Sample records for gaussian distribution function
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Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic.
Yokoyama, Jun'ichi
2014-01-01
After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student's t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case.
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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
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Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic
YOKOYAMA, Jun’ichi
2014-01-01
After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student’s t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case. PMID:25504231
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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.
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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.
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Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system.
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.
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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.
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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…
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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.
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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.
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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.
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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.
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Assessment of parametric uncertainty for groundwater reactive transport modeling,
Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun
2014-01-01
The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.
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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.
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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
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Double Wigner distribution function of a first-order optical system with a hard-edge aperture.
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.
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Non-Gaussian probabilistic MEG source localisation based on kernel density estimation☆
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
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Gaussian statistics for palaeomagnetic vectors
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.
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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.
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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.
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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.
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A Gaussian Model-Based Probabilistic Approach for Pulse Transit Time Estimation.
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.
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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.
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NASA Astrophysics Data System (ADS)
Schwartz, Craig R.; Thelen, Brian J.; Kenton, Arthur C.
1995-06-01
A statistical parametric multispectral sensor performance model was developed by ERIM to support mine field detection studies, multispectral sensor design/performance trade-off studies, and target detection algorithm development. The model assumes target detection algorithms and their performance models which are based on data assumed to obey multivariate Gaussian probability distribution functions (PDFs). The applicability of these algorithms and performance models can be generalized to data having non-Gaussian PDFs through the use of transforms which convert non-Gaussian data to Gaussian (or near-Gaussian) data. An example of one such transform is the Box-Cox power law transform. In practice, such a transform can be applied to non-Gaussian data prior to the introduction of a detection algorithm that is formally based on the assumption of multivariate Gaussian data. This paper presents an extension of these techniques to the case where the joint multivariate probability density function of the non-Gaussian input data is known, and where the joint estimate of the multivariate Gaussian statistics, under the Box-Cox transform, is desired. The jointly estimated multivariate Gaussian statistics can then be used to predict the performance of a target detection algorithm which has an associated Gaussian performance model.
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Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian.
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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Clark, Jeremy S C; Kaczmarczyk, Mariusz; Mongiało, Zbigniew; Ignaczak, Paweł; Czajkowski, Andrzej A; Klęsk, Przemysław; Ciechanowicz, Andrzej
2013-08-01
Gompertz-related distributions have dominated mortality studies for 187 years. However, nonrelated distributions also fit well to mortality data. These compete with the Gompertz and Gompertz-Makeham data when applied to data with varying extents of truncation, with no consensus as to preference. In contrast, Gaussian-related distributions are rarely applied, despite the fact that Lexis in 1879 suggested that the normal distribution itself fits well to the right of the mode. Study aims were therefore to compare skew-t fits to Human Mortality Database data, with Gompertz-nested distributions, by implementing maximum likelihood estimation functions (mle2, R package bbmle; coding given). Results showed skew-t fits obtained lower Bayesian information criterion values than Gompertz-nested distributions, applied to low-mortality country data, including 1711 and 1810 cohorts. As Gaussian-related distributions have now been found to have almost universal application to error theory, one conclusion could be that a Gaussian-related distribution might replace Gompertz-related distributions as the basis for mortality studies.
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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.
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Cheng, Mingjian; Guo, Ya; Li, Jiangting; Zheng, Xiaotong; Guo, Lixin
2018-04-20
We introduce an alternative distribution to the gamma-gamma (GG) distribution, called inverse Gaussian gamma (IGG) distribution, which can efficiently describe moderate-to-strong irradiance fluctuations. The proposed stochastic model is based on a modulation process between small- and large-scale irradiance fluctuations, which are modeled by gamma and inverse Gaussian distributions, respectively. The model parameters of the IGG distribution are directly related to atmospheric parameters. The accuracy of the fit among the IGG, log-normal, and GG distributions with the experimental probability density functions in moderate-to-strong turbulence are compared, and results indicate that the newly proposed IGG model provides an excellent fit to the experimental data. As the receiving diameter is comparable with the atmospheric coherence radius, the proposed IGG model can reproduce the shape of the experimental data, whereas the GG and LN models fail to match the experimental data. The fundamental channel statistics of a free-space optical communication system are also investigated in an IGG-distributed turbulent atmosphere, and a closed-form expression for the outage probability of the system is derived with Meijer's G-function.
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Leading non-Gaussian corrections for diffusion orientation distribution function.
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.
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Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function
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
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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.
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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.
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Theoretical study of sum-frequency vibrational spectroscopy on limonene surface
DOE Office of Scientific and Technical Information (OSTI.GOV)
Zheng, Ren-Hui, E-mail: zrh@iccas.ac.cn; Liu, Hao; Jing, Yuan-Yuan
2014-03-14
By combining molecule dynamics (MD) simulation and quantum chemistry computation, we calculate the surface sum-frequency vibrational spectroscopy (SFVS) of R-limonene molecules at the gas-liquid interface for SSP, PPP, and SPS polarization combinations. The distributions of the Euler angles are obtained using MD simulation, the ψ-distribution is between isotropic and Gaussian. Instead of the MD distributions, different analytical distributions such as the δ-function, Gaussian and isotropic distributions are applied to simulate surface SFVS. We find that different distributions significantly affect the absolute SFVS intensity and also influence on relative SFVS intensity, and the δ-function distribution should be used with caution whenmore » the orientation distribution is broad. Furthermore, the reason that the SPS signal is weak in reflected arrangement is discussed.« less
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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.
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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
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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.
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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.
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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.
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Evidence for criticality in financial data
NASA Astrophysics Data System (ADS)
Ruiz, G.; de Marcos, A. F.
2018-01-01
We provide evidence that cumulative distributions of absolute normalized returns for the 100 American companies with the highest market capitalization, uncover a critical behavior for different time scales Δt. Such cumulative distributions, in accordance with a variety of complex - and financial - systems, can be modeled by the cumulative distribution functions of q-Gaussians, the distribution function that, in the context of nonextensive statistical mechanics, maximizes a non-Boltzmannian entropy. These q-Gaussians are characterized by two parameters, namely ( q, β), that are uniquely defined by Δt. From these dependencies, we find a monotonic relationship between q and β, which can be seen as evidence of criticality. We numerically determine the various exponents which characterize this criticality.
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NASA Astrophysics Data System (ADS)
Krohn, Olivia; Armbruster, Aaron; Gao, Yongsheng; Atlas Collaboration
2017-01-01
Software tools developed for the purpose of modeling CERN LHC pp collision data to aid in its interpretation are presented. Some measurements are not adequately described by a Gaussian distribution; thus an interpretation assuming Gaussian uncertainties will inevitably introduce bias, necessitating analytical tools to recreate and evaluate non-Gaussian features. One example is the measurements of Higgs boson production rates in different decay channels, and the interpretation of these measurements. The ratios of data to Standard Model expectations (μ) for five arbitrary signals were modeled by building five Poisson distributions with mixed signal contributions such that the measured values of μ are correlated. Algorithms were designed to recreate probability distribution functions of μ as multi-variate Gaussians, where the standard deviation (σ) and correlation coefficients (ρ) are parametrized. There was good success with modeling 1-D likelihood contours of μ, and the multi-dimensional distributions were well modeled within 1- σ but the model began to diverge after 2- σ due to unmerited assumptions in developing ρ. Future plans to improve the algorithms and develop a user-friendly analysis package will also be discussed. NSF International Research Experiences for Students
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NASA Technical Reports Server (NTRS)
Leybold, H. A.
1971-01-01
Random numbers were generated with the aid of a digital computer and transformed such that the probability density function of a discrete random load history composed of these random numbers had one of the following non-Gaussian distributions: Poisson, binomial, log-normal, Weibull, and exponential. The resulting random load histories were analyzed to determine their peak statistics and were compared with cumulative peak maneuver-load distributions for fighter and transport aircraft in flight.
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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
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Some Modified Integrated Squared Error Procedures for Multivariate Normal Data.
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
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Gaussian Process Interpolation for Uncertainty Estimation in Image Registration
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
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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.
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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
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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.
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A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing
NASA Astrophysics Data System (ADS)
Zhou, Yuan; Rangarajan, Anand; Gader, Paul D.
2018-05-01
Hyperspectral unmixing while considering endmember variability is usually performed by the normal compositional model (NCM), where the endmembers for each pixel are assumed to be sampled from unimodal Gaussian distributions. However, in real applications, the distribution of a material is often not Gaussian. In this paper, we use Gaussian mixture models (GMM) to represent the endmember variability. We show, given the GMM starting premise, that the distribution of the mixed pixel (under the linear mixing model) is also a GMM (and this is shown from two perspectives). The first perspective originates from the random variable transformation and gives a conditional density function of the pixels given the abundances and GMM parameters. With proper smoothness and sparsity prior constraints on the abundances, the conditional density function leads to a standard maximum a posteriori (MAP) problem which can be solved using generalized expectation maximization. The second perspective originates from marginalizing over the endmembers in the GMM, which provides us with a foundation to solve for the endmembers at each pixel. Hence, our model can not only estimate the abundances and distribution parameters, but also the distinct endmember set for each pixel. We tested the proposed GMM on several synthetic and real datasets, and showed its potential by comparing it to current popular methods.
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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.
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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
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Automatic image equalization and contrast enhancement using Gaussian mixture modeling.
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.
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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.
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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%.
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Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong
2016-01-01
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. PMID:27187405
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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.
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The force distribution probability function for simple fluids by density functional theory.
Rickayzen, G; Heyes, D M
2013-02-28
Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.
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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.
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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.
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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.
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NASA Astrophysics Data System (ADS)
Yan, Qiushuang; Zhang, Jie; Fan, Chenqing; Wang, Jing; Meng, Junmin
2018-01-01
The collocated normalized radar backscattering cross-section measurements from the Global Precipitation Measurement (GPM) Ku-band precipitation radar (KuPR) and the winds from the moored buoys are used to study the effect of different sea-surface slope probability density functions (PDFs), including the Gaussian PDF, the Gram-Charlier PDF, and the Liu PDF, on the geometrical optics (GO) model predictions of the radar backscatter at low incidence angles (0 deg to 18 deg) at different sea states. First, the peakedness coefficient in the Liu distribution is determined using the collocations at the normal incidence angle, and the results indicate that the peakedness coefficient is a nonlinear function of the wind speed. Then, the performance of the modified Liu distribution, i.e., Liu distribution using the obtained peakedness coefficient estimate; the Gaussian distribution; and the Gram-Charlier distribution is analyzed. The results show that the GO model predictions with the modified Liu distribution agree best with the KuPR measurements, followed by the predictions with the Gaussian distribution, while the predictions with the Gram-Charlier distribution have larger differences as the total or the slick filtered, not the radar filtered, probability density is included in the distribution. The best-performing distribution changes with incidence angle and changes with wind speed.
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NASA Technical Reports Server (NTRS)
Mashiku, Alinda; Garrison, James L.; Carpenter, J. Russell
2012-01-01
The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.
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Efficiency-enhanced photon sieve using Gaussian/overlapping distribution of pinholes
DOE Office of Scientific and Technical Information (OSTI.GOV)
Sabatyan, A.; Mirzaie, S.
2011-04-10
A class of photon sieve is introduced whose structure is based on the overlapping pinholes in the innermost zones. This kind of distribution is produced by, for example, a particular form of Gaussian function. The focusing property of the proposed model was examined theoretically and experimentally. It is shown that under He-Ne laser and white light illumination, the focal spot size of this novel structure has considerably smaller FWHM than a photon sieve with randomly distributed pinholes and a Fresnel zone plate. In addition, secondary maxima have been suppressed effectively.
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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.
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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.
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Extended q -Gaussian and q -exponential distributions from gamma random variables
NASA Astrophysics Data System (ADS)
Budini, Adrián A.
2015-05-01
The family of q -Gaussian and q -exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q -Gaussian and q -exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q -Gaussian and modified q -exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.
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NASA Astrophysics Data System (ADS)
Huang, D.; Liu, Y.
2014-12-01
The effects of subgrid cloud variability on grid-average microphysical rates and radiative fluxes are examined by use of long-term retrieval products at the Tropical West Pacific (TWP), Southern Great Plains (SGP), and North Slope of Alaska (NSA) sites of the Department of Energy's Atmospheric Radiation Measurement (ARM) Program. Four commonly used distribution functions, the truncated Gaussian, Gamma, lognormal, and Weibull distributions, are constrained to have the same mean and standard deviation as observed cloud liquid water content. The PDFs are then used to upscale relevant physical processes to obtain grid-average process rates. It is found that the truncated Gaussian representation results in up to 30% mean bias in autoconversion rate whereas the mean bias for the lognormal representation is about 10%. The Gamma and Weibull distribution function performs the best for the grid-average autoconversion rate with the mean relative bias less than 5%. For radiative fluxes, the lognormal and truncated Gaussian representations perform better than the Gamma and Weibull representations. The results show that the optimal choice of subgrid cloud distribution function depends on the nonlinearity of the process of interest and thus there is no single distribution function that works best for all parameterizations. Examination of the scale (window size) dependence of the mean bias indicates that the bias in grid-average process rates monotonically increases with increasing window sizes, suggesting the increasing importance of subgrid variability with increasing grid sizes.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Takashima, Kengo; Yamamoto, Takahiro, E-mail: takahiro@rs.tus.ac.jp; Department of Liberal Arts
Conductance fluctuation of edge-disordered graphene nanoribbons (ED-GNRs) is examined using the non-equilibrium Green's function technique combined with the extended Hückel approximation. The mean free path λ and the localization length ξ of the ED-GNRs are determined to classify the quantum transport regimes. In the diffusive regime where the length L{sub c} of the ED-GNRs is much longer than λ and much shorter than ξ, the conductance histogram is given by a Gaussian distribution function with universal conductance fluctuation. In the localization regime where L{sub c}≫ξ, the histogram is no longer the universal Gaussian distribution but a lognormal distribution that characterizesmore » Anderson localization.« less
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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.
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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.
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Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density
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
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A Variational Approach to Simultaneous Image Segmentation and Bias Correction.
Zhang, Kaihua; Liu, Qingshan; Song, Huihui; Li, Xuelong
2015-08-01
This paper presents a novel variational approach for simultaneous estimation of bias field and segmentation of images with intensity inhomogeneity. We model intensity of inhomogeneous objects to be Gaussian distributed with different means and variances, and then introduce a sliding window to map the original image intensity onto another domain, where the intensity distribution of each object is still Gaussian but can be better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying the bias field with a piecewise constant signal within the sliding window. A maximum likelihood energy functional is then defined on each local region, which combines the bias field, the membership function of the object region, and the constant approximating the true signal from its corresponding object. The energy functional is then extended to the whole image domain by the Bayesian learning approach. An efficient iterative algorithm is proposed for energy minimization, via which the image segmentation and bias field correction are simultaneously achieved. Furthermore, the smoothness of the obtained optimal bias field is ensured by the normalized convolutions without extra cost. Experiments on real images demonstrated the superiority of the proposed algorithm to other state-of-the-art representative methods.
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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.
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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.
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Awazu, Akinori; Tanabe, Takahiro; Kamitani, Mari; Tezuka, Ayumi; Nagano, Atsushi J
2018-05-29
Gene expression levels exhibit stochastic variations among genetically identical organisms under the same environmental conditions. In many recent transcriptome analyses based on RNA sequencing (RNA-seq), variations in gene expression levels among replicates were assumed to follow a negative binomial distribution, although the physiological basis of this assumption remains unclear. In this study, RNA-seq data were obtained from Arabidopsis thaliana under eight conditions (21-27 replicates), and the characteristics of gene-dependent empirical probability density function (ePDF) profiles of gene expression levels were analyzed. For A. thaliana and Saccharomyces cerevisiae, various types of ePDF of gene expression levels were obtained that were classified as Gaussian, power law-like containing a long tail, or intermediate. These ePDF profiles were well fitted with a Gauss-power mixing distribution function derived from a simple model of a stochastic transcriptional network containing a feedback loop. The fitting function suggested that gene expression levels with long-tailed ePDFs would be strongly influenced by feedback regulation. Furthermore, the features of gene expression levels are correlated with their functions, with the levels of essential genes tending to follow a Gaussian-like ePDF while those of genes encoding nucleic acid-binding proteins and transcription factors exhibit long-tailed ePDF.
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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.
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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.
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Bayesian approach to non-Gaussian field statistics for diffusive broadband terahertz pulses.
Pearce, Jeremy; Jian, Zhongping; Mittleman, Daniel M
2005-11-01
We develop a closed-form expression for the probability distribution function for the field components of a diffusive broadband wave propagating through a random medium. We consider each spectral component to provide an individual observation of a random variable, the configurationally averaged spectral intensity. Since the intensity determines the variance of the field distribution at each frequency, this random variable serves as the Bayesian prior that determines the form of the non-Gaussian field statistics. This model agrees well with experimental results.
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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.
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The Unquiet State of Violent Relaxation
NASA Astrophysics Data System (ADS)
Henriksen, Richard
2005-08-01
In 1967 Lynden-Bell presented a statistical mechanical theory for the relaxation of collisionless systems. Since then this theory has been studied numerically and theoretically by many authors. Nakamura in 2000 gave an alternate theory that differed from that of Lynden- Bell by predicting a Gaussian equilibrium distribution function rather than Fermi-Dirac. More recently Henriksen in 2004 has used a coarsegraining technique on cosmological infall systems that also predicts a Gaussian equilibrium distribution function. These relaxed states are thought to occur from the centre of the system outwards. Simulations of cosmological cold dark-matter halos however persist in finding central density cusps (the NFWprofile), which are inconsistent with the predicted distribution functions and perhaps with the observations of some galaxies. Some numerical studies (e.g.Merrall & Henriksen 2003) that attempt to measure the distribution function of dark matter do find Gaussian functions, provided that the initial asymmetry is not too great. Moreover recent work at Queen's reported here by MacMillan, suggests that it is the growth of asymmetry during the infall that produces the cusped behaviour. So put briefly, the essential physics of dark-matter relaxation remains "obscure" as does the validity of the theoretical predictions. "Violent virialization" occurs rapidly, well before subscale relaxation, but the scale at which the relaxation stops (and why) remains unclear. I will present some results that argue for wave-particle relaxation (Landau damping as frequently suggested by Kandrup) and in addition I will suggest that the evolution of isolated systems is very different from that of systems constantly disturbed by infall. Isolated systems may become trapped in an unrelaxed state by the development or existence of multipolar internal structure. Nevertheless a suitable coarse graining of the system may restore the predicted distribution functions.
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FROM FINANCE TO COSMOLOGY: THE COPULA OF LARGE-SCALE STRUCTURE
DOE Office of Scientific and Technical Information (OSTI.GOV)
Scherrer, Robert J.; Berlind, Andreas A.; Mao, Qingqing
2010-01-01
Any multivariate distribution can be uniquely decomposed into marginal (one-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an important new methodology for analyzing the density field in large-scale structure. We derive the empirical two-point copula for the evolved dark matter density field. We find that this empirical copula is well approximated by a Gaussian copula. We consider the possibility that the full n-point copula is also Gaussian and describe some of the consequences of this hypothesis. Future directions for investigation are discussed.
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Statistical characterization of discrete conservative systems: The web map
NASA Astrophysics Data System (ADS)
Ruiz, Guiomar; Tirnakli, Ugur; Borges, Ernesto P.; Tsallis, Constantino
2017-10-01
We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional SB G[p (x ) ] =-k ∫d x p (x ) lnp (x ) . In contrast, possible ergodicity breakdown and transitory sticky dynamical behavior drag the map into the realm of generalized q statistics, based on the nonadditive entropic functional Sq[p (x ) ] =k 1/-∫d x [p(x ) ] q q -1 (q ∈R ;S1=SB G ). We statistically describe the system (probability distribution of the sum of successive iterates, sensitivity to the initial condition, and entropy production per unit time) for typical values of the parameter that controls the ergodicity of the map. For small (large) values of the external parameter K , we observe q -Gaussian distributions with q =1.935 ⋯ (Gaussian distributions), like for the standard map. In contrast, for intermediate values of K , we observe a different scenario, due to the fractal structure of the trajectories embedded in the chaotic sea. Long-standing non-Gaussian distributions are characterized in terms of the kurtosis and the box-counting dimension of chaotic sea.
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Revealing nonclassicality beyond Gaussian states via a single marginal distribution
Park, Jiyong; Lu, Yao; Lee, Jaehak; Shen, Yangchao; Zhang, Kuan; Zhang, Shuaining; Zubairy, Muhammad Suhail; Kim, Kihwan; Nha, Hyunchul
2017-01-01
A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential—a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis–independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement. PMID:28077456
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Revealing nonclassicality beyond Gaussian states via a single marginal distribution.
Park, Jiyong; Lu, Yao; Lee, Jaehak; Shen, Yangchao; Zhang, Kuan; Zhang, Shuaining; Zubairy, Muhammad Suhail; Kim, Kihwan; Nha, Hyunchul
2017-01-31
A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential-a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis-independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement.
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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.
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Fusion cross sections for reactions involving medium and heavy nucleus-nucleus systems
NASA Astrophysics Data System (ADS)
Atta, Debasis; Basu, D. N.
2014-12-01
Existing data on near-barrier fusion excitation functions of medium and heavy nucleus-nucleus systems have been analyzed by using a simple diffused-barrier formula derived assuming the Gaussian shape of the barrier-height distributions. The fusion cross section is obtained by folding the Gaussian barrier distribution with the classical expression for the fusion cross section for a fixed barrier. The energy dependence of the fusion cross section, thus obtained, provides good description to the existing data on near-barrier fusion and capture excitation functions for medium and heavy nucleus-nucleus systems. The theoretical values for the parameters of the barrier distribution are estimated which can be used for fusion or capture cross-section predictions that are especially important for planning experiments for synthesizing new superheavy elements.
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The maximum entropy method of moments and Bayesian probability theory
NASA Astrophysics Data System (ADS)
Bretthorst, G. Larry
2013-08-01
The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.
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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.
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Inflation in random Gaussian landscapes
DOE Office of Scientific and Technical Information (OSTI.GOV)
Masoumi, Ali; Vilenkin, Alexander; Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu
2017-05-01
We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations n {sub s} and its running α {sub s} . These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer frommore » potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.« less
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Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory
NASA Astrophysics Data System (ADS)
Pato, Mauricio P.; Oshanin, Gleb
2013-03-01
We study the probability distribution function P(β)n(w) of the Schmidt-like random variable w = x21/(∑j = 1nx2j/n), where xj, (j = 1, 2, …, n), are unordered eigenvalues of a given n × n β-Gaussian random matrix, β being the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual (randomly chosen) eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n → ∞ and for arbitrary β the distribution P(β)n(w) converges to the Marčenko-Pastur form, i.e. is defined as P_{n}^{( \\beta )}(w) \\sim \\sqrt{(4 - w)/w} for w ∈ [0, 4] and equals zero outside of the support, despite the fact that formally w is defined on the interval [0, n]. Furthermore, for Gaussian unitary ensembles (β = 2) we present exact explicit expressions for P(β = 2)n(w) which are valid for arbitrary n and analyse their behaviour.
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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.
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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,…
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SuperGaussian distribution functions in inhomogenous plasmas
NASA Astrophysics Data System (ADS)
Matte, Jean-Pierre
2008-11-01
In plasmas heated by a narrow laser beam, the shape of the distribution function is influenced by both the absorption, which tends to give a superGaussian (DLM) distribution function [1], and the effects of heat flow, which tends to make the distribution more Maxwellian, when the hot region is considerably wider than the laser beam [2]. Thus, it is only at early times that the deformation is as strong as predicted by our uniform intensity formula [1]. A large number of electron kinetic simulations of a finite width laser beam heating a uniform density plasma were performed with the electron kinetic code FPI [1] to study the competition between these two mechanisms. In some cases, the deformation is approximately given by this formula if we average the laser intensity over the entire plasma. This may explain why distributions were more Maxwellian than expected in some experiments [3]. [0pt] [1] J.-P. Matte et al., Plasma Phys. Contr. Fusion 30, 1665 (1988) [2] S. Brunner and E. Valeo, Phys. Plasmas 9, 923 (2002) [3] S.H. Glenzer et al., Phys. Rev. Lett. 82, 97 (1999).
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On the cause of the non-Gaussian distribution of residuals in geomagnetism
NASA Astrophysics Data System (ADS)
Hulot, G.; Khokhlov, A.
2017-12-01
To describe errors in the data, Gaussian distributions naturally come to mind. In many practical instances, indeed, Gaussian distributions are appropriate. In the broad field of geomagnetism, however, it has repeatedly been noted that residuals between data and models often display much sharper distributions, sometimes better described by a Laplace distribution. In the present study, we make the case that such non-Gaussian behaviors are very likely the result of what is known as mixture of distributions in the statistical literature. Mixtures arise as soon as the data do not follow a common distribution or are not properly normalized, the resulting global distribution being a mix of the various distributions followed by subsets of the data, or even individual datum. We provide examples of the way such mixtures can lead to distributions that are much sharper than Gaussian distributions and discuss the reasons why such mixtures are likely the cause of the non-Gaussian distributions observed in geomagnetism. We also show that when properly selecting sub-datasets based on geophysical criteria, statistical mixture can sometimes be avoided and much more Gaussian behaviors recovered. We conclude with some general recommendations and point out that although statistical mixture always tends to sharpen the resulting distribution, it does not necessarily lead to a Laplacian distribution. This needs to be taken into account when dealing with such non-Gaussian distributions.
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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.
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Photon-number statistics in resonance fluorescence
NASA Astrophysics Data System (ADS)
Lenstra, D.
1982-12-01
The theory of photon-number statistics in resonance fluorescence is treated, starting with the general formula for the emission probability of n photons during a given time interval T. The results fully confirm formerly obtained results by Cook that were based on the theory of atomic motion in a traveling wave. General expressions for the factorial moments are derived and explicit results for the mean and the variance are given. It is explicitly shown that the distribution function tends to a Gaussian when T becomes much larger than the natural lifetime of the excited atom. The speed of convergence towards the Gaussian is found to be typically slow, that is, the third normalized central moment (or the skewness) is proportional to T-12. However, numerical results illustrate that the overall features of the distribution function are already well represented by a Gaussian when T is larger than a few natural lifetimes only, at least if the intensity of the exciting field is not too small and its detuning is not too large.
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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.
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Fiori, Aldo; Volpi, Elena; Zarlenga, Antonio; Bohling, Geoffrey C
2015-08-01
The impact of the logconductivity (Y=ln K) distribution fY on transport at the MADE site is analyzed. Our principal interest is in non-Gaussian fY characterized by heavier tails than the Gaussian. Both the logconductivity moments and fY itself are inferred, taking advantage of the detailed measurements of Bohling et al. (2012). The resulting logconductivity distribution displays heavier tails than the Gaussian, although the departure from Gaussianity is not significant. The effect of the logconductivity distribution on the breakthrough curve (BTC) is studied through an analytical, physically based model. It is found that the non-Gaussianity of the MADE logconductivity distribution does not strongly affect the BTC. Counterintuitively, assuming heavier tailed distributions for Y, with same variance, leads to BTCs which are more symmetrical than those for the Gaussian fY, with less pronounced preferential flow. Results indicate that the impact of strongly non-Gaussian, heavy tailed distributions on solute transport in heterogeneous porous formations can be significant, especially in the presence of high heterogeneity, resulting in reduced preferential flow and retarded peak arrivals. Copyright © 2015 Elsevier B.V. All rights reserved.
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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.
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Bayes classification of terrain cover using normalized polarimetric data
NASA Technical Reports Server (NTRS)
Yueh, H. A.; Swartz, A. A.; Kong, J. A.; Shin, R. T.; Novak, L. M.
1988-01-01
The normalized polarimetric classifier (NPC) which uses only the relative magnitudes and phases of the polarimetric data is proposed for discrimination of terrain elements. The probability density functions (PDFs) of polarimetric data are assumed to have a complex Gaussian distribution, and the marginal PDF of the normalized polarimetric data is derived by adopting the Euclidean norm as the normalization function. The general form of the distance measure for the NPC is also obtained. It is demonstrated that for polarimetric data with an arbitrary PDF, the distance measure of NPC will be independent of the normalization function selected even when the classifier is mistrained. A complex Gaussian distribution is assumed for the polarimetric data consisting of grass and tree regions. The probability of error for the NPC is compared with those of several other single-feature classifiers. The classification error of NPCs is shown to be independent of the normalization function.
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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.
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Plasma Diffusion in Self-Consistent Fluctuations
NASA Technical Reports Server (NTRS)
Smets, R.; Belmont, G.; Aunai, N.
2012-01-01
The problem of particle diffusion in position space, as a consequence ofeleclromagnetic fluctuations is addressed. Numerical results obtained with a self-consistent hybrid code are presented, and a method to calculate diffusion coefficient in the direction perpendicular to the mean magnetic field is proposed. The diffusion is estimated for two different types of fluctuations. The first type (resuiting from an agyrotropic in itiai setting)is stationary, wide band white noise, and associated to Gaussian probability distribution function for the magnetic fluctuations. The second type (result ing from a Kelvin-Helmholtz instability) is non-stationary, with a power-law spectrum, and a non-Gaussian probabi lity distribution function. The results of the study allow revisiting the question of loading particles of solar wind origin in the Earth magnetosphere.
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NASA Astrophysics Data System (ADS)
Vlasov, M. N.; Kelley, M. C.; Hysell, D. L.
2013-06-01
Enhanced optical emissions observed during HF pumping are induced by electrons accelerated by high-power electromagnetic waves. Using measured emission intensities, the energy distribution of accelerated electrons can be inferred. Energy loss from the excitation of molecular nitrogen vibrational levels (the vibrational barrier) strongly influences the electron energy distribution (EED). In airglow calculations, compensation for electron depletion within the 2-3 eV energy range, induced by the vibrational barrier, can be achieved via electrons with an EED similar to a Gaussian distribution and energies higher than 3 eV. This EED has a peak within the 5-10 eV energy range. We show that the main EED features depend strongly on altitude and solar activity. An EED similar to a power law distribution can occur above 270-300 km altitude. Below 270 km altitude, a Gaussian distribution for energies between 3 eV and 10 eV, together with a power law distribution for energies higher than 10 eV, is indicated. A Gaussian distribution combined with an exponential function is needed below 230 km altitude. The transition altitude from Gaussian to power law distribution depends strongly on solar activity, increasing for high solar activity. Electrons accelerated during the initial collisionless stage can inhibit the depletion of fast electrons within the vibrational barrier range, an effect that strongly depends on altitude and solar activity. The approach, based on the effective root square electric field, enables EED calculation, providing the observed red-line intensities for low and high solar activities.
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Efficient Statistically Accurate Algorithms for the Fokker-Planck Equation in Large Dimensions
NASA Astrophysics Data System (ADS)
Chen, N.; Majda, A.
2017-12-01
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, which is based on an effective data assimilation framework, provides closed analytical formulae for determining the conditional Gaussian distributions in the high-dimensional subspace. Therefore, it is computationally efficient and accurate. The full non-Gaussian PDF of the system is then given by a Gaussian mixture. Different from the 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 a 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.
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Haeckel, Rainer; Wosniok, Werner
2010-10-01
The distribution of many quantities in laboratory medicine are considered to be Gaussian if they are symmetric, although, theoretically, a Gaussian distribution is not plausible for quantities that can attain only non-negative values. If a distribution is skewed, further specification of the type is required, which may be difficult to provide. Skewed (non-Gaussian) distributions found in clinical chemistry usually show only moderately large positive skewness (e.g., log-normal- and χ(2) distribution). The degree of skewness depends on the magnitude of the empirical biological variation (CV(e)), as demonstrated using the log-normal distribution. A Gaussian distribution with a small CV(e) (e.g., for plasma sodium) is very similar to a log-normal distribution with the same CV(e). In contrast, a relatively large CV(e) (e.g., plasma aspartate aminotransferase) leads to distinct differences between a Gaussian and a log-normal distribution. If the type of an empirical distribution is unknown, it is proposed that a log-normal distribution be assumed in such cases. This avoids distributional assumptions that are not plausible and does not contradict the observation that distributions with small biological variation look very similar to a Gaussian distribution.
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ExGUtils: A Python Package for Statistical Analysis With the ex-Gaussian Probability Density.
Moret-Tatay, Carmen; Gamermann, Daniel; Navarro-Pardo, Esperanza; Fernández de Córdoba Castellá, Pedro
2018-01-01
The study of reaction times and their underlying cognitive processes is an important field in Psychology. Reaction times are often modeled through the ex-Gaussian distribution, because it provides a good fit to multiple empirical data. The complexity of this distribution makes the use of computational tools an essential element. Therefore, there is a strong need for efficient and versatile computational tools for the research in this area. In this manuscript we discuss some mathematical details of the ex-Gaussian distribution and apply the ExGUtils package, a set of functions and numerical tools, programmed for python, developed for numerical analysis of data involving the ex-Gaussian probability density. In order to validate the package, we present an extensive analysis of fits obtained with it, discuss advantages and differences between the least squares and maximum likelihood methods and quantitatively evaluate the goodness of the obtained fits (which is usually an overlooked point in most literature in the area). The analysis done allows one to identify outliers in the empirical datasets and criteriously determine if there is a need for data trimming and at which points it should be done.
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ExGUtils: A Python Package for Statistical Analysis With the ex-Gaussian Probability Density
Moret-Tatay, Carmen; Gamermann, Daniel; Navarro-Pardo, Esperanza; Fernández de Córdoba Castellá, Pedro
2018-01-01
The study of reaction times and their underlying cognitive processes is an important field in Psychology. Reaction times are often modeled through the ex-Gaussian distribution, because it provides a good fit to multiple empirical data. The complexity of this distribution makes the use of computational tools an essential element. Therefore, there is a strong need for efficient and versatile computational tools for the research in this area. In this manuscript we discuss some mathematical details of the ex-Gaussian distribution and apply the ExGUtils package, a set of functions and numerical tools, programmed for python, developed for numerical analysis of data involving the ex-Gaussian probability density. In order to validate the package, we present an extensive analysis of fits obtained with it, discuss advantages and differences between the least squares and maximum likelihood methods and quantitatively evaluate the goodness of the obtained fits (which is usually an overlooked point in most literature in the area). The analysis done allows one to identify outliers in the empirical datasets and criteriously determine if there is a need for data trimming and at which points it should be done. PMID:29765345
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Exact posterior computation in non-conjugate Gaussian location-scale parameters models
NASA Astrophysics Data System (ADS)
Andrade, J. A. A.; Rathie, P. N.
2017-12-01
In Bayesian analysis the class of conjugate models allows to obtain exact posterior distributions, however this class quite restrictive in the sense that it involves only a few distributions. In fact, most of the practical applications involves non-conjugate models, thus approximate methods, such as the MCMC algorithms, are required. Although these methods can deal with quite complex structures, some practical problems can make their applications quite time demanding, for example, when we use heavy-tailed distributions, convergence may be difficult, also the Metropolis-Hastings algorithm can become very slow, in addition to the extra work inevitably required on choosing efficient candidate generator distributions. In this work, we draw attention to the special functions as a tools for Bayesian computation, we propose an alternative method for obtaining the posterior distribution in Gaussian non-conjugate models in an exact form. We use complex integration methods based on the H-function in order to obtain the posterior distribution and some of its posterior quantities in an explicit computable form. Two examples are provided in order to illustrate the theory.
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Gaussian copula as a likelihood function for environmental models
NASA Astrophysics Data System (ADS)
Wani, O.; Espadas, G.; Cecinati, F.; Rieckermann, J.
2017-12-01
Parameter estimation of environmental models always comes with uncertainty. To formally quantify this parametric uncertainty, a likelihood function needs to be formulated, which is defined as the probability of observations given fixed values of the parameter set. A likelihood function allows us to infer parameter values from observations using Bayes' theorem. The challenge is to formulate a likelihood function that reliably describes the error generating processes which lead to the observed monitoring data, such as rainfall and runoff. If the likelihood function is not representative of the error statistics, the parameter inference will give biased parameter values. Several uncertainty estimation methods that are currently being used employ Gaussian processes as a likelihood function, because of their favourable analytical properties. Box-Cox transformation is suggested to deal with non-symmetric and heteroscedastic errors e.g. for flow data which are typically more uncertain in high flows than in periods with low flows. Problem with transformations is that the results are conditional on hyper-parameters, for which it is difficult to formulate the analyst's belief a priori. In an attempt to address this problem, in this research work we suggest learning the nature of the error distribution from the errors made by the model in the "past" forecasts. We use a Gaussian copula to generate semiparametric error distributions . 1) We show that this copula can be then used as a likelihood function to infer parameters, breaking away from the practice of using multivariate normal distributions. Based on the results from a didactical example of predicting rainfall runoff, 2) we demonstrate that the copula captures the predictive uncertainty of the model. 3) Finally, we find that the properties of autocorrelation and heteroscedasticity of errors are captured well by the copula, eliminating the need to use transforms. In summary, our findings suggest that copulas are an interesting departure from the usage of fully parametric distributions as likelihood functions - and they could help us to better capture the statistical properties of errors and make more reliable predictions.
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A non-Gaussian option pricing model based on Kaniadakis exponential deformation
NASA Astrophysics Data System (ADS)
Moretto, Enrico; Pasquali, Sara; Trivellato, Barbara
2017-09-01
A way to make financial models effective is by letting them to represent the so called "fat tails", i.e., extreme changes in stock prices that are regarded as almost impossible by the standard Gaussian distribution. In this article, the Kaniadakis deformation of the usual exponential function is used to define a random noise source in the dynamics of price processes capable of capturing such real market phenomena.
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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.
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ERIC Educational Resources Information Center
Duerdoth, Ian
2009-01-01
The subject of uncertainties (sometimes called errors) is traditionally taught (to first-year science undergraduates) towards the end of a course on statistics that defines probability as the limit of many trials, and discusses probability distribution functions and the Gaussian distribution. We show how to introduce students to the concepts of…
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Fluctuations and intermittent poloidal transport in a simple toroidal plasma
DOE Office of Scientific and Technical Information (OSTI.GOV)
Goud, T. S.; Ganesh, R.; Saxena, Y. C.
In a simple magnetized toroidal plasma, fluctuation induced poloidal flux is found to be significant in magnitude. The probability distribution function of the fluctuation induced poloidal flux is observed to be strongly non-Gaussian in nature; however, in some cases, the distribution shows good agreement with the analytical form [Carreras et al., Phys. Plasmas 3, 2664 (1996)], assuming a coupling between the near Gaussian density and poloidal velocity fluctuations. The observed non-Gaussian nature of the fluctuation induced poloidal flux and other plasma parameters such as density and fluctuating poloidal velocity in this device is due to intermittent and bursty nature ofmore » poloidal transport. In the simple magnetized torus used here, such an intermittent fluctuation induced poloidal flux is found to play a crucial role in generating the poloidal flow.« less
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Zalvidea; Colautti; Sicre
2000-05-01
An analysis of the Strehl ratio and the optical transfer function as imaging quality parameters of optical elements with enhanced focal length is carried out by employing the Wigner distribution function. To this end, we use four different pupil functions: a full circular aperture, a hyper-Gaussian aperture, a quartic phase plate, and a logarithmic phase mask. A comparison is performed between the quality parameters and test images formed by these pupil functions at different defocus distances.
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Resampling methods in Microsoft Excel® for estimating reference intervals
Theodorsson, Elvar
2015-01-01
Computer- intensive resampling/bootstrap methods are feasible when calculating reference intervals from non-Gaussian or small reference samples. Microsoft Excel® in version 2010 or later includes natural functions, which lend themselves well to this purpose including recommended interpolation procedures for estimating 2.5 and 97.5 percentiles. The purpose of this paper is to introduce the reader to resampling estimation techniques in general and in using Microsoft Excel® 2010 for the purpose of estimating reference intervals in particular. Parametric methods are preferable to resampling methods when the distributions of observations in the reference samples is Gaussian or can transformed to that distribution even when the number of reference samples is less than 120. Resampling methods are appropriate when the distribution of data from the reference samples is non-Gaussian and in case the number of reference individuals and corresponding samples are in the order of 40. At least 500-1000 random samples with replacement should be taken from the results of measurement of the reference samples. PMID:26527366
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Resampling methods in Microsoft Excel® for estimating reference intervals.
Theodorsson, Elvar
2015-01-01
Computer-intensive resampling/bootstrap methods are feasible when calculating reference intervals from non-Gaussian or small reference samples. Microsoft Excel® in version 2010 or later includes natural functions, which lend themselves well to this purpose including recommended interpolation procedures for estimating 2.5 and 97.5 percentiles. The purpose of this paper is to introduce the reader to resampling estimation techniques in general and in using Microsoft Excel® 2010 for the purpose of estimating reference intervals in particular. Parametric methods are preferable to resampling methods when the distributions of observations in the reference samples is Gaussian or can transformed to that distribution even when the number of reference samples is less than 120. Resampling methods are appropriate when the distribution of data from the reference samples is non-Gaussian and in case the number of reference individuals and corresponding samples are in the order of 40. At least 500-1000 random samples with replacement should be taken from the results of measurement of the reference samples.
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Mabrouk, Rostom; Dubeau, François; Bentabet, Layachi
2013-01-01
Kinetic modeling of metabolic and physiologic cardiac processes in small animals requires an input function (IF) and a tissue time-activity curves (TACs). In this paper, we present a mathematical method based on independent component analysis (ICA) to extract the IF and the myocardium's TACs directly from dynamic positron emission tomography (PET) images. The method assumes a super-Gaussian distribution model for the blood activity, and a sub-Gaussian distribution model for the tissue activity. Our appreach was applied on 22 PET measurement sets of small animals, which were obtained from the three most frequently used cardiac radiotracers, namely: desoxy-fluoro-glucose ((18)F-FDG), [(13)N]-ammonia, and [(11)C]-acetate. Our study was extended to PET human measurements obtained with the Rubidium-82 ((82) Rb) radiotracer. The resolved mathematical IF values compare favorably to those derived from curves extracted from regions of interest (ROI), suggesting that the procedure presents a reliable alternative to serial blood sampling for small-animal cardiac PET studies.
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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.
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Non-Gaussian statistics of soliton timing jitter induced by amplifier noise.
Ho, Keang-Po
2003-11-15
Based on first-order perturbation theory of the soliton, the Gordon-Haus timing jitter induced by amplifier noise is found to be non-Gaussian distributed. Both frequency and timing jitter have larger tail probabilities than Gaussian distribution given by the linearized perturbation theory. The timing jitter has a larger discrepancy from Gaussian distribution than does the frequency jitter.
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NASA Astrophysics Data System (ADS)
Geloni, G.; Saldin, E. L.; Schneidmiller, E. A.; Yurkov, M. V.
2004-08-01
An effective and practical technique based on the detection of the coherent synchrotron radiation (CSR) spectrum can be used to characterize the profile function of ultra-short bunches. The CSR spectrum measurement has an important limitation: no spectral phase information is available, and the complete profile function cannot be obtained in general. In this paper we propose to use constrained deconvolution method for bunch profile reconstruction based on a priori-known information about formation of the electron bunch. Application of the method is illustrated with practically important example of a bunch formed in a single bunch-compressor. Downstream of the bunch compressor the bunch charge distribution is strongly non-Gaussian with a narrow leading peak and a long tail. The longitudinal bunch distribution is derived by measuring the bunch tail constant with a streak camera and by using a priory available information about profile function.
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Refractive laser beam shaping by means of a functional differential equation based design approach.
Duerr, Fabian; Thienpont, Hugo
2014-04-07
Many laser applications require specific irradiance distributions to ensure optimal performance. Geometric optical design methods based on numerical calculation of two plano-aspheric lenses have been thoroughly studied in the past. In this work, we present an alternative new design approach based on functional differential equations that allows direct calculation of the rotational symmetric lens profiles described by two-point Taylor polynomials. The formalism is used to design a Gaussian to flat-top irradiance beam shaping system but also to generate a more complex dark-hollow Gaussian (donut-like) irradiance distribution with zero intensity in the on-axis region. The presented ray tracing results confirm the high accuracy of both calculated solutions and emphasize the potential of this design approach for refractive beam shaping applications.
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ERIC Educational Resources Information Center
Ivancheva, Ludmila E.
2001-01-01
Discusses the concept of the hyperbolic or skew distribution as a universal statistical law in information science and socioeconomic studies. Topics include Zipf's law; Stankov's universal law; non-Gaussian distributions; and why most bibliometric and scientometric laws reveal characters of non-Gaussian distribution. (Author/LRW)
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NASA Astrophysics Data System (ADS)
Pires, Carlos A. L.; Ribeiro, Andreia F. S.
2017-02-01
We develop an expansion of space-distributed time series into statistically independent uncorrelated subspaces (statistical sources) of low-dimension and exhibiting enhanced non-Gaussian probability distributions with geometrically simple chosen shapes (projection pursuit rationale). The method relies upon a generalization of the principal component analysis that is optimal for Gaussian mixed signals and of the independent component analysis (ICA), optimized to split non-Gaussian scalar sources. The proposed method, supported by information theory concepts and methods, is the independent subspace analysis (ISA) that looks for multi-dimensional, intrinsically synergetic subspaces such as dyads (2D) and triads (3D), not separable by ICA. Basically, we optimize rotated variables maximizing certain nonlinear correlations (contrast functions) coming from the non-Gaussianity of the joint distribution. As a by-product, it provides nonlinear variable changes `unfolding' the subspaces into nearly Gaussian scalars of easier post-processing. Moreover, the new variables still work as nonlinear data exploratory indices of the non-Gaussian variability of the analysed climatic and geophysical fields. The method (ISA, followed by nonlinear unfolding) is tested into three datasets. The first one comes from the Lorenz'63 three-dimensional chaotic model, showing a clear separation into a non-Gaussian dyad plus an independent scalar. The second one is a mixture of propagating waves of random correlated phases in which the emergence of triadic wave resonances imprints a statistical signature in terms of a non-Gaussian non-separable triad. Finally the method is applied to the monthly variability of a high-dimensional quasi-geostrophic (QG) atmospheric model, applied to the Northern Hemispheric winter. We find that quite enhanced non-Gaussian dyads of parabolic shape, perform much better than the unrotated variables in which concerns the separation of the four model's centroid regimes (positive and negative phases of the Arctic Oscillation and of the North Atlantic Oscillation). Triads are also likely in the QG model but of weaker expression than dyads due to the imposed shape and dimension. The study emphasizes the existence of nonlinear dyadic and triadic nonlinear teleconnections.
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The Generation, Radiation and Prediction of Supersonic Jet Noise. Volume 1
1978-10-01
standard, Gaussian correlation function model can yield a good noise spectrum prediction (at 900), but the corresponding axial source distributions do not...forms for the turbulence cross-correlation function. Good agreement was obtained between measured and calculated far- field noise spectra. However, the...complementary error function profile (3.63) was found to provide a good fit to the axial velocity distribution tor a wide range of Mach numbers in the Initial
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Backscattering from a Gaussian distributed, perfectly conducting, rough surface
NASA Technical Reports Server (NTRS)
Brown, G. S.
1977-01-01
The problem of scattering by random surfaces possessing many scales of roughness is analyzed. The approach is applicable to bistatic scattering from dielectric surfaces, however, this specific analysis is restricted to backscattering from a perfectly conducting surface in order to more clearly illustrate the method. The surface is assumed to be Gaussian distributed so that the surface height can be split into large and small scale components, relative to the electromagnetic wavelength. A first order perturbation approach is employed wherein the scattering solution for the large scale structure is perturbed by the small scale diffraction effects. The scattering from the large scale structure is treated via geometrical optics techniques. The effect of the large scale surface structure is shown to be equivalent to a convolution in k-space of the height spectrum with the following: the shadowing function, a polarization and surface slope dependent function, and a Gaussian factor resulting from the unperturbed geometrical optics solution. This solution provides a continuous transition between the near normal incidence geometrical optics and wide angle Bragg scattering results.
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Statistics of initial density perturbations in heavy ion collisions and their fluid dynamic response
NASA Astrophysics Data System (ADS)
Floerchinger, Stefan; Wiedemann, Urs Achim
2014-08-01
An interesting opportunity to determine thermodynamic and transport properties in more detail is to identify generic statistical properties of initial density perturbations. Here we study event-by-event fluctuations in terms of correlation functions for two models that can be solved analytically. The first assumes Gaussian fluctuations around a distribution that is fixed by the collision geometry but leads to non-Gaussian features after averaging over the reaction plane orientation at non-zero impact parameter. In this context, we derive a three-parameter extension of the commonly used Bessel-Gaussian event-by-event distribution of harmonic flow coefficients. Secondly, we study a model of N independent point sources for which connected n-point correlation functions of initial perturbations scale like 1 /N n-1. This scaling is violated for non-central collisions in a way that can be characterized by its impact parameter dependence. We discuss to what extent these are generic properties that can be expected to hold for any model of initial conditions, and how this can improve the fluid dynamical analysis of heavy ion collisions.
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Statistics of Stokes variables for correlated Gaussian fields
DOE Office of Scientific and Technical Information (OSTI.GOV)
Eliyahu, D.
1994-09-01
The joint and marginal probability distribution functions of the Stokes variables are derived for correlated Gaussian fields [an extension of D. Eliyahu, Phys. Rev. E 47, 2881 (1993)]. The statistics depend only on the first moment (averaged) Stokes variables and have a universal form for [ital S][sub 1], [ital S][sub 2], and [ital S][sub 3]. The statistics of the variables describing the Cartesian coordinates of the Poincare sphere are given also.
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Flexible link functions in nonparametric binary regression with Gaussian process priors.
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.
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Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors
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
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Hirayama, S; Takayanagi, T; Fujii, Y
2014-06-15
Purpose: To present the validity of our beam modeling with double and triple Gaussian dose kernels for spot scanning proton beams in Nagoya Proton Therapy Center. This study investigates the conformance between the measurements and calculation results in absolute dose with two types of beam kernel. Methods: A dose kernel is one of the important input data required for the treatment planning software. The dose kernel is the 3D dose distribution of an infinitesimal pencil beam of protons in water and consists of integral depth doses and lateral distributions. We have adopted double and triple Gaussian model as lateral distributionmore » in order to take account of the large angle scattering due to nuclear reaction by fitting simulated inwater lateral dose profile for needle proton beam at various depths. The fitted parameters were interpolated as a function of depth in water and were stored as a separate look-up table for the each beam energy. The process of beam modeling is based on the method of MDACC [X.R.Zhu 2013]. Results: From the comparison results between the absolute doses calculated by double Gaussian model and those measured at the center of SOBP, the difference is increased up to 3.5% in the high-energy region because the large angle scattering due to nuclear reaction is not sufficiently considered at intermediate depths in the double Gaussian model. In case of employing triple Gaussian dose kernels, the measured absolute dose at the center of SOBP agrees with calculation within ±1% regardless of the SOBP width and maximum range. Conclusion: We have demonstrated the beam modeling results of dose distribution employing double and triple Gaussian dose kernel. Treatment planning system with the triple Gaussian dose kernel has been successfully verified and applied to the patient treatment with a spot scanning technique in Nagoya Proton Therapy Center.« less
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NASA Astrophysics Data System (ADS)
Park, Jong-Hyeok; Kim, Ki-Beom; Chang, Heon-Young
2014-08-01
Time series of drought indices has been considered mostly in view of temporal and spatial distributions of a drought index so far. Here we investigate the statistical properties of a daily Effective Drought Index (EDI) itself for Seoul, Busan, Daegu, Mokpo for the period of 100 years from 1913 to 2012. We have found that both in dry and wet seasons the distribution of EDI as a function of EDI follows the Gaussian function. In dry season the shape of the Gaussian function is characteristically broader than that in wet seasons. The total number of drought days during the period we have analyzed is related both to the mean value and more importantly to the standard deviation. We have also found that according to the distribution of the number of occasions where the EDI values of several consecutive days are all less than a threshold, the distribution follows the exponential distribution. The slope of the best fit becomes steeper not only as the critical EDI value becomes more negative but also as the number of consecutive days increases. The slope of the exponential distribution becomes steeper as the number of the city in which EDI is simultaneously less than a critical EDI in a row increases. Finally, we conclude by pointing out implications of our findings.
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NASA Astrophysics Data System (ADS)
Zhu, Kaicheng; Tang, Huiqin; Tang, Ying; Xia, Hui
2014-12-01
We proposed a scheme that converts a sine-Gaussian beam with an edge dislocation into a dark hollow beam with a vortex. Based on the gyrator transform (GT) relation, the closed-form field distribution of generalized sine-Gaussian beams passing through a GT system is derived; the intensity distribution and the corresponding phase distribution associated with the transforming generalized sine-Gaussian beams are analyzed. According to the numerical method, the distributions are graphically demonstrated and found that, for appropriate beam parameters and the GT angle, dark hollow vortex beams with topological charge 1 can be achieved using sine-Gaussian beams carrying an edge dislocation. Moreover, the orbital angular momentum content of a GT sine-Gaussian beam is analyzed. It is proved that the GT retains the odd- or even-order spiral harmonics structures of generalized sine-Gaussian beams in the transform process. In particular, it is wholly possible to convert an edge dislocation embedded in sine-Gaussian beams into a vortex with GT. The study also reveals that to obtain a dark hollow beam making use of GT of cos-Gaussian beams is impossible.
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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.
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Super-resolving random-Gaussian apodized photon sieve.
Sabatyan, Arash; Roshaninejad, Parisa
2012-09-10
A novel apodized photon sieve is presented in which random dense Gaussian distribution is implemented to modulate the pinhole density in each zone. The random distribution in dense Gaussian distribution causes intrazone discontinuities. Also, the dense Gaussian distribution generates a substantial number of pinholes in order to form a large degree of overlap between the holes in a few innermost zones of the photon sieve; thereby, clear zones are formed. The role of the discontinuities on the focusing properties of the photon sieve is examined as well. Analysis shows that secondary maxima have evidently been suppressed, transmission has increased enormously, and the central maxima width is approximately unchanged in comparison to the dense Gaussian distribution. Theoretical results have been completely verified by experiment.
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On focusing of a ring ripple on a Gaussian electromagnetic beam in a plasma
DOE Office of Scientific and Technical Information (OSTI.GOV)
Misra, Shikha; Mishra, S. K.
In this communication the authors have investigated the focusing of a ring ripple on a Gaussian electromagnetic beam propagating in a plasma, considering each of the three kinds of basic nonlinearities, namely, ponderomotive, collisional, and relativistic. In this analysis, the electric field profile of the propagating beam is assumed to be composed of the radial electric field distribution of the Gaussian beam as well as that of the ring ripple; a paraxial like approach has been adopted to analyze the characteristics of the propagation. Thus, one considers a unique dielectric function for the beam propagation and a radial field sensitivemore » diffraction term, appropriate to the vicinity of the maximum of the irradiance distribution of the ring ripple. Further, the variation of the phase associated with the beam on account of the r independent terms in the eikonal has also been accounted for.« less
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Quasi-electrostatic twisted waves in Lorentzian dusty plasmas
NASA Astrophysics Data System (ADS)
Arshad, Kashif; Lazar, M.; Poedts, S.
2018-07-01
The quasi electrostatic modes are investigated in non thermal dusty plasma using non-gyrotropic Kappa distribution in the presence of helical electric field. The Laguerre Gaussian (LG) mode function is employed to decompose the perturbed distribution function and helical electric field. The modified dielectric function is obtained for the dust ion acoustic (DIA) and dust acoustic (DA) twisted modes from the solution of Vlasov-Poisson equation. The threshold conditions for the growing modes is also illustrated.
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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.
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Linear velocity fields in non-Gaussian models for large-scale structure
NASA Technical Reports Server (NTRS)
Scherrer, Robert J.
1992-01-01
Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.
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NASA Astrophysics Data System (ADS)
Raymond, Neil; Iouchtchenko, Dmitri; Roy, Pierre-Nicholas; Nooijen, Marcel
2018-05-01
We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition function in a product basis of continuous nuclear and discrete electronic degrees of freedom without the use of any mapping schemes. We separate our Hamiltonian into a harmonic portion and a coupling portion; the partition function can then be calculated as the product of a Monte Carlo estimator (of the coupling contribution to the partition function) and a normalization factor (that is evaluated analytically). A Gaussian mixture model is used to evaluate the Monte Carlo estimator in a computationally efficient manner. Using two model systems, we demonstrate our approach to reduce the stochastic error associated with the Monte Carlo estimator. We show that the selection of the harmonic oscillators comprising the sampling distribution directly affects the efficiency of the method. Our results demonstrate that our path integral Monte Carlo method's deviation from exact Trotter calculations is dominated by the choice of the sampling distribution. By improving the sampling distribution, we can drastically reduce the stochastic error leading to lower computational cost.
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NASA Astrophysics Data System (ADS)
Sulyman, Alex; Chrystal, Colin; Haskey, Shaun; Burrell, Keith; Grierson, Brian
2017-10-01
The possible observation of non-Maxwellian ion distribution functions in the pedestal of DIII-D will be investigated with a synthetic diagnostic that accounts for the effect of finite neutral beam size. Ion distribution functions in tokamak plasmas are typically assumed to be Maxwellian, however non-Gaussian features observed in impurity charge exchange spectra have challenged this concept. Two possible explanations for these observations are spatial averaging over a finite beam size and a local ion distribution that is non-Maxwellian. Non-Maxwellian ion distribution functions could be driven by orbit loss effects in the edge of the plasma, and this has implications for momentum transport and intrinsic rotation. To investigate the potential effect of finite beam size on the observed spectra, a synthetic diagnostic has been created that uses FIDAsim to model beam and halo neutral density. Finite beam size effects are investigated for vertical and tangential views in the core and pedestal region with varying gradient scale lengths. Work supported in part by US DoE under the Science Undergraduate Laboratory Internship (SULI) program, DE-FC02-04ER54698, and DE-AC02-09CH11466.
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Non-Gaussian structure of B-mode polarization after delensing
DOE Office of Scientific and Technical Information (OSTI.GOV)
Namikawa, Toshiya; Nagata, Ryo, E-mail: namikawa@slac.stanford.edu, E-mail: rnagata@post.kek.jp
2015-10-01
The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less
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Non-Gaussian structure of B-mode polarization after delensing
NASA Astrophysics Data System (ADS)
Namikawa, Toshiya; Nagata, Ryo
2015-10-01
The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. In this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.
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Non-Gaussian structure of B-mode polarization after delensing
Namikawa, Toshiya; Nagata, Ryo
2015-10-01
The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. Furthermore, as a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less
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Gaussian noise and time-reversal symmetry in nonequilibrium Langevin models.
Vainstein, M H; Rubí, J M
2007-03-01
We show that in driven systems the Gaussian nature of the fluctuating force and time reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the probability distribution function, which can be shown to satisfy time-independent relations. We have corroborated this feature by explicitly analyzing a model for the stretching of a polymer and a model for a suspension of noninteracting Brownian particles in steady flow.
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Statistics of Advective Stretching in Three-dimensional Incompressible Flows
NASA Astrophysics Data System (ADS)
Subramanian, Natarajan; Kellogg, Louise H.; Turcotte, Donald L.
2009-09-01
We present a method to quantify kinematic stretching in incompressible, unsteady, isoviscous, three-dimensional flows. We extend the method of Kellogg and Turcotte (J. Geophys. Res. 95:421-432, 1990) to compute the axial stretching/thinning experienced by infinitesimal ellipsoidal strain markers in arbitrary three-dimensional incompressible flows and discuss the differences between our method and the computation of Finite Time Lyapunov Exponent (FTLE). We use the cellular flow model developed in Solomon and Mezic (Nature 425:376-380, 2003) to study the statistics of stretching in a three-dimensional unsteady cellular flow. We find that the probability density function of the logarithm of normalised cumulative stretching (log S) for a globally chaotic flow, with spatially heterogeneous stretching behavior, is not Gaussian and that the coefficient of variation of the Gaussian distribution does not decrease with time as t^{-1/2} . However, it is observed that stretching becomes exponential log S˜ t and the probability density function of log S becomes Gaussian when the time dependence of the flow and its three-dimensionality are increased to make the stretching behaviour of the flow more spatially uniform. We term these behaviors weak and strong chaotic mixing respectively. We find that for strongly chaotic mixing, the coefficient of variation of the Gaussian distribution decreases with time as t^{-1/2} . This behavior is consistent with a random multiplicative stretching process.
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Probabilistic inference using linear Gaussian importance sampling for hybrid Bayesian networks
NASA Astrophysics Data System (ADS)
Sun, Wei; Chang, K. C.
2005-05-01
Probabilistic inference for Bayesian networks is in general NP-hard using either exact algorithms or approximate methods. However, for very complex networks, only the approximate methods such as stochastic sampling could be used to provide a solution given any time constraint. There are several simulation methods currently available. They include logic sampling (the first proposed stochastic method for Bayesian networks, the likelihood weighting algorithm) the most commonly used simulation method because of its simplicity and efficiency, the Markov blanket scoring method, and the importance sampling algorithm. In this paper, we first briefly review and compare these available simulation methods, then we propose an improved importance sampling algorithm called linear Gaussian importance sampling algorithm for general hybrid model (LGIS). LGIS is aimed for hybrid Bayesian networks consisting of both discrete and continuous random variables with arbitrary distributions. It uses linear function and Gaussian additive noise to approximate the true conditional probability distribution for continuous variable given both its parents and evidence in a Bayesian network. One of the most important features of the newly developed method is that it can adaptively learn the optimal important function from the previous samples. We test the inference performance of LGIS using a 16-node linear Gaussian model and a 6-node general hybrid model. The performance comparison with other well-known methods such as Junction tree (JT) and likelihood weighting (LW) shows that LGIS-GHM is very promising.
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Schweiner, Frank; Laturner, Jeanine; Main, Jörg; Wunner, Günter
2017-11-01
Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) have analytical formulas for the level spacing distribution function been derived within random matrix theory. We investigate arbitrary crossovers in the triangle between all three statistics. To this aim we propose an according formula for the level spacing distribution function depending on two parameters. Comparing the behavior of our formula for the special cases of P→GUE, P→GOE, and GOE→GUE with the results from random matrix theory, we prove that these crossovers are described reasonably. Recent investigations by F. Schweiner et al. [Phys. Rev. E 95, 062205 (2017)2470-004510.1103/PhysRevE.95.062205] have shown that the Hamiltonian of magnetoexcitons in cubic semiconductors can exhibit all three statistics in dependence on the system parameters. Evaluating the numerical results for magnetoexcitons in dependence on the excitation energy and on a parameter connected with the cubic valence band structure and comparing the results with the formula proposed allows us to distinguish between regular and chaotic behavior as well as between existent or broken antiunitary symmetries. Increasing one of the two parameters, transitions between different crossovers, e.g., from the P→GOE to the P→GUE crossover, are observed and discussed.
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Work distributions for random sudden quantum quenches
NASA Astrophysics Data System (ADS)
Łobejko, Marcin; Łuczka, Jerzy; Talkner, Peter
2017-05-01
The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of Hermitian matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature. The same work distribution as for a sudden random quench is obtained for an adiabatic, i.e., infinitely slow, protocol connecting the same initial and final Hamiltonians.
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Dimension-independent likelihood-informed MCMC
Cui, Tiangang; Law, Kody J. H.; Marzouk, Youssef M.
2015-10-08
Many Bayesian inference problems require exploring the posterior distribution of highdimensional parameters that represent the discretization of an underlying function. Our work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. There are two distinct lines of research that intersect in the methods we develop here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian informationmore » and any associated lowdimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Finally, we use two nonlinear inverse problems in order to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.« less
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Exploring super-Gaussianity toward robust information-theoretical time delay estimation.
Petsatodis, Theodoros; Talantzis, Fotios; Boukis, Christos; Tan, Zheng-Hua; Prasad, Ramjee
2013-03-01
Time delay estimation (TDE) is a fundamental component of speaker localization and tracking algorithms. Most of the existing systems are based on the generalized cross-correlation method assuming gaussianity of the source. It has been shown that the distribution of speech, captured with far-field microphones, is highly varying, depending on the noise and reverberation conditions. Thus the performance of TDE is expected to fluctuate depending on the underlying assumption for the speech distribution, being also subject to multi-path reflections and competitive background noise. This paper investigates the effect upon TDE when modeling the source signal with different speech-based distributions. An information theoretical TDE method indirectly encapsulating higher order statistics (HOS) formed the basis of this work. The underlying assumption of Gaussian distributed source has been replaced by that of generalized Gaussian distribution that allows evaluating the problem under a larger set of speech-shaped distributions, ranging from Gaussian to Laplacian and Gamma. Closed forms of the univariate and multivariate entropy expressions of the generalized Gaussian distribution are derived to evaluate the TDE. The results indicate that TDE based on the specific criterion is independent of the underlying assumption for the distribution of the source, for the same covariance matrix.
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Gaussian functional regression for output prediction: Model assimilation and experimental design
NASA Astrophysics Data System (ADS)
Nguyen, N. C.; Peraire, J.
2016-03-01
In this paper, we introduce a Gaussian functional regression (GFR) technique that integrates multi-fidelity models with model reduction to efficiently predict the input-output relationship of a high-fidelity model. The GFR method combines the high-fidelity model with a low-fidelity model to provide an estimate of the output of the high-fidelity model in the form of a posterior distribution that can characterize uncertainty in the prediction. A reduced basis approximation is constructed upon the low-fidelity model and incorporated into the GFR method to yield an inexpensive posterior distribution of the output estimate. As this posterior distribution depends crucially on a set of training inputs at which the high-fidelity models are simulated, we develop a greedy sampling algorithm to select the training inputs. Our approach results in an output prediction model that inherits the fidelity of the high-fidelity model and has the computational complexity of the reduced basis approximation. Numerical results are presented to demonstrate the proposed approach.
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Full-wave generalizations of the fundamental Gaussian beam.
Seshadri, S R
2009-12-01
The basic full wave corresponding to the fundamental Gaussian beam was discovered for the outwardly propagating wave in a half-space by the introduction of a source in the complex space. There is a class of extended full waves all of which reduce to the same fundamental Gaussian beam in the appropriate limit. For the extended full Gaussian waves that include the basic full Gaussian wave as a special case, the sources are in the complex space on different planes transverse to the propagation direction. The sources are cylindrically symmetric Gaussian distributions centered at the origin of the transverse planes, the axis of symmetry being the propagation direction. For the special case of the basic full Gaussian wave, the source is a point source. The radiation intensity of the extended full Gaussian waves is determined and their characteristics are discussed and compared with those of the fundamental Gaussian beam. The extended full Gaussian waves are also obtained for the oppositely propagating outwardly directed waves in the second half-space. The radiation intensity distributions in the two half-spaces have reflection symmetry about the midplane. The radiation intensity distributions of the various extended full Gaussian waves are not significantly different. The power carried by the extended full Gaussian waves is evaluated and compared with that of the fundamental Gaussian beam.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
He Guangjun; Duan Wenshan; Tian Duoxiang
2008-04-15
For unmagnetized dusty plasma with many different dust grain species containing both hot isothermal electrons and ions, both the linear dispersion relation and the Kadomtsev-Petviashvili equation for small, but finite amplitude dust acoustic waves are obtained. The linear dispersion relation is investigated numerically. Furthermore, the variations of amplitude, width, and propagation velocity of the nonlinear solitary wave with an arbitrary dust size distribution function are studied as well. Moreover, both the power law distribution and the Gaussian distribution are approximately simulated by using appropriate arbitrary dust size distribution functions.
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Sailamul, Pachaya; Jang, Jaeson; Paik, Se-Bum
2017-12-01
Correlated neural activities such as synchronizations can significantly alter the characteristics of spike transfer between neural layers. However, it is not clear how this synchronization-dependent spike transfer can be affected by the structure of convergent feedforward wiring. To address this question, we implemented computer simulations of model neural networks: a source and a target layer connected with different types of convergent wiring rules. In the Gaussian-Gaussian (GG) model, both the connection probability and the strength are given as Gaussian distribution as a function of spatial distance. In the Uniform-Constant (UC) and Uniform-Exponential (UE) models, the connection probability density is a uniform constant within a certain range, but the connection strength is set as a constant value or an exponentially decaying function, respectively. Then we examined how the spike transfer function is modulated under these conditions, while static or synchronized input patterns were introduced to simulate different levels of feedforward spike synchronization. We observed that the synchronization-dependent modulation of the transfer function appeared noticeably different for each convergence condition. The modulation of the spike transfer function was largest in the UC model, and smallest in the UE model. Our analysis showed that this difference was induced by the different spike weight distributions that was generated from convergent synapses in each model. Our results suggest that, the structure of the feedforward convergence is a crucial factor for correlation-dependent spike control, thus must be considered important to understand the mechanism of information transfer in the brain.
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Dai, Huanping; Micheyl, Christophe
2015-05-01
Proportion correct (Pc) is a fundamental measure of task performance in psychophysics. The maximum Pc score that can be achieved by an optimal (maximum-likelihood) observer in a given task is of both theoretical and practical importance, because it sets an upper limit on human performance. Within the framework of signal detection theory, analytical solutions for computing the maximum Pc score have been established for several common experimental paradigms under the assumption of Gaussian additive internal noise. However, as the scope of applications of psychophysical signal detection theory expands, the need is growing for psychophysicists to compute maximum Pc scores for situations involving non-Gaussian (internal or stimulus-induced) noise. In this article, we provide a general formula for computing the maximum Pc in various psychophysical experimental paradigms for arbitrary probability distributions of sensory activity. Moreover, easy-to-use MATLAB code implementing the formula is provided. Practical applications of the formula are illustrated, and its accuracy is evaluated, for two paradigms and two types of probability distributions (uniform and Gaussian). The results demonstrate that Pc scores computed using the formula remain accurate even for continuous probability distributions, as long as the conversion from continuous probability density functions to discrete probability mass functions is supported by a sufficiently high sampling resolution. We hope that the exposition in this article, and the freely available MATLAB code, facilitates calculations of maximum performance for a wider range of experimental situations, as well as explorations of the impact of different assumptions concerning internal-noise distributions on maximum performance in psychophysical experiments.
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High quality Gaussian basis sets for fourth-row atoms
NASA Technical Reports Server (NTRS)
Partridge, Harry; Faegri, Knut, Jr.
1992-01-01
Energy optimized Gaussian basis sets of triple-zeta quality for the atoms Rb-Xe have been derived. Two series of basis sets are developed: (24s 16p 10d) and (26s 16p 10d) sets which were expanded to 13d and 19p functions as the 4d and 5p shells become occupied. For the atoms lighter than Cd, the (24s 16p 10d) sets with triple-zeta valence distributions are higher in energy than the corresponding double-zeta distribution. To ensure a triple-zeta distribution and a global energy minimum, the (26s 16p 10d) sets were derived. Total atomic energies from the largest basis sets are between 198 and 284 (mu)E(sub H) above the numerical Hartree-Fock energies.
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NASA Technical Reports Server (NTRS)
Garber, Donald P.
1993-01-01
A probability density function for the variability of ensemble averaged spectral estimates from helicopter acoustic signals in Gaussian background noise was evaluated. Numerical methods for calculating the density function and for determining confidence limits were explored. Density functions were predicted for both synthesized and experimental data and compared with observed spectral estimate variability.
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Petersen, Per H; Lund, Flemming; Fraser, Callum G; Sölétormos, György
2016-11-01
Background The distributions of within-subject biological variation are usually described as coefficients of variation, as are analytical performance specifications for bias, imprecision and other characteristics. Estimation of specifications required for reference change values is traditionally done using relationship between the batch-related changes during routine performance, described as Δbias, and the coefficients of variation for analytical imprecision (CV A ): the original theory is based on standard deviations or coefficients of variation calculated as if distributions were Gaussian. Methods The distribution of between-subject biological variation can generally be described as log-Gaussian. Moreover, recent analyses of within-subject biological variation suggest that many measurands have log-Gaussian distributions. In consequence, we generated a model for the estimation of analytical performance specifications for reference change value, with combination of Δbias and CV A based on log-Gaussian distributions of CV I as natural logarithms. The model was tested using plasma prolactin and glucose as examples. Results Analytical performance specifications for reference change value generated using the new model based on log-Gaussian distributions were practically identical with the traditional model based on Gaussian distributions. Conclusion The traditional and simple to apply model used to generate analytical performance specifications for reference change value, based on the use of coefficients of variation and assuming Gaussian distributions for both CV I and CV A , is generally useful.
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NASA Astrophysics Data System (ADS)
Lylova, A. N.; Sheldakova, Yu. V.; Kudryashov, A. V.; Samarkin, V. V.
2018-01-01
We consider the methods for modelling doughnut and super-Gaussian intensity distributions in the far field by means of deformable bimorph mirrors. A method for the rapid formation of a specified intensity distribution using a Shack - Hartmann sensor is proposed, and the results of the modelling of doughnut and super-Gaussian intensity distributions are presented.
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NASA Astrophysics Data System (ADS)
Sergeenko, N. P.
2017-11-01
An adequate statistical method should be developed in order to predict probabilistically the range of ionospheric parameters. This problem is solved in this paper. The time series of the critical frequency of the layer F2- foF2( t) were subjected to statistical processing. For the obtained samples {δ foF2}, statistical distributions and invariants up to the fourth order are calculated. The analysis shows that the distributions differ from the Gaussian law during the disturbances. At levels of sufficiently small probability distributions, there are arbitrarily large deviations from the model of the normal process. Therefore, it is attempted to describe statistical samples {δ foF2} based on the Poisson model. For the studied samples, the exponential characteristic function is selected under the assumption that time series are a superposition of some deterministic and random processes. Using the Fourier transform, the characteristic function is transformed into a nonholomorphic excessive-asymmetric probability-density function. The statistical distributions of the samples {δ foF2} calculated for the disturbed periods are compared with the obtained model distribution function. According to the Kolmogorov's criterion, the probabilities of the coincidence of a posteriori distributions with the theoretical ones are P 0.7-0.9. The conducted analysis makes it possible to draw a conclusion about the applicability of a model based on the Poisson random process for the statistical description and probabilistic variation estimates during heliogeophysical disturbances of the variations {δ foF2}.
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Fock expansion of multimode pure Gaussian states
DOE Office of Scientific and Technical Information (OSTI.GOV)
Cariolaro, Gianfranco; Pierobon, Gianfranco, E-mail: gianfranco.pierobon@unipd.it
2015-12-15
The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, asmore » shown for two-mode and three-mode Gaussian states.« less
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Modeling and statistical analysis of non-Gaussian random fields with heavy-tailed distributions.
Nezhadhaghighi, Mohsen Ghasemi; Nakhlband, Abbas
2017-04-01
In this paper, we investigate and develop an alternative approach to the numerical analysis and characterization of random fluctuations with the heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare fluctuations. We identify the heavy-tailed random fluctuations based on the scaling properties of the tail exponent of the PDF, power-law growth of qth order correlation function, and the self-similar properties of the contour lines in two-dimensional random fields. Moreover, this work leads to a substitution for the fractional Edwards-Wilkinson (EW) equation that works in the presence of μ-stable Lévy noise. Our proposed model explains the configuration dynamics of the systems with heavy-tailed correlated random fluctuations. We also present an alternative solution to the fractional EW equation in the presence of μ-stable Lévy noise in the steady state, which is implemented numerically, using the μ-stable fractional Lévy motion. Based on the analysis of the self-similar properties of contour loops, we numerically show that the scaling properties of contour loop ensembles can qualitatively and quantitatively distinguish non-Gaussian random fields from Gaussian random fluctuations.
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Statistical dynamics of regional populations and economies
NASA Astrophysics Data System (ADS)
Huo, Jie; Wang, Xu-Ming; Hao, Rui; Wang, Peng
Quantitative analysis of human behavior and social development is becoming a hot spot of some interdisciplinary studies. A statistical analysis on the population and GDP of 150 cities in China from 1990 to 2013 is conducted. The result indicates the cumulative probability distribution of the populations and that of the GDPs obeying the shifted power law, respectively. In order to understand these characteristics, a generalized Langevin equation describing variation of population is proposed, which is based on the correlations between population and GDP as well as the random fluctuations of the related factors. The equation is transformed into the Fokker-Plank equation to express the evolution of population distribution. The general solution demonstrates a transition of the distribution from the normal Gaussian distribution to a shifted power law, which suggests a critical point of time at which the transition takes place. The shifted power law distribution in the supercritical situation is qualitatively in accordance with the practical result. The distribution of the GDPs is derived from the well-known Cobb-Douglas production function. The result presents a change, in supercritical situation, from a shifted power law to the Gaussian distribution. This is a surprising result-the regional GDP distribution of our world will be the Gaussian distribution one day in the future. The discussions based on the changing trend of economic growth suggest it will be true. Therefore, these theoretical attempts may draw a historical picture of our society in the aspects of population and economy.
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Wang, Minghao; Yuan, Xiuhua; Ma, Donglin
2017-04-01
Nonuniformly correlated partially coherent beams (PCBs) have extraordinary propagation properties, making it possible to further improve the performance of free-space optical communications. In this paper, a series of PCBs with varying degrees of coherence in the radial direction, academically called radial partially coherent beams (RPCBs), are considered. RPCBs with arbitrary coherence distributions can be created by adjusting the amplitude profile of a spatial modulation function imposed on a uniformly correlated phase screen. Since RPCBs cannot be well characterized by the coherence length, a modulation depth factor is introduced as an indicator of the overall distribution of coherence. By wave optics simulation, free-space and atmospheric propagation properties of RPCBs with (inverse) Gaussian and super-Gaussian coherence distributions are examined in comparison with conventional Gaussian Schell-model beams. Furthermore, the impacts of varying central coherent areas are studied. Simulation results reveal that under comparable overall coherence, beams with a highly coherent core and a less coherent margin exhibit a smaller beam spread and greater on-axis intensity, which is mainly due to the self-focusing phenomenon right after the beam exits the transmitter. Particularly, those RPCBs with super-Gaussian coherence distributions will repeatedly focus during propagation, resulting in even greater intensities. Additionally, RPCBs also have a considerable ability to reduce scintillation. And it is demonstrated that those properties have made RPCBs very effective in improving the mean signal-to-noise ratio of small optical receivers, especially in relatively short, weakly fluctuating links.
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Hirayama, Shusuke; Takayanagi, Taisuke; Fujii, Yusuke; Fujimoto, Rintaro; Fujitaka, Shinichiro; Umezawa, Masumi; Nagamine, Yoshihiko; Hosaka, Masahiro; Yasui, Keisuke; Omachi, Chihiro; Toshito, Toshiyuki
2016-03-01
The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique. The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations. The authors investigated the difference between double and triple Gaussian kernel models. The authors found that the difference between the two studied kernel models appeared at mid-depths and the accuracy of predicting the double Gaussian model deteriorated at the low-dose bump that appeared at mid-depths. When the authors employed the double Gaussian kernel model, the accuracy of calculations for the absolute dose at the center of the SOBP varied with irradiation conditions and the maximum difference was 3.4%. In contrast, the results obtained from calculations with the triple Gaussian kernel model indicated good agreement with the measurements within ±1.1%, regardless of the irradiation conditions. The difference between the results obtained with the two types of studied kernel models was distinct in the high energy region. The accuracy of calculations with the double Gaussian kernel model varied with the field size and SOBP width because the accuracy of prediction with the double Gaussian model was insufficient at the low-dose bump. The evaluation was only qualitative under limited volumetric irradiation conditions. Further accumulation of measured data would be needed to quantitatively comprehend what influence the double and triple Gaussian kernel models had on the accuracy of dose calculations.
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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.
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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.
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Marko, Nicholas F.; Weil, Robert J.
2012-01-01
Introduction Gene expression data is often assumed to be normally-distributed, but this assumption has not been tested rigorously. We investigate the distribution of expression data in human cancer genomes and study the implications of deviations from the normal distribution for translational molecular oncology research. Methods We conducted a central moments analysis of five cancer genomes and performed empiric distribution fitting to examine the true distribution of expression data both on the complete-experiment and on the individual-gene levels. We used a variety of parametric and nonparametric methods to test the effects of deviations from normality on gene calling, functional annotation, and prospective molecular classification using a sixth cancer genome. Results Central moments analyses reveal statistically-significant deviations from normality in all of the analyzed cancer genomes. We observe as much as 37% variability in gene calling, 39% variability in functional annotation, and 30% variability in prospective, molecular tumor subclassification associated with this effect. Conclusions Cancer gene expression profiles are not normally-distributed, either on the complete-experiment or on the individual-gene level. Instead, they exhibit complex, heavy-tailed distributions characterized by statistically-significant skewness and kurtosis. The non-Gaussian distribution of this data affects identification of differentially-expressed genes, functional annotation, and prospective molecular classification. These effects may be reduced in some circumstances, although not completely eliminated, by using nonparametric analytics. This analysis highlights two unreliable assumptions of translational cancer gene expression analysis: that “small” departures from normality in the expression data distributions are analytically-insignificant and that “robust” gene-calling algorithms can fully compensate for these effects. PMID:23118863
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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.
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An alternative to the breeder's and Lande's equations.
Houchmandzadeh, Bahram
2014-01-10
The breeder's equation is a cornerstone of quantitative genetics, widely used in evolutionary modeling. Noting the mean phenotype in parental, selected parents, and the progeny by E(Z0), E(ZW), and E(Z1), this equation relates response to selection R = E(Z1) - E(Z0) to the selection differential S = E(ZW) - E(Z0) through a simple proportionality relation R = h(2)S, where the heritability coefficient h(2) is a simple function of genotype and environment factors variance. The validity of this relation relies strongly on the normal (Gaussian) distribution of the parent genotype, which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness (or selection) function is Gaussian with mean μ, an alternative, exact linear equation of the form R' = j(2)S' can be derived, regardless of the parental genotype distribution. Here R' = E(Z1) - μ and S' = E(ZW) - μ stand for the mean phenotypic lag with respect to the mean of the fitness function in the offspring and selected populations. The proportionality coefficient j(2) is a simple function of selection function and environment factors variance, but does not contain the genotype variance. To demonstrate this, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between them. These results generalize naturally to the concept of G matrix and the multivariate Lande's equation Δ(z) = GP(-1)S. The linearity coefficient of the alternative equation are not changed by Gaussian selection.
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Relative performance of selected detectors
NASA Astrophysics Data System (ADS)
Ranney, Kenneth I.; Khatri, Hiralal; Nguyen, Lam H.; Sichina, Jeffrey
2000-08-01
The quadratic polynomial detector (QPD) and the radial basis function (RBF) family of detectors -- including the Bayesian neural network (BNN) -- might well be considered workhorses within the field of automatic target detection (ATD). The QPD works reasonably well when the data is unimodal, and it also achieves the best possible performance if the underlying data follow a Gaussian distribution. The BNN, on the other hand, has been applied successfully in cases where the underlying data are assumed to follow a multimodal distribution. We compare the performance of a BNN detector and a QPD for various scenarios synthesized from a set of Gaussian probability density functions (pdfs). This data synthesis allows us to control parameters such as modality and correlation, which, in turn, enables us to create data sets that can probe the weaknesses of the detectors. We present results for different data scenarios and different detector architectures.
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Non-gaussianity versus nonlinearity of cosmological perturbations.
Verde, L
2001-06-01
Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.
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Generation of low-divergence laser beams
Kronberg, James W.
1993-01-01
Apparatus for transforming a conventional beam of coherent light, having a Gaussian energy distribution and relatively high divergence, into a beam in which the energy distribution approximates a single, non-zero-order Bessel function and which therefore has much lower divergence. The apparatus comprises a zone plate having transmitting and reflecting zones defined by the pattern of light interference produced by the combination of a beam of coherent light with a Gaussian energy distribution and one having such a Bessel distribution. The interference pattern between the two beams is a concentric array of multiple annuli, and is preferably recorded as a hologram. The hologram is then used to form the transmitting and reflecting zones by photo-etching portions of a reflecting layer deposited on a plate made of a transmitting material. A Bessel beam, containing approximately 50% of the energy of the incident beam, is produced by passing a Gaussian beam through such a Bessel zone plate. The reflected beam, also containing approximately 50% of the incident beam energy and having a Bessel energy distribution, can be redirected in the same direction and parallel to the transmitted beam. Alternatively, a filter similar to the Bessel zone plate can be placed within the resonator cavity of a conventional laser system having a front mirror and a rear mirror, preferably axially aligned with the mirrors and just inside the front mirror to generate Bessel energy distribution light beams at the laser source.
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NASA Astrophysics Data System (ADS)
Sato, Aki-Hiro
2010-12-01
This study considers q-Gaussian distributions and stochastic differential equations with both multiplicative and additive noises. In the M-dimensional case a q-Gaussian distribution can be theoretically derived as a stationary probability distribution of the multiplicative stochastic differential equation with both mutually independent multiplicative and additive noises. By using the proposed stochastic differential equation a method to evaluate a default probability under a given risk buffer is proposed.
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Investigation of non-Gaussian effects in the Brazilian option market
NASA Astrophysics Data System (ADS)
Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.
2018-04-01
An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.
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On Stabilizing the Variance of Dynamic Functional Brain Connectivity Time Series
Fransson, Peter
2016-01-01
Abstract Assessment of dynamic functional brain connectivity based on functional magnetic resonance imaging (fMRI) data is an increasingly popular strategy to investigate temporal dynamics of the brain's large-scale network architecture. Current practice when deriving connectivity estimates over time is to use the Fisher transformation, which aims to stabilize the variance of correlation values that fluctuate around varying true correlation values. It is, however, unclear how well the stabilization of signal variance performed by the Fisher transformation works for each connectivity time series, when the true correlation is assumed to be fluctuating. This is of importance because many subsequent analyses either assume or perform better when the time series have stable variance or adheres to an approximate Gaussian distribution. In this article, using simulations and analysis of resting-state fMRI data, we analyze the effect of applying different variance stabilization strategies on connectivity time series. We focus our investigation on the Fisher transformation, the Box–Cox (BC) transformation and an approach that combines both transformations. Our results show that, if the intention of stabilizing the variance is to use metrics on the time series, where stable variance or a Gaussian distribution is desired (e.g., clustering), the Fisher transformation is not optimal and may even skew connectivity time series away from being Gaussian. Furthermore, we show that the suboptimal performance of the Fisher transformation can be substantially improved by including an additional BC transformation after the dynamic functional connectivity time series has been Fisher transformed. PMID:27784176
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On Stabilizing the Variance of Dynamic Functional Brain Connectivity Time Series.
Thompson, William Hedley; Fransson, Peter
2016-12-01
Assessment of dynamic functional brain connectivity based on functional magnetic resonance imaging (fMRI) data is an increasingly popular strategy to investigate temporal dynamics of the brain's large-scale network architecture. Current practice when deriving connectivity estimates over time is to use the Fisher transformation, which aims to stabilize the variance of correlation values that fluctuate around varying true correlation values. It is, however, unclear how well the stabilization of signal variance performed by the Fisher transformation works for each connectivity time series, when the true correlation is assumed to be fluctuating. This is of importance because many subsequent analyses either assume or perform better when the time series have stable variance or adheres to an approximate Gaussian distribution. In this article, using simulations and analysis of resting-state fMRI data, we analyze the effect of applying different variance stabilization strategies on connectivity time series. We focus our investigation on the Fisher transformation, the Box-Cox (BC) transformation and an approach that combines both transformations. Our results show that, if the intention of stabilizing the variance is to use metrics on the time series, where stable variance or a Gaussian distribution is desired (e.g., clustering), the Fisher transformation is not optimal and may even skew connectivity time series away from being Gaussian. Furthermore, we show that the suboptimal performance of the Fisher transformation can be substantially improved by including an additional BC transformation after the dynamic functional connectivity time series has been Fisher transformed.
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Wigner functions for evanescent waves.
Petruccelli, Jonathan C; Tian, Lei; Oh, Se Baek; Barbastathis, George
2012-09-01
We propose phase space distributions, based on an extension of the Wigner distribution function, to describe fields of any state of coherence that contain evanescent components emitted into a half-space. The evanescent components of the field are described in an optical phase space of spatial position and complex-valued angle. Behavior of these distributions upon propagation is also considered, where the rapid decay of the evanescent components is associated with the exponential decay of the associated phase space distributions. To demonstrate the structure and behavior of these distributions, we consider the fields generated from total internal reflection of a Gaussian Schell-model beam at a planar interface.
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Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.
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.
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Korsgaard, Inge Riis; Lund, Mogens Sandø; Sorensen, Daniel; Gianola, Daniel; Madsen, Per; Jensen, Just
2003-01-01
A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed. PMID:12633531
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Park, Subok; Gallas, Bradon D; Badano, Aldo; Petrick, Nicholas A; Myers, Kyle J
2007-04-01
A previous study [J. Opt. Soc. Am. A22, 3 (2005)] has shown that human efficiency for detecting a Gaussian signal at a known location in non-Gaussian distributed lumpy backgrounds is approximately 4%. This human efficiency is much less than the reported 40% efficiency that has been documented for Gaussian-distributed lumpy backgrounds [J. Opt. Soc. Am. A16, 694 (1999) and J. Opt. Soc. Am. A18, 473 (2001)]. We conducted a psychophysical study with a number of changes, specifically in display-device calibration and data scaling, from the design of the aforementioned study. Human efficiency relative to the ideal observer was found again to be approximately 5%. Our variance analysis indicates that neither scaling nor display made a statistically significant difference in human performance for the task. We conclude that the non-Gaussian distributed lumpy background is a major factor in our low human-efficiency results.
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NASA Astrophysics Data System (ADS)
Drescher, A. C.; Gadgil, A. J.; Price, P. N.; Nazaroff, W. W.
Optical remote sensing and iterative computed tomography (CT) can be applied to measure the spatial distribution of gaseous pollutant concentrations. We conducted chamber experiments to test this combination of techniques using an open path Fourier transform infrared spectrometer (OP-FTIR) and a standard algebraic reconstruction technique (ART). Although ART converged to solutions that showed excellent agreement with the measured ray-integral concentrations, the solutions were inconsistent with simultaneously gathered point-sample concentration measurements. A new CT method was developed that combines (1) the superposition of bivariate Gaussians to represent the concentration distribution and (2) a simulated annealing minimization routine to find the parameters of the Gaussian basis functions that result in the best fit to the ray-integral concentration data. This method, named smooth basis function minimization (SBFM), generated reconstructions that agreed well, both qualitatively and quantitatively, with the concentration profiles generated from point sampling. We present an analysis of two sets of experimental data that compares the performance of ART and SBFM. We conclude that SBFM is a superior CT reconstruction method for practical indoor and outdoor air monitoring applications.
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Computer routines for probability distributions, random numbers, and related functions
Kirby, W.
1983-01-01
Use of previously coded and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main progress. The probability distributions provided include the beta, chi-square, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F. Other mathematical functions include the Bessel function, I sub o, gamma and log-gamma functions, error functions, and exponential integral. Auxiliary services include sorting and printer-plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)
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Computer routines for probability distributions, random numbers, and related functions
Kirby, W.H.
1980-01-01
Use of previously codes and tested subroutines simplifies and speeds up program development and testing. This report presents routines that can be used to calculate various probability distributions and other functions of importance in statistical hydrology. The routines are designed as general-purpose Fortran subroutines and functions to be called from user-written main programs. The probability distributions provided include the beta, chisquare, gamma, Gaussian (normal), Pearson Type III (tables and approximation), and Weibull. Also provided are the distributions of the Grubbs-Beck outlier test, Kolmogorov 's and Smirnov 's D, Student 's t, noncentral t (approximate), and Snedecor F tests. Other mathematical functions include the Bessel function I (subzero), gamma and log-gamma functions, error functions and exponential integral. Auxiliary services include sorting and printer plotting. Random number generators for uniform and normal numbers are provided and may be used with some of the above routines to generate numbers from other distributions. (USGS)
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Leverrier, Anthony; Grangier, Philippe; Laboratoire Charles Fabry, Institut d'Optique, CNRS, University Paris-Sud, Campus Polytechnique, RD 128, F-91127 Palaiseau Cedex
2010-06-15
In this article, we give a simple proof of the fact that the optimal collective attacks against continuous-variable quantum key distribution with a Gaussian modulation are Gaussian attacks. Our proof, which makes use of symmetry properties of the protocol in phase space, is particularly relevant for the finite-key analysis of the protocol and therefore for practical applications.
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Capacity of PPM on Gaussian and Webb Channels
NASA Technical Reports Server (NTRS)
Divsalar, D.; Dolinar, S.; Pollara, F.; Hamkins, J.
2000-01-01
This paper computes and compares the capacities of M-ary PPM on various idealized channels that approximate the optical communication channel: (1) the standard additive white Gaussian noise (AWGN) channel;(2) a more general AWGN channel (AWGN2) allowing different variances in signal and noise slots;(3) a Webb-distributed channel (Webb2);(4) a Webb+Gaussian channel, modeling Gaussian thermal noise added to Webb-distributed channel outputs.
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Focal ratio degradation: a new perspective
NASA Astrophysics Data System (ADS)
Haynes, Dionne M.; Withford, Michael J.; Dawes, Judith M.; Haynes, Roger; Bland-Hawthorn, Joss
2008-07-01
We have developed an alternative FRD empirical model for the parallel laser beam technique which can accommodate contributions from both scattering and modal diffusion. It is consistent with scattering inducing a Lorentzian contribution and modal diffusion inducing a Gaussian contribution. The convolution of these two functions produces a Voigt function which is shown to better simulate the observed behavior of the FRD distribution and provides a greatly improved fit over the standard Gaussian fitting approach. The Voigt model can also be used to quantify the amount of energy displaced by FRD, therefore allowing astronomical instrument scientists to identify, quantify and potentially minimize the various sources of FRD, and optimise the fiber and instrument performance.
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NASA Astrophysics Data System (ADS)
Cheng, Qin-Bo; Chen, Xi; Xu, Chong-Yu; Reinhardt-Imjela, Christian; Schulte, Achim
2014-11-01
In this study, the likelihood functions for uncertainty analysis of hydrological models are compared and improved through the following steps: (1) the equivalent relationship between the Nash-Sutcliffe Efficiency coefficient (NSE) and the likelihood function with Gaussian independent and identically distributed residuals is proved; (2) a new estimation method of the Box-Cox transformation (BC) parameter is developed to improve the effective elimination of the heteroscedasticity of model residuals; and (3) three likelihood functions-NSE, Generalized Error Distribution with BC (BC-GED) and Skew Generalized Error Distribution with BC (BC-SGED)-are applied for SWAT-WB-VSA (Soil and Water Assessment Tool - Water Balance - Variable Source Area) model calibration in the Baocun watershed, Eastern China. Performances of calibrated models are compared using the observed river discharges and groundwater levels. The result shows that the minimum variance constraint can effectively estimate the BC parameter. The form of the likelihood function significantly impacts on the calibrated parameters and the simulated results of high and low flow components. SWAT-WB-VSA with the NSE approach simulates flood well, but baseflow badly owing to the assumption of Gaussian error distribution, where the probability of the large error is low, but the small error around zero approximates equiprobability. By contrast, SWAT-WB-VSA with the BC-GED or BC-SGED approach mimics baseflow well, which is proved in the groundwater level simulation. The assumption of skewness of the error distribution may be unnecessary, because all the results of the BC-SGED approach are nearly the same as those of the BC-GED approach.
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Nonlocality of the original Einstein-Podolsky-Rosen state
NASA Astrophysics Data System (ADS)
Cohen, O.
1997-11-01
We examine the properties and behavior of the original Einstein-Podolsky-Rosen (EPR) wave function [Phys. Rev. 47, 777 (1935)] and related Gaussian-correlated wave functions. We assess the degree of entanglement of these wave functions and consider an argument of Bell [Ann. (N.Y.) Acad. Sci. 480, 263 (1986)] based on the Wigner phase-space distribution [Phys. Rev. 40, 749 (1932)], which implies that the original EPR correlations can accommodate a local hidden-variable description. We extend Bell's analysis to the related Gaussian wave functions. We then show that it is possible to identify definite nonlocal aspects for the original EPR state and related states. We describe possible experiments that would demonstrate these nonlocal features through violations of Bell inequalities. The implications of our results, and in particular their relevance for the causal interpretation of quantum mechanics, are considered.
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Long-range correlation in cosmic microwave background radiation.
Movahed, M Sadegh; Ghasemi, F; Rahvar, Sohrab; Tabar, M Reza Rahimi
2011-08-01
We investigate the statistical anisotropy and gaussianity of temperature fluctuations of Cosmic Microwave Background (CMB) radiation data from the Wilkinson Microwave Anisotropy Probe survey, using the Multifractal Detrended Fluctuation Analysis, Rescaled Range, and Scaled Windowed Variance methods. Multifractal Detrended Fluctuation Analysis shows that CMB fluctuations has a long-range correlation function with a multifractal behavior. By comparing the shuffled and surrogate series of CMB data, we conclude that the multifractality nature of the temperature fluctuation of CMB radiation is mainly due to the long-range correlations, and the map is consistent with a gaussian distribution.
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Statistical Modeling of Retinal Optical Coherence Tomography.
Amini, Zahra; Rabbani, Hossein
2016-06-01
In this paper, a new model for retinal Optical Coherence Tomography (OCT) images is proposed. This statistical model is based on introducing a nonlinear Gaussianization transform to convert the probability distribution function (pdf) of each OCT intra-retinal layer to a Gaussian distribution. The retina is a layered structure and in OCT each of these layers has a specific pdf which is corrupted by speckle noise, therefore a mixture model for statistical modeling of OCT images is proposed. A Normal-Laplace distribution, which is a convolution of a Laplace pdf and Gaussian noise, is proposed as the distribution of each component of this model. The reason for choosing Laplace pdf is the monotonically decaying behavior of OCT intensities in each layer for healthy cases. After fitting a mixture model to the data, each component is gaussianized and all of them are combined by Averaged Maximum A Posterior (AMAP) method. To demonstrate the ability of this method, a new contrast enhancement method based on this statistical model is proposed and tested on thirteen healthy 3D OCTs taken by the Topcon 3D OCT and five 3D OCTs from Age-related Macular Degeneration (AMD) patients, taken by Zeiss Cirrus HD-OCT. Comparing the results with two contending techniques, the prominence of the proposed method is demonstrated both visually and numerically. Furthermore, to prove the efficacy of the proposed method for a more direct and specific purpose, an improvement in the segmentation of intra-retinal layers using the proposed contrast enhancement method as a preprocessing step, is demonstrated.
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Ship Detection in SAR Image Based on the Alpha-stable Distribution
Wang, Changcheng; Liao, Mingsheng; Li, Xiaofeng
2008-01-01
This paper describes an improved Constant False Alarm Rate (CFAR) ship detection algorithm in spaceborne synthetic aperture radar (SAR) image based on Alpha-stable distribution model. Typically, the CFAR algorithm uses the Gaussian distribution model to describe statistical characteristics of a SAR image background clutter. However, the Gaussian distribution is only valid for multilook SAR images when several radar looks are averaged. As sea clutter in SAR images shows spiky or heavy-tailed characteristics, the Gaussian distribution often fails to describe background sea clutter. In this study, we replace the Gaussian distribution with the Alpha-stable distribution, which is widely used in impulsive or spiky signal processing, to describe the background sea clutter in SAR images. In our proposed algorithm, an initial step for detecting possible ship targets is employed. Then, similar to the typical two-parameter CFAR algorithm, a local process is applied to the pixel identified as possible target. A RADARSAT-1 image is used to validate this Alpha-stable distribution based algorithm. Meanwhile, known ship location data during the time of RADARSAT-1 SAR image acquisition is used to validate ship detection results. Validation results show improvements of the new CFAR algorithm based on the Alpha-stable distribution over the CFAR algorithm based on the Gaussian distribution. PMID:27873794
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Yi, Qu; Zhan-ming, Li; Er-chao, Li
2012-11-01
A new fault detection and diagnosis (FDD) problem via the output probability density functions (PDFs) for non-gausian stochastic distribution systems (SDSs) is investigated. The PDFs can be approximated by radial basis functions (RBFs) neural networks. Different from conventional FDD problems, the measured information for FDD is the output stochastic distributions and the stochastic variables involved are not confined to Gaussian ones. A (RBFs) neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighings of the RBFs neural network. In this work, a nonlinear adaptive observer-based fault detection and diagnosis algorithm is presented by introducing the tuning parameter so that the residual is as sensitive as possible to the fault. Stability and Convergency analysis is performed in fault detection and fault diagnosis analysis for the error dynamic system. At last, an illustrated example is given to demonstrate the efficiency of the proposed algorithm, and satisfactory results have been obtained. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.
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NASA Technical Reports Server (NTRS)
Huang, N. E.; Long, S. R.
1980-01-01
Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived from the Longuet-Higgins (1963) theory. It is found that, even for the highly non-Gaussian cases, the distribution function proposed by Longuet-Higgins still gives good approximations.
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Kleinert, H; Zatloukal, V
2013-11-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
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Accretion rates of protoplanets 2: Gaussian distribution of planestesimal velocities
NASA Technical Reports Server (NTRS)
Greenzweig, Yuval; Lissauer, Jack J.
1991-01-01
The growth rate of a protoplanet embedded in a uniform surface density disk of planetesimals having a triaxial Gaussian velocity distribution was calculated. The longitudes of the aspses and nodes of the planetesimals are uniformly distributed, and the protoplanet is on a circular orbit. The accretion rate in the two body approximation is enhanced by a factor of approximately 3, compared to the case where all planetesimals have eccentricity and inclination equal to the root mean square (RMS) values of those variables in the Gaussian distribution disk. Numerical three body integrations show comparable enhancements, except when the RMS initial planetesimal eccentricities are extremely small. This enhancement in accretion rate should be incorporated by all models, analytical or numerical, which assume a single random velocity for all planetesimals, in lieu of a Gaussian distribution.
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An Alternative to the Breeder’s and Lande’s Equations
Houchmandzadeh, Bahram
2013-01-01
The breeder’s equation is a cornerstone of quantitative genetics, widely used in evolutionary modeling. Noting the mean phenotype in parental, selected parents, and the progeny by E(Z0), E(ZW), and E(Z1), this equation relates response to selection R = E(Z1) − E(Z0) to the selection differential S = E(ZW) − E(Z0) through a simple proportionality relation R = h2S, where the heritability coefficient h2 is a simple function of genotype and environment factors variance. The validity of this relation relies strongly on the normal (Gaussian) distribution of the parent genotype, which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness (or selection) function is Gaussian with mean μ, an alternative, exact linear equation of the form R′ = j2S′ can be derived, regardless of the parental genotype distribution. Here R′ = E(Z1) − μ and S′ = E(ZW) − μ stand for the mean phenotypic lag with respect to the mean of the fitness function in the offspring and selected populations. The proportionality coefficient j2 is a simple function of selection function and environment factors variance, but does not contain the genotype variance. To demonstrate this, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between them. These results generalize naturally to the concept of G matrix and the multivariate Lande’s equation Δz¯=GP−1S. The linearity coefficient of the alternative equation are not changed by Gaussian selection. PMID:24212080
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Albin, Thomas J; Vink, Peter
2015-01-01
Anthropometric data are assumed to have a Gaussian (Normal) distribution, but if non-Gaussian, accommodation estimates are affected. When data are limited, users may choose to combine anthropometric elements by Combining Percentiles (CP) (adding or subtracting), despite known adverse effects. This study examined whether global anthropometric data are Gaussian distributed. It compared the Median Correlation Method (MCM) of combining anthropometric elements with unknown correlations to CP to determine if MCM provides better estimates of percentile values and accommodation. Percentile values of 604 male and female anthropometric data drawn from seven countries worldwide were expressed as standard scores. The standard scores were tested to determine if they were consistent with a Gaussian distribution. Empirical multipliers for determining percentile values were developed.In a test case, five anthropometric elements descriptive of seating were combined in addition and subtraction models. Percentile values were estimated for each model by CP, MCM with Gaussian distributed data, or MCM with empirically distributed data. The 5th and 95th percentile values of a dataset of global anthropometric data are shown to be asymmetrically distributed. MCM with empirical multipliers gave more accurate estimates of 5th and 95th percentiles values. Anthropometric data are not Gaussian distributed. The MCM method is more accurate than adding or subtracting percentiles.
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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.
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Tsallis non-extensive statistics and solar wind plasma complexity
NASA Astrophysics Data System (ADS)
Pavlos, G. P.; Iliopoulos, A. C.; Zastenker, G. N.; Zelenyi, L. M.; Karakatsanis, L. P.; Riazantseva, M. O.; Xenakis, M. N.; Pavlos, E. G.
2015-03-01
This article presents novel results revealing non-equilibrium phase transition processes in the solar wind plasma during a strong shock event, which took place on 26th September 2011. Solar wind plasma is a typical case of stochastic spatiotemporal distribution of physical state variables such as force fields (B → , E →) and matter fields (particle and current densities or bulk plasma distributions). This study shows clearly the non-extensive and non-Gaussian character of the solar wind plasma and the existence of multi-scale strong correlations from the microscopic to the macroscopic level. It also underlines the inefficiency of classical magneto-hydro-dynamic (MHD) or plasma statistical theories, based on the classical central limit theorem (CLT), to explain the complexity of the solar wind dynamics, since these theories include smooth and differentiable spatial-temporal functions (MHD theory) or Gaussian statistics (Boltzmann-Maxwell statistical mechanics). On the contrary, the results of this study indicate the presence of non-Gaussian non-extensive statistics with heavy tails probability distribution functions, which are related to the q-extension of CLT. Finally, the results of this study can be understood in the framework of modern theoretical concepts such as non-extensive statistical mechanics (Tsallis, 2009), fractal topology (Zelenyi and Milovanov, 2004), turbulence theory (Frisch, 1996), strange dynamics (Zaslavsky, 2002), percolation theory (Milovanov, 1997), anomalous diffusion theory and anomalous transport theory (Milovanov, 2001), fractional dynamics (Tarasov, 2013) and non-equilibrium phase transition theory (Chang, 1992).
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GaussianCpG: a Gaussian model for detection of CpG island in human genome sequences.
Yu, Ning; Guo, Xuan; Zelikovsky, Alexander; Pan, Yi
2017-05-24
As crucial markers in identifying biological elements and processes in mammalian genomes, CpG islands (CGI) play important roles in DNA methylation, gene regulation, epigenetic inheritance, gene mutation, chromosome inactivation and nuclesome retention. The generally accepted criteria of CGI rely on: (a) %G+C content is ≥ 50%, (b) the ratio of the observed CpG content and the expected CpG content is ≥ 0.6, and (c) the general length of CGI is greater than 200 nucleotides. Most existing computational methods for the prediction of CpG island are programmed on these rules. However, many experimentally verified CpG islands deviate from these artificial criteria. Experiments indicate that in many cases %G+C is < 50%, CpG obs /CpG exp varies, and the length of CGI ranges from eight nucleotides to a few thousand of nucleotides. It implies that CGI detection is not just a straightly statistical task and some unrevealed rules probably are hidden. A novel Gaussian model, GaussianCpG, is developed for detection of CpG islands on human genome. We analyze the energy distribution over genomic primary structure for each CpG site and adopt the parameters from statistics of Human genome. The evaluation results show that the new model can predict CpG islands efficiently by balancing both sensitivity and specificity over known human CGI data sets. Compared with other models, GaussianCpG can achieve better performance in CGI detection. Our Gaussian model aims to simplify the complex interaction between nucleotides. The model is computed not by the linear statistical method but by the Gaussian energy distribution and accumulation. The parameters of Gaussian function are not arbitrarily designated but deliberately chosen by optimizing the biological statistics. By using the pseudopotential analysis on CpG islands, the novel model is validated on both the real and artificial data sets.
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Mulkern, Robert V; Balasubramanian, Mukund; Mitsouras, Dimitrios
2014-07-30
To determine whether Lorentzian or Gaussian intra-voxel frequency distributions are better suited for modeling data acquired with gradient-echo sampling of single spin-echoes for the simultaneous characterization of irreversible and reversible relaxation rates. Clinical studies (e.g., of brain iron deposition) using such acquisition schemes have typically assumed Lorentzian distributions. Theoretical expressions of the time-domain spin-echo signal for intra-voxel Lorentzian and Gaussian distributions were used to fit data from a human brain scanned at both 1.5 Tesla (T) and 3T, resulting in maps of irreversible and reversible relaxation rates for each model. The relative merits of the Lorentzian versus Gaussian model were compared by means of quality of fit considerations. Lorentzian fits were equivalent to Gaussian fits primarily in regions of the brain where irreversible relaxation dominated. In the multiple brain regions where reversible relaxation effects become prominent, however, Gaussian fits were clearly superior. The widespread assumption that a Lorentzian distribution is suitable for quantitative transverse relaxation studies of the brain should be reconsidered, particularly at 3T and higher field strengths as reversible relaxation effects become more prominent. Gaussian distributions offer alternate fits of experimental data that should prove quite useful in general. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc. © 2014 Wiley Periodicals, Inc.
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NASA Astrophysics Data System (ADS)
Xiang, Shao-Hua; Wen, Wei; Zhao, Yu-Jing; Song, Ke-Hui
2018-04-01
We study the properties of the cumulants of multimode boson operators and introduce the phase-averaged quadrature cumulants as the measure of the non-Gaussianity of multimode quantum states. Using this measure, we investigate the non-Gaussianity of two classes of two-mode non-Gaussian states: photon-number entangled states and entangled coherent states traveling in a bosonic memory quantum channel. We show that such a channel can skew the distribution of two-mode quadrature variables, giving rise to a strongly non-Gaussian correlation. In addition, we provide a criterion to determine whether the distributions of these states are super- or sub-Gaussian.
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Modified Gaussian influence function of deformable mirror actuators.
Huang, Linhai; Rao, Changhui; Jiang, Wenhan
2008-01-07
A new deformable mirror influence function based on a Gaussian function is introduced to analyze the fitting capability of a deformable mirror. The modified expressions for both azimuthal and radial directions are presented based on the analysis of the residual error between a measured influence function and a Gaussian influence function. With a simplex search method, we further compare the fitting capability of our proposed influence function to fit the data produced by a Zygo interferometer with that of a Gaussian influence function. The result indicates that the modified Gaussian influence function provides much better performance in data fitting.
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Generation of low-divergence laser beams
Kronberg, J.W.
1993-09-14
Apparatus for transforming a conventional beam of coherent light, having a Gaussian energy distribution and relatively high divergence, into a beam in which the energy distribution approximates a single, non-zero-order Bessel function and which therefore has much lower divergence. The apparatus comprises a zone plate having transmitting and reflecting zones defined by the pattern of light interference produced by the combination of a beam of coherent light with a Gaussian energy distribution and one having such a Bessel distribution. The interference pattern between the two beams is a concentric array of multiple annuli, and is preferably recorded as a hologram. The hologram is then used to form the transmitting and reflecting zones by photo-etching portions of a reflecting layer deposited on a plate made of a transmitting material. A Bessel beam, containing approximately 50% of the energy of the incident beam, is produced by passing a Gaussian beam through such a Bessel zone plate. The reflected beam, also containing approximately 50% of the incident beam energy and having a Bessel energy distribution, can be redirected in the same direction and parallel to the transmitted beam. Alternatively, a filter similar to the Bessel zone plate can be placed within the resonator cavity of a conventional laser system having a front mirror and a rear mirror, preferably axially aligned with the mirrors and just inside the front mirror to generate Bessel energy distribution light beams at the laser source. 11 figures.
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Skewness and kurtosis analysis for non-Gaussian distributions
NASA Astrophysics Data System (ADS)
Celikoglu, Ahmet; Tirnakli, Ugur
2018-06-01
In this paper we address a number of pitfalls regarding the use of kurtosis as a measure of deviations from the Gaussian. We treat kurtosis in both its standard definition and that which arises in q-statistics, namely q-kurtosis. We have recently shown that the relation proposed by Cristelli et al. (2012) between skewness and kurtosis can only be verified for relatively small data sets, independently of the type of statistics chosen; however it fails for sufficiently large data sets, if the fourth moment of the distribution is finite. For infinite fourth moments, kurtosis is not defined as the size of the data set tends to infinity. For distributions with finite fourth moments, the size, N, of the data set for which the standard kurtosis saturates to a fixed value, depends on the deviation of the original distribution from the Gaussian. Nevertheless, using kurtosis as a criterion for deciding which distribution deviates further from the Gaussian can be misleading for small data sets, even for finite fourth moment distributions. Going over to q-statistics, we find that although the value of q-kurtosis is finite in the range of 0 < q < 3, this quantity is not useful for comparing different non-Gaussian distributed data sets, unless the appropriate q value, which truly characterizes the data set of interest, is chosen. Finally, we propose a method to determine the correct q value and thereby to compute the q-kurtosis of q-Gaussian distributed data sets.
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Stochastic space interval as a link between quantum randomness and macroscopic randomness?
NASA Astrophysics Data System (ADS)
Haug, Espen Gaarder; Hoff, Harald
2018-03-01
For many stochastic phenomena, we observe statistical distributions that have fat-tails and high-peaks compared to the Gaussian distribution. In this paper, we will explain how observable statistical distributions in the macroscopic world could be related to the randomness in the subatomic world. We show that fat-tailed (leptokurtic) phenomena in our everyday macroscopic world are ultimately rooted in Gaussian - or very close to Gaussian-distributed subatomic particle randomness, but they are not, in a strict sense, Gaussian distributions. By running a truly random experiment over a three and a half-year period, we observed a type of random behavior in trillions of photons. Combining our results with simple logic, we find that fat-tailed and high-peaked statistical distributions are exactly what we would expect to observe if the subatomic world is quantized and not continuously divisible. We extend our analysis to the fact that one typically observes fat-tails and high-peaks relative to the Gaussian distribution in stocks and commodity prices and many aspects of the natural world; these instances are all observable and documentable macro phenomena that strongly suggest that the ultimate building blocks of nature are discrete (e.g. they appear in quanta).
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Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene.
Oettinger, D; Mendoza, M; Herrmann, H J
2013-07-01
We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as the weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, which satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential the electronic fluid behaves as if it increases its effective viscosity.
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2010-06-01
GMKPF represents a better and more flexible alternative to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ...accurate results relative to GML and EML when the network delays are modeled in terms of a single non-Gaussian/non-exponential distribution or as a...to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ) estimators for clock offset estimation in non-Gaussian or non
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The statistics of peaks of Gaussian random fields. [cosmological density fluctuations
NASA Technical Reports Server (NTRS)
Bardeen, J. M.; Bond, J. R.; Kaiser, N.; Szalay, A. S.
1986-01-01
A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.
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On the efficacy of procedures to normalize Ex-Gaussian distributions.
Marmolejo-Ramos, Fernando; Cousineau, Denis; Benites, Luis; Maehara, Rocío
2014-01-01
Reaction time (RT) is one of the most common types of measure used in experimental psychology. Its distribution is not normal (Gaussian) but resembles a convolution of normal and exponential distributions (Ex-Gaussian). One of the major assumptions in parametric tests (such as ANOVAs) is that variables are normally distributed. Hence, it is acknowledged by many that the normality assumption is not met. This paper presents different procedures to normalize data sampled from an Ex-Gaussian distribution in such a way that they are suitable for parametric tests based on the normality assumption. Using simulation studies, various outlier elimination and transformation procedures were tested against the level of normality they provide. The results suggest that the transformation methods are better than elimination methods in normalizing positively skewed data and the more skewed the distribution then the transformation methods are more effective in normalizing such data. Specifically, transformation with parameter lambda -1 leads to the best results.
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Full stellar kinematical profiles of central parts of nearby galaxies
NASA Astrophysics Data System (ADS)
Vudragović, A.; Samurović, S.; Jovanović, M.
2016-09-01
Context. We present the largest catalog of detailed stellar kinematics of the central parts of nearby galaxies, which includes higher moments of the line-of-sight velocity distribution (LOSVD) function represented by the Gauss-Hermite series. The kinematics is measured on a sample of galaxies selected from the Arecibo Legacy Fast ALFA (Alfalfa) survey using spectroscopy from the Sloan Digital Sky Survey (SDSS DR7). Aims: The SDSS DR7 offers measurements of the LOSVD based on the assumption of a pure Gaussian shape of the broadening function caused by the combination of rotational and random motion of the stars in galaxies. We discuss the consequences of this oversimplification since the velocity dispersion, one of the measured quantities, often serves as the proxy to important modeling parameters such as the black-hole mass and the virial mass of galaxies. Methods: The publicly available pPXF code is used to calculate the full kinematical profile for the sample galaxies including higher moments of their LOSVD. Both observed and synthetic stellar libraries were used and the related template mismatch problem is discussed. Results: For the whole sample of 2180 nearby galaxies reflecting morphological distribution characteristic for the local Universe, we successfully recovered stellar kinematics of their central parts, including higher order moments of the LOSVD function, for signal-to-noise above 50. Conclusions: We show the consequences of the oversimplification of the LOSVD function with Gaussian function on the velocity dispersion for the empirical and the synthetic stellar library. For the empirical stellar library, this approximation leads to an increase in the virial mass of 13% on average, while for the synthetic library the effect is weaker, with an increase of 9% on average. Systematic erroneous estimates of the velocity dispersion comes from the use of the synthetic stellar library instead of the empirical one and is much larger than the value imposed by the use of the Gaussian function. Only after a careful analysis of the template mismatch problem does one need to address the issue of the deviation of the LOSVD from the Gaussian function. We also show that the kurtotic parameter describing symmetrical departures from the Gaussian seems to increase along the continuous morphological sequence from late- to early-type galaxies. The catalog is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/593/A40
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Raney Distributions and Random Matrix Theory
NASA Astrophysics Data System (ADS)
Forrester, Peter J.; Liu, Dang-Zheng
2015-03-01
Recent works have shown that the family of probability distributions with moments given by the Fuss-Catalan numbers permit a simple parameterized form for their density. We extend this result to the Raney distribution which by definition has its moments given by a generalization of the Fuss-Catalan numbers. Such computations begin with an algebraic equation satisfied by the Stieltjes transform, which we show can be derived from the linear differential equation satisfied by the characteristic polynomial of random matrix realizations of the Raney distribution. For the Fuss-Catalan distribution, an equilibrium problem characterizing the density is identified. The Stieltjes transform for the limiting spectral density of the singular values squared of the matrix product formed from inverse standard Gaussian matrices, and standard Gaussian matrices, is shown to satisfy a variant of the algebraic equation relating to the Raney distribution. Supported on , we show that it too permits a simple functional form upon the introduction of an appropriate choice of parameterization. As an application, the leading asymptotic form of the density as the endpoints of the support are approached is computed, and is shown to have some universal features.
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Comparing fixed and variable-width Gaussian networks.
Kůrková, Věra; Kainen, Paul C
2014-09-01
The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is proven that if two Gaussian RBF networks have the same input-output functions, then they must have the same numbers of units with the same centers and widths. Further, it is shown that while sets of input-output functions of Gaussian kernel networks with two different widths are disjoint, each such set is large enough to be a universal approximator. Embedding of RKHSs induced by "flatter" Gaussians into RKHSs induced by "sharper" Gaussians is described and growth of the ratios of norms on these spaces with increasing input dimension is estimated. Finally, large sets of argminima of error functionals in sets of input-output functions of Gaussian RBFs are described. Copyright © 2014 Elsevier Ltd. All rights reserved.
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Simulated laser fluorosensor signals from subsurface chlorophyll distributions
NASA Technical Reports Server (NTRS)
Venable, D. D.; Khatun, S.; Punjabi, A.; Poole, L.
1986-01-01
A semianalytic Monte Carlo model has been used to simulate laser fluorosensor signals returned from subsurface distributions of chlorophyll. This study assumes the only constituent of the ocean medium is the common coastal zone dinoflagellate Prorocentrum minimum. The concentration is represented by Gaussian distributions in which the location of the distribution maximum and the standard deviation are variable. Most of the qualitative features observed in the fluorescence signal for total chlorophyll concentrations up to 1.0 microg/liter can be accounted for with a simple analytic solution assuming a rectangular chlorophyll distribution function.
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Goerg, Georg M.
2015-01-01
I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert W × F X random variable depends on a tail parameter δ ≥ 0: for δ = 0, Y ≡ X, for δ > 0 Y has heavier tails than X. For X being Gaussian it reduces to Tukey's h distribution. The Lambert W function provides an explicit inverse transformation, which can thus remove heavy tails from observed data. It also provides closed-form expressions for the cumulative distribution (cdf) and probability density function (pdf). As a special case, these yield analytic expression for Tukey's h pdf and cdf. Parameters can be estimated by maximum likelihood and applications to S&P 500 log-returns demonstrate the usefulness of the presented methodology. The R package LambertW implements most of the introduced methodology and is publicly available on CRAN. PMID:26380372
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Comparisons of non-Gaussian statistical models in DNA methylation analysis.
Ma, Zhanyu; Teschendorff, Andrew E; Yu, Hong; Taghia, Jalil; Guo, Jun
2014-06-16
As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance.
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Comparisons of Non-Gaussian Statistical Models in DNA Methylation Analysis
Ma, Zhanyu; Teschendorff, Andrew E.; Yu, Hong; Taghia, Jalil; Guo, Jun
2014-01-01
As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance. PMID:24937687
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Some rules for polydimensional squeezing
NASA Technical Reports Server (NTRS)
Manko, Vladimir I.
1994-01-01
The review of the following results is presented: For mixed state light of N-mode electromagnetic field described by Wigner function which has generic Gaussian form, the photon distribution function is obtained and expressed explicitly in terms of Hermite polynomials of 2N-variables. The momenta of this distribution are calculated and expressed as functions of matrix invariants of the dispersion matrix. The role of new uncertainty relation depending on photon state mixing parameter is elucidated. New sum rules for Hermite polynomials of several variables are found. The photon statistics of polymode even and odd coherent light and squeezed polymode Schroedinger cat light is given explicitly. Photon distribution for polymode squeezed number states expressed in terms of multivariable Hermite polynomials is discussed.
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Edgeworth streaming model for redshift space distortions
NASA Astrophysics Data System (ADS)
Uhlemann, Cora; Kopp, Michael; Haugg, Thomas
2015-09-01
We derive the Edgeworth streaming model (ESM) for the redshift space correlation function starting from an arbitrary distribution function for biased tracers of dark matter by considering its two-point statistics and show that it reduces to the Gaussian streaming model (GSM) when neglecting non-Gaussianities. We test the accuracy of the GSM and ESM independent of perturbation theory using the Horizon Run 2 N -body halo catalog. While the monopole of the redshift space halo correlation function is well described by the GSM, higher multipoles improve upon including the leading order non-Gaussian correction in the ESM: the GSM quadrupole breaks down on scales below 30 Mpc /h whereas the ESM stays accurate to 2% within statistical errors down to 10 Mpc /h . To predict the scale-dependent functions entering the streaming model we employ convolution Lagrangian perturbation theory (CLPT) based on the dust model and local Lagrangian bias. Since dark matter halos carry an intrinsic length scale given by their Lagrangian radius, we extend CLPT to the coarse-grained dust model and consider two different smoothing approaches operating in Eulerian and Lagrangian space, respectively. The coarse graining in Eulerian space features modified fluid dynamics different from dust while the coarse graining in Lagrangian space is performed in the initial conditions with subsequent single-streaming dust dynamics, implemented by smoothing the initial power spectrum in the spirit of the truncated Zel'dovich approximation. Finally, we compare the predictions of the different coarse-grained models for the streaming model ingredients to N -body measurements and comment on the proper choice of both the tracer distribution function and the smoothing scale. Since the perturbative methods we considered are not yet accurate enough on small scales, the GSM is sufficient when applied to perturbation theory.
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Detecting Non-Gaussian and Lognormal Characteristics of Temperature and Water Vapor Mixing Ratio
NASA Astrophysics Data System (ADS)
Kliewer, A.; Fletcher, S. J.; Jones, A. S.; Forsythe, J. M.
2017-12-01
Many operational data assimilation and retrieval systems assume that the errors and variables come from a Gaussian distribution. This study builds upon previous results that shows that positive definite variables, specifically water vapor mixing ratio and temperature, can follow a non-Gaussian distribution and moreover a lognormal distribution. Previously, statistical testing procedures which included the Jarque-Bera test, the Shapiro-Wilk test, the Chi-squared goodness-of-fit test, and a composite test which incorporated the results of the former tests were employed to determine locations and time spans where atmospheric variables assume a non-Gaussian distribution. These tests are now investigated in a "sliding window" fashion in order to extend the testing procedure to near real-time. The analyzed 1-degree resolution data comes from the National Oceanic and Atmospheric Administration (NOAA) Global Forecast System (GFS) six hour forecast from the 0Z analysis. These results indicate the necessity of a Data Assimilation (DA) system to be able to properly use the lognormally-distributed variables in an appropriate Bayesian analysis that does not assume the variables are Gaussian.
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The distribution of cardiac troponin I in a population of healthy children: lessons for adults.
Koerbin, Gus; Potter, Julia M; Abhayaratna, Walter P; Telford, Richard D; Hickman, Peter E
2013-02-18
To describe the distribution of hs-cTnI in a large cohort of healthy children. As part of the LOOK study, blood was collected from a large cohort of healthy children on 3 separate occasions when the children were aged 8, 10 and 12years. Samples were stored at -80°C after collection and assayed after 1 freeze-thaw cycle using a pre-commercial release hs-cTnI assay from Abbott Diagnostics. More than 98% of the 12year-old children had cTnI above the LoD of 1.0ng/L. For the 212 boys the central 95% of results was distributed in a Gaussian fashion. For the 237 girls, the initial analysis was non-Gaussian, but after the elimination of 2 results, the pattern for girls was also Gaussian. In healthy children, cTnI is present in a Gaussian distribution. Even minor illnesses can cause some troponin release, distorting this Gaussian distribution. Copyright © 2012 Elsevier B.V. All rights reserved.
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Free energy calculations, enhanced by a Gaussian ansatz, for the "chemical work" distribution.
Boulougouris, Georgios C
2014-05-15
The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the "chemical work" of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the "irreversible" work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible "chemical work" minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the "chemical work," accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the "chemical work." For a more general free energy perturbation scheme that the Gaussian ansatz may not be valid, the free energy calculation can be expressed in terms of the moment generating function of the "chemical work" distribution. Copyright © 2014 Wiley Periodicals, Inc.
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Enhanced production of ψ (2 S ) mesons in heavy ion collisions
NASA Astrophysics Data System (ADS)
Cho, Sungtae
2015-05-01
I study the production of a ψ (2 S ) meson in heavy ion collisions. I evaluate Wigner functions for the ψ (2 S ) meson using both Gaussian and Coulomb wave functions, and investigate the wave function dependence in the ψ (2 S ) meson production by recombination of charm and anticharm quarks. The enhanced transverse momentum distribution of ψ (2 S ) mesons compared to that of J /ψ mesons, originated from wave function distributions of the ψ (2 S ) and J /ψ meson in momentum space, provides a plausible explanation for the recent measurement of the nuclear modification factor ratio between the ψ (2 S ) and J /ψ meson.
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NASA Astrophysics Data System (ADS)
Cecinati, F.; Wani, O.; Rico-Ramirez, M. A.
2017-11-01
Merging radar and rain gauge rainfall data is a technique used to improve the quality of spatial rainfall estimates and in particular the use of Kriging with External Drift (KED) is a very effective radar-rain gauge rainfall merging technique. However, kriging interpolations assume Gaussianity of the process. Rainfall has a strongly skewed, positive, probability distribution, characterized by a discontinuity due to intermittency. In KED rainfall residuals are used, implicitly calculated as the difference between rain gauge data and a linear function of the radar estimates. Rainfall residuals are non-Gaussian as well. The aim of this work is to evaluate the impact of applying KED to non-Gaussian rainfall residuals, and to assess the best techniques to improve Gaussianity. We compare Box-Cox transformations with λ parameters equal to 0.5, 0.25, and 0.1, Box-Cox with time-variant optimization of λ, normal score transformation, and a singularity analysis technique. The results suggest that Box-Cox with λ = 0.1 and the singularity analysis is not suitable for KED. Normal score transformation and Box-Cox with optimized λ, or λ = 0.25 produce satisfactory results in terms of Gaussianity of the residuals, probability distribution of the merged rainfall products, and rainfall estimate quality, when validated through cross-validation. However, it is observed that Box-Cox transformations are strongly dependent on the temporal and spatial variability of rainfall and on the units used for the rainfall intensity. Overall, applying transformations results in a quantitative improvement of the rainfall estimates only if the correct transformations for the specific data set are used.
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Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations
Del-Castillo-Negrete, Diego B.; Moradi, Sara; Anderson, Johan
2016-09-01
Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of -stable Levy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Levy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Levy fluctuations. The absolute value ofmore » the power law decay exponents are linearly proportional to the Levy index. Furthermore, the observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Levy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.« less
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Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations
NASA Astrophysics Data System (ADS)
Moradi, Sara; del-Castillo-Negrete, Diego; Anderson, Johan
2016-09-01
Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of α-stable Lévy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Lévy fluctuations. The absolute value of the power law decay exponents is linearly proportional to the Lévy index α. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Lévy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.
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Foster, Tobias
2011-09-01
A novel analytical and continuous density distribution function with a widely variable shape is reported and used to derive an analytical scattering form factor that allows us to universally describe the scattering from particles with the radial density profile of homogeneous spheres, shells, or core-shell particles. Composed by the sum of two Fermi-Dirac distribution functions, the shape of the density profile can be altered continuously from step-like via Gaussian-like or parabolic to asymptotically hyperbolic by varying a single "shape parameter", d. Using this density profile, the scattering form factor can be calculated numerically. An analytical form factor can be derived using an approximate expression for the original Fermi-Dirac distribution function. This approximation is accurate for sufficiently small rescaled shape parameters, d/R (R being the particle radius), up to values of d/R ≈ 0.1, and thus captures step-like, Gaussian-like, and parabolic as well as asymptotically hyperbolic profile shapes. It is expected that this form factor is particularly useful in a model-dependent analysis of small-angle scattering data since the applied continuous and analytical function for the particle density profile can be compared directly with the density profile extracted from the data by model-free approaches like the generalized inverse Fourier transform method. © 2011 American Chemical Society
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Helgesson, P; Sjöstrand, H
2017-11-01
Fitting a parametrized function to data is important for many researchers and scientists. If the model is non-linear and/or defect, it is not trivial to do correctly and to include an adequate uncertainty analysis. This work presents how the Levenberg-Marquardt algorithm for non-linear generalized least squares fitting can be used with a prior distribution for the parameters and how it can be combined with Gaussian processes to treat model defects. An example, where three peaks in a histogram are to be distinguished, is carefully studied. In particular, the probability r 1 for a nuclear reaction to end up in one out of two overlapping peaks is studied. Synthetic data are used to investigate effects of linearizations and other assumptions. For perfect Gaussian peaks, it is seen that the estimated parameters are distributed close to the truth with good covariance estimates. This assumes that the method is applied correctly; for example, prior knowledge should be implemented using a prior distribution and not by assuming that some parameters are perfectly known (if they are not). It is also important to update the data covariance matrix using the fit if the uncertainties depend on the expected value of the data (e.g., for Poisson counting statistics or relative uncertainties). If a model defect is added to the peaks, such that their shape is unknown, a fit which assumes perfect Gaussian peaks becomes unable to reproduce the data, and the results for r 1 become biased. It is, however, seen that it is possible to treat the model defect with a Gaussian process with a covariance function tailored for the situation, with hyper-parameters determined by leave-one-out cross validation. The resulting estimates for r 1 are virtually unbiased, and the uncertainty estimates agree very well with the underlying uncertainty.
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NASA Astrophysics Data System (ADS)
Helgesson, P.; Sjöstrand, H.
2017-11-01
Fitting a parametrized function to data is important for many researchers and scientists. If the model is non-linear and/or defect, it is not trivial to do correctly and to include an adequate uncertainty analysis. This work presents how the Levenberg-Marquardt algorithm for non-linear generalized least squares fitting can be used with a prior distribution for the parameters and how it can be combined with Gaussian processes to treat model defects. An example, where three peaks in a histogram are to be distinguished, is carefully studied. In particular, the probability r1 for a nuclear reaction to end up in one out of two overlapping peaks is studied. Synthetic data are used to investigate effects of linearizations and other assumptions. For perfect Gaussian peaks, it is seen that the estimated parameters are distributed close to the truth with good covariance estimates. This assumes that the method is applied correctly; for example, prior knowledge should be implemented using a prior distribution and not by assuming that some parameters are perfectly known (if they are not). It is also important to update the data covariance matrix using the fit if the uncertainties depend on the expected value of the data (e.g., for Poisson counting statistics or relative uncertainties). If a model defect is added to the peaks, such that their shape is unknown, a fit which assumes perfect Gaussian peaks becomes unable to reproduce the data, and the results for r1 become biased. It is, however, seen that it is possible to treat the model defect with a Gaussian process with a covariance function tailored for the situation, with hyper-parameters determined by leave-one-out cross validation. The resulting estimates for r1 are virtually unbiased, and the uncertainty estimates agree very well with the underlying uncertainty.
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ERIC Educational Resources Information Center
Steinhauser, Marco; Hubner, Ronald
2009-01-01
It has been suggested that performance in the Stroop task is influenced by response conflict as well as task conflict. The present study investigated the idea that both conflict types can be isolated by applying ex-Gaussian distribution analysis which decomposes response time into a Gaussian and an exponential component. Two experiments were…
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Hamby, D M
2002-01-01
Reconstructed meteorological data are often used in some form of long-term wind trajectory models for estimating the historical impacts of atmospheric emissions. Meteorological data for the straight-line Gaussian plume model are put into a joint frequency distribution, a three-dimensional array describing atmospheric wind direction, speed, and stability. Methods using the Gaussian model and joint frequency distribution inputs provide reasonable estimates of downwind concentration and have been shown to be accurate to within a factor of four. We have used multiple joint frequency distributions and probabilistic techniques to assess the Gaussian plume model and determine concentration-estimate uncertainty and model sensitivity. We examine the straight-line Gaussian model while calculating both sector-averaged and annual-averaged relative concentrations at various downwind distances. The sector-average concentration model was found to be most sensitive to wind speed, followed by horizontal dispersion (sigmaZ), the importance of which increases as stability increases. The Gaussian model is not sensitive to stack height uncertainty. Precision of the frequency data appears to be most important to meteorological inputs when calculations are made for near-field receptors, increasing as stack height increases.
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Comparison of Gaussian and non-Gaussian Atmospheric Profile Retrievals from Satellite Microwave Data
NASA Astrophysics Data System (ADS)
Kliewer, A.; Forsythe, J. M.; Fletcher, S. J.; Jones, A. S.
2017-12-01
The Cooperative Institute for Research in the Atmosphere at Colorado State University has recently developed two different versions of a mixed-distribution (lognormal combined with a Gaussian) based microwave temperature and mixing ratio retrieval system as well as the original Gaussian-based approach. These retrieval systems are based upon 1DVAR theory but have been adapted to use different descriptive statistics of the lognormal distribution to minimize the background errors. The input radiance data is from the AMSU-A and MHS instruments on the NOAA series of spacecraft. To help illustrate how the three retrievals are affected by the change in the distribution we are in the process of creating a new website to show the output from the different retrievals. Here we present initial results from different dynamical situations to show how the tool could be used by forecasters as well as for educators. However, as the new retrieved values are from a non-Gaussian based 1DVAR then they will display non-Gaussian behaviors that need to pass a quality control measure that is consistent with this distribution, and these new measures are presented here along with initial results for checking the retrievals.
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An Urban Diffusion Simulation Model for Carbon Monoxide
ERIC Educational Resources Information Center
Johnson, W. B.; And Others
1973-01-01
A relatively simple Gaussian-type diffusion simulation model for calculating urban carbon (CO) concentrations as a function of local meteorology and the distribution of traffic is described. The model can be used in two ways: in the synoptic mode and in the climatological mode. (Author/BL)
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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
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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. -
Idealized models of the joint probability distribution of wind speeds
NASA Astrophysics Data System (ADS)
Monahan, Adam H.
2018-05-01
The joint probability distribution of wind speeds at two separate locations in space or points in time completely characterizes the statistical dependence of these two quantities, providing more information than linear measures such as correlation. In this study, we consider two models of the joint distribution of wind speeds obtained from idealized models of the dependence structure of the horizontal wind velocity components. The bivariate Rice distribution follows from assuming that the wind components have Gaussian and isotropic fluctuations. The bivariate Weibull distribution arises from power law transformations of wind speeds corresponding to vector components with Gaussian, isotropic, mean-zero variability. Maximum likelihood estimates of these distributions are compared using wind speed data from the mid-troposphere, from different altitudes at the Cabauw tower in the Netherlands, and from scatterometer observations over the sea surface. While the bivariate Rice distribution is more flexible and can represent a broader class of dependence structures, the bivariate Weibull distribution is mathematically simpler and may be more convenient in many applications. The complexity of the mathematical expressions obtained for the joint distributions suggests that the development of explicit functional forms for multivariate speed distributions from distributions of the components will not be practical for more complicated dependence structure or more than two speed variables.
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Particle velocity distribution in a three-dimensional dusty plasma under microgravity conditions
NASA Astrophysics Data System (ADS)
Liu, Bin; Goree, J.; Pustylnik, M. Y.; Thomas, H. M.; Fortov, V. E.; Lipaev, A. M.; Usachev, A. D.; Molotkov, V. I.; Petrov, O. F.; Thoma, M. H.
2018-01-01
The velocity distribution function of dust particles immersed in a plasma was investigated under microgravity conditions. A three-dimensional (3D) cloud of polymer microspheres was suspended in a neon plasma, in the PK-4 instrument onboard the International Space Station (ISS). These dust particles were tracked using video microscopy in a cross section of the 3D dust cloud. The velocity distribution function (VDF) is found to have a non-Maxwellian shape with high-energy tails; it is fit well by a combination of low-energy Maxwellian core and a high-energy non-Gaussian Kappa-distribution halo. Similar non-Maxwellian VDFs are typically observed in space plasmas.
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NASA Astrophysics Data System (ADS)
Alekseev, V. A.; Krylova, D. D.
1996-02-01
The analytical investigation of Bloch equations is used to describe the main features of the 1D velocity selective coherent population trapping cooling scheme. For the initial stage of cooling the fraction of cooled atoms is derived in the case of a Gaussian initial velocity distribution. At very long times of interaction the fraction of cooled atoms and the velocity distribution function are described by simple analytical formulae and do not depend on the initial distribution. These results are in good agreement with those of Bardou, Bouchaud, Emile, Aspect and Cohen-Tannoudji based on statistical analysis in terms of Levy flights and with Monte-Carlo simulations of the process.
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Zheng, Xiliang; Wang, Jin
2015-01-01
We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics. PMID:25885453
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On the efficacy of procedures to normalize Ex-Gaussian distributions
Marmolejo-Ramos, Fernando; Cousineau, Denis; Benites, Luis; Maehara, Rocío
2015-01-01
Reaction time (RT) is one of the most common types of measure used in experimental psychology. Its distribution is not normal (Gaussian) but resembles a convolution of normal and exponential distributions (Ex-Gaussian). One of the major assumptions in parametric tests (such as ANOVAs) is that variables are normally distributed. Hence, it is acknowledged by many that the normality assumption is not met. This paper presents different procedures to normalize data sampled from an Ex-Gaussian distribution in such a way that they are suitable for parametric tests based on the normality assumption. Using simulation studies, various outlier elimination and transformation procedures were tested against the level of normality they provide. The results suggest that the transformation methods are better than elimination methods in normalizing positively skewed data and the more skewed the distribution then the transformation methods are more effective in normalizing such data. Specifically, transformation with parameter lambda -1 leads to the best results. PMID:25709588
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Ehrenfest model with large jumps in finance
NASA Astrophysics Data System (ADS)
Takahashi, Hisanao
2004-02-01
Changes (returns) in stock index prices and exchange rates for currencies are argued, based on empirical data, to obey a stable distribution with characteristic exponent α<2 for short sampling intervals and a Gaussian distribution for long sampling intervals. In order to explain this phenomenon, an Ehrenfest model with large jumps (ELJ) is introduced to explain the empirical density function of price changes for both short and long sampling intervals.
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Statistics of the geomagnetic secular variation for the past 5Ma
NASA Technical Reports Server (NTRS)
Constable, C. G.; Parker, R. L.
1986-01-01
A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.
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Statistics of the geomagnetic secular variation for the past 5 m.y
NASA Technical Reports Server (NTRS)
Constable, C. G.; Parker, R. L.
1988-01-01
A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.
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Bayesian nonparametric regression with varying residual density
Pati, Debdeep; Dunson, David B.
2013-01-01
We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking (PSB) scale mixtures and symmetrized PSB (sPSB) location-scale mixtures. Both priors restrict the residual density to be symmetric about zero, with the sPSB prior more flexible in allowing multimodal densities. We provide sufficient conditions to ensure strong posterior consistency in estimating the regression function under the sPSB prior, generalizing existing theory focused on parametric residual distributions. The PSB and sPSB priors are generalized to allow residual densities to change nonparametrically with predictors through incorporating Gaussian processes in the stick-breaking components. This leads to a robust Bayesian regression procedure that automatically down-weights outliers and influential observations in a locally-adaptive manner. Posterior computation relies on an efficient data augmentation exact block Gibbs sampler. The methods are illustrated using simulated and real data applications. PMID:24465053
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The MONET code for the evaluation of the dose in hadrontherapy
NASA Astrophysics Data System (ADS)
Embriaco, A.
2018-01-01
The MONET is a code for the computation of the 3D dose distribution for protons in water. For the lateral profile, MONET is based on the Molière theory of multiple Coulomb scattering. To take into account also the nuclear interactions, we add to this theory a Cauchy-Lorentz function, where the two parameters are obtained by a fit to a FLUKA simulation. We have implemented the Papoulis algorithm for the passage from the projected to a 2D lateral distribution. For the longitudinal profile, we have implemented a new calculation of the energy loss that is in good agreement with simulations. The inclusion of the straggling is based on the convolution of energy loss with a Gaussian function. In order to complete the longitudinal profile, also the nuclear contributions are included using a linear parametrization. The total dose profile is calculated in a 3D mesh by evaluating at each depth the 2D lateral distributions and by scaling them at the value of the energy deposition. We have compared MONET with FLUKA in two cases: a single Gaussian beam and a lateral scan. In both cases, we have obtained a good agreement for different energies of protons in water.
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Ellipsoids for anomaly detection in remote sensing imagery
NASA Astrophysics Data System (ADS)
Grosklos, Guenchik; Theiler, James
2015-05-01
For many target and anomaly detection algorithms, a key step is the estimation of a centroid (relatively easy) and a covariance matrix (somewhat harder) that characterize the background clutter. For a background that can be modeled as a multivariate Gaussian, the centroid and covariance lead to an explicit probability density function that can be used in likelihood ratio tests for optimal detection statistics. But ellipsoidal contours can characterize a much larger class of multivariate density function, and the ellipsoids that characterize the outer periphery of the distribution are most appropriate for detection in the low false alarm rate regime. Traditionally the sample mean and sample covariance are used to estimate ellipsoid location and shape, but these quantities are confounded both by large lever-arm outliers and non-Gaussian distributions within the ellipsoid of interest. This paper compares a variety of centroid and covariance estimation schemes with the aim of characterizing the periphery of the background distribution. In particular, we will consider a robust variant of the Khachiyan algorithm for minimum-volume enclosing ellipsoid. The performance of these different approaches is evaluated on multispectral and hyperspectral remote sensing imagery using coverage plots of ellipsoid volume versus false alarm rate.
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Fractional Gaussian model in global optimization
NASA Astrophysics Data System (ADS)
Dimri, V. P.; Srivastava, R. P.
2009-12-01
Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.
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NASA Astrophysics Data System (ADS)
Melis, Stefano
2015-01-01
We present a review of current Transverse Momentum Dependent (TMD) phenomenology focusing our attention on the unpolarized TMD parton distribution function and the Sivers function. The paper introduces and comments about the new Collins-Soper-Sterman (CSS) TMD evolution formalism [1]. We make use of a selection of results obtained by several groups to illustrate the achievements and the failures of the simple Gaussian approach and the TMD CSS evolution formalism.
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Symplectic evolution of Wigner functions in Markovian open systems.
Brodier, O; Almeida, A M Ozorio de
2004-01-01
The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.
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On the application of Rice's exceedance statistics to atmospheric turbulence.
NASA Technical Reports Server (NTRS)
Chen, W. Y.
1972-01-01
Discrepancies produced by the application of Rice's exceedance statistics to atmospheric turbulence are examined. First- and second-order densities from several data sources have been measured for this purpose. Particular care was paid to each selection of turbulence that provides stationary mean and variance over the entire segment. Results show that even for a stationary segment of turbulence, the process is still highly non-Gaussian, in spite of a Gaussian appearance for its first-order distribution. Data also indicate strongly non-Gaussian second-order distributions. It is therefore concluded that even stationary atmospheric turbulence with a normal first-order distribution cannot be considered a Gaussian process, and consequently the application of Rice's exceedance statistics should be approached with caution.
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Gaussian polarizable-ion tight binding.
Boleininger, Max; Guilbert, Anne Ay; Horsfield, Andrew P
2016-10-14
To interpret ultrafast dynamics experiments on large molecules, computer simulation is required due to the complex response to the laser field. We present a method capable of efficiently computing the static electronic response of large systems to external electric fields. This is achieved by extending the density-functional tight binding method to include larger basis sets and by multipole expansion of the charge density into electrostatically interacting Gaussian distributions. Polarizabilities for a range of hydrocarbon molecules are computed for a multipole expansion up to quadrupole order, giving excellent agreement with experimental values, with average errors similar to those from density functional theory, but at a small fraction of the cost. We apply the model in conjunction with the polarizable-point-dipoles model to estimate the internal fields in amorphous poly(3-hexylthiophene-2,5-diyl).
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Gaussian polarizable-ion tight binding
NASA Astrophysics Data System (ADS)
Boleininger, Max; Guilbert, Anne AY; Horsfield, Andrew P.
2016-10-01
To interpret ultrafast dynamics experiments on large molecules, computer simulation is required due to the complex response to the laser field. We present a method capable of efficiently computing the static electronic response of large systems to external electric fields. This is achieved by extending the density-functional tight binding method to include larger basis sets and by multipole expansion of the charge density into electrostatically interacting Gaussian distributions. Polarizabilities for a range of hydrocarbon molecules are computed for a multipole expansion up to quadrupole order, giving excellent agreement with experimental values, with average errors similar to those from density functional theory, but at a small fraction of the cost. We apply the model in conjunction with the polarizable-point-dipoles model to estimate the internal fields in amorphous poly(3-hexylthiophene-2,5-diyl).
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On estimating the phase of periodic waveform in additive Gaussian noise, part 2
NASA Astrophysics Data System (ADS)
Rauch, L. L.
1984-11-01
Motivated by advances in signal processing technology that support more complex algorithms, a new look is taken at the problem of estimating the phase and other parameters of a periodic waveform in additive Gaussian noise. The general problem was introduced and the maximum a posteriori probability criterion with signal space interpretation was used to obtain the structures of optimum and some suboptimum phase estimators for known constant frequency and unknown constant phase with an a priori distribution. Optimal algorithms are obtained for some cases where the frequency is a parameterized function of time with the unknown parameters and phase having a joint a priori distribution. In the last section, the intrinsic and extrinsic geometry of hypersurfaces is introduced to provide insight to the estimation problem for the small noise and large noise cases.
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Ultrasound beam transmission using a discretely orthogonal Gaussian aperture basis
NASA Astrophysics Data System (ADS)
Roberts, R. A.
2018-04-01
Work is reported on development of a computational model for ultrasound beam transmission at an arbitrary geometry transmission interface for generally anisotropic materials. The work addresses problems encountered when the fundamental assumptions of ray theory do not hold, thereby introducing errors into ray-theory-based transmission models. Specifically, problems occur when the asymptotic integral analysis underlying ray theory encounters multiple stationary phase points in close proximity, due to focusing caused by concavity on either the entry surface or a material slowness surface. The approach presented here projects integrands over both the transducer aperture and the entry surface beam footprint onto a Gaussian-derived basis set, thereby distributing the integral over a summation of second-order phase integrals which are amenable to single stationary phase point analysis. Significantly, convergence is assured provided a sufficiently fine distribution of basis functions is used.
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On Estimating the Phase of Periodic Waveform in Additive Gaussian Noise, Part 2
NASA Technical Reports Server (NTRS)
Rauch, L. L.
1984-01-01
Motivated by advances in signal processing technology that support more complex algorithms, a new look is taken at the problem of estimating the phase and other parameters of a periodic waveform in additive Gaussian noise. The general problem was introduced and the maximum a posteriori probability criterion with signal space interpretation was used to obtain the structures of optimum and some suboptimum phase estimators for known constant frequency and unknown constant phase with an a priori distribution. Optimal algorithms are obtained for some cases where the frequency is a parameterized function of time with the unknown parameters and phase having a joint a priori distribution. In the last section, the intrinsic and extrinsic geometry of hypersurfaces is introduced to provide insight to the estimation problem for the small noise and large noise cases.
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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
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The heliolongitudinal distribution of solar flares associated with solar proton events.
Smart, D F; Shea, M A
1996-01-01
We find that the heliolongitudinal distribution of solar flares associated with earth-observed solar proton events is a function of the particle measurement energy. For solar proton events containing fluxes with energies exceeding 1 GeV, we find a Gaussian distribution about the probable root of the Archimedean spiral favorable propagation path leading from the earth to the sun. This distribution is modified as the detection threshold is lowered. For > 100 MeV solar proton events with fluxes > or = 10 protons (cm2-sec-ster)-1 we find the distribution becomes wider with a secondary peak near the solar central meridian. When the threshold is lowered to 10 MeV the distribution further evolves. For > 10 MeV solar proton events having a flux threshold at 10 protons (cm2-sec-ster)-1 the distribution can be considered to be a composite of two Gaussians. One distribution is centered about the probable root of the Archimedean spiral favorable propagation path leading from the earth to the sun, and the other is centered about the solar central meridian. For large flux solar proton events, those with flux threshold of 1000 (cm2-sec-ster)-1 at energies > 10 MeV, we find the distribution is rather flat for about 40 degrees either side of central meridian.
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Finite Larmor radius effects on weak turbulence transport
NASA Astrophysics Data System (ADS)
Kryukov, N.; Martinell, J. J.
2018-06-01
Transport of test particles in two-dimensional weak turbulence with waves propagating along the poloidal direction is studied using a reduced model. Finite Larmor radius (FLR) effects are included by gyroaveraging over one particle orbit. For low wave amplitudes the motion is mostly regular with particles trapped in the potential wells. As the amplitude increases the trajectories become chaotic and the Larmor radius modifies the orbits. For a thermal distribution of Finite Larmor radii the particle distribution function (PDF) is Gaussian for small th$ (thermal gyroradius) but becomes non-Gaussian for large th$ . However, the time scaling of transport is diffusive, as characterized by a linear dependence of the variance of the PDF with time. An explanation for this behaviour is presented that provides an expression for an effective diffusion coefficient and reproduces the numerical results for large wave amplitudes which implies generalized chaos. When a shear flow is added in the direction of wave propagation, a modified model is obtained that produces free-streaming particle trajectories in addition to trapped ones; these contribute to ballistic transport for low wave amplitude but produce super-ballistic transport in the chaotic regime. As in the previous case, the PDF is Gaussian for low th$ becoming non-Gaussian as it increases. The perpendicular transport presents the same behaviour as in the case with no flow but the diffusion is faster in the presence of the flow.
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NASA Astrophysics Data System (ADS)
Waubke, Holger; Kasess, Christian H.
2016-11-01
Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.
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Wigner Function Reconstruction in Levitated Optomechanics
NASA Astrophysics Data System (ADS)
Rashid, Muddassar; Toroš, Marko; Ulbricht, Hendrik
2017-10-01
We demonstrate the reconstruction of theWigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical systems even under the efect of continuous measurement by the trapping laser light. We describe the opto-mechanical coupling for the case of the particle trapped by a free-space focused laser beam, explicitly for the case without an optical cavity. We use the scheme to reconstruct the Wigner function of experimental data in perfect agreement with the expected Gaussian distribution of a thermal state of motion. This opens a route for quantum state preparation in levitated optomechanics.
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NASA Astrophysics Data System (ADS)
Del Pozzo, W.; Berry, C. P. L.; Ghosh, A.; Haines, T. S. F.; Singer, L. P.; Vecchio, A.
2018-06-01
We reconstruct posterior distributions for the position (sky area and distance) of a simulated set of binary neutron-star gravitational-waves signals observed with Advanced LIGO and Advanced Virgo. We use a Dirichlet Process Gaussian-mixture model, a fully Bayesian non-parametric method that can be used to estimate probability density functions with a flexible set of assumptions. The ability to reliably reconstruct the source position is important for multimessenger astronomy, as recently demonstrated with GW170817. We show that for detector networks comparable to the early operation of Advanced LIGO and Advanced Virgo, typical localization volumes are ˜104-105 Mpc3 corresponding to ˜102-103 potential host galaxies. The localization volume is a strong function of the network signal-to-noise ratio, scaling roughly ∝ϱnet-6. Fractional localizations improve with the addition of further detectors to the network. Our Dirichlet Process Gaussian-mixture model can be adopted for localizing events detected during future gravitational-wave observing runs, and used to facilitate prompt multimessenger follow-up.
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Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C
2016-02-01
A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.
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NASA Technical Reports Server (NTRS)
Mcclelland, J.; Silk, J.
1979-01-01
The evolution of the two-point correlation function for the large-scale distribution of galaxies in an expanding universe is studied on the assumption that the perturbation densities lie in a Gaussian distribution centered on any given mass scale. The perturbations are evolved according to the Friedmann equation, and the correlation function for the resulting distribution of perturbations at the present epoch is calculated. It is found that: (1) the computed correlation function gives a satisfactory fit to the observed function in cosmological models with a density parameter (Omega) of approximately unity, provided that a certain free parameter is suitably adjusted; (2) the power-law slope in the nonlinear regime reflects the initial fluctuation spectrum, provided that the density profile of individual perturbations declines more rapidly than the -2.4 power of distance; and (3) both positive and negative contributions to the correlation function are predicted for cosmological models with Omega less than unity.
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Ligation site in proteins recognized in silico
Brylinski, Michal; Konieczny, Leszek; Roterman, Irena
2006-01-01
Recognition of a ligation site in a protein molecule is important for identifying its biological activity. The model for in silico recognition of ligation sites in proteins is presented. The idealized hydrophobic core stabilizing protein structure is represented by a three-dimensional Gaussian function. The experimentally observed distribution of hydrophobicity compared with the theoretical distribution reveals differences. The area of high differences indicates the ligation site. Availability http://bioinformatics.cm-uj.krakow.pl/activesite PMID:17597871
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NASA Astrophysics Data System (ADS)
Klimenko, V. V.
2017-12-01
We obtain expressions for the probabilities of the normal-noise spikes with the Gaussian correlation function and for the probability density of the inter-spike intervals. As distinct from the delta-correlated noise, in which the intervals are distributed by the exponential law, the probability of the subsequent spike depends on the previous spike and the interval-distribution law deviates from the exponential one for a finite noise-correlation time (frequency-bandwidth restriction). This deviation is the most pronounced for a low detection threshold. Similarity of the behaviors of the distributions of the inter-discharge intervals in a thundercloud and the noise spikes for the varying repetition rate of the discharges/spikes, which is determined by the ratio of the detection threshold to the root-mean-square value of noise, is observed. The results of this work can be useful for the quantitative description of the statistical characteristics of the noise spikes and studying the role of fluctuations for the discharge emergence in a thundercloud.
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NASA Astrophysics Data System (ADS)
Drescher, Anushka C.; Yost, Michael G.; Park, Doo Y.; Levine, Steven P.; Gadgil, Ashok J.; Fischer, Marc L.; Nazaroff, William W.
1995-05-01
Optical remote sensing and iterative computed tomography (CT) can be combined to measure the spatial distribution of gaseous pollutant concentrations in a plane. We have conducted chamber experiments to test this combination of techniques using an Open Path Fourier Transform Infrared Spectrometer (OP-FTIR) and a standard algebraic reconstruction technique (ART). ART was found to converge to solutions that showed excellent agreement with the ray integral concentrations measured by the FTIR but were inconsistent with simultaneously gathered point sample concentration measurements. A new CT method was developed based on (a) the superposition of bivariate Gaussians to model the concentration distribution and (b) a simulated annealing minimization routine to find the parameters of the Gaussians that resulted in the best fit to the ray integral concentration data. This new method, named smooth basis function minimization (SBFM) generated reconstructions that agreed well, both qualitatively and quantitatively, with the concentration profiles generated from point sampling. We present one set of illustrative experimental data to compare the performance of ART and SBFM.
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Lévy flight with absorption: A model for diffusing diffusivity with long tails
NASA Astrophysics Data System (ADS)
Jain, Rohit; Sebastian, K. L.
2017-03-01
We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016), 10.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e.,
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DOE Office of Scientific and Technical Information (OSTI.GOV)
S., Juan Manuel Franco; Cywiak, Moises; Cywiak, David
2015-06-24
A homodyne profiler is used for recording the intensity distribution of focused non-truncated Gaussian beams. The spatial distributions are obtained at planes in the vicinity of the back-focal plane of a focusing lens placed at different distances from a He–Ne laser beam with a Gaussian intensity profile. Comparisons of the experimental data with those obtained from the analytical equations for an ideal focusing lens allow us to propose formulae to fine-tune the quadratic term in the Fresnel Gaussian shape invariant at each interface of the propagated field. Furthermore, we give analytical expressions to calculate adequately the propagation of the fieldmore » through an optical system.« less
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The area of isodensity contours in cosmological models and galaxy surveys
NASA Technical Reports Server (NTRS)
Ryden, Barbara S.; Melott, Adrian L.; Craig, David A.; Gott, J. Richard, III; Weinberg, David H.
1989-01-01
The contour crossing statistic, defined as the mean number of times per unit length that a straight line drawn through the field crosses a given contour, is applied to model density fields and to smoothed samples of galaxies. Models in which the matter is in a bubble structure, in a filamentary net, or in clusters can be distinguished from Gaussian density distributions. The shape of the contour crossing curve in the initially Gaussian fields considered remains Gaussian after gravitational evolution and biasing, as long as the smoothing length is longer than the mass correlation length. With a smoothing length of 5/h Mpc, models containing cosmic strings are indistinguishable from Gaussian distributions. Cosmic explosion models are significantly non-Gaussian, having a bubbly structure. Samples from the CfA survey and the Haynes and Giovanelli (1986) survey are more strongly non-Gaussian at a smoothing length of 6/h Mpc than any of the models examined. At a smoothing length of 12/h Mpc, the Haynes and Giovanelli sample appears Gaussian.
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Skewness in large-scale structure and non-Gaussian initial conditions
NASA Technical Reports Server (NTRS)
Fry, J. N.; Scherrer, Robert J.
1994-01-01
We compute the skewness of the galaxy distribution arising from the nonlinear evolution of arbitrary non-Gaussian intial conditions to second order in perturbation theory including the effects of nonlinear biasing. The result contains a term identical to that for a Gaussian initial distribution plus terms which depend on the skewness and kurtosis of the initial conditions. The results are model dependent; we present calculations for several toy models. At late times, the leading contribution from the initial skewness decays away relative to the other terms and becomes increasingly unimportant, but the contribution from initial kurtosis, previously overlooked, has the same time dependence as the Gaussian terms. Observations of a linear dependence of the normalized skewness on the rms density fluctuation therefore do not necessarily rule out initially non-Gaussian models. We also show that with non-Gaussian initial conditions the first correction to linear theory for the mean square density fluctuation is larger than for Gaussian models.
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NASA Astrophysics Data System (ADS)
Weitzen, J. A.; Bourque, S.; Ostergaard, J. C.; Bench, P. M.; Baily, A. D.
1991-04-01
Analysis of data from recent experiments leads to the observation that distributions of underdense meteor trail peak signal amplitudes differ from classic predictions. In this paper the distribution of trail amplitudes in decibels relative 1 W (dBw) is considered, and it is shown that Lindberg's theorem can be used to apply central limit arguments to this problem. It is illustrated that a Gaussian model for the distribution of the logarithm of the peak received signal level of underdense trails provides a better fit to data than classic approaches. Distributions of underdense meteor trail amplitudes at five frequencies are compared to a Gaussian distribution and the classic model. Implications of the Gaussian assumption on the design of communication systems are discussed.
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Large-scale velocities and primordial non-Gaussianity
DOE Office of Scientific and Technical Information (OSTI.GOV)
Schmidt, Fabian
2010-09-15
We study the peculiar velocities of density peaks in the presence of primordial non-Gaussianity. Rare, high-density peaks in the initial density field can be identified with tracers such as galaxies and clusters in the evolved matter distribution. The distribution of relative velocities of peaks is derived in the large-scale limit using two different approaches based on a local biasing scheme. Both approaches agree, and show that halos still stream with the dark matter locally as well as statistically, i.e. they do not acquire a velocity bias. Nonetheless, even a moderate degree of (not necessarily local) non-Gaussianity induces a significant skewnessmore » ({approx}0.1-0.2) in the relative velocity distribution, making it a potentially interesting probe of non-Gaussianity on intermediate to large scales. We also study two-point correlations in redshift space. The well-known Kaiser formula is still a good approximation on large scales, if the Gaussian halo bias is replaced with its (scale-dependent) non-Gaussian generalization. However, there are additional terms not encompassed by this simple formula which become relevant on smaller scales (k > or approx. 0.01h/Mpc). Depending on the allowed level of non-Gaussianity, these could be of relevance for future large spectroscopic surveys.« less
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Redshift-space distortions with the halo occupation distribution - II. Analytic model
NASA Astrophysics Data System (ADS)
Tinker, Jeremy L.
2007-01-01
We present an analytic model for the galaxy two-point correlation function in redshift space. The cosmological parameters of the model are the matter density Ωm, power spectrum normalization σ8, and velocity bias of galaxies αv, circumventing the linear theory distortion parameter β and eliminating nuisance parameters for non-linearities. The model is constructed within the framework of the halo occupation distribution (HOD), which quantifies galaxy bias on linear and non-linear scales. We model one-halo pairwise velocities by assuming that satellite galaxy velocities follow a Gaussian distribution with dispersion proportional to the virial dispersion of the host halo. Two-halo velocity statistics are a combination of virial motions and host halo motions. The velocity distribution function (DF) of halo pairs is a complex function with skewness and kurtosis that vary substantially with scale. Using a series of collisionless N-body simulations, we demonstrate that the shape of the velocity DF is determined primarily by the distribution of local densities around a halo pair, and at fixed density the velocity DF is close to Gaussian and nearly independent of halo mass. We calibrate a model for the conditional probability function of densities around halo pairs on these simulations. With this model, the full shape of the halo velocity DF can be accurately calculated as a function of halo mass, radial separation, angle and cosmology. The HOD approach to redshift-space distortions utilizes clustering data from linear to non-linear scales to break the standard degeneracies inherent in previous models of redshift-space clustering. The parameters of the occupation function are well constrained by real-space clustering alone, separating constraints on bias and cosmology. We demonstrate the ability of the model to separately constrain Ωm,σ8 and αv in models that are constructed to have the same value of β at large scales as well as the same finger-of-god distortions at small scales.
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Gyrator transform of Gaussian beams with phase difference and generation of hollow beam
NASA Astrophysics Data System (ADS)
Xiao, Zhiyu; Xia, Hui; Yu, Tao; Xie, Ding; Xie, Wenke
2018-03-01
The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω 0. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.
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Gyrator transform of Gaussian beams with phase difference and generation of hollow beam
NASA Astrophysics Data System (ADS)
Xiao, Zhiyu; Xia, Hui; Yu, Tao; Xie, Ding; Xie, Wenke
2018-06-01
The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω 0. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.
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Tahir, M Ramzan; Tran, Quang X; Nikulin, Mikhail S
2017-05-30
We studied the problem of testing a hypothesized distribution in survival regression models when the data is right censored and survival times are influenced by covariates. A modified chi-squared type test, known as Nikulin-Rao-Robson statistic, is applied for the comparison of accelerated failure time models. This statistic is used to test the goodness-of-fit for hypertabastic survival model and four other unimodal hazard rate functions. The results of simulation study showed that the hypertabastic distribution can be used as an alternative to log-logistic and log-normal distribution. In statistical modeling, because of its flexible shape of hazard functions, this distribution can also be used as a competitor of Birnbaum-Saunders and inverse Gaussian distributions. The results for the real data application are shown. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.
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Kollins, Scott H; McClernon, F Joseph; Epstein, Jeff N
2009-02-01
Smoking abstinence differentially affects cognitive functioning in smokers with ADHD, compared to non-ADHD smokers. Alternative approaches for analyzing reaction time data from these tasks may further elucidate important group differences. Adults smoking > or = 15 cigarettes with (n=12) or without (n=14) a diagnosis of ADHD completed a continuous performance task (CPT) during two sessions under two separate laboratory conditions--a 'Satiated' condition wherein participants smoked up to and during the session; and an 'Abstinent' condition, in which participants were abstinent overnight and during the session. Reaction time (RT) distributions from the CPT were modeled to fit an ex-Gaussian distribution. The indicator of central tendency for RT from the normal component of the RT distribution (mu) showed a main effect of Group (ADHD < Control) and a Group x Session interaction (ADHD group RTs decreased when abstinent). RT standard deviation for the normal component of the distribution (sigma) showed no effects. The ex-Gaussian parameter tau, which describes the mean and standard deviation of the non-normal component of the distribution, showed significant effects of session (Abstinent > Satiated), Group x Session interaction (ADHD increased significantly under Abstinent condition compared to Control), and a trend toward a main effect of Group (ADHD > Control). Alternative approaches to analyzing RT data provide a more detailed description of the effects of smoking abstinence in ADHD and non-ADHD smokers and results differ from analyses using more traditional approaches. These findings have implications for understanding the neuropsychopharmacology of nicotine and nicotine withdrawal.
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New method for calculating the coupling coefficient in graded index optical fibers
NASA Astrophysics Data System (ADS)
Savović, Svetislav; Djordjevich, Alexandar
2018-05-01
A simple method is proposed for determining the mode coupling coefficient D in graded index multimode optical fibers. It only requires observation of the output modal power distribution P(m, z) for one fiber length z as the Gaussian launching modal power distribution changes, with the Gaussian input light distribution centered along the graded index optical fiber axis (θ0 = 0) without radial offset (r0 = 0). A similar method we previously proposed for calculating the coupling coefficient D in a step-index multimode optical fibers where the output angular power distributions P(θ, z) for one fiber length z with the Gaussian input light distribution launched centrally along the step-index optical fiber axis (θ0 = 0) is needed to be known.
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NASA Astrophysics Data System (ADS)
Aygun, M.; Kucuk, Y.; Boztosun, I.; Ibraheem, Awad A.
2010-12-01
The elastic scattering angular distributions of 6He projectile on different medium and heavy mass target nuclei including 12C, 27Al, 58Ni, 64Zn, 65Cu, 197Au, 208Pb and 209Bi have been examined by using the few-body and Gaussian-shaped density distributions at various energies. The microscopic real parts of the complex nuclear optical potential have been obtained by using the double-folding model for each of the density distributions and the phenomenological imaginary potentials have been taken as the Woods-Saxon type. Comparative results of the few-body and Gaussian-shaped density distributions together with the experimental data are presented within the framework of the optical model.
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NASA Astrophysics Data System (ADS)
Marrocco, Michele
2007-11-01
Fluorescence correlation spectroscopy is fundamental in many physical, chemical and biological studies of molecular diffusion. However, the concept of fluorescence correlation is founded on the assumption that the analytical description of the correlation decay of diffusion can be achieved if the spatial profile of the detected volume obeys a three-dimensional Gaussian distribution. In the present Letter, the analytical result is instead proven for the fundamental Gaussian-Lorentzian profile.
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Sugita, Mitsuro; Weatherbee, Andrew; Bizheva, Kostadinka; Popov, Ivan; Vitkin, Alex
2016-07-01
The probability density function (PDF) of light scattering intensity can be used to characterize the scattering medium. We have recently shown that in optical coherence tomography (OCT), a PDF formalism can be sensitive to the number of scatterers in the probed scattering volume and can be represented by the K-distribution, a functional descriptor for non-Gaussian scattering statistics. Expanding on this initial finding, here we examine polystyrene microsphere phantoms with different sphere sizes and concentrations, and also human skin and fingernail in vivo. It is demonstrated that the K-distribution offers an accurate representation for the measured OCT PDFs. The behavior of the shape parameter of K-distribution that best fits the OCT scattering results is investigated in detail, and the applicability of this methodology for biological tissue characterization is demonstrated and discussed.
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Bingi, Jayachandra; Murukeshan, Vadakke Matham
2015-12-18
Laser speckle pattern is a granular structure formed due to random coherent wavelet interference and generally considered as noise in optical systems including photolithography. Contrary to this, in this paper, we use the speckle pattern to generate predictable and controlled Gaussian random structures and quasi-random structures photo-lithographically. The random structures made using this proposed speckle lithography technique are quantified based on speckle statistics, radial distribution function (RDF) and fast Fourier transform (FFT). The control over the speckle size, density and speckle clustering facilitates the successful fabrication of black silicon with different surface structures. The controllability and tunability of randomness makes this technique a robust method for fabricating predictable 2D Gaussian random structures and black silicon structures. These structures can enhance the light trapping significantly in solar cells and hence enable improved energy harvesting. Further, this technique can enable efficient fabrication of disordered photonic structures and random media based devices.
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USDA-ARS?s Scientific Manuscript database
Hyperspectral scattering provides an effective means for characterizing light scattering in the fruit and is thus promising for noninvasive assessment of apple firmness and soluble solids content (SSC). A critical problem encountered in application of hyperspectral scattering technology is analyzing...
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Statistical analysis of passenger-crowding in bus transport network of Harbin
NASA Astrophysics Data System (ADS)
Hu, Baoyu; Feng, Shumin; Li, Jinyang; Zhao, Hu
2018-01-01
Passenger flow data is indispensable but rare in the study of public transport networks. In this study, we focus on the passenger-crowding characteristics of the bus transport network of Harbin (BTN-H) based on passenger flow investigation. The three frequency histograms for all the uplinks and downlinks in Harbin are presented, including passengers on the bus at each section, crowding coefficients, and position parameters of crowded sections. The differences in crowding position are analyzed on each route. The distributions of degree and crowding degree (in directed space L) follow an exponential law. The new finding indicates that there are many stations with few crowded sections and a few stations with many crowded sections. The distributions of path length and crowded length (in directed space P) are presented based on the minimum transfer times, and it is found that they can be fitted by a composite Gaussian function and a Gaussian function, respectively. The stations and paths can be divided into three crowd levels. We conclude that BTN-H is crowded from a network-based perspective.
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NASA Astrophysics Data System (ADS)
Chakrabarty, Ayan; Wang, Feng; Sun, Kai; Wei, Qi-Huo
Prior studies have shown that low symmetry particles such as micro-boomerangs exhibit behaviour of Brownian motion rather different from that of high symmetry particles because convenient tracking points (TPs) are usually inconsistent with the center of hydrodynamic stress (CoH) where the translational and rotational motions are decoupled. In this paper we study the effects of the translation-rotation coupling on the displacement probability distribution functions (PDFs) of the boomerang colloid particles with symmetric arms. By tracking the motions of different points on the particle symmetry axis, we show that as the distance between the TP and the CoH is increased, the effects of translation-rotation coupling becomes pronounced, making the short-time 2D PDF for fixed initial orientation to change from elliptical to crescent shape and the angle averaged PDFs from ellipsoidal-particle-like PDF to a shape with a Gaussian top and long displacement tails. We also observed that at long times the PDFs revert to Gaussian. This crescent shape of 2D PDF provides a clear physical picture of the non-zero mean displacements observed in boomerangs particles.
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NASA Astrophysics Data System (ADS)
Palenčár, Rudolf; Sopkuliak, Peter; Palenčár, Jakub; Ďuriš, Stanislav; Suroviak, Emil; Halaj, Martin
2017-06-01
Evaluation of uncertainties of the temperature measurement by standard platinum resistance thermometer calibrated at the defining fixed points according to ITS-90 is a problem that can be solved in different ways. The paper presents a procedure based on the propagation of distributions using the Monte Carlo method. The procedure employs generation of pseudo-random numbers for the input variables of resistances at the defining fixed points, supposing the multivariate Gaussian distribution for input quantities. This allows taking into account the correlations among resistances at the defining fixed points. Assumption of Gaussian probability density function is acceptable, with respect to the several sources of uncertainties of resistances. In the case of uncorrelated resistances at the defining fixed points, the method is applicable to any probability density function. Validation of the law of propagation of uncertainty using the Monte Carlo method is presented on the example of specific data for 25 Ω standard platinum resistance thermometer in the temperature range from 0 to 660 °C. Using this example, we demonstrate suitability of the method by validation of its results.
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NASA Astrophysics Data System (ADS)
Jenkins, Colleen; Jordan, Jay; Carlson, Jeff
2007-02-01
This paper presents parameter estimation techniques useful for detecting background changes in a video sequence with extreme foreground activity. A specific application of interest is automated detection of the covert placement of threats (e.g., a briefcase bomb) inside crowded public facilities. We propose that a histogram of pixel intensity acquired from a fixed mounted camera over time for a series of images will be a mixture of two Gaussian functions: the foreground probability distribution function and background probability distribution function. We will use Pearson's Method of Moments to separate the two probability distribution functions. The background function can then be "remembered" and changes in the background can be detected. Subsequent comparisons of background estimates are used to detect changes. Changes are flagged to alert security forces to the presence and location of potential threats. Results are presented that indicate the significant potential for robust parameter estimation techniques as applied to video surveillance.
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NASA Astrophysics Data System (ADS)
Sposini, Vittoria; Chechkin, Aleksei V.; Seno, Flavio; Pagnini, Gianni; Metzler, Ralf
2018-04-01
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.
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Theory and generation of conditional, scalable sub-Gaussian random fields
NASA Astrophysics Data System (ADS)
Panzeri, M.; Riva, M.; Guadagnini, A.; Neuman, S. P.
2016-03-01
Many earth and environmental (as well as a host of other) variables, Y, and their spatial (or temporal) increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture key aspects of such non-Gaussian scaling by treating Y and/or ΔY as sub-Gaussian random fields (or processes). This however left unaddressed the empirical finding that whereas sample frequency distributions of Y tend to display relatively mild non-Gaussian peaks and tails, those of ΔY often reveal peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we proposed a generalized sub-Gaussian model (GSG) which resolves this apparent inconsistency between the statistical scaling behaviors of observed variables and their increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. Most importantly, we demonstrated the feasibility of estimating all parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments, ΔY. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random fields, introduce two approximate versions of this algorithm to reduce CPU time, and explore them on one and two-dimensional synthetic test cases.
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NASA Technical Reports Server (NTRS)
Kihm, Frederic; Rizzi, Stephen A.; Ferguson, Neil S.; Halfpenny, Andrew
2013-01-01
High cycle fatigue of metals typically occurs through long term exposure to time varying loads which, although modest in amplitude, give rise to microscopic cracks that can ultimately propagate to failure. The fatigue life of a component is primarily dependent on the stress amplitude response at critical failure locations. For most vibration tests, it is common to assume a Gaussian distribution of both the input acceleration and stress response. In real life, however, it is common to experience non-Gaussian acceleration input, and this can cause the response to be non-Gaussian. Examples of non-Gaussian loads include road irregularities such as potholes in the automotive world or turbulent boundary layer pressure fluctuations for the aerospace sector or more generally wind, wave or high amplitude acoustic loads. The paper first reviews some of the methods used to generate non-Gaussian excitation signals with a given power spectral density and kurtosis. The kurtosis of the response is examined once the signal is passed through a linear time invariant system. Finally an algorithm is presented that determines the output kurtosis based upon the input kurtosis, the input power spectral density and the frequency response function of the system. The algorithm is validated using numerical simulations. Direct applications of these results include improved fatigue life estimations and a method to accelerate shaker tests by generating high kurtosis, non-Gaussian drive signals.
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Lodewyck, Jérôme; Debuisschert, Thierry; García-Patrón, Raúl; Tualle-Brouri, Rosa; Cerf, Nicolas J; Grangier, Philippe
2007-01-19
An intercept-resend attack on a continuous-variable quantum-key-distribution protocol is investigated experimentally. By varying the interception fraction, one can implement a family of attacks where the eavesdropper totally controls the channel parameters. In general, such attacks add excess noise in the channel, and may also result in non-Gaussian output distributions. We implement and characterize the measurements needed to detect these attacks, and evaluate experimentally the information rates available to the legitimate users and the eavesdropper. The results are consistent with the optimality of Gaussian attacks resulting from the security proofs.
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The Gaussian Laser Angular Distribution in HYDRA's 3D Laser Ray Trace Package
DOE Office of Scientific and Technical Information (OSTI.GOV)
Sepke, Scott M.
In this note, the angular distribution of rays launched by the 3D LZR ray trace package is derived for Gaussian beams (npower==2) with bm model=3±. Beams with bm model=+3 have a nearly at distribution, and beams with bm model=-3 have a nearly linear distribution when the spot size is large compared to the wavelength.
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Clerkin, L.; Kirk, D.; Manera, M.; ...
2016-08-30
It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (kappa_WL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the Counts in Cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey (DES) Science Verification data over 139 deg^2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirmmore » that the galaxy density contrast distribution is well modeled by a lognormal PDF convolved with Poisson noise at angular scales from 10-40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as kappa_WL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the kappa_WL distribution is well modeled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fit chi^2/DOF of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07 respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.« less
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NASA Astrophysics Data System (ADS)
Clerkin, L.; Kirk, D.; Manera, M.; Lahav, O.; Abdalla, F.; Amara, A.; Bacon, D.; Chang, C.; Gaztañaga, E.; Hawken, A.; Jain, B.; Joachimi, B.; Vikram, V.; Abbott, T.; Allam, S.; Armstrong, R.; Benoit-Lévy, A.; Bernstein, G. M.; Bernstein, R. A.; Bertin, E.; Brooks, D.; Burke, D. L.; Rosell, A. Carnero; Carrasco Kind, M.; Crocce, M.; Cunha, C. E.; D'Andrea, C. B.; da Costa, L. N.; Desai, S.; Diehl, H. T.; Dietrich, J. P.; Eifler, T. F.; Evrard, A. E.; Flaugher, B.; Fosalba, P.; Frieman, J.; Gerdes, D. W.; Gruen, D.; Gruendl, R. A.; Gutierrez, G.; Honscheid, K.; James, D. J.; Kent, S.; Kuehn, K.; Kuropatkin, N.; Lima, M.; Melchior, P.; Miquel, R.; Nord, B.; Plazas, A. A.; Romer, A. K.; Roodman, A.; Sanchez, E.; Schubnell, M.; Sevilla-Noarbe, I.; Smith, R. C.; Soares-Santos, M.; Sobreira, F.; Suchyta, E.; Swanson, M. E. C.; Tarle, G.; Walker, A. R.
2017-04-01
It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (κWL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the counts-in-cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey Science Verification data over 139 deg2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirm that the galaxy density contrast distribution is well modelled by a lognormal PDF convolved with Poisson noise at angular scales from 10 to 40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as κWL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the κWL distribution is well modelled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fitting χ2/dof of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07, respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check, we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.
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LASER BIOLOGY AND MEDICINE: Light scattering study of rheumatoid arthritis
NASA Astrophysics Data System (ADS)
Beuthan, J.; Netz, U.; Minet, O.; Klose, Annerose D.; Hielscher, A. H.; Scheel, A.; Henniger, J.; Müller, G.
2002-11-01
The distribution of light scattered by finger joints is studied in the near-IR region. It is shown that variations in the optical parameters of the tissue (scattering coefficient μs, absorption coefficient μa, and anisotropy factor g) depend on the presence of the rheumatoid arthritis (RA). At the first stage, the distribution of scattered light was measured in diaphanoscopic experiments. The convolution of a Gaussian error function with the scattering phase function proved to be a good approximation of the data obtained. Then, a new method was developed for the reconstruction of distribution of optical parameters in the finger cross section. Model tests of the quality of this reconstruction method show good results.
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NASA Astrophysics Data System (ADS)
Takeuchi, Tsutomu T.
2010-08-01
We provide an analytic method to construct a bivariate distribution function (DF) with given marginal distributions and correlation coefficient. We introduce a convenient mathematical tool, called a copula, to connect two DFs with any prescribed dependence structure. If the correlation of two variables is weak (Pearson's correlation coefficient |ρ| < 1/3), the Farlie-Gumbel-Morgenstern (FGM) copula provides an intuitive and natural way to construct such a bivariate DF. When the linear correlation is stronger, the FGM copula cannot work anymore. In this case, we propose using a Gaussian copula, which connects two given marginals and is directly related to the linear correlation coefficient between two variables. Using the copulas, we construct the bivariate luminosity function (BLF) and discuss its statistical properties. We focus especially on the far-infrared-far-ulatraviolet (FUV-FIR) BLF, since these two wavelength regions are related to star-formation (SF) activity. Though both the FUV and FIR are related to SF activity, the univariate LFs have a very different functional form: the former is well described by the Schechter function whilst the latter has a much more extended power-law-like luminous end. We construct the FUV-FIR BLFs using the FGM and Gaussian copulas with different strengths of correlation, and examine their statistical properties. We then discuss some further possible applications of the BLF: the problem of a multiband flux-limited sample selection, the construction of the star-formation rate (SFR) function, and the construction of the stellar mass of galaxies (M*)-specific SFR (SFR/M*) relation. The copulas turn out to be a very useful tool to investigate all these issues, especially for including complicated selection effects.
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Gas and Dust Structures of the Protoplanetary Disk around HD 142527
NASA Astrophysics Data System (ADS)
Momose, M.; Muto, T.; Hanawa, T.; Fukagawa, M.; Tsukagoshi, T.; Saigo, K.; Kataoka, A.; Nomura, H.; Takeuchi, T.; Akiyama, E.; Ohashi, N.; Fujiwara, H.; Shibai, H.; Kitamura, Y.; Inutsuka, S.; Kobayashi, H.; Honda, M.; Aso, Y.; Takahashi, S. Z.
2015-12-01
HD142527 is a Herbig Fe star accompanied by a disk with ring-like structure. We derive the distributions of dust and gas separately by model fitting and discuss the spatial variation of gas-to-dust mass ratio in the disk. The radial distribution of dust is well approximated by a Gaussian function, while the gas is roughly followed by a power-law distribution between 110 and 400 AU in radius, which is significantly more extended than dust. G/d may reach the order of unity at the northern peak.
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Accretion rates of protoplanets. II - Gaussian distributions of planetesimal velocities
NASA Technical Reports Server (NTRS)
Greenzweig, Yuval; Lissauer, Jack J.
1992-01-01
In the present growth-rate calculations for a protoplanet that is embedded in a disk of planetesimals with triaxial Gaussian velocity dispersion and uniform surface density, the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is found to be enhanced by a factor of about 3 relative to the case where all planetesimals' eccentricities and inclinations are equal to the rms values of those disk variables having locally Gaussian velocity dispersion. This accretion-rate enhancement should be incorporated by all models that assume a single random velocity for all planetesimals in lieu of a Gaussian distribution.
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Study on typhoon characteristic based on bridge health monitoring system.
Wang, Xu; Chen, Bin; Sun, Dezhang; Wu, Yinqiang
2014-01-01
Through the wind velocity and direction monitoring system installed on Jiubao Bridge of Qiantang River, Hangzhou city, Zhejiang province, China, a full range of wind velocity and direction data was collected during typhoon HAIKUI in 2012. Based on these data, it was found that, at higher observed elevation, turbulence intensity is lower, and the variation tendency of longitudinal and lateral turbulence intensities with mean wind speeds is basically the same. Gust factor goes higher with increasing mean wind speed, and the change rate obviously decreases as wind speed goes down and an inconspicuous increase occurs when wind speed is high. The change of peak factor is inconspicuous with increasing time and mean wind speed. The probability density function (PDF) of fluctuating wind speed follows Gaussian distribution. Turbulence integral scale increases with mean wind speed, and its PDF does not follow Gaussian distribution. The power spectrum of observation fluctuating velocity is in accordance with Von Karman spectrum.
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Dynamic design of ecological monitoring networks for non-Gaussian spatio-temporal data
Wikle, C.K.; Royle, J. Andrew
2005-01-01
Many ecological processes exhibit spatial structure that changes over time in a coherent, dynamical fashion. This dynamical component is often ignored in the design of spatial monitoring networks. Furthermore, ecological variables related to processes such as habitat are often non-Gaussian (e.g. Poisson or log-normal). We demonstrate that a simulation-based design approach can be used in settings where the data distribution is from a spatio-temporal exponential family. The key random component in the conditional mean function from this distribution is then a spatio-temporal dynamic process. Given the computational burden of estimating the expected utility of various designs in this setting, we utilize an extended Kalman filter approximation to facilitate implementation. The approach is motivated by, and demonstrated on, the problem of selecting sampling locations to estimate July brood counts in the prairie pothole region of the U.S.
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Near-field spectral shift of a zero-order Bessel beam scattered from a spherical particle
NASA Astrophysics Data System (ADS)
Chen, Feinan; Li, Jia; Belafhal, Abdelmajid; Chafiq, Abdelghani; Sun, Xiaobing
2018-06-01
Within the accuracy of the first-order Born approximation, expressions are derived for the near-zone spectrum of a zero-order Bessel beam scattered from a spherical particle whose correlation function satisfies a Gaussian distribution. The dependence of the spectral shift and spectral switch of the scattered field on the effective size of the scattering potential (ESSP) are determined by numerical simulations. It is shown that the spectral shift of the scattered field does not occur along the longitudinal propagation direction. Furthermore, when the medium’s ESSP is comparable with the central wavelength of the beam, the spectrum of the scattered field loses the Gaussian distribution and exhibits a blue shift as the reference point sufficiently far away from central origin. These results may have prospective applications in guiding tiny particles when the near-zone spectrums of scattered beams are captured and analyzed.
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A Geostatistical Scaling Approach for the Generation of Non Gaussian Random Variables and Increments
NASA Astrophysics Data System (ADS)
Guadagnini, Alberto; Neuman, Shlomo P.; Riva, Monica; Panzeri, Marco
2016-04-01
We address manifestations of non-Gaussian statistical scaling displayed by many variables, Y, and their (spatial or temporal) increments. Evidence of such behavior includes symmetry of increment distributions at all separation distances (or lags) with sharp peaks and heavy tails which tend to decay asymptotically as lag increases. Variables reported to exhibit such distributions include quantities of direct relevance to hydrogeological sciences, e.g. porosity, log permeability, electrical resistivity, soil and sediment texture, sediment transport rate, rainfall, measured and simulated turbulent fluid velocity, and other. No model known to us captures all of the documented statistical scaling behaviors in a unique and consistent manner. We recently proposed a generalized sub-Gaussian model (GSG) which reconciles within a unique theoretical framework the probability distributions of a target variable and its increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. In this context, we demonstrated the feasibility of estimating all key parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random field, and explore them on one- and two-dimensional synthetic test cases.
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Statistical properties and correlation functions for drift waves
NASA Technical Reports Server (NTRS)
Horton, W.
1986-01-01
The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.
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Lin, H-Y; Gau, S S-F; Huang-Gu, S L; Shang, C-Y; Wu, Y-H; Tseng, W-Y I
2014-06-01
Increased intra-individual variability (IIV) in reaction time (RT) across various tasks is one ubiquitous neuropsychological finding in attention deficit hyperactivity disorder (ADHD). However, neurobiological underpinnings of IIV in individuals with ADHD have not yet been fully delineated. The ex-Gaussian distribution has been proved to capture IIV in RT. The authors explored the three parameters [μ (mu), σ (sigma), τ (tau)] of an ex-Gaussian RT distribution derived from the Conners' continuous performance test (CCPT) and their correlations with the microstructural integrity of the frontostriatal-caudate tracts and the cingulum bundles. We assessed 28 youths with ADHD (8-17 years; 25 males) and 28 age-, sex-, IQ- and handedness-matched typically developing (TD) youths using the CCPT, Wechsler Intelligence Scale for Children, 3rd edition and magnetic resonance imaging (MRI). Microstructural integrity, indexed by generalized fractional anisotropy (GFA), was measured by diffusion spectrum imaging tractrography on a 3-T MRI system. Youths with ADHD had larger σ (s.d. of Gaussian distribution) and τ (mean of exponential distribution) and reduced GFA in four bilateral frontostriatal tracts. With increased inter-stimulus intervals of CCPT, the magnitude of greater τ in ADHD than TD increased. In ADHD youths, the cingulum bundles and frontostriatal integrity were associated with three ex-Gaussian parameters and with μ (mean of Gaussian distribution) and τ, respectively; while only frontostriatal GFA was associated with μ and τ in TD youths. Our findings suggest the crucial role of the integrity of the cingulum bundles in accounting for IIV in ADHD. Involvement of different brain systems in mediating IIV may relate to a distinctive pathophysiological processing and/or adaptive compensatory mechanism.
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An estimation of distribution method for infrared target detection based on Copulas
NASA Astrophysics Data System (ADS)
Wang, Shuo; Zhang, Yiqun
2015-10-01
Track-before-detect (TBD) based target detection involves a hypothesis test of merit functions which measure each track as a possible target track. Its accuracy depends on the precision of the distribution of merit functions, which determines the threshold for a test. Generally, merit functions are regarded Gaussian, and on this basis the distribution is estimated, which is true for most methods such as the multiple hypothesis tracking (MHT). However, merit functions for some other methods such as the dynamic programming algorithm (DPA) are non-Guassian and cross-correlated. Since existing methods cannot reasonably measure the correlation, the exact distribution can hardly be estimated. If merit functions are assumed Guassian and independent, the error between an actual distribution and its approximation may occasionally over 30 percent, and is divergent by propagation. Hence, in this paper, we propose a novel estimation of distribution method based on Copulas, by which the distribution can be estimated precisely, where the error is less than 1 percent without propagation. Moreover, the estimation merely depends on the form of merit functions and the structure of a tracking algorithm, and is invariant to measurements. Thus, the distribution can be estimated in advance, greatly reducing the demand for real-time calculation of distribution functions.
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Why noise is useful in functional and neural mechanisms of interval timing?
2013-01-01
Background The ability to estimate durations in the seconds-to-minutes range - interval timing - is essential for survival, adaptation and its impairment leads to severe cognitive and/or motor dysfunctions. The response rate near a memorized duration has a Gaussian shape centered on the to-be-timed interval (criterion time). The width of the Gaussian-like distribution of responses increases linearly with the criterion time, i.e., interval timing obeys the scalar property. Results We presented analytical and numerical results based on the striatal beat frequency (SBF) model showing that parameter variability (noise) mimics behavioral data. A key functional block of the SBF model is the set of oscillators that provide the time base for the entire timing network. The implementation of the oscillators block as simplified phase (cosine) oscillators has the additional advantage that is analytically tractable. We also checked numerically that the scalar property emerges in the presence of memory variability by using biophysically realistic Morris-Lecar oscillators. First, we predicted analytically and tested numerically that in a noise-free SBF model the output function could be approximated by a Gaussian. However, in a noise-free SBF model the width of the Gaussian envelope is independent of the criterion time, which violates the scalar property. We showed analytically and verified numerically that small fluctuations of the memorized criterion time leads to scalar property of interval timing. Conclusions Noise is ubiquitous in the form of small fluctuations of intrinsic frequencies of the neural oscillators, the errors in recording/retrieving stored information related to criterion time, fluctuation in neurotransmitters’ concentration, etc. Our model suggests that the biological noise plays an essential functional role in the SBF interval timing. PMID:23924391
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Computations of Eisenstein series on Fuchsian groups
NASA Astrophysics Data System (ADS)
Avelin, Helen
2008-09-01
We present numerical investigations of the value distribution and distribution of Fourier coefficients of the Eisenstein series E(z;s) on arithmetic and non-arithmetic Fuchsian groups. Our numerics indicate a Gaussian limit value distribution for a real-valued rotation of E(z;s) as operatorname{Re} sD1/2 , operatorname{Im} sto infty and also, on non-arithmetic groups, a complex Gaussian limit distribution for E(z;s) when operatorname{Re} s>1/2 near 1/2 and operatorname{Im} sto infty , at least if we allow operatorname{Re} sto 1/2 at some rate. Furthermore, on non-arithmetic groups and for fixed s with operatorname{Re} s ge 1/2 near 1/2 , our numerics indicate a Gaussian limit distribution for the appropriately normalized Fourier coefficients.
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Fusion of Imaging and Inertial Sensors for Navigation
2006-09-01
combat operations. The Global Positioning System (GPS) was fielded in the 1980’s and first used for precision navigation and targeting in combat...equations [37]. Consider the homogeneous nonlinear differential equation ẋ(t) = f [x(t),u(t), t] ; x(t0) = x0 (2.4) For a given input function , u0(t...differential equation is a time-varying probability density function . The Kalman filter derivation assumes Gaussian distributions for all random
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{Phi}{sup 4} kinks: Statistical mechanics
DOE Office of Scientific and Technical Information (OSTI.GOV)
Habib, S.
1995-12-31
Some recent investigations of the thermal equilibrium properties of kinks in a 1+1-dimensional, classical {phi}{sup 4} field theory are reviewed. The distribution function, kink density, correlation function, and certain thermodynamic quantities were studied both theoretically and via large scale simulations. A simple double Gaussian variational approach within the transfer operator formalism was shown to give good results in the intermediate temperature range where the dilute gas theory is known to fail.
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NASA Astrophysics Data System (ADS)
Uchida, Y.; Takada, E.; Fujisaki, A.; Kikuchi, T.; Ogawa, K.; Isobe, M.
2017-08-01
A method to stochastically discriminate neutron and γ-ray signals measured with a stilbene organic scintillator is proposed. Each pulse signal was stochastically categorized into two groups: neutron and γ-ray. In previous work, the Expectation Maximization (EM) algorithm was used with the assumption that the measured data followed a Gaussian mixture distribution. It was shown that probabilistic discrimination between these groups is possible. Moreover, by setting the initial parameters for the Gaussian mixture distribution with a k-means algorithm, the possibility of automatic discrimination was demonstrated. In this study, the Student's t-mixture distribution was used as a probabilistic distribution with the EM algorithm to improve the robustness against the effect of outliers caused by pileup of the signals. To validate the proposed method, the figures of merit (FOMs) were compared for the EM algorithm assuming a t-mixture distribution and a Gaussian mixture distribution. The t-mixture distribution resulted in an improvement of the FOMs compared with the Gaussian mixture distribution. The proposed data processing technique is a promising tool not only for neutron and γ-ray discrimination in fusion experiments but also in other fields, for example, homeland security, cancer therapy with high energy particles, nuclear reactor decommissioning, pattern recognition, and so on.
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Simple reaction time in 8-9-year old children environmentally exposed to PCBs.
Šovčíková, Eva; Wimmerová, Soňa; Strémy, Maximilián; Kotianová, Janette; Loffredo, Christopher A; Murínová, Ľubica Palkovičová; Chovancová, Jana; Čonka, Kamil; Lancz, Kinga; Trnovec, Tomáš
2015-12-01
Simple reaction time (SRT) has been studied in children exposed to polychlorinated biphenyls (PCBs), with variable results. In the current work we examined SRT in 146 boys and 161 girls, aged 8.53 ± 0.65 years (mean ± SD), exposed to PCBs in the environment of eastern Slovakia. We divided the children into tertiles with regard to increasing PCB serum concentration. The mean ± SEM serum concentration of the sum of 15 PCB congeners was 191.15 ± 5.39, 419.23 ± 8.47, and 1315.12 ± 92.57 ng/g lipids in children of the first, second, and third tertiles, respectively. We created probability distribution plots for each child from their multiple trials of the SRT testing. We fitted response time distributions from all valid trials with the ex-Gaussian function, a convolution of a normal and an additional exponential function, providing estimates of three independent parameters μ, σ, and τ. μ is the mean of the normal component, σ is the standard deviation of the normal component, and τ is the mean of the exponential component. Group response time distributions were calculated using the Vincent averaging technique. A Q-Q plot comparing probability distribution of the first vs. third tertile indicated that deviation of the quantiles of the latter tertile from those of the former begins at the 40th percentile and does not show a positive acceleration. This was confirmed in comparison of the ex-Gaussian parameters of these two tertiles adjusted for sex, age, Raven IQ of the child, mother's and father's education, behavior at home and school, and BMI: the results showed that the parameters μ and τ significantly (p ≤ 0.05) increased with PCB exposure. Similar increases of the ex-Gaussian parameter τ in children suffering from ADHD have been previously reported and interpreted as intermittent attentional lapses, but were not seen in our cohort. Our study has confirmed that environmental exposure of children to PCBs is associated with prolongation of simple reaction time reflecting impairment of cognitive functions. Copyright © 2015 Elsevier Inc. All rights reserved.
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Gaussian fluctuation of the diffusion exponent of virus capsid in a living cell nucleus
NASA Astrophysics Data System (ADS)
Itto, Yuichi
2018-05-01
In their work [4], Bosse et al. experimentally showed that virus capsid exhibits not only normal diffusion but also anomalous diffusion in nucleus of a living cell. There, it was found that the distribution of fluctuations of the diffusion exponent characterizing them takes the Gaussian form, which is, quite remarkably, the same form for two different types of the virus. This suggests high robustness of such fluctuations. Here, the statistical property of local fluctuations of the diffusion exponent of the virus capsid in the nucleus is studied. A maximum-entropy-principle approach (originally proposed for a different virus in a different cell) is applied for obtaining the fluctuation distribution of the exponent. Largeness of the number of blocks identified with local areas of interchromatin corrals is also examined based on the experimental data. It is shown that the Gaussian distribution of the local fluctuations can be derived, in accordance with the above form. In addition, it is quantified how the fluctuation distribution on a long time scale is different from the Gaussian distribution.
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Castillo-Barnes, Diego; Peis, Ignacio; Martínez-Murcia, Francisco J.; Segovia, Fermín; Illán, Ignacio A.; Górriz, Juan M.; Ramírez, Javier; Salas-Gonzalez, Diego
2017-01-01
A wide range of segmentation approaches assumes that intensity histograms extracted from magnetic resonance images (MRI) have a distribution for each brain tissue that can be modeled by a Gaussian distribution or a mixture of them. Nevertheless, intensity histograms of White Matter and Gray Matter are not symmetric and they exhibit heavy tails. In this work, we present a hidden Markov random field model with expectation maximization (EM-HMRF) modeling the components using the α-stable distribution. The proposed model is a generalization of the widely used EM-HMRF algorithm with Gaussian distributions. We test the α-stable EM-HMRF model in synthetic data and brain MRI data. The proposed methodology presents two main advantages: Firstly, it is more robust to outliers. Secondly, we obtain similar results than using Gaussian when the Gaussian assumption holds. This approach is able to model the spatial dependence between neighboring voxels in tomographic brain MRI. PMID:29209194
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Zeng, Yuehua
2018-01-01
The Uniform California Earthquake Rupture Forecast v.3 (UCERF3) model (Field et al., 2014) considers epistemic uncertainty in fault‐slip rate via the inclusion of multiple rate models based on geologic and/or geodetic data. However, these slip rates are commonly clustered about their mean value and do not reflect the broader distribution of possible rates and associated probabilities. Here, we consider both a double‐truncated 2σ Gaussian and a boxcar distribution of slip rates and use a Monte Carlo simulation to sample the entire range of the distribution for California fault‐slip rates. We compute the seismic hazard following the methodology and logic‐tree branch weights applied to the 2014 national seismic hazard model (NSHM) for the western U.S. region (Petersen et al., 2014, 2015). By applying a new approach developed in this study to the probabilistic seismic hazard analysis (PSHA) using precomputed rates of exceedance from each fault as a Green’s function, we reduce the computer time by about 10^5‐fold and apply it to the mean PSHA estimates with 1000 Monte Carlo samples of fault‐slip rates to compare with results calculated using only the mean or preferred slip rates. The difference in the mean probabilistic peak ground motion corresponding to a 2% in 50‐yr probability of exceedance is less than 1% on average over all of California for both the Gaussian and boxcar probability distributions for slip‐rate uncertainty but reaches about 18% in areas near faults compared with that calculated using the mean or preferred slip rates. The average uncertainties in 1σ peak ground‐motion level are 5.5% and 7.3% of the mean with the relative maximum uncertainties of 53% and 63% for the Gaussian and boxcar probability density function (PDF), respectively.
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A non-gaussian model of continuous atmospheric turbulence for use in aircraft design
NASA Technical Reports Server (NTRS)
Reeves, P. M.; Joppa, R. G.; Ganzer, V. M.
1976-01-01
A non-Gaussian model of atmospheric turbulence is presented and analyzed. The model is restricted to the regions of the atmosphere where the turbulence is steady or continuous, and the assumptions of homogeneity and stationarity are justified. Also spatial distribution of turbulence is neglected, so the model consists of three independent, stationary stochastic processes which represent the vertical, lateral, and longitudinal gust components. The non-Gaussian and Gaussian models are compared with experimental data, and it is shown that the Gaussian model underestimates the number of high velocity gusts which occur in the atmosphere, while the non-Gaussian model can be adjusted to match the observed high velocity gusts more satisfactorily. Application of the proposed model to aircraft response is investigated, with particular attention to the response power spectral density, the probability distribution, and the level crossing frequency. A numerical example is presented which illustrates the application of the non-Gaussian model to the study of an aircraft autopilot system. Listings and sample results of a number of computer programs used in working with the model are included.
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NASA Astrophysics Data System (ADS)
Jain, Varun; Biesinger, Mark C.; Linford, Matthew R.
2018-07-01
X-ray photoelectron spectroscopy (XPS) is arguably the most important vacuum technique for surface chemical analysis, and peak fitting is an indispensable part of XPS data analysis. Functions that have been widely explored and used in XPS peak fitting include the Gaussian, Lorentzian, Gaussian-Lorentzian sum (GLS), Gaussian-Lorentzian product (GLP), and Voigt functions, where the Voigt function is a convolution of a Gaussian and a Lorentzian function. In this article we discuss these functions from a graphical perspective. Arguments based on convolution and the Central Limit Theorem are made to justify the use of functions that are intermediate between pure Gaussians and pure Lorentzians in XPS peak fitting. Mathematical forms for the GLS and GLP functions are presented with a mixing parameter m. Plots are shown for GLS and GLP functions with mixing parameters ranging from 0 to 1. There are fundamental differences between the GLS and GLP functions. The GLS function better follows the 'wings' of the Lorentzian, while these 'wings' are suppressed in the GLP. That is, these two functions are not interchangeable. The GLS and GLP functions are compared to the Voigt function, where the GLS is shown to be a decent approximation of it. Practically, both the GLS and the GLP functions can be useful for XPS peak fitting. Examples of the uses of these functions are provided herein.
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Log-amplitude statistics for Beck-Cohen superstatistics
NASA Astrophysics Data System (ADS)
Kiyono, Ken; Konno, Hidetoshi
2013-05-01
As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for χ2, inverse χ2, and log-normal superstatistical distributions. Furthermore, we show that χ2 and inverse χ2 superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the q-Gaussian distribution with q=5/3 and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the χ2 superstatistical distribution with degree 2.
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Log-normal distribution from a process that is not multiplicative but is additive.
Mouri, Hideaki
2013-10-01
The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal distribution. Although the sum tends eventually to a Gaussian distribution, the distribution of the sum is always close to a log-normal distribution rather than to any Gaussian distribution if the summands are numerous enough. This is in contrast to the current consensus that any log-normal distribution is due to a product of random variables, i.e., a multiplicative process, or equivalently to nonlinearity of the system. In fact, the log-normal distribution is also observable for a sum, i.e., an additive process that is typical of linear systems. We show conditions for such a sum, an analytical example, and an application to random scalar fields such as those of turbulence.
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The effect of unresolved contaminant stars on the cross-matching of photometric catalogues
NASA Astrophysics Data System (ADS)
Wilson, Tom J.; Naylor, Tim
2017-07-01
A fundamental process in astrophysics is the matching of two photometric catalogues. It is crucial that the correct objects be paired, and that their photometry does not suffer from any spurious additional flux. We compare the positions of sources in Wide-field Infrared Survey Explorer (WISE), INT Photometric H α Survey, Two Micron All Sky Survey and AAVSO Photometric All Sky Survey with Gaia Data Release 1 astrometric positions. We find that the separations are described by a combination of a Gaussian distribution, wider than naively assumed based on their quoted uncertainties, and a large wing, which some authors ascribe to proper motions. We show that this is caused by flux contamination from blended stars not treated separately. We provide linear fits between the quoted Gaussian uncertainty and the core fit to the separation distributions. We show that at least one in three of the stars in the faint half of a given catalogue will suffer from flux contamination above the 1 per cent level when the density of catalogue objects per point spread function area is above approximately 0.005. This has important implications for the creation of composite catalogues. It is important for any closest neighbour matches as there will be a given fraction of matches that are flux contaminated, while some matches will be missed due to significant astrometric perturbation by faint contaminants. In the case of probability-based matching, this contamination affects the probability density function of matches as a function of distance. This effect results in up to 50 per cent fewer counterparts being returned as matches, assuming Gaussian astrometric uncertainties for WISE-Gaia matching in crowded Galactic plane regions, compared with a closest neighbour match.
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Critical density of a soliton gas
DOE Office of Scientific and Technical Information (OSTI.GOV)
El, G. A., E-mail: g.el@lboro.ac.uk
We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schrödinger operator associated with the Korteweg–de Vries soliton gas dynamics. As a by-product of our derivation, we find the speed of sound in the soliton gas with Gaussian spectral distribution function.
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Critical density of a soliton gas
NASA Astrophysics Data System (ADS)
El, G. A.
2016-02-01
We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schrödinger operator associated with the Korteweg-de Vries soliton gas dynamics. As a by-product of our derivation, we find the speed of sound in the soliton gas with Gaussian spectral distribution function.
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Target Recognition in Ultra-Wideband SAR Imagery
1994-08-01
Poles in a Transfer Function for Real Frequency Informa- tion," Lawrence Livermore Laboratory, UCRL -52050 (April 1974). 24. V. K Jain, T. K. Sarker, and...0.777 Gaussian 0.849 1 5,265 0.978 93 Distribution Adrnnstr ARPAJASTO Defris Techi Info Ctr Attn T DePersia Attn DTIC-DDA (2 copies) 3701 N Fairfax Dr
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Bit-Wise Arithmetic Coding For Compression Of Data
NASA Technical Reports Server (NTRS)
Kiely, Aaron
1996-01-01
Bit-wise arithmetic coding is data-compression scheme intended especially for use with uniformly quantized data from source with Gaussian, Laplacian, or similar probability distribution function. Code words of fixed length, and bits treated as being independent. Scheme serves as means of progressive transmission or of overcoming buffer-overflow or rate constraint limitations sometimes arising when data compression used.
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Liu, Chengyu; Zheng, Dingchang; Zhao, Lina; Liu, Changchun
2014-01-01
It has been reported that Gaussian functions could accurately and reliably model both carotid and radial artery pressure waveforms (CAPW and RAPW). However, the physiological relevance of the characteristic features from the modeled Gaussian functions has been little investigated. This study thus aimed to determine characteristic features from the Gaussian functions and to make comparisons of them between normal subjects and heart failure patients. Fifty-six normal subjects and 51 patients with heart failure were studied with the CAPW and RAPW signals recorded simultaneously. The two signals were normalized first and then modeled by three positive Gaussian functions, with their peak amplitude, peak time, and half-width determined. Comparisons of these features were finally made between the two groups. Results indicated that the peak amplitude of the first Gaussian curve was significantly decreased in heart failure patients compared with normal subjects (P<0.001). Significantly increased peak amplitude of the second Gaussian curves (P<0.001) and significantly shortened peak times of the second and third Gaussian curves (both P<0.001) were also presented in heart failure patients. These results were true for both CAPW and RAPW signals, indicating the clinical significance of the Gaussian modeling, which should provide essential tools for further understanding the underlying physiological mechanisms of the artery pressure waveform.
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Balderson, M J; Brown, D W; Quirk, S; Ghasroddashti, E; Kirkby, C
2012-07-01
Clinical outcome studies with clear and objective endpoints are necessary to make informed radiotherapy treatment decisions. Commonly, clinical outcomes are established after lengthy and costly clinical trials are performed and the data are analyzed and published. One the challenges with obtaining meaningful data from clinical trials is that by the time the information gets to the medical profession the results may be less clinically relevant than when the trial began, An alternative approach is to estimate clinical outcomes through patient population modeling. We are developing a mathematical tool that uses Monte Carlo techniques to simulate variations in planned and delivered dose distributions of prostate patients receiving radiotherapy. Ultimately, our simulation will calculate a distribution of Tumor Control Probabilities (TCPs) for a population of patients treated under a given protocol. Such distributions can serve as a metric for comparing different treatment modalities, planning and setup approaches, and machine parameter settings or tolerances with respect to outcomes on broad patient populations. It may also help researchers understand differences one might expect to find before actually doing the clinical trial. As a first step and for the focus of this abstract we wanted to see if we could answer the question: "Can a population of dose distributions of prostate patients be accurately modeled by a set of randomly generated Gaussian functions?" Our results have demonstrated that using a set of randomly generated Gaussian functions can simulate a distribution of prostate patients. © 2012 American Association of Physicists in Medicine.
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Irradiation direction from texture
NASA Astrophysics Data System (ADS)
Koenderink, Jan J.; Pont, Sylvia C.
2003-10-01
We present a theory of image texture resulting from the shading of corrugated (three-dimensional textured) surfaces, Lambertian on the micro scale, in the domain of geometrical optics. The derivation applies to isotropic Gaussian random surfaces, under collimated illumination, in normal view. The theory predicts the structure tensors from either the gradient or the Hessian of the image intensity and allows inferences of the direction of irradiation of the surface. Although the assumptions appear prima facie rather restrictive, even for surfaces that are not at all Gaussian, with the bidirectional reflectance distribution function far from Lambertian and vignetting and multiple scattering present, we empirically recover the direction of irradiation with an accuracy of a few degrees.
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Color Histogram Diffusion for Image Enhancement
NASA Technical Reports Server (NTRS)
Kim, Taemin
2011-01-01
Various color histogram equalization (CHE) methods have been proposed to extend grayscale histogram equalization (GHE) for color images. In this paper a new method called histogram diffusion that extends the GHE method to arbitrary dimensions is proposed. Ranges in a histogram are specified as overlapping bars of uniform heights and variable widths which are proportional to their frequencies. This diagram is called the vistogram. As an alternative approach to GHE, the squared error of the vistogram from the uniform distribution is minimized. Each bar in the vistogram is approximated by a Gaussian function. Gaussian particles in the vistoram diffuse as a nonlinear autonomous system of ordinary differential equations. CHE results of color images showed that the approach is effective.
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NASA Astrophysics Data System (ADS)
Uhlemann, C.; Pajer, E.; Pichon, C.; Nishimichi, T.; Codis, S.; Bernardeau, F.
2018-03-01
Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point probability distribution function and the two-point clustering of spherically averaged cosmic densities (sphere bias). Sphere bias extends the idea of halo bias to intermediate density environments and voids as underdense regions. In the presence of primordial non-Gaussianity, sphere bias displays a strong scale dependence relevant for both high- and low-density regions, which is predicted analytically. The statistics of densities in spheres are built to model primordial non-Gaussianity via an initial skewness with a scale dependence that depends on the bispectrum of the underlying model. The analytical formulas with the measured non-linear dark matter variance as input are successfully tested against numerical simulations. For local non-Gaussianity with a range from fNL = -100 to +100, they are found to agree within 2 per cent or better for densities ρ ∈ [0.5, 3] in spheres of radius 15 Mpc h-1 down to z = 0.35. The validity of the large deviation statistics formalism is thereby established for all observationally relevant local-type departures from perfectly Gaussian initial conditions. The corresponding estimators for the amplitude of the non-linear variance σ8 and primordial skewness fNL are validated using a fiducial joint maximum likelihood experiment. The influence of observational effects and the prospects for a future detection of primordial non-Gaussianity from joint one- and two-point densities-in-spheres statistics are discussed.
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Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States
NASA Astrophysics Data System (ADS)
Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas
2017-11-01
Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.
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Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States.
Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas
2017-11-03
Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.
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Steinhauser, Marco; Hübner, Ronald
2009-10-01
It has been suggested that performance in the Stroop task is influenced by response conflict as well as task conflict. The present study investigated the idea that both conflict types can be isolated by applying ex-Gaussian distribution analysis which decomposes response time into a Gaussian and an exponential component. Two experiments were conducted in which manual versions of a standard Stroop task (Experiment 1) and a separated Stroop task (Experiment 2) were performed under task-switching conditions. Effects of response congruency and stimulus bivalency were used to measure response conflict and task conflict, respectively. Ex-Gaussian analysis revealed that response conflict was mainly observed in the Gaussian component, whereas task conflict was stronger in the exponential component. Moreover, task conflict in the exponential component was selectively enhanced under task-switching conditions. The results suggest that ex-Gaussian analysis can be used as a tool to isolate different conflict types in the Stroop task. PsycINFO Database Record (c) 2009 APA, all rights reserved.
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Model for non-Gaussian intraday stock returns
NASA Astrophysics Data System (ADS)
Gerig, Austin; Vicente, Javier; Fuentes, Miguel A.
2009-12-01
Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations (called intraday returns) and verify the model using a large database for several stocks traded on the London Stock Exchange. We provide evidence that the return distribution for these stocks is non-Gaussian and similar in shape and that the distribution appears stable over intraday time scales. We explain these results by assuming the volatility of returns is constant intraday but varies over longer periods such that its inverse square follows a gamma distribution. This produces returns that are Student distributed for intraday time scales. The predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution.
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Payne, Brennan R; Stine-Morrow, Elizabeth A L
2014-06-01
We report a secondary data analysis investigating age differences in the effects of clause and sentence wrap-up on reading time distributions during sentence comprehension. Residual word-by-word self-paced reading times were fit to the ex-Gaussian distribution to examine age differences in the effects of clause and sentence wrap-up on both the location and shape of participants' reaction time (RT) distributions. The ex-Gaussian distribution showed good fit to the data in both younger and older adults. Sentence wrap-up increased the central tendency, the variability, and the tail of the distribution, and these effects were exaggerated among the old. In contrast, clause wrap-up influenced the tail of the distribution only, and did so differentially for older adults. Effects were confirmed via nonparametric vincentile plots. Individual differences in visual acuity, working memory, speed of processing, and verbal ability were differentially related to ex-Gaussian parameters reflecting wrap-up effects on underlying reading time distributions. These findings argue against simple pause mechanisms to explain end-of-clause and end-of-sentence reading time patterns; rather, the findings are consistent with a cognitively effortful view of wrap-up and suggest that age and individual differences in attentional allocation to semantic integration during reading, as revealed by RT distribution analyses, play an important role in sentence understanding. PsycINFO Database Record (c) 2014 APA, all rights reserved.
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Moutsopoulou, Karolina; Waszak, Florian
2012-04-01
The differential effects of task and response conflict in priming paradigms where associations are strengthened between a stimulus, a task, and a response have been demonstrated in recent years with neuroimaging methods. However, such effects are not easily disentangled with only measurements of behavior, such as reaction times (RTs). Here, we report the application of ex-Gaussian distribution analysis on task-switching RT data and show that conflict related to stimulus-response associations retrieved after a switch of tasks is reflected in the Gaussian component. By contrast, conflict related to the retrieval of stimulus-task associations is reflected in the exponential component. Our data confirm that the retrieval of stimulus-task and -response associations affects behavior differently. Ex-Gaussian distribution analysis is a useful tool for pulling apart these different levels of associative priming that are not distinguishable in analyses of RT means.
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Incorporating Skew into RMS Surface Roughness Probability Distribution
NASA Technical Reports Server (NTRS)
Stahl, Mark T.; Stahl, H. Philip.
2013-01-01
The standard treatment of RMS surface roughness data is the application of a Gaussian probability distribution. This handling of surface roughness ignores the skew present in the surface and overestimates the most probable RMS of the surface, the mode. Using experimental data we confirm the Gaussian distribution overestimates the mode and application of an asymmetric distribution provides a better fit. Implementing the proposed asymmetric distribution into the optical manufacturing process would reduce the polishing time required to meet surface roughness specifications.
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An Improved Algorithm to Generate a Wi-Fi Fingerprint Database for Indoor Positioning
Chen, Lina; Li, Binghao; Zhao, Kai; Rizos, Chris; Zheng, Zhengqi
2013-01-01
The major problem of Wi-Fi fingerprint-based positioning technology is the signal strength fingerprint database creation and maintenance. The significant temporal variation of received signal strength (RSS) is the main factor responsible for the positioning error. A probabilistic approach can be used, but the RSS distribution is required. The Gaussian distribution or an empirically-derived distribution (histogram) is typically used. However, these distributions are either not always correct or require a large amount of data for each reference point. Double peaks of the RSS distribution have been observed in experiments at some reference points. In this paper a new algorithm based on an improved double-peak Gaussian distribution is proposed. Kurtosis testing is used to decide if this new distribution, or the normal Gaussian distribution, should be applied. Test results show that the proposed algorithm can significantly improve the positioning accuracy, as well as reduce the workload of the off-line data training phase. PMID:23966197
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An improved algorithm to generate a Wi-Fi fingerprint database for indoor positioning.
Chen, Lina; Li, Binghao; Zhao, Kai; Rizos, Chris; Zheng, Zhengqi
2013-08-21
The major problem of Wi-Fi fingerprint-based positioning technology is the signal strength fingerprint database creation and maintenance. The significant temporal variation of received signal strength (RSS) is the main factor responsible for the positioning error. A probabilistic approach can be used, but the RSS distribution is required. The Gaussian distribution or an empirically-derived distribution (histogram) is typically used. However, these distributions are either not always correct or require a large amount of data for each reference point. Double peaks of the RSS distribution have been observed in experiments at some reference points. In this paper a new algorithm based on an improved double-peak Gaussian distribution is proposed. Kurtosis testing is used to decide if this new distribution, or the normal Gaussian distribution, should be applied. Test results show that the proposed algorithm can significantly improve the positioning accuracy, as well as reduce the workload of the off-line data training phase.
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NASA Astrophysics Data System (ADS)
Gao, Li
2015-07-01
We study the evolution of the distribution of consumption of individuals in the majority population in China during the period 1995-2012 and find that its probability density functions (PDFs) obey the rule Pc(x) = K(x - μ) e-(x - μ)2/2σ2. We also find (i) that the PDFs and the individual income distribution appear to be identical, (ii) that the peaks of the PDFs of the individual consumption distribution are consistently on the low side of the PDFs of the income distribution, and (iii) that the average of the marginal propensity to consume (MPC) is large, MPC bar = 0.77, indicating that in the majority population individual consumption is low and strongly dependent on income. The long right tail of the PDFs of consumption indicates that few people in China are participating in the high consumption economy, and that consumption inequality is high. After comparing the PDFs of consumption with the PDFs of income we obtain the PDFs of residual wealth during the period 1995-2012, which exhibit a Gaussian distribution. We use an agent-based kinetic wealth-exchange model (KWEM) to simulate this evolutional process and find that this Gaussian distribution indicates a strong propensity to save rather than spend. This may be due to an anticipation of such large potential outlays as housing, education, and health care in the context of an inadequate welfare support system.
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Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments
NASA Astrophysics Data System (ADS)
Ghosh, Surya K.; Cherstvy, Andrey G.; Grebenkov, Denis S.; Metzler, Ralf
2016-01-01
A topic of intense current investigation pursues the question of how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of extensive simulations of the motion of a finite sized tracer particle in a heterogeneously crowded environment made up of quenched distributions of monodisperse crowders of varying sizes in finite circular two-dimensional domains. For given spatial distributions of monodisperse crowders we demonstrate how anomalous diffusion with strongly non-Gaussian features arises in this model system. We investigate both biologically relevant situations of particles released either at the surface of an inner domain or at the outer boundary, exhibiting distinctly different features of the observed anomalous diffusion for heterogeneous distributions of crowders. Specifically we reveal an asymmetric spreading of tracers even at moderate crowding. In addition to the mean squared displacement (MSD) and local diffusion exponent we investigate the magnitude and the amplitude scatter of the time averaged MSD of individual tracer trajectories, the non-Gaussianity parameter, and the van Hove correlation function. We also quantify how the average tracer diffusivity varies with the position in the domain with a heterogeneous radial distribution of crowders and examine the behaviour of the survival probability and the dynamics of the tracer survival probability. Inter alia, the systems we investigate are related to the passive transport of lipid molecules and proteins in two-dimensional crowded membranes or the motion in colloidal solutions or emulsions in effectively two-dimensional geometries, as well as inside supercrowded, surface adhered cells.
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Kollins, Scott H.; McClernon, F. Joseph; Epstein, Jeff N.
2009-01-01
Smoking abstinence differentially affects cognitive functioning in smokers with ADHD, compared to non-ADHD smokers. Alternative approaches for analyzing reaction time data from these tasks may further elucidate important group differences. Adults smoking ≥15 cigarettes with (n = 12) or without (n = 14) a diagnosis of ADHD completed a continuous performance task (CPT) during two sessions under two separate laboratory conditions—a ‘Satiated’ condition wherein participants smoked up to and during the session; and an ‘Abstinent’ condition, in which participants were abstinent overnight and during the session. Reaction time (RT) distributions from the CPT were modeled to fit an ex-Gaussian distribution. The indicator of central tendency for RT from the normal component of the RT distribution (mu) showed a main effect of Group (ADHD
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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.
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Light scattering study of rheumatoid arthritis
DOE Office of Scientific and Technical Information (OSTI.GOV)
Beuthan, J; Netz, U; Minet, O
The distribution of light scattered by finger joints is studied in the near-IR region. It is shown that variations in the optical parameters of the tissue (scattering coefficient {mu}{sub s}, absorption coefficient {mu}{sub a}, and anisotropy factor g) depend on the presence of the rheumatoid arthritis (RA). At the first stage, the distribution of scattered light was measured in diaphanoscopic experiments. The convolution of a Gaussian error function with the scattering phase function proved to be a good approximation of the data obtained. Then, a new method was developed for the reconstruction of distribution of optical parameters in the fingermore » cross section. Model tests of the quality of this reconstruction method show good results. (laser biology and medicine)« less
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NASA Astrophysics Data System (ADS)
Brodyn, M. S.; Starkov, V. N.
2007-07-01
It is shown that in laser experiments performed by using an 'imperfect' setup when instrumental distortions are considerable, sufficiently accurate results can be obtained by the modern methods of computational physics. It is found for the first time that a new instrumental function — the 'cap' function — a 'sister' of a Gaussian curve proved to be demanded namely in laser experiments. A new mathematical model of a measurement path and carefully performed computational experiment show that a light beam transmitted through a mesoporous film has actually a narrower intensity distribution than the detected beam, and the amplitude of the real intensity distribution is twice as large as that for measured intensity distributions.
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Local Gaussian operations can enhance continuous-variable entanglement distillation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Zhang Shengli; Loock, Peter van; Institute of Theoretical Physics I, Universitaet Erlangen-Nuernberg, Staudtstrasse 7/B2, DE-91058 Erlangen
2011-12-15
Entanglement distillation is a fundamental building block in long-distance quantum communication. Though known to be useless on their own for distilling Gaussian entangled states, local Gaussian operations may still help to improve non-Gaussian entanglement distillation schemes. Here we show that by applying local squeezing operations both the performance and the efficiency of existing distillation protocols can be enhanced. We find that such an enhancement through local Gaussian unitaries can be obtained even when the initially shared Gaussian entangled states are mixed, as, for instance, after their distribution through a lossy-fiber communication channel.
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Nongaussian distribution curve of heterophorias among children.
Letourneau, J E; Giroux, R
1991-02-01
The purpose of this study was to measure the distribution curve of horizontal and vertical phorias among children. Kolmogorov-Smirnov goodness of fit tests showed that these distribution curves were not Gaussian among (N = 2048) 6- to 13-year-old children. The distribution curve of horizontal phoria at far and of vertical phorias at far and at near were leptokurtic; the distribution curve of horizontal phoria at near was platykurtic. No variation of the distribution curve of heterophorias with age was observed. Comparisons of any individual findings with the general distribution curve should take the nonGaussian distribution curve of heterophorias into account.
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Statistics and topology of the COBE differential microwave radiometer first-year sky maps
NASA Technical Reports Server (NTRS)
Smoot, G. F.; Tenorio, L.; Banday, A. J.; Kogut, A.; Wright, E. L.; Hinshaw, G.; Bennett, C. L.
1994-01-01
We use statistical and topological quantities to test the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) first-year sky maps against the hypothesis that the observed temperature fluctuations reflect Gaussian initial density perturbations with random phases. Recent papers discuss specific quantities as discriminators between Gaussian and non-Gaussian behavior, but the treatment of instrumental noise on the data is largely ignored. The presence of noise in the data biases many statistical quantities in a manner dependent on both the noise properties and the unknown cosmic microwave background temperature field. Appropriate weighting schemes can minimize this effect, but it cannot be completely eliminated. Analytic expressions are presented for these biases, and Monte Carlo simulations are used to assess the best strategy for determining cosmologically interesting information from noisy data. The genus is a robust discriminator that can be used to estimate the power-law quadrupole-normalized amplitude, Q(sub rms-PS), independently of the two-point correlation function. The genus of the DMR data is consistent with Gaussian initial fluctuations with Q(sub rms-PS) = (15.7 +/- 2.2) - (6.6 +/- 0.3)(n - 1) micro-K, where n is the power-law index. Fitting the rms temperature variations at various smoothing angles gives Q(sub rms-PS) = 13.2 +/- 2.5 micro-K and n = 1.7(sup (+0.3) sub (-0.6)). While consistent with Gaussian fluctuations, the first year data are only sufficient to rule out strongly non-Gaussian distributions of fluctuations.
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Detailed noise statistics for an optically preamplified direct detection receiver
NASA Astrophysics Data System (ADS)
Danielsen, Soeren Lykke; Mikkelsen, Benny; Durhuus, Terji; Joergensen, Carsten; Stubkjaer, Kristian E.
We describe the exact statistics of an optically preamplified direct detection receiver by means of the moment generating function. The theory allows an arbitrary shaped electrical filter in the receiver circuit. The moment generating function (MGF) allows for a precise calculation of the error rate by using the inverse Fast Fourier transform (FFT). The exact results are compared with the usual Gaussian approximation (GA), the saddlepoint approximation (SAP) and the modified Chernoff bound (MCB). This comparison shows that the noise is not Gaussian distributed for all values of the optical amplifier gain. In the region from 20-30 dB gain, calculations shows that the GA underestimates the receiver sensitivity while the SAP is very close to the results of our exact model. Using the MGF derived in the article we then find the optimal bandwidth of the electrical filter in the receiver circuit and calculate the sensitivity degradation due to inter symbol interference (ISI).
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NASA Astrophysics Data System (ADS)
Shukri, Seyfan Kelil
2017-01-01
We have done Kinetic Monte Carlo (KMC) simulations to investigate the effect of charge carrier density on the electrical conductivity and carrier mobility in disordered organic semiconductors using a lattice model. The density of state (DOS) of the system are considered to be Gaussian and exponential. Our simulations reveal that the mobility of the charge carrier increases with charge carrier density for both DOSs. In contrast, the mobility of charge carriers decreases as the disorder increases. In addition the shape of the DOS has a significance effect on the charge transport properties as a function of density which are clearly seen. On the other hand, for the same distribution width and at low carrier density, the change occurred on the conductivity and mobility for a Gaussian DOS is more pronounced than that for the exponential DOS.
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A new probability distribution model of turbulent irradiance based on Born perturbation theory
NASA Astrophysics Data System (ADS)
Wang, Hongxing; Liu, Min; Hu, Hao; Wang, Qian; Liu, Xiguo
2010-10-01
The subject of the PDF (Probability Density Function) of the irradiance fluctuations in a turbulent atmosphere is still unsettled. Theory reliably describes the behavior in the weak turbulence regime, but theoretical description in the strong and whole turbulence regimes are still controversial. Based on Born perturbation theory, the physical manifestations and correlations of three typical PDF models (Rice-Nakagami, exponential-Bessel and negative-exponential distribution) were theoretically analyzed. It is shown that these models can be derived by separately making circular-Gaussian, strong-turbulence and strong-turbulence-circular-Gaussian approximations in Born perturbation theory, which denies the viewpoint that the Rice-Nakagami model is only applicable in the extremely weak turbulence regime and provides theoretical arguments for choosing rational models in practical applications. In addition, a common shortcoming of the three models is that they are all approximations. A new model, called the Maclaurin-spread distribution, is proposed without any approximation except for assuming the correlation coefficient to be zero. So, it is considered that the new model can exactly reflect the Born perturbation theory. Simulated results prove the accuracy of this new model.
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A survey of kernel-type estimators for copula and their applications
NASA Astrophysics Data System (ADS)
Sumarjaya, I. W.
2017-10-01
Copulas have been widely used to model nonlinear dependence structure. Main applications of copulas include areas such as finance, insurance, hydrology, rainfall to name but a few. The flexibility of copula allows researchers to model dependence structure beyond Gaussian distribution. Basically, a copula is a function that couples multivariate distribution functions to their one-dimensional marginal distribution functions. In general, there are three methods to estimate copula. These are parametric, nonparametric, and semiparametric method. In this article we survey kernel-type estimators for copula such as mirror reflection kernel, beta kernel, transformation method and local likelihood transformation method. Then, we apply these kernel methods to three stock indexes in Asia. The results of our analysis suggest that, albeit variation in information criterion values, the local likelihood transformation method performs better than the other kernel methods.
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Demonstration of Monogamy Relations for Einstein-Podolsky-Rosen Steering in Gaussian Cluster States.
Deng, Xiaowei; Xiang, Yu; Tian, Caixing; Adesso, Gerardo; He, Qiongyi; Gong, Qihuang; Su, Xiaolong; Xie, Changde; Peng, Kunchi
2017-06-09
Understanding how quantum resources can be quantified and distributed over many parties has profound applications in quantum communication. As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. By reconstructing the covariance matrix of a continuous variable four-mode square Gaussian cluster state subject to asymmetric loss, we quantify the amount of bipartite steering with a variable number of modes per party, and verify recently introduced monogamy relations for Gaussian steerability, which establish quantitative constraints on the security of information shared among different parties. We observe a very rich structure for the steering distribution, and demonstrate one-way EPR steering of the cluster state under Gaussian measurements, as well as one-to-multimode steering. Our experiment paves the way for exploiting EPR steering in Gaussian cluster states as a valuable resource for multiparty quantum information tasks.
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Demonstration of Monogamy Relations for Einstein-Podolsky-Rosen Steering in Gaussian Cluster States
NASA Astrophysics Data System (ADS)
Deng, Xiaowei; Xiang, Yu; Tian, Caixing; Adesso, Gerardo; He, Qiongyi; Gong, Qihuang; Su, Xiaolong; Xie, Changde; Peng, Kunchi
2017-06-01
Understanding how quantum resources can be quantified and distributed over many parties has profound applications in quantum communication. As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. By reconstructing the covariance matrix of a continuous variable four-mode square Gaussian cluster state subject to asymmetric loss, we quantify the amount of bipartite steering with a variable number of modes per party, and verify recently introduced monogamy relations for Gaussian steerability, which establish quantitative constraints on the security of information shared among different parties. We observe a very rich structure for the steering distribution, and demonstrate one-way EPR steering of the cluster state under Gaussian measurements, as well as one-to-multimode steering. Our experiment paves the way for exploiting EPR steering in Gaussian cluster states as a valuable resource for multiparty quantum information tasks.
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The Self-Organization of a Spoken Word
Holden, John G.; Rajaraman, Srinivasan
2012-01-01
Pronunciation time probability density and hazard functions from large speeded word naming data sets were assessed for empirical patterns consistent with multiplicative and reciprocal feedback dynamics – interaction dominant dynamics. Lognormal and inverse power law distributions are associated with multiplicative and interdependent dynamics in many natural systems. Mixtures of lognormal and inverse power law distributions offered better descriptions of the participant’s distributions than the ex-Gaussian or ex-Wald – alternatives corresponding to additive, superposed, component processes. The evidence for interaction dominant dynamics suggests fundamental links between the observed coordinative synergies that support speech production and the shapes of pronunciation time distributions. PMID:22783213
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Xiao, A.; Borland, M.
Both intra-beamscattering (IBS) and the Touschek effect become prominent formulti-bend-achromat- (MBA-) based ultra-low-emittance storage rings. To mitigate the transverse emittance degradation and obtain a reasonably long beam lifetime, a higher harmonic rf cavity (HHC) is often proposed to lengthen the bunch. The use of such a cavity results in a non-gaussian longitudinal distribution. However, common methods for computing IBS and Touschek scattering assume Gaussian distributions. Modifications have been made to several simulation codes that are part of the elegant [1] toolkit to allow these computations for arbitrary longitudinal distributions. After describing thesemodifications, we review the results of detailed simulations formore » the proposed hybrid seven-bend-achromat (H7BA) upgrade lattice [2] for the Advanced Photon Source.« less
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Distilling Gaussian states with Gaussian operations is impossible.
Eisert, J; Scheel, S; Plenio, M B
2002-09-23
We show that no distillation protocol for Gaussian quantum states exists that relies on (i) arbitrary local unitary operations that preserve the Gaussian character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local Gaussian unitary operations on two symmetric identically prepared copies. This is in contrast to the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time. The ramifications for the distribution of Gaussian states over large distances will be outlined. We also comment on the generality of the approach and sketch the most general form of a Gaussian local operation with classical communication in a bipartite setting.
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Zhang, Xiaoping; Nieforth, Keith; Lang, Jean-Marie; Rouzier-Panis, Regine; Reynes, Jacques; Dorr, Albert; Kolis, Stanley; Stiles, Mark R; Kinchelow, Tosca; Patel, Indravadan H
2002-07-01
Enfuvirtide (T-20) is the first of a novel class of human immunodeficiency virus (HIV) drugs that block gp41-mediated viral fusion to host cells. The objectives of this study were to develop a structural pharmacokinetic model that would adequately characterize the absorption and disposition of enfuvirtide pharmacokinetics after both intravenous and subcutaneous administration and to evaluate the dose proportionality of enfuvirtide pharmacokinetic parameters at a subcutaneous dose higher than that currently used in phase III studies. Twelve patients with HIV infection received 4 single doses of enfuvirtide separated by a 1-week washout period in an open-label, randomized, 4-way crossover fashion. The doses studied were 90 mg (intravenous) and 45 mg, 90 mg, and 180 mg (subcutaneous). Serial blood samples were collected up to 48 hours after each dose. Plasma enfuvirtide concentrations were measured with use of a validated liquid chromatography-tandem mass spectrometry method. Enfuvirtide plasma concentration-time data after subcutaneous administration were well described by an inverse Gaussian density function-input model linked to a 2-compartment open distribution model with first-order elimination from the central compartment. The model-derived mean pharmacokinetic parameters (+/-SD) were volume of distribution of the central compartment (3.8 +/- 0.8 L), volume of distribution of the peripheral compartment (1.7 +/- 0.6 L), total clearance (1.44 +/- 0.30 L/h), intercompartmental distribution (2.3 +/- 1.1 L/h), bioavailability (89% +/- 11%), and mean absorption time (7.26 hours, 8.65 hours, and 9.79 hours for the 45-mg, 90-mg, and 180-mg dose groups, respectively). The terminal half-life increased from 3.46 to 4.35 hours for the subcutaneous dose range from 45 to 180 mg. An inverse Gaussian density function-input model linked to a 2-compartment open distribution model with first-order elimination from the central compartment was appropriate to describe complex absorption and disposition kinetics of enfuvirtide plasma concentration-time data after subcutaneous administration to patients with HIV infection. Enfuvirtide was nearly completely absorbed from subcutaneous depot, and pharmacokinetic parameters were linear up to a dose of 180 mg in this study.
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Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution.
García-Patrón, Raúl; Cerf, Nicolas J
2006-11-10
A fully general approach to the security analysis of continuous-variable quantum key distribution (CV-QKD) is presented. Provided that the quantum channel is estimated via the covariance matrix of the quadratures, Gaussian attacks are shown to be optimal against all collective eavesdropping strategies. The proof is made strikingly simple by combining a physical model of measurement, an entanglement-based description of CV-QKD, and a recent powerful result on the extremality of Gaussian states [M. M. Wolf, Phys. Rev. Lett. 96, 080502 (2006)10.1103/PhysRevLett.96.080502].
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Continuous-variable quantum-key-distribution protocols with a non-Gaussian modulation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Leverrier, Anthony; Grangier, Philippe; Laboratoire Charles Fabry, Institut d'Optique, CNRS, Univ. Paris-Sud, Campus Polytechnique, RD 128, F-91127 Palaiseau Cedex
2011-04-15
In this paper, we consider continuous-variable quantum-key-distribution (QKD) protocols which use non-Gaussian modulations. These specific modulation schemes are compatible with very efficient error-correction procedures, hence allowing the protocols to outperform previous protocols in terms of achievable range. In their simplest implementation, these protocols are secure for any linear quantum channels (hence against Gaussian attacks). We also show how the use of decoy states makes the protocols secure against arbitrary collective attacks, which implies their unconditional security in the asymptotic limit.
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Gaussian-input Gaussian mixture model for representing density maps and atomic models.
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.
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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.
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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.
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Long-distance continuous-variable quantum key distribution with a Gaussian modulation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Jouguet, Paul; SeQureNet, 23 avenue d'Italie, F-75013 Paris; Kunz-Jacques, Sebastien
2011-12-15
We designed high-efficiency error correcting codes allowing us to extract an errorless secret key in a continuous-variable quantum key distribution (CVQKD) protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an additive white Gaussian noise channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a CVQKD with a Gaussian modulation, giving a secret key rate of about 10{sup -3} bit per pulse at amore » distance of 120 km for reasonable physical parameters.« less
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The location-, word-, and arrow-based Simon effects: An ex-Gaussian analysis.
Luo, Chunming; Proctor, Robert W
2018-04-01
Task-irrelevant spatial information, conveyed by stimulus location, location word, or arrow direction, can influence the response to task-relevant attributes, generating the location-, word-, and arrow-based Simon effects. We examined whether different mechanisms are involved in the generation of these Simon effects by fitting a mathematical ex-Gaussian function to empirical response time (RT) distributions. Specifically, we tested whether which ex-Gaussian parameters (μ, σ, and τ) show Simon effects and whether the location-, word, and arrow-based effects are on different parameters. Results show that the location-based Simon effect occurred on mean RT and μ but not on τ, and a reverse Simon effect occurred on σ. In contrast, a positive word-based Simon effect was obtained on all these measures (including σ), and a positive arrow-based Simon effect was evident on mean RT, σ, and τ but not μ. The arrow-based Simon effect was not different from the word-based Simon effect on τ or σ but was on μ and mean RT. These distinct results on mean RT and ex-Gaussian parameters provide evidence that spatial information conveyed by the various location modes are different in the time-course of activation.
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NASA Astrophysics Data System (ADS)
Wolfsteiner, Peter; Breuer, Werner
2013-10-01
The assessment of fatigue load under random vibrations is usually based on load spectra. Typically they are computed with counting methods (e.g. Rainflow) based on a time domain signal. Alternatively methods are available (e.g. Dirlik) enabling the estimation of load spectra directly from power spectral densities (PSDs) of the corresponding time signals; the knowledge of the time signal is then not necessary. These PSD based methods have the enormous advantage that if for example the signal to assess results from a finite element method based vibration analysis, the computation time of the simulation of PSDs in the frequency domain outmatches by far the simulation of time signals in the time domain. This is especially true for random vibrations with very long signals in the time domain. The disadvantage of the PSD based simulation of vibrations and also the PSD based load spectra estimation is their limitation to Gaussian distributed time signals. Deviations from this Gaussian distribution cause relevant deviations in the estimated load spectra. In these cases usually only computation time intensive time domain calculations produce accurate results. This paper presents a method dealing with non-Gaussian signals with real statistical properties that is still able to use the efficient PSD approach with its computation time advantages. Essentially it is based on a decomposition of the non-Gaussian signal in Gaussian distributed parts. The PSDs of these rearranged signals are then used to perform usual PSD analyses. In particular, detailed methods are described for the decomposition of time signals and the derivation of PSDs and cross power spectral densities (CPSDs) from multiple real measurements without using inaccurate standard procedures. Furthermore the basic intention is to design a general and integrated method that is not just able to analyse a certain single load case for a small time interval, but to generate representative PSD and CPSD spectra replacing extensive measured loads in time domain without losing the necessary accuracy for the fatigue load results. These long measurements may even represent the whole application range of the railway vehicle. The presented work demonstrates the application of this method to railway vehicle components subjected to random vibrations caused by the wheel rail contact. Extensive measurements of axle box accelerations have been used to verify the proposed procedure for this class of railway vehicle applications. The linearity is not a real limitation, because the structural vibrations caused by the random excitations are usually small for rail vehicle applications. The impact of nonlinearities is usually covered by separate nonlinear models and only needed for the deterministic part of the loads. Linear vibration systems subjected to Gaussian vibrations respond with vibrations having also a Gaussian distribution. A non-Gaussian distribution in the excitation signal produces also a non-Gaussian response with statistical properties different from these excitations. A drawback is the fact that there is no simple mathematical relation between excitation and response concerning these deviations from the Gaussian distribution (see e.g. Ito calculus [6], which is usually not part of commercial codes!). There are a couple of well-established procedures for the prediction of fatigue load spectra from PSDs designed for Gaussian loads (see [4]); the question of the impact of non-Gaussian distributions on the fatigue load prediction has been studied for decades (see e.g. [3,4,11-13]) and is still subject of the ongoing research; e.g. [13] proposed a procedure, capable of considering non-Gaussian broadbanded loads. It is based on the knowledge of the response PSD and some statistical data, defining the non-Gaussian character of the underlying time signal. As already described above, these statistical data are usually not available for a PSD vibration response that has been calculated in the frequency domain. Summarizing the above and considering the fact of having highly non-Gaussian excitations on railway vehicles caused by the wheel rail contact means that the fast PSD analysis in the frequency domain cannot be combined with load spectra prediction methods for PSDs.
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A fast elitism Gaussian estimation of distribution algorithm and application for PID optimization.
Xu, Qingyang; Zhang, Chengjin; Zhang, Li
2014-01-01
Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA.
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A Fast Elitism Gaussian Estimation of Distribution Algorithm and Application for PID Optimization
Xu, Qingyang; Zhang, Chengjin; Zhang, Li
2014-01-01
Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA. PMID:24892059
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Chen, Tianju; Zhang, Jinzhi; Wu, Jinhu
2016-07-01
The kinetic and energy productions of pyrolysis of a lignocellulosic biomass were investigated using a three-parallel Gaussian distribution method in this work. The pyrolysis experiment of the pine sawdust was performed using a thermogravimetric-mass spectroscopy (TG-MS) analyzer. A three-parallel Gaussian distributed activation energy model (DAEM)-reaction model was used to describe thermal decomposition behaviors of the three components, hemicellulose, cellulose and lignin. The first, second and third pseudocomponents represent the fractions of hemicellulose, cellulose and lignin, respectively. It was found that the model is capable of predicting the pyrolysis behavior of the pine sawdust. The activation energy distribution peaks for the three pseudo-components were centered at 186.8, 197.5 and 203.9kJmol(-1) for the pine sawdust, respectively. The evolution profiles of H2, CH4, CO, and CO2 were well predicted using the three-parallel Gaussian distribution model. In addition, the chemical composition of bio-oil was also obtained by pyrolysis-gas chromatography/mass spectrometry instrument (Py-GC/MS). Copyright © 2016 Elsevier Ltd. All rights reserved.
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León, Larry F; Cai, Tianxi
2012-04-01
In this paper we develop model checking techniques for assessing functional form specifications of covariates in censored linear regression models. These procedures are based on a censored data analog to taking cumulative sums of "robust" residuals over the space of the covariate under investigation. These cumulative sums are formed by integrating certain Kaplan-Meier estimators and may be viewed as "robust" censored data analogs to the processes considered by Lin, Wei & Ying (2002). The null distributions of these stochastic processes can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be generated by computer simulation. Each observed process can then be graphically compared with a few realizations from the Gaussian process. We also develop formal test statistics for numerical comparison. Such comparisons enable one to assess objectively whether an apparent trend seen in a residual plot reects model misspecification or natural variation. We illustrate the methods with a well known dataset. In addition, we examine the finite sample performance of the proposed test statistics in simulation experiments. In our simulation experiments, the proposed test statistics have good power of detecting misspecification while at the same time controlling the size of the test.
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Model-checking techniques based on cumulative residuals.
Lin, D Y; Wei, L J; Ying, Z
2002-03-01
Residuals have long been used for graphical and numerical examinations of the adequacy of regression models. Conventional residual analysis based on the plots of raw residuals or their smoothed curves is highly subjective, whereas most numerical goodness-of-fit tests provide little information about the nature of model misspecification. In this paper, we develop objective and informative model-checking techniques by taking the cumulative sums of residuals over certain coordinates (e.g., covariates or fitted values) or by considering some related aggregates of residuals, such as moving sums and moving averages. For a variety of statistical models and data structures, including generalized linear models with independent or dependent observations, the distributions of these stochastic processes tinder the assumed model can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be easily generated by computer simulation. Each observed process can then be compared, both graphically and numerically, with a number of realizations from the Gaussian process. Such comparisons enable one to assess objectively whether a trend seen in a residual plot reflects model misspecification or natural variation. The proposed techniques are particularly useful in checking the functional form of a covariate and the link function. Illustrations with several medical studies are provided.
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Chakrabarty, Ayan; Wang, Feng; Sun, Kai; Wei, Qi-Huo
2016-05-11
Prior studies have shown that low symmetry particles such as micro-boomerangs exhibit behaviour of Brownian motion rather different from that of high symmetry particles because convenient tracking points (TPs) are usually inconsistent with their center of hydrodynamic stress (CoH) where the translational and rotational motions are decoupled. In this paper we study the effects of the translation-rotation coupling on the displacement probability distribution functions (PDFs) of the boomerang colloid particles with symmetric arm length. By tracking the motions of different points on the particle symmetry axis, we show that as the distance between the TP and the CoH is increased, the effects of translation-rotation coupling becomes pronounced, making the short-time 2D PDF for fixed initial orientation to change from elliptical, to bean and then to crescent shape, and the angle averaged PDFs change from ellipsoidal-particle-like PDF to a shape with a Gaussian top and long displacement tails. We also observed that at long times the PDFs revert to Gaussian. These 2D PDF shapes provide a clear physical picture of the non-zero mean displacements observed in boomerangs particles.
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Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures
DOE Office of Scientific and Technical Information (OSTI.GOV)
Procacci, Piero
2015-04-21
In this paper, we present an improved method for obtaining unbiased estimates of the free energy difference between two thermodynamic states using the work distribution measured in nonequilibrium driven experiments connecting these states. The method is based on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, whose normal components are identical in either direction of the nonequilibrium process, with weights regulated by the Crooks theorem. Using the prototypical example for the driven unfolding/folding of deca-alanine, we show that the predicted behavior of the forward and reverse work distributions, assuming a combination of onlymore » two Gaussian components with Crooks derived weights, explains surprisingly well the striking asymmetry in the observed distributions at fast pulling speeds. The proposed methodology opens the way for a perfectly parallel implementation of Jarzynski-based free energy calculations in complex systems.« less
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Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon.
McConnell, Robert; Zhang, Hao; Hu, Jiazhong; Ćuk, Senka; Vuletić, Vladan
2015-03-26
Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized, but these states display Gaussian spin distribution functions with a non-negative Wigner quasiprobability distribution function. Non-Gaussian entangled states have been produced in small ensembles of ions, and very recently in large atomic ensembles. Here we generate entanglement in a large atomic ensemble via an interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function--an important hallmark of non-classicality--and verify an entanglement depth (the minimum number of mutually entangled atoms) of 2,910 ± 190 out of 3,100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. Although the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing. More generally, our results demonstrate the power of heralded methods for entanglement generation, and illustrate how the information contained in a single photon can drastically alter the quantum state of a large system.
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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.
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Propagation of Ince-Gaussian beams in a thermal lens medium
NASA Astrophysics Data System (ADS)
Xu, Ting; Wang, Shaomin
2006-09-01
The propagation of Ince-Gaussian beams in a thermal lens medium is studied in this paper. Based on the ABCD matrix for Gaussian beams passing through a thermal lens medium, distinct expressions for the beam transverse intensity distributions and the longitudinal phase shift are deduced and discussed. Similar to Laguerre and Hermite-Gaussian beams, Ince-Gaussian beams, which constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation, can also be used in other inhomogeneous media such as lenslike media and saturated absorption media.
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Bingi, Jayachandra; Murukeshan, Vadakke Matham
2015-01-01
Laser speckle pattern is a granular structure formed due to random coherent wavelet interference and generally considered as noise in optical systems including photolithography. Contrary to this, in this paper, we use the speckle pattern to generate predictable and controlled Gaussian random structures and quasi-random structures photo-lithographically. The random structures made using this proposed speckle lithography technique are quantified based on speckle statistics, radial distribution function (RDF) and fast Fourier transform (FFT). The control over the speckle size, density and speckle clustering facilitates the successful fabrication of black silicon with different surface structures. The controllability and tunability of randomness makes this technique a robust method for fabricating predictable 2D Gaussian random structures and black silicon structures. These structures can enhance the light trapping significantly in solar cells and hence enable improved energy harvesting. Further, this technique can enable efficient fabrication of disordered photonic structures and random media based devices. PMID:26679513
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Langevin dynamics for ramified structures
NASA Astrophysics Data System (ADS)
Méndez, Vicenç; Iomin, Alexander; Horsthemke, Werner; Campos, Daniel
2017-06-01
We propose a generalized Langevin formalism to describe transport in combs and similar ramified structures. Our approach consists of a Langevin equation without drift for the motion along the backbone. The motion along the secondary branches may be described either by a Langevin equation or by other types of random processes. The mean square displacement (MSD) along the backbone characterizes the transport through the ramified structure. We derive a general analytical expression for this observable in terms of the probability distribution function of the motion along the secondary branches. We apply our result to various types of motion along the secondary branches of finite or infinite length, such as subdiffusion, superdiffusion, and Langevin dynamics with colored Gaussian noise and with non-Gaussian white noise. Monte Carlo simulations show excellent agreement with the analytical results. The MSD for the case of Gaussian noise is shown to be independent of the noise color. We conclude by generalizing our analytical expression for the MSD to the case where each secondary branch is n dimensional.
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Color image enhancement based on particle swarm optimization with Gaussian mixture
NASA Astrophysics Data System (ADS)
Kattakkalil Subhashdas, Shibudas; Choi, Bong-Seok; Yoo, Ji-Hoon; Ha, Yeong-Ho
2015-01-01
This paper proposes a Gaussian mixture based image enhancement method which uses particle swarm optimization (PSO) to have an edge over other contemporary methods. The proposed method uses the guassian mixture model to model the lightness histogram of the input image in CIEL*a*b* space. The intersection points of the guassian components in the model are used to partition the lightness histogram. . The enhanced lightness image is generated by transforming the lightness value in each interval to appropriate output interval according to the transformation function that depends on PSO optimized parameters, weight and standard deviation of Gaussian component and cumulative distribution of the input histogram interval. In addition, chroma compensation is applied to the resulting image to reduce washout appearance. Experimental results show that the proposed method produces a better enhanced image compared to the traditional methods. Moreover, the enhanced image is free from several side effects such as washout appearance, information loss and gradation artifacts.
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Comment on "Universal relation between skewness and kurtosis in complex dynamics"
NASA Astrophysics Data System (ADS)
Celikoglu, Ahmet; Tirnakli, Ugur
2015-12-01
In a recent paper [M. Cristelli, A. Zaccaria, and L. Pietronero, Phys. Rev. E 85, 066108 (2012), 10.1103/PhysRevE.85.066108], the authors analyzed the relation between skewness and kurtosis for complex dynamical systems, and they identified two power-law regimes of non-Gaussianity, one of which scales with an exponent of 2 and the other with 4 /3 . They concluded that the observed relation is a universal fact in complex dynamical systems. In this Comment, we test the proposed universal relation between skewness and kurtosis with a large number of synthetic data, and we show that in fact it is not a universal relation and originates only due to the small number of data points in the datasets considered. The proposed relation is tested using a family of non-Gaussian distribution known as q -Gaussians. We show that this relation disappears for sufficiently large datasets provided that the fourth moment of the distribution is finite. We find that kurtosis saturates to a single value, which is of course different from the Gaussian case (K =3 ), as the number of data is increased, and this indicates that the kurtosis will converge to a finite single value if all moments of the distribution up to fourth are finite. The converged kurtosis value for the finite fourth-moment distributions and the number of data points needed to reach this value depend on the deviation of the original distribution from the Gaussian case.
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NASA Astrophysics Data System (ADS)
Červený, Vlastislav; Pšenčík, Ivan
2017-08-01
Integral superposition of Gaussian beams is a useful generalization of the standard ray theory. It removes some of the deficiencies of the ray theory like its failure to describe properly behaviour of waves in caustic regions. It also leads to a more efficient computation of seismic wavefields since it does not require the time-consuming two-point ray tracing. We present the formula for a high-frequency elementary Green function expressed in terms of the integral superposition of Gaussian beams for inhomogeneous, isotropic or anisotropic, layered structures, based on the dynamic ray tracing (DRT) in Cartesian coordinates. For the evaluation of the superposition formula, it is sufficient to solve the DRT in Cartesian coordinates just for the point-source initial conditions. Moreover, instead of seeking 3 × 3 paraxial matrices in Cartesian coordinates, it is sufficient to seek just 3 × 2 parts of these matrices. The presented formulae can be used for the computation of the elementary Green function corresponding to an arbitrary direct, multiply reflected/transmitted, unconverted or converted, independently propagating elementary wave of any of the three modes, P, S1 and S2. Receivers distributed along or in a vicinity of a target surface may be situated at an arbitrary part of the medium, including ray-theory shadow regions. The elementary Green function formula can be used as a basis for the computation of wavefields generated by various types of point sources (explosive, moment tensor).
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Monogamy inequality for distributed gaussian entanglement.
Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio
2007-02-02
We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.
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Robust Gaussian Graphical Modeling via l1 Penalization
Sun, Hokeun; Li, Hongzhe
2012-01-01
Summary Gaussian graphical models have been widely used as an effective method for studying the conditional independency structure among genes and for constructing genetic networks. However, gene expression data typically have heavier tails or more outlying observations than the standard Gaussian distribution. Such outliers in gene expression data can lead to wrong inference on the dependency structure among the genes. We propose a l1 penalized estimation procedure for the sparse Gaussian graphical models that is robustified against possible outliers. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its own likelihood. An efficient computational algorithm based on the coordinate gradient descent method is developed to obtain the minimizer of the negative penalized robustified-likelihood, where nonzero elements of the concentration matrix represents the graphical links among the genes. After the graphical structure is obtained, we re-estimate the positive definite concentration matrix using an iterative proportional fitting algorithm. Through simulations, we demonstrate that the proposed robust method performs much better than the graphical Lasso for the Gaussian graphical models in terms of both graph structure selection and estimation when outliers are present. We apply the robust estimation procedure to an analysis of yeast gene expression data and show that the resulting graph has better biological interpretation than that obtained from the graphical Lasso. PMID:23020775
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Muthu Rama Krishnan, M; Shah, Pratik; Chakraborty, Chandan; Ray, Ajoy K
2012-04-01
The objective of this paper is to provide an improved technique, which can assist oncopathologists in correct screening of oral precancerous conditions specially oral submucous fibrosis (OSF) with significant accuracy on the basis of collagen fibres in the sub-epithelial connective tissue. The proposed scheme is composed of collagen fibres segmentation, its textural feature extraction and selection, screening perfomance enhancement under Gaussian transformation and finally classification. In this study, collagen fibres are segmented on R,G,B color channels using back-probagation neural network from 60 normal and 59 OSF histological images followed by histogram specification for reducing the stain intensity variation. Henceforth, textural features of collgen area are extracted using fractal approaches viz., differential box counting and brownian motion curve . Feature selection is done using Kullback-Leibler (KL) divergence criterion and the screening performance is evaluated based on various statistical tests to conform Gaussian nature. Here, the screening performance is enhanced under Gaussian transformation of the non-Gaussian features using hybrid distribution. Moreover, the routine screening is designed based on two statistical classifiers viz., Bayesian classification and support vector machines (SVM) to classify normal and OSF. It is observed that SVM with linear kernel function provides better classification accuracy (91.64%) as compared to Bayesian classifier. The addition of fractal features of collagen under Gaussian transformation improves Bayesian classifier's performance from 80.69% to 90.75%. Results are here studied and discussed.
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Optimality of Gaussian attacks in continuous-variable quantum cryptography.
Navascués, Miguel; Grosshans, Frédéric; Acín, Antonio
2006-11-10
We analyze the asymptotic security of the family of Gaussian modulated quantum key distribution protocols for continuous-variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.
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Capacity and optimal collusion attack channels for Gaussian fingerprinting games
NASA Astrophysics Data System (ADS)
Wang, Ying; Moulin, Pierre
2007-02-01
In content fingerprinting, the same media covertext - image, video, audio, or text - is distributed to many users. A fingerprint, a mark unique to each user, is embedded into each copy of the distributed covertext. In a collusion attack, two or more users may combine their copies in an attempt to "remove" their fingerprints and forge a pirated copy. To trace the forgery back to members of the coalition, we need fingerprinting codes that can reliably identify the fingerprints of those members. Researchers have been focusing on designing or testing fingerprints for Gaussian host signals and the mean square error (MSE) distortion under some classes of collusion attacks, in terms of the detector's error probability in detecting collusion members. For example, under the assumptions of Gaussian fingerprints and Gaussian attacks (the fingerprinted signals are averaged and then the result is passed through a Gaussian test channel), Moulin and Briassouli1 derived optimal strategies in a game-theoretic framework that uses the detector's error probability as the performance measure for a binary decision problem (whether a user participates in the collusion attack or not); Stone2 and Zhao et al. 3 studied average and other non-linear collusion attacks for Gaussian-like fingerprints; Wang et al. 4 stated that the average collusion attack is the most efficient one for orthogonal fingerprints; Kiyavash and Moulin 5 derived a mathematical proof of the optimality of the average collusion attack under some assumptions. In this paper, we also consider Gaussian cover signals, the MSE distortion, and memoryless collusion attacks. We do not make any assumption about the fingerprinting codes used other than an embedding distortion constraint. Also, our only assumptions about the attack channel are an expected distortion constraint, a memoryless constraint, and a fairness constraint. That is, the colluders are allowed to use any arbitrary nonlinear strategy subject to the above constraints. Under those constraints on the fingerprint embedder and the colluders, fingerprinting capacity is obtained as the solution of a mutual-information game involving probability density functions (pdf's) designed by the embedder and the colluders. We show that the optimal fingerprinting strategy is a Gaussian test channel where the fingerprinted signal is the sum of an attenuated version of the cover signal plus a Gaussian information-bearing noise, and the optimal collusion strategy is to average fingerprinted signals possessed by all the colluders and pass the averaged copy through a Gaussian test channel. The capacity result and the optimal strategies are the same for both the private and public games. In the former scenario, the original covertext is available to the decoder, while in the latter setup, the original covertext is available to the encoder but not to the decoder.
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Voice-onset time and buzz-onset time identification: A ROC analysis
NASA Astrophysics Data System (ADS)
Lopez-Bascuas, Luis E.; Rosner, Burton S.; Garcia-Albea, Jose E.
2004-05-01
Previous studies have employed signal detection theory to analyze data from speech and nonspeech experiments. Typically, signal distributions were assumed to be Gaussian. Schouten and van Hessen [J. Acoust. Soc. Am. 104, 2980-2990 (1998)] explicitly tested this assumption for an intensity continuum and a speech continuum. They measured response distributions directly and, assuming an interval scale, concluded that the Gaussian assumption held for both continua. However, Pastore and Macmillan [J. Acoust. Soc. Am. 111, 2432 (2002)] applied ROC analysis to Schouten and van Hessen's data, assuming only an ordinal scale. Their ROC curves suppported the Gaussian assumption for the nonspeech signals only. Previously, Lopez-Bascuas [Proc. Audit. Bas. Speech Percept., 158-161 (1997)] found evidence with a rating scale procedure that the Gaussian model was inadequate for a voice-onset time continuum but not for a noise-buzz continuum. Both continua contained ten stimuli with asynchronies ranging from -35 ms to +55 ms. ROC curves (double-probability plots) are now reported for each pair of adjacent stimuli on the two continua. Both speech and nonspeech ROCs often appeared nonlinear, indicating non-Gaussian signal distributions under the usual zero-variance assumption for response criteria.
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NASA Technical Reports Server (NTRS)
Freilich, M. H.; Pawka, S. S.
1987-01-01
The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman (1957), the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxy(tot). In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum-likelihood estimator for a posterior estimation is outlined.
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White Gaussian Noise - Models for Engineers
NASA Astrophysics Data System (ADS)
Jondral, Friedrich K.
2018-04-01
This paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.
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Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas
NASA Astrophysics Data System (ADS)
Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.
2010-03-01
We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.
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Time-frequency distributions for propulsion-system diagnostics
NASA Astrophysics Data System (ADS)
Griffin, Michael E.; Tulpule, Sharayu
1991-12-01
The Wigner distribution and its smoothed versions, i.e., Choi-Williams and Gaussian kernels, are evaluated for propulsion system diagnostics. The approach is intended for off-line kernel design by using the ambiguity domain to select the appropriate Gaussian kernel. The features produced by the Wigner distribution and its smoothed versions correlate remarkably well with documented failure indications. The selection of the kernel on the other hand is very subjective for our unstructured data.
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Steve P. Verrill; James W. Evans; David E. Kretschmann; Cherilyn A. Hatfield
2014-01-01
Two important wood properties are the modulus of elasticity (MOE) and the modulus of rupture (MOR). In the past, the statistical distribution of the MOE has often been modeled as Gaussian, and that of the MOR as lognormal or as a two- or three-parameter Weibull distribution. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior...
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Lin, Guoxing
2016-11-21
Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) techniques have been increasingly used to study anomalous diffusion in nuclear magnetic resonance and magnetic resonance imaging. However, the interpretation of PFG anomalous diffusion is complicated. Moreover, the exact signal attenuation expression including the finite gradient pulse width effect has not been obtained based on fractional derivatives for PFG anomalous diffusion. In this paper, a new method, a Mainardi-Luchko-Pagnini (MLP) phase distribution approximation, is proposed to describe PFG fractional diffusion. MLP phase distribution is a non-Gaussian phase distribution. From the fractional derivative model, both the probability density function (PDF) of a spin in real space and the PDF of the spin's accumulating phase shift in virtual phase space are MLP distributions. The MLP phase distribution leads to a Mittag-Leffler function based PFG signal attenuation, which differs significantly from the exponential attenuation for normal diffusion and from the stretched exponential attenuation for fractional diffusion based on the fractal derivative model. A complete signal attenuation expression E α (-D f b α,β * ) including the finite gradient pulse width effect was obtained and it can handle all three types of PFG fractional diffusions. The result was also extended in a straightforward way to give a signal attenuation expression of fractional diffusion in PFG intramolecular multiple quantum coherence experiments, which has an n β dependence upon the order of coherence which is different from the familiar n 2 dependence in normal diffusion. The results obtained in this study are in agreement with the results from the literature. The results in this paper provide a set of new, convenient approximation formalisms to interpret complex PFG fractional diffusion experiments.
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A computer program for uncertainty analysis integrating regression and Bayesian methods
Lu, Dan; Ye, Ming; Hill, Mary C.; Poeter, Eileen P.; Curtis, Gary
2014-01-01
This work develops a new functionality in UCODE_2014 to evaluate Bayesian credible intervals using the Markov Chain Monte Carlo (MCMC) method. The MCMC capability in UCODE_2014 is based on the FORTRAN version of the differential evolution adaptive Metropolis (DREAM) algorithm of Vrugt et al. (2009), which estimates the posterior probability density function of model parameters in high-dimensional and multimodal sampling problems. The UCODE MCMC capability provides eleven prior probability distributions and three ways to initialize the sampling process. It evaluates parametric and predictive uncertainties and it has parallel computing capability based on multiple chains to accelerate the sampling process. This paper tests and demonstrates the MCMC capability using a 10-dimensional multimodal mathematical function, a 100-dimensional Gaussian function, and a groundwater reactive transport model. The use of the MCMC capability is made straightforward and flexible by adopting the JUPITER API protocol. With the new MCMC capability, UCODE_2014 can be used to calculate three types of uncertainty intervals, which all can account for prior information: (1) linear confidence intervals which require linearity and Gaussian error assumptions and typically 10s–100s of highly parallelizable model runs after optimization, (2) nonlinear confidence intervals which require a smooth objective function surface and Gaussian observation error assumptions and typically 100s–1,000s of partially parallelizable model runs after optimization, and (3) MCMC Bayesian credible intervals which require few assumptions and commonly 10,000s–100,000s or more partially parallelizable model runs. Ready access allows users to select methods best suited to their work, and to compare methods in many circumstances.
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NASA Astrophysics Data System (ADS)
Nie, Yongming; Li, Xiujian; Qi, Junli; Ma, Haotong; Liao, Jiali; Yang, Jiankun; Hu, Wenhua
2012-03-01
Based on the refractive beam shaping system, the transformation of a quasi-Gaussian beam into a dark hollow Gaussian beam by a phase-only liquid crystal spatial light modulator (LC-SLM) is proposed. According to the energy conservation and constant optical path principle, the phase distribution of the aspheric lens and the phase-only LC-SLM can modulate the wave-front properly to generate the hollow beam. The numerical simulation results indicate that, the dark hollow intensity distribution of the output shaped beam can be maintained well for a certain propagation distance during which the dark region will not decrease whereas the ideal hollow Gaussian beam will do. By designing the phase modulation profile, which loaded into the LC-SLM carefully, the experimental results indicate that the dark hollow intensity distribution of the output shaped beam can be maintained well even at a distance much more than 550 mm from the LC-SLM, which agree with the numerical simulation results.
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NASA Astrophysics Data System (ADS)
Malyutin, A. A.
2007-03-01
Modes of a laser with plano-spherical degenerate and nondegenerate resonators are calculated upon diode pumping producing the Gaussian gain distribution in the active medium. Axially symmetric and off-axis pumpings are considered. It is shown that in the first case the lowest Hermite-Gaussian mode is excited with the largest weight both in the degenerate and nondegenerate resonator if the pump level is sufficiently high or the characteristic size wg of the amplifying region greatly exceeds the mode radius w0. The high-order Ince-Gaussian modes are excited upon weak off-axis pumping in the nondegenerate resonator both in the absence and presence of the symmetry of the gain distribution with respect to the resonator axis. It is found that when the level of off-axis symmetric pumping of the resonator is high enough, modes with the parameters of the TEM00 mode periodically propagating over a closed path in the resonator can exist. The explanation of this effect is given.
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Gaussian curvature directs the distribution of spontaneous curvature on bilayer membrane necks.
Chabanon, Morgan; Rangamani, Padmini
2018-03-28
Formation of membrane necks is crucial for fission and fusion in lipid bilayers. In this work, we seek to answer the following fundamental question: what is the relationship between protein-induced spontaneous mean curvature and the Gaussian curvature at a membrane neck? Using an augmented Helfrich model for lipid bilayers to include membrane-protein interaction, we solve the shape equation on catenoids to find the field of spontaneous curvature that satisfies mechanical equilibrium of membrane necks. In this case, the shape equation reduces to a variable coefficient Helmholtz equation for spontaneous curvature, where the source term is proportional to the Gaussian curvature. We show how this latter quantity is responsible for non-uniform distribution of spontaneous curvature in minimal surfaces. We then explore the energetics of catenoids with different spontaneous curvature boundary conditions and geometric asymmetries to show how heterogeneities in spontaneous curvature distribution can couple with Gaussian curvature to result in membrane necks of different geometries.
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Four Theorems on the Psychometric Function
May, Keith A.; Solomon, Joshua A.
2013-01-01
In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, . This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull “slope” parameter, , can be approximated by , where is the of the Weibull function that fits best to the cumulative noise distribution, and depends on the transducer. We derive general expressions for and , from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when , . We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4–0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of for contrast discrimination suggests that, if internal noise is stimulus-independent, it has lower kurtosis than a Gaussian. PMID:24124456
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Characterization of Adrenal Adenoma by Gaussian Model-Based Algorithm.
Hsu, Larson D; Wang, Carolyn L; Clark, Toshimasa J
2016-01-01
We confirmed that computed tomography (CT) attenuation values of pixels in an adrenal nodule approximate a Gaussian distribution. Building on this and the previously described histogram analysis method, we created an algorithm that uses mean and standard deviation to estimate the percentage of negative attenuation pixels in an adrenal nodule, thereby allowing differentiation of adenomas and nonadenomas. The institutional review board approved both components of this study in which we developed and then validated our criteria. In the first, we retrospectively assessed CT attenuation values of adrenal nodules for normality using a 2-sample Kolmogorov-Smirnov test. In the second, we evaluated a separate cohort of patients with adrenal nodules using both the conventional 10HU unit mean attenuation method and our Gaussian model-based algorithm. We compared the sensitivities of the 2 methods using McNemar's test. A total of 183 of 185 observations (98.9%) demonstrated a Gaussian distribution in adrenal nodule pixel attenuation values. The sensitivity and specificity of our Gaussian model-based algorithm for identifying adrenal adenoma were 86.1% and 83.3%, respectively. The sensitivity and specificity of the mean attenuation method were 53.2% and 94.4%, respectively. The sensitivities of the 2 methods were significantly different (P value < 0.001). In conclusion, the CT attenuation values within an adrenal nodule follow a Gaussian distribution. Our Gaussian model-based algorithm can characterize adrenal adenomas with higher sensitivity than the conventional mean attenuation method. The use of our algorithm, which does not require additional postprocessing, may increase workflow efficiency and reduce unnecessary workup of benign nodules. Copyright © 2016 Elsevier Inc. All rights reserved.
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Apodization of two-dimensional pupils with aberrations
NASA Astrophysics Data System (ADS)
Reddy, Andra Naresh Kumar; Hashemi, Mahdieh; Khonina, Svetlana Nikolaevna
2018-06-01
The technique proposed to enhance the resolution of the point spread function (PSF) of an optical system underneath defocussing and spherical aberrations. The method of approach is based on the amplitude and phase masking in a ring aperture for modifying the light intensity distribution in the Gaussian focal plane (YD = 0) and in the defocussed planes (YD= π and YD= 2π ). The width of the annulus modifies the distribution of the light intensity in the side lobes of the resultant PSF. In the presence of an asymmetry in the phase of the annulus, the Hanning amplitude apodizer [cos(π β ρ )] employed in the pupil function can modify the spatial distribution of light in the maximum defocussed plane ({Y}D = 2π ), results in PSF with improved resolution.
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EM in high-dimensional spaces.
Draper, Bruce A; Elliott, Daniel L; Hayes, Jeremy; Baek, Kyungim
2005-06-01
This paper considers fitting a mixture of Gaussians model to high-dimensional data in scenarios where there are fewer data samples than feature dimensions. Issues that arise when using principal component analysis (PCA) to represent Gaussian distributions inside Expectation-Maximization (EM) are addressed, and a practical algorithm results. Unlike other algorithms that have been proposed, this algorithm does not try to compress the data to fit low-dimensional models. Instead, it models Gaussian distributions in the (N - 1)-dimensional space spanned by the N data samples. We are able to show that this algorithm converges on data sets where low-dimensional techniques do not.
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Non-gaussian statistics of pencil beam surveys
NASA Technical Reports Server (NTRS)
Amendola, Luca
1994-01-01
We study the effect of the non-Gaussian clustering of galaxies on the statistics of pencil beam surveys. We derive the probability from the power spectrum peaks by means of Edgeworth expansion and find that the higher order moments of the galaxy distribution play a dominant role. The probability of obtaining the 128 Mpc/h periodicity found in pencil beam surveys is raised by more than one order of magnitude, up to 1%. Further data are needed to decide if non-Gaussian distribution alone is sufficient to explain the 128 Mpc/h periodicity, or if extra large-scale power is necessary.
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Irradiance tailoring by fractional Fourier transform of a radial Gaussian beam array
NASA Astrophysics Data System (ADS)
Zhou, Pu; Wang, Xiaolin; Ma, Yanxing; Ma, Haotong; Liu, Zejin
2011-03-01
The fractional Fourier transform (FRFT) is applied to a radial Gaussian beam array. Analytical formula is derived for the irradiance distribution of coherent and incoherent radial Gaussian beam array in FRFT domain using Collins integral formula. It is revealed that the irradiance pattern can be tailored to be controllable dark-hollow, flat-topped and Gaussian beam pattern by changing of the fractional order of FRFT and the coherent state of the laser array.
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Irradiance tailoring by fractional Fourier transform of a radial Gaussian beam array
NASA Astrophysics Data System (ADS)
Zhou, Pu; Wang, Xiaolin; Ma, Yanxing; Ma, Haotong; Liu, Zejin
2010-07-01
The fractional Fourier transform (FRFT) is applied to a radial Gaussian beam array. Analytical formula is derived for the irradiance distribution of coherent and incoherent radial Gaussian beam array in FRFT domain using Collins integral formula. It is revealed that the irradiance pattern can be tailored to be controllable dark-hollow, flat-topped and Gaussian beam pattern by changing of the fractional order of FRFT and the coherent state of the laser array.
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Diffusion of active chiral particles
NASA Astrophysics Data System (ADS)
Sevilla, Francisco J.
2016-12-01
The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v ̂ at time t , and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.
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Zadpoor, Amir A
2015-03-01
Mechanical characterization of biological tissues and biomaterials at the nano-scale is often performed using nanoindentation experiments. The different constituents of the characterized materials will then appear in the histogram that shows the probability of measuring a certain range of mechanical properties. An objective technique is needed to separate the probability distributions that are mixed together in such a histogram. In this paper, finite mixture models (FMMs) are proposed as a tool capable of performing such types of analysis. Finite Gaussian mixture models assume that the measured probability distribution is a weighted combination of a finite number of Gaussian distributions with separate mean and standard deviation values. Dedicated optimization algorithms are available for fitting such a weighted mixture model to experimental data. Moreover, certain objective criteria are available to determine the optimum number of Gaussian distributions. In this paper, FMMs are used for interpreting the probability distribution functions representing the distributions of the elastic moduli of osteoarthritic human cartilage and co-polymeric microspheres. As for cartilage experiments, FMMs indicate that at least three mixture components are needed for describing the measured histogram. While the mechanical properties of the softer mixture components, often assumed to be associated with Glycosaminoglycans, were found to be more or less constant regardless of whether two or three mixture components were used, those of the second mixture component (i.e. collagen network) considerably changed depending on the number of mixture components. Regarding the co-polymeric microspheres, the optimum number of mixture components estimated by the FMM theory, i.e. 3, nicely matches the number of co-polymeric components used in the structure of the polymer. The computer programs used for the presented analyses are made freely available online for other researchers to use. Copyright © 2014 Elsevier B.V. All rights reserved.
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Random medium model for cusping of plane waves.
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.
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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.
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Ferragut, Erik M.; Laska, Jason A.; Bridges, Robert A.
2016-06-07
A system is described for receiving a stream of events and scoring the events based on anomalousness and maliciousness (or other classification). The system can include a plurality of anomaly detectors that together implement an algorithm to identify low-probability events and detect atypical traffic patterns. The anomaly detector provides for comparability of disparate sources of data (e.g., network flow data and firewall logs.) Additionally, the anomaly detector allows for regulatability, meaning that the algorithm can be user configurable to adjust a number of false alerts. The anomaly detector can be used for a variety of probability density functions, including normal Gaussian distributions, irregular distributions, as well as functions associated with continuous or discrete variables.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Passos de Figueiredo, Leandro, E-mail: leandrop.fgr@gmail.com; Grana, Dario; Santos, Marcio
We propose a Bayesian approach for seismic inversion to estimate acoustic impedance, porosity and lithofacies within the reservoir conditioned to post-stack seismic and well data. The link between elastic and petrophysical properties is given by a joint prior distribution for the logarithm of impedance and porosity, based on a rock-physics model. The well conditioning is performed through a background model obtained by well log interpolation. Two different approaches are presented: in the first approach, the prior is defined by a single Gaussian distribution, whereas in the second approach it is defined by a Gaussian mixture to represent the well datamore » multimodal distribution and link the Gaussian components to different geological lithofacies. The forward model is based on a linearized convolutional model. For the single Gaussian case, we obtain an analytical expression for the posterior distribution, resulting in a fast algorithm to compute the solution of the inverse problem, i.e. the posterior distribution of acoustic impedance and porosity as well as the facies probability given the observed data. For the Gaussian mixture prior, it is not possible to obtain the distributions analytically, hence we propose a Gibbs algorithm to perform the posterior sampling and obtain several reservoir model realizations, allowing an uncertainty analysis of the estimated properties and lithofacies. Both methodologies are applied to a real seismic dataset with three wells to obtain 3D models of acoustic impedance, porosity and lithofacies. The methodologies are validated through a blind well test and compared to a standard Bayesian inversion approach. Using the probability of the reservoir lithofacies, we also compute a 3D isosurface probability model of the main oil reservoir in the studied field.« less
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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.
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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
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Mean intensity of the vortex Bessel-Gaussian beam in turbulent atmosphere
NASA Astrophysics Data System (ADS)
Lukin, Igor P.
2017-11-01
In this work the question of stability of the vortex Bessel-Gaussian optical beams formed in turbulent atmosphere is theoretically considered. The detailed analysis of features of spatial structure of distribution of mean intensity of vortex Bessel-Gaussian optical beams in turbulent atmosphere are analyzed. The quantitative criterion of possibility of formation of vortex Bessel-Gaussian optical beams in turbulent atmosphere is derived. It is shown that stability of the form of a vortex Bessel-Gaussian optical beam during propagation in turbulent atmosphere increases with increase of value of a topological charge of this optical beam.
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Gaussian model for emission rate measurement of heated plumes using hyperspectral data
NASA Astrophysics Data System (ADS)
Grauer, Samuel J.; Conrad, Bradley M.; Miguel, Rodrigo B.; Daun, Kyle J.
2018-02-01
This paper presents a novel model for measuring the emission rate of a heated gas plume using hyperspectral data from an FTIR imaging spectrometer. The radiative transfer equation (RTE) is used to relate the spectral intensity of a pixel to presumed Gaussian distributions of volume fraction and temperature within the plume, along a line-of-sight that corresponds to the pixel, whereas previous techniques exclusively presume uniform distributions for these parameters. Estimates of volume fraction and temperature are converted to a column density by integrating the local molecular density along each path. Image correlation velocimetry is then employed on raw spectral intensity images to estimate the volume-weighted normal velocity at each pixel. Finally, integrating the product of velocity and column density along a control surface yields an estimate of the instantaneous emission rate. For validation, emission rate estimates were derived from synthetic hyperspectral images of a heated methane plume, generated using data from a large-eddy simulation. Calculating the RTE with Gaussian distributions of volume fraction and temperature, instead of uniform distributions, improved the accuracy of column density measurement by 14%. Moreover, the mean methane emission rate measured using our approach was within 4% of the ground truth. These results support the use of Gaussian distributions of thermodynamic properties in calculation of the RTE for optical gas diagnostics.
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Chaudret, Robin; Gresh, Nohad; Narth, Christophe; Lagardère, Louis; Darden, Thomas A; Cisneros, G Andrés; Piquemal, Jean-Philip
2014-09-04
We demonstrate as a proof of principle the capabilities of a novel hybrid MM'/MM polarizable force field to integrate short-range quantum effects in molecular mechanics (MM) through the use of Gaussian electrostatics. This lead to a further gain in accuracy in the representation of the first coordination shell of metal ions. It uses advanced electrostatics and couples two point dipole polarizable force fields, namely, the Gaussian electrostatic model (GEM), a model based on density fitting, which uses fitted electronic densities to evaluate nonbonded interactions, and SIBFA (sum of interactions between fragments ab initio computed), which resorts to distributed multipoles. To understand the benefits of the use of Gaussian electrostatics, we evaluate first the accuracy of GEM, which is a pure density-based Gaussian electrostatics model on a test Ca(II)-H2O complex. GEM is shown to further improve the agreement of MM polarization with ab initio reference results. Indeed, GEM introduces nonclassical effects by modeling the short-range quantum behavior of electric fields and therefore enables a straightforward (and selective) inclusion of the sole overlap-dependent exchange-polarization repulsive contribution by means of a Gaussian damping function acting on the GEM fields. The S/G-1 scheme is then introduced. Upon limiting the use of Gaussian electrostatics to metal centers only, it is shown to be able to capture the dominant quantum effects at play on the metal coordination sphere. S/G-1 is able to accurately reproduce ab initio total interaction energies within closed-shell metal complexes regarding each individual contribution including the separate contributions of induction, polarization, and charge-transfer. Applications of the method are provided for various systems including the HIV-1 NCp7-Zn(II) metalloprotein. S/G-1 is then extended to heavy metal complexes. Tested on Hg(II) water complexes, S/G-1 is shown to accurately model polarization up to quadrupolar response level. This opens up the possibility of embodying explicit scalar relativistic effects in molecular mechanics thanks to the direct transferability of ab initio pseudopotentials. Therefore, incorporating GEM-like electron density for a metal cation enable the introduction of nonambiguous short-range quantum effects within any point-dipole based polarizable force field without the need of an extensive parametrization.
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q-Gaussian distributions of leverage returns, first stopping times, and default risk valuations
NASA Astrophysics Data System (ADS)
Katz, Yuri A.; Tian, Li
2013-10-01
We study the probability distributions of daily leverage returns of 520 North American industrial companies that survive de-listing during the financial crisis, 2006-2012. We provide evidence that distributions of unbiased leverage returns of all individual firms belong to the class of q-Gaussian distributions with the Tsallis entropic parameter within the interval 1
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On the mass function of stars growing in a flocculent medium
NASA Astrophysics Data System (ADS)
Maschberger, Th.
2013-12-01
Stars form in regions of very inhomogeneous densities and may have chaotic orbital motions. This leads to a time variation of the accretion rate, which will spread the masses over some mass range. We investigate the mass distribution functions that arise from fluctuating accretion rates in non-linear accretion, ṁ ∝ mα. The distribution functions evolve in time and develop a power-law tail attached to a lognormal body, like in numerical simulations of star formation. Small fluctuations may be modelled by a Gaussian and develop a power-law tail ∝ m-α at the high-mass side for α > 1 and at the low-mass side for α < 1. Large fluctuations require that their distribution is strictly positive, for example, lognormal. For positive fluctuations the mass distribution function develops the power-law tail always at the high-mass hand side, independent of α larger or smaller than unity. Furthermore, we discuss Bondi-Hoyle accretion in a supersonically turbulent medium, the range of parameters for which non-linear stochastic growth could shape the stellar initial mass function, as well as the effects of a distribution of initial masses and growth times.
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Ploetz, Elizabeth A; Karunaweera, Sadish; Smith, Paul E
2015-01-28
Fluctuation solution theory has provided an alternative view of many liquid mixture properties in terms of particle number fluctuations. The particle number fluctuations can also be related to integrals of the corresponding two body distribution functions between molecular pairs in order to provide a more physical picture of solution behavior and molecule affinities. Here, we extend this type of approach to provide expressions for higher order triplet and quadruplet fluctuations, and thereby integrals over the corresponding distribution functions, all of which can be obtained from available experimental thermodynamic data. The fluctuations and integrals are then determined using the International Association for the Properties of Water and Steam Formulation 1995 (IAPWS-95) equation of state for the liquid phase of pure water. The results indicate small, but significant, deviations from a Gaussian distribution for the molecules in this system. The pressure and temperature dependence of the fluctuations and integrals, as well as the limiting behavior as one approaches both the triple point and the critical point, are also examined.
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NASA Astrophysics Data System (ADS)
Ploetz, Elizabeth A.; Karunaweera, Sadish; Smith, Paul E.
2015-01-01
Fluctuation solution theory has provided an alternative view of many liquid mixture properties in terms of particle number fluctuations. The particle number fluctuations can also be related to integrals of the corresponding two body distribution functions between molecular pairs in order to provide a more physical picture of solution behavior and molecule affinities. Here, we extend this type of approach to provide expressions for higher order triplet and quadruplet fluctuations, and thereby integrals over the corresponding distribution functions, all of which can be obtained from available experimental thermodynamic data. The fluctuations and integrals are then determined using the International Association for the Properties of Water and Steam Formulation 1995 (IAPWS-95) equation of state for the liquid phase of pure water. The results indicate small, but significant, deviations from a Gaussian distribution for the molecules in this system. The pressure and temperature dependence of the fluctuations and integrals, as well as the limiting behavior as one approaches both the triple point and the critical point, are also examined.
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Axion excursions of the landscape during inflation
NASA Astrophysics Data System (ADS)
Palma, Gonzalo A.; Riquelme, Walter
2017-07-01
Because of their quantum fluctuations, axion fields had a chance to experience field excursions traversing many minima of their potentials during inflation. We study this situation by analyzing the dynamics of an axion field ψ , present during inflation, with a periodic potential given by v (ψ )=Λ4[1 -cos (ψ /f )]. By assuming that the vacuum expectation value of the field is stabilized at one of its minima, say, ψ =0 , we compute every n -point correlation function of ψ up to first order in Λ4 using the in-in formalism. This computation allows us to identify the distribution function describing the probability of measuring ψ at a particular amplitude during inflation. Because ψ is able to tunnel between the barriers of the potential, we find that the probability distribution function consists of a non-Gaussian multimodal distribution such that the probability of measuring ψ at a minimum of v (ψ ) different from ψ =0 increases with time. As a result, at the end of inflation, different patches of the Universe are characterized by different values of the axion field amplitude, leading to important cosmological phenomenology: (a) Isocurvature fluctuations induced by the axion at the end of inflation could be highly non-Gaussian. (b) If the axion defines the strength of standard model couplings, then one is led to a concrete realization of the multiverse. (c) If the axion corresponds to dark matter, one is led to the possibility that, within our observable Universe, dark matter started with a nontrivial initial condition, implying novel signatures for future surveys.
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Integrating impairments in reaction time and executive function using a diffusion model framework
Karalunas, Sarah L.; Huang-Pollock, Cynthia L.
2013-01-01
Using Ratcliff’s diffusion model and ex-Gaussian decomposition, we directly evaluate the role individual differences in reaction time (RT) distribution components play in the prediction of inhibitory control and working memory (WM) capacity in children with and without ADHD. Children with (n=92, x̄ age= 10.2 years, 67% male) and without ADHD (n=62, x̄ age=10.6 years, 46% male) completed four tasks of WM and a stop signal reaction time (SSRT) task. Children with ADHD had smaller WM capacities and less efficient inhibitory control. Diffusion model analyses revealed that children with ADHD had slower drift rates (v) and faster non-decision times (Ter), but there were no group differences in boundary separations (a). Similarly, using an ex-Gaussian approach, children with ADHD had larger τ values than non-ADHD controls, but did not differ in µ or σ distribution components. Drift rate mediated the association between ADHD status and performance on both inhibitory control and WM capacity. τ also mediated the ADHD-executive function impairment associations; however, models were a poorer fit to the data. Impaired performance on RT and executive functioning tasks has long been associated with childhood ADHD. Both are believed to be important cognitive mechanisms to the disorder. We demonstrate here that drift rate, or the speed at which information accumulates towards a decision, is able to explain both. PMID:23334775
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Fisher information and Cramér-Rao lower bound for experimental design in parallel imaging.
Bouhrara, Mustapha; Spencer, Richard G
2018-06-01
The Cramér-Rao lower bound (CRLB) is widely used in the design of magnetic resonance (MR) experiments for parameter estimation. Previous work has considered only Gaussian or Rician noise distributions in this calculation. However, the noise distribution for multi-coil acquisitions, such as in parallel imaging, obeys the noncentral χ-distribution under many circumstances. The purpose of this paper is to present the CRLB calculation for parameter estimation from multi-coil acquisitions. We perform explicit calculations of Fisher matrix elements and the associated CRLB for noise distributions following the noncentral χ-distribution. The special case of diffusion kurtosis is examined as an important example. For comparison with analytic results, Monte Carlo (MC) simulations were conducted to evaluate experimental minimum standard deviations (SDs) in the estimation of diffusion kurtosis model parameters. Results were obtained for a range of signal-to-noise ratios (SNRs), and for both the conventional case of Gaussian noise distribution and noncentral χ-distribution with different numbers of coils, m. At low-to-moderate SNR, the noncentral χ-distribution deviates substantially from the Gaussian distribution. Our results indicate that this departure is more pronounced for larger values of m. As expected, the minimum SDs (i.e., CRLB) in derived diffusion kurtosis model parameters assuming a noncentral χ-distribution provided a closer match to the MC simulations as compared to the Gaussian results. Estimates of minimum variance for parameter estimation and experimental design provided by the CRLB must account for the noncentral χ-distribution of noise in multi-coil acquisitions, especially in the low-to-moderate SNR regime. Magn Reson Med 79:3249-3255, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Sirunyan, Albert M; et al.
Event-by-event fluctuations in the elliptic-flow coefficientmore » $$v_2$$ are studied in PbPb collisions at $$\\sqrt{s_{_\\text{NN}}} = 5.02$$ TeV using the CMS detector at the CERN LHC. Elliptic-flow probability distributions $${p}(v_2)$$ for charged particles with transverse momentum 0.3$$< p_\\mathrm{T} <$$3.0 GeV and pseudorapidity $$| \\eta | <$$ 1.0 are determined for different collision centrality classes. The moments of the $${p}(v_2)$$ distributions are used to calculate the $$v_{2}$$ coefficients based on cumulant orders 2, 4, 6, and 8. A rank ordering of the higher-order cumulant results and nonzero standardized skewness values obtained for the $${p}(v_2)$$ distributions indicate non-Gaussian initial-state fluctuation behavior. Bessel-Gaussian and elliptic power fits to the flow distributions are studied to characterize the initial-state spatial anisotropy.« less
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Poisson-Gaussian Noise Analysis and Estimation for Low-Dose X-ray Images in the NSCT Domain.
Lee, Sangyoon; Lee, Min Seok; Kang, Moon Gi
2018-03-29
The noise distribution of images obtained by X-ray sensors in low-dosage situations can be analyzed using the Poisson and Gaussian mixture model. Multiscale conversion is one of the most popular noise reduction methods used in recent years. Estimation of the noise distribution of each subband in the multiscale domain is the most important factor in performing noise reduction, with non-subsampled contourlet transform (NSCT) representing an effective method for scale and direction decomposition. In this study, we use artificially generated noise to analyze and estimate the Poisson-Gaussian noise of low-dose X-ray images in the NSCT domain. The noise distribution of the subband coefficients is analyzed using the noiseless low-band coefficients and the variance of the noisy subband coefficients. The noise-after-transform also follows a Poisson-Gaussian distribution, and the relationship between the noise parameters of the subband and the full-band image is identified. We then analyze noise of actual images to validate the theoretical analysis. Comparison of the proposed noise estimation method with an existing noise reduction method confirms that the proposed method outperforms traditional methods.
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Poisson–Gaussian Noise Analysis and Estimation for Low-Dose X-ray Images in the NSCT Domain
Lee, Sangyoon; Lee, Min Seok; Kang, Moon Gi
2018-01-01
The noise distribution of images obtained by X-ray sensors in low-dosage situations can be analyzed using the Poisson and Gaussian mixture model. Multiscale conversion is one of the most popular noise reduction methods used in recent years. Estimation of the noise distribution of each subband in the multiscale domain is the most important factor in performing noise reduction, with non-subsampled contourlet transform (NSCT) representing an effective method for scale and direction decomposition. In this study, we use artificially generated noise to analyze and estimate the Poisson–Gaussian noise of low-dose X-ray images in the NSCT domain. The noise distribution of the subband coefficients is analyzed using the noiseless low-band coefficients and the variance of the noisy subband coefficients. The noise-after-transform also follows a Poisson–Gaussian distribution, and the relationship between the noise parameters of the subband and the full-band image is identified. We then analyze noise of actual images to validate the theoretical analysis. Comparison of the proposed noise estimation method with an existing noise reduction method confirms that the proposed method outperforms traditional methods. PMID:29596335
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Nucleon form factors in generalized parton distributions at high momentum transfers
NASA Astrophysics Data System (ADS)
Sattary Nikkhoo, Negin; Shojaei, Mohammad Reza
2018-05-01
This paper aims at calculating the elastic form factors for a nucleon by considering the extended Regge and modified Gaussian ansatzes based on the generalized parton distributions. To reach this goal, we have considered three different parton distribution functions (PDFs) and have compared the obtained results among them for high momentum transfer ranges. Minimum free parameters have been applied in our parametrization. After achieving the form factors, we calculate the electric radius and the transversely unpolarized and polarized densities for the nucleon. Furthermore, we obtain the impact-parameter-dependent PDFs. Finally, we compare our obtained data with the results of previous studies.
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Incoherent vector mesons production in PbPb ultraperipheral collisions at the LHC
NASA Astrophysics Data System (ADS)
Xie, Ya-Ping; Chen, Xurong
2017-03-01
The incoherent rapidity distributions of vector mesons are computed in dipole model in PbPb ultraperipheral collisions at the CERN Large Hadron Collider (LHC). The IIM model fitted from newer data is employed in the dipole amplitude. The Boosted Gaussian and Gaus-LC wave functions for vector mesons are implemented in the calculations as well. Predictions for the J / ψ, ψ (2 s), ρ and ϕ incoherent rapidity distributions are evaluated and compared with experimental data and other theoretical predictions in this paper. We obtain closer predictions of the incoherent rapidity distributions for J / ψ than previous calculations in the IIM model.
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Exclusive photoproduction of vector mesons in proton-lead ultraperipheral collisions at the LHC
NASA Astrophysics Data System (ADS)
Xie, Ya-Ping; Chen, Xurong
2018-02-01
Rapidity distributions of vector mesons are computed in dipole model proton-lead ultraperipheral collisions (UPCs) at the CERN Larger Hadron Collider (LHC). The dipole model framework is implemented in the calculations of cross sections in the photon-hadron interaction. The bCGC model and Boosted Gaussian wave functions are employed in the scattering amplitude. We obtain predictions of rapidity distributions of J / ψ meson proton-lead ultraperipheral collisions. The predictions give a good description to the experimental data of ALICE. The rapidity distributions of ϕ, ω and ψ (2 s) mesons in proton-lead ultraperipheral collisions are also presented in this paper.
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Kinetic Theory of quasi-electrostatic waves in non-gyrotropic plasmas
NASA Astrophysics Data System (ADS)
Arshad, K.; Poedts, S.; Lazar, M.
2017-12-01
The orbital angular momentum (OAM) is a trait of helically phased light or helical (twisted) electric field. Lasers carrying orbital angular momentum (OAM) revolutionized many scientific and technological paradigms like microscopy, imaging and ionospheric radar facility to analyze three dimensional plasma dynamics in ionosphere, ultra-intense twisted laser pulses, twisted gravitational waves and astrophysics. This trend has also been investigated in plasma physics. Laguerre-Gaussian type solutions are predicted for magnetic tornadoes and Alfvénic tornadoes which exhibit spiral, split and ring-like morphologies. The ring shape morphology is ideal to fit the observed solar corona, solar atmosphere and Earth's ionosphere. The orbital angular momentum indicates the mediation of electrostatic and electromagnetic waves in new phenomena like Raman and Brillouin scattering. A few years ago, some new effects have been included in studies of orbital angular momentum in plasma regimes such as wave-particle interaction in the presence of helical electric field. Therefore, kinetic studies are carried out to investigate the Landau damping of the waves and growth of the instabilities in the presence helical electric field carrying orbital angular momentum for the Maxwellian distributed plasmas. Recently, a well suited approach involving a kappa distribution function has been adopted to model the twisted space plasmas. This leads to the development of new theoretical grounds for the study of Lorentzian or kappa distributed twisted Langmuir, ion acoustic, dust ion acoustic and dust acoustic modes. The quasi-electrostatic twisted waves have been studied now for the non-gyrotropic dusty plasmas in the presence of the orbital angular momentum of the helical electric field using Generalized Lorentzian or kappa distribution function. The Laguerre-Gaussian (LG) mode function is employed to decompose the perturbed distribution function and electric field into planar (longitudinal) and non-planar (azimuthal) components. The modified Vlasov and Poisson equations are solved to obtain the dielectric function for quasi-electrostatic twisted modes the non-gyrotropic dusty plasmas. Some numerical and graphical analysis is also illustrated for the better understanding of the twisted non-gyrotropic plasmas.
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What are the Shapes of Response Time Distributions in Visual Search?
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
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The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise
NASA Astrophysics Data System (ADS)
Guo, Qin; Sun, Zhongkui; Xu, Wei
2016-05-01
The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.
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Hermite-Gaussian beams with self-forming spiral phase distribution
NASA Astrophysics Data System (ADS)
Zinchik, Alexander A.; Muzychenko, Yana B.
2014-05-01
Spiral laser beams is a family of laser beams that preserve the structural stability up to scale and rotate with the propagation. Properties of spiral beams are of practical interest for laser technology, medicine and biotechnology. Researchers use a spiral beams for movement and manipulation of microparticles. Spiral beams have a complicated phase distribution in cross section. This paper describes the results of analytical and computer simulation of Hermite-Gaussian beams with self-forming spiral phase distribution. In the simulation used a laser beam consisting of the sum of the two modes HG TEMnm and TEMn1m1. The coefficients n1, n, m1, m were varied. Additional phase depending from the coefficients n, m, m1, n1 imposed on the resulting beam. As a result, formed the Hermite Gaussian beam phase distribution which takes the form of a spiral in the process of distribution. For modeling was used VirtualLab 5.0 (manufacturer LightTrans GmbH).
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Large-deviation properties of Brownian motion with dry friction.
Chen, Yaming; Just, Wolfram
2014-10-01
We investigate piecewise-linear stochastic models with regard to the probability distribution of functionals of the stochastic processes, a question that occurs frequently in large deviation theory. The functionals that we are looking into in detail are related to the time a stochastic process spends at a phase space point or in a phase space region, as well as to the motion with inertia. For a Langevin equation with discontinuous drift, we extend the so-called backward Fokker-Planck technique for non-negative support functionals to arbitrary support functionals, to derive explicit expressions for the moments of the functional. Explicit solutions for the moments and for the distribution of the so-called local time, the occupation time, and the displacement are derived for the Brownian motion with dry friction, including quantitative measures to characterize deviation from Gaussian behavior in the asymptotic long time limit.
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Effects of beam irregularity on uniform scanning
NASA Astrophysics Data System (ADS)
Kim, Chang Hyeuk; Jang, Sea duk; Yang, Tae-Keun
2016-09-01
An active scanning beam delivery method has many advantages in particle beam applications. For the beam is to be successfully delivered to the target volume by using the active scanning technique, the dose uniformity must be considered and should be at least 2.5% in the case of therapy application. During beam irradiation, many beam parameters affect the 2-dimensional uniformity at the target layer. A basic assumption in the beam irradiation planning stage is that the shape of the beam is symmetric and follows a Gaussian distribution. In this study, a pure Gaussian-shaped beam distribution was distorted by adding parasitic Gaussian distribution. An appropriate uniform scanning condition was deduced by using a quantitative analysis based on the gamma value of the distorted beam and 2-dimensional uniformities.
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Stress-induced electric current fluctuations in rocks: a superstatistical model
NASA Astrophysics Data System (ADS)
Cartwright-Taylor, Alexis; Vallianatos, Filippos; Sammonds, Peter
2017-04-01
We recorded spontaneous electric current flow in non-piezoelectric Carrara marble samples during triaxial deformation. Mechanical data, ultrasonic velocities and acoustic emissions were acquired simultaneously with electric current to constrain the relationship between electric current flow, differential stress and damage. Under strain-controlled loading, spontaneous electric current signals (nA) were generated and sustained under all conditions tested. In dry samples, a detectable electric current arises only during dilatancy and the overall signal is correlated with the damage induced by microcracking. Our results show that fracture plays a key role in the generation of electric currents in deforming rocks (Cartwright-Taylor et al., in prep). We also analysed the high-frequency fluctuations of these electric current signals and found that they are not normally distributed - they exhibit power-law tails (Cartwright-Taylor et al., 2014). We modelled these distributions with q-Gaussian statistics, derived by maximising the Tsallis entropy. This definition of entropy is particularly applicable to systems which are strongly correlated and far from equilibrium. Good agreement, at all experimental conditions, between the distributions of electric current fluctuations and the q-Gaussian function with q-values far from one, illustrates the highly correlated, fractal nature of the electric source network within the samples and provides further evidence that the source of the electric signals is the developing fractal network of cracks. It has been shown (Beck, 2001) that q-Gaussian distributions can arise from the superposition of local relaxations in the presence of a slowly varying driving force, thus providing a dynamic reason for the appearance of Tsallis statistics in systems with a fluctuating energy dissipation rate. So, the probability distribution for a dynamic variable, u under some external slow forcing, β, can be obtained as a superposition of temporary local equilibrium processes whose variance fluctuates over time. The appearance of q-Gaussian statistics are caused by the fluctuating β parameter, which effectively models the fluctuating energy dissipation rate in the system. This concept is known as superstatistics and is physically relevant for modelling driven non-equilibrium systems where the environmental conditions fluctuate on a large scale. The idea is that the environmental variable, such as temperature or pressure, changes so slowly that a rapidly fluctuating variable within that environment has time to relax back to equilibrium between each change in the environment. The application of superstatistical techniques to our experimental electric current fluctuations show that they can indeed be described, to good approximation, by the superposition of local Gaussian processes with fluctuating variance. We conclude, then, that the measured electric current fluctuates in response to intermittent energy dissipation and is driven to varying temporary local equilibria during deformation by the variations in stress intensity. The advantage of this technique is that, once the model has been established to be a good description of the system in question, the average β parameter (a measure of the average energy dissipation rate) for the system can be obtained simply from the macroscopic q-Gaussian distribution parameters.
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NASA Astrophysics Data System (ADS)
Bovy Jo; Hogg, David W.; Roweis, Sam T.
2011-06-01
We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation-Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point carries an individual d-dimensional uncertainty covariance and has unique missing data properties. This algorithm reconstructs the error-deconvolved or "underlying" distribution function common to all samples, even when the individual data points are samples from different distributions, obtained by convolving the underlying distribution with the heteroskedastic uncertainty distribution of the data point and projecting out the missing data directions. We show how this basic algorithm can be extended with conjugate priors on all of the model parameters and a "split-and-"erge- procedure designed to avoid local maxima of the likelihood. We demonstrate the full method by applying it to the problem of inferring the three-dimensional veloc! ity distribution of stars near the Sun from noisy two-dimensional, transverse velocity measurements from the Hipparcos satellite.
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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.
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Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models
NASA Astrophysics Data System (ADS)
Yang, Linxiao; Fang, Jun; Duan, Huiping; Li, Hongbin; Zeng, Bing
2018-06-01
The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.
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Hayashi, Norio; Miyati, Tosiaki; Takanaga, Masako; Ohno, Naoki; Hamaguchi, Takashi; Kozaka, Kazuto; Sanada, Shigeru; Yamamoto, Tomoyuki; Matsui, Osamu
2011-01-01
In the direction where the phased array coil used in parallel magnetic resonance imaging (MRI) is perpendicular to the arrangement, sensitivity falls significantly. Moreover, in a 3.0 tesla (3T) abdominal MRI, the quality of the image is reduced by changes in the relaxation time, reinforcement of the magnetic susceptibility effect, etc. In a 3T MRI, which has a high resonant frequency, the signal of the depths (central part) is reduced in the trunk part. SCIC, which is sensitivity correction processing, has inadequate correction processing, such as that edges are emphasized and the central part is corrected. Therefore, we used 3T with a Gaussian distribution. The uneven compensation processing for sensitivity of an abdomen MR image was considered. The correction processing consisted of the following methods. 1) The center of gravity of the domain of the human body in an abdomen MR image was calculated. 2) The correction coefficient map was created from the center of gravity using the Gaussian distribution. 3) The sensitivity correction image was created from the correction coefficient map and the original picture image. Using the Gaussian correction to process the image, the uniformity calculated using the NEMA method was improved significantly compared to the original image of a phantom. In a visual evaluation by radiologists, the uniformity was improved significantly using the Gaussian correction processing. Because of the homogeneous improvement of the abdomen image taken using 3T MRI, the Gaussian correction processing is considered to be a very useful technique.
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Hydrologic risk analysis in the Yangtze River basin through coupling Gaussian mixtures into copulas
NASA Astrophysics Data System (ADS)
Fan, Y. R.; Huang, W. W.; Huang, G. H.; Li, Y. P.; Huang, K.; Li, Z.
2016-02-01
In this study, a bivariate hydrologic risk framework is proposed through coupling Gaussian mixtures into copulas, leading to a coupled GMM-copula method. In the coupled GMM-Copula method, the marginal distributions of flood peak, volume and duration are quantified through Gaussian mixture models and the joint probability distributions of flood peak-volume, peak-duration and volume-duration are established through copulas. The bivariate hydrologic risk is then derived based on the joint return period of flood variable pairs. The proposed method is applied to the risk analysis for the Yichang station on the main stream of the Yangtze River, China. The results indicate that (i) the bivariate risk for flood peak-volume would keep constant for the flood volume less than 1.0 × 105 m3/s day, but present a significant decreasing trend for the flood volume larger than 1.7 × 105 m3/s day; and (ii) the bivariate risk for flood peak-duration would not change significantly for the flood duration less than 8 days, and then decrease significantly as duration value become larger. The probability density functions (pdfs) of the flood volume and duration conditional on flood peak can also be generated through the fitted copulas. The results indicate that the conditional pdfs of flood volume and duration follow bimodal distributions, with the occurrence frequency of the first vertex decreasing and the latter one increasing as the increase of flood peak. The obtained conclusions from the bivariate hydrologic analysis can provide decision support for flood control and mitigation.
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MSEE: Stochastic Cognitive Linguistic Behavior Models for Semantic Sensing
2013-09-01
recognition, a Gaussian Process Dynamic Model with Social Network Analysis (GPDM-SNA) for a small human group action recognition, an extended GPDM-SNA...44 3.2. Small Human Group Activity Modeling Based on Gaussian Process Dynamic Model and Social Network Analysis (SN-GPDM...51 Approved for public release; distribution unlimited. 3 3.2.3. Gaussian Process Dynamical Model and
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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…
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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.
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Analysis of low altitude atmospheric turbulence data measured in flight
NASA Technical Reports Server (NTRS)
Ganzer, V. M.; Joppa, R. G.; Vanderwees, G.
1977-01-01
All three components of turbulence were measured simultaneously in flight at each wing tip of a Beech D-18 aircraft. The flights were conducted at low altitude, 30.5 - 61.0 meters (100-200 ft.), over water in the presence of wind driven turbulence. Statistical properties of flight measured turbulence were compared with Gaussian and non-Gaussian turbulence models. Spatial characteristics of the turbulence were analyzed using the data from flight perpendicular and parallel to the wind. The probability density distributions of the vertical gusts show distinctly non-Gaussian characteristics. The distributions of the longitudinal and lateral gusts are generally Gaussian. The power spectra compare in the inertial subrange at some points better with the Dryden spectrum, while at other points the von Karman spectrum is a better approximation. In the low frequency range the data show peaks or dips in the power spectral density. The cross between vertical gusts in the direction of the mean wind were compared with a matched non-Gaussian model. The real component of the cross spectrum is in general close to the non-Gaussian model. The imaginary component, however, indicated a larger phase shift between these two gust components than was found in previous research.
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Local spectrum analysis of field propagation in an anisotropic medium. Part I. Time-harmonic fields.
Tinkelman, Igor; Melamed, Timor
2005-06-01
The phase-space beam summation is a general analytical framework for local analysis and modeling of radiation from extended source distributions. In this formulation, the field is expressed as a superposition of beam propagators that emanate from all points in the source domain and in all directions. In this Part I of a two-part investigation, the theory is extended to include propagation in anisotropic medium characterized by a generic wave-number profile for time-harmonic fields; in a companion paper [J. Opt. Soc. Am. A 22, 1208 (2005)], the theory is extended to time-dependent fields. The propagation characteristics of the beam propagators in a homogeneous anisotropic medium are considered. With use of Gaussian windows for the local processing of either ordinary or extraordinary electromagnetic field distributions, the field is represented by a phase-space spectral distribution in which the propagating elements are Gaussian beams that are formulated by using Gaussian plane-wave spectral distributions over the extended source plane. By applying saddle-point asymptotics, we extract the Gaussian beam phenomenology in the anisotropic environment. The resulting field is parameterized in terms of the spatial evolution of the beam curvature, beam width, etc., which are mapped to local geometrical properties of the generic wave-number profile. The general results are applied to the special case of uniaxial crystal, and it is found that the asymptotics for the Gaussian beam propagators, as well as the physical phenomenology attached, perform remarkably well.
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Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft
NASA Technical Reports Server (NTRS)
Carpenter, J. Russell
1999-01-01
A distributed satellite formation, modeled as an arbitrary number of fully connected nodes in a network, could be controlled using a decentralized controller framework that distributes operations in parallel over the network. For such problems, a solution that minimizes data transmission requirements, in the context of linear-quadratic-Gaussian (LQG) control theory, was given by Speyer. This approach is advantageous because it is non-hierarchical, detected failures gracefully degrade system performance, fewer local computations are required than for a centralized controller, and it is optimal with respect to the standard LQG cost function. Disadvantages of the approach are the need for a fully connected communications network, the total operations performed over all the nodes are greater than for a centralized controller, and the approach is formulated for linear time-invariant systems. To investigate the feasibility of the decentralized approach to satellite formation flying, a simple centralized LQG design for a spacecraft orbit control problem is adapted to the decentralized framework. The simple design uses a fixed reference trajectory (an equatorial, Keplerian, circular orbit), and by appropriate choice of coordinates and measurements is formulated as a linear time-invariant system.
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Transport of cosmic-ray protons in intermittent heliospheric turbulence: Model and simulations
DOE Office of Scientific and Technical Information (OSTI.GOV)
Alouani-Bibi, Fathallah; Le Roux, Jakobus A., E-mail: fb0006@uah.edu
The transport of charged energetic particles in the presence of strong intermittent heliospheric turbulence is computationally analyzed based on known properties of the interplanetary magnetic field and solar wind plasma at 1 astronomical unit. The turbulence is assumed to be static, composite, and quasi-three-dimensional with a varying energy distribution between a one-dimensional Alfvénic (slab) and a structured two-dimensional component. The spatial fluctuations of the turbulent magnetic field are modeled either as homogeneous with a Gaussian probability distribution function (PDF), or as intermittent on large and small scales with a q-Gaussian PDF. Simulations showed that energetic particle diffusion coefficients both parallelmore » and perpendicular to the background magnetic field are significantly affected by intermittency in the turbulence. This effect is especially strong for parallel transport where for large-scale intermittency results show an extended phase of subdiffusive parallel transport during which cross-field transport diffusion dominates. The effects of intermittency are found to depend on particle rigidity and the fraction of slab energy in the turbulence, yielding a perpendicular to parallel mean free path ratio close to 1 for large-scale intermittency. Investigation of higher order transport moments (kurtosis) indicates that non-Gaussian statistical properties of the intermittent turbulent magnetic field are present in the parallel transport, especially for low rigidity particles at all times.« less
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NASA Astrophysics Data System (ADS)
Magalhães, S.; Fialho, M.; Peres, M.; Lorenz, K.; Alves, E.
2016-04-01
In this work radial symmetric x-ray diffraction scans of Al0.15Ga0.85N thin films implanted with Tm ions were measured to determine the lattice deformation and crystal quality as functions of depth. The alloys were implanted with 300 keV Tm with 10° off-set to the sample normal to avoid channelling, with fluences varying between 1013 Tm cm-2 and 5 × 1015 Tm cm-2. Simulations of the radial 2θ-ω scans were performed under the frame of the dynamical theory of x-ray diffraction assuming Gaussian distributions of the lattice strain induced by implantation defects. The structure factor of the individual layers is multiplied by a static Debye-Waller factor in order to take into account the effect of lattice disorder due to implantation. For higher fluences two asymmetric Gaussians are required to describe well the experimental diffractograms, although a single asymmetric Gaussian profile for the deformation is found in the sample implanted with 1013 Tm cm-2. After thermal treatment at 1200 °C, the crystal quality partially recovers as seen in a reduction of the amplitude of the deformation maximum as well as the total thickness of the deformed layer. Furthermore, no evidence of changes with respect to the virgin crystal mosaicity is found after implantation and annealing.
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Permutation modulation for quantization and information reconciliation in CV-QKD systems
NASA Astrophysics Data System (ADS)
Daneshgaran, Fred; Mondin, Marina; Olia, Khashayar
2017-08-01
This paper is focused on the problem of Information Reconciliation (IR) for continuous variable Quantum Key Distribution (QKD). The main problem is quantization and assignment of labels to the samples of the Gaussian variables observed at Alice and Bob. Trouble is that most of the samples, assuming that the Gaussian variable is zero mean which is de-facto the case, tend to have small magnitudes and are easily disturbed by noise. Transmission over longer and longer distances increases the losses corresponding to a lower effective Signal to Noise Ratio (SNR) exasperating the problem. Here we propose to use Permutation Modulation (PM) as a means of quantization of Gaussian vectors at Alice and Bob over a d-dimensional space with d ≫ 1. The goal is to achieve the necessary coding efficiency to extend the achievable range of continuous variable QKD by quantizing over larger and larger dimensions. Fractional bit rate per sample is easily achieved using PM at very reasonable computational cost. Ordered statistics is used extensively throughout the development from generation of the seed vector in PM to analysis of error rates associated with the signs of the Gaussian samples at Alice and Bob as a function of the magnitude of the observed samples at Bob.
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The tensor distribution function.
Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M
2009-01-01
Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.
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Modeling methods for merging computational and experimental aerodynamic pressure data
NASA Astrophysics Data System (ADS)
Haderlie, Jacob C.
This research describes a process to model surface pressure data sets as a function of wing geometry from computational and wind tunnel sources and then merge them into a single predicted value. The described merging process will enable engineers to integrate these data sets with the goal of utilizing the advantages of each data source while overcoming the limitations of both; this provides a single, combined data set to support analysis and design. The main challenge with this process is accurately representing each data source everywhere on the wing. Additionally, this effort demonstrates methods to model wind tunnel pressure data as a function of angle of attack as an initial step towards a merging process that uses both location on the wing and flow conditions (e.g., angle of attack, flow velocity or Reynold's number) as independent variables. This surrogate model of pressure as a function of angle of attack can be useful for engineers that need to predict the location of zero-order discontinuities, e.g., flow separation or normal shocks. Because, to the author's best knowledge, there is no published, well-established merging method for aerodynamic pressure data (here, the coefficient of pressure Cp), this work identifies promising modeling and merging methods, and then makes a critical comparison of these methods. Surrogate models represent the pressure data for both data sets. Cubic B-spline surrogate models represent the computational simulation results. Machine learning and multi-fidelity surrogate models represent the experimental data. This research compares three surrogates for the experimental data (sequential--a.k.a. online--Gaussian processes, batch Gaussian processes, and multi-fidelity additive corrector) on the merits of accuracy and computational cost. The Gaussian process (GP) methods employ cubic B-spline CFD surrogates as a model basis function to build a surrogate model of the WT data, and this usage of the CFD surrogate in building the WT data could serve as a "merging" because the resulting WT pressure prediction uses information from both sources. In the GP approach, this model basis function concept seems to place more "weight" on the Cp values from the wind tunnel (WT) because the GP surrogate uses the CFD to approximate the WT data values. Conversely, the computationally inexpensive additive corrector method uses the CFD B-spline surrogate to define the shape of the spanwise distribution of the Cp while minimizing prediction error at all spanwise locations for a given arc length position; this, too, combines information from both sources to make a prediction of the 2-D WT-based Cp distribution, but the additive corrector approach gives more weight to the CFD prediction than to the WT data. Three surrogate models of the experimental data as a function of angle of attack are also compared for accuracy and computational cost. These surrogates are a single Gaussian process model (a single "expert"), product of experts, and generalized product of experts. The merging approach provides a single pressure distribution that combines experimental and computational data. The batch Gaussian process method provides a relatively accurate surrogate that is computationally acceptable, and can receive wind tunnel data from port locations that are not necessarily parallel to a variable direction. On the other hand, the sequential Gaussian process and additive corrector methods must receive a sufficient number of data points aligned with one direction, e.g., from pressure port bands (tap rows) aligned with the freestream. The generalized product of experts best represents wind tunnel pressure as a function of angle of attack, but at higher computational cost than the single expert approach. The format of the application data from computational and experimental sources in this work precluded the merging process from including flow condition variables (e.g., angle of attack) in the independent variables, so the merging process is only conducted in the wing geometry variables of arc length and span. The merging process of Cp data allows a more "hands-off" approach to aircraft design and analysis, (i.e., not as many engineers needed to debate the Cp distribution shape) and generates Cp predictions at any location on the wing. However, the cost with these benefits are engineer time (learning how to build surrogates), computational time in constructing the surrogates, and surrogate accuracy (surrogates introduce error into data predictions). This dissertation effort used the Trap Wing / First AIAA CFD High-Lift Prediction Workshop as a relevant transonic wing with a multi-element high-lift system, and this work identified that the batch GP model for the WT data and the B-spline surrogate for the CFD might best be combined using expert belief weights to describe Cp as a function of location on the wing element surface. (Abstract shortened by ProQuest.).
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NASA Astrophysics Data System (ADS)
Liu, Pusheng; Lü, Baida
2007-04-01
By using the vectorial Debye diffraction theory, phase singularities of high numerical aperture (NA) dark-hollow Gaussian beams in the focal region are studied. The dependence of phase singularities on the truncation parameter δ and semi-aperture angle α (or equally, NA) is illustrated numerically. A comparison of phase singularities of high NA dark-hollow Gaussian beams with those of scalar paraxial Gaussian beams and high NA Gaussian beams is made. For high NA dark-hollow Gaussian beams the beam order n additionally affects the spatial distribution of phase singularities, and there exist phase singularities outside the focal plane, which may be created or annihilated by variation of the semi-aperture angle in a certain region.
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Quantification of Gaussian quantum steering.
Kogias, Ioannis; Lee, Antony R; Ragy, Sammy; Adesso, Gerardo
2015-02-13
Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible.
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Multipartite Gaussian steering: Monogamy constraints and quantum cryptography applications
NASA Astrophysics Data System (ADS)
Xiang, Yu; Kogias, Ioannis; Adesso, Gerardo; He, Qiongyi
2017-01-01
We derive laws for the distribution of quantum steering among different parties in multipartite Gaussian states under Gaussian measurements. We prove that a monogamy relation akin to the generalized Coffman-Kundu-Wootters inequality holds quantitatively for a recently introduced measure of Gaussian steering. We then define the residual Gaussian steering, stemming from the monogamy inequality, as an indicator of collective steering-type correlations. For pure three-mode Gaussian states, the residual acts as a quantifier of genuine multipartite steering, and is interpreted operationally in terms of the guaranteed key rate in the task of secure quantum secret sharing. Optimal resource states for the latter protocol are identified, and their possible experimental implementation discussed. Our results pin down the role of multipartite steering for quantum communication.
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Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere.
Chen, Rong; Liu, Lin; Zhu, Shijun; Wu, Gaofeng; Wang, Fei; Cai, Yangjian
2014-01-27
Laguerre-Gaussian Schell-model (LGSM) beam was proposed in theory [Opt. Lett.38, 91 (2013 Opt. Lett.38, 1814 (2013)] just recently. In this paper, we study the propagation of a LGSM beam in turbulent atmosphere. Analytical expressions for the cross-spectral density and the second-order moments of the Wigner distribution function of a LGSM beam in turbulent atmosphere are derived. The statistical properties, such as the degree of coherence and the propagation factor, of a LGSM beam in turbulent atmosphere are studied in detail. It is found that a LGSM beam with larger mode order n is less affected by turbulence than a LGSM beam with smaller mode order n or a GSM beam under certain condition, which will be useful in free-space optical communications.
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Using Fuzzy Gaussian Inference and Genetic Programming to Classify 3D Human Motions
NASA Astrophysics Data System (ADS)
Khoury, Mehdi; Liu, Honghai
This research introduces and builds on the concept of Fuzzy Gaussian Inference (FGI) (Khoury and Liu in Proceedings of UKCI, 2008 and IEEE Workshop on Robotic Intelligence in Informationally Structured Space (RiiSS 2009), 2009) as a novel way to build Fuzzy Membership Functions that map to hidden Probability Distributions underlying human motions. This method is now combined with a Genetic Programming Fuzzy rule-based system in order to classify boxing moves from natural human Motion Capture data. In this experiment, FGI alone is able to recognise seven different boxing stances simultaneously with an accuracy superior to a GMM-based classifier. Results seem to indicate that adding an evolutionary Fuzzy Inference Engine on top of FGI improves the accuracy of the classifier in a consistent way.
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Optimization of removal function in computer controlled optical surfacing
NASA Astrophysics Data System (ADS)
Chen, Xi; Guo, Peiji; Ren, Jianfeng
2010-10-01
The technical principle of computer controlled optical surfacing (CCOS) and the common method of optimizing removal function that is used in CCOS are introduced in this paper. A new optimizing method time-sharing synthesis of removal function is proposed to solve problems of the removal function being far away from Gaussian type and slow approaching of the removal function error that encountered in the mode of planet motion or translation-rotation. Detailed time-sharing synthesis of using six removal functions is discussed. For a given region on the workpiece, six positions are selected as the centers of the removal function; polishing tool controlled by the executive system of CCOS revolves around each centre to complete a cycle in proper order. The overall removal function obtained by the time-sharing process is the ratio of total material removal in six cycles to time duration of the six cycles, which depends on the arrangement and distribution of the six removal functions. Simulations on the synthesized overall removal functions under two different modes of motion, i.e., planet motion and translation-rotation are performed from which the optimized combination of tool parameters and distribution of time-sharing synthesis removal functions are obtained. The evaluation function when optimizing is determined by an approaching factor which is defined as the ratio of the material removal within the area of half of the polishing tool coverage from the polishing center to the total material removal within the full polishing tool coverage area. After optimization, it is found that the optimized removal function obtained by time-sharing synthesis is closer to the ideal Gaussian type removal function than those by the traditional methods. The time-sharing synthesis method of the removal function provides an efficient way to increase the convergence speed of the surface error in CCOS for the fabrication of aspheric optical surfaces, and to reduce the intermediate- and high-frequency error.
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The Non-Gaussian Nature of Prostate Motion Based on Real-Time Intrafraction Tracking
DOE Office of Scientific and Technical Information (OSTI.GOV)
Lin, Yuting; Liu, Tian; Yang, Wells
2013-10-01
Purpose: The objective of this work is to test the validity of the Gaussian approximation for prostate motion through characterization of its spatial distribution. Methods and Materials: Real-time intrafraction prostate motion was observed using Calypso 4-dimensional (4D) nonradioactive electromagnetic tracking system. We report the results from a total of 1024 fractions from 31 prostate cancer patients. First, the correlation of prostate motion in right/left (RL), anteroposterior (AP), and superoinferior (SI) direction were determined using Pearson's correlation of coefficient. Then the spatial distribution of prostate motion was analyzed for individual fraction, individual patient including all fractions, and all patients including allmore » fractions. The displacement in RL, AP, SI, oblique, or total direction is fitted into a Gaussian distribution, and a Lilliefors test was used to evaluate the validity of the hypothesis that the displacement is normally distributed. Results: There is high correlation in AP/SI direction (61% of fractions with medium or strong correlation). This is consistent with the longitudinal oblique motion of the prostate, and likely the effect from respiration on an organ confined within the genitourinary diaphragm with the rectum sitting posteriorly and bladder sitting superiorly. In all directions, the non-Gaussian distribution is more common for individual fraction, individual patient including all fractions, and all patients including all fractions. The spatial distribution of prostate motion shows an elongated shape in oblique direction, indicating a higher range of motion in the AP and SI directions. Conclusions: Our results showed that the prostate motion is highly correlated in AP and SI direction, indicating an oblique motion preference. In addition, the spatial distribution of prostate motion is elongated in an oblique direction, indicating that the organ motion dosimetric modeling using Gaussian kernel may need to be modified to account for the particular organ motion character of prostate.« less
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The non-Gaussian nature of prostate motion based on real-time intrafraction tracking.
Lin, Yuting; Liu, Tian; Yang, Wells; Yang, Xiaofeng; Khan, Mohammad K
2013-10-01
The objective of this work is to test the validity of the Gaussian approximation for prostate motion through characterization of its spatial distribution. Real-time intrafraction prostate motion was observed using Calypso 4-dimensional (4D) nonradioactive electromagnetic tracking system. We report the results from a total of 1024 fractions from 31 prostate cancer patients. First, the correlation of prostate motion in right/left (RL), anteroposterior (AP), and superoinferior (SI) direction were determined using Pearson's correlation of coefficient. Then the spatial distribution of prostate motion was analyzed for individual fraction, individual patient including all fractions, and all patients including all fractions. The displacement in RL, AP, SI, oblique, or total direction is fitted into a Gaussian distribution, and a Lilliefors test was used to evaluate the validity of the hypothesis that the displacement is normally distributed. There is high correlation in AP/SI direction (61% of fractions with medium or strong correlation). This is consistent with the longitudinal oblique motion of the prostate, and likely the effect from respiration on an organ confined within the genitourinary diaphragm with the rectum sitting posteriorly and bladder sitting superiorly. In all directions, the non-Gaussian distribution is more common for individual fraction, individual patient including all fractions, and all patients including all fractions. The spatial distribution of prostate motion shows an elongated shape in oblique direction, indicating a higher range of motion in the AP and SI directions. Our results showed that the prostate motion is highly correlated in AP and SI direction, indicating an oblique motion preference. In addition, the spatial distribution of prostate motion is elongated in an oblique direction, indicating that the organ motion dosimetric modeling using Gaussian kernel may need to be modified to account for the particular organ motion character of prostate. Copyright © 2013 Elsevier Inc. All rights reserved.
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Stochastic characteristics and Second Law violations of atomic fluids in Couette flow
NASA Astrophysics Data System (ADS)
Raghavan, Bharath V.; Karimi, Pouyan; Ostoja-Starzewski, Martin
2018-04-01
Using Non-equilibrium Molecular Dynamics (NEMD) simulations, we study the statistical properties of an atomic fluid undergoing planar Couette flow, in which particles interact via a Lennard-Jones potential. We draw a connection between local density contrast and temporal fluctuations in the shear stress, which arise naturally through the equivalence between the dissipation function and entropy production according to the fluctuation theorem. We focus on the shear stress and the spatio-temporal density fluctuations and study the autocorrelations and spectral densities of the shear stress. The bispectral density of the shear stress is used to measure the degree of departure from a Gaussian model and the degree of nonlinearity induced in the system owing to the applied strain rate. More evidence is provided by the probability density function of the shear stress. We use the Information Theory to account for the departure from Gaussian statistics and to develop a more general probability distribution function that captures this broad range of effects. By accounting for negative shear stress increments, we show how this distribution preserves the violations of the Second Law of Thermodynamics observed in planar Couette flow of atomic fluids, and also how it captures the non-Gaussian nature of the system by allowing for non-zero higher moments. We also demonstrate how the temperature affects the band-width of the shear-stress and how the density affects its Power Spectral Density, thus determining the conditions under which the shear-stress acts is a narrow-band or wide-band random process. We show that changes in the statistical characteristics of the parameters of interest occur at a critical strain rate at which an ordering transition occurs in the fluid causing shear thinning and affecting its stability. A critical strain rate of this kind is also predicted by the Loose-Hess stability criterion.
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Statistical properties of multi-theta polymer chains
NASA Astrophysics Data System (ADS)
Uehara, Erica; Deguchi, Tetsuo
2018-04-01
We study statistical properties of polymer chains with complex structures whose chemical connectivities are expressed by graphs. The multi-theta curve of m subchains with two branch points connected by them is one of the simplest graphs among those graphs having closed paths, i.e. loops. We denoted it by θm , and for m = 2 it is given by a ring. We derive analytically the pair distribution function and the scattering function for the θm -shaped polymer chains consisting of m Gaussian random walks of n steps. Surprisingly, it is shown rigorously that the mean-square radius of gyration for the Gaussian θm -shaped polymer chain does not depend on the number m of subchains if each subchain has the same fixed number of steps. For m = 3 we show the Kratky plot for the theta-shaped polymer chain consisting of hard cylindrical segments by the Monte-Carlo method including reflection at trivalent vertices.
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Yang, Yanzheng; Zhu, Qiuan; Peng, Changhui; Wang, Han; Xue, Wei; Lin, Guanghui; Wen, Zhongming; Chang, Jie; Wang, Meng; Liu, Guobin; Li, Shiqing
2016-01-01
Increasing evidence indicates that current dynamic global vegetation models (DGVMs) have suffered from insufficient realism and are difficult to improve, particularly because they are built on plant functional type (PFT) schemes. Therefore, new approaches, such as plant trait-based methods, are urgently needed to replace PFT schemes when predicting the distribution of vegetation and investigating vegetation sensitivity. As an important direction towards constructing next-generation DGVMs based on plant functional traits, we propose a novel approach for modelling vegetation distributions and analysing vegetation sensitivity through trait-climate relationships in China. The results demonstrated that a Gaussian mixture model (GMM) trained with a LMA-Nmass-LAI data combination yielded an accuracy of 72.82% in simulating vegetation distribution, providing more detailed parameter information regarding community structures and ecosystem functions. The new approach also performed well in analyses of vegetation sensitivity to different climatic scenarios. Although the trait-climate relationship is not the only candidate useful for predicting vegetation distributions and analysing climatic sensitivity, it sheds new light on the development of next-generation trait-based DGVMs. PMID:27052108
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Scheven, U M
2013-12-01
This paper describes a new variant of established stimulated echo pulse sequences, and an analytical method for determining diffusion or dispersion coefficients for Gaussian or non-Gaussian displacement distributions. The unipolar displacement encoding PFGSTE sequence uses trapezoidal gradient pulses of equal amplitude g and equal ramp rates throughout while sampling positive and negative halves of q-space. Usefully, the equal gradient amplitudes and gradient ramp rates help to reduce the impact of experimental artefacts caused by residual amplifier transients, eddy currents, or ferromagnetic hysteresis in components of the NMR magnet. The pulse sequence was validated with measurements of diffusion in water and of dispersion in flow through a packing of spheres. The analytical method introduced here permits the robust determination of the variance of non-Gaussian, dispersive displacement distributions. The noise sensitivity of the analytical method is shown to be negligible, using a demonstration experiment with a non-Gaussian longitudinal displacement distribution, measured on flow through a packing of mono-sized spheres. Copyright © 2013 Elsevier Inc. All rights reserved.
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Following a trend with an exponential moving average: Analytical results for a Gaussian model
NASA Astrophysics Data System (ADS)
Grebenkov, Denis S.; Serror, Jeremy
2014-01-01
We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both auto-correlation level and transaction costs. Theoretical results are illustrated on the Dow Jones index.
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Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian
NASA Astrophysics Data System (ADS)
Teneng, Dean
2013-09-01
We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.
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Gu, Shoou-Lian Hwang; Gau, Susan Shur-Fen; Tzang, Shyh-Weir; Hsu, Wen-Yau
2013-11-01
We investigated the three parameters (mu, sigma, tau) of ex-Gaussian distribution of RT derived from the Conners' continuous performance test (CCPT) and examined the moderating effects of the energetic factors (the inter-stimulus intervals (ISIs) and Blocks) among these three parameters, especially tau, an index describing the positive skew of RT distribution. We assessed 195 adolescents with DSM-IV ADHD, and 90 typically developing (TD) adolescents, aged 10-16. Participants and their parents received psychiatric interviews to confirm the diagnosis of ADHD and other psychiatric disorders. Participants also received intelligence (WISC-III) and CCPT assessments. We found that participants with ADHD had a smaller mu, and larger tau. As the ISI/Block increased, the magnitude of group difference in tau increased. Among the three ex-Gaussian parameters, tau was positively associated with omission errors, and mu was negatively associated with commission errors. The moderating effects of ISIs and Blocks on tau parameters suggested that the ex-Gaussian parameters could offer more information about the attention state in vigilance task, especially in ADHD. Copyright © 2013 Elsevier Ltd. All rights reserved.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Goulianos, K.; /Rockefeller U.
The charged multiplicity distributions of the diffractive and non-diffractive components of hadronic interactions, as well as those of hadronic states produced in other reactions, are described well by a universal Gaussian function that depends only on the available mass for pionization, has a maximum at n{sub o} {approx_equal} 2M{sup 1/2}, where M is the available mass in GeV, and a peak to width ratio n{sub o}/D {approx_equal} 2.
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Molecular dynamics study on glycolic acid in the physiological salt solution
NASA Astrophysics Data System (ADS)
Matsunaga, S.
2018-05-01
Molecular dynamics (MD) study on glycolic acid in the physiological salt solution has been performed, which is a model of a biofuel cell. The structure and charge distribution of glycolic acid in aqueous solution used in MD is beforehand optimized by Gaussian09 utilizing the density functional theory. MD is performed in the NTV constant condition, i.e. the number of particles, temperature, and volume of MD cell are definite. The structure difference of the glycolic acid and oxalic acid is detected by the water distribution around the molecules using the pair distribution functions, gij(r), and the frequency dependent diffusion coefficients, Di(ν). The anomalous dielectric constant of the solution, i.e. about 12 times larger than that of water, has been obtained, which may be attributed to the ion pair formation in the solution.
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NASA Astrophysics Data System (ADS)
Zhou, Yali; Zhang, Qizhi; Yin, Yixin
2015-05-01
In this paper, active control of impulsive noise with symmetric α-stable (SαS) distribution is studied. A general step-size normalized filtered-x Least Mean Square (FxLMS) algorithm is developed based on the analysis of existing algorithms, and the Gaussian distribution function is used to normalize the step size. Compared with existing algorithms, the proposed algorithm needs neither the parameter selection and thresholds estimation nor the process of cost function selection and complex gradient computation. Computer simulations have been carried out to suggest that the proposed algorithm is effective for attenuating SαS impulsive noise, and then the proposed algorithm has been implemented in an experimental ANC system. Experimental results show that the proposed scheme has good performance for SαS impulsive noise attenuation.
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Statistical properties of two sine waves in Gaussian noise.
NASA Technical Reports Server (NTRS)
Esposito, R.; Wilson, L. R.
1973-01-01
A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).
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Color-magnitude distribution of face-on nearby galaxies in Sloan digital sky survey DR7
DOE Office of Scientific and Technical Information (OSTI.GOV)
Jin, Shuo-Wen; Feng, Long-Long; Gu, Qiusheng
2014-05-20
We have analyzed the distributions in the color-magnitude diagram (CMD) of a large sample of face-on galaxies to minimize the effect of dust extinctions on galaxy color. About 300,000 galaxies with log (a/b) < 0.2 and redshift z < 0.2 are selected from the Sloan Digital Sky Survey DR7 catalog. Two methods are employed to investigate the distributions of galaxies in the CMD, including one-dimensional (1D) Gaussian fitting to the distributions in individual magnitude bins and two-dimensional (2D) Gaussian mixture model (GMM) fitting to galaxies as a whole. We find that in the 1D fitting, two Gaussians are not enoughmore » to fit galaxies with the excess present between the blue cloud and the red sequence. The fitting to this excess defines the center of the green valley in the local universe to be (u – r){sub 0.1} = –0.121M {sub r,} 0{sub .1} – 0.061. The fraction of blue cloud and red sequence galaxies turns over around M {sub r,} {sub 0.1} ∼ –20.1 mag, corresponding to stellar mass of 3 × 10{sup 10} M {sub ☉}. For the 2D GMM fitting, a total of four Gaussians are required, one for the blue cloud, one for the red sequence, and the additional two for the green valley. The fact that two Gaussians are needed to describe the distributions of galaxies in the green valley is consistent with some models that argue for two different evolutionary paths from the blue cloud to the red sequence.« less
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Receiver design for SPAD-based VLC systems under Poisson-Gaussian mixed noise model.
Mao, Tianqi; Wang, Zhaocheng; Wang, Qi
2017-01-23
Single-photon avalanche diode (SPAD) is a promising photosensor because of its high sensitivity to optical signals in weak illuminance environment. Recently, it has drawn much attention from researchers in visible light communications (VLC). However, existing literature only deals with the simplified channel model, which only considers the effects of Poisson noise introduced by SPAD, but neglects other noise sources. Specifically, when an analog SPAD detector is applied, there exists Gaussian thermal noise generated by the transimpedance amplifier (TIA) and the digital-to-analog converter (D/A). Therefore, in this paper, we propose an SPAD-based VLC system with pulse-amplitude-modulation (PAM) under Poisson-Gaussian mixed noise model, where Gaussian-distributed thermal noise at the receiver is also investigated. The closed-form conditional likelihood of received signals is derived using the Laplace transform and the saddle-point approximation method, and the corresponding quasi-maximum-likelihood (quasi-ML) detector is proposed. Furthermore, the Poisson-Gaussian-distributed signals are converted to Gaussian variables with the aid of the generalized Anscombe transform (GAT), leading to an equivalent additive white Gaussian noise (AWGN) channel, and a hard-decision-based detector is invoked. Simulation results demonstrate that, the proposed GAT-based detector can reduce the computational complexity with marginal performance loss compared with the proposed quasi-ML detector, and both detectors are capable of accurately demodulating the SPAD-based PAM signals.
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Ince-Gaussian series representation of the two-dimensional fractional Fourier transform.
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.
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Spin-Hall effect in the scattering of structured light from plasmonic nanowire
NASA Astrophysics Data System (ADS)
Sharma, Deepak K.; Kumar, Vijay; Vasista, Adarsh B.; Chaubey, Shailendra K.; Kumar, G. V. Pavan
2018-06-01
Spin-orbit interactions are subwavelength phenomena which can potentially lead to numerous device related applications in nanophotonics. Here, we report Spin-Hall effect in the forward scattering of Hermite-Gaussian and Gaussian beams from a plasmonic nanowire. Asymmetric scattered radiation distribution was observed for circularly polarized beams. Asymmetry in the scattered radiation distribution changes the sign when the polarization handedness inverts. We found a significant enhancement in the Spin-Hall effect for Hermite-Gaussian beam as compared to Gaussian beam for constant input power. The difference between scattered powers perpendicular to the long axis of the plasmonic nanowire was used to quantify the enhancement. In addition to it, nodal line of HG beam acts as the marker for the Spin-Hall shift. Numerical calculations corroborate experimental observations and suggest that the Spin flow component of Poynting vector associated with the circular polarization is responsible for the Spin-Hall effect and its enhancement.
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NASA Astrophysics Data System (ADS)
Chu, X. X.; Liu, Z. J.; Wu, Y.
2008-07-01
Based on the Huygens-Fresnel integral, the properties of a circular flattened Gaussian beam through a stigmatic optical system in turbulent atmosphere are investigated. Analytical formulas for the average intensity are derived. As elementary examples, the average intensity distributions of a collimated circular flattened Gaussian beam and a focused circular flattened Gaussian beam through a simple optical system are studied. To see the effects of the optical system on the propagation, the average intensity distributions of the beam for direct propagation are also studied. From the analysis, comparison and numerical calculation we can see that there are many differences between the two propagations. These differences are due to the geometrical magnification of the optical system, different diffraction and different turbulence-induced spreading. Namely, an optical system not only affects the diffraction but also affects the turbulence-induced spreading.
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A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment.
Kumar, P; Kumar, Dinesh; Rai, K N
2015-01-01
The success of hyperthermia in the treatment of cancer depends on the precise prediction and control of temperature. It was absolutely a necessity for hyperthermia treatment planning to understand the temperature distribution within living biological tissues. In this paper, dual-phase-lag model of bio-heat transfer has been studied using Gaussian distribution source term under most generalized boundary condition during hyperthermia treatment. An approximate analytical solution of the present problem has been done by Finite element wavelet Galerkin method which uses Legendre wavelet as a basis function. Multi-resolution analysis of Legendre wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. The whole analysis is presented in dimensionless form. The dual-phase-lag model of bio-heat transfer has compared with Pennes and Thermal wave model of bio-heat transfer and it has been found that large differences in the temperature at the hyperthermia position and time to achieve the hyperthermia temperature exist, when we increase the value of τT. Particular cases when surface subjected to boundary condition of 1st, 2nd and 3rd kind are discussed in detail. The use of dual-phase-lag model of bio-heat transfer and finite element wavelet Galerkin method as a solution method helps in precise prediction of temperature. Gaussian distribution source term helps in control of temperature during hyperthermia treatment. So, it makes this study more useful for clinical applications. Copyright © 2015 Elsevier Ltd. All rights reserved.
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Line-edge roughness performance targets for EUV lithography
NASA Astrophysics Data System (ADS)
Brunner, Timothy A.; Chen, Xuemei; Gabor, Allen; Higgins, Craig; Sun, Lei; Mack, Chris A.
2017-03-01
Our paper will use stochastic simulations to explore how EUV pattern roughness can cause device failure through rare events, so-called "black swans". We examine the impact of stochastic noise on the yield of simple wiring patterns with 36nm pitch, corresponding to 7nm node logic, using a local Critical Dimension (CD)-based fail criteria Contact hole failures are examined in a similar way. For our nominal EUV process, local CD uniformity variation and local Pattern Placement Error variation was observed, but no pattern failures were seen in the modest (few thousand) number of features simulated. We degraded the image quality by incorporating Moving Standard Deviation (MSD) blurring to degrade the Image Log-Slope (ILS), and were able to find conditions where pattern failures were observed. We determined the Line Width Roughness (LWR) value as a function of the ILS. By use of an artificial "step function" image degraded by various MSD blur, we were able to extend the LWR vs ILS curve into regimes that might be available for future EUV imagery. As we decreased the image quality, we observed LWR grow and also began to see pattern failures. For high image quality, we saw CD distributions that were symmetrical and close to Gaussian in shape. Lower image quality caused CD distributions that were asymmetric, with "fat tails" on the low CD side (under-exposed) which were associated with pattern failures. Similar non-Gaussian CD distributions were associated with image conditions that caused missing contact holes, i.e. CD=0.
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Przybytek, Michal; Helgaker, Trygve
2013-08-07
We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.
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Vibrational analysis and quantum chemical calculations of 2,2‧-bipyridine Zinc(II) halide complexes
NASA Astrophysics Data System (ADS)
Ozel, Aysen E.; Kecel, Serda; Akyuz, Sevim
2007-05-01
In this study the molecular structure and vibrational spectra of Zn(2,2'-bipyridine)X 2 (X = Cl and Br) complexes were studied in their ground states by computational vibrational study and scaled quantum mechanical (SQM) analysis. The geometry optimization, vibrational wavenumber and intensity calculations of free and coordinated 2,2'-bipyridine were carried out with the Gaussian03 program package by using Hartree-Fock (HF) and Density Functional Theory (DFT) with B3LYP functional and 6-31G (d,p) basis set. The total energy distributions (TED) of the vibrational modes were calculated by using Scaled Quantum Mechanical (SQM) analysis. Fundamentals were characterised by their total energy distributions. Coordination sensitive modes of 2,2'-bipyridine were determined.
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Richardson, Magnus J E; Gerstner, Wulfram
2005-04-01
The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.
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Numerical solution of transport equation for applications in environmental hydraulics and hydrology
NASA Astrophysics Data System (ADS)
Rashidul Islam, M.; Hanif Chaudhry, M.
1997-04-01
The advective term in the one-dimensional transport equation, when numerically discretized, produces artificial diffusion. To minimize such artificial diffusion, which vanishes only for Courant number equal to unity, transport owing to advection has been modeled separately. The numerical solution of the advection equation for a Gaussian initial distribution is well established; however, large oscillations are observed when applied to an initial distribution with sleep gradients, such as trapezoidal distribution of a constituent or propagation of mass from a continuous input. In this study, the application of seven finite-difference schemes and one polynomial interpolation scheme is investigated to solve the transport equation for both Gaussian and non-Gaussian (trapezoidal) initial distributions. The results obtained from the numerical schemes are compared with the exact solutions. A constant advective velocity is assumed throughout the transport process. For a Gaussian distribution initial condition, all eight schemes give excellent results, except the Lax scheme which is diffusive. In application to the trapezoidal initial distribution, explicit finite-difference schemes prove to be superior to implicit finite-difference schemes because the latter produce large numerical oscillations near the steep gradients. The Warming-Kutler-Lomax (WKL) explicit scheme is found to be better among this group. The Hermite polynomial interpolation scheme yields the best result for a trapezoidal distribution among all eight schemes investigated. The second-order accurate schemes are sufficiently accurate for most practical problems, but the solution of unusual problems (concentration with steep gradient) requires the application of higher-order (e.g. third- and fourth-order) accurate schemes.
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A novel multitarget model of radiation-induced cell killing based on the Gaussian distribution.
Zhao, Lei; Mi, Dong; Sun, Yeqing
2017-05-07
The multitarget version of the traditional target theory based on the Poisson distribution is still used to describe the dose-survival curves of cells after ionizing radiation in radiobiology and radiotherapy. However, noting that the usual ionizing radiation damage is the result of two sequential stochastic processes, the probability distribution of the damage number per cell should follow a compound Poisson distribution, like e.g. Neyman's distribution of type A (N. A.). In consideration of that the Gaussian distribution can be considered as the approximation of the N. A. in the case of high flux, a multitarget model based on the Gaussian distribution is proposed to describe the cell inactivation effects in low linear energy transfer (LET) radiation with high dose-rate. Theoretical analysis and experimental data fitting indicate that the present theory is superior to the traditional multitarget model and similar to the Linear - Quadratic (LQ) model in describing the biological effects of low-LET radiation with high dose-rate, and the parameter ratio in the present model can be used as an alternative indicator to reflect the radiation damage and radiosensitivity of the cells. Copyright © 2017 Elsevier Ltd. All rights reserved.
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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.
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Biktashev, Vadim N
2014-04-01
We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.
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Continuous-variable quantum key distribution with Gaussian source noise
DOE Office of Scientific and Technical Information (OSTI.GOV)
Shen Yujie; Peng Xiang; Yang Jian
2011-05-15
Source noise affects the security of continuous-variable quantum key distribution (CV QKD) and is difficult to analyze. We propose a model to characterize Gaussian source noise through introducing a neutral party (Fred) who induces the noise with a general unitary transformation. Without knowing Fred's exact state, we derive the security bounds for both reverse and direct reconciliations and show that the bound for reverse reconciliation is tight.
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NASA Astrophysics Data System (ADS)
Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.
2006-11-01
The simulation of biological systems by means of current empirical force fields presents shortcomings due to their lack of accuracy, especially in the description of the nonbonded terms. We have previously introduced a force field based on density fitting termed the Gaussian electrostatic model-0 (GEM-0) J.-P. Piquemal et al. [J. Chem. Phys. 124, 104101 (2006)] that improves the description of the nonbonded interactions. GEM-0 relies on density fitting methodology to reproduce each contribution of the constrained space orbital variation (CSOV) energy decomposition scheme, by expanding the electronic density of the molecule in s-type Gaussian functions centered at specific sites. In the present contribution we extend the Coulomb and exchange components of the force field to auxiliary basis sets of arbitrary angular momentum. Since the basis functions with higher angular momentum have directionality, a reference molecular frame (local frame) formalism is employed for the rotation of the fitted expansion coefficients. In all cases the intermolecular interaction energies are calculated by means of Hermite Gaussian functions using the McMurchie-Davidson [J. Comput. Phys. 26, 218 (1978)] recursion to calculate all the required integrals. Furthermore, the use of Hermite Gaussian functions allows a point multipole decomposition determination at each expansion site. Additionally, the issue of computational speed is investigated by reciprocal space based formalisms which include the particle mesh Ewald (PME) and fast Fourier-Poisson (FFP) methods. Frozen-core (Coulomb and exchange-repulsion) intermolecular interaction results for ten stationary points on the water dimer potential-energy surface, as well as a one-dimensional surface scan for the canonical water dimer, formamide, stacked benzene, and benzene water dimers, are presented. All results show reasonable agreement with the corresponding CSOV calculated reference contributions, around 0.1 and 0.15kcal/mol error for Coulomb and exchange, respectively. Timing results for single Coulomb energy-force calculations for (H2O)n, n =64, 128, 256, 512, and 1024, in periodic boundary conditions with PME and FFP at two different rms force tolerances are also presented. For the small and intermediate auxiliaries, PME shows faster times than FFP at both accuracies and the advantage of PME widens at higher accuracy, while for the largest auxiliary, the opposite occurs.
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Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.
2007-01-01
The simulation of biological systems by means of current empirical force fields presents shortcomings due to their lack of accuracy, especially in the description of the nonbonded terms. We have previously introduced a force field based on density fitting termed the Gaussian electrostatic model-0 (GEM-0) J.-P. Piquemal et al. [J. Chem. Phys. 124, 104101 (2006)] that improves the description of the nonbonded interactions. GEM-0 relies on density fitting methodology to reproduce each contribution of the constrained space orbital variation (CSOV) energy decomposition scheme, by expanding the electronic density of the molecule in s-type Gaussian functions centered at specific sites. In the present contribution we extend the Coulomb and exchange components of the force field to auxiliary basis sets of arbitrary angular momentum. Since the basis functions with higher angular momentum have directionality, a reference molecular frame (local frame) formalism is employed for the rotation of the fitted expansion coefficients. In all cases the intermolecular interaction energies are calculated by means of Hermite Gaussian functions using the McMurchie-Davidson [J. Comput. Phys. 26, 218 (1978)] recursion to calculate all the required integrals. Furthermore, the use of Hermite Gaussian functions allows a point multipole decomposition determination at each expansion site. Additionally, the issue of computational speed is investigated by reciprocal space based formalisms which include the particle mesh Ewald (PME) and fast Fourier-Poisson (FFP) methods. Frozen-core (Coulomb and exchange-repulsion) intermolecular interaction results for ten stationary points on the water dimer potential-energy surface, as well as a one-dimensional surface scan for the canonical water dimer, formamide, stacked benzene, and benzene water dimers, are presented. All results show reasonable agreement with the corresponding CSOV calculated reference contributions, around 0.1 and 0.15 kcal/mol error for Coulomb and exchange, respectively. Timing results for single Coulomb energy-force calculations for (H2O)n, n=64, 128, 256, 512, and 1024, in periodic boundary conditions with PME and FFP at two different rms force tolerances are also presented. For the small and intermediate auxiliaries, PME shows faster times than FFP at both accuracies and the advantage of PME widens at higher accuracy, while for the largest auxiliary, the opposite occurs. PMID:17115732
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Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.
Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi
2015-02-01
We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.
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Gibbs sampling on large lattice with GMRF
NASA Astrophysics Data System (ADS)
Marcotte, Denis; Allard, Denis
2018-02-01
Gibbs sampling is routinely used to sample truncated Gaussian distributions. These distributions naturally occur when associating latent Gaussian fields to category fields obtained by discrete simulation methods like multipoint, sequential indicator simulation and object-based simulation. The latent Gaussians are often used in data assimilation and history matching algorithms. When the Gibbs sampling is applied on a large lattice, the computing cost can become prohibitive. The usual practice of using local neighborhoods is unsatisfying as it can diverge and it does not reproduce exactly the desired covariance. A better approach is to use Gaussian Markov Random Fields (GMRF) which enables to compute the conditional distributions at any point without having to compute and invert the full covariance matrix. As the GMRF is locally defined, it allows simultaneous updating of all points that do not share neighbors (coding sets). We propose a new simultaneous Gibbs updating strategy on coding sets that can be efficiently computed by convolution and applied with an acceptance/rejection method in the truncated case. We study empirically the speed of convergence, the effect of choice of boundary conditions, of the correlation range and of GMRF smoothness. We show that the convergence is slower in the Gaussian case on the torus than for the finite case studied in the literature. However, in the truncated Gaussian case, we show that short scale correlation is quickly restored and the conditioning categories at each lattice point imprint the long scale correlation. Hence our approach enables to realistically apply Gibbs sampling on large 2D or 3D lattice with the desired GMRF covariance.
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NASA Astrophysics Data System (ADS)
Boyer, Denis; Pineda, Inti
2016-02-01
Among Markovian processes, the hallmark of Lévy flights is superdiffusion, or faster-than-Brownian dynamics. Here we show that Lévy laws, as well as Gaussian distributions, can also be the limit distributions of processes with long-range memory that exhibit very slow diffusion, logarithmic in time. These processes are path dependent and anomalous motion emerges from frequent relocations to already visited sites. We show how the central limit theorem is modified in this context, keeping the usual distinction between analytic and nonanalytic characteristic functions. A fluctuation-dissipation relation is also derived. Our results may have important applications in the study of animal and human displacements.
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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.
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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.
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The effect of spherical aberration on the phase singularities of focused dark-hollow Gaussian beams
NASA Astrophysics Data System (ADS)
Luo, Yamei; Lü, Baida
2009-06-01
The phase singularities of focused dark-hollow Gaussian beams in the presence of spherical aberration are studied. It is shown that the evolution behavior of phase singularities of focused dark-hollow Gaussian beams in the focal region depends not only on the truncation parameter and beam order, but also on the spherical aberration. The spherical aberration leads to an asymmetric spatial distribution of singularities outside the focal plane and to a shift of singularities near the focal plane. The reorganization process of singularities and spatial distribution of singularities are additionally dependent on the sign of the spherical aberration. The results are illustrated by numerical examples.
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Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J
2017-01-01
Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D , observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄ . When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model.
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Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J.
2017-01-01
Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D, observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄. When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model. PMID:28989561