted estimator may be much more efficient than the unrestricted one. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Effect of central obscuration on the LDR point spread function

NASA Technical Reports Server (NTRS)

Vanzyl, Jakob J.

1988-01-01

It is well known that Gaussian apodization of an aperture reduces the sidelobe levels of its point spread function (PSF). In the limit where the standard deviation of the Gaussian function is much smaller than the diameter of the aperture, the sidelobes completely disappear. However, when Gaussian apodization is applied to the Large Deployable Reflector (LDR) array consisting of 84 hexagonal panels, it is found that the sidelobe level only decreases by about 2.5 dB. The reason for this is explained. The PSF is shown for an array consisting of 91 uniformly illuminated hexagonal apertures; this array is identical to the LDR array, except that the central hole in the LDR array is filled with seven additional panels. For comparison, the PSF of the uniformly illuminated LDR array is shown. Notice that it is already evident that the sidelobe structure of the LDR array is different from that of the full array of 91 panels. The PSF's of the same two arrays are shown, but with the illumination apodized with a Gaussian function to have 20 dB tapering at the edges of the arrays. While the sidelobes of the full array have decreased dramatically, those of the LDR array changed in structure, but stayed at almost the same level. This result is not completely surprising, since the Gaussian apodization tends to emphasize the contributions from the central portion of the array; exactly where the hole in the LDR array is located. The two most important conclusions are: the size of the central hole should be minimized, and a simple Gaussian apodization scheme to suppress the sidelobes in the PSF should not be used. A more suitable apodization scheme would be a Gaussian annular ring.

Geographically weighted regression model on poverty indicator

NASA Astrophysics Data System (ADS)

Slamet, I.; Nugroho, N. F. T. A.; Muslich

2017-12-01

In this research, we applied geographically weighted regression (GWR) for analyzing the poverty in Central Java. We consider Gaussian Kernel as weighted function. The GWR uses the diagonal matrix resulted from calculating kernel Gaussian function as a weighted function in the regression model. The kernel weights is used to handle spatial effects on the data so that a model can be obtained for each location. The purpose of this paper is to model of poverty percentage data in Central Java province using GWR with Gaussian kernel weighted function and to determine the influencing factors in each regency/city in Central Java province. Based on the research, we obtained geographically weighted regression model with Gaussian kernel weighted function on poverty percentage data in Central Java province. We found that percentage of population working as farmers, population growth rate, percentage of households with regular sanitation, and BPJS beneficiaries are the variables that affect the percentage of poverty in Central Java province. In this research, we found the determination coefficient R2 are 68.64%. There are two categories of district which are influenced by different of significance factors.

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.

An empirical analysis of the distribution of overshoots in a stationary Gaussian stochastic process

NASA Technical Reports Server (NTRS)

Carter, M. C.; Madison, M. W.

1973-01-01

The frequency distribution of overshoots in a stationary Gaussian stochastic process is analyzed. The primary processes involved in this analysis are computer simulation and statistical estimation. Computer simulation is used to simulate stationary Gaussian stochastic processes that have selected autocorrelation functions. An analysis of the simulation results reveals a frequency distribution for overshoots with a functional dependence on the mean and variance of the process. Statistical estimation is then used to estimate the mean and variance of a process. It is shown that for an autocorrelation function, the mean and the variance for the number of overshoots, a frequency distribution for overshoots can be estimated.

The influence of non-Gaussian distribution functions on the time-dependent perpendicular transport of energetic particles

NASA Astrophysics Data System (ADS)

Lasuik, J.; Shalchi, A.

2018-06-01

In the current paper we explore the influence of the assumed particle statistics on the transport of energetic particles across a mean magnetic field. In previous work the assumption of a Gaussian distribution function was standard, although there have been known cases for which the transport is non-Gaussian. In the present work we combine a kappa distribution with the ordinary differential equation provided by the so-called unified non-linear transport theory. We then compute running perpendicular diffusion coefficients for different values of κ and turbulence configurations. We show that changing the parameter κ slightly increases or decreases the perpendicular diffusion coefficient depending on the considered turbulence configuration. Since these changes are small, we conclude that the assumed statistics is less significant in particle transport theory. The results obtained in the current paper support to use a Gaussian distribution function as usually done in particle transport theory.

Truncated Gaussians as tolerance sets

NASA Technical Reports Server (NTRS)

Cozman, Fabio; Krotkov, Eric

1994-01-01

This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.

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…

Detection of nonlinear transfer functions by the use of Gaussian statistics

NASA Technical Reports Server (NTRS)

Sheppard, J. G.

1972-01-01

The possibility of using on-line signal statistics to detect electronic equipment nonlinearities is discussed. The results of an investigation using Gaussian statistics are presented, and a nonlinearity test that uses ratios of the moments of a Gaussian random variable is developed and discussed. An outline for further investigation is presented.

Age-Associated Changes in the Spectral and Statistical Parameters of Surface Electromyogram of Tibialis Anterior

PubMed Central

2016-01-01

Age-related neuromuscular change of Tibialis Anterior (TA) is a leading cause of muscle strength decline among the elderly. This study has established the baseline for age-associated changes in sEMG of TA at different levels of voluntary contraction. We have investigated the use of Gaussianity and maximal power of the power spectral density (PSD) as suitable features to identify age-associated changes in the surface electromyogram (sEMG). Eighteen younger (20–30 years) and 18 older (60–85 years) cohorts completed two trials of isometric dorsiflexion at four different force levels between 10% and 50% of the maximal voluntary contraction. Gaussianity and maximal power of the PSD of sEMG were determined. Results show a significant increase in sEMG's maximal power of the PSD and Gaussianity with increase in force for both cohorts. It was also observed that older cohorts had higher maximal power of the PSD and lower Gaussianity. These age-related differences observed in the PSD and Gaussianity could be due to motor unit remodelling. This can be useful for noninvasive tracking of age-associated neuromuscular changes. PMID:27610379

A Gaussian Model-Based Probabilistic Approach for Pulse Transit Time Estimation.

PubMed

Jang, Dae-Geun; Park, Seung-Hun; Hahn, Minsoo

2016-01-01

In this paper, we propose a new probabilistic approach to pulse transit time (PTT) estimation using a Gaussian distribution model. It is motivated basically by the hypothesis that PTTs normalized by RR intervals follow the Gaussian distribution. To verify the hypothesis, we demonstrate the effects of arterial compliance on the normalized PTTs using the Moens-Korteweg equation. Furthermore, we observe a Gaussian distribution of the normalized PTTs on real data. In order to estimate the PTT using the hypothesis, we first assumed that R-waves in the electrocardiogram (ECG) can be correctly identified. The R-waves limit searching ranges to detect pulse peaks in the photoplethysmogram (PPG) and to synchronize the results with cardiac beats--i.e., the peaks of the PPG are extracted within the corresponding RR interval of the ECG as pulse peak candidates. Their probabilities of being the actual pulse peak are then calculated using a Gaussian probability function. The parameters of the Gaussian function are automatically updated when a new pulse peak is identified. This update makes the probability function adaptive to variations of cardiac cycles. Finally, the pulse peak is identified as the candidate with the highest probability. The proposed approach is tested on a database where ECG and PPG waveforms are collected simultaneously during the submaximal bicycle ergometer exercise test. The results are promising, suggesting that the method provides a simple but more accurate PTT estimation in real applications.

Equivalent peak resolution: characterization of the extent of separation for two components based on their relative peak overlap.

PubMed

Dvořák, Martin; Svobodová, Jana; Dubský, Pavel; Riesová, Martina; Vigh, Gyula; Gaš, Bohuslav

2015-03-01

Although the classical formula of peak resolution was derived to characterize the extent of separation only for Gaussian peaks of equal areas, it is often used even when the peaks follow non-Gaussian distributions and/or have unequal areas. This practice can result in misleading information about the extent of separation in terms of the severity of peak overlap. We propose here the use of the equivalent peak resolution value, a term based on relative peak overlap, to characterize the extent of separation that had been achieved. The definition of equivalent peak resolution is not constrained either by the form(s) of the concentration distribution function(s) of the peaks (Gaussian or non-Gaussian) or the relative area of the peaks. The equivalent peak resolution value and the classically defined peak resolution value are numerically identical when the separated peaks are Gaussian and have identical areas and SDs. Using our new freeware program, Resolution Analyzer, one can calculate both the classically defined and the equivalent peak resolution values. With the help of this tool, we demonstrate here that the classical peak resolution values mischaracterize the extent of peak overlap even when the peaks are Gaussian but have different areas. We show that under ideal conditions of the separation process, the relative peak overlap value is easily accessible by fitting the overall peak profile as the sum of two Gaussian functions. The applicability of the new approach is demonstrated on real separations. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Gaussian Boson Sampling.

PubMed

Hamilton, Craig S; Kruse, Regina; Sansoni, Linda; Barkhofen, Sonja; Silberhorn, Christine; Jex, Igor

2017-10-27

Boson sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require universal control over the quantum system, which favors current photonic experimental platforms. Here, we introduce Gaussian Boson sampling, a classically hard-to-solve problem that uses squeezed states as a nonclassical resource. We relate the probability to measure specific photon patterns from a general Gaussian state in the Fock basis to a matrix function called the Hafnian, which answers the last remaining question of sampling from Gaussian states. Based on this result, we design Gaussian Boson sampling, a #P hard problem, using squeezed states. This demonstrates that Boson sampling from Gaussian states is possible, with significant advantages in the photon generation probability, compared to existing protocols.

Carcass Functions in Variational Calculations for Few-Body Systems

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

Donchev, A.G.; Kalachev, S.A.; Kolesnikov, N.N.

For variational calculations of molecular and nuclear systems involving a few particles, it is proposed to use carcass basis functions that generalize exponential and Gaussian trial functions. It is shown that the matrix elements of the Hamiltonian are expressed in a closed form for a Coulomb potential, as well as for other popular particle-interaction potentials. The use of such carcass functions in two-center Coulomb problems reduces, in relation to other methods, the number of terms in a variational expansion by a few orders of magnitude at a commensurate or even higher accuracy. The efficiency of the method is illustrated bymore » calculations of the three-particle Coulomb systems {mu}{mu}e, ppe, dde, and tte and the four-particle molecular systems H{sub 2} and HeH{sup +} of various isotopic composition. By considering the example of the {sub {lambda}}{sup 9}Be hypernucleus, it is shown that the proposed method can be used in calculating nuclear systems as well.« less

Some Modified Integrated Squared Error Procedures for Multivariate Normal Data.

DTIC Science & Technology

1982-06-01

p-dimensional Gaussian. There are a number of measures of qualitative robustness but the most important is the influence function . Most of the other...measures are derived from the influence function . The influence function is simply proportional to the score function (Huber, 1981, p. 45 ). The... influence function at the p-variate Gaussian distribution Np (UV) is as -1P IC(x; ,N) = IE&) ;-") sD=XV = (I+c) (p+2)(x-p) exp(- ! (x-p) TV-.1-)) (3.6

A Systematic Approach for Understanding Slater-Gaussian Functions in Computational Chemistry

ERIC Educational Resources Information Center

Stewart, Brianna; Hylton, Derrick J.; Ravi, Natarajan

2013-01-01

A systematic way to understand the intricacies of quantum mechanical computations done by a software package known as "Gaussian" is undertaken via an undergraduate research project. These computations involve the evaluation of key parameters in a fitting procedure to express a Slater-type orbital (STO) function in terms of the linear…

Leading non-Gaussian corrections for diffusion orientation distribution function.

PubMed

Jensen, Jens H; Helpern, Joseph A; Tabesh, Ali

2014-02-01

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed from the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves on the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. 2013 John Wiley & Sons, Ltd.

Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function

PubMed Central

Jensen, Jens H.; Helpern, Joseph A.; Tabesh, Ali

2014-01-01

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed out of the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves upon the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common. PMID:24738143

Elegant Gaussian beams for enhanced optical manipulation

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

Alpmann, Christina, E-mail: c.alpmann@uni-muenster.de; Schöler, Christoph; Denz, Cornelia

2015-06-15

Generation of micro- and nanostructured complex light beams attains increasing impact in photonics and laser applications. In this contribution, we demonstrate the implementation and experimental realization of the relatively unknown, but highly versatile class of complex-valued Elegant Hermite- and Laguerre-Gaussian beams. These beams create higher trapping forces compared to standard Gaussian light fields due to their propagation changing properties. We demonstrate optical trapping and alignment of complex functional particles as nanocontainers with standard and Elegant Gaussian light beams. Elegant Gaussian beams will inspire manifold applications in optical manipulation, direct laser writing, or microscopy, where the design of the point-spread functionmore » is relevant.« less

Correlation functions from a unified variational principle: Trial Lie groups

NASA Astrophysics Data System (ADS)

Balian, R.; Vénéroni, M.

2015-11-01

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie-Poisson structure. At second order, the variational expression for two-time correlation functions separates-as does its exact counterpart-the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.

Using an iterative eigensolver to compute vibrational energies with phase-spaced localized basis functions.

PubMed

Brown, James; Carrington, Tucker

2015-07-28

Although phase-space localized Gaussians are themselves poor basis functions, they can be used to effectively contract a discrete variable representation basis [A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett. 109, 070402 (2012)]. This works despite the fact that elements of the Hamiltonian and overlap matrices labelled by discarded Gaussians are not small. By formulating the matrix problem as a regular (i.e., not a generalized) matrix eigenvalue problem, we show that it is possible to use an iterative eigensolver to compute vibrational energy levels in the Gaussian basis.

Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions.

PubMed

Yura, Harold T; Hanson, Steen G

2012-04-01

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative examples with relevance for optics are given.

Multi-pose facial correction based on Gaussian process with combined kernel function

NASA Astrophysics Data System (ADS)

Shi, Shuyan; Ji, Ruirui; Zhang, Fan

2018-04-01

In order to improve the recognition rate of various postures, this paper proposes a method of facial correction based on Gaussian Process which build a nonlinear regression model between the front and the side face with combined kernel function. The face images with horizontal angle from -45° to +45° can be properly corrected to front faces. Finally, Support Vector Machine is employed for face recognition. Experiments on CAS PEAL R1 face database show that Gaussian process can weaken the influence of pose changes and improve the accuracy of face recognition to certain extent.

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.

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.

The optimal on-source region size for detections with counting-type telescopes

NASA Astrophysics Data System (ADS)

Klepser, S.

2017-03-01

Source detection in counting type experiments such as Cherenkov telescopes often involves the application of the classical Eq. (17) from the paper of Li & Ma (1983) to discrete on- and off-source regions. The on-source region is typically a circular area with radius θ in which the signal is expected to appear with the shape of the instrument point spread function (PSF). This paper addresses the question of what is the θ that maximises the probability of detection for a given PSF width and background event density. In the high count number limit and assuming a Gaussian PSF profile, the optimum is found to be at ζ∞2 ≈ 2.51 times the squared PSF width σPSF392. While this number is shown to be a good choice in many cases, a dynamic formula for cases of lower count numbers, which favour larger on-source regions, is given. The recipe to get to this parametrisation can also be applied to cases with a non-Gaussian PSF. This result can standardise and simplify analysis procedures, reduce trials and eliminate the need for experience-based ad hoc cut definitions or expensive case-by-case Monte Carlo simulations.

Tables Of Gaussian-Type Orbital Basis Functions

NASA Technical Reports Server (NTRS)

Partridge, Harry

1992-01-01

NASA technical memorandum contains tables of estimated Hartree-Fock wave functions for atoms lithium through neon and potassium through krypton. Sets contain optimized Gaussian-type orbital exponents and coefficients, and near Hartree-Fock quality. Orbital exponents optimized by minimizing restricted Hartree-Fock energy via scaled Newton-Raphson scheme in which Hessian evaluated numerically by use of analytically determined gradients.

Complete stability of delayed recurrent neural networks with Gaussian activation functions.

PubMed

Liu, Peng; Zeng, Zhigang; Wang, Jun

2017-01-01

This paper addresses the complete stability of delayed recurrent neural networks with Gaussian activation functions. By means of the geometrical properties of Gaussian function and algebraic properties of nonsingular M-matrix, some sufficient conditions are obtained to ensure that for an n-neuron neural network, there are exactly 3 k equilibrium points with 0≤k≤n, among which 2 k and 3 k -2 k equilibrium points are locally exponentially stable and unstable, respectively. Moreover, it concludes that all the states converge to one of the equilibrium points; i.e., the neural networks are completely stable. The derived conditions herein can be easily tested. Finally, a numerical example is given to illustrate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Operational quantification of continuous-variable correlations.

PubMed

Rodó, Carles; Adesso, Gerardo; Sanpera, Anna

2008-03-21

We quantify correlations (quantum and/or classical) between two continuous-variable modes as the maximal number of correlated bits extracted via local quadrature measurements. On Gaussian states, such "bit quadrature correlations" majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, photon-subtracted states, and mixtures of Gaussian states, the bit correlations are shown to be a monotonic function of the negativity. This quantification yields a feasible, operational way to measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a complete state tomography.

Gaussian Mixture Model of Heart Rate Variability

PubMed Central

Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

2012-01-01

Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters. PMID:22666386

Capacity and precision in an animal model of visual short-term memory.

PubMed

Lara, Antonio H; Wallis, Jonathan D

2012-03-14

Temporary storage of information in visual short-term memory (VSTM) is a key component of many complex cognitive abilities. However, it is highly limited in capacity. Understanding the neurophysiological nature of this capacity limit will require a valid animal model of VSTM. We used a multiple-item color change detection task to measure macaque monkeys' VSTM capacity. Subjects' performance deteriorated and reaction times increased as a function of the number of items in memory. Additionally, we measured the precision of the memory representations by varying the distance between sample and test colors. In trials with similar sample and test colors, subjects made more errors compared to trials with highly discriminable colors. We modeled the error distribution as a Gaussian function and used this to estimate the precision of VSTM representations. We found that as the number of items in memory increases the precision of the representations decreases dramatically. Additionally, we found that focusing attention on one of the objects increases the precision with which that object is stored and degrades the precision of the remaining. These results are in line with recent findings in human psychophysics and provide a solid foundation for understanding the neurophysiological nature of the capacity limit of VSTM.

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.

Flexible link functions in nonparametric binary regression with Gaussian process priors.

PubMed

Li, Dan; Wang, Xia; Lin, Lizhen; Dey, Dipak K

2016-09-01

In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function. © 2015, The International Biometric Society.

Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors

PubMed Central

Li, Dan; Lin, Lizhen; Dey, Dipak K.

2015-01-01

Summary In many scientific fields, it is a common practice to collect a sequence of 0-1 binary responses from a subject across time, space, or a collection of covariates. Researchers are interested in finding out how the expected binary outcome is related to covariates, and aim at better prediction in the future 0-1 outcomes. Gaussian processes have been widely used to model nonlinear systems; in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes. A critical issue in modeling binary response data is the appropriate choice of link functions. Commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness. To address this limitation, we propose a flexible binary regression model which combines a generalized extreme value link function with a Gaussian process prior on the latent structure. Bayesian computation is employed in model estimation. Posterior consistency of the resulting posterior distribution is demonstrated. The flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples. Empirical results show that the proposed model outperforms a set of alternative models, which only have either a Gaussian process prior on the latent regression function or a Dirichlet prior on the link function. PMID:26686333

Fitted Hanbury-Brown Twiss radii versus space-time variances in flow-dominated models

NASA Astrophysics Data System (ADS)

Frodermann, Evan; Heinz, Ulrich; Lisa, Michael Annan

2006-04-01

The inability of otherwise successful dynamical models to reproduce the Hanbury-Brown Twiss (HBT) radii extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the RHIC HBT Puzzle. Most comparisons between models and experiment exploit the fact that for Gaussian sources the HBT radii agree with certain combinations of the space-time widths of the source that can be directly computed from the emission function without having to evaluate, at significant expense, the two-particle correlation function. We here study the validity of this approach for realistic emission function models, some of which exhibit significant deviations from simple Gaussian behavior. By Fourier transforming the emission function, we compute the two-particle correlation function, and fit it with a Gaussian to partially mimic the procedure used for measured correlation functions. We describe a novel algorithm to perform this Gaussian fit analytically. We find that for realistic hydrodynamic models the HBT radii extracted from this procedure agree better with the data than the values previously extracted from the space-time widths of the emission function. Although serious discrepancies between the calculated and the measured HBT radii remain, we show that a more apples-to-apples comparison of models with data can play an important role in any eventually successful theoretical description of RHIC HBT data.

Fitted Hanbury-Brown-Twiss radii versus space-time variances in flow-dominated models

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

Frodermann, Evan; Heinz, Ulrich; Lisa, Michael Annan

2006-04-15

The inability of otherwise successful dynamical models to reproduce the Hanbury-Brown-Twiss (HBT) radii extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the RHIC HBT Puzzle. Most comparisons between models and experiment exploit the fact that for Gaussian sources the HBT radii agree with certain combinations of the space-time widths of the source that can be directly computed from the emission function without having to evaluate, at significant expense, the two-particle correlation function. We here study the validity of this approach for realistic emission function models, some of which exhibit significant deviations from simplemore » Gaussian behavior. By Fourier transforming the emission function, we compute the two-particle correlation function, and fit it with a Gaussian to partially mimic the procedure used for measured correlation functions. We describe a novel algorithm to perform this Gaussian fit analytically. We find that for realistic hydrodynamic models the HBT radii extracted from this procedure agree better with the data than the values previously extracted from the space-time widths of the emission function. Although serious discrepancies between the calculated and the measured HBT radii remain, we show that a more apples-to-apples comparison of models with data can play an important role in any eventually successful theoretical description of RHIC HBT data.« less

Gaussian-Beam Laser-Resonator Program

NASA Technical Reports Server (NTRS)

Cross, Patricia L.; Bair, Clayton H.; Barnes, Norman

1989-01-01

Gaussian Beam Laser Resonator Program models laser resonators by use of Gaussian-beam-propagation techniques. Used to determine radii of beams as functions of position in laser resonators. Algorithm used in program has three major components. First, ray-transfer matrix for laser resonator must be calculated. Next, initial parameters of beam calculated. Finally, propagation of beam through optical elements computed. Written in Microsoft FORTRAN (Version 4.01).

Exact evaluations of some Meijer G-functions and probability of all eigenvalues real for the product of two Gaussian matrices

NASA Astrophysics Data System (ADS)

Kumar, Santosh

2015-11-01

We provide a proof to a recent conjecture by Forrester (2014 J. Phys. A: Math. Theor. 47 065202) regarding the algebraic and arithmetic structure of Meijer G-functions which appear in the expression for probability of all eigenvalues real for the product of two real Gaussian matrices. In the process we come across several interesting identities involving Meijer G-functions.

Precise Determination of the Absorption Maximum in Wide Bands

ERIC Educational Resources Information Center

Eriksson, Karl-Hugo; And Others

1977-01-01

A precise method of determining absorption maxima where Gaussian functions occur is described. The method is based on a logarithmic transformation of the Gaussian equation and is suited for a mini-computer. (MR)

On the numbers of images of two stochastic gravitational lensing models

NASA Astrophysics Data System (ADS)

Wei, Ang

2017-02-01

We study two gravitational lensing models with Gaussian randomness: the continuous mass fluctuation model and the floating black hole model. The lens equations of these models are related to certain random harmonic functions. Using Rice's formula and Gaussian techniques, we obtain the expected numbers of zeros of these functions, which indicate the amounts of images in the corresponding lens systems.

What are the Shapes of Response Time Distributions in Visual Search?

PubMed Central

Palmer, Evan M.; Horowitz, Todd S.; Torralba, Antonio; Wolfe, Jeremy M.

2011-01-01

Many visual search experiments measure reaction time (RT) as their primary dependent variable. Analyses typically focus on mean (or median) RT. However, given enough data, the RT distribution can be a rich source of information. For this paper, we collected about 500 trials per cell per observer for both target-present and target-absent displays in each of three classic search tasks: feature search, with the target defined by color; conjunction search, with the target defined by both color and orientation; and spatial configuration search for a 2 among distractor 5s. This large data set allows us to characterize the RT distributions in detail. We present the raw RT distributions and fit several psychologically motivated functions (ex-Gaussian, ex-Wald, Gamma, and Weibull) to the data. We analyze and interpret parameter trends from these four functions within the context of theories of visual search. PMID:21090905

Model-free estimation of the psychometric function

PubMed Central

Żychaluk, Kamila; Foster, David H.

2009-01-01

A subject's response to the strength of a stimulus is described by the psychometric function, from which summary measures, such as a threshold or slope, may be derived. Traditionally, this function is estimated by fitting a parametric model to the experimental data, usually the proportion of successful trials at each stimulus level. Common models include the Gaussian and Weibull cumulative distribution functions. This approach works well if the model is correct, but it can mislead if not. In practice, the correct model is rarely known. Here, a nonparametric approach based on local linear fitting is advocated. No assumption is made about the true model underlying the data, except that the function is smooth. The critical role of the bandwidth is identified, and its optimum value estimated by a cross-validation procedure. As a demonstration, seven vision and hearing data sets were fitted by the local linear method and by several parametric models. The local linear method frequently performed better and never worse than the parametric ones. Supplemental materials for this article can be downloaded from app.psychonomic-journals.org/content/supplemental. PMID:19633355

Synthesis and analysis of discriminators under influence of broadband non-Gaussian noise

NASA Astrophysics Data System (ADS)

Artyushenko, V. M.; Volovach, V. I.

2018-01-01

We considered the problems of the synthesis and analysis of discriminators, when the useful signal is exposed to non-Gaussian additive broadband noise. It is shown that in this case, the discriminator of the tracking meter should contain the nonlinear transformation unit, the characteristics of which are determined by the Fisher information relative to the probability density function of the mixture of non-Gaussian broadband noise and mismatch errors. The parameters of the discriminatory and phase characteristics of the discriminators working under the above conditions are obtained. It is shown that the efficiency of non-linear processing depends on the ratio of power of FM noise to the power of Gaussian noise. The analysis of the information loss of signal transformation caused by the linear section of discriminatory characteristics of the unit of nonlinear transformations of the discriminator is carried out. It is shown that the average slope of the nonlinear transformation characteristic is determined by the Fisher information relative to the probability density function of the mixture of non-Gaussian noise and mismatch errors.

Multi-task Gaussian process for imputing missing data in multi-trait and multi-environment trials.

PubMed

Hori, Tomoaki; Montcho, David; Agbangla, Clement; Ebana, Kaworu; Futakuchi, Koichi; Iwata, Hiroyoshi

2016-11-01

A method based on a multi-task Gaussian process using self-measuring similarity gave increased accuracy for imputing missing phenotypic data in multi-trait and multi-environment trials. Multi-environmental trial (MET) data often encounter the problem of missing data. Accurate imputation of missing data makes subsequent analysis more effective and the results easier to understand. Moreover, accurate imputation may help to reduce the cost of phenotyping for thinned-out lines tested in METs. METs are generally performed for multiple traits that are correlated to each other. Correlation among traits can be useful information for imputation, but single-trait-based methods cannot utilize information shared by traits that are correlated. In this paper, we propose imputation methods based on a multi-task Gaussian process (MTGP) using self-measuring similarity kernels reflecting relationships among traits, genotypes, and environments. This framework allows us to use genetic correlation among multi-trait multi-environment data and also to combine MET data and marker genotype data. We compared the accuracy of three MTGP methods and iterative regularized PCA using rice MET data. Two scenarios for the generation of missing data at various missing rates were considered. The MTGP performed a better imputation accuracy than regularized PCA, especially at high missing rates. Under the 'uniform' scenario, in which missing data arise randomly, inclusion of marker genotype data in the imputation increased the imputation accuracy at high missing rates. Under the 'fiber' scenario, in which missing data arise in all traits for some combinations between genotypes and environments, the inclusion of marker genotype data decreased the imputation accuracy for most traits while increasing the accuracy in a few traits remarkably. The proposed methods will be useful for solving the missing data problem in MET data.

Weighted Feature Gaussian Kernel SVM for Emotion Recognition

PubMed Central

Jia, Qingxuan

2016-01-01

Emotion recognition with weighted feature based on facial expression is a challenging research topic and has attracted great attention in the past few years. This paper presents a novel method, utilizing subregion recognition rate to weight kernel function. First, we divide the facial expression image into some uniform subregions and calculate corresponding recognition rate and weight. Then, we get a weighted feature Gaussian kernel function and construct a classifier based on Support Vector Machine (SVM). At last, the experimental results suggest that the approach based on weighted feature Gaussian kernel function has good performance on the correct rate in emotion recognition. The experiments on the extended Cohn-Kanade (CK+) dataset show that our method has achieved encouraging recognition results compared to the state-of-the-art methods. PMID:27807443

On Nonlinear Functionals of Random Spherical Eigenfunctions

NASA Astrophysics Data System (ADS)

Marinucci, Domenico; Wigman, Igor

2014-05-01

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

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.

Video Shot Boundary Detection Using QR-Decomposition and Gaussian Transition Detection

NASA Astrophysics Data System (ADS)

Amiri, Ali; Fathy, Mahmood

2010-12-01

This article explores the problem of video shot boundary detection and examines a novel shot boundary detection algorithm by using QR-decomposition and modeling of gradual transitions by Gaussian functions. Specifically, the authors attend to the challenges of detecting gradual shots and extracting appropriate spatiotemporal features that affect the ability of algorithms to efficiently detect shot boundaries. The algorithm utilizes the properties of QR-decomposition and extracts a block-wise probability function that illustrates the probability of video frames to be in shot transitions. The probability function has abrupt changes in hard cut transitions, and semi-Gaussian behavior in gradual transitions. The algorithm detects these transitions by analyzing the probability function. Finally, we will report the results of the experiments using large-scale test sets provided by the TRECVID 2006, which has assessments for hard cut and gradual shot boundary detection. These results confirm the high performance of the proposed algorithm.

Variational method for calculating the binding energy of the base state of an impurity D- centered on a quantum dot of GaAs-Ga1-xAlxAs

NASA Astrophysics Data System (ADS)

Durán-Flórez, F.; Caicedo, L. C.; Gonzalez, J. E.

2018-04-01

In quantum mechanics it is very difficult to obtain exact solutions, therefore, it is necessary to resort to tools and methods that facilitate the calculations of the solutions of these systems, one of these methods is the variational method that consists in proposing a wave function that depend on several parameters that are adjusted to get close to the exact solution. Authors in the past have performed calculations applying this method using exponential and Gaussian orbital functions with linear and quadratic correlation factors. In this paper, a Gaussian function with a linear correlation factor is proposed, for the calculation of the binding energy of an impurity D ‑ centered on a quantum dot of radius r, the Gaussian function is dependent on the radius of the quantum dot.

Non-Gaussian probabilistic MEG source localisation based on kernel density estimation☆

PubMed Central

Mohseni, Hamid R.; Kringelbach, Morten L.; Woolrich, Mark W.; Baker, Adam; Aziz, Tipu Z.; Probert-Smith, Penny

2014-01-01

There is strong evidence to suggest that data recorded from magnetoencephalography (MEG) follows a non-Gaussian distribution. However, existing standard methods for source localisation model the data using only second order statistics, and therefore use the inherent assumption of a Gaussian distribution. In this paper, we present a new general method for non-Gaussian source estimation of stationary signals for localising brain activity from MEG data. By providing a Bayesian formulation for MEG source localisation, we show that the source probability density function (pdf), which is not necessarily Gaussian, can be estimated using multivariate kernel density estimators. In the case of Gaussian data, the solution of the method is equivalent to that of widely used linearly constrained minimum variance (LCMV) beamformer. The method is also extended to handle data with highly correlated sources using the marginal distribution of the estimated joint distribution, which, in the case of Gaussian measurements, corresponds to the null-beamformer. The proposed non-Gaussian source localisation approach is shown to give better spatial estimates than the LCMV beamformer, both in simulations incorporating non-Gaussian signals, and in real MEG measurements of auditory and visual evoked responses, where the highly correlated sources are known to be difficult to estimate. PMID:24055702

Normal form decomposition for Gaussian-to-Gaussian superoperators

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

De Palma, Giacomo; INFN, Pisa; Mari, Andrea

2015-05-15

In this paper, we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non-positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms ofmore » their action on the characteristic function of the inputs. For the special case of one-mode mappings, we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.« less

Axial acoustic radiation force on a sphere in Gaussian field

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

Wu, Rongrong; Liu, Xiaozhou, E-mail: xzliu@nju.edu.cn; Gong, Xiufen

2015-10-28

Based on the finite series method, the acoustical radiation force resulting from a Gaussian beam incident on a spherical object is investigated analytically. When the position of the particles deviating from the center of the beam, the Gaussian beam is expanded as a spherical function at the center of the particles and the expanded coefficients of the Gaussian beam is calculated. The analytical expression of the acoustic radiation force on spherical particles deviating from the Gaussian beam center is deduced. The acoustic radiation force affected by the acoustic frequency and the offset distance from the Gaussian beam center is investigated.more » Results have been presented for Gaussian beams with different wavelengths and it has been shown that the interaction of a Gaussian beam with a sphere can result in attractive axial force under specific operational conditions. Results indicate the capability of manipulating and separating spherical spheres based on their mechanical and acoustical properties, the results provided here may provide a theoretical basis for development of single-beam acoustical tweezers.« less

Beam wander characteristics of flat-topped, dark hollow, cos and cosh-Gaussian, J0- and I0- Bessel Gaussian beams propagating in turbulent atmosphere: a review

NASA Astrophysics Data System (ADS)

Eyyuboğlu, Halil T.; Baykal, Yahya; Çil, Celal Z.; Korotkova, Olga; Cai, Yangjian

2010-02-01

In this paper we review our work done in the evaluations of the root mean square (rms) beam wander characteristics of the flat-topped, dark hollow, cos-and cosh Gaussian, J0-Bessel Gaussian and the I0-Bessel Gaussian beams in atmospheric turbulence. Our formulation is based on the wave-treatment approach, where not only the beam sizes but the source beam profiles are taken into account as well. In this approach the first and the second statistical moments are obtained from the Rytov series under weak atmospheric turbulence conditions and the beam size are determined as a function of the propagation distance. It is found that after propagating in atmospheric turbulence, under certain conditions, the collimated flat-topped, dark hollow, cos- and cosh Gaussian, J0-Bessel Gaussian and the I0-Bessel Gaussian beams have smaller rms beam wander compared to that of the Gaussian beam. The beam wander of these beams are analyzed against the propagation distance, source spot sizes, and against specific beam parameters related to the individual beam such as the relative amplitude factors of the constituent beams, the flatness parameters, the beam orders, the displacement parameters, the width parameters, and are compared against the corresponding Gaussian beam.

Mean intensity of the fundamental Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

In the given article mean intensity of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is studied. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian beam of optical radiation. Distributions of mean intensity of a fundamental Bessel- Gaussian beam optical beam in longitudinal and transverse to a direction of propagation of optical radiation are investigated in detail. Influence of atmospheric turbulence on change of radius of the central part of a Bessel optical beam is estimated. Values of parameters at which it is possible to generate in turbulent atmosphere a nondiffracting pseudo-Bessel optical beam by means of a fundamental Bessel-Gaussian optical beam are established.

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.

Poly-Gaussian model of randomly rough surface in rarefied gas flow

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

Aksenova, Olga A.; Khalidov, Iskander A.

2014-12-09

Surface roughness is simulated by the model of non-Gaussian random process. Our results for the scattering of rarefied gas atoms from a rough surface using modified approach to the DSMC calculation of rarefied gas flow near a rough surface are developed and generalized applying the poly-Gaussian model representing probability density as the mixture of Gaussian densities. The transformation of the scattering function due to the roughness is characterized by the roughness operator. Simulating rough surface of the walls by the poly-Gaussian random field expressed as integrated Wiener process, we derive a representation of the roughness operator that can be appliedmore » in numerical DSMC methods as well as in analytical investigations.« less

Tests for Gaussianity of the MAXIMA-1 cosmic microwave background map.

PubMed

Wu, J H; Balbi, A; Borrill, J; Ferreira, P G; Hanany, S; Jaffe, A H; Lee, A T; Rabii, B; Richards, P L; Smoot, G F; Stompor, R; Winant, C D

2001-12-17

Gaussianity of the cosmological perturbations is one of the key predictions of standard inflation, but it is violated by other models of structure formation such as cosmic defects. We present the first test of the Gaussianity of the cosmic microwave background (CMB) on subdegree angular scales, where deviations from Gaussianity are most likely to occur. We apply the methods of moments, cumulants, the Kolmogorov test, the chi(2) test, and Minkowski functionals in eigen, real, Wiener-filtered, and signal-whitened spaces, to the MAXIMA-1 CMB anisotropy data. We find that the data, which probe angular scales between 10 arcmin and 5 deg, are consistent with Gaussianity. These results show consistency with the standard inflation and place constraints on the existence of cosmic defects.

Matrix elements of explicitly correlated Gaussian basis functions with arbitrary angular momentum

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

Joyce, Tennesse; Varga, Kálmán

2016-05-14

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with arbitrary angular momentum is presented. The calculations are checked on several excited states of three and four electron systems. The presented formalism can be used as unified framework for high accuracy calculations of properties of small atoms and molecules.

Effects of scale-dependent non-Gaussianity on cosmological structures

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

LoVerde, Marilena; Miller, Amber; Shandera, Sarah

2008-04-15

The detection of primordial non-Gaussianity could provide a powerful means to test various inflationary scenarios. Although scale-invariant non-Gaussianity (often described by the f{sub NL} formalism) is currently best constrained by the CMB, single-field models with changing sound speed can have strongly scale-dependent non-Gaussianity. Such models could evade the CMB constraints but still have important effects at scales responsible for the formation of cosmological objects such as clusters and galaxies. We compute the effect of scale-dependent primordial non-Gaussianity on cluster number counts as a function of redshift, using a simple ansatz to model scale-dependent features. We forecast constraints on these modelsmore » achievable with forthcoming datasets. We also examine consequences for the galaxy bispectrum. Our results are relevant for the Dirac-Born-Infeld model of brane inflation, where the scale dependence of the non-Gaussianity is directly related to the geometry of the extra dimensions.« less

Bivariate- distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems.

PubMed

Kota, V K B; Chavda, N D; Sahu, R

2006-04-01

Interacting many-particle systems with a mean-field one-body part plus a chaos generating random two-body interaction having strength lambda exhibit Poisson to Gaussian orthogonal ensemble and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and strength functions with transition points marked by lambda = lambda c and lambda = lambda F, respectively; lambda F > lambda c. For these systems a theory for the matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with lambda > lambda F, in terms of orbital occupation numbers, level densities, and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using a bivariate-t distribution, the theory extends below from the Gaussian regime to the BW regime up to lambda = lambda c. This is well tested in numerical calculations for 6 spinless fermions in 12 single-particle states.

Anomalous and non-Gaussian diffusion in Hertzian spheres

NASA Astrophysics Data System (ADS)

Ouyang, Wenze; Sun, Bin; Sun, Zhiwei; Xu, Shenghua

2018-09-01

By means of molecular dynamics simulations, we study the non-Gaussian diffusion in the fluid of Hertzian spheres. The time dependent non-Gaussian parameter, as an indicator of the dynamic heterogeneity, is increased with the increasing of temperature. When the temperature is high enough, the dynamic heterogeneity becomes very significant, and it seems counterintuitive that the maximum of non-Gaussian parameter and the position of its peak decrease monotonically with the increasing of density. By fitting the curves of self intermediate scattering function, we find that the character relaxation time τα is surprisingly not coupled with the time τmax where the non-Gaussian parameter reaches to a maximum. The intriguing features of non-Gaussian diffusion at high enough temperatures can be associated with the weakly correlated mean-field behavior of Hertzian spheres. Especially the time τmax is nearly inversely proportional to the density at extremely high temperatures.

Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.

Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

In this paper the theoretical research of coherent properties of the vortex Bessel-Gaussian optical beams propagating in turbulent atmosphere are developed. The approach to the analysis of this problem is based on the analytical solution of the equation for the transverse second-order mutual coherence function of a field of optical radiation. The behavior of integral scale of coherence degree of vortex Bessel-Gaussian optical beams depending on parameters of an optical beam and characteristics of turbulent atmosphere is particularly considered. It is shown that the integral scale of coherence degree of a vortex Bessel-Gaussian optical beam essentially depends on value of a topological charge of a vortex optical beam. With increase in a topological charge of a vortex Bessel-Gaussian optical beam the value of integral scale of coherence degree of a vortex Bessel-Gaussian optical beam are decreased.

Investigating Einstein-Podolsky-Rosen steering of continuous-variable bipartite states by non-Gaussian pseudospin measurements

NASA Astrophysics Data System (ADS)

Xiang, Yu; Xu, Buqing; Mišta, Ladislav; Tufarelli, Tommaso; He, Qiongyi; Adesso, Gerardo

2017-10-01

Einstein-Podolsky-Rosen (EPR) steering is an asymmetric form of correlations which is intermediate between quantum entanglement and Bell nonlocality, and can be exploited as a resource for quantum communication with one untrusted party. In particular, steering of continuous-variable Gaussian states has been extensively studied theoretically and experimentally, as a fundamental manifestation of the EPR paradox. While most of these studies focused on quadrature measurements for steering detection, two recent works revealed that there exist Gaussian states which are only steerable by suitable non-Gaussian measurements. In this paper we perform a systematic investigation of EPR steering of bipartite Gaussian states by pseudospin measurements, complementing and extending previous findings. We first derive the density-matrix elements of two-mode squeezed thermal Gaussian states in the Fock basis, which may be of independent interest. We then use such a representation to investigate steering of these states as detected by a simple nonlinear criterion, based on second moments of the correlation matrix constructed from pseudospin operators. This analysis reveals previously unexplored regimes where non-Gaussian measurements are shown to be more effective than Gaussian ones to witness steering of Gaussian states in the presence of local noise. We further consider an alternative set of pseudospin observables, whose expectation value can be expressed more compactly in terms of Wigner functions for all two-mode Gaussian states. However, according to the adopted criterion, these observables are found to be always less sensitive than conventional Gaussian observables for steering detection. Finally, we investigate continuous-variable Werner states, which are non-Gaussian mixtures of Gaussian states, and find that pseudospin measurements are always more effective than Gaussian ones to reveal their steerability. Our results provide useful insights on the role of non-Gaussian measurements in characterizing quantum correlations of Gaussian and non-Gaussian states of continuous-variable quantum systems.

Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian.

PubMed

Ginzburg, D; Mann, A

2014-03-10

A Lie algebraic method for propagation of the Wigner quasi-distribution function (QDF) under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of QDFs, which we call the "Gaussian class." This class contains as special cases the well-known Wigner, Husimi, Glauber, and Kirkwood-Rihaczek QDFs. We present some examples of the calculation of the time evolution of those functions.

Laser plasma x-ray line spectra fitted using the Pearson VII function

NASA Astrophysics Data System (ADS)

Michette, A. G.; Pfauntsch, S. J.

2000-05-01

The Pearson VII function, which is more general than the Gaussian, Lorentzian and other profiles, is used to fit the x-ray spectral lines produced in a laser-generated plasma, instead of the more usual, but computationally expensive, Voigt function. The mean full-width half-maximum of the fitted lines is 0.102+/-0.014 nm, entirely consistent with the value expected from geometrical considerations, and the fitted line profiles are generally inconsistent with being either Lorentzian or Gaussian.

Linear Scaling Density Functional Calculations with Gaussian Orbitals

NASA Technical Reports Server (NTRS)

Scuseria, Gustavo E.

1999-01-01

Recent advances in linear scaling algorithms that circumvent the computational bottlenecks of large-scale electronic structure simulations make it possible to carry out density functional calculations with Gaussian orbitals on molecules containing more than 1000 atoms and 15000 basis functions using current workstations and personal computers. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.

Lower bounds to energies for cusped-gaussian wavefunctions. [hydrogen atom ground state

NASA Technical Reports Server (NTRS)

Eaves, J. O.; Walsh, B. C.; Steiner, E.

1974-01-01

Calculations for the ground states of H, He, and Be, conducted by Steiner and Sykes (1972), show that the inclusion of a very small number of cusp functions can lead to a substantial enhancement of the quality of the Gaussian basis used in molecular wavefunction computations. The properties of the cusped-Gaussian basis are investigated by a calculation of lower bounds concerning the ground state energy of the hydrogen atom.

Study protocol: effect of playful training on functional abilities of older adults - a randomized controlled trial.

PubMed

Jessen, Jari Due; Lund, Henrik Hautop

2017-01-19

Loss of functional capabilities due to inactivity is one of the most common reasons for fall accidents, and it has been well established that loss of capabilities can be effectively reduced by physical activity. Pilot studies indicate a possible improvement in functional abilities of community dwelling elderly as a result of short-term playing with an exergame system in the form of interactive modular tiles. Such playful training may be motivational to perform and viewed by the subjects to offer life-fulfilling quality, while providing improvement in physical abilities, e.g. related to prevent fall accidents. The RCT will test for a variety of health parameters of community-dwelling elderly playing on interactive modular tiles. The study will be a single blinded, randomized controlled trial with 60 community-dwelling adults 70+ years. The trial will consist an intervention group of 30 participants training with the interactive modular tiles, and a control group of 30 participants that will receive the usual care provided to non-patient elderly. The intervention period will be 12 weeks. The intervention group will perform group training (4-5 individuals for 1 h training session with each participant receiving 13 min training) on the interactive tiles twice a week. Follow-up tests include 6-min Walk Test (6MWT), the 8-ft Timed Up & Go Test (TUG), and the Chair-Stand Test (CS) from the Senior Fitness Test, along with balancing tests (static test on Wii Board and Line Walk test). Secondary outcomes related to adherence, motivation and acceptability will be investigated through semi-structured interviews. Data will be collected from pre- and post-tests. Data will be analyzed for statistically significant differences by checking that there is a Gaussian distribution and then using paired t-test, otherwise using Wilcoxon signed-rank test. "Intention to treat" analysis will be done. The trial tests for increased mobility, agility, balancing and general fitness of community-dwelling elderly as a result of playing, in this case on modular interactive tiles. A positive outcome may help preventing loss of functional capabilities due to inactivity. ClinicalTrials.gov: Nr. NCT02496702 , Initial Release date 7/7-2015.

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.

Assessment of refractive index of pigments by Gaussian fitting of light backscattering data in context of the liquid immersion method.

PubMed

Niskanen, Ilpo; Peiponen, Kai-Erik; Räty, Jukka

2010-05-01

Using a multifunction spectrophotometer, the refractive index of a pigment can be estimated by measuring the backscattering of light from the pigment in immersion liquids having slightly different refractive indices. A simple theoretical Gaussian function model related to the optical path distribution is introduced that makes it possible to describe quantitatively the backscattering signal from transparent pigments using a set of only a few immersion liquids. With the aid of the data fitting by a Gaussian function, the measurement time of the refractive index of the pigment can be reduced. The backscattering measurement technique is suggested to be useful in industrial measurement environments of pigments.

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

Fuzzy Logic Controller Design for A Robot Grasping System with Different Membership Functions

NASA Astrophysics Data System (ADS)

Ahmad, Hamzah; Razali, Saifudin; Rusllim Mohamed, Mohd

2013-12-01

This paper investigates the effects of the membership function to the object grasping for a three fingered gripper system. The performance of three famously used membership functions is compared to identify their behavior in lifting a defined object shape. MATLAB Simulink and SimMechanics toolboxes are used to examine the performance. Our preliminary results proposed that the Gaussian membership function surpassed the two other membership functions; triangular and trapezoid memberships especially in the context of firmer grasping and less time consumption during operations. Therefore, Gaussian membership function could be the best solution when time consumption and firmer grasp are considered.

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.

Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski functionals

NASA Astrophysics Data System (ADS)

Buchert, Thomas; France, Martin J.; Steiner, Frank

2017-05-01

Despite the wealth of Planck results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of NG the lack of complete data introduces model-dependences. Aiming at detecting the NGs of the CMB temperature anisotropy δ T , while paying particular attention to a model-independent quantification of NGs, our analysis is based upon statistical and morphological univariate descriptors, respectively: the probability density function P(δ T) , related to v0, the first Minkowski Functional (MF), and the two other MFs, v1 and v2. From their analytical Gaussian predictions we build the discrepancy functions {{ Δ }k} (k  =  P, 0, 1, 2) which are applied to an ensemble of 105 CMB realization maps of the Λ CDM model and to the Planck CMB maps. In our analysis we use general Hermite expansions of the {{ Δ }k} up to the 12th order, where the coefficients are explicitly given in terms of cumulants. Assuming hierarchical ordering of the cumulants, we obtain the perturbative expansions generalizing the second order expansions of Matsubara to arbitrary order in the standard deviation {σ0} for P(δ T) and v0, where the perturbative expansion coefficients are explicitly given in terms of complete Bell polynomials. The comparison of the Hermite expansions and the perturbative expansions is performed for the Λ CDM map sample and the Planck data. We confirm the weak level of non-Gaussianity (1-2)σ of the foreground corrected masked Planck 2015 maps.

Effects of blood pressure and sex on the change of wave reflection: evidence from Gaussian fitting method for radial artery pressure waveform.

PubMed

Liu, Chengyu; Zhao, Lina; Liu, Changchun

2014-01-01

An early return of the reflected component in the arterial pulse has been recognized as an important indicator of cardiovascular risk. This study aimed to determine the effects of blood pressure and sex factor on the change of wave reflection using Gaussian fitting method. One hundred and ninety subjects were enrolled. They were classified into four blood pressure categories based on the systolic blood pressures (i.e., ≤ 110, 111-120, 121-130 and ≥ 131 mmHg). Each blood pressure category was also stratified for sex factor. Electrocardiogram (ECG) and radial artery pressure waveforms (RAPW) signals were recorded for each subject. Ten consecutive pulse episodes from the RAPW signal were extracted and normalized. Each normalized pulse episode was fitted by three Gaussian functions. Both the peak position and peak height of the first and second Gaussian functions, as well as the peak position interval and peak height ratio, were used as the evaluation indices of wave reflection. Two-way ANOVA results showed that with the increased blood pressure, the peak position of the second Gaussian significantly shorten (P < 0.01), the peak height of the first Gaussian significantly decreased (P < 0.01) and the peak height of the second Gaussian significantly increased (P < 0.01), inducing the significantly decreased peak position interval and significantly increased peak height ratio (both P < 0.01). Sex factor had no significant effect on all evaluation indices (all P > 0.05). Moreover, the interaction between sex and blood pressure factors also had no significant effect on all evaluation indices (all P > 0.05). These results showed that blood pressure has significant effect on the change of wave reflection when using the recently developed Gaussian fitting method, whereas sex has no significant effect. The results also suggested that the Gaussian fitting method could be used as a new approach for assessing the arterial wave reflection.

Metasurface-assisted orbital angular momentum carrying Bessel-Gaussian Laser: proposal and simulation.

PubMed

Zhou, Nan; Wang, Jian

2018-05-23

Bessel-Gaussian beams have distinct properties of suppressed diffraction divergence and self-reconstruction. In this paper, we propose and simulate metasurface-assisted orbital angular momentum (OAM) carrying Bessel-Gaussian laser. The laser can be regarded as a Fabry-Perot cavity formed by one partially transparent output plane mirror and the other metasurface-based reflector mirror. The gain medium of Nd:YVO 4 enables the lasing wavelength at 1064 nm with a 808 nm laser serving as the pump. The sub-wavelength structure of metasurface facilitates flexible spatial light manipulation. The compact metasurface-based reflector provides combined phase functions of an axicon and a spherical mirror. By appropriately selecting the size of output mirror and inserting mode-selection element in the laser cavity, different orders of OAM-carrying Bessel-Gaussian lasing modes are achievable. The lasing Bessel-Gaussian 0 , Bessel-Gaussian 01 + , Bessel-Gaussian 02 + and Bessel-Gaussian 03 + modes have high fidelities of ~0.889, ~0.889, ~0.881 and ~0.879, respectively. The metasurface fabrication tolerance and the dependence of threshold power and output lasing power on the length of gain medium, beam radius of pump and transmittance of output mirror are also discussed. The obtained results show successful implementation of metasurface-assisted OAM-carrying Bessel-Gaussian laser with favorable performance. The metasurface-assisted OAM-carrying Bessel-Gaussian laser may find wide OAM-enabled communication and non-communication applications.

Increased intra-individual reaction time variability in cocaine-dependent subjects: role of cocaine-related cues.

PubMed

Liu, Shijing; Lane, Scott D; Schmitz, Joy M; Green, Charles E; Cunningham, Kathryn A; Moeller, F Gerard

2012-02-01

Neuroimaging data suggest that impaired performance on response inhibition and information processing tests in cocaine-dependent subjects is related to prefrontal and frontal cortical dysfunction and that dysfunction in these brain areas may underlie some aspects of cocaine addiction. In subjects with attention-deficit hyperactivity disorder and other psychiatric disorders, the Intra-Individual Reaction Time Variability (IIRTV) has been associated with frontal cortical dysfunction. In the present study, we evaluated IIRTV parameters in cocaine-dependent subjects vs. controls using a cocaine Stroop task. Fifty control and 123 cocaine-dependent subjects compiled from three studies completed a cocaine Stroop task. Standard deviation (SD) and coefficient of variation (CV) for reaction times (RT) were calculated for both trials with neutral and trials with cocaine-related words. The parameters mu, sigma, and tau were calculated using an ex-Gaussian analysis employed to characterize variability in RTs. The ex-Gaussian analysis divides the RTs into normal (mu, sigma) and exponential (tau) components. Using robust regression analysis, cocaine-dependent subjects showed greater SD, CV and Tau on trials with cocaine-related words compared to controls (p<0.05). However, in trials with neutral words, there was no evidence of group differences in any IIRTV parameters (p>0.05). The Wilcoxon matched-pairs signed-rank test showed that for cocaine-dependent subjects, both SD and tau were larger in trials with cocaine-related words than in trials with neutral words (p<0.05). The observation that only cocaine-related words increased IIRTV in cocaine-dependent subjects suggests that cocaine-related stimuli might disrupt information processing subserved by prefrontal and frontal cortical circuits. Copyright © 2011 Elsevier Ltd. All rights reserved.

Atomoxetine could improve intra-individual variability in drug-naïve adults with attention-deficit/hyperactivity disorder comparably with methylphenidate: A head-to-head randomized clinical trial.

PubMed

Ni, Hsing-Chang; Hwang Gu, Shoou-Lian; Lin, Hsiang-Yuan; Lin, Yu-Ju; Yang, Li-Kuang; Huang, Hui-Chun; Gau, Susan Shur-Fen

2016-05-01

Intra-individual variability in reaction time (IIV-RT) is common in individuals with attention-deficit/hyperactivity disorder (ADHD). It can be improved by stimulants. However, the effects of atomoxetine on IIV-RT are inconclusive. We aimed to investigate the effects of atomoxetine on IIV-RT, and directly compared its efficacy with methylphenidate in adults with ADHD. An 8-10 week, open-label, head-to-head, randomized clinical trial was conducted in 52 drug-naïve adults with ADHD, who were randomly assigned to two treatment groups: immediate-release methylphenidate (n=26) thrice daily (10-20 mg per dose) and atomoxetine once daily (n=26) (0.5-1.2 mg/kg/day). IIV-RT, derived from the Conners' continuous performance test (CCPT), was represented by the Gaussian (reaction time standard error, RTSE) and ex-Gaussian models (sigma and tau). Other neuropsychological functions, including response errors and mean of reaction time, were also measured. Participants received CCPT assessments at baseline and week 8-10 (60.4±6.3 days). We found comparable improvements in performances of CCPT between the immediate-release methylphenidate- and atomoxetine-treated groups. Both medications significantly improved IIV-RT in terms of reducing tau values with comparable efficacy. In addition, both medications significantly improved inhibitory control by reducing commission errors. Our results provide evidence to support that atomoxetine could improve IIV-RT and inhibitory control, of comparable efficacy with immediate-release methylphenidate, in drug-naïve adults with ADHD. Shared and unique mechanisms underpinning these medication effects on IIV-RT awaits further investigation. © The Author(s) 2016.

Photonic generation of FCC-compliant UWB pulses based on modified Gaussian quadruplet and incoherent wavelength-to-time conversion

NASA Astrophysics Data System (ADS)

Mu, Hongqian; Wang, Muguang; Tang, Yu; Zhang, Jing; Jian, Shuisheng

2018-03-01

A novel scheme for the generation of FCC-compliant UWB pulse is proposed based on modified Gaussian quadruplet and incoherent wavelength-to-time conversion. The modified Gaussian quadruplet is synthesized based on linear sum of a broad Gaussian pulse and two narrow Gaussian pulses with the same pulse-width and amplitude peak. Within specific parameter range, FCC-compliant UWB with spectral power efficiency of higher than 39.9% can be achieved. In order to realize the designed waveform, a UWB generator based on spectral shaping and incoherent wavelength-to-time mapping is proposed. The spectral shaper is composed of a Gaussian filter and a programmable filter. Single-mode fiber functions as both dispersion device and transmission medium. Balanced photodetection is employed to combine linearly the broad Gaussian pulse and two narrow Gaussian pulses, and at same time to suppress pulse pedestals that result in low-frequency components. The proposed UWB generator can be reconfigured for UWB doublet by operating the programmable filter as a single-band Gaussian filter. The feasibility of proposed UWB generator is demonstrated experimentally. Measured UWB pulses match well with simulation results. FCC-compliant quadruplet with 10-dB bandwidth of 6.88-GHz, fractional bandwidth of 106.8% and power efficiency of 51% is achieved.

Non-Gaussianity in a quasiclassical electronic circuit

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi J.; Hayakawa, Hisao

2017-05-01

We study the non-Gaussian dynamics of a quasiclassical electronic circuit coupled to a mesoscopic conductor. Non-Gaussian noise accompanying the nonequilibrium transport through the conductor significantly modifies the stationary probability density function (PDF) of the flux in the dissipative circuit. We incorporate weak quantum fluctuation of the dissipative LC circuit with a stochastic method and evaluate the quantum correction of the stationary PDF. Furthermore, an inverse formula to infer the statistical properties of the non-Gaussian noise from the stationary PDF is derived in the classical-quantum crossover regime. The quantum correction is indispensable to correctly estimate the microscopic transfer events in the QPC with the quasiclassical inverse formula.

Second order Pseudo-gaussian shaper

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

Beche, Jean-Francois

2002-11-22

The purpose of this document is to provide a calculus spreadsheet for the design of second-order pseudo-gaussian shapers. A very interesting reference is given by C.H. Mosher ''Pseudo-Gaussian Transfer Functions with Superlative Recovery'', IEEE TNS Volume 23, p. 226-228 (1976). Fred Goulding and Don Landis have studied the structure of those filters and their implementation and this document will outline the calculation leading to the relation between the coefficients of the filter. The general equation of the second order pseudo-gaussian filter is: f(t) = P{sub 0} {center_dot} e{sup -3kt} {center_dot} sin{sup 2}(kt). The parameter k is a normalization factor.

Non-Gaussian PDF Modeling of Turbulent Boundary Layer Fluctuating Pressure Excitation

NASA Technical Reports Server (NTRS)

Steinwolf, Alexander; Rizzi, Stephen A.

2003-01-01

The purpose of the study is to investigate properties of the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the exterior of a supersonic transport aircraft. It is shown that fluctuating pressure PDFs differ from the Gaussian distribution even for surface conditions having no significant discontinuities. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations upstream of forward-facing step discontinuities and downstream of aft-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. Various analytical PDF distributions are used and further developed to model this behavior.

Quantum non-Gaussianity and quantification of nonclassicality

NASA Astrophysics Data System (ADS)

Kühn, B.; Vogel, W.

2018-05-01

The algebraic quantification of nonclassicality, which naturally arises from the quantum superposition principle, is related to properties of regular nonclassicality quasiprobabilities. The latter are obtained by non-Gaussian filtering of the Glauber-Sudarshan P function. They yield lower bounds for the degree of nonclassicality. We also derive bounds for convex combinations of Gaussian states for certifying quantum non-Gaussianity directly from the experimentally accessible nonclassicality quasiprobabilities. Other quantum-state representations, such as s -parametrized quasiprobabilities, insufficiently indicate or even fail to directly uncover detailed information on the properties of quantum states. As an example, our approach is applied to multi-photon-added squeezed vacuum states.

How to model moon signals using 2-dimensional Gaussian function: Classroom activity for measuring nighttime cloud cover

NASA Astrophysics Data System (ADS)

Gacal, G. F. B.; Lagrosas, N.

2016-12-01

Nowadays, cameras are commonly used by students. In this study, we use this instrument to look at moon signals and relate these signals to Gaussian functions. To implement this as a classroom activity, students need computers, computer software to visualize signals, and moon images. A normalized Gaussian function is often used to represent probability density functions of normal distribution. It is described by its mean m and standard deviation s. The smaller standard deviation implies less spread from the mean. For the 2-dimensional Gaussian function, the mean can be described by coordinates (x0, y0), while the standard deviations can be described by sx and sy. In modelling moon signals obtained from sky-cameras, the position of the mean (x0, y0) is solved by locating the coordinates of the maximum signal of the moon. The two standard deviations are the mean square weighted deviation based from the sum of total pixel values of all rows/columns. If visualized in three dimensions, the 2D Gaussian function appears as a 3D bell surface (Fig. 1a). This shape is similar to the pixel value distribution of moon signals as captured by a sky-camera. An example of this is illustrated in Fig 1b taken around 22:20 (local time) of January 31, 2015. The local time is 8 hours ahead of coordinated universal time (UTC). This image is produced by a commercial camera (Canon Powershot A2300) with 1s exposure time, f-stop of f/2.8, and 5mm focal length. One has to chose a camera with high sensitivity when operated at nighttime to effectively detect these signals. Fig. 1b is obtained by converting the red-green-blue (RGB) photo to grayscale values. The grayscale values are then converted to a double data type matrix. The last conversion process is implemented for the purpose of having the same scales for both Gaussian model and pixel distribution of raw signals. Subtraction of the Gaussian model from the raw data produces a moonless image as shown in Fig. 1c. This moonless image can be used for quantifying cloud cover as captured by ordinary cameras (Gacal et al, 2016). Cloud cover can be defined as the ratio of number of pixels whose values exceeds 0.07 and the total number of pixels. In this particular image, cloud cover value is 0.67.

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.

Disappearance of Anisotropic Intermittency in Large-amplitude MHD Turbulence and Its Comparison with Small-amplitude MHD Turbulence

NASA Astrophysics Data System (ADS)

Yang, Liping; Zhang, Lei; He, Jiansen; Tu, Chuanyi; Li, Shengtai; Wang, Xin; Wang, Linghua

2018-03-01

Multi-order structure functions in the solar wind are reported to display a monofractal scaling when sampled parallel to the local magnetic field and a multifractal scaling when measured perpendicularly. Whether and to what extent will the scaling anisotropy be weakened by the enhancement of turbulence amplitude relative to the background magnetic strength? In this study, based on two runs of the magnetohydrodynamic (MHD) turbulence simulation with different relative levels of turbulence amplitude, we investigate and compare the scaling of multi-order magnetic structure functions and magnetic probability distribution functions (PDFs) as well as their dependence on the direction of the local field. The numerical results show that for the case of large-amplitude MHD turbulence, the multi-order structure functions display a multifractal scaling at all angles to the local magnetic field, with PDFs deviating significantly from the Gaussian distribution and a flatness larger than 3 at all angles. In contrast, for the case of small-amplitude MHD turbulence, the multi-order structure functions and PDFs have different features in the quasi-parallel and quasi-perpendicular directions: a monofractal scaling and Gaussian-like distribution in the former, and a conversion of a monofractal scaling and Gaussian-like distribution into a multifractal scaling and non-Gaussian tail distribution in the latter. These results hint that when intermittencies are abundant and intense, the multifractal scaling in the structure functions can appear even if it is in the quasi-parallel direction; otherwise, the monofractal scaling in the structure functions remains even if it is in the quasi-perpendicular direction.

Separation of the low-frequency atmospheric variability into non-Gaussian multidimensional sources by Independent Subspace Analysis

NASA Astrophysics Data System (ADS)

Pires, Carlos; Ribeiro, Andreia

2016-04-01

An efficient nonlinear method of statistical source separation of space-distributed non-Gaussian distributed data is proposed. The method relies in the so called Independent Subspace Analysis (ISA), being tested on a long time-series of the stream-function field of an atmospheric quasi-geostrophic 3-level model (QG3) simulating the winter's monthly variability of the Northern Hemisphere. ISA generalizes the Independent Component Analysis (ICA) by looking for multidimensional and minimally dependent, uncorrelated and non-Gaussian distributed statistical sources among the rotated projections or subspaces of the multivariate probability distribution of the leading principal components of the working field whereas ICA restrict to scalar sources. The rationale of that technique relies upon the projection pursuit technique, looking for data projections of enhanced interest. In order to accomplish the decomposition, we maximize measures of the sources' non-Gaussianity by contrast functions which are given by squares of nonlinear, cross-cumulant-based correlations involving the variables spanning the sources. Therefore sources are sought matching certain nonlinear data structures. The maximized contrast function is built in such a way that it provides the minimization of the mean square of the residuals of certain nonlinear regressions. The issuing residuals, followed by spherization, provide a new set of nonlinear variable changes that are at once uncorrelated, quasi-independent and quasi-Gaussian, representing an advantage with respect to the Independent Components (scalar sources) obtained by ICA where the non-Gaussianity is concentrated into the non-Gaussian scalar sources. The new scalar sources obtained by the above process encompass the attractor's curvature thus providing improved nonlinear model indices of the low-frequency atmospheric variability which is useful since large circulation indices are nonlinearly correlated. The non-Gaussian tested sources (dyads and triads, respectively of two and three dimensions) lead to a dense data concentration along certain curves or surfaces, nearby which the clusters' centroids of the joint probability density function tend to be located. That favors a better splitting of the QG3 atmospheric model's weather regimes: the positive and negative phases of the Arctic Oscillation and positive and negative phases of the North Atlantic Oscillation. The leading model's non-Gaussian dyad is associated to a positive correlation between: 1) the squared anomaly of the extratropical jet-stream and 2) the meridional jet-stream meandering. Triadic sources coming from maximized third-order cross cumulants between pairwise uncorrelated components reveal situations of triadic wave resonance and nonlinear triadic teleconnections, only possible thanks to joint non-Gaussianity. That kind of triadic synergies are accounted for an Information-Theoretic measure: the Interaction Information. The dominant model's triad occurs between anomalies of: 1) the North Pole anomaly pressure 2) the jet-stream intensity at the Eastern North-American boundary and 3) the jet-stream intensity at the Eastern Asian boundary. Publication supported by project FCT UID/GEO/50019/2013 - Instituto Dom Luiz.

On the evaluation of derivatives of Gaussian integrals

NASA Technical Reports Server (NTRS)

Helgaker, Trygve; Taylor, Peter R.

1992-01-01

We show that by a suitable change of variables, the derivatives of molecular integrals over Gaussian-type functions required for analytic energy derivatives can be evaluated with significantly less computational effort than current formulations. The reduction in effort increases with the order of differentiation.

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

McKemmish, Laura K., E-mail: laura.mckemmish@gmail.com; Research School of Chemistry, Australian National University, Canberra

Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RAMPITUP. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or verymore » large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.« less

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.

Four tails problems for dynamical collapse theories

NASA Astrophysics Data System (ADS)

McQueen, Kelvin J.

2015-02-01

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory.

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.

Design and implementation of an optical Gaussian noise generator

NASA Astrophysics Data System (ADS)

Za~O, Leonardo; Loss, Gustavo; Coelho, Rosângela

2009-08-01

A design of a fast and accurate optical Gaussian noise generator is proposed and demonstrated. The noise sample generation is based on the Box-Muller algorithm. The functions implementation was performed on a high-speed Altera Stratix EP1S25 field-programmable gate array (FPGA) development kit. It enabled the generation of 150 million 16-bit noise samples per second. The Gaussian noise generator required only 7.4% of the FPGA logic elements, 1.2% of the RAM memory, 0.04% of the ROM memory, and a laser source. The optical pulses were generated by a laser source externally modulated by the data bit samples using the frequency-shift keying technique. The accuracy of the noise samples was evaluated for different sequences size and confidence intervals. The noise sample pattern was validated by the Bhattacharyya distance (Bd) and the autocorrelation function. The results showed that the proposed design of the optical Gaussian noise generator is very promising to evaluate the performance of optical communications channels with very low bit-error-rate values.

Tensor Minkowski Functionals for random fields on the sphere

NASA Astrophysics Data System (ADS)

Chingangbam, Pravabati; Yogendran, K. P.; Joby, P. K.; Ganesan, Vidhya; Appleby, Stephen; Park, Changbom

2017-12-01

We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We outline a method to compute the tensor-valued Minkowski Functionals numerically for any random field on the sphere. Then we obtain analytic expressions for the ensemble expectation values of the matrix elements for isotropic Gaussian and Rayleigh fields. The results hold on flat as well as any curved space with affine connection. We elucidate the way in which the matrix elements encode information about the Gaussian nature and statistical isotropy (or departure from isotropy) of the field. Finally, we apply the method to maps of the Galactic foreground emissions from the 2015 PLANCK data and demonstrate their high level of statistical anisotropy and departure from Gaussianity.

Large-scale 3D galaxy correlation function and non-Gaussianity

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

Raccanelli, Alvise; Doré, Olivier; Bertacca, Daniele

We investigate the properties of the 2-point galaxy correlation function at very large scales, including all geometric and local relativistic effects --- wide-angle effects, redshift space distortions, Doppler terms and Sachs-Wolfe type terms in the gravitational potentials. The general three-dimensional correlation function has a nonzero dipole and octupole, in addition to the even multipoles of the flat-sky limit. We study how corrections due to primordial non-Gaussianity and General Relativity affect the multipolar expansion, and we show that they are of similar magnitude (when f{sub NL} is small), so that a relativistic approach is needed. Furthermore, we look at how large-scalemore » corrections depend on the model for the growth rate in the context of modified gravity, and we discuss how a modified growth can affect the non-Gaussian signal in the multipoles.« less

Comparison between photon annihilation-then-creation and photon creation-then-annihilation thermal states: Non-classical and non-Gaussian properties

NASA Astrophysics Data System (ADS)

Xu, Xue-Xiang; Yuan, Hong-Chun; Wang, Yan

2014-07-01

We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal state (TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number, Mandel Q-parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.

Gaussian vs non-Gaussian turbulence: impact on wind turbine loads

NASA Astrophysics Data System (ADS)

Berg, J.; Mann, J.; Natarajan, A.; Patton, E. G.

2014-12-01

In wind energy applications the turbulent velocity field of the Atmospheric Boundary Layer (ABL) is often characterised by Gaussian probability density functions. When estimating the dynamical loads on wind turbines this has been the rule more than anything else. From numerous studies in the laboratory, in Direct Numerical Simulations, and from in-situ measurements of the ABL we know, however, that turbulence is not purely Gaussian: the smallest and fastest scales often exhibit extreme behaviour characterised by strong non-Gaussian statistics. In this contribution we want to investigate whether these non-Gaussian effects are important when determining wind turbine loads, and hence of utmost importance to the design criteria and lifetime of a wind turbine. We devise a method based on Principal Orthogonal Decomposition where non-Gaussian velocity fields generated by high-resolution pseudo-spectral Large-Eddy Simulation (LES) of the ABL are transformed so that they maintain the exact same second-order statistics including variations of the statistics with height, but are otherwise Gaussian. In that way we can investigate in isolation the question whether it is important for wind turbine loads to include non-Gaussian properties of atmospheric turbulence. As an illustration the Figure show both a non-Gaussian velocity field (left) from our LES, and its transformed Gaussian Counterpart (right). Whereas the horizontal velocity components (top) look close to identical, the vertical components (bottom) are not: the non-Gaussian case is much more fluid-like (like in a sketch by Michelangelo). The question is then: Does the wind turbine see this? Using the load simulation software HAWC2 with both the non-Gaussian and newly constructed Gaussian fields, respectively, we show that the Fatigue loads and most of the Extreme loads are unaltered when using non-Gaussian velocity fields. The turbine thus acts like a low-pass filter which average out the non-Gaussian behaviour on time scales close to and faster than the revolution time of the turbine. For a few of the Extreme load estimations there is, on the other hand, a tendency that non-Gaussian effects increase the overall dynamical load, and hence can be of importance in wind energy load estimations.

Capacity and precision in an animal model of visual short-term memory

PubMed Central

Lara, Antonio H.; Wallis, Jonathan D.

2013-01-01

Temporary storage of information in visual short-term memory (VSTM) is a key component of many complex cognitive abilities. However, it is highly limited in capacity. Understanding the neurophysiological nature of this capacity limit will require a valid animal model of VSTM. We used a multiple-item color change detection task to measure macaque monkeys’ VSTM capacity. Subjects’ performance deteriorated and reaction times increased as a function of the number of items in memory. Additionally, we measured the precision of the memory representations by varying the distance between sample and test colors. In trials with similar sample and test colors, subjects made more errors compared to trials with highly discriminable colors. We modeled the error distribution as a Gaussian function and used this to estimate the precision of VSTM representations. We found that as the number of items in memory increases the precision of the representations decreases dramatically. Additionally, we found that focusing attention on one of the objects increases the precision with which that object is stored and degrading the precision of the remaining. These results are in line with recent findings in human psychophysics and provide a solid foundation for understanding the neurophysiological nature of the capacity limit of VSTM. PMID:22419756

An effective introduction to structural crystallography using 1D Gaussian atoms

NASA Astrophysics Data System (ADS)

Smith, Emily; Evans, Gwyndaf; Foadi, James

2017-11-01

The most important quantitative aspects of computational structural crystallography can be introduced in a satisfactory way using 1D truncated and periodic Gaussian functions to represent the atoms in a crystal lattice. This paper describes in detail and demonstrates 1D structural crystallography starting with the definition of such truncated Gaussians. The availability of the computer programme CRONE makes possible the repetition of the examples provided in the paper as well as the creation of new ones.

Elegant Ince—Gaussian breathers in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

2012-06-01

A novel class of optical breathers, called elegant Ince—Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell's mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schrödinger equation.

Regression Models for the Analysis of Longitudinal Gaussian Data from Multiple Sources

PubMed Central

O’Brien, Liam M.; Fitzmaurice, Garrett M.

2006-01-01

We present a regression model for the joint analysis of longitudinal multiple source Gaussian data. Longitudinal multiple source data arise when repeated measurements are taken from two or more sources, and each source provides a measure of the same underlying variable and on the same scale. This type of data generally produces a relatively large number of observations per subject; thus estimation of an unstructured covariance matrix often may not be possible. We consider two methods by which parsimonious models for the covariance can be obtained for longitudinal multiple source data. The methods are illustrated with an example of multiple informant data arising from a longitudinal interventional trial in psychiatry. PMID:15726666

On the robustness of the q-Gaussian family

NASA Astrophysics Data System (ADS)

Sicuro, Gabriele; Tempesta, Piergiulio; Rodríguez, Antonio; Tsallis, Constantino

2015-12-01

We introduce three deformations, called α-, β- and γ-deformation respectively, of a N-body probabilistic model, first proposed by Rodríguez et al. (2008), having q-Gaussians as N → ∞ limiting probability distributions. The proposed α- and β-deformations are asymptotically scale-invariant, whereas the γ-deformation is not. We prove that, for both α- and β-deformations, the resulting deformed triangles still have q-Gaussians as limiting distributions, with a value of q independent (dependent) on the deformation parameter in the α-case (β-case). In contrast, the γ-case, where we have used the celebrated Q-numbers and the Gauss binomial coefficients, yields other limiting probability distribution functions, outside the q-Gaussian family. These results suggest that scale-invariance might play an important role regarding the robustness of the q-Gaussian family.

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.

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.

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…

Application of genetic algorithm for the simultaneous identification of atmospheric pollution sources

NASA Astrophysics Data System (ADS)

Cantelli, A.; D'Orta, F.; Cattini, A.; Sebastianelli, F.; Cedola, L.

2015-08-01

A computational model is developed for retrieving the positions and the emission rates of unknown pollution sources, under steady state conditions, starting from the measurements of the concentration of the pollutants. The approach is based on the minimization of a fitness function employing a genetic algorithm paradigm. The model is tested considering both pollutant concentrations generated through a Gaussian model in 25 points in a 3-D test case domain (1000m × 1000m × 50 m) and experimental data such as the Prairie Grass field experiments data in which about 600 receptors were located along five concentric semicircle arcs and the Fusion Field Trials 2007. The results show that the computational model is capable to efficiently retrieve up to three different unknown sources.

Fresnel zone plate with apodized aperture for hard X-ray Gaussian beam optics.

PubMed

Takeuchi, Akihisa; Uesugi, Kentaro; Suzuki, Yoshio; Itabashi, Seiichi; Oda, Masatoshi

2017-05-01

Fresnel zone plates with apodized apertures [apodization FZPs (A-FZPs)] have been developed to realise Gaussian beam optics in the hard X-ray region. The designed zone depth of A-FZPs gradually decreases from the center to peripheral regions. Such a zone structure forms a Gaussian-like smooth-shouldered aperture function which optically behaves as an apodization filter and produces a Gaussian-like focusing spot profile. Optical properties of two types of A-FZP, i.e. a circular type and a one-dimensional type, have been evaluated by using a microbeam knife-edge scan test, and have been carefully compared with those of normal FZP optics. Advantages of using A-FZPs are introduced.

Ensemble Kalman filtering in presence of inequality constraints

NASA Astrophysics Data System (ADS)

van Leeuwen, P. J.

2009-04-01

Kalman filtering is presence of constraints is an active area of research. Based on the Gaussian assumption for the probability-density functions, it looks hard to bring in extra constraints in the formalism. On the other hand, in geophysical systems we often encounter constraints related to e.g. the underlying physics or chemistry, which are violated by the Gaussian assumption. For instance, concentrations are always non-negative, model layers have non-negative thickness, and sea-ice concentration is between 0 and 1. Several methods to bring inequality constraints into the Kalman-filter formalism have been proposed. One of them is probability density function (pdf) truncation, in which the Gaussian mass from the non-allowed part of the variables is just equally distributed over the pdf where the variables are alolwed, as proposed by Shimada et al. 1998. However, a problem with this method is that the probability that e.g. the sea-ice concentration is zero, is zero! The new method proposed here does not have this drawback. It assumes that the probability-density function is a truncated Gaussian, but the truncated mass is not distributed equally over all allowed values of the variables, but put into a delta distribution at the truncation point. This delta distribution can easily be handled with in Bayes theorem, leading to posterior probability density functions that are also truncated Gaussians with delta distributions at the truncation location. In this way a much better representation of the system is obtained, while still keeping most of the benefits of the Kalman-filter formalism. In the full Kalman filter the formalism is prohibitively expensive in large-scale systems, but efficient implementation is possible in ensemble variants of the kalman filter. Applications to low-dimensional systems and large-scale systems will be discussed.

Antimicrobial peptides and induced membrane curvature: geometry, coordination chemistry, and molecular engineering

PubMed Central

Schmidt, Nathan W.; Wong, Gerard C. L.

2013-01-01

Short cationic, amphipathic antimicrobial peptides are multi-functional molecules that have roles in host defense as direct microbicides and modulators of the immune response. While a general mechanism of microbicidal activity involves the selective disruption and permeabilization of cell membranes, the relationships between peptide sequence and membrane activity are still under investigation. Here, we review the diverse functions that AMPs collectively have in host defense, and show that these functions can be multiplexed with a membrane mechanism of activity derived from the generation of negative Gaussian membrane curvature. As AMPs preferentially generate this curvature in model bacterial cell membranes, the selective generation of negative Gaussian curvature provides AMPs with a broad mechanism to target microbial membranes. The amino acid constraints placed on AMPs by the geometric requirement to induce negative Gaussian curvature are consistent with known AMP sequences. This ‘saddle-splay curvature selection rule’ is not strongly restrictive so AMPs have significant compositional freedom to multiplex membrane activity with other useful functions. The observation that certain proteins involved in cellular processes which require negative Gaussian curvature contain domains with similar motifs as AMPs, suggests this rule may be applicable to other curvature-generating proteins. Since our saddle-splay curvature design rule is based upon both a mechanism of activity and the existing motifs of natural AMPs, we believe it will assist the development of synthetic antimicrobials. PMID:24778573

Effect of Coulomb friction on orientational correlation and velocity distribution functions in a sheared dilute granular gas.

PubMed

Gayen, Bishakhdatta; Alam, Meheboob

2011-08-01

From particle simulations of a sheared frictional granular gas, we show that the Coulomb friction can have dramatic effects on orientational correlation as well as on both the translational and angular velocity distribution functions even in the Boltzmann (dilute) limit. The dependence of orientational correlation on friction coefficient (μ) is found to be nonmonotonic, and the Coulomb friction plays a dual role of enhancing or diminishing the orientational correlation, depending on the value of the tangential restitution coefficient (which characterizes the roughness of particles). From the sticking limit (i.e., with no sliding contact) of rough particles, decreasing the Coulomb friction is found to reduce the density and spatial velocity correlations which, together with diminished orientational correlation for small enough μ, are responsible for the transition from non-gaussian to gaussian distribution functions in the double limit of small friction (μ→0) and nearly elastic particles (e→1). This double limit in fact corresponds to perfectly smooth particles, and hence the maxwellian (gaussian) is indeed a solution of the Boltzmann equation for a frictional granular gas in the limit of elastic collisions and zero Coulomb friction at any roughness. The high-velocity tails of both distribution functions seem to follow stretched exponentials even in the presence of Coulomb friction, and the related velocity exponents deviate strongly from a gaussian with increasing friction.

Non-Gaussian bias: insights from discrete density peaks

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

Desjacques, Vincent; Riotto, Antonio; Gong, Jinn-Ouk, E-mail: Vincent.Desjacques@unige.ch, E-mail: jinn-ouk.gong@apctp.org, E-mail: Antonio.Riotto@unige.ch

2013-09-01

Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastlymore » simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out that statistics of thresholded regions can be computed using the same formalism. Our results suggest that halo clustering statistics can be modelled consistently (in the sense that the Gaussian and non-Gaussian bias factors agree with peak-background split expectations) from a Lagrangian bias relation only if the latter is specified as a set of constraints imposed on the linear density field. This is clearly not the case of standard Lagrangian local bias. Therefore, one is led to consider additional variables beyond the local mass overdensity.« less

Analysis of Flow and Transport in non-Gaussian Heterogeneous Formations Using a Generalized Sub-Gaussian Model

NASA Astrophysics Data System (ADS)

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

2016-12-01

Environmental quantities such as log hydraulic conductivity (or transmissivity), Y(x) = ln K(x), and their spatial (or temporal) increments, ΔY, are known to be generally non-Gaussian. Documented evidence of such behavior includes symmetry of increment distributions at all separation scales (or lags) between incremental values of Y with sharp peaks and heavy tails that decay asymptotically as lag increases. This statistical scaling occurs in porous as well as fractured media characterized by either one or a hierarchy of spatial correlation scales. In hierarchical media one observes a range of additional statistical ΔY scaling phenomena, all of which are captured comprehensibly by a novel generalized sub-Gaussian (GSG) model. In this model Y forms a mixture Y(x) = U(x) G(x) of single- or multi-scale Gaussian processes G having random variances, U being a non-negative subordinator independent of G. Elsewhere we developed ways to generate unconditional and conditional random realizations of isotropic or anisotropic GSG fields which can be embedded in numerical Monte Carlo flow and transport simulations. Here we present and discuss expressions for probability distribution functions of Y and ΔY as well as their lead statistical moments. We then focus on a simple flow setting of mean uniform steady state flow in an unbounded, two-dimensional domain, exploring ways in which non-Gaussian heterogeneity affects stochastic flow and transport descriptions. Our expressions represent (a) lead order autocovariance and cross-covariance functions of hydraulic head, velocity and advective particle displacement as well as (b) analogues of preasymptotic and asymptotic Fickian dispersion coefficients. We compare them with corresponding expressions developed in the literature for Gaussian Y.

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

NASA Technical Reports Server (NTRS)

Isar, Aurelian

1995-01-01

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

Coherent mode decomposition using mixed Wigner functions of Hermite-Gaussian beams.

PubMed

Tanaka, Takashi

2017-04-15

A new method of coherent mode decomposition (CMD) is proposed that is based on a Wigner-function representation of Hermite-Gaussian beams. In contrast to the well-known method using the cross spectral density (CSD), it directly determines the mode functions and their weights without solving the eigenvalue problem. This facilitates the CMD of partially coherent light whose Wigner functions (and thus CSDs) are not separable, in which case the conventional CMD requires solving an eigenvalue problem with a large matrix and thus is numerically formidable. An example is shown regarding the CMD of synchrotron radiation, one of the most important applications of the proposed method.

Progress in calculating the potential energy surface of H3+.

PubMed

Adamowicz, Ludwik; Pavanello, Michele

2012-11-13

The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H(3)(+) ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh-Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H(3)(+) rovibrational spectrum is reproduced at the 0.1 cm(-1) accuracy level up to 16,600 cm(-1) above the ground state.

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

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.

A novel Gaussian-Sinc mixed basis set for electronic structure calculations

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

Jerke, Jonathan L.; Lee, Young; Tymczak, C. J.

2015-08-14

A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree–Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the “localized” and “delocalized” regions. A basis set for each region is combined to make a new basis methodology—a lattice of orthonormal sinc functions is used to represent the “delocalized” regions and the atom-centered Gaussian functions are used to represent the “localized” regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definablemore » and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree–Fock energies for atoms up to neon, the diatomic systems H{sub 2}, O{sub 2}, and N{sub 2}, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species.« less

The Laplace method for probability measures in Banach spaces

NASA Astrophysics Data System (ADS)

Piterbarg, V. I.; Fatalov, V. R.

1995-12-01

Contents §1. Introduction Chapter I. Asymptotic analysis of continual integrals in Banach space, depending on a large parameter §2. The large deviation principle and logarithmic asymptotics of continual integrals §3. Exact asymptotics of Gaussian integrals in Banach spaces: the Laplace method 3.1. The Laplace method for Gaussian integrals taken over the whole Hilbert space: isolated minimum points ([167], I) 3.2. The Laplace method for Gaussian integrals in Hilbert space: the manifold of minimum points ([167], II) 3.3. The Laplace method for Gaussian integrals in Banach space ([90], [174], [176]) 3.4. Exact asymptotics of large deviations of Gaussian norms §4. The Laplace method for distributions of sums of independent random elements with values in Banach space 4.1. The case of a non-degenerate minimum point ([137], I) 4.2. A degenerate isolated minimum point and the manifold of minimum points ([137], II) §5. Further examples 5.1. The Laplace method for the local time functional of a Markov symmetric process ([217]) 5.2. The Laplace method for diffusion processes, a finite number of non-degenerate minimum points ([116]) 5.3. Asymptotics of large deviations for Brownian motion in the Hölder norm 5.4. Non-asymptotic expansion of a strong stable law in Hilbert space ([41]) Chapter II. The double sum method - a version of the Laplace method in the space of continuous functions §6. Pickands' method of double sums 6.1. General situations 6.2. Asymptotics of the distribution of the maximum of a Gaussian stationary process 6.3. Asymptotics of the probability of a large excursion of a Gaussian non-stationary process §7. Probabilities of large deviations of trajectories of Gaussian fields 7.1. Homogeneous fields and fields with constant dispersion 7.2. Finitely many maximum points of dispersion 7.3. Manifold of maximum points of dispersion 7.4. Asymptotics of distributions of maxima of Wiener fields §8. Exact asymptotics of large deviations of the norm of Gaussian vectors and processes with values in the spaces L_k^p and l^2. Gaussian fields with the set of parameters in Hilbert space 8.1 Exact asymptotics of the distribution of the l_k^p-norm of a Gaussian finite-dimensional vector with dependent coordinates, p > 1 8.2. Exact asymptotics of probabilities of high excursions of trajectories of processes of type \\chi^2 8.3. Asymptotics of the probabilities of large deviations of Gaussian processes with a set of parameters in Hilbert space [74] 8.4. Asymptotics of distributions of maxima of the norms of l^2-valued Gaussian processes 8.5. Exact asymptotics of large deviations for the l^2-valued Ornstein-Uhlenbeck process Bibliography

A Model of Self-Monitoring Blood Glucose Measurement Error.

PubMed

Vettoretti, Martina; Facchinetti, Andrea; Sparacino, Giovanni; Cobelli, Claudio

2017-07-01

A reliable model of the probability density function (PDF) of self-monitoring of blood glucose (SMBG) measurement error would be important for several applications in diabetes, like testing in silico insulin therapies. In the literature, the PDF of SMBG error is usually described by a Gaussian function, whose symmetry and simplicity are unable to properly describe the variability of experimental data. Here, we propose a new methodology to derive more realistic models of SMBG error PDF. The blood glucose range is divided into zones where error (absolute or relative) presents a constant standard deviation (SD). In each zone, a suitable PDF model is fitted by maximum-likelihood to experimental data. Model validation is performed by goodness-of-fit tests. The method is tested on two databases collected by the One Touch Ultra 2 (OTU2; Lifescan Inc, Milpitas, CA) and the Bayer Contour Next USB (BCN; Bayer HealthCare LLC, Diabetes Care, Whippany, NJ). In both cases, skew-normal and exponential models are used to describe the distribution of errors and outliers, respectively. Two zones were identified: zone 1 with constant SD absolute error; zone 2 with constant SD relative error. Goodness-of-fit tests confirmed that identified PDF models are valid and superior to Gaussian models used so far in the literature. The proposed methodology allows to derive realistic models of SMBG error PDF. These models can be used in several investigations of present interest in the scientific community, for example, to perform in silico clinical trials to compare SMBG-based with nonadjunctive CGM-based insulin treatments.

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.

Performance assessment of density functional methods with Gaussian and Slater basis sets using 7σ orbital momentum distributions of N2O

NASA Astrophysics Data System (ADS)

Wang, Feng; Pang, Wenning; Duffy, Patrick

2012-12-01

Performance of a number of commonly used density functional methods in chemistry (B3LYP, Bhandh, BP86, PW91, VWN, LB94, PBe0, SAOP and X3LYP and the Hartree-Fock (HF) method) has been assessed using orbital momentum distributions of the 7σ orbital of nitrous oxide (NNO), which models electron behaviour in a chemically significant region. The density functional methods are combined with a number of Gaussian basis sets (Pople's 6-31G*, 6-311G**, DGauss TZVP and Dunning's aug-cc-pVTZ as well as even-tempered Slater basis sets, namely, et-DZPp, et-QZ3P, et-QZ+5P and et-pVQZ). Orbital momentum distributions of the 7σ orbital in the ground electronic state of NNO, which are obtained from a Fourier transform into momentum space from single point electronic calculations employing the above models, are compared with experimental measurement of the same orbital from electron momentum spectroscopy (EMS). The present study reveals information on performance of (a) the density functional methods, (b) Gaussian and Slater basis sets, (c) combinations of the density functional methods and basis sets, that is, the models, (d) orbital momentum distributions, rather than a group of specific molecular properties and (e) the entire region of chemical significance of the orbital. It is found that discrepancies of this orbital between the measured and the calculated occur in the small momentum region (i.e. large r region). In general, Slater basis sets achieve better overall performance than the Gaussian basis sets. Performance of the Gaussian basis sets varies noticeably when combining with different Vxc functionals, but Dunning's augcc-pVTZ basis set achieves the best performance for the momentum distributions of this orbital. The overall performance of the B3LYP and BP86 models is similar to newer models such as X3LYP and SAOP. The present study also demonstrates that the combinations of the density functional methods and the basis sets indeed make a difference in the quality of the calculated orbitals.

Long-range corrected density functional theory with accelerated Hartree-Fock exchange integration using a two-Gaussian operator [LC-ωPBE(2Gau)].

PubMed

Song, Jong-Won; Hirao, Kimihiko

2015-10-14

Since the advent of hybrid functional in 1993, it has become a main quantum chemical tool for the calculation of energies and properties of molecular systems. Following the introduction of long-range corrected hybrid scheme for density functional theory a decade later, the applicability of the hybrid functional has been further amplified due to the resulting increased performance on orbital energy, excitation energy, non-linear optical property, barrier height, and so on. Nevertheless, the high cost associated with the evaluation of Hartree-Fock (HF) exchange integrals remains a bottleneck for the broader and more active applications of hybrid functionals to large molecular and periodic systems. Here, we propose a very simple yet efficient method for the computation of long-range corrected hybrid scheme. It uses a modified two-Gaussian attenuating operator instead of the error function for the long-range HF exchange integral. As a result, the two-Gaussian HF operator, which mimics the shape of the error function operator, reduces computational time dramatically (e.g., about 14 times acceleration in C diamond calculation using periodic boundary condition) and enables lower scaling with system size, while maintaining the improved features of the long-range corrected density functional theory.

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.

All-electron density functional calculation on insulin with quasi-canonical localized orbitals.

PubMed

Inaba, Toru; Tahara, Saisei; Nisikawa, Nobutaka; Kashiwagi, Hiroshi; Sato, Fumitoshi

2005-07-30

An all-electron density functional (DF) calculation on insulin was performed by the Gaussian-based DF program, ProteinDF. Quasi-canonical localized orbitals (QCLOs) were used to improve the initial guess for the self-consistent field (SCF) calculation. All calculations were carried out by parallel computing on eight processors of an Itanium2 cluster (SGI Altix3700) with a theoretical peak performance of 41.6 GFlops. It took 35 h for the whole calculation. Insulin is a protein hormone consisting of two peptide chains linked by three disulfide bonds. The numbers of residues, atoms, electrons, orbitals, and auxiliary functions are 51, 790, 3078, 4439, and 8060, respectively. An all-electron DF calculation on insulin was successfully carried out, starting from connected QCLOs. Regardless of a large molecule with complicated topology, the differences in the total energy and the Mulliken atomic charge between initial and converged wavefunctions were very small. The calculation proceeded smoothly without any trial and error, suggesting that this is a promising method to obtain SCF convergence on large molecules such as proteins.

The Form, and Some Robustness Properties of Integrated Distance Estimators for Linear Models, Applied to Some Published Data Sets.

DTIC Science & Technology

1982-06-01

observation in our framework is the pair (y,x) with x considered given. The influence function for 52 at the Gaussian distribution with mean xB and variance...3/2 - (1+22)o2 2) 1+2x\\/2 x’) 2(3-9) (1+2X) This influence function is bounded in the residual y-xS, and redescends to an asymptote greater than...version of the influence function for B at the Gaussian distribution, given the x. and x, is defined as the normalized differenceJ (see Barnett and

Cosine-Gaussian Schell-model sources.

PubMed

Mei, Zhangrong; Korotkova, Olga

2013-07-15

We introduce a new class of partially coherent sources of Schell type with cosine-Gaussian spectral degree of coherence and confirm that such sources are physically genuine. Further, we derive the expression for the cross-spectral density function of a beam generated by the novel source propagating in free space and analyze the evolution of the spectral density and the spectral degree of coherence. It is shown that at sufficiently large distances from the source the degree of coherence of the propagating beam assumes Gaussian shape while the spectral density takes on the dark-hollow profile.

Intermittent nature of solar wind turbulence near the Earth's bow shock: phase coherence and non-Gaussianity.

PubMed

Koga, D; Chian, A C-L; Miranda, R A; Rempel, E L

2007-04-01

The link between phase coherence and non-Gaussian statistics is investigated using magnetic field data observed in the solar wind turbulence near the Earth's bow shock. The phase coherence index Cphi, which characterizes the degree of phase correlation (i.e., nonlinear wave-wave interactions) among scales, displays a behavior similar to kurtosis and reflects a departure from Gaussianity in the probability density functions of magnetic field fluctuations. This demonstrates that nonlinear interactions among scales are the origin of intermittency in the magnetic field turbulence.

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.

Statistical description of turbulent transport for flux driven toroidal plasmas

NASA Astrophysics Data System (ADS)

Anderson, J.; Imadera, K.; Kishimoto, Y.; Li, J. Q.; Nordman, H.

2017-06-01

A novel methodology to analyze non-Gaussian probability distribution functions (PDFs) of intermittent turbulent transport in global full-f gyrokinetic simulations is presented. In this work, the auto-regressive integrated moving average (ARIMA) model is applied to time series data of intermittent turbulent heat transport to separate noise and oscillatory trends, allowing for the extraction of non-Gaussian features of the PDFs. It was shown that non-Gaussian tails of the PDFs from first principles based gyrokinetic simulations agree with an analytical estimation based on a two fluid model.

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.

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

PubMed

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

Lensing of the CMB: non-Gaussian aspects.

PubMed

Zaldarriaga, M

2001-06-01

We compute the small angle limit of the three- and four-point function of the cosmic microwave background (CMB) temperature induced by the gravitational lensing effect by the large-scale structure of the universe. We relate the non-Gaussian aspects presented in this paper with those in our previous studies of the lensing effects. We interpret the statistics proposed in previous work in terms of different configurations of the four-point function and show how they relate to the statistic that maximizes the S/N.

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

Phase retrieval of images using Gaussian radial bases.

PubMed

Trahan, Russell; Hyland, David

2013-12-20

Here, the possibility of a noniterative solution to the phase retrieval problem is explored. A new look is taken at the phase retrieval problem that reveals that knowledge of a diffraction pattern's frequency components is enough to recover the image without projective iterations. This occurs when the image is formed using Gaussian bases that give the convenience of a continuous Fourier transform existing in a compact form where square pixels do not. The Gaussian bases are appropriate when circular apertures are used to detect the diffraction pattern because of their optical transfer functions, as discussed briefly. An algorithm is derived that is capable of recovering an image formed by Gaussian bases from only the Fourier transform's modulus, without background constraints. A practical example is shown.

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.

Gaussian-windowed frame based method of moments formulation of surface-integral-equation for extended apertures

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

Shlivinski, A., E-mail: amirshli@ee.bgu.ac.il; Lomakin, V., E-mail: vlomakin@eng.ucsd.edu

2016-03-01

Scattering or coupling of electromagnetic beam-field at a surface discontinuity separating two homogeneous or inhomogeneous media with different propagation characteristics is formulated using surface integral equation, which are solved by the Method of Moments with the aid of the Gabor-based Gaussian window frame set of basis and testing functions. The application of the Gaussian window frame provides (i) a mathematically exact and robust tool for spatial-spectral phase-space formulation and analysis of the problem; (ii) a system of linear equations in a transmission-line like form relating mode-like wave objects of one medium with mode-like wave objects of the second medium; (iii)more » furthermore, an appropriate setting of the frame parameters yields mode-like wave objects that blend plane wave properties (as if solving in the spectral domain) with Green's function properties (as if solving in the spatial domain); and (iv) a representation of the scattered field with Gaussian-beam propagators that may be used in many large (in terms of wavelengths) systems.« less

Log-amplitude variance and wave structure function: A new perspective for Gaussian beams

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

Miller, W.B.; Ricklin, J.C.; Andrews, L.C.

1993-04-01

Two naturally linked pairs of nondimensional parameters are identified such that either pair, together with wavelength and path length, completely specifies the diffractive propagation environment for a lowest-order paraxial Gaussian beam. Both parameter pairs are intuitive, and within the context of locally homogeneous and isotropic turbulence they reflect the long-recognized importance of the Fresnel zone size in the behavior of Rytov propagation statistics. These parameter pairs, called, respectively, the transmitter and receiver parameters, also provide a change in perspective in the analysis of optical turbulence effects on Gaussian beams by unifying a number of behavioral traits previously observed or predicted,more » and they create an environment in which the determination of limiting interrelationships between beam forms is especially simple. The fundamental nature of the parameter pairs becomes apparent in the derived analytical expressions for the log-amplitude variance and the wave structure function. These expressions verify general optical turbulence-related characteristics predicted for Gaussian beams, provide additional insights into beam-wave behavior, and are convenient tools for beam-wave analysis. 22 refs., 10 figs., 2 tabs.« less

DC and analog/RF performance optimisation of source pocket dual work function TFET

NASA Astrophysics Data System (ADS)

Raad, Bhagwan Ram; Sharma, Dheeraj; Kondekar, Pravin; Nigam, Kaushal; Baronia, Sagar

2017-12-01

We investigate a systematic study of source pocket tunnel field-effect transistor (SP TFET) with dual work function of single gate material by using uniform and Gaussian doping profile in the drain region for ultra-low power high frequency high speed applications. For this, a n+ doped region is created near the source/channel junction to decrease the depletion width results in improvement of ON-state current. However, the dual work function of the double gate is used for enhancement of the device performance in terms of DC and analog/RF parameters. Further, to improve the high frequency performance of the device, Gaussian doping profile is considered in the drain region with different characteristic lengths which decreases the gate to drain capacitance and leads to drastic improvement in analog/RF figures of merit. Furthermore, the optimisation is performed with different concentrations for uniform and Gaussian drain doping profile and for various sectional length of lower work function of the gate electrode. Finally, the effect of temperature variation on the device performance is demonstrated.

Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density

DOE PAGES

Smallwood, David O.

1997-01-01

The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs) of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power) spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general casemore » of matching a target probability density function using a zero memory nonlinear (ZMNL) function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV) are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.« less

A Prediction Model for Functional Outcomes in Spinal Cord Disorder Patients Using Gaussian Process Regression.

PubMed

Lee, Sunghoon Ivan; Mortazavi, Bobak; Hoffman, Haydn A; Lu, Derek S; Li, Charles; Paak, Brian H; Garst, Jordan H; Razaghy, Mehrdad; Espinal, Marie; Park, Eunjeong; Lu, Daniel C; Sarrafzadeh, Majid

2016-01-01

Predicting the functional outcomes of spinal cord disorder patients after medical treatments, such as a surgical operation, has always been of great interest. Accurate posttreatment prediction is especially beneficial for clinicians, patients, care givers, and therapists. This paper introduces a prediction method for postoperative functional outcomes by a novel use of Gaussian process regression. The proposed method specifically considers the restricted value range of the target variables by modeling the Gaussian process based on a truncated Normal distribution, which significantly improves the prediction results. The prediction has been made in assistance with target tracking examinations using a highly portable and inexpensive handgrip device, which greatly contributes to the prediction performance. The proposed method has been validated through a dataset collected from a clinical cohort pilot involving 15 patients with cervical spinal cord disorder. The results show that the proposed method can accurately predict postoperative functional outcomes, Oswestry disability index and target tracking scores, based on the patient's preoperative information with a mean absolute error of 0.079 and 0.014 (out of 1.0), respectively.

Effect of asymmetric concentration profile on thermal conductivity in Ge/SiGe superlattices

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

Hahn, Konstanze R., E-mail: konstanze.hahn@dsf.unica.it; Cecchi, Stefano; Colombo, Luciano

2016-05-16

The effect of the chemical composition in Si/Ge-based superlattices on their thermal conductivity has been investigated using molecular dynamics simulations. Simulation cells of Ge/SiGe superlattices have been generated with different concentration profiles such that the Si concentration follows a step-like, a tooth-saw, a Gaussian, and a gamma-type function in direction of the heat flux. The step-like and tooth-saw profiles mimic ideally sharp interfaces, whereas Gaussian and gamma-type profiles are smooth functions imitating atomic diffusion at the interface as obtained experimentally. Symmetry effects have been investigated comparing the symmetric profiles of the step-like and the Gaussian function to the asymmetric profilesmore » of the tooth-saw and the gamma-type function. At longer sample length and similar degree of interdiffusion, the thermal conductivity is found to be lower in asymmetric profiles. Furthermore, it is found that with smooth concentration profiles where atomic diffusion at the interface takes place the thermal conductivity is higher compared to systems with atomically sharp concentration profiles.« less

Realistic continuous-variable quantum teleportation with non-Gaussian resources

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

Dell'Anno, F.; De Siena, S.; CNR-INFM Coherentia, Napoli, Italy, and CNISM and INFN Sezione di Napoli, Gruppo Collegato di Salerno, Baronissi, SA

2010-01-15

We present a comprehensive investigation of nonideal continuous-variable quantum teleportation implemented with entangled non-Gaussian resources. We discuss in a unified framework the main decoherence mechanisms, including imperfect Bell measurements and propagation of optical fields in lossy fibers, applying the formalism of the characteristic function. By exploiting appropriate displacement strategies, we compute analytically the success probability of teleportation for input coherent states and two classes of non-Gaussian entangled resources: two-mode squeezed Bell-like states (that include as particular cases photon-added and photon-subtracted de-Gaussified states), and two-mode squeezed catlike states. We discuss the optimization procedure on the free parameters of the non-Gaussian resourcesmore » at fixed values of the squeezing and of the experimental quantities determining the inefficiencies of the nonideal protocol. It is found that non-Gaussian resources enhance significantly the efficiency of teleportation and are more robust against decoherence than the corresponding Gaussian ones. Partial information on the alphabet of input states allows further significant improvement in the performance of the nonideal teleportation protocol.« less

Separation of components from a scale mixture of Gaussian white noises

NASA Astrophysics Data System (ADS)

Vamoş, Călin; Crăciun, Maria

2010-05-01

The time evolution of a physical quantity associated with a thermodynamic system whose equilibrium fluctuations are modulated in amplitude by a slowly varying phenomenon can be modeled as the product of a Gaussian white noise {Zt} and a stochastic process with strictly positive values {Vt} referred to as volatility. The probability density function (pdf) of the process Xt=VtZt is a scale mixture of Gaussian white noises expressed as a time average of Gaussian distributions weighted by the pdf of the volatility. The separation of the two components of {Xt} can be achieved by imposing the condition that the absolute values of the estimated white noise be uncorrelated. We apply this method to the time series of the returns of the daily S&P500 index, which has also been analyzed by means of the superstatistics method that imposes the condition that the estimated white noise be Gaussian. The advantage of our method is that this financial time series is processed without partitioning or removal of the extreme events and the estimated white noise becomes almost Gaussian only as result of the uncorrelation condition.

On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak-lensing likelihoods

NASA Astrophysics Data System (ADS)

Sellentin, Elena; Heavens, Alan F.

2018-01-01

We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmological data, is supported by simulated survey data. We define test statistics, based on a novel method that first destroys Gaussian correlations in a data set, and then measures the non-Gaussian correlations that remain. This procedure flags pairs of data points that depend on each other in a non-Gaussian fashion, and thereby identifies where the assumption of a Gaussian likelihood breaks down. Using this diagnosis, we find that non-Gaussian correlations in the CFHTLenS cosmic shear correlation functions are significant. With a simple exclusion of the most contaminated data points, the posterior for s8 is shifted without broadening, but we find no significant reduction in the tension with s8 derived from Planck cosmic microwave background data. However, we also show that the one-point distributions of the correlation statistics are noticeably skewed, such that sound weak-lensing data sets are intrinsically likely to lead to a systematically low lensing amplitude being inferred. The detected non-Gaussianities get larger with increasing angular scale such that for future wide-angle surveys such as Euclid or LSST, with their very small statistical errors, the large-scale modes are expected to be increasingly affected. The shifts in posteriors may then not be negligible and we recommend that these diagnostic tests be run as part of future analyses.

Q (Alpha) Function and Squeezing Effect

NASA Technical Reports Server (NTRS)

Yunjie, Xia; Xianghe, Kong; Kezhu, Yan; Wanping, Chen

1996-01-01

The relation of squeezing and Q(alpha) function is discussed in this paper. By means of Q function, the squeezing of field with gaussian Q(alpha) function or negative P(a)function is also discussed in detail.

The effects of the one-step replica symmetry breaking on the Sherrington-Kirkpatrick spin glass model in the presence of random field with a joint Gaussian probability density function for the exchange interactions and random fields

NASA Astrophysics Data System (ADS)

Hadjiagapiou, Ioannis A.; Velonakis, Ioannis N.

2018-07-01

The Sherrington-Kirkpatrick Ising spin glass model, in the presence of a random magnetic field, is investigated within the framework of the one-step replica symmetry breaking. The two random variables (exchange integral interaction Jij and random magnetic field hi) are drawn from a joint Gaussian probability density function characterized by a correlation coefficient ρ, assuming positive and negative values. The thermodynamic properties, the three different phase diagrams and system's parameters are computed with respect to the natural parameters of the joint Gaussian probability density function at non-zero and zero temperatures. The low temperature negative entropy controversy, a result of the replica symmetry approach, has been partly remedied in the current study, leading to a less negative result. In addition, the present system possesses two successive spin glass phase transitions with characteristic temperatures.

Mixed-effects Gaussian process functional regression models with application to dose-response curve prediction.

PubMed

Shi, J Q; Wang, B; Will, E J; West, R M

2012-11-20

We propose a new semiparametric model for functional regression analysis, combining a parametric mixed-effects model with a nonparametric Gaussian process regression model, namely a mixed-effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose-response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose-response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient-specific treatment regime. Copyright © 2012 John Wiley & Sons, Ltd.

Robust signal recovery using the prolate spherical wave functions and maximum correntropy criterion

NASA Astrophysics Data System (ADS)

Zou, Cuiming; Kou, Kit Ian

2018-05-01

Signal recovery is one of the most important problem in signal processing. This paper proposes a novel signal recovery method based on prolate spherical wave functions (PSWFs). PSWFs are a kind of special functions, which have been proved having good performance in signal recovery. However, the existing PSWFs based recovery methods used the mean square error (MSE) criterion, which depends on the Gaussianity assumption of the noise distributions. For the non-Gaussian noises, such as impulsive noise or outliers, the MSE criterion is sensitive, which may lead to large reconstruction error. Unlike the existing PSWFs based recovery methods, our proposed PSWFs based recovery method employs the maximum correntropy criterion (MCC), which is independent of the noise distribution. The proposed method can reduce the impact of the large and non-Gaussian noises. The experimental results on synthetic signals with various types of noises show that the proposed MCC based signal recovery method has better robust property against various noises compared to other existing methods.

A comparative study of nonparametric methods for pattern recognition

NASA Technical Reports Server (NTRS)

Hahn, S. F.; Nelson, G. D.

1972-01-01

The applied research discussed in this report determines and compares the correct classification percentage of the nonparametric sign test, Wilcoxon's signed rank test, and K-class classifier with the performance of the Bayes classifier. The performance is determined for data which have Gaussian, Laplacian and Rayleigh probability density functions. The correct classification percentage is shown graphically for differences in modes and/or means of the probability density functions for four, eight and sixteen samples. The K-class classifier performed very well with respect to the other classifiers used. Since the K-class classifier is a nonparametric technique, it usually performed better than the Bayes classifier which assumes the data to be Gaussian even though it may not be. The K-class classifier has the advantage over the Bayes in that it works well with non-Gaussian data without having to determine the probability density function of the data. It should be noted that the data in this experiment was always unimodal.

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

NASA Astrophysics Data System (ADS)

Arendt, V.; Shalchi, A.

2018-06-01

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

SU-G-IeP3-08: Image Reconstruction for Scanning Imaging System Based On Shape-Modulated Point Spreading Function

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

Wang, Ruixing; Yang, LV; Xu, Kele

Purpose: Deconvolution is a widely used tool in the field of image reconstruction algorithm when the linear imaging system has been blurred by the imperfect system transfer function. However, due to the nature of Gaussian-liked distribution for point spread function (PSF), the components with coherent high frequency in the image are hard to restored in most of the previous scanning imaging system, even the relatively accurate PSF is acquired. We propose a novel method for deconvolution of images which are obtained by using shape-modulated PSF. Methods: We use two different types of PSF - Gaussian shape and donut shape -more » to convolute the original image in order to simulate the process of scanning imaging. By employing deconvolution of the two images with corresponding given priors, the image quality of the deblurred images are compared. Then we find the critical size of the donut shape compared with the Gaussian shape which has similar deconvolution results. Through calculation of tightened focusing process using radially polarized beam, such size of donut is achievable under same conditions. Results: The effects of different relative size of donut and Gaussian shapes are investigated. When the full width at half maximum (FWHM) ratio of donut and Gaussian shape is set about 1.83, similar resolution results are obtained through our deconvolution method. Decreasing the size of donut will favor the deconvolution method. A mask with both amplitude and phase modulation is used to create a donut-shaped PSF compared with the non-modulated Gaussian PSF. Donut with size smaller than our critical value is obtained. Conclusion: The utility of donutshaped PSF are proved useful and achievable in the imaging and deconvolution processing, which is expected to have potential practical applications in high resolution imaging for biological samples.« less

Gaussian windows: A tool for exploring multivariate data

NASA Technical Reports Server (NTRS)

Jaeckel, Louis A.

1990-01-01

Presented here is a method for interactively exploring a large set of quantitative multivariate data, in order to estimate the shape of the underlying density function. It is assumed that the density function is more or less smooth, but no other specific assumptions are made concerning its structure. The local structure of the data in a given region may be examined by viewing the data through a Gaussian window, whose location and shape are chosen by the user. A Gaussian window is defined by giving each data point a weight based on a multivariate Gaussian function. The weighted sample mean and sample covariance matrix are then computed, using the weights attached to the data points. These quantities are used to compute an estimate of the shape of the density function in the window region. The local structure of the data is described by a method similar to the method of principal components. By taking many such local views of the data, we can form an idea of the structure of the data set. The method is applicable in any number of dimensions. The method can be used to find and describe simple structural features such as peaks, valleys, and saddle points in the density function, and also extended structures in higher dimensions. With some practice, we can apply our geometrical intuition to these structural features in any number of dimensions, so that we can think about and describe the structure of the data. Since the computations involved are relatively simple, the method can easily be implemented on a small computer.

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.

Anisotropic non-gaussianity from rotational symmetry breaking excited initial states

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

Ashoorioon, Amjad; Casadio, Roberto; Dipartimento di Fisica e Astronomia, Alma Mater Università di Bologna,via Irnerio 46, 40126 Bologna

2016-12-01

If the initial quantum state of the primordial perturbations broke rotational invariance, that would be seen as a statistical anisotropy in the angular correlations of the cosmic microwave background radiation (CMBR) temperature fluctuations. This can be described by a general parameterisation of the initial conditions that takes into account the possible direction-dependence of both the amplitude and the phase of particle creation during inflation. The leading effect in the CMBR two-point function is typically a quadrupole modulation, whose coefficient is analytically constrained here to be |B|≲0.06. The CMBR three-point function then acquires enhanced non-gaussianity, especially for the local configurations. Inmore » the large occupation number limit, a distinctive prediction is a modulation of the non-gaussianity around a mean value depending on the angle that short and long wavelength modes make with the preferred direction. The maximal variations with respect to the mean value occur for the configurations which are coplanar with the preferred direction and the amplitude of the non-gaussianity increases (decreases) for the short wavelength modes aligned with (perpendicular to) the preferred direction. For a high scale model of inflation with maximally pumped up isotropic occupation and ϵ≃0.01 the difference between these two configurations is about 0.27, which could be detectable in the future. For purely anisotropic particle creation, the non-Gaussianity can be larger and its anisotropic feature very sharp. The non-gaussianity can then reach f{sub NL}∼30 in the preferred direction while disappearing from the correlations in the orthogonal plane.« less

Cigar-shaped quarkonia under strong magnetic field

NASA Astrophysics Data System (ADS)

Suzuki, Kei; Yoshida, Tetsuya

2016-03-01

Heavy quarkonia in a homogeneous magnetic field are analyzed by using a potential model with constituent quarks. To obtain anisotropic wave functions and corresponding eigenvalues, the cylindrical Gaussian expansion method is applied, where the anisotropic wave functions are expanded by a Gaussian basis in the cylindrical coordinates. Deformation of the wave functions and the mass shifts of the S-wave heavy quarkonia (ηc, J /ψ , ηc(2 S ), ψ (2 S ) and bottomonia) are examined for the wide range of external magnetic field. The spatial structure of the wave functions changes drastically as adjacent energy levels cross each other. Possible observables in heavy-ion collision experiments and future lattice QCD simulations are also discussed.

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

Balian, R., E-mail: roger.balian@cea.fr; Vénéroni, M.

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces themore » original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie–Poisson structure. At second order, the variational expression for two-time correlation functions separates–as does its exact counterpart–the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.« less

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.

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.

PAREMD: A parallel program for the evaluation of momentum space properties of atoms and molecules

NASA Astrophysics Data System (ADS)

Meena, Deep Raj; Gadre, Shridhar R.; Balanarayan, P.

2018-03-01

The present work describes a code for evaluating the electron momentum density (EMD), its moments and the associated Shannon information entropy for a multi-electron molecular system. The code works specifically for electronic wave functions obtained from traditional electronic structure packages such as GAMESS and GAUSSIAN. For the momentum space orbitals, the general expression for Gaussian basis sets in position space is analytically Fourier transformed to momentum space Gaussian basis functions. The molecular orbital coefficients of the wave function are taken as an input from the output file of the electronic structure calculation. The analytic expressions of EMD are evaluated over a fine grid and the accuracy of the code is verified by a normalization check and a numerical kinetic energy evaluation which is compared with the analytic kinetic energy given by the electronic structure package. Apart from electron momentum density, electron density in position space has also been integrated into this package. The program is written in C++ and is executed through a Shell script. It is also tuned for multicore machines with shared memory through OpenMP. The program has been tested for a variety of molecules and correlated methods such as CISD, Møller-Plesset second order (MP2) theory and density functional methods. For correlated methods, the PAREMD program uses natural spin orbitals as an input. The program has been benchmarked for a variety of Gaussian basis sets for different molecules showing a linear speedup on a parallel architecture.

The semantic Stroop effect: An ex-Gaussian analysis.

PubMed

White, Darcy; Risko, Evan F; Besner, Derek

2016-10-01

Previous analyses of the standard Stroop effect (which typically uses color words that form part of the response set) have documented effects on mean reaction times in hundreds of experiments in the literature. Less well known is the fact that ex-Gaussian analyses reveal that such effects are seen in (a) the mean of the normal distribution (mu), as well as in (b) the standard deviation of the normal distribution (sigma) and (c) the tail (tau). No ex-Gaussian analysis exists in the literature with respect to the semantically based Stroop effect (which contrasts incongruent color-associated words with, e.g., neutral controls). In the present experiments, we investigated whether the semantically based Stroop effect is also seen in the three ex-Gaussian parameters. Replicating previous reports, color naming was slower when the color was carried by an irrelevant (but incongruent) color-associated word (e.g., sky, tomato) than when the control items consisted of neutral words (e.g., keg, palace) in each of four experiments. An ex-Gaussian analysis revealed that this semantically based Stroop effect was restricted to the arithmetic mean and mu; no semantic Stroop effect was observed in tau. These data are consistent with the views (1) that there is a clear difference in the source of the semantic Stroop effect, as compared to the standard Stroop effect (evidenced by the presence vs. absence of an effect on tau), and (2) that interference associated with response competition on incongruent trials in tau is absent in the semantic Stroop effect.

Double Wigner distribution function of a first-order optical system with a hard-edge aperture.

PubMed

Pan, Weiqing

2008-01-01

The effect of an apertured optical system on Wigner distribution can be expressed as a superposition integral of the input Wigner distribution function and the double Wigner distribution function of the apertured optical system. By introducing a hard aperture function into a finite sum of complex Gaussian functions, the double Wigner distribution functions of a first-order optical system with a hard aperture outside and inside it are derived. As an example of application, the analytical expressions of the Wigner distribution for a Gaussian beam passing through a spatial filtering optical system with an internal hard aperture are obtained. The analytical results are also compared with the numerical integral results, and they show that the analytical results are proper and ascendant.

Comparative Analysis of Membership Function on Mamdani Fuzzy Inference System for Decision Making

NASA Astrophysics Data System (ADS)

harliana, Putri; Rahim, Robbi

2017-12-01

Membership function is a curve that shows mapping the input data points into the value or degree of membership which has an interval between 0 and 1. One way to get membership value is through a function approach. There are some membership functions can be used on mamdani fuzzy inference system. They are triangular, trapezoid, singleton, sigmoid, Gaussian, etc. In this paper only discuss three membership functions, are triangular, trapezoid and Gaussian. These three membership functions will be compared to see the difference in parameter values and results obtained. For case study in this paper is admission of students at popular school. There are three variable can be used, they are students’ report, IQ score and parents’ income. Which will then be created if-then rules.

Apertured averaged scintillation of fully and partially coherent Gaussian, annular Gaussian, flat toped and dark hollow beams

NASA Astrophysics Data System (ADS)

Eyyuboğlu, Halil T.

2015-03-01

Apertured averaged scintillation requires the evaluation of rather complicated irradiance covariance function. Here we develop a much simpler numerical method based on our earlier introduced semi-analytic approach. Using this method, we calculate aperture averaged scintillation of fully and partially coherent Gaussian, annular Gaussian flat topped and dark hollow beams. For comparison, the principles of equal source beam power and normalizing the aperture averaged scintillation with respect to received power are applied. Our results indicate that for fully coherent beams, upon adjusting the aperture sizes to capture 10 and 20% of the equal source power, Gaussian beam needs the largest aperture opening, yielding the lowest aperture average scintillation, whilst the opposite occurs for annular Gaussian and dark hollow beams. When assessed on the basis of received power normalized aperture averaged scintillation, fixed propagation distance and aperture size, annular Gaussian and dark hollow beams seem to have the lowest scintillation. Just like the case of point-like scintillation, partially coherent beams will offer less aperture averaged scintillation in comparison to fully coherent beams. But this performance improvement relies on larger aperture openings. Upon normalizing the aperture averaged scintillation with respect to received power, fully coherent beams become more advantageous than partially coherent ones.

Automatic image equalization and contrast enhancement using Gaussian mixture modeling.

PubMed

Celik, Turgay; Tjahjadi, Tardi

2012-01-01

In this paper, we propose an adaptive image equalization algorithm that automatically enhances the contrast in an input image. The algorithm uses the Gaussian mixture model to model the image gray-level distribution, and the intersection points of the Gaussian components in the model are used to partition the dynamic range of the image into input gray-level intervals. The contrast equalized image is generated by transforming the pixels' gray levels in each input interval to the appropriate output gray-level interval according to the dominant Gaussian component and the cumulative distribution function of the input interval. To take account of the hypothesis that homogeneous regions in the image represent homogeneous silences (or set of Gaussian components) in the image histogram, the Gaussian components with small variances are weighted with smaller values than the Gaussian components with larger variances, and the gray-level distribution is also used to weight the components in the mapping of the input interval to the output interval. Experimental results show that the proposed algorithm produces better or comparable enhanced images than several state-of-the-art algorithms. Unlike the other algorithms, the proposed algorithm is free of parameter setting for a given dynamic range of the enhanced image and can be applied to a wide range of image types.

Addendum to foundations of multidimensional wave field signal theory: Gaussian source function

NASA Astrophysics Data System (ADS)

Baddour, Natalie

2018-02-01

Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011)], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.

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.

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

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

Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu; Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089; Ghanem, Roger G., E-mail: ghanem@usc.edu

2017-07-15

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

NASA Astrophysics Data System (ADS)

Tsilifis, Panagiotis; Ghanem, Roger G.

2017-07-01

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Gaussian statistics for palaeomagnetic vectors

USGS Publications Warehouse

Love, J.J.; Constable, C.G.

2003-01-01

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Re??union, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Gaussian statistics for palaeomagnetic vectors

NASA Astrophysics Data System (ADS)

Love, J. J.; Constable, C. G.

2003-03-01

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimodal) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Réunion, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Stable Lévy motion with inverse Gaussian subordinator

NASA Astrophysics Data System (ADS)

Kumar, A.; Wyłomańska, A.; Gajda, J.

2017-09-01

In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.

Ince Gaussian beams in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Deng, Dongmei; Guo, Qi

2008-07-01

Based on the Snyder-Mitchell model that describes the beam propagation in strongly nonlocal nonlinear media, the close forms of Ince-Gaussian (IG) beams have been found. The transverse structures of the IG beams are described by the product of the Ince polynomials and the Gaussian function. Depending on the input power of the beams, the IG beams can be either a soliton state or a breather state. The IG beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian beams. The IG vortex beams can be constructed by a linear combination of the even and odd IG beams. The transverse intensity pattern of IG vortex beams consists of elliptic rings, whose number and ellipticity can be controlled, and a phase displaying a number of in-line vortices, each with a unitary topological charge. The analytical solutions of the IG beams are confirmed by the numerical simulations of the nonlocal nonlinear Schr\\rm \\ddot{o} dinger equation.

Sufficient condition for a quantum state to be genuinely quantum non-Gaussian

NASA Astrophysics Data System (ADS)

Happ, L.; Efremov, M. A.; Nha, H.; Schleich, W. P.

2018-02-01

We show that the expectation value of the operator \\hat{{ \\mathcal O }}\\equiv \\exp (-c{\\hat{x}}2)+\\exp (-c{\\hat{p}}2) defined by the position and momentum operators \\hat{x} and \\hat{p} with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states that cannot be represented as a mixture of Gaussian states. Our condition can be readily tested employing a highly efficient homodyne detection which unlike quantum-state tomography requires the measurements of only two orthogonal quadratures. We demonstrate that our method is even able to detect quantum non-Gaussian states with positive–definite Wigner functions. This situation cannot be addressed in terms of the negativity of the phase-space distribution. Moreover, we demonstrate that our condition can characterize quantum non-Gaussianity for the class of superposition states consisting of a vacuum and integer multiples of four photons under more than 50 % signal attenuation.

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.

AUTONOMOUS GAUSSIAN DECOMPOSITION

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

Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.

2015-04-15

We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocitymore » width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.« less

Recent advances in scalable non-Gaussian geostatistics: The generalized sub-Gaussian model

NASA Astrophysics Data System (ADS)

Guadagnini, Alberto; Riva, Monica; Neuman, Shlomo P.

2018-07-01

Geostatistical analysis has been introduced over half a century ago to allow quantifying seemingly random spatial variations in earth quantities such as rock mineral content or permeability. The traditional approach has been to view such quantities as multivariate Gaussian random functions characterized by one or a few well-defined spatial correlation scales. There is, however, mounting evidence that many spatially varying quantities exhibit non-Gaussian behavior over a multiplicity of scales. The purpose of this minireview is not to paint a broad picture of the subject and its treatment in the literature. Instead, we focus on very recent advances in the recognition and analysis of this ubiquitous phenomenon, which transcends hydrology and the Earth sciences, brought about largely by our own work. In particular, we use porosity data from a deep borehole to illustrate typical aspects of such scalable non-Gaussian behavior, describe a very recent theoretical model that (for the first time) captures all these behavioral aspects in a comprehensive manner, show how this allows generating random realizations of the quantity conditional on sampled values, point toward ways of incorporating scalable non-Gaussian behavior in hydrologic analysis, highlight the significance of doing so, and list open questions requiring further research.

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

A DS-UWB Cognitive Radio System Based on Bridge Function Smart Codes

NASA Astrophysics Data System (ADS)

Xu, Yafei; Hong, Sheng; Zhao, Guodong; Zhang, Fengyuan; di, Jinshan; Zhang, Qishan

This paper proposes a direct-sequence UWB Gaussian pulse of cognitive radio systems based on bridge function smart sequence matrix and the Gaussian pulse. As the system uses the spreading sequence code, that is the bridge function smart code sequence, the zero correlation zones (ZCZs) which the bridge function sequences' auto-correlation functions had, could reduce multipath fading of the pulse interference. The Modulated channel signal was sent into the IEEE 802.15.3a UWB channel. We analysis the ZCZs's inhibition to the interference multipath interference (MPI), as one of the main system sources interferences. The simulation in SIMULINK/MATLAB is described in detail. The result shows the system has better performance by comparison with that employing Walsh sequence square matrix, and it was verified by the formula in principle.

Estimating Mixture of Gaussian Processes by Kernel Smoothing

PubMed Central

Huang, Mian; Li, Runze; Wang, Hansheng; Yao, Weixin

2014-01-01

When the functional data are not homogeneous, e.g., there exist multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimation procedure for the Mixture of Gaussian Processes, to incorporate both functional and inhomogeneous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. The model is shown to be identifiable, and can be estimated efficiently by a combination of the ideas from EM algorithm, kernel regression, and functional principal component analysis. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset. PMID:24976675

Sparkle model for AM1 calculation of lanthanide complexes: improved parameters for europium.

PubMed

Rocha, Gerd B; Freire, Ricardo O; Da Costa, Nivan B; De Sá, Gilberto F; Simas, Alfredo M

2004-04-05

In the present work, we sought to improve our sparkle model for the calculation of lanthanide complexes, SMLC,in various ways: (i) inclusion of the europium atomic mass, (ii) reparametrization of the model within AM1 from a new response function including all distances of the coordination polyhedron for tris(acetylacetonate)(1,10-phenanthroline) europium(III), (iii) implementation of the model in the software package MOPAC93r2, and (iv) inclusion of spherical Gaussian functions in the expression which computes the core-core repulsion energy. The parametrization results indicate that SMLC II is superior to the previous version of the model because Gaussian functions proved essential if one requires a better description of the geometries of the complexes. In order to validate our parametrization, we carried out calculations on 96 europium(III) complexes, selected from Cambridge Structural Database 2003, and compared our predicted ground state geometries with the experimental ones. Our results show that this new parametrization of the SMLC model, with the inclusion of spherical Gaussian functions in the core-core repulsion energy, is better capable of predicting the Eu-ligand distances than the previous version. The unsigned mean error for all interatomic distances Eu-L, in all 96 complexes, which, for the original SMLC is 0.3564 A, is lowered to 0.1993 A when the model was parametrized with the inclusion of two Gaussian functions. Our results also indicate that this model is more applicable to europium complexes with beta-diketone ligands. As such, we conclude that this improved model can be considered a powerful tool for the study of lanthanide complexes and their applications, such as the modeling of light conversion molecular devices.

The non-Gaussian joint probability density function of slope and elevation for a nonlinear gravity wave field. [in ocean surface

NASA Technical Reports Server (NTRS)

Huang, N. E.; Long, S. R.; Bliven, L. F.; Tung, C.-C.

1984-01-01

On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared with a series of carefully controlled laboratory observations, and good agreement is noted. Furthermore, the laboratory wind wave field observations indicate that the capillary or capillary-gravity waves may not be the dominant components in determining the total roughness of the wave field. Thus, the analytic results, though derived specifically for the gravity waves, may have more general applications.

The Strategy for Time Dependent Quantum Mechanical Calculations Using a Gaussian Wave Packet Representation of the Wave Function.

DTIC Science & Technology

1985-01-01

a number of problems chosen so that the risk of SHM break-down wa.s minimized. A beautiful example is the absorption coefficient of a...the aporo~ cimation We consider here the case of one normalized Gaussian, to isolate the effects of LilA from those of the neglect of the *Interaction

Comparing Alternative Kernels for the Kernel Method of Test Equating: Gaussian, Logistic, and Uniform Kernels. Research Report. ETS RR-08-12

ERIC Educational Resources Information Center

Lee, Yi-Hsuan; von Davier, Alina A.

2008-01-01

The kernel equating method (von Davier, Holland, & Thayer, 2004) is based on a flexible family of equipercentile-like equating functions that use a Gaussian kernel to continuize the discrete score distributions. While the classical equipercentile, or percentile-rank, equating method carries out the continuization step by linear interpolation,…

When Does a Good Working Memory Counteract Proactive Interference? Surprising Evidence from a Probe Recognition Task

ERIC Educational Resources Information Center

Cowan, Nelson; Saults, J. Scott

2013-01-01

It is often proposed that individuals with high working memory span overcome proactive interference (PI) from previous trials, saving working memory for task-relevant items. We examined this hypothesis in word-list probe recognition. We found no difference in PI related to span. Instead, ex-Gaussian analysis of reaction time showed speed…

Dynamic heterogeneity and conditional statistics of non-Gaussian temperature fluctuations in turbulent thermal convection

NASA Astrophysics Data System (ADS)

He, Xiaozhou; Wang, Yin; Tong, Penger

2018-05-01

Non-Gaussian fluctuations with an exponential tail in their probability density function (PDF) are often observed in nonequilibrium steady states (NESSs) and one does not understand why they appear so often. Turbulent Rayleigh-Bénard convection (RBC) is an example of such a NESS, in which the measured PDF P (δ T ) of temperature fluctuations δ T in the central region of the flow has a long exponential tail. Here we show that because of the dynamic heterogeneity in RBC, the exponential PDF is generated by a convolution of a set of dynamics modes conditioned on a constant local thermal dissipation rate ɛ . The conditional PDF G (δ T |ɛ ) of δ T under a constant ɛ is found to be of Gaussian form and its variance σT2 for different values of ɛ follows an exponential distribution. The convolution of the two distribution functions gives rise to the exponential PDF P (δ T ) . This work thus provides a physical mechanism of the observed exponential distribution of δ T in RBC and also sheds light on the origin of non-Gaussian fluctuations in other NESSs.

Assessment of a Three-Dimensional Line-of-Response Probability Density Function System Matrix for PET

PubMed Central

Yao, Rutao; Ramachandra, Ranjith M.; Mahajan, Neeraj; Rathod, Vinay; Gunasekar, Noel; Panse, Ashish; Ma, Tianyu; Jian, Yiqiang; Yan, Jianhua; Carson, Richard E.

2012-01-01

To achieve optimal PET image reconstruction through better system modeling, we developed a system matrix that is based on the probability density function for each line of response (LOR-PDF). The LOR-PDFs are grouped by LOR-to-detector incident angles to form a highly compact system matrix. The system matrix was implemented in the MOLAR list mode reconstruction algorithm for a small animal PET scanner. The impact of LOR-PDF on reconstructed image quality was assessed qualitatively as well as quantitatively in terms of contrast recovery coefficient (CRC) and coefficient of variance (COV), and its performance was compared with a fixed Gaussian (iso-Gaussian) line spread function. The LOR-PDFs of 3 coincidence signal emitting sources, 1) ideal positron emitter that emits perfect back-to-back γ rays (γγ) in air; 2) fluorine-18 (18F) nuclide in water; and 3) oxygen-15 (15O) nuclide in water, were derived, and assessed with simulated and experimental phantom data. The derived LOR-PDFs showed anisotropic and asymmetric characteristics dependent on LOR-detector angle, coincidence emitting source, and the medium, consistent with common PET physical principles. The comparison of the iso-Gaussian function and LOR-PDF showed that: 1) without positron range and acolinearity effects, the LOR-PDF achieved better or similar trade-offs of contrast recovery and noise for objects of 4-mm radius or larger, and this advantage extended to smaller objects (e.g. 2-mm radius sphere, 0.6-mm radius hot-rods) at higher iteration numbers; and 2) with positron range and acolinearity effects, the iso-Gaussian achieved similar or better resolution recovery depending on the significance of positron range effect. We conclude that the 3-D LOR-PDF approach is an effective method to generate an accurate and compact system matrix. However, when used directly in expectation-maximization based list-mode iterative reconstruction algorithms such as MOLAR, its superiority is not clear. For this application, using an iso-Gaussian function in MOLAR is a simple but effective technique for PET reconstruction. PMID:23032702

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.

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.

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.

Complete ensemble local mean decomposition with adaptive noise and its application to fault diagnosis for rolling bearings

NASA Astrophysics Data System (ADS)

Wang, Lei; Liu, Zhiwen; Miao, Qiang; Zhang, Xin

2018-06-01

Mode mixing resulting from intermittent signals is an annoying problem associated with the local mean decomposition (LMD) method. Based on noise-assisted approach, ensemble local mean decomposition (ELMD) method alleviates the mode mixing issue of LMD to some degree. However, the product functions (PFs) produced by ELMD often contain considerable residual noise, and thus a relatively large number of ensemble trials are required to eliminate the residual noise. Furthermore, since different realizations of Gaussian white noise are added to the original signal, different trials may generate different number of PFs, making it difficult to take ensemble mean. In this paper, a novel method is proposed called complete ensemble local mean decomposition with adaptive noise (CELMDAN) to solve these two problems. The method adds a particular and adaptive noise at every decomposition stage for each trial. Moreover, a unique residue is obtained after separating each PF, and the obtained residue is used as input for the next stage. Two simulated signals are analyzed to illustrate the advantages of CELMDAN in comparison to ELMD and CEEMDAN. To further demonstrate the efficiency of CELMDAN, the method is applied to diagnose faults for rolling bearings in an experimental case and an engineering case. The diagnosis results indicate that CELMDAN can extract more fault characteristic information with less interference than ELMD.

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.

Fast Gaussian kernel learning for classification tasks based on specially structured global optimization.

PubMed

Zhong, Shangping; Chen, Tianshun; He, Fengying; Niu, Yuzhen

2014-09-01

For a practical pattern classification task solved by kernel methods, the computing time is mainly spent on kernel learning (or training). However, the current kernel learning approaches are based on local optimization techniques, and hard to have good time performances, especially for large datasets. Thus the existing algorithms cannot be easily extended to large-scale tasks. In this paper, we present a fast Gaussian kernel learning method by solving a specially structured global optimization (SSGO) problem. We optimize the Gaussian kernel function by using the formulated kernel target alignment criterion, which is a difference of increasing (d.i.) functions. Through using a power-transformation based convexification method, the objective criterion can be represented as a difference of convex (d.c.) functions with a fixed power-transformation parameter. And the objective programming problem can then be converted to a SSGO problem: globally minimizing a concave function over a convex set. The SSGO problem is classical and has good solvability. Thus, to find the global optimal solution efficiently, we can adopt the improved Hoffman's outer approximation method, which need not repeat the searching procedure with different starting points to locate the best local minimum. Also, the proposed method can be proven to converge to the global solution for any classification task. We evaluate the proposed method on twenty benchmark datasets, and compare it with four other Gaussian kernel learning methods. Experimental results show that the proposed method stably achieves both good time-efficiency performance and good classification performance. Copyright © 2014 Elsevier Ltd. All rights reserved.

Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L =1

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2008-03-01

In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L =1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

Energy and energy gradient matrix elements with N-particle explicitly correlated complex Gaussian basis functions with L=1.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2008-03-21

In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N-particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

Crossing statistics of laser light scattered through a nanofluid.

PubMed

Arshadi Pirlar, M; Movahed, S M S; Razzaghi, D; Karimzadeh, R

2017-09-01

In this paper, we investigate the crossing statistics of speckle patterns formed in the Fresnel diffraction region by a laser beam scattering through a nanofluid. We extend zero-crossing statistics to assess the dynamical properties of the nanofluid. According to the joint probability density function of laser beam fluctuation and its time derivative, the theoretical frameworks for Gaussian and non-Gaussian regimes are revisited. We count the number of crossings not only at zero level but also for all available thresholds to determine the average speed of moving particles. Using a probabilistic framework in determining crossing statistics, a priori Gaussianity is not essentially considered; therefore, even in the presence of deviation from Gaussian fluctuation, this modified approach is capable of computing relevant quantities, such as mean value of speed, more precisely. Generalized total crossing, which represents the weighted summation of crossings for all thresholds to quantify small deviation from Gaussian statistics, is introduced. This criterion can also manipulate the contribution of noises and trends to infer reliable physical quantities. The characteristic time scale for having successive crossings at a given threshold is defined. In our experimental setup, we find that increasing sample temperature leads to more consistency between Gaussian and perturbative non-Gaussian predictions. The maximum number of crossings does not necessarily occur at mean level, indicating that we should take into account other levels in addition to zero level to achieve more accurate assessments.

Efficient statistically accurate algorithms for the Fokker-Planck equation in large dimensions

NASA Astrophysics Data System (ADS)

Chen, Nan; Majda, Andrew J.

2018-02-01

Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing the fat tailed highly intermittent probability density functions (PDFs) of complex systems in turbulence, neuroscience and excitable media. In this article, efficient statistically accurate algorithms are developed for solving both the transient and the equilibrium solutions of Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures. The algorithms involve a hybrid strategy that requires only a small number of ensembles. Here, a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious non-parametric Gaussian kernel density estimation in the remaining low-dimensional subspace. Particularly, the parametric method provides closed analytical formulae for determining the conditional Gaussian distributions in the high-dimensional subspace and is therefore computationally efficient and accurate. The full non-Gaussian PDF of the system is then given by a Gaussian mixture. Different from traditional particle methods, each conditional Gaussian distribution here covers a significant portion of the high-dimensional PDF. Therefore a small number of ensembles is sufficient to recover the full PDF, which overcomes the curse of dimensionality. Notably, the mixture distribution has significant skill in capturing the transient behavior with fat tails of the high-dimensional non-Gaussian PDFs, and this facilitates the algorithms in accurately describing the intermittency and extreme events in complex turbulent systems. It is shown in a stringent set of test problems that the method only requires an order of O (100) ensembles to successfully recover the highly non-Gaussian transient PDFs in up to 6 dimensions with only small errors.

Invariant polarimetric contrast parameters of light with Gaussian fluctuations in three dimensions.

PubMed

Réfrégier, Philippe; Roche, Muriel; Goudail, François

2006-01-01

We propose a rigorous definition of the minimal set of parameters that characterize the difference between two partially polarized states of light whose electric fields vary in three dimensions with Gaussian fluctuations. Although two such states are a priori defined by eighteen parameters, we demonstrate that the performance of processing tasks such as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by three scalar functions of these parameters. These functions define a "polarimetric contrast" that simplifies the analysis and the specification of processing techniques on polarimetric signals and images. This result can also be used to analyze the definition of the degree of polarization of a three-dimensional state of light with Gaussian fluctuations in comparison, with respect to its polarimetric contrast parameters, with a totally depolarized light. We show that these contrast parameters are a simple function of the degrees of polarization previously proposed by Barakat [Opt. Acta 30, 1171 (1983)] and Setälä et al. [Phys. Rev. Lett. 88, 123902 (2002)]. Finally, we analyze the dimension of the set of contrast parameters in different particular situations.

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.

How to calculate H3 better.

PubMed

Pavanello, Michele; Tung, Wei-Cheng; Adamowicz, Ludwik

2009-11-14

Efficient optimization of the basis set is key to achieving a very high accuracy in variational calculations of molecular systems employing basis functions that are explicitly dependent on the interelectron distances. In this work we present a method for a systematic enlargement of basis sets of explicitly correlated functions based on the iterative-complement-interaction approach developed by Nakatsuji [Phys. Rev. Lett. 93, 030403 (2004)]. We illustrate the performance of the method in the variational calculations of H(3) where we use explicitly correlated Gaussian functions with shifted centers. The total variational energy (-1.674 547 421 Hartree) and the binding energy (-15.74 cm(-1)) obtained in the calculation with 1000 Gaussians are the most accurate results to date.

Characterization, parameter estimation, and aircraft response statistics of atmospheric turbulence

NASA Technical Reports Server (NTRS)

Mark, W. D.

1981-01-01

A nonGaussian three component model of atmospheric turbulence is postulated that accounts for readily observable features of turbulence velocity records, their autocorrelation functions, and their spectra. Methods for computing probability density functions and mean exceedance rates of a generic aircraft response variable are developed using nonGaussian turbulence characterizations readily extracted from velocity recordings. A maximum likelihood method is developed for optimal estimation of the integral scale and intensity of records possessing von Karman transverse of longitudinal spectra. Formulas for the variances of such parameter estimates are developed. The maximum likelihood and least-square approaches are combined to yield a method for estimating the autocorrelation function parameters of a two component model for turbulence.

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.

Probing the statistics of primordial fluctuations and their evolution

NASA Technical Reports Server (NTRS)

Gaztanaga, Enrique; Yokoyama, Jun'ichi

1993-01-01

The statistical distribution of fluctuations on various scales is analyzed in terms of the counts in cells of smoothed density fields, using volume-limited samples of galaxy redshift catalogs. It is shown that the distribution on large scales, with volume average of the two-point correlation function of the smoothed field less than about 0.05, is consistent with Gaussian. Statistics are shown to agree remarkably well with the negative binomial distribution, which has hierarchial correlations and a Gaussian behavior at large scales. If these observed properties correspond to the matter distribution, they suggest that our universe started with Gaussian fluctuations and evolved keeping hierarchial form.

Rational-operator-based depth-from-defocus approach to scene reconstruction.

PubMed

Li, Ang; Staunton, Richard; Tjahjadi, Tardi

2013-09-01

This paper presents a rational-operator-based approach to depth from defocus (DfD) for the reconstruction of three-dimensional scenes from two-dimensional images, which enables fast DfD computation that is independent of scene textures. Two variants of the approach, one using the Gaussian rational operators (ROs) that are based on the Gaussian point spread function (PSF) and the second based on the generalized Gaussian PSF, are considered. A novel DfD correction method is also presented to further improve the performance of the approach. Experimental results are considered for real scenes and show that both approaches outperform existing RO-based methods.

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.

Numerical modeling of macrodispersion in heterogeneous media: a comparison of multi-Gaussian and non-multi-Gaussian models

NASA Astrophysics Data System (ADS)

Wen, Xian-Huan; Gómez-Hernández, J. Jaime

1998-03-01

The macrodispersion of an inert solute in a 2-D heterogeneous porous media is estimated numerically in a series of fields of varying heterogeneity. Four different random function (RF) models are used to model log-transmissivity (ln T) spatial variability, and for each of these models, ln T variance is varied from 0.1 to 2.0. The four RF models share the same univariate Gaussian histogram and the same isotropic covariance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme values (both high and low) are spatially uncorrelated. The other three models are non-multi-Gaussian: model B with high connectivity of high extreme values, model C with high connectivity of low extreme values, and model D with high connectivities of both high and low extreme values. Residence time distributions (RTDs) and macrodispersivities (longitudinal and transverse) are computed on ln T fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RTDs and macrodispersivities for the multi-Gaussian model are in good agreement with analytically derived values using first-order theories for log-transmissivity variance up to 2.0. The results from the non-multi-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when ln T variance is small. RTDs in non-multi-Gaussian realizations with high connectivity at high extreme values display earlier breakthrough than in multi-Gaussian realizations, whereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian realizations are, in general, larger than in the multi-Gaussian ones, while transverse macrodispersivities in the non-multi-Gaussian realizations can be larger or smaller than in the multi-Gaussian ones depending on the type of connectivity at extreme values. Comparing the numerical results for different flow directions, it is confirmed that macrodispersivities in multi-Gaussian realizations with isotropic spatial correlation are not flow direction-dependent. Macrodispersivities in the non-multi-Gaussian realizations, however, are flow direction-dependent although the covariance of ln T is isotropic (the same for all four models). It is important to account for high connectivities at extreme transmissivity values, a likely situation in some geological formations. Some of the discrepancies between first-order-based analytical results and field-scale tracer test data may be due to the existence of highly connected paths of extreme conductivity values.

Magnetism in all-carbon nanostructures with negative Gaussian curvature.

PubMed

Park, Noejung; Yoon, Mina; Berber, Savas; Ihm, Jisoon; Osawa, Eiji; Tománek, David

2003-12-05

We apply the ab initio spin density functional theory to study magnetism in all-carbon nanostructures. We find that particular systems, which are related to schwarzite and contain no undercoordinated carbon atoms, carry a net magnetic moment in the ground state. We postulate that, in this and other nonalternant aromatic systems with negative Gaussian curvature, unpaired spins can be introduced by sterically protected carbon radicals.

Quantum Monte Carlo calculations of NiO

NASA Astrophysics Data System (ADS)

Maezono, Ryo; Towler, Mike D.; Needs, Richard. J.

2008-03-01

We describe variational and diffusion quantum Monte Carlo (VMC and DMC) calculations [1] of NiO using a 1024-electron simulation cell. We have used a smooth, norm-conserving, Dirac-Fock pseudopotential [2] in our work. Our trial wave functions were of Slater-Jastrow form, containing orbitals generated in Gaussian-basis UHF periodic calculations. Jastrow factor is optimized using variance minimization with optimized cutoff lengths using the same scheme as our previous work. [4] We apply the lattice regulated scheme [5] to evaluate non-local pseudopotentials in DMC and find the scheme improves the smoothness of the energy-volume curve. [1] CASINO ver.2.1 User Manual, University of Cambridge (2007). [2] J.R. Trail et.al., J. Chem. Phys. 122, 014112 (2005). [3] CRYSTAL98 User's Manual, University of Torino (1998). [4] Ryo Maezono et.al., Phys. Rev. Lett., 98, 025701 (2007). [5] Michele Casula, Phys. Rev. B 74, 161102R (2006).

Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers

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

Stanke, Monika, E-mail: monika@fizyka.umk.pl; Palikot, Ewa, E-mail: epalikot@doktorant.umk.pl; Adamowicz, Ludwik, E-mail: ludwik@email.arizona.edu

2016-05-07

Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H{sub 2} and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.

Bivariate sub-Gaussian model for stock index returns

NASA Astrophysics Data System (ADS)

Jabłońska-Sabuka, Matylda; Teuerle, Marek; Wyłomańska, Agnieszka

2017-11-01

Financial time series are commonly modeled with methods assuming data normality. However, the real distribution can be nontrivial, also not having an explicitly formulated probability density function. In this work we introduce novel parameter estimation and high-powered distribution testing methods which do not rely on closed form densities, but use the characteristic functions for comparison. The approach applied to a pair of stock index returns demonstrates that such a bivariate vector can be a sample coming from a bivariate sub-Gaussian distribution. The methods presented here can be applied to any nontrivially distributed financial data, among others.

An empirical analysis of the distribution of the duration of overshoots in a stationary gaussian stochastic process

NASA Technical Reports Server (NTRS)

Parrish, R. S.; Carter, M. C.

1974-01-01

This analysis utilizes computer simulation and statistical estimation. Realizations of stationary gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrelation parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters was estimated. Thus, given the autocorrelation parameter, crossing level, mean, and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time was calculated.

The analysis of ensembles of moderately saturated interstellar lines

NASA Technical Reports Server (NTRS)

Jenkins, E. B.

1986-01-01

It is shown that the combined equivalent widths for a large population of Gaussian-like interstellar line components, each with different central optical depths tau(0) and velocity dispersions b, exhibit a curve of growth (COG) which closely mimics that of a single, pure Gaussian distribution in velocity. Two parametric distributions functions for the line populations are considered: a bivariate Gaussian for tau(0) and b and a power law distribution for tau(0) combined with a Gaussian dispersion for b. First, COGs for populations having an extremely large number of nonoverlapping components are derived, and the implications are shown by focusing on the doublet-ratio analysis for a pair of lines whose f-values differ by a factor of two. The consequences of having, instead of an almost infinite number of lines, a relatively small collection of components added together for each member of a doublet are examined. The theory of how the equivalent widths grow for populations of overlapping Gaussian profiles is developed. Examples of the composite COG analysis applied to existing collections of high-resolution interstellar line data are presented.

The formation of cosmic structure in a texture-seeded cold dark matter cosmogony

NASA Technical Reports Server (NTRS)

Gooding, Andrew K.; Park, Changbom; Spergel, David N.; Turok, Neil; Gott, Richard, III

1992-01-01

The growth of density fluctuations induced by global texture in an Omega = 1 cold dark matter (CDM) cosmogony is calculated. The resulting power spectra are in good agreement with each other, with more power on large scales than in the standard inflation plus CDM model. Calculation of related statistics (two-point correlation functions, mass variances, cosmic Mach number) indicates that the texture plus CDM model compares more favorably than standard CDM with observations of large-scale structure. Texture produces coherent velocity fields on large scales, as observed. Excessive small-scale velocity dispersions, and voids less empty than those observed may be remedied by including baryonic physics. The topology of the cosmic structure agrees well with observation. The non-Gaussian texture induced density fluctuations lead to earlier nonlinear object formation than in Gaussian models and may also be more compatible with recent evidence that the galaxy density field is non-Gaussian on large scales. On smaller scales the density field is strongly non-Gaussian, but this appears to be primarily due to nonlinear gravitational clustering. The velocity field on smaller scales is surprisingly Gaussian.

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.

A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment.

PubMed

Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong

2016-05-13

In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student's t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods.

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.

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

Nunes, Rafael C.; Abreu, Everton M.C.; Neto, Jorge Ananias

Based on the relationship between thermodynamics and gravity we propose, with the aid of Verlinde's formalism, an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe. This description takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there through non-gaussian statistical theories proposed by Tsallis and Kaniadakis. The effect of these non-gaussian statistics in the cosmological context is to change the strength of the gravitational constant. In this paper, we consider the w CDM model modified by the non-gaussian statistics and investigate the compatibility of these non-gaussian modificationmore » with the cosmological observations. In order to analyze in which extend the cosmological data constrain these non-extensive statistics, we will use type Ia supernovae, baryon acoustic oscillations, Hubble expansion rate function and the linear growth of matter density perturbations data. We show that Tsallis' statistics is favored at 1σ confidence level.« less

A new method for the identification of non-Gaussian line profiles in elliptical galaxies

NASA Technical Reports Server (NTRS)

Van Der Marel, Roeland P.; Franx, Marijn

1993-01-01

A new parameterization for the line profiles of elliptical galaxies, the Gauss-Hermite series, is proposed. This approach expands the line profile as a sum of orthogonal functions which minimizes the correlations between the errors in the parameters of the fit. This method also make use of the fact that Gaussians provide good low-order fits to observed line profiles. The method yields measurements of the line strength, mean radial velocity, and the velocity dispersion as well as two extra parameters, h3 and h4, that measure asymmetric and symmetric deviations of the line profiles from a Gaussian, respectively. The new method was used to derive profiles for three elliptical galaxies which all have asymmetric line profiles on the major axis with symmetric deviations from a Gaussian. Results confirm that elliptical galaxies have complex structures due to their complex formation history.

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.

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 NEW METHOD OF PEAK DETECTION FOR ANALYSIS OF COMPREHENSIVE TWO-DIMENSIONAL GAS CHROMATOGRAPHY MASS SPECTROMETRY DATA.

PubMed

Kim, Seongho; Ouyang, Ming; Jeong, Jaesik; Shen, Changyu; Zhang, Xiang

2014-06-01

We develop a novel peak detection algorithm for the analysis of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (GC×GC-TOF MS) data using normal-exponential-Bernoulli (NEB) and mixture probability models. The algorithm first performs baseline correction and denoising simultaneously using the NEB model, which also defines peak regions. Peaks are then picked using a mixture of probability distribution to deal with the co-eluting peaks. Peak merging is further carried out based on the mass spectral similarities among the peaks within the same peak group. The algorithm is evaluated using experimental data to study the effect of different cut-offs of the conditional Bayes factors and the effect of different mixture models including Poisson, truncated Gaussian, Gaussian, Gamma, and exponentially modified Gaussian (EMG) distributions, and the optimal version is introduced using a trial-and-error approach. We then compare the new algorithm with two existing algorithms in terms of compound identification. Data analysis shows that the developed algorithm can detect the peaks with lower false discovery rates than the existing algorithms, and a less complicated peak picking model is a promising alternative to the more complicated and widely used EMG mixture models.

When does a good working memory counteract proactive interference? Surprising evidence from a probe recognition task.

PubMed

Cowan, Nelson; Saults, J Scott

2013-02-01

It is often proposed that individuals with high working memory span overcome proactive interference (PI) from previous trials, saving working memory for task-relevant items. We examined this hypothesis in word-list probe recognition. We found no difference in PI related to span. Instead, ex-gaussian analysis of reaction time showed speed advantages for high spans specific to short lists (3 or 4 items) but absent from longer lists (6 or 8 items). We suggest that high-span advantages in reaction time are based on finesse during easy trials, not on overcoming PI. 2013 APA, all rights reserved

Theoretical analysis of non-Gaussian heterogeneity effects on subsurface flow and transport

NASA Astrophysics Data System (ADS)

Riva, Monica; Guadagnini, Alberto; Neuman, Shlomo P.

2017-04-01

Much of the stochastic groundwater literature is devoted to the analysis of flow and transport in Gaussian or multi-Gaussian log hydraulic conductivity (or transmissivity) fields, Y(x)=ln\\func K(x) (x being a position vector), characterized by one or (less frequently) a multiplicity of spatial correlation scales. Yet Y and many other variables and their (spatial or temporal) increments, ΔY, are known to be generally non-Gaussian. One common manifestation of non-Gaussianity is that whereas frequency distributions of Y often exhibit mild peaks and light tails, those of increments ΔY are generally symmetric with peaks that grow sharper, and tails that become heavier, as separation scale or lag between pairs of Y values decreases. A statistical model that captures these disparate, scale-dependent distributions of Y and ΔY in a unified and consistent manner has been recently proposed by us. This new "generalized sub-Gaussian (GSG)" model has the form Y(x)=U(x)G(x) where G(x) is (generally, but not necessarily) a multiscale Gaussian random field and U(x) is a nonnegative subordinator independent of G. The purpose of this paper is to explore analytically, in an elementary manner, lead-order effects that non-Gaussian heterogeneity described by the GSG model have on the stochastic description of flow and transport. Recognizing that perturbation expansion of hydraulic conductivity K=eY diverges when Y is sub-Gaussian, we render the expansion convergent by truncating Y's domain of definition. We then demonstrate theoretically and illustrate by way of numerical examples that, as the domain of truncation expands, (a) the variance of truncated Y (denoted by Yt) approaches that of Y and (b) the pdf (and thereby moments) of Yt increments approach those of Y increments and, as a consequence, the variogram of Yt approaches that of Y. This in turn guarantees that perturbing Kt=etY to second order in σYt (the standard deviation of Yt) yields results which approach those we obtain upon perturbing K=eY to second order in σY even as the corresponding series diverges. Our analysis is rendered mathematically tractable by considering mean-uniform steady state flow in an unbounded, two-dimensional domain of mildly heterogeneous Y with a single-scale function G having an isotropic exponential covariance. Results consist of expressions for (a) lead-order autocovariance and cross-covariance functions of hydraulic head, velocity, and advective particle displacement and (b) analogues of preasymptotic as well as asymptotic Fickian dispersion coefficients. We compare these theoretically and graphically with corresponding expressions developed in the literature for Gaussian Y. We find the former to differ from the latter by a factor k = /2 ( <> denoting ensemble expectation) and the GSG covariance of longitudinal velocity to contain an additional nugget term depending on this same factor. In the limit as Y becomes Gaussian, k reduces to one and the nugget term drops out.