Sample records for gaussian random fields
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Zentner, I.; Ferré, G., E-mail: gregoire.ferre@ponts.org; Poirion, F.
2016-06-01
In this paper, a new method for the identification and simulation of non-Gaussian and non-stationary stochastic fields given a database is proposed. It is based on two successive biorthogonal decompositions aiming at representing spatio–temporal stochastic fields. The proposed double expansion allows to build the model even in the case of large-size problems by separating the time, space and random parts of the field. A Gaussian kernel estimator is used to simulate the high dimensional set of random variables appearing in the decomposition. The capability of the method to reproduce the non-stationary and non-Gaussian features of random phenomena is illustrated bymore » applications to earthquakes (seismic ground motion) and sea states (wave heights).« less
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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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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)
Ding, Jian; Li, Li
2018-05-01
We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.
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NASA Astrophysics Data System (ADS)
Ding, Jian; Li, Li
2018-06-01
We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.
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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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Testing for a Signal with Unknown Location and Scale in a Stationary Gaussian Random Field
1994-01-07
Secondary 60D05, 52A22. Key words and phrases. Euler characteristic, integral geometry, image analysis , Gaussian fields, volume of tubes. SUMMARY We...words and phrases. Euler characteristic, integral geometry. image analysis . Gaussian fields. volume of tubes. 20. AMST RACT (Coith..o an revmreo ef* It
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Random scalar fields and hyperuniformity
NASA Astrophysics Data System (ADS)
Ma, Zheng; Torquato, Salvatore
2017-06-01
Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystals and liquids. Hyperuniform systems have attracted recent attention because they are endowed with novel transport and optical properties. Recently, the hyperuniformity concept has been generalized to characterize two-phase media, scalar fields, and random vector fields. In this paper, we devise methods to explicitly construct hyperuniform scalar fields. Specifically, we analyze spatial patterns generated from Gaussian random fields, which have been used to model the microwave background radiation and heterogeneous materials, the Cahn-Hilliard equation for spinodal decomposition, and Swift-Hohenberg equations that have been used to model emergent pattern formation, including Rayleigh-Bénard convection. We show that the Gaussian random scalar fields can be constructed to be hyperuniform. We also numerically study the time evolution of spinodal decomposition patterns and demonstrate that they are hyperuniform in the scaling regime. Moreover, we find that labyrinth-like patterns generated by the Swift-Hohenberg equation are effectively hyperuniform. We show that thresholding (level-cutting) a hyperuniform Gaussian random field to produce a two-phase random medium tends to destroy the hyperuniformity of the progenitor scalar field. We then propose guidelines to achieve effectively hyperuniform two-phase media derived from thresholded non-Gaussian fields. Our investigation paves the way for new research directions to characterize the large-structure spatial patterns that arise in physics, chemistry, biology, and ecology. Moreover, our theoretical results are expected to guide experimentalists to synthesize new classes of hyperuniform materials with novel physical properties via coarsening processes and using state-of-the-art techniques, such as stereolithography and 3D printing.
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NASA Astrophysics Data System (ADS)
Hadjiagapiou, Ioannis A.; Velonakis, Ioannis N.
2018-07-01
The Sherrington-Kirkpatrick Ising spin glass model, in the presence of a random magnetic field, is investigated within the framework of the one-step replica symmetry breaking. The two random variables (exchange integral interaction Jij and random magnetic field hi) are drawn from a joint Gaussian probability density function characterized by a correlation coefficient ρ, assuming positive and negative values. The thermodynamic properties, the three different phase diagrams and system's parameters are computed with respect to the natural parameters of the joint Gaussian probability density function at non-zero and zero temperatures. The low temperature negative entropy controversy, a result of the replica symmetry approach, has been partly remedied in the current study, leading to a less negative result. In addition, the present system possesses two successive spin glass phase transitions with characteristic temperatures.
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Non-Gaussian Multi-resolution Modeling of Magnetosphere-Ionosphere Coupling Processes
NASA Astrophysics Data System (ADS)
Fan, M.; Paul, D.; Lee, T. C. M.; Matsuo, T.
2016-12-01
The most dynamic coupling between the magnetosphere and ionosphere occurs in the Earth's polar atmosphere. Our objective is to model scale-dependent stochastic characteristics of high-latitude ionospheric electric fields that originate from solar wind magnetosphere-ionosphere interactions. The Earth's high-latitude ionospheric electric field exhibits considerable variability, with increasing non-Gaussian characteristics at decreasing spatio-temporal scales. Accurately representing the underlying stochastic physical process through random field modeling is crucial not only for scientific understanding of the energy, momentum and mass exchanges between the Earth's magnetosphere and ionosphere, but also for modern technological systems including telecommunication, navigation, positioning and satellite tracking. While a lot of efforts have been made to characterize the large-scale variability of the electric field in the context of Gaussian processes, no attempt has been made so far to model the small-scale non-Gaussian stochastic process observed in the high-latitude ionosphere. We construct a novel random field model using spherical needlets as building blocks. The double localization of spherical needlets in both spatial and frequency domains enables the model to capture the non-Gaussian and multi-resolutional characteristics of the small-scale variability. The estimation procedure is computationally feasible due to the utilization of an adaptive Gibbs sampler. We apply the proposed methodology to the computational simulation output from the Lyon-Fedder-Mobarry (LFM) global magnetohydrodynamics (MHD) magnetosphere model. Our non-Gaussian multi-resolution model results in characterizing significantly more energy associated with the small-scale ionospheric electric field variability in comparison to Gaussian models. By accurately representing unaccounted-for additional energy and momentum sources to the Earth's upper atmosphere, our novel random field modeling approach will provide a viable remedy to the current numerical models' systematic biases resulting from the underestimation of high-latitude energy and momentum sources.
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Is the Non-Dipole Magnetic Field Random?
NASA Technical Reports Server (NTRS)
Walker, Andrew D.; Backus, George E.
1996-01-01
Statistical modelling of the Earth's magnetic field B has a long history. In particular, the spherical harmonic coefficients of scalar fields derived from B can be treated as Gaussian random variables. In this paper, we give examples of highly organized fields whose spherical harmonic coefficients pass tests for independent Gaussian random variables. The fact that coefficients at some depth may be usefully summarized as independent samples from a normal distribution need not imply that there really is some physical, random process at that depth. In fact, the field can be extremely structured and still be regarded for some purposes as random. In this paper, we examined the radial magnetic field B(sub r) produced by the core, but the results apply to any scalar field on the core-mantle boundary (CMB) which determines B outside the CMB.
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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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A New Algorithm with Plane Waves and Wavelets for Random Velocity Fields with Many Spatial Scales
NASA Astrophysics Data System (ADS)
Elliott, Frank W.; Majda, Andrew J.
1995-03-01
A new Monte Carlo algorithm for constructing and sampling stationary isotropic Gaussian random fields with power-law energy spectrum, infrared divergence, and fractal self-similar scaling is developed here. The theoretical basis for this algorithm involves the fact that such a random field is well approximated by a superposition of random one-dimensional plane waves involving a fixed finite number of directions. In general each one-dimensional plane wave is the sum of a random shear layer and a random acoustical wave. These one-dimensional random plane waves are then simulated by a wavelet Monte Carlo method for a single space variable developed recently by the authors. The computational results reported in this paper demonstrate remarkable low variance and economical representation of such Gaussian random fields through this new algorithm. In particular, the velocity structure function for an imcorepressible isotropic Gaussian random field in two space dimensions with the Kolmogoroff spectrum can be simulated accurately over 12 decades with only 100 realizations of the algorithm with the scaling exponent accurate to 1.1% and the constant prefactor accurate to 6%; in fact, the exponent of the velocity structure function can be computed over 12 decades within 3.3% with only 10 realizations. Furthermore, only 46,592 active computational elements are utilized in each realization to achieve these results for 12 decades of scaling behavior.
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Poly-Gaussian model of randomly rough surface in rarefied gas flow
DOE Office of Scientific and Technical Information (OSTI.GOV)
Aksenova, Olga A.; Khalidov, Iskander A.
2014-12-09
Surface roughness is simulated by the model of non-Gaussian random process. Our results for the scattering of rarefied gas atoms from a rough surface using modified approach to the DSMC calculation of rarefied gas flow near a rough surface are developed and generalized applying the poly-Gaussian model representing probability density as the mixture of Gaussian densities. The transformation of the scattering function due to the roughness is characterized by the roughness operator. Simulating rough surface of the walls by the poly-Gaussian random field expressed as integrated Wiener process, we derive a representation of the roughness operator that can be appliedmore » in numerical DSMC methods as well as in analytical investigations.« less
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Reduced Wiener Chaos representation of random fields via basis adaptation and projection
DOE Office of Scientific and Technical Information (OSTI.GOV)
Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu; Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089; Ghanem, Roger G., E-mail: ghanem@usc.edu
2017-07-15
A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.
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Reduced Wiener Chaos representation of random fields via basis adaptation and projection
NASA Astrophysics Data System (ADS)
Tsilifis, Panagiotis; Ghanem, Roger G.
2017-07-01
A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.
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Discretisation Schemes for Level Sets of Planar Gaussian Fields
NASA Astrophysics Data System (ADS)
Beliaev, D.; Muirhead, S.
2018-01-01
Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic compact manifolds. Our work is motivated by questions about the geometry of such random functions, in particular relating to the structure of their nodal and level sets. We study four discretisation schemes that extract information about level sets of planar Gaussian fields. Each scheme recovers information up to a different level of precision, and each requires a maximum mesh-size in order to be valid with high probability. The first two schemes are generalisations and enhancements of similar schemes that have appeared in the literature (Beffara and Gayet in Publ Math IHES, 2017. https://doi.org/10.1007/s10240-017-0093-0; Mischaikow and Wanner in Ann Appl Probab 17:980-1018, 2007); these give complete topological information about the level sets on either a local or global scale. As an application, we improve the results in Beffara and Gayet (2017) on Russo-Seymour-Welsh estimates for the nodal set of positively-correlated planar Gaussian fields. The third and fourth schemes are, to the best of our knowledge, completely new. The third scheme is specific to the nodal set of the random plane wave, and provides global topological information about the nodal set up to `visible ambiguities'. The fourth scheme gives a way to approximate the mean number of excursion domains of planar Gaussian fields.
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Connectivity ranking of heterogeneous random conductivity models
NASA Astrophysics Data System (ADS)
Rizzo, C. B.; de Barros, F.
2017-12-01
To overcome the challenges associated with hydrogeological data scarcity, the hydraulic conductivity (K) field is often represented by a spatial random process. The state-of-the-art provides several methods to generate 2D or 3D random K-fields, such as the classic multi-Gaussian fields or non-Gaussian fields, training image-based fields and object-based fields. We provide a systematic comparison of these models based on their connectivity. We use the minimum hydraulic resistance as a connectivity measure, which it has been found to be strictly correlated with early time arrival of dissolved contaminants. A computationally efficient graph-based algorithm is employed, allowing a stochastic treatment of the minimum hydraulic resistance through a Monte-Carlo approach and therefore enabling the computation of its uncertainty. The results show the impact of geostatistical parameters on the connectivity for each group of random fields, being able to rank the fields according to their minimum hydraulic resistance.
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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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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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NASA Astrophysics Data System (ADS)
Rychlik, Igor; Mao, Wengang
2018-02-01
The wind speed variability in the North Atlantic has been successfully modelled using a spatio-temporal transformed Gaussian field. However, this type of model does not correctly describe the extreme wind speeds attributed to tropical storms and hurricanes. In this study, the transformed Gaussian model is further developed to include the occurrence of severe storms. In this new model, random components are added to the transformed Gaussian field to model rare events with extreme wind speeds. The resulting random field is locally stationary and homogeneous. The localized dependence structure is described by time- and space-dependent parameters. The parameters have a natural physical interpretation. To exemplify its application, the model is fitted to the ECMWF ERA-Interim reanalysis data set. The model is applied to compute long-term wind speed distributions and return values, e.g., 100- or 1000-year extreme wind speeds, and to simulate random wind speed time series at a fixed location or spatio-temporal wind fields around that location.
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On Nonlinear Functionals of Random Spherical Eigenfunctions
NASA Astrophysics Data System (ADS)
Marinucci, Domenico; Wigman, Igor
2014-05-01
We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.
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Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel
2016-07-20
A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of fieldmore » and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.« less
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel
A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of fieldmore » and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.« less
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Stochastic inflation lattice simulations - Ultra-large scale structure of the universe
NASA Technical Reports Server (NTRS)
Salopek, D. S.
1991-01-01
Non-Gaussian fluctuations for structure formation may arise in inflation from the nonlinear interaction of long wavelength gravitational and scalar fields. Long wavelength fields have spatial gradients, a (exp -1), small compared to the Hubble radius, and they are described in terms of classical random fields that are fed by short wavelength quantum noise. Lattice Langevin calculations are given for a toy model with a scalar field interacting with an exponential potential where one can obtain exact analytic solutions of the Fokker-Planck equation. For single scalar field models that are consistent with current microwave background fluctuations, the fluctuations are Gaussian. However, for scales much larger than our observable Universe, one expects large metric fluctuations that are non-Gaussian. This example illuminates non-Gaussian models involving multiple scalar fields which are consistent with current microwave background limits.
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Entropy of level-cut random Gaussian structures at different volume fractions
NASA Astrophysics Data System (ADS)
Marčelja, Stjepan
2017-10-01
Cutting random Gaussian fields at a given level can create a variety of morphologically different two- or several-phase structures that have often been used to describe physical systems. The entropy of such structures depends on the covariance function of the generating Gaussian random field, which in turn depends on its spectral density. But the entropy of level-cut structures also depends on the volume fractions of different phases, which is determined by the selection of the cutting level. This dependence has been neglected in earlier work. We evaluate the entropy of several lattice models to show that, even in the cases of strongly coupled systems, the dependence of the entropy of level-cut structures on molar fractions of the constituents scales with the simple ideal noninteracting system formula. In the last section, we discuss the application of the results to binary or ternary fluids and microemulsions.
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Kernel-Correlated Levy Field Driven Forward Rate and Application to Derivative Pricing
DOE Office of Scientific and Technical Information (OSTI.GOV)
Bo Lijun; Wang Yongjin; Yang Xuewei, E-mail: xwyangnk@yahoo.com.cn
2013-08-01
We propose a term structure of forward rates driven by a kernel-correlated Levy random field under the HJM framework. The kernel-correlated Levy random field is composed of a kernel-correlated Gaussian random field and a centered Poisson random measure. We shall give a criterion to preclude arbitrage under the risk-neutral pricing measure. As applications, an interest rate derivative with general payoff functional is priced under this pricing measure.
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Possible Statistics of Two Coupled Random Fields: Application to Passive Scalar
NASA Technical Reports Server (NTRS)
Dubrulle, B.; He, Guo-Wei; Bushnell, Dennis M. (Technical Monitor)
2000-01-01
We use the relativity postulate of scale invariance to derive the similarity transformations between two coupled scale-invariant random elds at different scales. We nd the equations leading to the scaling exponents. This formulation is applied to the case of passive scalars advected i) by a random Gaussian velocity field; and ii) by a turbulent velocity field. In the Gaussian case, we show that the passive scalar increments follow a log-Levy distribution generalizing Kraichnan's solution and, in an appropriate limit, a log-normal distribution. In the turbulent case, we show that when the velocity increments follow a log-Poisson statistics, the passive scalar increments follow a statistics close to log-Poisson. This result explains the experimental observations of Ruiz et al. about the temperature increments.
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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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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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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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Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field
NASA Astrophysics Data System (ADS)
Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra
2017-10-01
In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.
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Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field.
Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra
2017-10-28
In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.
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NASA Astrophysics Data System (ADS)
Libera, A.; de Barros, F.; Riva, M.; Guadagnini, A.
2016-12-01
Managing contaminated groundwater systems is an arduous task for multiple reasons. First, subsurface hydraulic properties are heterogeneous and the high costs associated with site characterization leads to data scarcity (therefore, model predictions are uncertain). Second, it is common for water agencies to schedule groundwater extraction through a temporal sequence of pumping rates to maximize the benefits to anthropogenic activities and minimize the environmental footprint of the withdrawal operations. The temporal variability in pumping rates and aquifer heterogeneity affect dilution rates of contaminant plumes and chemical concentration breakthrough curves (BTCs) at the well. While contaminant transport under steady-state pumping is widely studied, the manner in which a given time-varying pumping schedule affects contaminant plume behavior is tackled only marginally. At the same time, most studies focus on the impact of Gaussian random hydraulic conductivity (K) fields on transport. Here, we systematically analyze the significance of the random space function (RSF) model characterizing K in the presence of distinct pumping operations on the uncertainty of the concentration BTC at the operating well. We juxtapose Monte Carlo based numerical results associated with two models: (a) a recently proposed Generalized Sub-Gaussian model which allows capturing non-Gaussian statistical scaling features of RSFs such as hydraulic conductivity, and (b) the commonly used Gaussian field approximation. Our novel results include an appraisal of the coupled effect of (a) the model employed to depict the random spatial variability of K and (b) transient flow regime, as induced by a temporally varying pumping schedule, on the concentration BTC at the operating well. We systematically quantify the sensitivity of the uncertainty in the contaminant BTC to the RSF model adopted for K (non-Gaussian or Gaussian) in the presence of diverse well pumping schedules. Results contribute to determine conditions under which any of these two key factors prevails on the other.
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Multi-fidelity Gaussian process regression for prediction of random fields
DOE Office of Scientific and Technical Information (OSTI.GOV)
Parussini, L.; Venturi, D., E-mail: venturi@ucsc.edu; Perdikaris, P.
We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgersmore » equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.« less
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Subcritical Multiplicative Chaos for Regularized Counting Statistics from Random Matrix Theory
NASA Astrophysics Data System (ADS)
Lambert, Gaultier; Ostrovsky, Dmitry; Simm, Nick
2018-05-01
For an {N × N} Haar distributed random unitary matrix U N , we consider the random field defined by counting the number of eigenvalues of U N in a mesoscopic arc centered at the point u on the unit circle. We prove that after regularizing at a small scale {ɛN > 0}, the renormalized exponential of this field converges as N \\to ∞ to a Gaussian multiplicative chaos measure in the whole subcritical phase. We discuss implications of this result for obtaining a lower bound on the maximum of the field. We also show that the moments of the total mass converge to a Selberg-like integral and by taking a further limit as the size of the arc diverges, we establish part of the conjectures in Ostrovsky (Nonlinearity 29(2):426-464, 2016). By an analogous construction, we prove that the multiplicative chaos measure coming from the sine process has the same distribution, which strongly suggests that this limiting object should be universal. Our approach to the L 1-phase is based on a generalization of the construction in Berestycki (Electron Commun Probab 22(27):12, 2017) to random fields which are only asymptotically Gaussian. In particular, our method could have applications to other random fields coming from either random matrix theory or a different context.
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Dynamical transition for a particle in a squared Gaussian potential
NASA Astrophysics Data System (ADS)
Touya, C.; Dean, D. S.
2007-02-01
We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by ψ = phi2/2 where phi is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.
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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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A Gaussian random field model for similarity-based smoothing in Bayesian disease mapping.
Baptista, Helena; Mendes, Jorge M; MacNab, Ying C; Xavier, Miguel; Caldas-de-Almeida, José
2016-08-01
Conditionally specified Gaussian Markov random field (GMRF) models with adjacency-based neighbourhood weight matrix, commonly known as neighbourhood-based GMRF models, have been the mainstream approach to spatial smoothing in Bayesian disease mapping. In the present paper, we propose a conditionally specified Gaussian random field (GRF) model with a similarity-based non-spatial weight matrix to facilitate non-spatial smoothing in Bayesian disease mapping. The model, named similarity-based GRF, is motivated for modelling disease mapping data in situations where the underlying small area relative risks and the associated determinant factors do not vary systematically in space, and the similarity is defined by "similarity" with respect to the associated disease determinant factors. The neighbourhood-based GMRF and the similarity-based GRF are compared and accessed via a simulation study and by two case studies, using new data on alcohol abuse in Portugal collected by the World Mental Health Survey Initiative and the well-known lip cancer data in Scotland. In the presence of disease data with no evidence of positive spatial correlation, the simulation study showed a consistent gain in efficiency from the similarity-based GRF, compared with the adjacency-based GMRF with the determinant risk factors as covariate. This new approach broadens the scope of the existing conditional autocorrelation models. © The Author(s) 2016.
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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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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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Non-Gaussian microwave background fluctuations from nonlinear gravitational effects
NASA Technical Reports Server (NTRS)
Salopek, D. S.; Kunstatter, G. (Editor)
1991-01-01
Whether the statistics of primordial fluctuations for structure formation are Gaussian or otherwise may be determined if the Cosmic Background Explorer (COBE) Satellite makes a detection of the cosmic microwave-background temperature anisotropy delta T(sub CMB)/T(sub CMB). Non-Gaussian fluctuations may be generated in the chaotic inflationary model if two scalar fields interact nonlinearly with gravity. Theoretical contour maps are calculated for the resulting Sachs-Wolfe temperature fluctuations at large angular scales (greater than 3 degrees). In the long-wavelength approximation, one can confidently determine the nonlinear evolution of quantum noise with gravity during the inflationary epoch because: (1) different spatial points are no longer in causal contact; and (2) quantum gravity corrections are typically small-- it is sufficient to model the system using classical random fields. If the potential for two scalar fields V(phi sub 1, phi sub 2) possesses a sharp feature, then non-Gaussian fluctuations may arise. An explicit model is given where cold spots in delta T(sub CMB)/T(sub CMB) maps are suppressed as compared to the Gaussian case. The fluctuations are essentially scale-invariant.
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Najafi, M N; Nezhadhaghighi, M Ghasemi
2017-03-01
We characterize the carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity in zero gate voltage. We provide detailed analysis on the resulting spatially inhomogeneous electron gas, taking into account the particle-particle interaction and the remote Coulomb disorder on an equal footing within the Thomas-Fermi-Dirac theory. We present some general features of the carrier density probability measure of the graphene sheet. We also show that, when viewed as a random surface, the electron-hole puddles at zero chemical potential show peculiar self-similar statistical properties. Although the disorder potential is chosen to be Gaussian, we show that the charge field is non-Gaussian with unusual Kondev relations, which can be regarded as a new class of two-dimensional random-field surfaces. Using Schramm-Loewner (SLE) evolution, we numerically demonstrate that the ungated graphene has conformal invariance and the random zero-charge density contours are SLE_{κ} with κ=1.8±0.2, consistent with c=-3 conformal field theory.
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Adzhemyan, L Ts; Antonov, N V; Honkonen, J; Kim, T L
2005-01-01
The field theoretic renormalization group and operator-product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the Navier-Stokes equation, subject to an external random stirring force with the correlation function proportional to delta(t- t')k(4-d-2epsilon). It is shown that the scalar field is intermittent already for small epsilon, its structure functions display anomalous scaling behavior, and the corresponding exponents can be systematically calculated as series in epsilon. The practical calculation is accomplished to order epsilon2 (two-loop approximation), including anisotropic sectors. As for the well-known Kraichnan rapid-change model, the anomalous scaling results from the existence in the model of composite fields (operators) with negative scaling dimensions, identified with the anomalous exponents. Thus the mechanism of the origin of anomalous scaling appears similar for the Gaussian model with zero correlation time and the non-Gaussian model with finite correlation time. It should be emphasized that, in contrast to Gaussian velocity ensembles with finite correlation time, the model and the perturbation theory discussed here are manifestly Galilean covariant. The relevance of these results for real passive advection and comparison with the Gaussian models and experiments are briefly discussed.
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Relativistic diffusive motion in random electromagnetic fields
NASA Astrophysics Data System (ADS)
Haba, Z.
2011-08-01
We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Jüttner equilibrium at the inverse temperature β-1 = mc2. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).
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A stochastic-geometric model of soil variation in Pleistocene patterned ground
NASA Astrophysics Data System (ADS)
Lark, Murray; Meerschman, Eef; Van Meirvenne, Marc
2013-04-01
In this paper we examine the spatial variability of soil in parent material with complex spatial structure which arises from complex non-linear geomorphic processes. We show that this variability can be better-modelled by a stochastic-geometric model than by a standard Gaussian random field. The benefits of the new model are seen in the reproduction of features of the target variable which influence processes like water movement and pollutant dispersal. Complex non-linear processes in the soil give rise to properties with non-Gaussian distributions. Even under a transformation to approximate marginal normality, such variables may have a more complex spatial structure than the Gaussian random field model of geostatistics can accommodate. In particular the extent to which extreme values of the variable are connected in spatially coherent regions may be misrepresented. As a result, for example, geostatistical simulation generally fails to reproduce the pathways for preferential flow in an environment where coarse infill of former fluvial channels or coarse alluvium of braided streams creates pathways for rapid movement of water. Multiple point geostatistics has been developed to deal with this problem. Multiple point methods proceed by sampling from a set of training images which can be assumed to reproduce the non-Gaussian behaviour of the target variable. The challenge is to identify appropriate sources of such images. In this paper we consider a mode of soil variation in which the soil varies continuously, exhibiting short-range lateral trends induced by local effects of the factors of soil formation which vary across the region of interest in an unpredictable way. The trends in soil variation are therefore only apparent locally, and the soil variation at regional scale appears random. We propose a stochastic-geometric model for this mode of soil variation called the Continuous Local Trend (CLT) model. We consider a case study of soil formed in relict patterned ground with pronounced lateral textural variations arising from the presence of infilled ice-wedges of Pleistocene origin. We show how knowledge of the pedogenetic processes in this environment, along with some simple descriptive statistics, can be used to select and fit a CLT model for the apparent electrical conductivity (ECa) of the soil. We use the model to simulate realizations of the CLT process, and compare these with realizations of a fitted Gaussian random field. We show how statistics that summarize the spatial coherence of regions with small values of ECa, which are expected to have coarse texture and so larger saturated hydraulic conductivity, are better reproduced by the CLT model than by the Gaussian random field. This suggests that the CLT model could be used to generate an unlimited supply of training images to allow multiple point geostatistical simulation or prediction of this or similar variables.
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Response of space shuttle insulation panels to acoustic noise pressure
NASA Technical Reports Server (NTRS)
Vaicaitis, R.
1976-01-01
The response of reusable space shuttle insulation panels to random acoustic pressure fields are studied. The basic analytical approach in formulating the governing equations of motion uses a Rayleigh-Ritz technique. The input pressure field is modeled as a stationary Gaussian random process for which the cross-spectral density function is known empirically from experimental measurements. The response calculations are performed in both frequency and time domain.
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Cluster mass inference via random field theory.
Zhang, Hui; Nichols, Thomas E; Johnson, Timothy D
2009-01-01
Cluster extent and voxel intensity are two widely used statistics in neuroimaging inference. Cluster extent is sensitive to spatially extended signals while voxel intensity is better for intense but focal signals. In order to leverage strength from both statistics, several nonparametric permutation methods have been proposed to combine the two methods. Simulation studies have shown that of the different cluster permutation methods, the cluster mass statistic is generally the best. However, to date, there is no parametric cluster mass inference available. In this paper, we propose a cluster mass inference method based on random field theory (RFT). We develop this method for Gaussian images, evaluate it on Gaussian and Gaussianized t-statistic images and investigate its statistical properties via simulation studies and real data. Simulation results show that the method is valid under the null hypothesis and demonstrate that it can be more powerful than the cluster extent inference method. Further, analyses with a single subject and a group fMRI dataset demonstrate better power than traditional cluster size inference, and good accuracy relative to a gold-standard permutation test.
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Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs
NASA Astrophysics Data System (ADS)
Reddy, Tulasi Ram; Vadlamani, Sreekar; Yogeshwaran, D.
2018-04-01
Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of α -mixing (for local statistics) and exponential α -mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.
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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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NASA Astrophysics Data System (ADS)
Troncossi, M.; Di Sante, R.; Rivola, A.
2016-10-01
In the field of vibration qualification testing, random excitations are typically imposed on the tested system in terms of a power spectral density (PSD) profile. This is the one of the most popular ways to control the shaker or slip table for durability tests. However, these excitations (and the corresponding system responses) exhibit a Gaussian probability distribution, whereas not all real-life excitations are Gaussian, causing the response to be also non-Gaussian. In order to introduce non-Gaussian peaks, a further parameter, i.e., kurtosis, has to be controlled in addition to the PSD. However, depending on the specimen behaviour and input signal characteristics, the use of non-Gaussian excitations with high kurtosis and a given PSD does not automatically imply a non-Gaussian stress response. For an experimental investigation of these coupled features, suitable measurement methods need to be developed in order to estimate the stress amplitude response at critical failure locations and consequently evaluate the input signals most representative for real-life, non-Gaussian excitations. In this paper, a simple test rig with a notched cantilevered specimen was developed to measure the response and examine the kurtosis values in the case of stationary Gaussian, stationary non-Gaussian, and burst non-Gaussian excitation signals. The laser Doppler vibrometry technique was used in this type of test for the first time, in order to estimate the specimen stress amplitude response as proportional to the differential displacement measured at the notch section ends. A method based on the use of measurements using accelerometers to correct for the occasional signal dropouts occurring during the experiment is described. The results demonstrate the ability of the test procedure to evaluate the output signal features and therefore to select the most appropriate input signal for the fatigue test.
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Cosmic Rays in Intermittent Magnetic Fields
DOE Office of Scientific and Technical Information (OSTI.GOV)
Shukurov, Anvar; Seta, Amit; Bushby, Paul J.
The propagation of cosmic rays in turbulent magnetic fields is a diffusive process driven by the scattering of the charged particles by random magnetic fluctuations. Such fields are usually highly intermittent, consisting of intense magnetic filaments and ribbons surrounded by weaker, unstructured fluctuations. Studies of cosmic-ray propagation have largely overlooked intermittency, instead adopting Gaussian random magnetic fields. Using test particle simulations, we calculate cosmic-ray diffusivity in intermittent, dynamo-generated magnetic fields. The results are compared with those obtained from non-intermittent magnetic fields having identical power spectra. The presence of magnetic intermittency significantly enhances cosmic-ray diffusion over a wide range of particlemore » energies. We demonstrate that the results can be interpreted in terms of a correlated random walk.« less
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EVOLUTION OF THE MAGNETIC FIELD LINE DIFFUSION COEFFICIENT AND NON-GAUSSIAN STATISTICS
DOE Office of Scientific and Technical Information (OSTI.GOV)
Snodin, A. P.; Ruffolo, D.; Matthaeus, W. H.
The magnetic field line random walk (FLRW) plays an important role in the transport of energy and particles in turbulent plasmas. For magnetic fluctuations that are transverse or almost transverse to a large-scale mean magnetic field, theories describing the FLRW usually predict asymptotic diffusion of magnetic field lines perpendicular to the mean field. Such theories often depend on the assumption that one can relate the Lagrangian and Eulerian statistics of the magnetic field via Corrsin’s hypothesis, and additionally take the distribution of magnetic field line displacements to be Gaussian. Here we take an ordinary differential equation (ODE) model with thesemore » underlying assumptions and test how well it describes the evolution of the magnetic field line diffusion coefficient in 2D+slab magnetic turbulence, by comparisons to computer simulations that do not involve such assumptions. In addition, we directly test the accuracy of the Corrsin approximation to the Lagrangian correlation. Over much of the studied parameter space we find that the ODE model is in fairly good agreement with computer simulations, in terms of both the evolution and asymptotic values of the diffusion coefficient. When there is poor agreement, we show that this can be largely attributed to the failure of Corrsin’s hypothesis rather than the assumption of Gaussian statistics of field line displacements. The degree of non-Gaussianity, which we measure in terms of the kurtosis, appears to be an indicator of how well Corrsin’s approximation works.« less
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Osborn, Sarah; Zulian, Patrick; Benson, Thomas; ...
2018-01-30
This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Osborn, Sarah; Zulian, Patrick; Benson, Thomas
This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less
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Inflation with a graceful exit in a random landscape
NASA Astrophysics Data System (ADS)
Pedro, F. G.; Westphal, A.
2017-03-01
We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N ≪ 10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
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Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows
NASA Technical Reports Server (NTRS)
He, Guowei; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
The Eulerian mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An Eulerian mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.
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Topology of large-scale structure in seeded hot dark matter models
NASA Technical Reports Server (NTRS)
Beaky, Matthew M.; Scherrer, Robert J.; Villumsen, Jens V.
1992-01-01
The topology of the isodensity surfaces in seeded hot dark matter models, in which static seed masses provide the density perturbations in a universe dominated by massive neutrinos is examined. When smoothed with a Gaussian window, the linear initial conditions in these models show no trace of non-Gaussian behavior for r0 equal to or greater than 5 Mpc (h = 1/2), except for very low seed densities, which show a shift toward isolated peaks. An approximate analytic expression is given for the genus curve expected in linear density fields from randomly distributed seed masses. The evolved models have a Gaussian topology for r0 = 10 Mpc, but show a shift toward a cellular topology with r0 = 5 Mpc; Gaussian models with an identical power spectrum show the same behavior.
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Peebles, P. J. E.
1998-01-01
It is argued that within the standard Big Bang cosmological model the bulk of the mass of the luminous parts of the large galaxies likely had been assembled by redshift z ∼ 10. Galaxy assembly this early would be difficult to fit in the widely discussed adiabatic cold dark matter model for structure formation, but it could agree with an isocurvature version in which the cold dark matter is the remnant of a massive scalar field frozen (or squeezed) from quantum fluctuations during inflation. The squeezed field fluctuations would be Gaussian with zero mean, and the distribution of the field mass therefore would be the square of a random Gaussian process. This offers a possibly interesting new direction for the numerical exploration of models for cosmic structure formation. PMID:9419326
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A New Non-gaussian Turbulent Wind Field Generator to Estimate Design-Loads of Wind-Turbines
NASA Astrophysics Data System (ADS)
Schaffarczyk, A. P.; Gontier, H.; Kleinhans, D.; Friedrich, R.
Climate change and finite fossil fuel resources make it urgent to turn into electricity generation from mostly renewable energies. One major part will play wind-energy supplied by wind-turbines of rated power up to 10 MW. For their design and development wind field models have to be used. The standard models are based on the empirical spectra, for example by von Karman or Kaimal. From investigation of measured data it is clear that gusts are underrepresented in such models. Based on some fundamental discoveries of the nature of turbulence by Friedrich [1] derived from the Navier-Stokes equation directly, we used the concept of Continuous Time Random Walks to construct three dimensional wind fields obeying non-Gaussian statistics. These wind fields were used to estimate critical fatigue loads necessary within the certification process. Calculations are carried out with an implementation of a beam-model (FLEX5) for two types of state-of-the-art wind turbines The authors considered the edgewise and flapwise blade-root bending moments as well as tilt moment at tower top due to the standard wind field models and our new non-Gaussian wind field model. Clear differences in the loads were found.
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Antonov, N V; Kostenko, M M
2014-12-01
The field theoretic renormalization group and the operator product expansion are applied to two models of passive scalar quantities (the density and the tracer fields) advected by a random turbulent velocity field. The latter is governed by the Navier-Stokes equation for compressible fluid, subject to external random force with the covariance ∝δ(t-t')k(4-d-y), where d is the dimension of space and y is an arbitrary exponent. The original stochastic problems are reformulated as multiplicatively renormalizable field theoretic models; the corresponding renormalization group equations possess infrared attractive fixed points. It is shown that various correlation functions of the scalar field, its powers and gradients, demonstrate anomalous scaling behavior in the inertial-convective range already for small values of y. The corresponding anomalous exponents, identified with scaling (critical) dimensions of certain composite fields ("operators" in the quantum-field terminology), can be systematically calculated as series in y. The practical calculation is performed in the leading one-loop approximation, including exponents in anisotropic contributions. It should be emphasized that, in contrast to Gaussian ensembles with finite correlation time, the model and the perturbation theory presented here are manifestly Galilean covariant. The validity of the one-loop approximation and comparison with Gaussian models are briefly discussed.
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Multi-field inflation with a random potential
NASA Astrophysics Data System (ADS)
Tye, S.-H. Henry; Xu, Jiajun; Zhang, Yang
2009-04-01
Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian-like motion with a drift in the D-dimensional field space, allowing entropic perturbation modes to continuously and randomly feed into the adiabatic mode. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario where the stochastic scatterings are frequent but mild, the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, in which the coarse-grained motion of the inflaton is significantly slowed down by the scatterings, leads to rich phenomenologies. The power spectrum exhibits primordial fluctuations on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and have been smoothed out by binning of data points. With more data coming in the future, we expect these features can be detected or falsified. On the other hand the tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced by the large ratio of the Brownian-like motion speed over the drift speed. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, and is negligible in the weakly random scenario. However, non-Gaussianity can possibly be enhanced by resonant effects in the strongly random scenario or arise from the entropic perturbations during the onset of (p)reheating if the background inflaton trajectory exhibits particular properties. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.
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Direct Simulation of Multiple Scattering by Discrete Random Media Illuminated by Gaussian Beams
NASA Technical Reports Server (NTRS)
Mackowski, Daniel W.; Mishchenko, Michael I.
2011-01-01
The conventional orientation-averaging procedure developed in the framework of the superposition T-matrix approach is generalized to include the case of illumination by a Gaussian beam (GB). The resulting computer code is parallelized and used to perform extensive numerically exact calculations of electromagnetic scattering by volumes of discrete random medium consisting of monodisperse spherical particles. The size parameters of the scattering volumes are 40, 50, and 60, while their packing density is fixed at 5%. We demonstrate that all scattering patterns observed in the far-field zone of a random multisphere target and their evolution with decreasing width of the incident GB can be interpreted in terms of idealized theoretical concepts such as forward-scattering interference, coherent backscattering (CB), and diffuse multiple scattering. It is shown that the increasing violation of electromagnetic reciprocity with decreasing GB width suppresses and eventually eradicates all observable manifestations of CB. This result supplements the previous demonstration of the effects of broken reciprocity in the case of magneto-optically active particles subjected to an external magnetic field.
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Transport of Charged Particles in Turbulent Magnetic Fields
NASA Astrophysics Data System (ADS)
Parashar, T.; Subedi, P.; Sonsrettee, W.; Blasi, P.; Ruffolo, D. J.; Matthaeus, W. H.; Montgomery, D.; Chuychai, P.; Dmitruk, P.; Wan, M.; Chhiber, R.
2017-12-01
Magnetic fields permeate the Universe. They are found in planets, stars, galaxies, and the intergalactic medium. The magnetic field found in these astrophysical systems are usually chaotic, disordered, and turbulent. The investigation of the transport of cosmic rays in magnetic turbulence is a subject of considerable interest. One of the important aspects of cosmic ray transport is to understand their diffusive behavior and to calculate the diffusion coefficient in the presence of these turbulent fields. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here, we will particularly focus on calculating diffusion coefficients of charged particles and magnetic field lines in a fully three-dimensional isotropic turbulent magnetic field with no mean field, which may be pertinent to many astrophysical situations. For charged particles in isotropic turbulence we identify different ranges of particle energy depending upon the ratio of the Larmor radius of the charged particle to the characteristic outer length scale of the turbulence. Different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. The theoretical ideas are tested against results of detailed numerical experiments using Monte-Carlo simulations of particle propagation in stochastic magnetic fields. We also discuss two different methods of generating random magnetic field to study charged particle propagation using numerical simulation. One method is the usual way of generating random fields with a specified power law in wavenumber space, using Gaussian random variables. Turbulence, however, is non-Gaussian, with variability that comes in bursts called intermittency. We therefore devise a way to generate synthetic intermittent fields which have many properties of realistic turbulence. Possible applications of such synthetically generated intermittent fields are discussed.
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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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Model studies of the beam-filling error for rain-rate retrieval with microwave radiometers
NASA Technical Reports Server (NTRS)
Ha, Eunho; North, Gerald R.
1995-01-01
Low-frequency (less than 20 GHz) single-channel microwave retrievals of rain rate encounter the problem of beam-filling error. This error stems from the fact that the relationship between microwave brightness temperature and rain rate is nonlinear, coupled with the fact that the field of view is large or comparable to important scales of variability of the rain field. This means that one may not simply insert the area average of the brightness temperature into the formula for rain rate without incurring both bias and random error. The statistical heterogeneity of the rain-rate field in the footprint of the instrument is key to determining the nature of these errors. This paper makes use of a series of random rain-rate fields to study the size of the bias and random error associated with beam filling. A number of examples are analyzed in detail: the binomially distributed field, the gamma, the Gaussian, the mixed gamma, the lognormal, and the mixed lognormal ('mixed' here means there is a finite probability of no rain rate at a point of space-time). Of particular interest are the applicability of a simple error formula due to Chiu and collaborators and a formula that might hold in the large field of view limit. It is found that the simple formula holds for Gaussian rain-rate fields but begins to fail for highly skewed fields such as the mixed lognormal. While not conclusively demonstrated here, it is suggested that the notionof climatologically adjusting the retrievals to remove the beam-filling bias is a reasonable proposition.
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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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DOE Office of Scientific and Technical Information (OSTI.GOV)
Rossi, Matteo A. C., E-mail: matteo.rossi@unimi.it; Paris, Matteo G. A., E-mail: matteo.paris@fisica.unimi.it; CNISM, Unità Milano Statale, I-20133 Milano
2016-01-14
We address the interaction of single- and two-qubit systems with an external transverse fluctuating field and analyze in detail the dynamical decoherence induced by Gaussian noise and random telegraph noise (RTN). Upon exploiting the exact RTN solution of the time-dependent von Neumann equation, we analyze in detail the behavior of quantum correlations and prove the non-Markovianity of the dynamical map in the full parameter range, i.e., for either fast or slow noise. The dynamics induced by Gaussian noise is studied numerically and compared to the RTN solution, showing the existence of (state dependent) regions of the parameter space where themore » two noises lead to very similar dynamics. We show that the effects of RTN noise and of Gaussian noise are different, i.e., the spectrum alone is not enough to summarize the noise effects, but the dynamics under the effect of one kind of noise may be simulated with high fidelity by the other one.« less
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Analog model for quantum gravity effects: phonons in random fluids.
Krein, G; Menezes, G; Svaiter, N F
2010-09-24
We describe an analog model for quantum gravity effects in condensed matter physics. The situation discussed is that of phonons propagating in a fluid with a random velocity wave equation. We consider that there are random fluctuations in the reciprocal of the bulk modulus of the system and study free phonons in the presence of Gaussian colored noise with zero mean. We show that, in this model, after performing the random averages over the noise function a free conventional scalar quantum field theory describing free phonons becomes a self-interacting model.
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Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.
Lukin, Igor P
2016-04-20
The orbital angular momentum of vortex Bessel-Gaussian beams propagating in turbulent atmosphere is studied theoretically. The field of an optical beam is determined through the solution of the paraxial wave equation for a randomly inhomogeneous medium with fluctuations of the refraction index of the turbulent atmosphere. Peculiarities in the behavior of the total power of the vortex Bessel-Gaussian beam at the receiver (or transmitter) are examined. The dependence of the total power of the vortex Bessel-Gaussian beam on optical beam parameters, namely, the transverse wave number of optical radiation, amplitude factor radius, and, especially, topological charge of the optical beam, is analyzed in detail. It turns out that the mean value of the orbital angular momentum of the vortex Bessel-Gaussian beam remains constant during propagation in the turbulent atmosphere. It is shown that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam propagating in turbulent atmosphere calculated with the "mean-intensity" approximation is equal to zero identically. Thus, it is possible to declare confidently that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam in turbulent atmosphere is not very large.
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Random waves in the brain: Symmetries and defect generation in the visual cortex
NASA Astrophysics Data System (ADS)
Schnabel, M.; Kaschube, M.; Löwel, S.; Wolf, F.
2007-06-01
How orientation maps in the visual cortex of the brain develop is a matter of long standing debate. Experimental and theoretical evidence suggests that their development represents an activity-dependent self-organization process. Theoretical analysis [1] exploring this hypothesis predicted that maps at an early developmental stage are realizations of Gaussian random fields exhibiting a rigorous lower bound for their densities of topological defects, called pinwheels. As a consequence, lower pinwheel densities, if observed in adult animals, are predicted to develop through the motion and annihilation of pinwheel pairs. Despite of being valid for a large class of developmental models this result depends on the symmetries of the models and thus of the predicted random field ensembles. In [1] invariance of the orientation map's statistical properties under independent space rotations and orientation shifts was assumed. However, full rotation symmetry appears to be broken by interactions of cortical neurons, e.g. selective couplings between groups of neurons with collinear orientation preferences [2]. A recently proposed new symmetry, called shift-twist symmetry [3], stating that spatial rotations have to occur together with orientation shifts in order to be an appropriate symmetry transformation, is more consistent with this organization. Here we generalize our random field approach to this important symmetry class. We propose a new class of shift-twist symmetric Gaussian random fields and derive the general correlation functions of this ensemble. It turns out that despite strong effects of the shift-twist symmetry on the structure of the correlation functions and on the map layout the lower bound on the pinwheel densities remains unaffected, predicting pinwheel annihilation in systems with low pinwheel densities.
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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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Statistics of the epoch of reionization 21-cm signal - I. Power spectrum error-covariance
NASA Astrophysics Data System (ADS)
Mondal, Rajesh; Bharadwaj, Somnath; Majumdar, Suman
2016-02-01
The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has a significant impact on the error variance of its power spectrum P(k). We have used a large ensemble of seminumerical simulations and an analytical model to estimate the effect of this non-Gaussianity on the entire error-covariance matrix {C}ij. Our analytical model shows that {C}ij has contributions from two sources. One is the usual variance for a Gaussian random field which scales inversely of the number of modes that goes into the estimation of P(k). The other is the trispectrum of the signal. Using the simulated 21-cm Signal Ensemble, an ensemble of the Randomized Signal and Ensembles of Gaussian Random Ensembles we have quantified the effect of the trispectrum on the error variance {C}II. We find that its relative contribution is comparable to or larger than that of the Gaussian term for the k range 0.3 ≤ k ≤ 1.0 Mpc-1, and can be even ˜200 times larger at k ˜ 5 Mpc-1. We also establish that the off-diagonal terms of {C}ij have statistically significant non-zero values which arise purely from the trispectrum. This further signifies that the error in different k modes are not independent. We find a strong correlation between the errors at large k values (≥0.5 Mpc-1), and a weak correlation between the smallest and largest k values. There is also a small anticorrelation between the errors in the smallest and intermediate k values. These results are relevant for the k range that will be probed by the current and upcoming EoR 21-cm experiments.
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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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Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d
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Deterministic Mean-Field Ensemble Kalman Filtering
DOE Office of Scientific and Technical Information (OSTI.GOV)
Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d
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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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Bayesian spatial transformation models with applications in neuroimaging data
Miranda, Michelle F.; Zhu, Hongtu; Ibrahim, Joseph G.
2013-01-01
Summary The aim of this paper is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. Our STMs include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov Random Field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder. PMID:24128143
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Vyas, Manan; Kota, V K B; Chavda, N D
2010-03-01
Finite interacting Fermi systems with a mean-field and a chaos generating two-body interaction are modeled by one plus two-body embedded Gaussian orthogonal ensemble of random matrices with spin degree of freedom [called EGOE(1+2)-s]. Numerical calculations are used to demonstrate that, as lambda , the strength of the interaction (measured in the units of the average spacing of the single-particle levels defining the mean-field), increases, generically there is Poisson to GOE transition in level fluctuations, Breit-Wigner to Gaussian transition in strength functions (also called local density of states) and also a duality region where information entropy will be the same in both the mean-field and interaction defined basis. Spin dependence of the transition points lambda_{c} , lambdaF, and lambdad , respectively, is described using the propagator for the spectral variances and the formula for the propagator is derived. We further establish that the duality region corresponds to a region of thermalization. For this purpose we compared the single-particle entropy defined by the occupancies of the single-particle orbitals with thermodynamic entropy and information entropy for various lambda values and they are very close to each other at lambda=lambdad.
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NASA Astrophysics Data System (ADS)
Vanmarcke, Erik
1983-03-01
Random variation over space and time is one of the few attributes that might safely be predicted as characterizing almost any given complex system. Random fields or "distributed disorder systems" confront astronomers, physicists, geologists, meteorologists, biologists, and other natural scientists. They appear in the artifacts developed by electrical, mechanical, civil, and other engineers. They even underlie the processes of social and economic change. The purpose of this book is to bring together existing and new methodologies of random field theory and indicate how they can be applied to these diverse areas where a "deterministic treatment is inefficient and conventional statistics insufficient." Many new results and methods are included. After outlining the extent and characteristics of the random field approach, the book reviews the classical theory of multidimensional random processes and introduces basic probability concepts and methods in the random field context. It next gives a concise amount of the second-order analysis of homogeneous random fields, in both the space-time domain and the wave number-frequency domain. This is followed by a chapter on spectral moments and related measures of disorder and on level excursions and extremes of Gaussian and related random fields. After developing a new framework of analysis based on local averages of one-, two-, and n-dimensional processes, the book concludes with a chapter discussing ramifications in the important areas of estimation, prediction, and control. The mathematical prerequisite has been held to basic college-level calculus.
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NASA Astrophysics Data System (ADS)
Cao, Xiangyu; Fyodorov, Yan V.; Le Doussal, Pierre
2018-02-01
We address systematically an apparent nonphysical behavior of the free-energy moment generating function for several instances of the logarithmically correlated models: the fractional Brownian motion with Hurst index H =0 (fBm0) (and its bridge version), a one-dimensional model appearing in decaying Burgers turbulence with log-correlated initial conditions and, finally, the two-dimensional log-correlated random-energy model (logREM) introduced in Cao et al. [Phys. Rev. Lett. 118, 090601 (2017), 10.1103/PhysRevLett.118.090601] based on the two-dimensional Gaussian free field with background charges and directly related to the Liouville field theory. All these models share anomalously large fluctuations of the associated free energy, with a variance proportional to the log of the system size. We argue that a seemingly nonphysical vanishing of the moment generating function for some values of parameters is related to the termination point transition (i.e., prefreezing). We study the associated universal log corrections in the frozen phase, both for logREMs and for the standard REM, filling a gap in the literature. For the above mentioned integrable instances of logREMs, we predict the nontrivial free-energy cumulants describing non-Gaussian fluctuations on the top of the Gaussian with extensive variance. Some of the predictions are tested numerically.
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NASA Astrophysics Data System (ADS)
Dwivedi, Prashant Povel; Kumar, Challa Sesha Sai Pavan; Choi, Hee Joo; Cha, Myoungsik
2016-02-01
Random duty-cycle error (RDE) is inherent in the fabrication of ferroelectric quasi-phase-matching (QPM) gratings. Although a small RDE may not affect the nonlinearity of QPM devices, it enhances non-phase-matched parasitic harmonic generations, limiting the device performance in some applications. Recently, we demonstrated a simple method for measuring the RDE in QPM gratings by analyzing the far-field diffraction pattern obtained by uniform illumination (Dwivedi et al. in Opt Express 21:30221-30226, 2013). In the present study, we used a Gaussian beam illumination for the diffraction experiment to measure noise spectra that are less affected by the pedestals of the strong diffraction orders. Our results were compared with our calculations based on a random grating model, demonstrating improved resolution in the RDE estimation.
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NASA Astrophysics Data System (ADS)
Ye, Junye; le Roux, Jakobus A.; Arthur, Aaron D.
2016-08-01
We study the physics of locally born interstellar pickup proton acceleration at the nearly perpendicular solar wind termination shock (SWTS) in the presence of a random magnetic field spiral angle using a focused transport model. Guided by Voyager 2 observations, the spiral angle is modeled with a q-Gaussian distribution. The spiral angle fluctuations, which are used to generate the perpendicular diffusion of pickup protons across the SWTS, play a key role in enabling efficient injection and rapid diffusive shock acceleration (DSA) when these particles follow field lines. Our simulations suggest that variation of both the shape (q-value) and the standard deviation (σ-value) of the q-Gaussian distribution significantly affect the injection speed, pitch-angle anisotropy, radial distribution, and the efficiency of the DSA of pickup protons at the SWTS. For example, increasing q and especially reducing σ enhances the DSA rate.
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Kinetic field theory: exact free evolution of Gaussian phase-space correlations
NASA Astrophysics Data System (ADS)
Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2018-04-01
In recent work we developed a description of cosmic large-scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial correlations between particles sampled from random Gaussian density and velocity fields have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correlations between all phase-space coordinates exactly by adopting a diagrammatic language for the different forms of correlations, directly inspired by the Mayer cluster expansion. We will demonstrate that explicit expressions for phase-space density cumulants of arbitrary n-point order, which fully capture the non-linear coupling of free streaming kinematics due to initial correlations, can be obtained from a simple set of Feynman rules. These cumulants will be the foundation for future investigations of perturbation theory in particle interactions.
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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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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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NASA Astrophysics Data System (ADS)
Granato, Enzo
2017-11-01
We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass, and a Gaussian phase glass. The first two models describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field, while the last two describe the effects of random negative Josephson-junction couplings or π junctions. Monte Carlo simulations in the path-integral representation of the models are used to determine the critical exponents and the universal conductivity at the quantum phase transition. The gauge- and flux-glass models display the same critical behavior, within the estimated numerical uncertainties. Similar agreement is found for the binary and Gaussian phase-glass models. Despite the different symmetries and disorder correlations, we find that the universal conductivity of these models is approximately the same. In particular, the ratio of this value to that of the pure model agrees with recent experiments on nanohole thin-film superconductors in a magnetic field, in the large disorder limit.
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Analysis of randomly time varying systems by gaussian closure technique
NASA Astrophysics Data System (ADS)
Dash, P. K.; Iyengar, R. N.
1982-07-01
The Gaussian probability closure technique is applied to study the random response of multidegree of freedom stochastically time varying systems under non-Gaussian excitations. Under the assumption that the response, the coefficient and the excitation processes are jointly Gaussian, deterministic equations are derived for the first two response moments. It is further shown that this technique leads to the best Gaussian estimate in a minimum mean square error sense. An example problem is solved which demonstrates the capability of this technique for handling non-linearity, stochastic system parameters and amplitude limited responses in a unified manner. Numerical results obtained through the Gaussian closure technique compare well with the exact solutions.
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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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DOE Office of Scientific and Technical Information (OSTI.GOV)
Ruban, V. P., E-mail: ruban@itp.ac.ru
2015-05-15
The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less
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Bayesian spatial transformation models with applications in neuroimaging data.
Miranda, Michelle F; Zhu, Hongtu; Ibrahim, Joseph G
2013-12-01
The aim of this article is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. The proposed STM include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov random field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder. © 2013, The International Biometric Society.
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An Interactive Image Segmentation Method in Hand Gesture Recognition
Chen, Disi; Li, Gongfa; Sun, Ying; Kong, Jianyi; Jiang, Guozhang; Tang, Heng; Ju, Zhaojie; Yu, Hui; Liu, Honghai
2017-01-01
In order to improve the recognition rate of hand gestures a new interactive image segmentation method for hand gesture recognition is presented, and popular methods, e.g., Graph cut, Random walker, Interactive image segmentation using geodesic star convexity, are studied in this article. The Gaussian Mixture Model was employed for image modelling and the iteration of Expectation Maximum algorithm learns the parameters of Gaussian Mixture Model. We apply a Gibbs random field to the image segmentation and minimize the Gibbs Energy using Min-cut theorem to find the optimal segmentation. The segmentation result of our method is tested on an image dataset and compared with other methods by estimating the region accuracy and boundary accuracy. Finally five kinds of hand gestures in different backgrounds are tested on our experimental platform, and the sparse representation algorithm is used, proving that the segmentation of hand gesture images helps to improve the recognition accuracy. PMID:28134818
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Almost sure convergence in quantum spin glasses
DOE Office of Scientific and Technical Information (OSTI.GOV)
Buzinski, David, E-mail: dab197@case.edu; Meckes, Elizabeth, E-mail: elizabeth.meckes@case.edu
2015-12-15
Recently, Keating, Linden, and Wells [Markov Processes Relat. Fields 21(3), 537-555 (2015)] showed that the density of states measure of a nearest-neighbor quantum spin glass model is approximately Gaussian when the number of particles is large. The density of states measure is the ensemble average of the empirical spectral measure of a random matrix; in this paper, we use concentration of measure and entropy techniques together with the result of Keating, Linden, and Wells to show that in fact the empirical spectral measure of such a random matrix is almost surely approximately Gaussian itself with no ensemble averaging. We alsomore » extend this result to a spherical quantum spin glass model and to the more general coupling geometries investigated by Erdős and Schröder [Math. Phys., Anal. Geom. 17(3-4), 441–464 (2014)].« less
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A novel approach to assess the treatment response using Gaussian random field in PET
DOE Office of Scientific and Technical Information (OSTI.GOV)
Wang, Mengdie; Guo, Ning; Hu, Guangshu
2016-02-15
Purpose: The assessment of early therapeutic response to anticancer therapy is vital for treatment planning and patient management in clinic. With the development of personal treatment plan, the early treatment response, especially before any anatomically apparent changes after treatment, becomes urgent need in clinic. Positron emission tomography (PET) imaging serves an important role in clinical oncology for tumor detection, staging, and therapy response assessment. Many studies on therapy response involve interpretation of differences between two PET images, usually in terms of standardized uptake values (SUVs). However, the quantitative accuracy of this measurement is limited. This work proposes a statistically robustmore » approach for therapy response assessment based on Gaussian random field (GRF) to provide a statistically more meaningful scale to evaluate therapy effects. Methods: The authors propose a new criterion for therapeutic assessment by incorporating image noise into traditional SUV method. An analytical method based on the approximate expressions of the Fisher information matrix was applied to model the variance of individual pixels in reconstructed images. A zero mean unit variance GRF under the null hypothesis (no response to therapy) was obtained by normalizing each pixel of the post-therapy image with the mean and standard deviation of the pretherapy image. The performance of the proposed method was evaluated by Monte Carlo simulation, where XCAT phantoms (128{sup 2} pixels) with lesions of various diameters (2–6 mm), multiple tumor-to-background contrasts (3–10), and different changes in intensity (6.25%–30%) were used. The receiver operating characteristic curves and the corresponding areas under the curve were computed for both the proposed method and the traditional methods whose figure of merit is the percentage change of SUVs. The formula for the false positive rate (FPR) estimation was developed for the proposed therapy response assessment utilizing local average method based on random field. The accuracy of the estimation was validated in terms of Euler distance and correlation coefficient. Results: It is shown that the performance of therapy response assessment is significantly improved by the introduction of variance with a higher area under the curve (97.3%) than SUVmean (91.4%) and SUVmax (82.0%). In addition, the FPR estimation serves as a good prediction for the specificity of the proposed method, consistent with simulation outcome with ∼1 correlation coefficient. Conclusions: In this work, the authors developed a method to evaluate therapy response from PET images, which were modeled as Gaussian random field. The digital phantom simulations demonstrated that the proposed method achieved a large reduction in statistical variability through incorporating knowledge of the variance of the original Gaussian random field. The proposed method has the potential to enable prediction of early treatment response and shows promise for application to clinical practice. In future work, the authors will report on the robustness of the estimation theory for application to clinical practice of therapy response evaluation, which pertains to binary discrimination tasks at a fixed location in the image such as detection of small and weak lesion.« less
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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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NASA Astrophysics Data System (ADS)
Musenge, Eustasius; Chirwa, Tobias Freeman; Kahn, Kathleen; Vounatsou, Penelope
2013-06-01
Longitudinal mortality data with few deaths usually have problems of zero-inflation. This paper presents and applies two Bayesian models which cater for zero-inflation, spatial and temporal random effects. To reduce the computational burden experienced when a large number of geo-locations are treated as a Gaussian field (GF) we transformed the field to a Gaussian Markov Random Fields (GMRF) by triangulation. We then modelled the spatial random effects using the Stochastic Partial Differential Equations (SPDEs). Inference was done using a computationally efficient alternative to Markov chain Monte Carlo (MCMC) called Integrated Nested Laplace Approximation (INLA) suited for GMRF. The models were applied to data from 71,057 children aged 0 to under 10 years from rural north-east South Africa living in 15,703 households over the years 1992-2010. We found protective effects on HIV/TB mortality due to greater birth weight, older age and more antenatal clinic visits during pregnancy (adjusted RR (95% CI)): 0.73(0.53;0.99), 0.18(0.14;0.22) and 0.96(0.94;0.97) respectively. Therefore childhood HIV/TB mortality could be reduced if mothers are better catered for during pregnancy as this can reduce mother-to-child transmissions and contribute to improved birth weights. The INLA and SPDE approaches are computationally good alternatives in modelling large multilevel spatiotemporal GMRF data structures.
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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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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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Finding SDSS Galaxy Clusters in 4-dimensional Color Space Using the False Discovery Rate
NASA Astrophysics Data System (ADS)
Nichol, R. C.; Miller, C. J.; Reichart, D.; Wasserman, L.; Genovese, C.; SDSS Collaboration
2000-12-01
We describe a recently developed statistical technique that provides a meaningful cut-off in probability-based decision making. We are concerned with multiple testing, where each test produces a well-defined probability (or p-value). By well-known, we mean that the null hypothesis used to determine the p-value is fully understood and appropriate. The method is entitled False Discovery Rate (FDR) and its largest advantage over other measures is that it allows one to specify a maximal amount of acceptable error. As an example of this tool, we apply FDR to a four-dimensional clustering algorithm using SDSS data. For each galaxy (or test galaxy), we count the number of neighbors that fit within one standard deviation of a four dimensional Gaussian centered on that test galaxy. The mean and standard deviation of that Gaussian are determined from the colors and errors of the test galaxy. We then take that same Gaussian and place it on a random selection of n galaxies and make a similar count. In the limit of large n, we expect the median count around these random galaxies to represent a typical field galaxy. For every test galaxy we determine the probability (or p-value) that it is a field galaxy based on these counts. A low p-value implies that the test galaxy is in a cluster environment. Once we have a p-value for every galaxy, we use FDR to determine at what level we should make our probability cut-off. Once this cut-off is made, we have a final sample of galaxies that are cluster-like galaxies. Using FDR, we also know the maximum amount of field contamination in our cluster galaxy sample. We present our preliminary galaxy clustering results using these methods.
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Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices
Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan; Gross, Sam; Hills, Gage; Hornstein, Michael; Lakkam, Milinda; Lee, Jason; Li, Jian; Liu, Linxi; Sing-Long, Carlos; Marx, Mike; Mittal, Akshay; Monajemi, Hatef; No, Albert; Omrani, Reza; Pekelis, Leonid; Qin, Junjie; Raines, Kevin; Ryu, Ernest; Saxe, Andrew; Shi, Dai; Siilats, Keith; Strauss, David; Tang, Gary; Wang, Chaojun; Zhou, Zoey; Zhu, Zhen
2013-01-01
In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions. PMID:23277588
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NASA Astrophysics Data System (ADS)
Watkinson, Catherine A.; Majumdar, Suman; Pritchard, Jonathan R.; Mondal, Rajesh
2017-12-01
In this paper, we establish the accuracy and robustness of a fast estimator for the bispectrum - the 'FFT-bispectrum estimator'. The implementation of the estimator presented here offers speed and simplicity benefits over a direct-measurement approach. We also generalize the derivation so it may be easily be applied to any order polyspectra, such as the trispectrum, with the cost of only a handful of Fast-Fourier Transforms (FFTs). All lower order statistics can also be calculated simultaneously for little extra cost. To test the estimator, we make use of a non-linear density field, and for a more strongly non-Gaussian test case, we use a toy-model of reionization in which ionized bubbles at a given redshift are all of equal size and are randomly distributed. Our tests find that the FFT-estimator remains accurate over a wide range of k, and so should be extremely useful for analysis of 21-cm observations. The speed of the FFT-bispectrum estimator makes it suitable for sampling applications, such as Bayesian inference. The algorithm we describe should prove valuable in the analysis of simulations and observations, and whilst, we apply it within the field of cosmology, this estimator is useful in any field that deals with non-Gaussian data.
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A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields
Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto
2017-10-26
In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less
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A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields
DOE Office of Scientific and Technical Information (OSTI.GOV)
Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto
In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less
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Two-dimensional Topology of the Two-Degree Field Galaxy Redshift Survey
NASA Astrophysics Data System (ADS)
Hoyle, Fiona; Vogeley, Michael S.; Gott, J. Richard, III
2002-05-01
We study the topology of the publicly available data released by the Two Degree Field Galaxy Redshift Survey team (2dF GRS). The 2dF GRS data contain over 100,000 galaxy redshifts with a magnitude limit of bJ=19.45 and is the largest such survey to date. The data lie over a wide range of right ascension (75° strips) but only within a narrow range of declination (10° and 15° strips). This allows measurements of the two-dimensional genus to be made. We find that the genus curves of the north Galactic pole (NGP) and south Galactic pole (SGP) are slightly different. The NGP displays a slight meatball shift topology, whereas the SGP displays a bubble-like topology. The current SGP data also have a slightly higher genus amplitude. In both cases, a slight excess of overdense regions is found over underdense regions. We assess the significance of these features using mock catalogs drawn from the Virgo Consortium's Hubble volume ΛCDM z=0 simulation. We find that differences between the NGP and SGP genus curves are only significant at the 1 σ level. The average genus curve of the 2dF GRS agrees well with that extracted from the ΛCDM mock catalogs. We also use the simulations to assess how the current incompleteness of the survey (the strips are not completely filled in) affects the measurement of the genus and find that we are not sensitive to the geometry; there are enough data in the current sample to trace the isolated high- and low-density regions. We compare the amplitude of the 2dF GRS genus curve to the amplitude of the genus curve of a Gaussian random field that we construct to have the same power spectrum as the 2dF GRS. In previous three-dimensional analyses, it was found that the genus curve of observed samples was lower than the Gaussian random field curve, presumably because of high-order correlations present in the data. However, we find that the 2dF GRS genus curve has an amplitude that is slightly higher than that of the power-spectrum-matched Gaussian random field. We suggest that in two dimensions the genus measurement is less sensitive to nonlinear effects because of the effective smoothing over the thickness of the slice.
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Fluctuations of the partition function in the generalized random energy model with external field
NASA Astrophysics Data System (ADS)
Bovier, Anton; Klimovsky, Anton
2008-12-01
We study Derrida's generalized random energy model (GREM) in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters. We find that the fluctuations are described by a hierarchical structure which is obtained by a certain coarse graining of the initial hierarchical structure of the GREM with external field. We provide an explicit formula for the free energy of the model. We also derive some large deviation results providing an expression for the free energy in a class of models with Gaussian Hamiltonians and external field. Finally, we prove that the coarse-grained parts of the system emerging in the thermodynamic limit tend to have a certain optimal magnetization, as prescribed by the strength of the external field and by parameters of the GREM.
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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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Micromagnetic Simulation of Thermal Effects in Magnetic Nanostructures
2003-01-01
NiFe magnetic nano- elements are calculated. INTRODUCTION With decreasing size of magnetic nanostructures thermal effects become increasingly important...thermal field. The thermal field is assumed to be a Gaussian random process with the following statistical properties : (H,,,(t))=0 and (H,I.(t),H,.1(t...following property DI " =VE(M’’) - [VE(M"’)• t] t =0, for k =1.m (12) 186 The optimal path can be found using an iterative scheme. In each iteration step the
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Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA
DOE Office of Scientific and Technical Information (OSTI.GOV)
Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao
2017-10-18
Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less
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Simulating and mapping spatial complexity using multi-scale techniques
De Cola, L.
1994-01-01
A central problem in spatial analysis is the mapping of data for complex spatial fields using relatively simple data structures, such as those of a conventional GIS. This complexity can be measured using such indices as multi-scale variance, which reflects spatial autocorrelation, and multi-fractal dimension, which characterizes the values of fields. These indices are computed for three spatial processes: Gaussian noise, a simple mathematical function, and data for a random walk. Fractal analysis is then used to produce a vegetation map of the central region of California based on a satellite image. This analysis suggests that real world data lie on a continuum between the simple and the random, and that a major GIS challenge is the scientific representation and understanding of rapidly changing multi-scale fields. -Author
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NASA Astrophysics Data System (ADS)
Jeffs, Brian D.; Christou, Julian C.
1998-09-01
This paper addresses post processing for resolution enhancement of sequences of short exposure adaptive optics (AO) images of space objects. The unknown residual blur is removed using Bayesian maximum a posteriori blind image restoration techniques. In the problem formulation, both the true image and the unknown blur psf's are represented by the flexible generalized Gaussian Markov random field (GGMRF) model. The GGMRF probability density function provides a natural mechanism for expressing available prior information about the image and blur. Incorporating such prior knowledge in the deconvolution optimization is crucial for the success of blind restoration algorithms. For example, space objects often contain sharp edge boundaries and geometric structures, while the residual blur psf in the corresponding partially corrected AO image is spectrally band limited, and exhibits while the residual blur psf in the corresponding partially corrected AO image is spectrally band limited, and exhibits smoothed, random , texture-like features on a peaked central core. By properly choosing parameters, GGMRF models can accurately represent both the blur psf and the object, and serve to regularize the deconvolution problem. These two GGMRF models also serve as discriminator functions to separate blur and object in the solution. Algorithm performance is demonstrated with examples from synthetic AO images. Results indicate significant resolution enhancement when applied to partially corrected AO images. An efficient computational algorithm is described.
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The Topology of Large-Scale Structure in the 1.2 Jy IRAS Redshift Survey
NASA Astrophysics Data System (ADS)
Protogeros, Zacharias A. M.; Weinberg, David H.
1997-11-01
We measure the topology (genus) of isodensity contour surfaces in volume-limited subsets of the 1.2 Jy IRAS redshift survey, for smoothing scales λ = 4, 7, and 12 h-1 Mpc. At 12 h-1 Mpc, the observed genus curve has a symmetric form similar to that predicted for a Gaussian random field. At the shorter smoothing lengths, the observed genus curve shows a modest shift in the direction of an isolated cluster or ``meatball'' topology. We use mock catalogs drawn from cosmological N-body simulations to investigate the systematic biases that affect topology measurements in samples of this size and to determine the full covariance matrix of the expected random errors. We incorporate the error correlations into our evaluations of theoretical models, obtaining both frequentist assessments of absolute goodness of fit and Bayesian assessments of models' relative likelihoods. We compare the observed topology of the 1.2 Jy survey to the predictions of dynamically evolved, unbiased, gravitational instability models that have Gaussian initial conditions. The model with an n = -1 power-law initial power spectrum achieves the best overall agreement with the data, though models with a low-density cold dark matter power spectrum and an n = 0 power-law spectrum are also consistent. The observed topology is inconsistent with an initially Gaussian model that has n = -2, and it is strongly inconsistent with a Voronoi foam model, which has a non-Gaussian, bubble topology.
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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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Prequantum classical statistical field theory: background field as a source of everything?
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2011-07-01
Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie's "double solution" approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson's stochastic QM and its generalization by Davidson, 't Hooft's models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrodinger. There is no quantum particles at all, only waves. In particular, photons are simply wave-pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special "prequantum fields": the electron field, the neutron field, and so on. PCSFT claims that (sooner or later) people will be able to measure components of these fields: components of the "photonic field" (the classical electromagnetic field of low intensity), electronic field, neutronic field, and so on. At the moment we are able to produce quantum correlations as correlations of classical Gaussian random fields. In this paper we are interested in mathematical and physical reasons of usage of Gaussian fields. We consider prequantum signals (corresponding to quantum systems) as composed of a huge number of wave-pulses (on very fine prequantum time scale). We speculate that the prequantum background field (the field of "vacuum fluctuations") might play the role of a source of such pulses, i.e., the source of everything.
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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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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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Generalized expectation-maximization segmentation of brain MR images
NASA Astrophysics Data System (ADS)
Devalkeneer, Arnaud A.; Robe, Pierre A.; Verly, Jacques G.; Phillips, Christophe L. M.
2006-03-01
Manual segmentation of medical images is unpractical because it is time consuming, not reproducible, and prone to human error. It is also very difficult to take into account the 3D nature of the images. Thus, semi- or fully-automatic methods are of great interest. Current segmentation algorithms based on an Expectation- Maximization (EM) procedure present some limitations. The algorithm by Ashburner et al., 2005, does not allow multichannel inputs, e.g. two MR images of different contrast, and does not use spatial constraints between adjacent voxels, e.g. Markov random field (MRF) constraints. The solution of Van Leemput et al., 1999, employs a simplified model (mixture coefficients are not estimated and only one Gaussian is used by tissue class, with three for the image background). We have thus implemented an algorithm that combines the features of these two approaches: multichannel inputs, intensity bias correction, multi-Gaussian histogram model, and Markov random field (MRF) constraints. Our proposed method classifies tissues in three iterative main stages by way of a Generalized-EM (GEM) algorithm: (1) estimation of the Gaussian parameters modeling the histogram of the images, (2) correction of image intensity non-uniformity, and (3) modification of prior classification knowledge by MRF techniques. The goal of the GEM algorithm is to maximize the log-likelihood across the classes and voxels. Our segmentation algorithm was validated on synthetic data (with the Dice metric criterion) and real data (by a neurosurgeon) and compared to the original algorithms by Ashburner et al. and Van Leemput et al. Our combined approach leads to more robust and accurate segmentation.
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Recent advances in scalable non-Gaussian geostatistics: The generalized sub-Gaussian model
NASA Astrophysics Data System (ADS)
Guadagnini, Alberto; Riva, Monica; Neuman, Shlomo P.
2018-07-01
Geostatistical analysis has been introduced over half a century ago to allow quantifying seemingly random spatial variations in earth quantities such as rock mineral content or permeability. The traditional approach has been to view such quantities as multivariate Gaussian random functions characterized by one or a few well-defined spatial correlation scales. There is, however, mounting evidence that many spatially varying quantities exhibit non-Gaussian behavior over a multiplicity of scales. The purpose of this minireview is not to paint a broad picture of the subject and its treatment in the literature. Instead, we focus on very recent advances in the recognition and analysis of this ubiquitous phenomenon, which transcends hydrology and the Earth sciences, brought about largely by our own work. In particular, we use porosity data from a deep borehole to illustrate typical aspects of such scalable non-Gaussian behavior, describe a very recent theoretical model that (for the first time) captures all these behavioral aspects in a comprehensive manner, show how this allows generating random realizations of the quantity conditional on sampled values, point toward ways of incorporating scalable non-Gaussian behavior in hydrologic analysis, highlight the significance of doing so, and list open questions requiring further research.
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Some Metric Properties of Planar Gaussian Free Field
NASA Astrophysics Data System (ADS)
Goswami, Subhajit
In this thesis we study the properties of some metrics arising from two-dimensional Gaussian free field (GFF), namely the Liouville first-passage percolation (Liouville FPP), the Liouville graph distance and an effective resistance metric. In Chapter 1, we define these metrics as well as discuss the motivations for studying them. Roughly speaking, Liouville FPP is the shortest path metric in a planar domain D where the length of a path P is given by ∫Pe gammah(z)|dz| where h is the GFF on D and gamma > 0. In Chapter 2, we present an upper bound on the expected Liouville FPP distance between two typical points for small values of gamma (the near-Euclidean regime). A similar upper bound is derived in Chapter 3 for the Liouville graph distance which is, roughly, the minimal number of Euclidean balls with comparable Liouville quantum gravity (LQG) measure whose union contains a continuous path between two endpoints. Our bounds seem to be in disagreement with Watabiki's prediction (1993) on the random metric of Liouville quantum gravity in this regime. The contents of these two chapters are based on a joint work with Jian Ding. In Chapter 4, we derive some asymptotic estimates for effective resistances on a random network which is defined as follows. Given any gamma > 0 and for eta = {etav}v∈Z2 denoting a sample of the two-dimensional discrete Gaussian free field on Z2 pinned at the origin, we equip the edge ( u, v) with conductance egamma(etau + eta v). The metric structure of effective resistance plays a crucial role in our proof of the main result in Chapter 4. The primary motivation behind this metric is to understand the random walk on Z 2 where the edge (u, v) has weight egamma(etau + etav). Using the estimates from Chapter 4 we show in Chapter 5 that for almost every eta, this random walk is recurrent and that, with probability tending to 1 as T → infinity, the return probability at time 2T decays as T-1+o(1). In addition, we prove a version of subdiffusive behavior by showing that the expected exit time from a ball of radius N scales as Npsi(gamma)+o(1) with psi(gamma) > 2 for all gamma > 0. The contents of these chapters are based on a joint work with Marek Biskup and Jian Ding.
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Detection of Gauss-Markov Random Fields with Nearest-Neighbor Dependency
2010-01-01
sgn(Y )C log n, o.w, (45b) where sgn is the sign function and C > 0 is a constant. Consider the functionals H ′2, φ ′ 2 by replacing Yn with Zn in H2...Gaussian signal processing, and has held visiting faculty positions at INP , Toulouse. He is currently with the US Army Research Laboratory where his work
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Topology of large-scale structure. IV - Topology in two dimensions
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Cohen, Alexander P.; Hamilton, Andrew J. S.; Gott, J. Richard, III; Weinberg, David H.
1989-01-01
In a recent series of papers, an algorithm was developed for quantitatively measuring the topology of the large-scale structure of the universe and this algorithm was applied to numerical models and to three-dimensional observational data sets. In this paper, it is shown that topological information can be derived from a two-dimensional cross section of a density field, and analytic expressions are given for a Gaussian random field. The application of a two-dimensional numerical algorithm for measuring topology to cross sections of three-dimensional models is demonstrated.
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Palacios, Julia A; Minin, Vladimir N
2013-03-01
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method. Copyright © 2013, The International Biometric Society.
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Gaussian vs non-Gaussian turbulence: impact on wind turbine loads
NASA Astrophysics Data System (ADS)
Berg, J.; Mann, J.; Natarajan, A.; Patton, E. G.
2014-12-01
In wind energy applications the turbulent velocity field of the Atmospheric Boundary Layer (ABL) is often characterised by Gaussian probability density functions. When estimating the dynamical loads on wind turbines this has been the rule more than anything else. From numerous studies in the laboratory, in Direct Numerical Simulations, and from in-situ measurements of the ABL we know, however, that turbulence is not purely Gaussian: the smallest and fastest scales often exhibit extreme behaviour characterised by strong non-Gaussian statistics. In this contribution we want to investigate whether these non-Gaussian effects are important when determining wind turbine loads, and hence of utmost importance to the design criteria and lifetime of a wind turbine. We devise a method based on Principal Orthogonal Decomposition where non-Gaussian velocity fields generated by high-resolution pseudo-spectral Large-Eddy Simulation (LES) of the ABL are transformed so that they maintain the exact same second-order statistics including variations of the statistics with height, but are otherwise Gaussian. In that way we can investigate in isolation the question whether it is important for wind turbine loads to include non-Gaussian properties of atmospheric turbulence. As an illustration the Figure show both a non-Gaussian velocity field (left) from our LES, and its transformed Gaussian Counterpart (right). Whereas the horizontal velocity components (top) look close to identical, the vertical components (bottom) are not: the non-Gaussian case is much more fluid-like (like in a sketch by Michelangelo). The question is then: Does the wind turbine see this? Using the load simulation software HAWC2 with both the non-Gaussian and newly constructed Gaussian fields, respectively, we show that the Fatigue loads and most of the Extreme loads are unaltered when using non-Gaussian velocity fields. The turbine thus acts like a low-pass filter which average out the non-Gaussian behaviour on time scales close to and faster than the revolution time of the turbine. For a few of the Extreme load estimations there is, on the other hand, a tendency that non-Gaussian effects increase the overall dynamical load, and hence can be of importance in wind energy load estimations.
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Enhanced backscattering through a deep random phase screen
NASA Astrophysics Data System (ADS)
Jakeman, E.
1988-10-01
The statistical properties of radiation scattered by a system consisting of a plane mirror placed in the Fresnel region behind a smoothly varying deep random-phase screen with off-axis beam illumination are studied. It is found that two mechanisms cause enhanced scattering around the backward direction, according to the mirror position with respect to the focusing plane of the screen. In all of the plane mirror geometries considered, the scattered field remains a complex Gaussian process with a spatial coherence function identical to that expected for a single screen, and a speckle size smaller than the width of backscatter enhancement.
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Fermi problem in disordered systems
NASA Astrophysics Data System (ADS)
Menezes, G.; Svaiter, N. F.; de Mello, H. R.; Zarro, C. A. D.
2017-10-01
We revisit the Fermi two-atom problem in the framework of disordered systems. In our model, we consider a two-qubit system linearly coupled with a quantum massless scalar field. We analyze the energy transfer between the qubits under different experimental perspectives. In addition, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that the classical notion of causality emerges only in the wave zone in the presence of random fluctuations of the light cone. Possible repercussions are discussed.
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Modelling past land use using archaeological and pollen data
NASA Astrophysics Data System (ADS)
Pirzamanbein, Behnaz; Lindström, johan; Poska, Anneli; Gaillard-Lemdahl, Marie-José
2016-04-01
Accurate maps of past land use are necessary for studying the impact of anthropogenic land-cover changes on climate and biodiversity. We develop a Bayesian hierarchical model to reconstruct the land use using Gaussian Markov random fields. The model uses two observations sets: 1) archaeological data, representing human settlements, urbanization and agricultural findings; and 2) pollen-based land estimates of the three land-cover types Coniferous forest, Broadleaved forest and Unforested/Open land. The pollen based estimates are obtained from the REVEALS model, based on pollen counts from lakes and bogs. Our developed model uses the sparse pollen-based estimations to reconstruct the spatial continuous cover of three land cover types. Using the open-land component and the archaeological data, the extent of land-use is reconstructed. The model is applied on three time periods - centred around 1900 CE, 1000 and, 4000 BCE over Sweden for which both pollen-based estimates and archaeological data are available. To estimate the model parameters and land use, a block updated Markov chain Monte Carlo (MCMC) algorithm is applied. Using the MCMC posterior samples uncertainties in land-use predictions are computed. Due to lack of good historic land use data, model results are evaluated by cross-validation. Keywords. Spatial reconstruction, Gaussian Markov random field, Fossil pollen records, Archaeological data, Human land-use, Prediction uncertainty
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NASA Astrophysics Data System (ADS)
Maleki, Mohammad; Emery, Xavier
2017-12-01
In mineral resources evaluation, the joint simulation of a quantitative variable, such as a metal grade, and a categorical variable, such as a rock type, is challenging when one wants to reproduce spatial trends of the rock type domains, a feature that makes a stationarity assumption questionable. To address this problem, this work presents methodological and practical proposals for jointly simulating a grade and a rock type, when the former is represented by the transform of a stationary Gaussian random field and the latter is obtained by truncating an intrinsic random field of order k with Gaussian generalized increments. The proposals concern both the inference of the model parameters and the construction of realizations conditioned to existing data. The main difficulty is the identification of the spatial correlation structure, for which a semi-automated algorithm is designed, based on a least squares fitting of the data-to-data indicator covariances and grade-indicator cross-covariances. The proposed models and algorithms are applied to jointly simulate the copper grade and the rock type in a Chilean porphyry copper deposit. The results show their ability to reproduce the gradual transitions of the grade when crossing a rock type boundary, as well as the spatial zonation of the rock type.
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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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Aksenov, Valerii P; Kolosov, Valeriy V; Pogutsa, Cheslav E
2014-06-10
The propagation of laser beams having orbital angular momenta (OAM) in the turbulent atmosphere is studied numerically. The variance of random wandering of these beams is investigated with the use of the Monte Carlo technique. It is found that, among various types of vortex laser beams, such as the Laguerre-Gaussian (LG) beam, modified Bessel-Gaussian beam, and hypergeometric Gaussian beam, having identical initial effective radii and OAM, the LG beam occupying the largest effective volume in space is the most stable one.
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Temporal self-splitting of optical pulses
NASA Astrophysics Data System (ADS)
Ding, Chaoliang; Koivurova, Matias; Turunen, Jari; Pan, Liuzhan
2018-05-01
We present mathematical models for temporally and spectrally partially coherent pulse trains with Laguerre-Gaussian and Hermite-Gaussian Schell-model statistics as extensions of the standard Gaussian Schell model for pulse trains. We derive propagation formulas of both classes of pulsed fields in linearly dispersive media and in temporal optical systems. It is found that, in general, both types of fields exhibit time-domain self-splitting upon propagation. The Laguerre-Gaussian model leads to multiply peaked pulses, while the Hermite-Gaussian model leads to doubly peaked pulses, in the temporal far field (in dispersive media) or at the Fourier plane of a temporal system. In both model fields the character of the self-splitting phenomenon depends both on the degree of temporal and spectral coherence and on the power spectrum of the field.
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Optical vortices as potential indicators of biophysical dynamics
NASA Astrophysics Data System (ADS)
Majumdar, Anindya; Kirkpatrick, Sean J.
2017-03-01
Laser speckle patterns are granular patterns produced as a result of random interference of light waves. Optical vortices (OVs) are phase singularities in such speckle fields, characterized by zero intensity and an undefined phase. Decorrelation of the speckle fields causes these OVs to move in both time and space. In this work, a variety of parameters of these OVs have been studied. The speckle fields were simulated to undergo three distinct decorrelation behaviors- Gaussian, Lorentzian and constant decorrelations. Different decorrelation behaviors represent different dynamics. For example, Lorentzian and Gaussian decorrelations represent Brownian and ordered motions, respectively. Typical dynamical systems in biophysics are generally argued to be a combination of these. For each of the decorrelation behaviors under study, the vortex trails were tracked while varying the rate of decorrelation. Parameters such as the decorrelation length, average trail length and the deviation of the vortices as they traversed in the speckle field, were studied. Empirical studies were also performed to define the distinction between trails arising from different speckle decorrelation behaviors. The initial studies under stationary speckle fields were followed up by similar studies on shifting fields. A new idea to employ Poincaŕe plots in speckle analysis has also been introduced. Our studies indicate that tracking OVs can be a potential method to study cell and tissue dynamics.
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On the Response of a Nonlinear Structure to High Kurtosis Non-Gaussian Random Loadings
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam; Turner, Travis L.
2011-01-01
This paper is a follow-on to recent work by the authors in which the response and high-cycle fatigue of a nonlinear structure subject to non-Gaussian loadings was found to vary markedly depending on the nature of the loading. There it was found that a non-Gaussian loading having a steady rate of short-duration, high-excursion peaks produced essentially the same response as would have been incurred by a Gaussian loading. In contrast, a non-Gaussian loading having the same kurtosis, but with bursts of high-excursion peaks was found to elicit a much greater response. This work is meant to answer the question of when consideration of a loading probability distribution other than Gaussian is important. The approach entailed nonlinear numerical simulation of a beam structure under Gaussian and non-Gaussian random excitations. Whether the structure responded in a Gaussian or non-Gaussian manner was determined by adherence to, or violations of, the Central Limit Theorem. Over a practical range of damping, it was found that the linear response to a non-Gaussian loading was Gaussian when the period of the system impulse response is much greater than the rate of peaks in the loading. Lower damping reduced the kurtosis, but only when the linear response was non-Gaussian. In the nonlinear regime, the response was found to be non-Gaussian for all loadings. The effect of a spring-hardening type of nonlinearity was found to limit extreme values and thereby lower the kurtosis relative to the linear response regime. In this case, lower damping gave rise to greater nonlinearity, resulting in lower kurtosis than a higher level of damping.
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Phase retrieval in generalized optical interferometry systems.
Farriss, Wesley E; Fienup, James R; Malhotra, Tanya; Vamivakas, A Nick
2018-02-05
Modal analysis of an optical field via generalized interferometry (GI) is a novel technique that treats said field as a linear superposition of transverse modes and recovers the amplitudes of modal weighting coefficients. We use phase retrieval by nonlinear optimization to recover the phase of these modal weighting coefficients. Information diversity increases the robustness of the algorithm by better constraining the solution. Additionally, multiple sets of random starting phase values assist the algorithm in overcoming local minima. The algorithm was able to recover nearly all coefficient phases for simulated fields consisting of up to 21 superpositioned Hermite Gaussian modes from simulated data and proved to be resilient to shot noise.
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On the Bar Pattern Speed Determination of NGC 3367
NASA Astrophysics Data System (ADS)
Gabbasov, R. F.; Repetto, P.; Rosado, M.
2009-09-01
An important dynamic parameter of barred galaxies is the bar pattern speed, Ω P . Among several methods that are used for the determination of Ω P , the Tremaine-Weinberg method has the advantage of model independence and accuracy. In this work, we apply the method to a simulated bar including gas dynamics and study the effect of two-dimensional spectroscopy data quality on robustness of the method. We added white noise and a Gaussian random field to the data and measured the corresponding errors in Ω P . We found that a signal to noise ratio in surface density ~5 introduces errors of ~20% for the Gaussian noise, while for the white noise the corresponding errors reach ~50%. At the same time, the velocity field is less sensitive to contamination. On the basis of the performed study, we applied the method to the NGC 3367 spiral galaxy using Hα Fabry-Pérot interferometry data. We found Ω P = 43 ± 6 km s-1 kpc-1 for this galaxy.
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Coupling the Gaussian Free Fields with Free and with Zero Boundary Conditions via Common Level Lines
NASA Astrophysics Data System (ADS)
Qian, Wei; Werner, Wendelin
2018-06-01
We point out a new simple way to couple the Gaussian Free Field (GFF) with free boundary conditions in a two-dimensional domain with the GFF with zero boundary conditions in the same domain: Starting from the latter, one just has to sample at random all the signs of the height gaps on its boundary-touching zero-level lines (these signs are alternating for the zero-boundary GFF) in order to obtain a free boundary GFF. Constructions and couplings of the free boundary GFF and its level lines via soups of reflected Brownian loops and their clusters are also discussed. Such considerations show for instance that in a domain with an axis of symmetry, if one looks at the overlay of a single usual Conformal Loop Ensemble CLE3 with its own symmetric image, one obtains the CLE4-type collection of level lines of a GFF with mixed zero/free boundary conditions in the half-domain.
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Nonperturbative quantization of the electroweak model's electrodynamic sector
NASA Astrophysics Data System (ADS)
Fry, M. P.
2015-04-01
Consider the Euclidean functional integral representation of any physical process in the electroweak model. Integrating out the fermion degrees of freedom introduces 24 fermion determinants. These multiply the Gaussian functional measures of the Maxwell, Z , W , and Higgs fields to give an effective functional measure. Suppose the functional integral over the Maxwell field is attempted first. This paper is concerned with the large amplitude behavior of the Maxwell effective measure. It is assumed that the large amplitude variation of this measure is insensitive to the presence of the Z , W , and H fields; they are assumed to be a subdominant perturbation of the large amplitude Maxwell sector. Accordingly, we need only examine the large amplitude variation of a single QED fermion determinant. To facilitate this the Schwinger proper time representation of this determinant is decomposed into a sum of three terms. The advantage of this is that the separate terms can be nonperturbatively estimated for a measurable class of large amplitude random fields in four dimensions. It is found that the QED fermion determinant grows faster than exp [c e2∫d4x Fμν 2] , c >0 , in the absence of zero mode supporting random background potentials. This raises doubt on whether the QED fermion determinant is integrable with any Gaussian measure whose support does not include zero mode supporting potentials. Including zero mode supporting background potentials can result in a decaying exponential growth of the fermion determinant. This is prima facie evidence that Maxwellian zero modes are necessary for the nonperturbative quantization of QED and, by implication, for the nonperturbative quantization of the electroweak model.
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Distillation of squeezing from non-Gaussian quantum states.
Heersink, J; Marquardt, Ch; Dong, R; Filip, R; Lorenz, S; Leuchs, G; Andersen, U L
2006-06-30
We show that single copy distillation of squeezing from continuous variable non-Gaussian states is possible using linear optics and conditional homodyne detection. A specific non-Gaussian noise source, corresponding to a random linear displacement, is investigated experimentally. Conditioning the signal on a tap measurement, we observe probabilistic recovery of squeezing.
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Analysis of speckle and material properties in laider tracer
NASA Astrophysics Data System (ADS)
Ross, Jacob W.; Rigling, Brian D.; Watson, Edward A.
2017-04-01
The SAL simulation tool Laider Tracer models speckle: the random variation in intensity of an incident light beam across a rough surface. Within Laider Tracer, the speckle field is modeled as a 2-D array of jointly Gaussian random variables projected via ray tracing onto the scene of interest. Originally, all materials in Laider Tracer were treated as ideal diffuse scatterers, for which the far-field return computed uses the Lambertian Bidirectional Reflectance Distribution Function (BRDF). As presented here, we implement material properties into Laider Tracer via the Non-conventional Exploitation Factors Data System: a database of properties for thousands of different materials sampled at various wavelengths and incident angles. We verify the intensity behavior as a function of incident angle after material properties are added to the simulation.
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Geostatistical risk estimation at waste disposal sites in the presence of hot spots.
Komnitsas, Kostas; Modis, Kostas
2009-05-30
The present paper aims to estimate risk by using geostatistics at the wider coal mining/waste disposal site of Belkovskaya, Tula region, in Russia. In this area the presence of hot spots causes a spatial trend in the mean value of the random field and a non-Gaussian data distribution. Prior to application of geostatistics, subtraction of trend and appropriate smoothing and transformation of the data into a Gaussian form were carried out; risk maps were then generated for the wider study area in order to assess the probability of exceeding risk thresholds. Finally, the present paper discusses the need for homogenization of soil risk thresholds regarding hazardous elements that will enhance reliability of risk estimation and enable application of appropriate rehabilitation actions in contaminated areas.
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The fast algorithm of spark in compressive sensing
NASA Astrophysics Data System (ADS)
Xie, Meihua; Yan, Fengxia
2017-01-01
Compressed Sensing (CS) is an advanced theory on signal sampling and reconstruction. In CS theory, the reconstruction condition of signal is an important theory problem, and spark is a good index to study this problem. But the computation of spark is NP hard. In this paper, we study the problem of computing spark. For some special matrixes, for example, the Gaussian random matrix and 0-1 random matrix, we obtain some conclusions. Furthermore, for Gaussian random matrix with fewer rows than columns, we prove that its spark equals to the number of its rows plus one with probability 1. For general matrix, two methods are given to compute its spark. One is the method of directly searching and the other is the method of dual-tree searching. By simulating 24 Gaussian random matrixes and 18 0-1 random matrixes, we tested the computation time of these two methods. Numerical results showed that the dual-tree searching method had higher efficiency than directly searching, especially for those matrixes which has as much as rows and columns.
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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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Gaussian Random Fields Methods for Fork-Join Network with Synchronization Constraints
2014-12-22
substantial efforts were dedicated to the study of the max-plus recursions [21, 3, 12]. More recently, Atar et al. [2] have studied a fork-join...feedback and NES, Atar et al. [2] show that a dynamic priority discipline achieves throughput optimal- ity asymptotically in the conventional heavy...2011) Patient flow in hospitals: a data-based queueing-science perspective. Submitted to Stochastic Systems, 20. [2] R. Atar , A. Mandelbaum and A
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On the numbers of images of two stochastic gravitational lensing models
NASA Astrophysics Data System (ADS)
Wei, Ang
2017-02-01
We study two gravitational lensing models with Gaussian randomness: the continuous mass fluctuation model and the floating black hole model. The lens equations of these models are related to certain random harmonic functions. Using Rice's formula and Gaussian techniques, we obtain the expected numbers of zeros of these functions, which indicate the amounts of images in the corresponding lens systems.
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Random Process Simulation for stochastic fatigue analysis. Ph.D. Thesis - Rice Univ., Houston, Tex.
NASA Technical Reports Server (NTRS)
Larsen, Curtis E.
1988-01-01
A simulation technique is described which directly synthesizes the extrema of a random process and is more efficient than the Gaussian simulation method. Such a technique is particularly useful in stochastic fatigue analysis because the required stress range moment E(R sup m), is a function only of the extrema of the random stress process. The family of autoregressive moving average (ARMA) models is reviewed and an autoregressive model is presented for modeling the extrema of any random process which has a unimodal power spectral density (psd). The proposed autoregressive technique is found to produce rainflow stress range moments which compare favorably with those computed by the Gaussian technique and to average 11.7 times faster than the Gaussian technique. The autoregressive technique is also adapted for processes having bimodal psd's. The adaptation involves using two autoregressive processes to simulate the extrema due to each mode and the superposition of these two extrema sequences. The proposed autoregressive superposition technique is 9 to 13 times faster than the Gaussian technique and produces comparable values for E(R sup m) for bimodal psd's having the frequency of one mode at least 2.5 times that of the other mode.
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Detection of nonlinear transfer functions by the use of Gaussian statistics
NASA Technical Reports Server (NTRS)
Sheppard, J. G.
1972-01-01
The possibility of using on-line signal statistics to detect electronic equipment nonlinearities is discussed. The results of an investigation using Gaussian statistics are presented, and a nonlinearity test that uses ratios of the moments of a Gaussian random variable is developed and discussed. An outline for further investigation is presented.
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Circularly symmetric cusped random beams in free space and atmospheric turbulence.
Wang, Fei; Korotkova, Olga
2017-03-06
A class of random stationary, scalar sources producing cusped average intensity profiles (i.e. profiles with concave curvature) in the far field is introduced by modeling the source degree of coherence as a Fractional Multi-Gaussian-correlated Schell-Model (FMGSM) function with rotational symmetry. The average intensity (spectral density) generated by such sources is investigated on propagation in free space and isotropic and homogeneous atmospheric turbulence. It is found that the FMGSM beam can retain the cusped shape on propagation at least in weak or moderate turbulence regimes; however, strong turbulence completely suppresses the cusped intensity profile. Under the same atmospheric conditions the spectral density of the FMGSM beam at the receiver is found to be much higher than that of the conventional Gaussian Schell-model (GSM) beam within the narrow central area, implying that for relatively small collecting apertures the power-in-bucket of the FMGSM beam is higher than that of the GSM beam. Our results are of importance to energy delivery, Free-Space Optical communications and imaging in the atmosphere.
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Spectral turning bands for efficient Gaussian random fields generation on GPUs and accelerators
NASA Astrophysics Data System (ADS)
Hunger, L.; Cosenza, B.; Kimeswenger, S.; Fahringer, T.
2015-11-01
A random field (RF) is a set of correlated random variables associated with different spatial locations. RF generation algorithms are of crucial importance for many scientific areas, such as astrophysics, geostatistics, computer graphics, and many others. Current approaches commonly make use of 3D fast Fourier transform (FFT), which does not scale well for RF bigger than the available memory; they are also limited to regular rectilinear meshes. We introduce random field generation with the turning band method (RAFT), an RF generation algorithm based on the turning band method that is optimized for massively parallel hardware such as GPUs and accelerators. Our algorithm replaces the 3D FFT with a lower-order, one-dimensional FFT followed by a projection step and is further optimized with loop unrolling and blocking. RAFT can easily generate RF on non-regular (non-uniform) meshes and efficiently produce fields with mesh sizes bigger than the available device memory by using a streaming, out-of-core approach. Our algorithm generates RF with the correct statistical behavior and is tested on a variety of modern hardware, such as NVIDIA Tesla, AMD FirePro and Intel Phi. RAFT is faster than the traditional methods on regular meshes and has been successfully applied to two real case scenarios: planetary nebulae and cosmological simulations.
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NASA Astrophysics Data System (ADS)
Voss, Sebastian; Zimmermann, Beate; Zimmermann, Alexander
2016-04-01
In the last three decades, an increasing number of studies analyzed spatial patterns in throughfall to investigate the consequences of rainfall redistribution for biogeochemical and hydrological processes in forests. In the majority of cases, variograms were used to characterize the spatial properties of the throughfall data. The estimation of the variogram from sample data requires an appropriate sampling scheme: most importantly, a large sample and an appropriate layout of sampling locations that often has to serve both variogram estimation and geostatistical prediction. While some recommendations on these aspects exist, they focus on Gaussian data and high ratios of the variogram range to the extent of the study area. However, many hydrological data, and throughfall data in particular, do not follow a Gaussian distribution. In this study, we examined the effect of extent, sample size, sampling design, and calculation methods on variogram estimation of throughfall data. For our investigation, we first generated non-Gaussian random fields based on throughfall data with heavy outliers. Subsequently, we sampled the fields with three extents (plots with edge lengths of 25 m, 50 m, and 100 m), four common sampling designs (two grid-based layouts, transect and random sampling), and five sample sizes (50, 100, 150, 200, 400). We then estimated the variogram parameters by method-of-moments and residual maximum likelihood. Our key findings are threefold. First, the choice of the extent has a substantial influence on the estimation of the variogram. A comparatively small ratio of the extent to the correlation length is beneficial for variogram estimation. Second, a combination of a minimum sample size of 150, a design that ensures the sampling of small distances and variogram estimation by residual maximum likelihood offers a good compromise between accuracy and efficiency. Third, studies relying on method-of-moments based variogram estimation may have to employ at least 200 sampling points for reliable variogram estimates. These suggested sample sizes exceed the numbers recommended by studies dealing with Gaussian data by up to 100 %. Given that most previous throughfall studies relied on method-of-moments variogram estimation and sample sizes << 200, our current knowledge about throughfall spatial variability stands on shaky ground.
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NASA Astrophysics Data System (ADS)
Voss, Sebastian; Zimmermann, Beate; Zimmermann, Alexander
2016-09-01
In the last decades, an increasing number of studies analyzed spatial patterns in throughfall by means of variograms. The estimation of the variogram from sample data requires an appropriate sampling scheme: most importantly, a large sample and a layout of sampling locations that often has to serve both variogram estimation and geostatistical prediction. While some recommendations on these aspects exist, they focus on Gaussian data and high ratios of the variogram range to the extent of the study area. However, many hydrological data, and throughfall data in particular, do not follow a Gaussian distribution. In this study, we examined the effect of extent, sample size, sampling design, and calculation method on variogram estimation of throughfall data. For our investigation, we first generated non-Gaussian random fields based on throughfall data with large outliers. Subsequently, we sampled the fields with three extents (plots with edge lengths of 25 m, 50 m, and 100 m), four common sampling designs (two grid-based layouts, transect and random sampling) and five sample sizes (50, 100, 150, 200, 400). We then estimated the variogram parameters by method-of-moments (non-robust and robust estimators) and residual maximum likelihood. Our key findings are threefold. First, the choice of the extent has a substantial influence on the estimation of the variogram. A comparatively small ratio of the extent to the correlation length is beneficial for variogram estimation. Second, a combination of a minimum sample size of 150, a design that ensures the sampling of small distances and variogram estimation by residual maximum likelihood offers a good compromise between accuracy and efficiency. Third, studies relying on method-of-moments based variogram estimation may have to employ at least 200 sampling points for reliable variogram estimates. These suggested sample sizes exceed the number recommended by studies dealing with Gaussian data by up to 100 %. Given that most previous throughfall studies relied on method-of-moments variogram estimation and sample sizes ≪200, currently available data are prone to large uncertainties.
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Ensemble solute transport in two-dimensional operator-scaling random fields
NASA Astrophysics Data System (ADS)
Monnig, Nathan D.; Benson, David A.; Meerschaert, Mark M.
2008-02-01
Motivated by field measurements of aquifer hydraulic conductivity (K), recent techniques were developed to construct anisotropic fractal random fields in which the scaling, or self-similarity parameter, varies with direction and is defined by a matrix. Ensemble numerical results are analyzed for solute transport through these two-dimensional "operator-scaling" fractional Brownian motion ln(K) fields. Both the longitudinal and transverse Hurst coefficients, as well as the "radius of isotropy" are important to both plume growth rates and the timing and duration of breakthrough. It is possible to create operator-scaling fractional Brownian motion fields that have more "continuity" or stratification in the direction of transport. The effects on a conservative solute plume are continually faster-than-Fickian growth rates, highly non-Gaussian shapes, and a heavier tail early in the breakthrough curve. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rates never exceed A. Mercado's (1967) purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent superstratified growth must be the result of other demonstrable factors, such as initial plume size.
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Efficient 3D porous microstructure reconstruction via Gaussian random field and hybrid optimization.
Jiang, Z; Chen, W; Burkhart, C
2013-11-01
Obtaining an accurate three-dimensional (3D) structure of a porous microstructure is important for assessing the material properties based on finite element analysis. Whereas directly obtaining 3D images of the microstructure is impractical under many circumstances, two sets of methods have been developed in literature to generate (reconstruct) 3D microstructure from its 2D images: one characterizes the microstructure based on certain statistical descriptors, typically two-point correlation function and cluster correlation function, and then performs an optimization process to build a 3D structure that matches those statistical descriptors; the other method models the microstructure using stochastic models like a Gaussian random field and generates a 3D structure directly from the function. The former obtains a relatively accurate 3D microstructure, but computationally the optimization process can be very intensive, especially for problems with large image size; the latter generates a 3D microstructure quickly but sacrifices the accuracy due to issues in numerical implementations. A hybrid optimization approach of modelling the 3D porous microstructure of random isotropic two-phase materials is proposed in this paper, which combines the two sets of methods and hence maintains the accuracy of the correlation-based method with improved efficiency. The proposed technique is verified for 3D reconstructions based on silica polymer composite images with different volume fractions. A comparison of the reconstructed microstructures and the optimization histories for both the original correlation-based method and our hybrid approach demonstrates the improved efficiency of the approach. © 2013 The Authors Journal of Microscopy © 2013 Royal Microscopical Society.
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New constraints on modelling the random magnetic field of the MW
NASA Astrophysics Data System (ADS)
Beck, Marcus C.; Beck, Alexander M.; Beck, Rainer; Dolag, Klaus; Strong, Andrew W.; Nielaba, Peter
2016-05-01
We extend the description of the isotropic and anisotropic random component of the small-scale magnetic field within the existing magnetic field model of the Milky Way from Jansson & Farrar, by including random realizations of the small-scale component. Using a magnetic-field power spectrum with Gaussian random fields, the NE2001 model for the thermal electrons and the Galactic cosmic-ray electron distribution from the current GALPROP model we derive full-sky maps for the total and polarized synchrotron intensity as well as the Faraday rotation-measure distribution. While previous work assumed that small-scale fluctuations average out along the line-of-sight or which only computed ensemble averages of random fields, we show that these fluctuations need to be carefully taken into account. Comparing with observational data we obtain not only good agreement with 408 MHz total and WMAP7 22 GHz polarized intensity emission maps, but also an improved agreement with Galactic foreground rotation-measure maps and power spectra, whose amplitude and shape strongly depend on the parameters of the random field. We demonstrate that a correlation length of 0≈22 pc (05 pc being a 5σ lower limit) is needed to match the slope of the observed power spectrum of Galactic foreground rotation-measure maps. Using multiple realizations allows us also to infer errors on individual observables. We find that previously-used amplitudes for random and anisotropic random magnetic field components need to be rescaled by factors of ≈0.3 and 0.6 to account for the new small-scale contributions. Our model predicts a rotation measure of -2.8±7.1 rad/m2 and 04.4±11. rad/m2 for the north and south Galactic poles respectively, in good agreement with observations. Applying our model to deflections of ultra-high-energy cosmic rays we infer a mean deflection of ≈3.5±1.1 degree for 60 EeV protons arriving from CenA.
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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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Weakly anomalous diffusion with non-Gaussian propagators
NASA Astrophysics Data System (ADS)
Cressoni, J. C.; Viswanathan, G. M.; Ferreira, A. S.; da Silva, M. A. A.
2012-08-01
A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H≈1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H=1/2 but with a non-Gaussian propagator.
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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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Generalized expression for optical source fields
NASA Astrophysics Data System (ADS)
Kamacıoğlu, Canan; Baykal, Yahya
2012-09-01
A generalized optical beam expression is developed that presents the majority of the existing optical source fields such as Bessel, Laguerre-Gaussian, dark hollow, bottle, super Gaussian, Lorentz, super-Lorentz, flat-topped, Hermite-sinusoidal-Gaussian, sinusoidal-Gaussian, annular, Gauss-Legendre, vortex, also their higher order modes with their truncated, elegant and elliptical versions. Source intensity profiles derived from the generalized optical source beam fields are checked to match the intensity profiles of many individual known beam types. Source intensities for several interesting beam combinations are presented. Our generalized optical source beam field expression can be used to examine both the source characteristics and the propagation properties of many different optical beams in a single formulation.
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NASA Astrophysics Data System (ADS)
Selim, M. M.; Bezák, V.
2003-06-01
The one-dimensional version of the radiative transfer problem (i.e. the so-called rod model) is analysed with a Gaussian random extinction function (x). Then the optical length X = 0 Ldx(x) is a Gaussian random variable. The transmission and reflection coefficients, T(X) and R(X), are taken as infinite series. When these series (and also when the series representing T 2(X), T 2(X), R(X)T(X), etc.) are averaged, term by term, according to the Gaussian statistics, the series become divergent after averaging. As it was shown in a former paper by the authors (in Acta Physica Slovaca (2003)), a rectification can be managed when a `modified' Gaussian probability density function is used, equal to zero for X > 0 and proportional to the standard Gaussian probability density for X > 0. In the present paper, the authors put forward an alternative, showing that if the m.s.r. of X is sufficiently small in comparison with & $bar X$ ; , the standard Gaussian averaging is well functional provided that the summation in the series representing the variable T m-j (X)R j (X) (m = 1,2,..., j = 1,...,m) is truncated at a well-chosen finite term. The authors exemplify their analysis by some numerical calculations.
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Alexanderian, Alen; Zhu, Liang; Salloum, Maher; Ma, Ronghui; Yu, Meilin
2017-09-01
In this study, statistical models are developed for modeling uncertain heterogeneous permeability and porosity in tumors, and the resulting uncertainties in pressure and velocity fields during an intratumoral injection are quantified using a nonintrusive spectral uncertainty quantification (UQ) method. Specifically, the uncertain permeability is modeled as a log-Gaussian random field, represented using a truncated Karhunen-Lòeve (KL) expansion, and the uncertain porosity is modeled as a log-normal random variable. The efficacy of the developed statistical models is validated by simulating the concentration fields with permeability and porosity of different uncertainty levels. The irregularity in the concentration field bears reasonable visual agreement with that in MicroCT images from experiments. The pressure and velocity fields are represented using polynomial chaos (PC) expansions to enable efficient computation of their statistical properties. The coefficients in the PC expansion are computed using a nonintrusive spectral projection method with the Smolyak sparse quadrature. The developed UQ approach is then used to quantify the uncertainties in the random pressure and velocity fields. A global sensitivity analysis is also performed to assess the contribution of individual KL modes of the log-permeability field to the total variance of the pressure field. It is demonstrated that the developed UQ approach can effectively quantify the flow uncertainties induced by uncertain material properties of the tumor.
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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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Topology in two dimensions. II - The Abell and ACO cluster catalogues
NASA Astrophysics Data System (ADS)
Plionis, Manolis; Valdarnini, Riccardo; Coles, Peter
1992-09-01
We apply a method for quantifying the topology of projected galaxy clustering to the Abell and ACO catalogues of rich clusters. We use numerical simulations to quantify the statistical bias involved in using high peaks to define the large-scale structure, and we use the results obtained to correct our observational determinations for this known selection effect and also for possible errors introduced by boundary effects. We find that the Abell cluster sample is consistent with clusters being identified with high peaks of a Gaussian random field, but that the ACO shows a slight meatball shift away from the Gaussian behavior over and above that expected purely from the high-peak selection. The most conservative explanation of this effect is that it is caused by some artefact of the procedure used to select the clusters in the two samples.
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The influence of statistical properties of Fourier coefficients on random Gaussian surfaces.
de Castro, C P; Luković, M; Andrade, R F S; Herrmann, H J
2017-05-16
Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently establish the presence of scale invariance. We show that this symmetry is not affected by the distribution of the modulus of the Fourier coefficients. Furthermore, we investigate the role of the Fourier phases of random surfaces. In particular, we show how the surface is affected by a non-uniform distribution of phases.
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NASA Astrophysics Data System (ADS)
Zhang, Hong; Hou, Rui; Yi, Lei; Meng, Juan; Pan, Zhisong; Zhou, Yuhuan
2016-07-01
The accurate identification of encrypted data stream helps to regulate illegal data, detect network attacks and protect users' information. In this paper, a novel encrypted data stream identification algorithm is introduced. The proposed method is based on randomness characteristics of encrypted data stream. We use a l1-norm regularized logistic regression to improve sparse representation of randomness features and Fuzzy Gaussian Mixture Model (FGMM) to improve identification accuracy. Experimental results demonstrate that the method can be adopted as an effective technique for encrypted data stream identification.
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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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Self-Consistent Field Theory of Gaussian Ring Polymers
NASA Astrophysics Data System (ADS)
Kim, Jaeup; Yang, Yong-Biao; Lee, Won Bo
2012-02-01
Ring polymers, being free from chain ends, have fundamental importance in understanding the polymer statics and dynamics which are strongly influenced by the chain end effects. At a glance, their theoretical treatment may not seem particularly difficult, but the absence of chain ends and the topological constraints make the problem non-trivial, which results in limited success in the analytical or semi-analytical formulation of ring polymer theory. Here, I present a self-consistent field theory (SCFT) formalism of Gaussian (topologically unconstrained) ring polymers for the first time. The resulting static property of homogeneous and inhomogeneous ring polymers are compared with the random phase approximation (RPA) results. The critical point for ring homopolymer system is exactly the same as the linear polymer case, χN = 2, since a critical point does not depend on local structures of polymers. The critical point for ring diblock copolymer melts is χN 17.795, which is approximately 1.7 times of that of linear diblock copolymer melts, χN 10.495. The difference is due to the ring structure constraint.
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Large-scale structure in the Southern Sky Redshift Survey
NASA Technical Reports Server (NTRS)
Park, Changbom; Gott, J. R., III; Da Costa, L. N.
1992-01-01
The power spectrum from the Southern Sky Redshift Survey and the CfA samples are measured in order to explore the amplitude of fluctuation in the galaxy density. At lambda of less than or equal to 30/h Mpc the observed power spectrum is quite consistent with the standard CDM model. At larger scales the data indicate an excess of power over the standard CDM model. The observed power spectrum from these optical galaxy samples is in good agreement with that drawn from the sparsely sampled IRAS galaxies. The shape of the power spectrum is also studied by examining the relation between the genus per unit volume and the smoothing length. It is found that, over Gaussian smoothing scales from 6 to 14/h Mpc, the power spectrum has a slope of about -1. The topology of the galaxy density field is studied by measuring the shift of the genus curve from the Gaussian case. Over all smoothing scales studied, the observed genus curves are consistent with a random phase distribution of the galaxy density field, as predicted by the inflationary scenarios.
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Virial expansion for almost diagonal random matrices
NASA Astrophysics Data System (ADS)
Yevtushenko, Oleg; Kravtsov, Vladimir E.
2003-08-01
Energy level statistics of Hermitian random matrices hat H with Gaussian independent random entries Higeqj is studied for a generic ensemble of almost diagonal random matrices with langle|Hii|2rangle ~ 1 and langle|Hi\
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The meta-Gaussian Bayesian Processor of forecasts and associated preliminary experiments
NASA Astrophysics Data System (ADS)
Chen, Fajing; Jiao, Meiyan; Chen, Jing
2013-04-01
Public weather services are trending toward providing users with probabilistic weather forecasts, in place of traditional deterministic forecasts. Probabilistic forecasting techniques are continually being improved to optimize available forecasting information. The Bayesian Processor of Forecast (BPF), a new statistical method for probabilistic forecast, can transform a deterministic forecast into a probabilistic forecast according to the historical statistical relationship between observations and forecasts generated by that forecasting system. This technique accounts for the typical forecasting performance of a deterministic forecasting system in quantifying the forecast uncertainty. The meta-Gaussian likelihood model is suitable for a variety of stochastic dependence structures with monotone likelihood ratios. The meta-Gaussian BPF adopting this kind of likelihood model can therefore be applied across many fields, including meteorology and hydrology. The Bayes theorem with two continuous random variables and the normal-linear BPF are briefly introduced. The meta-Gaussian BPF for a continuous predictand using a single predictor is then presented and discussed. The performance of the meta-Gaussian BPF is tested in a preliminary experiment. Control forecasts of daily surface temperature at 0000 UTC at Changsha and Wuhan stations are used as the deterministic forecast data. These control forecasts are taken from ensemble predictions with a 96-h lead time generated by the National Meteorological Center of the China Meteorological Administration, the European Centre for Medium-Range Weather Forecasts, and the US National Centers for Environmental Prediction during January 2008. The results of the experiment show that the meta-Gaussian BPF can transform a deterministic control forecast of surface temperature from any one of the three ensemble predictions into a useful probabilistic forecast of surface temperature. These probabilistic forecasts quantify the uncertainty of the control forecast; accordingly, the performance of the probabilistic forecasts differs based on the source of the underlying deterministic control forecasts.
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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
In the landscape perspective, our Universe begins with a quantum tunneling from an eternally-inflating parent vacuum, followed by a period of slow-roll inflation. We investigate the tunneling process and calculate the probability distribution for the initial conditions and for the number of e-folds of slow-roll inflation, modeling the landscape by a small-field one-dimensional random Gaussian potential. We find that such a landscape is fully consistent with observations, but the probability for future detection of spatial curvature is rather low, P ∼ 10{sup −3}.
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Hot spots in the microwave sky
NASA Technical Reports Server (NTRS)
Vittorio, Nicola; Juszkiewicz, Roman
1987-01-01
Tha assumption that the cosmic background fluctuations can be approximated as a random Gaussian field implies specific predictions for the radiation temperature pattern. Using this assumption, the abundances and angular sizes are calculated for regions of various levels of brightness expected to appear in the sky. Different observational strategies are assessed in the context of these results. Calculations for both large-angle and small-angle anisotropy generated by scale-invariant fluctuations in a flat universe are presented. Also discussed are simple generalizations to open cosmological models.
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Stochastic uncertainty analysis for unconfined flow systems
Liu, Gaisheng; Zhang, Dongxiao; Lu, Zhiming
2006-01-01
A new stochastic approach proposed by Zhang and Lu (2004), called the Karhunen‐Loeve decomposition‐based moment equation (KLME), has been extended to solving nonlinear, unconfined flow problems in randomly heterogeneous aquifers. This approach is on the basis of an innovative combination of Karhunen‐Loeve decomposition, polynomial expansion, and perturbation methods. The random log‐transformed hydraulic conductivity field (lnKS) is first expanded into a series in terms of orthogonal Gaussian standard random variables with their coefficients obtained as the eigenvalues and eigenfunctions of the covariance function of lnKS. Next, head h is decomposed as a perturbation expansion series Σh(m), where h(m) represents the mth‐order head term with respect to the standard deviation of lnKS. Then h(m) is further expanded into a polynomial series of m products of orthogonal Gaussian standard random variables whose coefficients hi1,i2,...,im(m) are deterministic and solved sequentially from low to high expansion orders using MODFLOW‐2000. Finally, the statistics of head and flux are computed using simple algebraic operations on hi1,i2,...,im(m). A series of numerical test results in 2‐D and 3‐D unconfined flow systems indicated that the KLME approach is effective in estimating the mean and (co)variance of both heads and fluxes and requires much less computational effort as compared to the traditional Monte Carlo simulation technique.
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NASA Astrophysics Data System (ADS)
Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing; Walker, Paul D.
2017-02-01
This paper proposes an uncertain modelling and computational method to analyze dynamic responses of rigid-flexible multibody systems (or mechanisms) with random geometry and material properties. Firstly, the deterministic model for the rigid-flexible multibody system is built with the absolute node coordinate formula (ANCF), in which the flexible parts are modeled by using ANCF elements, while the rigid parts are described by ANCF reference nodes (ANCF-RNs). Secondly, uncertainty for the geometry of rigid parts is expressed as uniform random variables, while the uncertainty for the material properties of flexible parts is modeled as a continuous random field, which is further discretized to Gaussian random variables using a series expansion method. Finally, a non-intrusive numerical method is developed to solve the dynamic equations of systems involving both types of random variables, which systematically integrates the deterministic generalized-α solver with Latin Hypercube sampling (LHS) and Polynomial Chaos (PC) expansion. The benchmark slider-crank mechanism is used as a numerical example to demonstrate the characteristics of the proposed method.
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Monte Carlo modeling of spatial coherence: free-space diffraction
Fischer, David G.; Prahl, Scott A.; Duncan, Donald D.
2008-01-01
We present a Monte Carlo method for propagating partially coherent fields through complex deterministic optical systems. A Gaussian copula is used to synthesize a random source with an arbitrary spatial coherence function. Physical optics and Monte Carlo predictions of the first- and second-order statistics of the field are shown for coherent and partially coherent sources for free-space propagation, imaging using a binary Fresnel zone plate, and propagation through a limiting aperture. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. Convergence criteria are presented for judging the quality of the Monte Carlo predictions. PMID:18830335
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Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile
NASA Astrophysics Data System (ADS)
Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.
2012-09-01
Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.
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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. -
NASA Astrophysics Data System (ADS)
Crevillén-García, D.; Power, H.
2017-08-01
In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log-Gaussian random field by using direct Karhunen-Loéve decompositions. The random terms in such expansions represent the coefficients in the equations. Numerical calculations demonstrating the effectiveness of each of the methods are presented. A comparison of the computational cost incurred by each of the methods for three different tolerances is provided. The accuracy of the approaches is quantified via the mean square error.
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Crevillén-García, D; Power, H
2017-08-01
In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log-Gaussian random field by using direct Karhunen-Loéve decompositions. The random terms in such expansions represent the coefficients in the equations. Numerical calculations demonstrating the effectiveness of each of the methods are presented. A comparison of the computational cost incurred by each of the methods for three different tolerances is provided. The accuracy of the approaches is quantified via the mean square error.
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Power, H.
2017-01-01
In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log-Gaussian random field by using direct Karhunen–Loéve decompositions. The random terms in such expansions represent the coefficients in the equations. Numerical calculations demonstrating the effectiveness of each of the methods are presented. A comparison of the computational cost incurred by each of the methods for three different tolerances is provided. The accuracy of the approaches is quantified via the mean square error. PMID:28878974
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Robustifying blind image deblurring methods by simple filters
NASA Astrophysics Data System (ADS)
Liu, Yan; Zeng, Xiangrong; Huangpeng, Qizi; Fan, Jun; Zhou, Jinglun; Feng, Jing
2016-07-01
The state-of-the-art blind image deblurring (BID) methods are sensitive to noise, and most of them can deal with only small levels of Gaussian noise. In this paper, we use simple filters to present a robust BID framework which is able to robustify exiting BID methods to high-level Gaussian noise or/and Non-Gaussian noise. Experiments on images in presence of Gaussian noise, impulse noise (salt-and-pepper noise and random-valued noise) and mixed Gaussian-impulse noise, and a real-world blurry and noisy image show that the proposed method can faster estimate sharper kernels and better images, than that obtained by other methods.
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Large-scale magnetic fields, non-Gaussianity, and gravitational waves from inflation
NASA Astrophysics Data System (ADS)
Bamba, Kazuharu
2017-12-01
We explore the generation of large-scale magnetic fields in the so-called moduli inflation. The hypercharge electromagnetic fields couple to not only a scalar field but also a pseudoscalar one, so that the conformal invariance of the hypercharge electromagnetic fields can be broken. We explicitly analyze the strength of the magnetic fields on the Hubble horizon scale at the present time, the local non-Gaussianity of the curvature perturbations originating from the massive gauge fields, and the tensor-to-scalar ratio of the density perturbations. As a consequence, we find that the local non-Gaussianity and the tensor-to-scalar ratio are compatible with the recent Planck results.
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NASA Astrophysics Data System (ADS)
Cheraghalizadeh, Jafar; Najafi, Morteza N.; Mohammadzadeh, Hossein
2018-05-01
The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize the correlations between the MNPs we have used the Ising model with an artificial temperature T that controls the number of MNPs as well as their correlations. In the T → 0 limit, one retrieves the Gaussian free field (GFF), and in the finite temperature the problem is equivalent to a GFF in iso-potential islands. The problem is argued to be equivalent to a scale-invariant random surface with some critical exponents which vary with T and correspondingly are correlation-dependent. Two type of observables have been considered: local and global quantities. We have observed that the MNPs soften the random potential and reduce its statistical fluctuations. This softening is observed in the local as well as the geometrical quantities. The correlation function of the electrostatic and its total variance are observed to be logarithmic just like the GFF, i.e. the roughness exponent remains zero for all temperatures, whereas the proportionality constants scale with T - T c . The fractal dimension of iso-potential lines ( D f ), the exponent of the distribution function of the gyration radius ( τ r ), and the loop lengths ( τ l ), and also the exponent of the loop Green function x l change in terms of T - T c in a power-law fashion, with some critical exponents reported in the text. Importantly we have observed that D f ( T) - D f ( T c ) 1/√ ξ( T), in which ξ( T) is the spin correlation length in the Ising model.
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Anomalous transport in fluid field with random waiting time depending on the preceding jump length
NASA Astrophysics Data System (ADS)
Zhang, Hong; Li, Guo-Hua
2016-11-01
Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. Project supported by the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414) and the Opening Foundation of Geomathematics Key Laboratory of Sichuan Province, China (Grant No. scsxdz2013009).
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Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates
Gill, Mandev S.; Lemey, Philippe; Bennett, Shannon N.; Biek, Roman; Suchard, Marc A.
2016-01-01
Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics and evolutionary biology. Kingman’s coalescent process enables inference of past population dynamics directly from molecular sequence data, and researchers have developed a number of flexible coalescent-based models for Bayesian nonparametric estimation of the effective population size as a function of time. Major goals of demographic reconstruction include identifying driving factors of effective population size, and understanding the association between the effective population size and such factors. Building upon Bayesian nonparametric coalescent-based approaches, we introduce a flexible framework that incorporates time-varying covariates that exploit Gaussian Markov random fields to achieve temporal smoothing of effective population size trajectories. To approximate the posterior distribution, we adapt efficient Markov chain Monte Carlo algorithms designed for highly structured Gaussian models. Incorporating covariates into the demographic inference framework enables the modeling of associations between the effective population size and covariates while accounting for uncertainty in population histories. Furthermore, it can lead to more precise estimates of population dynamics. We apply our model to four examples. We reconstruct the demographic history of raccoon rabies in North America and find a significant association with the spatiotemporal spread of the outbreak. Next, we examine the effective population size trajectory of the DENV-4 virus in Puerto Rico along with viral isolate count data and find similar cyclic patterns. We compare the population history of the HIV-1 CRF02_AG clade in Cameroon with HIV incidence and prevalence data and find that the effective population size is more reflective of incidence rate. Finally, we explore the hypothesis that the population dynamics of musk ox during the Late Quaternary period were related to climate change. [Coalescent; effective population size; Gaussian Markov random fields; phylodynamics; phylogenetics; population genetics. PMID:27368344
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Normal and tumoral melanocytes exhibit q-Gaussian random search patterns.
da Silva, Priscila C A; Rosembach, Tiago V; Santos, Anésia A; Rocha, Márcio S; Martins, Marcelo L
2014-01-01
In multicellular organisms, cell motility is central in all morphogenetic processes, tissue maintenance, wound healing and immune surveillance. Hence, failures in its regulation potentiates numerous diseases. Here, cell migration assays on plastic 2D surfaces were performed using normal (Melan A) and tumoral (B16F10) murine melanocytes in random motility conditions. The trajectories of the centroids of the cell perimeters were tracked through time-lapse microscopy. The statistics of these trajectories was analyzed by building velocity and turn angle distributions, as well as velocity autocorrelations and the scaling of mean-squared displacements. We find that these cells exhibit a crossover from a normal to a super-diffusive motion without angular persistence at long time scales. Moreover, these melanocytes move with non-Gaussian velocity distributions. This major finding indicates that amongst those animal cells supposedly migrating through Lévy walks, some of them can instead perform q-Gaussian walks. Furthermore, our results reveal that B16F10 cells infected by mycoplasmas exhibit essentially the same diffusivity than their healthy counterparts. Finally, a q-Gaussian random walk model was proposed to account for these melanocytic migratory traits. Simulations based on this model correctly describe the crossover to super-diffusivity in the cell migration tracks.
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NASA Astrophysics Data System (ADS)
Gott, J. Richard, III
1998-09-01
Topology may play an important role in cosmology in several different ways. First, Einstein's field equations tell us about the local geometry of the universe but not about its topology. Therefore, the universe may be multiply connected. Inflation predicts that the fluctuations that made clusters and groups of galaxies arose from random quantum fluctuations in the early universe. These should be Gaussian random phase. This can be tested by quantitatively measuring the topology of large-scale structure in the universe using the genus statistic. If the original fluctuations were Gaussian random phase then the structure we see today should have a spongelike topology. A number of studies by our group and others have shown that this is indeed the case. Future tests using the Sloan Digital Sky Survey should be possible. Microwave background fluctuations should also exhibit a characteristic symmetric pattern of hot and cold spots. The COBE data are consistent with this pattern and the MAP and PLANCK satellites should provide a definitive test. If the original inflationary state was metastable then it should decay by making an infinite number of open inflationary bubble universes. This model makes a specific prediction for the power spectrum of fluctuations in the microwave background which can be checked by the MAP and PLANCK satellites. Finally, Gott and Li have proposed how a multiply connected cosmology with an early epoch of closed timelike curves might allow the universe to be its own mother.
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Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory
DOE Office of Scientific and Technical Information (OSTI.GOV)
Shalchi, A.; Negrea, M.; Petrisor, I.
2016-07-15
We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficientsmore » and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.« less
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Scattering of electromagnetic wave by the layer with one-dimensional random inhomogeneities
NASA Astrophysics Data System (ADS)
Kogan, Lev; Zaboronkova, Tatiana; Grigoriev, Gennadii., IV.
A great deal of attention has been paid to the study of probability characteristics of electro-magnetic waves scattered by one-dimensional fluctuations of medium dielectric permittivity. However, the problem of a determination of a density of a probability and average intensity of the field inside the stochastically inhomogeneous medium with arbitrary extension of fluc-tuations has not been considered yet. It is the purpose of the present report to find and to analyze the indicated functions for the plane electromagnetic wave scattered by the layer with one-dimensional fluctuations of permittivity. We assumed that the length and the amplitude of individual fluctuations as well the interval between them are random quantities. All of indi-cated fluctuation parameters are supposed as independent random values possessing Gaussian distribution. We considered the stationary time cases both small-scale and large-scale rarefied inhomogeneities. Mathematically such problem can be reduced to the solution of integral Fred-holm equation of second kind for Hertz potential (U). Using the decomposition of the field into the series of multiply scattered waves we obtained the expression for a probability density of the field of the plane wave and determined the moments of the scattered field. We have shown that all odd moments of the centered field (U-¡U¿) are equal to zero and the even moments depend on the intensity. It was obtained that the probability density of the field possesses the Gaussian distribution. The average field is small compared with the standard fluctuation of scattered field for all considered cases of inhomogeneities. The value of average intensity of the field is an order of a standard of fluctuations of field intensity and drops with increases the inhomogeneities length in the case of small-scale inhomogeneities. The behavior of average intensity is more complicated in the case of large-scale medium inhomogeneities. The value of average intensity is the oscillating function versus the average fluctuations length if the standard of fluctuations of inhomogeneities length is greater then the wave length. When the standard of fluctuations of medium inhomogeneities extension is smaller then the wave length, the av-erage intensity value weakly depends from the average fluctuations extension. The obtained results may be used for analysis of the electromagnetic wave propagation into the media with the fluctuating parameters caused by such factors as leafs of trees, cumulus, internal gravity waves with a chaotic phase and etc. Acknowledgment: This work was supported by the Russian Foundation for Basic Research (projects 08-02-97026 and 09-05-00450).
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Smirnov, V.N.; Strokovskii, G.A.
An analytical form of expansion coefficients of a diffracted field for an arbitrary Hermite-Gaussian beam in an alien Hermite-Gaussian basis is obtained. A possible physical interpretation of the well-known Young phenomenological diffraction principle and experiments on diffraction of Hermite-Gaussian beams of the lowest types (n = 0 - 5) from half-plane are discussed. The case of nearly homogenous expansion corresponding to misalignment and mismatch of optical systems is also analyzed. 7 refs., 2 figs.
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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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NASA Astrophysics Data System (ADS)
Wang, Kai; Cao, Qing; Zhang, Huifang; Shen, Pengcheng; Xing, Lujing
2018-06-01
Based on the TE01 mode of a rectangular metal waveguide and the Gaussian mode of a fiber, we propose the cos-Gaussian mode of a terahertz rectangular metal waveguide filled with multiple slices of dielectric. First, we consider a rectangular metal waveguide filled with an ideal graded-index dielectric along one direction. Furthermore, we replace the graded-index dielectric with multiple slices of dielectric according to the effective medium theory. The modal field, the effective index, and the coupling efficiency of this waveguide are investigated. It is found that the approximately linearly polarized electric field is Gaussian along one dimensionality and cosine along the other one. In addition, the low loss and high coupling efficiency with a Gaussian beam can be acquired at 0.9 THz. By optimization, the coupling efficiency could reach 88.5%.
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Strength functions, entropies, and duality in weakly to strongly interacting fermionic systems.
Angom, D; Ghosh, S; Kota, V K B
2004-01-01
We revisit statistical wave function properties of finite systems of interacting fermions in the light of strength functions and their participation ratio and information entropy. For weakly interacting fermions in a mean-field with random two-body interactions of increasing strength lambda, the strength functions F(k) (E) are well known to change, in the regime where level fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We propose an ansatz for the function describing this transition which we use to investigate the participation ratio xi(2) and the information entropy S(info) during this crossover, thereby extending the known behavior valid in the Gaussian domain into much of the Breit-Wigner domain. Our method also allows us to derive the scaling law lambda(d) approximately 1/sqrt[m] ( m is number of fermions) for the duality point lambda= lambda(d), where F(k) (E), xi(2), and S(info) in both the weak ( lambda=0 ) and strong mixing ( lambda= infinity ) basis coincide. As an application, the ansatz function for strength functions is used in describing the Breit-Wigner to Gaussian transition seen in neutral atoms CeI to SmI with valence electrons changing from 4 to 8.
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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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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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Large-scale modeling of rain fields from a rain cell deterministic model
NASA Astrophysics Data System (ADS)
FéRal, Laurent; Sauvageot, Henri; Castanet, Laurent; Lemorton, JoëL.; Cornet, FréDéRic; Leconte, Katia
2006-04-01
A methodology to simulate two-dimensional rain rate fields at large scale (1000 × 1000 km2, the scale of a satellite telecommunication beam or a terrestrial fixed broadband wireless access network) is proposed. It relies on a rain rate field cellular decomposition. At small scale (˜20 × 20 km2), the rain field is split up into its macroscopic components, the rain cells, described by the Hybrid Cell (HYCELL) cellular model. At midscale (˜150 × 150 km2), the rain field results from the conglomeration of rain cells modeled by HYCELL. To account for the rain cell spatial distribution at midscale, the latter is modeled by a doubly aggregative isotropic random walk, the optimal parameterization of which is derived from radar observations at midscale. The extension of the simulation area from the midscale to the large scale (1000 × 1000 km2) requires the modeling of the weather frontal area. The latter is first modeled by a Gaussian field with anisotropic covariance function. The Gaussian field is then turned into a binary field, giving the large-scale locations over which it is raining. This transformation requires the definition of the rain occupation rate over large-scale areas. Its probability distribution is determined from observations by the French operational radar network ARAMIS. The coupling with the rain field modeling at midscale is immediate whenever the large-scale field is split up into midscale subareas. The rain field thus generated accounts for the local CDF at each point, defining a structure spatially correlated at small scale, midscale, and large scale. It is then suggested that this approach be used by system designers to evaluate diversity gain, terrestrial path attenuation, or slant path attenuation for different azimuth and elevation angle directions.
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Thermodynamical Limit for Correlated Gaussian Random Energy Models
NASA Astrophysics Data System (ADS)
Contucci, P.; Esposti, M. Degli; Giardinà, C.; Graffi, S.
Let {EΣ(N)}ΣΣN be a family of |ΣN|=2N centered unit Gaussian random variables defined by the covariance matrix CN of elements cN(Σ,τ):=Av(EΣ(N)Eτ(N)) and the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition N=N1+N2, and all pairs (Σ,τ)ΣN×ΣN:
where πk(Σ),k=1,2 are the projections of ΣΣN into ΣNk. The condition is explicitly verified for the Sherrington-Kirkpatrick, the even p-spin, the Derrida REM and the Derrida-Gardner GREM models. -
The formation of cosmic structure in a texture-seeded cold dark matter cosmogony
NASA Technical Reports Server (NTRS)
Gooding, Andrew K.; Park, Changbom; Spergel, David N.; Turok, Neil; Gott, Richard, III
1992-01-01
The growth of density fluctuations induced by global texture in an Omega = 1 cold dark matter (CDM) cosmogony is calculated. The resulting power spectra are in good agreement with each other, with more power on large scales than in the standard inflation plus CDM model. Calculation of related statistics (two-point correlation functions, mass variances, cosmic Mach number) indicates that the texture plus CDM model compares more favorably than standard CDM with observations of large-scale structure. Texture produces coherent velocity fields on large scales, as observed. Excessive small-scale velocity dispersions, and voids less empty than those observed may be remedied by including baryonic physics. The topology of the cosmic structure agrees well with observation. The non-Gaussian texture induced density fluctuations lead to earlier nonlinear object formation than in Gaussian models and may also be more compatible with recent evidence that the galaxy density field is non-Gaussian on large scales. On smaller scales the density field is strongly non-Gaussian, but this appears to be primarily due to nonlinear gravitational clustering. The velocity field on smaller scales is surprisingly Gaussian.
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A 2D Gaussian-Beam-Based Method for Modeling the Dichroic Surfaces of Quasi-Optical Systems
NASA Astrophysics Data System (ADS)
Elis, Kevin; Chabory, Alexandre; Sokoloff, Jérôme; Bolioli, Sylvain
2016-08-01
In this article, we propose an approach in the spectral domain to treat the interaction of a field with a dichroic surface in two dimensions. For a Gaussian beam illumination of the surface, the reflected and transmitted fields are approximated by one reflected and one transmitted Gaussian beams. Their characteristics are determined by means of a matching in the spectral domain, which requires a second-order approximation of the dichroic surface response when excited by plane waves. This approximation is of the same order as the one used in Gaussian beam shooting algorithm to model curved interfaces associated with lenses, reflector, etc. The method uses general analytical formulations for the GBs that depend either on a paraxial or far-field approximation. Numerical experiments are led to test the efficiency of the method in terms of accuracy and computation time. They include a parametric study and a case for which the illumination is provided by a horn antenna. For the latter, the incident field is firstly expressed as a sum of Gaussian beams by means of Gabor frames.
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Koga, D; Chian, A C-L; Miranda, R A; Rempel, E L
2007-04-01
The link between phase coherence and non-Gaussian statistics is investigated using magnetic field data observed in the solar wind turbulence near the Earth's bow shock. The phase coherence index Cphi, which characterizes the degree of phase correlation (i.e., nonlinear wave-wave interactions) among scales, displays a behavior similar to kurtosis and reflects a departure from Gaussianity in the probability density functions of magnetic field fluctuations. This demonstrates that nonlinear interactions among scales are the origin of intermittency in the magnetic field turbulence.
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Assessing Gaussian Assumption of PMU Measurement Error Using Field Data
Wang, Shaobu; Zhao, Junbo; Huang, Zhenyu; ...
2017-10-13
Gaussian PMU measurement error has been assumed for many power system applications, such as state estimation, oscillatory modes monitoring, voltage stability analysis, to cite a few. This letter proposes a simple yet effective approach to assess this assumption by using the stability property of a probability distribution and the concept of redundant measurement. Extensive results using field PMU data from WECC system reveal that the Gaussian assumption is questionable.
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Horizon in random matrix theory, the Hawking radiation, and flow of cold atoms.
Franchini, Fabio; Kravtsov, Vladimir E
2009-10-16
We propose a Gaussian scalar field theory in a curved 2D metric with an event horizon as the low-energy effective theory for a weakly confined, invariant random matrix ensemble (RME). The presence of an event horizon naturally generates a bath of Hawking radiation, which introduces a finite temperature in the model in a nontrivial way. A similar mapping with a gravitational analogue model has been constructed for a Bose-Einstein condensate (BEC) pushed to flow at a velocity higher than its speed of sound, with Hawking radiation as sound waves propagating over the cold atoms. Our work suggests a threefold connection between a moving BEC system, black-hole physics and unconventional RMEs with possible experimental applications.
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Statistical crossover characterization of the heterotic localized-extended transition.
Ugajin, Ryuichi
2003-07-01
We investigated the spectral statistics of a quantum particle in a superlattice consisting of a disordered layer and a clean layer, possibly accompanied by random magnetic fields. Because a disordered layer has localized states and a clean layer has extended states, our quantum system shows a heterotic phase of an Anderson insulator and a normal metal. As the ratio of the volume of these two layers changes, the spectral statistics change from Poissonian to one of the Gaussian ensembles which characterize quantum chaos. A crossover distribution specified by two parameters is introduced to distinguish the transition from an integrable system to a quantum chaotic system during the heterotic phase from an Anderson transition in which the degree of random potentials is homogenous.
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Correlations of RMT characteristic polynomials and integrability: Hermitean matrices
DOE Office of Scientific and Technical Information (OSTI.GOV)
Osipov, Vladimir Al., E-mail: Vladimir.Osipov@uni-due.d; Kanzieper, Eugene, E-mail: Eugene.Kanzieper@hit.ac.i; Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100
Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general theory of {tau} functions, we (i) identify a zoo of hierarchical relations satisfied by {tau} functions in an abstract infinite-dimensional space and (ii) present a technology to translate these relations into hierarchically structured nonlinear differential equations describing the correlation functions of characteristic polynomials in the physical, spectral space. Implications of this formalism for fermionic, bosonic, and supersymmetric variations of zero-dimensional replica field theories are discussed at length. A particular emphasismore » is placed on the phenomenon of fermionic-bosonic factorisation of random-matrix-theory correlation functions.« less
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Gaussian-reflectivity mirror resonator for a high-power transverse-flow CO2 laser.
Ling, Dongxiong; Chen, Junruo; Li, Junchang
2006-05-01
A Gaussian-reflectivity mirror resonator is proposed to achieve high-quality laser beams. To analyze the laser fields in a Gaussian-reflectivity mirror resonator, the diffraction integral equations of a Gaussian-reflectivity mirror resonator are converted to the finite-sum matrix equations. Consequently, according to the Fox-Li laser self-reproducing principle, we describe the mode fields and their losses in the proposed resonator as eigenvectors and eigenvalues of a transfer matrix. The conclusion can be drawn from the numerical results that, if a Gaussian-reflectivity mirror is adopted for a plano-concave resonator, a fundamental mode can easily be obtained from a transverse-flow CO2 laser and high-quality laser beams can be expected.
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Percolation Analysis of a Wiener Reconstruction of the IRAS 1.2 Jy Redshift Catalog
NASA Astrophysics Data System (ADS)
Yess, Capp; Shandarin, Sergei F.; Fisher, Karl B.
1997-01-01
We present percolation analyses of Wiener reconstructions of the IRAS 1.2 Jy redshift survey. There are 10 reconstructions of galaxy density fields in real space spanning the range β = 0.1-1.0, where β = Ω0.6/b, Ω is the present dimensionless density, and b is the bias factor. Our method uses the growth of the largest cluster statistic to characterize the topology of a density field, where Gaussian randomized versions of the reconstructions are used as standards for analysis. For the reconstruction volume of radius R ~ 100 h-1 Mpc, percolation analysis reveals a slight ``meatball'' topology for the real space, galaxy distribution of the IRAS survey.
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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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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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Wilhelm, Jan; Seewald, Patrick; Del Ben, Mauro; Hutter, Jürg
2016-12-13
We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring [Formula: see text] operations and [Formula: see text] memory. The method is based on the resolution of the identity (RI) with the overlap metric, a reformulation of RI-RPA in the Gaussian basis, imaginary time, and imaginary frequency integration techniques, and the use of sparse linear algebra. Additional memory reduction without extra computations can be achieved by an iterative scheme that overcomes the memory bottleneck of canonical RPA implementations. We report a massively parallel implementation that is the key for the application to large systems. Finally, cubic-scaling RPA is applied to a thousand water molecules using a correlation-consistent triple-ζ quality basis.
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NASA Astrophysics Data System (ADS)
Cascio, David M.
1988-05-01
States of nature or observed data are often stochastically modelled as Gaussian random variables. At times it is desirable to transmit this information from a source to a destination with minimal distortion. Complicating this objective is the possible presence of an adversary attempting to disrupt this communication. In this report, solutions are provided to a class of minimax and maximin decision problems, which involve the transmission of a Gaussian random variable over a communications channel corrupted by both additive Gaussian noise and probabilistic jamming noise. The jamming noise is termed probabilistic in the sense that with nonzero probability 1-P, the jamming noise is prevented from corrupting the channel. We shall seek to obtain optimal linear encoder-decoder policies which minimize given quadratic distortion measures.
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specsim: A Fortran-77 program for conditional spectral simulation in 3D
NASA Astrophysics Data System (ADS)
Yao, Tingting
1998-12-01
A Fortran 77 program, specsim, is presented for conditional spectral simulation in 3D domains. The traditional Fourier integral method allows generating random fields with a given covariance spectrum. Conditioning to local data is achieved by an iterative identification of the conditional phase information. A flowchart of the program is given to illustrate the implementation procedures of the program. A 3D case study is presented to demonstrate application of the program. A comparison with the traditional sequential Gaussian simulation algorithm emphasizes the advantages and drawbacks of the proposed algorithm.
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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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NASA Astrophysics Data System (ADS)
Kang, Yan-Mei; Chen, Xi; Lin, Xu-Dong; Tan, Ning
The mean first passage time (MFPT) in a phenomenological gene transcriptional regulatory model with non-Gaussian noise is analytically investigated based on the singular perturbation technique. The effect of the non-Gaussian noise on the phenomenon of stochastic resonance (SR) is then disclosed based on a new combination of adiabatic elimination and linear response approximation. Compared with the results in the Gaussian noise case, it is found that bounded non-Gaussian noise inhibits the transition between different concentrations of protein, while heavy-tailed non-Gaussian noise accelerates the transition. It is also found that the optimal noise intensity for SR in the heavy-tailed noise case is smaller, while the optimal noise intensity in the bounded noise case is larger. These observations can be explained by the heavy-tailed noise easing random transitions.
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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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Studies on system and measuring method of far-field beam divergency in near field by Ronchi ruling
NASA Astrophysics Data System (ADS)
Zhou, Chenbo; Yang, Li; Ma, Wenli; Yan, Peiying; Fan, Tianquan; He, Shangfeng
1996-10-01
Up to now, as large as seven times of Rayleigh-range or more is needed in measuring the far-field Gaussian beam divergency. This method is very inconvenient for the determination of the output beam divergency of the industrial product such as He-Ne lasers and the measuring unit will occupy a large space. The measurement and the measuring accuracy will be greatly influenced by the environment. Application of the Ronchi ruling to the measurement of far-field divergency of Gaussian beam in near-field is analyzed in the paper. The theoretical research and the experiments show that this measuring method is convenient in industrial application. The measuring system consists of a precision mechanical unit which scans Gaussian beam with a microdisplaced Ronchi ruling, a signal sampling system, a single-chip microcomputer data processing system and an electronic unit with microprinter output. The characteristics of the system is stable and the repeatability errors of the system are low. The spot size and far-field divergency of visible Gaussian laser beam can be measured with the system.
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Randomized central limit theorems: A unified theory.
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
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Randomized central limit theorems: A unified theory
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2010-08-01
The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.
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Feinauer, Christoph; Procaccini, Andrea; Zecchina, Riccardo; Weigt, Martin; Pagnani, Andrea
2014-01-01
In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our method aims at extracting such constraints from rapidly accumulating sequence data, and thereby at inferring protein structure and function from sequence information alone. Recently, global statistical inference methods (e.g. direct-coupling analysis, sparse inverse covariance estimation) have achieved a breakthrough towards this aim, and their predictions have been successfully implemented into tertiary and quaternary protein structure prediction methods. However, due to the discrete nature of the underlying variable (amino-acids), exact inference requires exponential time in the protein length, and efficient approximations are needed for practical applicability. Here we propose a very efficient multivariate Gaussian modeling approach as a variant of direct-coupling analysis: the discrete amino-acid variables are replaced by continuous Gaussian random variables. The resulting statistical inference problem is efficiently and exactly solvable. We show that the quality of inference is comparable or superior to the one achieved by mean-field approximations to inference with discrete variables, as done by direct-coupling analysis. This is true for (i) the prediction of residue-residue contacts in proteins, and (ii) the identification of protein-protein interaction partner in bacterial signal transduction. An implementation of our multivariate Gaussian approach is available at the website http://areeweb.polito.it/ricerca/cmp/code. PMID:24663061
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Generic evolution of mixing in heterogeneous media
NASA Astrophysics Data System (ADS)
De Dreuzy, J.; Carrera, J.; Dentz, M.; Le Borgne, T.
2011-12-01
Mixing in heterogeneous media results from the competition bewteen flow fluctuations and local scale diffusion. Flow fluctuations quickly create concentration contrasts and thus heterogeneity of the concentration field, which is slowly homogenized by local scale diffusion. Mixing first deviates from Gaussian mixing, which represents the potential mixing induced by spreading before approaching it. This deviation fundamentally expresses the evolution of the interaction between spreading and local scale diffusion. We characterize it by the ratio γ of the non-Gaussian to the Gaussian mixing states. We define the Gaussian mixing state as the integrated squared concentration of the Gaussian plume that has the same longitudinal dispersion as the real plume. The non-Gaussian mixing state is the difference between the overall mixing state defined as the integrated squared concentration and the Gaussian mixing state. The main advantage of this definition is to use the full knowledge previously acquired on dispersion for characterizing mixing even when the solute concentration field is highly non Gaussian. Using high precision numerical simulations, we show that γ quickly increases, peaks and slowly decreases. γ can be derived from two scales characterizing spreading and local mixing, at least for large flux-weighted solute injection conditions into classically log-normal Gaussian correlated permeability fields. The spreading scale is directly related to the longitudinal dispersion. The local mixing scale is the largest scale over which solute concentrations can be considered locally uniform. More generally, beyond the characteristics of its maximum, γ turns out to have a highly generic scaling form. Its fast increase and slow decrease depend neither on the heterogeneity level, nor on the ratio of diffusion to advection, nor on the injection conditions. They might even not depend on the particularities of the flow fields as the same generic features also prevail for Taylor dispersion. This generic characterization of mixing can offer new ways to set up transport equations that honor not only advection and spreading (dispersion), but also mixing.
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Random mechanics: Nonlinear vibrations, turbulences, seisms, swells, fatigue
NASA Astrophysics Data System (ADS)
Kree, P.; Soize, C.
The random modeling of physical phenomena, together with probabilistic methods for the numerical calculation of random mechanical forces, are analytically explored. Attention is given to theoretical examinations such as probabilistic concepts, linear filtering techniques, and trajectory statistics. Applications of the methods to structures experiencing atmospheric turbulence, the quantification of turbulence, and the dynamic responses of the structures are considered. A probabilistic approach is taken to study the effects of earthquakes on structures and to the forces exerted by ocean waves on marine structures. Theoretical analyses by means of vector spaces and stochastic modeling are reviewed, as are Markovian formulations of Gaussian processes and the definition of stochastic differential equations. Finally, random vibrations with a variable number of links and linear oscillators undergoing the square of Gaussian processes are investigated.
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Dimension from covariance matrices.
Carroll, T L; Byers, J M
2017-02-01
We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.
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NASA Astrophysics Data System (ADS)
Buldyrev, S.; Davis, A.; Marshak, A.; Stanley, H. E.
2001-12-01
Two-stream radiation transport models, as used in all current GCM parameterization schemes, are mathematically equivalent to ``standard'' diffusion theory where the physical picture is a slow propagation of the diffuse radiation by Gaussian random walks. The space/time spread (technically, the Green function) of this diffusion process is described exactly by a Gaussian distribution; from the statistical physics viewpoint, this follows from the convergence of the sum of many (rescaled) steps between scattering events with a finite variance. This Gaussian picture follows directly from first principles (the radiative transfer equation) under the assumptions of horizontal uniformity and large optical depth, i.e., there is a homogeneous plane-parallel cloud somewhere in the column. The first-order effect of 3D variability of cloudiness, the main source of scattering, is to perturb the distribution of single steps between scatterings which, modulo the ``1-g'' rescaling, can be assumed effectively isotropic. The most natural generalization of the Gaussian distribution is the 1-parameter family of symmetric Lévy-stable distributions because the sum of many zero-mean random variables with infinite variance, but finite moments of order q < α (0 < α < 2), converge to them. It has been shown on heuristic grounds that for these Lévy-based random walks the typical number of scatterings is now (1-g)τ α for transmitted light. The appearance of a non-rational exponent is why this is referred to as ``anomalous'' diffusion. Note that standard/Gaussian diffusion is retrieved in the limit α = 2-. Lévy transport theory has been successfully used in the statistical physics literature to investigate a wide variety of systems with strongly nonlinear dynamics; these applications range from random advection in turbulent fluids to the erratic behavior of financial time-series and, most recently, self-regulating ecological systems. We will briefly survey the state-of-the-art observations that offer compelling empirical support for the Lévy/anomalous diffusion model in atmospheric radiation: (1) high-resolution spectroscopy of differential absorption in the O2 A-band from ground; (2) temporal transient records of lightning strokes transmitted through clouds to a sensitive detector in space; and (3) the Gamma-distributions of optical depths derived from Landsat cloud scenes at 30-m resolution. We will then introduce a rigorous analytical formulation of Lévy/anomalous transport through finite media based on fractional derivatives and Sonin calculus. A remarkable result from this new theoretical development is an extremal property of the α = 1+ case (divergent mean-free-path), as is observed in the cloudy atmosphere. Finally, we will discuss the implications of anomalous transport theory for bulk 3D effects on the current enhanced absorption problem as well as its role as the basis of a next-generation GCM radiation parameterization.
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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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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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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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Characteristics of level-spacing statistics in chaotic graphene billiards.
Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2011-03-01
A fundamental result in nonrelativistic quantum nonlinear dynamics is that the spectral statistics of quantum systems that possess no geometric symmetry, but whose classical dynamics are chaotic, are described by those of the Gaussian orthogonal ensemble (GOE) or the Gaussian unitary ensemble (GUE), in the presence or absence of time-reversal symmetry, respectively. For massless spin-half particles such as neutrinos in relativistic quantum mechanics in a chaotic billiard, the seminal work of Berry and Mondragon established the GUE nature of the level-spacing statistics, due to the combination of the chirality of Dirac particles and the confinement, which breaks the time-reversal symmetry. A question is whether the GOE or the GUE statistics can be observed in experimentally accessible, relativistic quantum systems. We demonstrate, using graphene confinements in which the quasiparticle motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are persistently those of GOE random matrices. We present extensive numerical evidence obtained from the tight-binding approach and a physical explanation for the GOE statistics. We also find that the presence of a weak magnetic field switches the statistics to those of GUE. For a strong magnetic field, Landau levels become influential, causing the level-spacing distribution to deviate markedly from the random-matrix predictions. Issues addressed also include the effects of a number of realistic factors on level-spacing statistics such as next nearest-neighbor interactions, different lattice orientations, enhanced hopping energy for atoms on the boundary, and staggered potential due to graphene-substrate interactions.
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On the connectivity of the cosmic web: theory and implications for cosmology and galaxy formation
NASA Astrophysics Data System (ADS)
Codis, Sandrine; Pogosyan, Dmitri; Pichon, Christophe
2018-06-01
Cosmic connectivity and multiplicity, i.e. the number of filaments globally or locally connected to a given cluster is a natural probe of the growth of structure and in particular of the nature of dark energy. It is also a critical ingredient driving the assembly history of galaxies as it controls mass and angular momentum accretion. The connectivity of the cosmic web is investigated here via the persistent skeleton. This tool identifies topologically the ridges of the cosmic landscape which allows us to investigate how the nodes of the cosmic web are connected together. When applied to Gaussian random fields corresponding to the high redshift universe, it is found that on average the nodes are connected to exactly κ = 4 neighbours in two dimensions and ˜6.1 in three dimensions. Investigating spatial dimensions up to d = 6, typical departures from a cubic lattice κ = 2d are shown to scale like the power 7/4 of the dimension. These numbers strongly depend on the height of the peaks: the higher the peak the larger the connectivity. Predictions from first principles based on peak theory are shown to reproduce well the connectivity and multiplicity of Gaussian random fields and cosmological simulations. As an illustration, connectivity is quantified in galaxy lensing convergence maps and large dark haloes catalogues. As a function of redshift and scale the mean connectivity decreases in a cosmology-dependent way. As a function of halo mass it scales like 10/3 times the log of the mass. Implications on galactic scales are discussed.
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Batool, Nazre; Chellappa, Rama
2014-09-01
Facial retouching is widely used in media and entertainment industry. Professional software usually require a minimum level of user expertise to achieve the desirable results. In this paper, we present an algorithm to detect facial wrinkles/imperfection. We believe that any such algorithm would be amenable to facial retouching applications. The detection of wrinkles/imperfections can allow these skin features to be processed differently than the surrounding skin without much user interaction. For detection, Gabor filter responses along with texture orientation field are used as image features. A bimodal Gaussian mixture model (GMM) represents distributions of Gabor features of normal skin versus skin imperfections. Then, a Markov random field model is used to incorporate the spatial relationships among neighboring pixels for their GMM distributions and texture orientations. An expectation-maximization algorithm then classifies skin versus skin wrinkles/imperfections. Once detected automatically, wrinkles/imperfections are removed completely instead of being blended or blurred. We propose an exemplar-based constrained texture synthesis algorithm to inpaint irregularly shaped gaps left by the removal of detected wrinkles/imperfections. We present results conducted on images downloaded from the Internet to show the efficacy of our algorithms.
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Non-Gaussian quantum states generation and robust quantum non-Gaussianity via squeezing field
NASA Astrophysics Data System (ADS)
Tang, Xu-Bing; Gao, Fang; Wang, Yao-Xiong; Kuang, Sen; Shuang, Feng
2015-03-01
Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaussian operations (namely subtracting and adding a single photon), we propose a scheme to generate non-Gaussian quantum states named single-photon-added and -subtracted coherent (SPASC) superposition states by implementing Bell measurements, and then investigate the corresponding nonclassical features. By squeezed the input field, we demonstrate that robustness of non-Gaussianity can be improved. Controllable phase space distribution offers the possibility to approximately generate a displaced coherent superposition states (DCSS). The fidelity can reach up to F ≥ 0.98 and F ≥ 0.90 for size of amplitude z = 1.53 and 2.36, respectively. Project supported by the National Natural Science Foundation of China (Grant Nos. 61203061 and 61074052), the Outstanding Young Talent Foundation of Anhui Province, China (Grant No. 2012SQRL040), and the Natural Science Foundation of Anhui Province, China (Grant No. KJ2012Z035).
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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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NASA Astrophysics Data System (ADS)
Mazzoleni, Paolo; Matta, Fabio; Zappa, Emanuele; Sutton, Michael A.; Cigada, Alfredo
2015-03-01
This paper discusses the effect of pre-processing image blurring on the uncertainty of two-dimensional digital image correlation (DIC) measurements for the specific case of numerically-designed speckle patterns having particles with well-defined and consistent shape, size and spacing. Such patterns are more suitable for large measurement surfaces on large-scale specimens than traditional spray-painted random patterns without well-defined particles. The methodology consists of numerical simulations where Gaussian digital filters with varying standard deviation are applied to a reference speckle pattern. To simplify the pattern application process for large areas and increase contrast to reduce measurement uncertainty, the speckle shape, mean size and on-center spacing were selected to be representative of numerically-designed patterns that can be applied on large surfaces through different techniques (e.g., spray-painting through stencils). Such 'designer patterns' are characterized by well-defined regions of non-zero frequency content and non-zero peaks, and are fundamentally different from typical spray-painted patterns whose frequency content exhibits near-zero peaks. The effect of blurring filters is examined for constant, linear, quadratic and cubic displacement fields. Maximum strains between ±250 and ±20,000 με are simulated, thus covering a relevant range for structural materials subjected to service and ultimate stresses. The robustness of the simulation procedure is verified experimentally using a physical speckle pattern subjected to constant displacements. The stability of the relation between standard deviation of the Gaussian filter and measurement uncertainty is assessed for linear displacement fields at varying image noise levels, subset size, and frequency content of the speckle pattern. It is shown that bias error as well as measurement uncertainty are minimized through Gaussian pre-filtering. This finding does not apply to typical spray-painted patterns without well-defined particles, for which image blurring is only beneficial in reducing bias errors.
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Propagation of a general-type beam through a truncated fractional Fourier transform optical system.
Zhao, Chengliang; Cai, Yangjian
2010-03-01
Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Mackowski, Daniel W.; Mishchenko, Michael I.
The conventional orientation-averaging procedure developed in the framework of the superposition T-matrix approach is generalized to include the case of illumination by a Gaussian beam (GB). The resulting computer code is parallelized and used to perform extensive numerically exact calculations of electromagnetic scattering by volumes of discrete random medium consisting of monodisperse spherical particles. The size parameters of the scattering volumes are 40, 50, and 60, while their packing density is fixed at 5%. We demonstrate that all scattering patterns observed in the far-field zone of a random multisphere target and their evolution with decreasing width of the incident GBmore » can be interpreted in terms of idealized theoretical concepts such as forward-scattering interference, coherent backscattering (CB), and diffuse multiple scattering. It is shown that the increasing violation of electromagnetic reciprocity with decreasing GB width suppresses and eventually eradicates all observable manifestations of CB. This result supplements the previous demonstration of the effects of broken reciprocity in the case of magneto-optically active particles subjected to an external magnetic field.« less
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Gaussian random bridges and a geometric model for information equilibrium
NASA Astrophysics Data System (ADS)
Mengütürk, Levent Ali
2018-03-01
The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.
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NASA Astrophysics Data System (ADS)
Bamba, Kazuharu
2015-02-01
The generation of large-scale magnetic fields in inflationary cosmology is explored, in particular, in a kind of moduli inflation motivated by racetrack inflation in the context of the type IIB string theory. In this model, the conformal invariance of the hypercharge electromagnetic fields is broken thanks to the coupling of both the scalar and pseudoscalar fields to the hypercharge electromagnetic fields. The following three cosmological observable quantities are first evaluated: the current magnetic field strength on the Hubble horizon scale, which is much smaller than the upper limit from the backreaction problem, local non-Gaussianity of the curvature perturbations due to the existence of the massive gauge fields, and the tensor-to-scalar ratio. It is explicitly demonstrated that the resultant values of local non-Gaussianity and the tensor-to-scalar ratio are consistent with the Planck data.
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Topology of microwave background fluctuations - Theory
NASA Technical Reports Server (NTRS)
Gott, J. Richard, III; Park, Changbom; Bies, William E.; Bennett, David P.; Juszkiewicz, Roman
1990-01-01
Topological measures are used to characterize the microwave background temperature fluctuations produced by 'standard' scenarios (Gaussian) and by cosmic strings (non-Gaussian). Three topological quantities: total area of the excursion regions, total length, and total curvature (genus) of the isotemperature contours, are studied for simulated Gaussian microwave background anisotropy maps and then compared with those of the non-Gaussian anisotropy pattern produced by cosmic strings. In general, the temperature gradient field shows the non-Gaussian behavior of the string map more distinctively than the temperature field for all topology measures. The total contour length and the genus are found to be more sensitive to the existence of a stringy pattern than the usual temperature histogram. Situations when instrumental noise is superposed on the map, are considered to find the critical signal-to-noise ratio for which strings can be detected.
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A brain MRI bias field correction method created in the Gaussian multi-scale space
NASA Astrophysics Data System (ADS)
Chen, Mingsheng; Qin, Mingxin
2017-07-01
A pre-processing step is needed to correct for the bias field signal before submitting corrupted MR images to such image-processing algorithms. This study presents a new bias field correction method. The method creates a Gaussian multi-scale space by the convolution of the inhomogeneous MR image with a two-dimensional Gaussian function. In the multi-Gaussian space, the method retrieves the image details from the differentiation of the original image and convolution image. Then, it obtains an image whose inhomogeneity is eliminated by the weighted sum of image details in each layer in the space. Next, the bias field-corrected MR image is retrieved after the Υ correction, which enhances the contrast and brightness of the inhomogeneity-eliminated MR image. We have tested the approach on T1 MRI and T2 MRI with varying bias field levels and have achieved satisfactory results. Comparison experiments with popular software have demonstrated superior performance of the proposed method in terms of quantitative indices, especially an improvement in subsequent image segmentation.
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Accounting for crustal magnetization in models of the core magnetic field
NASA Technical Reports Server (NTRS)
Jackson, Andrew
1990-01-01
The problem of determining the magnetic field originating in the earth's core in the presence of remanent and induced magnetization is considered. The effect of remanent magnetization in the crust on satellite measurements of the core magnetic field is investigated. The crust as a zero-mean stationary Gaussian random process is modelled using an idea proposed by Parker (1988). It is shown that the matrix of second-order statistics is proportional to the Gram matrix, which depends only on the inner-products of the appropriate Green's functions, and that at a typical satellite altitude of 400 km the data are correlated out to an angular separation of approximately 15 deg. Accurate and efficient means of calculating the matrix elements are given. It is shown that the variance of measurements of the radial component of a magnetic field due to the crust is expected to be approximately twice that in horizontal components.
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NASA Astrophysics Data System (ADS)
Semchishen, Vladimir A.; Mrochen, Michael; Seminogov, Vladimir N.; Panchenko, Vladislav Y.; Seiler, Theo
1998-04-01
Purpose: The increasing interest in a homogeneous Gaussian light beam profile for applications in ophthalmology e.g. photorefractive keratectomy (PRK) requests simple optical systems with low energy losses. Therefore, we developed the Light Shaping Beam Homogenizer (LSBH) working from UV up to mid-IR. Method: The irregular microlenses structure on a quartz surface was fabricated by using photolithography, chemical etching and chemical polishing processes. This created a three dimensional structure on the quartz substrate characterized in case of a Gaussian beam by random law distribution of individual irregularities tilts. The LSBH was realized for the 193 nm and the 2.94 micrometer wavelengths. Simulation results obtained by 3-D analysis for an arbitrary incident light beam were compared to experimental results. Results: The correlation to a numerical Gaussian fit is better than 94% with high uniformity for an incident beam with an intensity modulation of nearly 100%. In the far field the cross section of the beam shows always rotation symmetry. Transmittance and damage threshold of the LSBH are only dependent on the substrate characteristics. Conclusions: considering our experimental and simulation results it is possible to control the angular distribution of the beam intensity after LSBH with higher efficiency compared to diffraction or holographic optical elements.
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PHYSICS OF NON-GAUSSIAN FIELDS AND THE COSMOLOGICAL GENUS STATISTIC
DOE Office of Scientific and Technical Information (OSTI.GOV)
James, J. Berian, E-mail: berian@berkeley.edu
2012-05-20
We report a technique to calculate the impact of distinct physical processes inducing non-Gaussianity on the cosmological density field. A natural decomposition of the cosmic genus statistic into an orthogonal polynomial sequence allows complete expression of the scale-dependent evolution of the topology of large-scale structure, in which effects including galaxy bias, nonlinear gravitational evolution, and primordial non-Gaussianity may be delineated. The relationship of this decomposition to previous methods for analyzing the genus statistic is briefly considered and the following applications are made: (1) the expression of certain systematics affecting topological measurements, (2) the quantification of broad deformations from Gaussianity thatmore » appear in the genus statistic as measured in the Horizon Run simulation, and (3) the study of the evolution of the genus curve for simulations with primordial non-Gaussianity. These advances improve the treatment of flux-limited galaxy catalogs for use with this measurement and further the use of the genus statistic as a tool for exploring non-Gaussianity.« less
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Horizon in Random Matrix Theory, the Hawking Radiation, and Flow of Cold Atoms
DOE Office of Scientific and Technical Information (OSTI.GOV)
Franchini, Fabio; Kravtsov, Vladimir E.
2009-10-16
We propose a Gaussian scalar field theory in a curved 2D metric with an event horizon as the low-energy effective theory for a weakly confined, invariant random matrix ensemble (RME). The presence of an event horizon naturally generates a bath of Hawking radiation, which introduces a finite temperature in the model in a nontrivial way. A similar mapping with a gravitational analogue model has been constructed for a Bose-Einstein condensate (BEC) pushed to flow at a velocity higher than its speed of sound, with Hawking radiation as sound waves propagating over the cold atoms. Our work suggests a threefold connectionmore » between a moving BEC system, black-hole physics and unconventional RMEs with possible experimental applications.« less
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A unified perturbation expansion for surface scattering
NASA Technical Reports Server (NTRS)
Rodriguez, Ernesto; Kim, Yunjin
1992-01-01
Starting with the extinction theorem, a perturbation expansion which, to first and second orders, converges over a wider domain than the small perturbation expansion and the momentum transfer expansion is presented. It is shown that, in the appropriate limits, both of these theories, as well as the two-scale expansion, are recovered. There is no adjustable parameter, such as a spectral split, in the theory. This theory is applied to random rough surfaces and derive analytic expressions for the coherent field and the bistatic cross section. Finally, a numerical test of the theory against method of moments results for Gaussian random rough surfaces with a power law spectrum is given. These results show that the expansion is ramarkably accurate over a large range of surface heights and slopes for both horizontal and vertical polarization.
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A path-level exact parallelization strategy for sequential simulation
NASA Astrophysics Data System (ADS)
Peredo, Oscar F.; Baeza, Daniel; Ortiz, Julián M.; Herrero, José R.
2018-01-01
Sequential Simulation is a well known method in geostatistical modelling. Following the Bayesian approach for simulation of conditionally dependent random events, Sequential Indicator Simulation (SIS) method draws simulated values for K categories (categorical case) or classes defined by K different thresholds (continuous case). Similarly, Sequential Gaussian Simulation (SGS) method draws simulated values from a multivariate Gaussian field. In this work, a path-level approach to parallelize SIS and SGS methods is presented. A first stage of re-arrangement of the simulation path is performed, followed by a second stage of parallel simulation for non-conflicting nodes. A key advantage of the proposed parallelization method is to generate identical realizations as with the original non-parallelized methods. Case studies are presented using two sequential simulation codes from GSLIB: SISIM and SGSIM. Execution time and speedup results are shown for large-scale domains, with many categories and maximum kriging neighbours in each case, achieving high speedup results in the best scenarios using 16 threads of execution in a single machine.
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NASA Astrophysics Data System (ADS)
Schnyder, Simon K.; Skinner, Thomas O. E.; Thorneywork, Alice L.; Aarts, Dirk G. A. L.; Horbach, Jürgen; Dullens, Roel P. A.
2017-03-01
A binary mixture of superparamagnetic colloidal particles is confined between glass plates such that the large particles become fixed and provide a two-dimensional disordered matrix for the still mobile small particles, which form a fluid. By varying fluid and matrix area fractions and tuning the interactions between the superparamagnetic particles via an external magnetic field, different regions of the state diagram are explored. The mobile particles exhibit delocalized dynamics at small matrix area fractions and localized motion at high matrix area fractions, and the localization transition is rounded by the soft interactions [T. O. E. Skinner et al., Phys. Rev. Lett. 111, 128301 (2013), 10.1103/PhysRevLett.111.128301]. Expanding on previous work, we find the dynamics of the tracers to be strongly heterogeneous and show that molecular dynamics simulations of an ideal gas confined in a fixed matrix exhibit similar behavior. The simulations show how these soft interactions make the dynamics more heterogeneous compared to the disordered Lorentz gas and lead to strong non-Gaussian fluctuations.
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Controlling the stability of nonlinear optical modes via electromagnetically induced transparency
NASA Astrophysics Data System (ADS)
Zhang, Kun; Liang, Yi-zeng; Lin, Ji; Li, Hui-jun
2018-02-01
We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having Λ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schrödinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.
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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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Complexity transitions in global algorithms for sparse linear systems over finite fields
NASA Astrophysics Data System (ADS)
Braunstein, A.; Leone, M.; Ricci-Tersenghi, F.; Zecchina, R.
2002-09-01
We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois field modulo q. Using tools from statistical mechanics we are able to identify phase transitions in the structure of the solution space and to connect them to the changes in the performance of a global algorithm, namely Gaussian elimination. Crossing phase boundaries produces a dramatic increase in memory and CPU requirements necessary for the algorithms. In turn, this causes the saturation of the upper bounds for the running time. We illustrate the results on the specific problem of integer factorization, which is of central interest for deciphering messages encrypted with the RSA cryptosystem.
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A Multiple Sphere T-Matrix Fortran Code for Use on Parallel Computer Clusters
NASA Technical Reports Server (NTRS)
Mackowski, D. W.; Mishchenko, M. I.
2011-01-01
A general-purpose Fortran-90 code for calculation of the electromagnetic scattering and absorption properties of multiple sphere clusters is described. The code can calculate the efficiency factors and scattering matrix elements of the cluster for either fixed or random orientation with respect to the incident beam and for plane wave or localized- approximation Gaussian incident fields. In addition, the code can calculate maps of the electric field both interior and exterior to the spheres.The code is written with message passing interface instructions to enable the use on distributed memory compute clusters, and for such platforms the code can make feasible the calculation of absorption, scattering, and general EM characteristics of systems containing several thousand spheres.
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Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains
NASA Astrophysics Data System (ADS)
Formentin, M.; Külske, C.; Reichenbachs, A.
2012-01-01
We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that for a degenerate non-reversible chain this CLT approximation is not enough, and that the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.
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φq-field theory for portfolio optimization: “fat tails” and nonlinear correlations
NASA Astrophysics Data System (ADS)
Sornette, D.; Simonetti, P.; Andersen, J. V.
2000-08-01
Physics and finance are both fundamentally based on the theory of random walks (and their generalizations to higher dimensions) and on the collective behavior of large numbers of correlated variables. The archetype examplifying this situation in finance is the portfolio optimization problem in which one desires to diversify on a set of possibly dependent assets to optimize the return and minimize the risks. The standard mean-variance solution introduced by Markovitz and its subsequent developments is basically a mean-field Gaussian solution. It has severe limitations for practical applications due to the strongly non-Gaussian structure of distributions and the nonlinear dependence between assets. Here, we present in details a general analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto Gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a nonlinear covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good conditioning. The portfolio distribution is then obtained as the solution of a mapping to a so-called φq field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The interaction (non-mean field) structure in this field theory is a direct consequence of the non-Gaussian nature of the distribution of asset price returns. We find that minimizing the portfolio variance (i.e. the relatively “small” risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive empirical tests are presented on the foreign exchange market that validate satisfactorily the theory. For “fat tail” distributions, we show that an adequate prediction of the risks of a portfolio relies much more on the correct description of the tail structure rather than on their correlations. For the case of asymmetric return distributions, our theory allows us to generalize the return-risk efficient frontier concept to incorporate the dimensions of large risks embedded in the tail of the asset distributions. We demonstrate that it is often possible to increase the portfolio return while decreasing the large risks as quantified by the fourth and higher-order cumulants. Exact theoretical formulas are validated by empirical tests.
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Emergence of Multiscaling in a Random-Force Stirred Fluid
NASA Astrophysics Data System (ADS)
Yakhot, Victor; Donzis, Diego
2017-07-01
We consider the transition to strong turbulence in an infinite fluid stirred by a Gaussian random force. The transition is defined as a first appearance of anomalous scaling of normalized moments of velocity derivatives (dissipation rates) emerging from the low-Reynolds-number Gaussian background. It is shown that, due to multiscaling, strongly intermittent rare events can be quantitatively described in terms of an infinite number of different "Reynolds numbers" reflecting a multitude of anomalous scaling exponents. The theoretically predicted transition disappears at Rλ≤3 . The developed theory is in quantitative agreement with the outcome of large-scale numerical simulations.
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Scattering of Gaussian Beams by Disordered Particulate Media
NASA Technical Reports Server (NTRS)
Mishchenko, Michael I.; Dlugach, Janna M.
2016-01-01
A frequently observed characteristic of electromagnetic scattering by a disordered particulate medium is the absence of pronounced speckles in angular patterns of the scattered light. It is known that such diffuse speckle-free scattering patterns can be caused by averaging over randomly changing particle positions and/or over a finite spectral range. To get further insight into the possible physical causes of the absence of speckles, we use the numerically exact superposition T-matrix solver of the Maxwell equations and analyze the scattering of plane-wave and Gaussian beams by representative multi-sphere groups. We show that phase and amplitude variations across an incident Gaussian beam do not serve to extinguish the pronounced speckle pattern typical of plane-wave illumination of a fixed multi-particle group. Averaging over random particle positions and/or over a finite spectral range is still required to generate the classical diffuse speckle-free regime.
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Cosmic microwave background bispectrum from primordial magnetic fields on large angular scales.
Seshadri, T R; Subramanian, Kandaswamy
2009-08-21
Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher-order effect. We propose a novel probe of stochastic primordial magnetic fields that exploits the characteristic CMB non-Gaussianity that they induce. We compute the CMB bispectrum (b(l1l2l3)) induced by such fields on large angular scales. We find a typical value of l1(l1 + 1)l3(l3 + 1)b(l1l2l3) approximately 10(-22), for magnetic fields of strength B0 approximately 3 nG and with a nearly scale invariant magnetic spectrum. Observational limits on the bispectrum allow us to set upper limits on B0 approximately 35 nG.
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Numerical Schemes for Dynamically Orthogonal Equations of Stochastic Fluid and Ocean Flows
2011-11-03
stages of the simulation (see §5.1). Also, because the pdf is discrete, we calculate the mo- ments using the biased estimator CYiYj ≈ 1q ∑ r Yr,iYr,j...independent random variables. For problems that require large p (e.g. non-Gaussian) and large s (e.g. large ocean or fluid simulations ), the number of...Sc = ν̂/K̂ is the Schmidt number which is the ratio of kinematic viscosity ν̂ to molecular diffusivity K̂ for the density field, ĝ′ = ĝ (ρ̂max−ρ̂min
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Large angle nonmechanical laser beam steering at 4.6 μm using a digital micromirror device
NASA Astrophysics Data System (ADS)
Lindle, James Ryan; Watnik, Abbie T.
2018-02-01
Large angle, nonmechanical beam steering is demonstrated at 4.62 μm using the digital light processing technology. A 42-deg steering range is demonstrated, limited by the field-of-view of the recollimating lens. The measured diffraction efficiency is 8.1% on-axis and falls-off with a sin2 dependence with the steering angle. However, within the 42-deg steering range, the power varied less than 25%. The profile of the steered laser beam is Gaussian with a divergence of 5.2 mrad. Multibeam, randomly addressable beam steering, is also demonstrated.
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Embedded random matrix ensembles from nuclear structure and their recent applications
NASA Astrophysics Data System (ADS)
Kota, V. K. B.; Chavda, N. D.
Embedded random matrix ensembles generated by random interactions (of low body rank and usually two-body) in the presence of a one-body mean field, introduced in nuclear structure physics, are now established to be indispensable in describing statistical properties of a large number of isolated finite quantum many-particle systems. Lie algebra symmetries of the interactions, as identified from nuclear shell model and the interacting boson model, led to the introduction of a variety of embedded ensembles (EEs). These ensembles with a mean field and chaos generating two-body interaction generate in three different stages, delocalization of wave functions in the Fock space of the mean-field basis states. The last stage corresponds to what one may call thermalization and complex nuclei, as seen from many shell model calculations, lie in this region. Besides briefly describing them, their recent applications to nuclear structure are presented and they are (i) nuclear level densities with interactions; (ii) orbit occupancies; (iii) neutrinoless double beta decay nuclear transition matrix elements as transition strengths. In addition, their applications are also presented briefly that go beyond nuclear structure and they are (i) fidelity, decoherence, entanglement and thermalization in isolated finite quantum systems with interactions; (ii) quantum transport in disordered networks connected by many-body interactions with centrosymmetry; (iii) semicircle to Gaussian transition in eigenvalue densities with k-body random interactions and its relation to the Sachdev-Ye-Kitaev (SYK) model for majorana fermions.
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Vortex-Core Reversal Dynamics: Towards Vortex Random Access Memory
NASA Astrophysics Data System (ADS)
Kim, Sang-Koog
2011-03-01
An energy-efficient, ultrahigh-density, ultrafast, and nonvolatile solid-state universal memory is a long-held dream in the field of information-storage technology. The magnetic random access memory (MRAM) along with a spin-transfer-torque switching mechanism is a strong candidate-means of realizing that dream, given its nonvolatility, infinite endurance, and fast random access. Magnetic vortices in patterned soft magnetic dots promise ground-breaking applications in information-storage devices, owing to the very stable twofold ground states of either their upward or downward core magnetization orientation and plausible core switching by in-plane alternating magnetic fields or spin-polarized currents. However, two technologically most important but very challenging issues --- low-power recording and reliable selection of each memory cell with already existing cross-point architectures --- have not yet been resolved for the basic operations in information storage, that is, writing (recording) and readout. Here, we experimentally demonstrate a magnetic vortex random access memory (VRAM) in the basic cross-point architecture. This unique VRAM offers reliable cell selection and low-power-consumption control of switching of out-of-plane core magnetizations using specially designed rotating magnetic fields generated by two orthogonal and unipolar Gaussian-pulse currents along with optimized pulse width and time delay. Our achievement of a new device based on a new material, that is, a medium composed of patterned vortex-state disks, together with the new physics on ultrafast vortex-core switching dynamics, can stimulate further fruitful research on MRAMs that are based on vortex-state dot arrays.
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CMB B-mode auto-bispectrum produced by primordial gravitational waves
NASA Astrophysics Data System (ADS)
Tahara, Hiroaki W. H.; Yokoyama, Jun'ichi
2018-01-01
Gravitational waves from inflation induce polarization patterns in the cosmic microwave background (CMB). It is known that there are only two types of non-Gaussianities of the gravitational waves in the most general covariant scalar field theory having second-order field equations, namely, generalized G-inflation. One originates from the inherent non-Gaussianity in general relativity, and the other from a derivative coupling between the Einstein tensor and the scalar field. We calculate polarization bispectra induced by these non-Gaussianities by transforming them into separable forms by virtue of the Laplace transformation. It is shown that future experiments can constrain the new one but cannot detect the general relativistic one.
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A qualitative assessment of a random process proposed as an atmospheric turbulence model
NASA Technical Reports Server (NTRS)
Sidwell, K.
1977-01-01
A random process is formed by the product of two Gaussian processes and the sum of that product with a third Gaussian process. The resulting total random process is interpreted as the sum of an amplitude modulated process and a slowly varying, random mean value. The properties of the process are examined, including an interpretation of the process in terms of the physical structure of atmospheric motions. The inclusion of the mean value variation gives an improved representation of the properties of atmospheric motions, since the resulting process can account for the differences in the statistical properties of atmospheric velocity components and their gradients. The application of the process to atmospheric turbulence problems, including the response of aircraft dynamic systems, is examined. The effects of the mean value variation upon aircraft loads are small in most cases, but can be important in the measurement and interpretation of atmospheric turbulence data.
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Generalized Ince Gaussian beams
NASA Astrophysics Data System (ADS)
Bandres, Miguel A.; Gutiérrez-Vega, Julio C.
2006-08-01
In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.
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High-resolution moisture profiles from full-waveform probabilistic inversion of TDR signals
NASA Astrophysics Data System (ADS)
Laloy, Eric; Huisman, Johan Alexander; Jacques, Diederik
2014-11-01
This study presents an novel Bayesian inversion scheme for high-dimensional undetermined TDR waveform inversion. The methodology quantifies uncertainty in the moisture content distribution, using a Gaussian Markov random field (GMRF) prior as regularization operator. A spatial resolution of 1 cm along a 70-cm long TDR probe is considered for the inferred moisture content. Numerical testing shows that the proposed inversion approach works very well in case of a perfect model and Gaussian measurement errors. Real-world application results are generally satisfying. For a series of TDR measurements made during imbibition and evaporation from a laboratory soil column, the average root-mean-square error (RMSE) between maximum a posteriori (MAP) moisture distribution and reference TDR measurements is 0.04 cm3 cm-3. This RMSE value reduces to less than 0.02 cm3 cm-3 for a field application in a podzol soil. The observed model-data discrepancies are primarily due to model inadequacy, such as our simplified modeling of the bulk soil electrical conductivity profile. Among the important issues that should be addressed in future work are the explicit inference of the soil electrical conductivity profile along with the other sampled variables, the modeling of the temperature-dependence of the coaxial cable properties and the definition of an appropriate statistical model of the residual errors.
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Biasing and the search for primordial non-Gaussianity beyond the local type
DOE Office of Scientific and Technical Information (OSTI.GOV)
Gleyzes, Jérôme; De Putter, Roland; Doré, Olivier
Primordial non-Gaussianity encodes valuable information about the physics of inflation, including the spectrum of particles and interactions. Significant improvements in our understanding of non-Gaussanity beyond Planck require information from large-scale structure. The most promising approach to utilize this information comes from the scale-dependent bias of halos. For local non-Gaussanity, the improvements available are well studied but the potential for non-Gaussianity beyond the local type, including equilateral and quasi-single field inflation, is much less well understood. In this paper, we forecast the capabilities of large-scale structure surveys to detect general non-Gaussianity through galaxy/halo power spectra. We study how non-Gaussanity can bemore » distinguished from a general biasing model and where the information is encoded. For quasi-single field inflation, significant improvements over Planck are possible in some regions of parameter space. We also show that the multi-tracer technique can significantly improve the sensitivity for all non-Gaussianity types, providing up to an order of magnitude improvement for equilateral non-Gaussianity over the single-tracer measurement.« less
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Kurtosis, skewness, and non-Gaussian cosmological density perturbations
NASA Technical Reports Server (NTRS)
Luo, Xiaochun; Schramm, David N.
1993-01-01
Cosmological topological defects as well as some nonstandard inflation models can give rise to non-Gaussian density perturbations. Skewness and kurtosis are the third and fourth moments that measure the deviation of a distribution from a Gaussian. Measurement of these moments for the cosmological density field and for the microwave background temperature anisotropy can provide a test of the Gaussian nature of the primordial fluctuation spectrum. In the case of the density field, the importance of measuring the kurtosis is stressed since it will be preserved through the weakly nonlinear gravitational evolution epoch. Current constraints on skewness and kurtosis of primeval perturbations are obtained from the observed density contrast on small scales and from recent COBE observations of temperature anisotropies on large scales. It is also shown how, in principle, future microwave anisotropy experiments might be able to reveal the initial skewness and kurtosis. It is shown that present data argue that if the initial spectrum is adiabatic, then it is probably Gaussian, but non-Gaussian isocurvature fluctuations are still allowed, and these are what topological defects provide.
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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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Primordial non-Gaussianity and reionization
NASA Astrophysics Data System (ADS)
Lidz, Adam; Baxter, Eric J.; Adshead, Peter; Dodelson, Scott
2013-07-01
The statistical properties of the primordial perturbations contain clues about their origins. Although the Planck collaboration has recently obtained tight constraints on primordial non-Gaussianity from cosmic microwave background measurements, it is still worthwhile to mine upcoming data sets in an effort to place independent or competitive limits. The ionized bubbles that formed at redshift z˜6-20 during the epoch of reionization were seeded by primordial overdensities, and so the statistics of the ionization field at high redshift are related to the statistics of the primordial field. Here we model the effect of primordial non-Gaussianity on the reionization field. The epoch and duration of reionization are affected, as are the sizes of the ionized bubbles, but these changes are degenerate with variations in the properties of the ionizing sources and the surrounding intergalactic medium. A more promising signature is the power spectrum of the spatial fluctuations in the ionization field, which may be probed by upcoming 21 cm surveys. This has the expected 1/k2 dependence on large scales, characteristic of a biased tracer of the matter field. We project how well upcoming 21 cm observations will be able to disentangle this signal from foreground contamination. Although foreground cleaning inevitably removes the large-scale modes most impacted by primordial non-Gaussianity, we find that primordial non-Gaussianity can be separated from foreground contamination for a narrow range of length scales. In principle, futuristic redshifted 21 cm surveys may allow constraints competitive with Planck.
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fNL‑gNL mixing in the matter density field at higher orders
NASA Astrophysics Data System (ADS)
Gressel, Hedda A.; Bruni, Marco
2018-06-01
In this paper we examine how primordial non-Gaussianity contributes to nonlinear perturbative orders in the expansion of the density field at large scales in the matter dominated era. General Relativity is an intrinsically nonlinear theory, establishing a nonlinear relation between the metric and the density field. Representing the metric perturbations with the curvature perturbation ζ, it is known that nonlinearity produces effective non-Gaussian terms in the nonlinear perturbations of the matter density field δ, even if the primordial ζ is Gaussian. Here we generalise these results to the case of a non-Gaussian primordial ζ. Using a standard parametrization of primordial non-Gaussianity in ζ in terms of fNL, gNL, hNL\\ldots , we show how at higher order (from third and higher) nonlinearity also produces a mixing of these contributions to the density field at large scales, e.g. both fNL and gNL contribute to the third order in δ. This is the main result of this paper. Our analysis is based on the synergy between a gradient expansion (aka long-wavelength approximation) and standard perturbation theory at higher order. In essence, mathematically the equations for the gradient expansion are equivalent to those of first order perturbation theory, thus first-order results convert into gradient expansion results and, vice versa, the gradient expansion can be used to derive results in perturbation theory at higher order and large scales.
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A High Performance Bayesian Computing Framework for Spatiotemporal Uncertainty Modeling
NASA Astrophysics Data System (ADS)
Cao, G.
2015-12-01
All types of spatiotemporal measurements are subject to uncertainty. With spatiotemporal data becomes increasingly involved in scientific research and decision making, it is important to appropriately model the impact of uncertainty. Quantitatively modeling spatiotemporal uncertainty, however, is a challenging problem considering the complex dependence and dataheterogeneities.State-space models provide a unifying and intuitive framework for dynamic systems modeling. In this paper, we aim to extend the conventional state-space models for uncertainty modeling in space-time contexts while accounting for spatiotemporal effects and data heterogeneities. Gaussian Markov Random Field (GMRF) models, also known as conditional autoregressive models, are arguably the most commonly used methods for modeling of spatially dependent data. GMRF models basically assume that a geo-referenced variable primarily depends on its neighborhood (Markov property), and the spatial dependence structure is described via a precision matrix. Recent study has shown that GMRFs are efficient approximation to the commonly used Gaussian fields (e.g., Kriging), and compared with Gaussian fields, GMRFs enjoy a series of appealing features, such as fast computation and easily accounting for heterogeneities in spatial data (e.g, point and areal). This paper represents each spatial dataset as a GMRF and integrates them into a state-space form to statistically model the temporal dynamics. Different types of spatial measurements (e.g., categorical, count or continuous), can be accounted for by according link functions. A fast alternative to MCMC framework, so-called Integrated Nested Laplace Approximation (INLA), was adopted for model inference.Preliminary case studies will be conducted to showcase the advantages of the described framework. In the first case, we apply the proposed method for modeling the water table elevation of Ogallala aquifer over the past decades. In the second case, we analyze the drought impacts in Texas counties in the past years, where the spatiotemporal dynamics are represented in areal data.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Li, Y; Hsi, W; Zhao, J
2016-06-15
Purpose: The Gaussian model for the lateral profiles in air is crucial for an accurate treatment planning system. The field size dependence of dose and the lateral beam profiles of scanning proton and carbon ion beams are due mainly to particles undergoing multiple Coulomb scattering in the beam line components and secondary particles produced by nuclear interactions in the target, both of which depend upon the energy and species of the beam. In this work, lateral profile shape parameters were fitted to measurements of field size dependence dose at the center of field size in air. Methods: Previous studies havemore » employed empirical fits to measured profile data to significantly reduce the QA time required for measurements. From this approach to derive the weight and sigma of lateral profiles in air, empirical model formulations were simulated for three selected energies for both proton and carbon beams. Results: The 20%–80% lateral penumbras predicted by the double model for proton and single model for carbon with the error functions agreed with the measurements within 1 mm. The standard deviation between measured and fitted field size dependence of dose for empirical model in air has a maximum accuracy of 0.74% for proton with double Gaussian, and of 0.57% for carbon with single Gaussian. Conclusion: We have demonstrated that the double Gaussian model of lateral beam profiles is significantly better than the single Gaussian model for proton while a single Gaussian model is sufficient for carbon. The empirical equation may be used to double check the separately obtained model that is currently used by the planning system. The empirical model in air for dose of spot scanning proton and carbon ion beams cannot be directly used for irregular shaped patient fields, but can be to provide reference values for clinical use and quality assurance.« less
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NASA Astrophysics Data System (ADS)
Huang, Xingguo; Sun, Hui
2018-05-01
Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss-Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.
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Porous media flux sensitivity to pore-scale geostatistics: A bottom-up approach
NASA Astrophysics Data System (ADS)
Di Palma, P. R.; Guyennon, N.; Heße, F.; Romano, E.
2017-04-01
Macroscopic properties of flow through porous media can be directly computed by solving the Navier-Stokes equations at the scales related to the actual flow processes, while considering the porous structures in an explicit way. The aim of this paper is to investigate the effects of the pore-scale spatial distribution on seepage velocity through numerical simulations of 3D fluid flow performed by the lattice Boltzmann method. To this end, we generate multiple random Gaussian fields whose spatial correlation follows an assigned semi-variogram function. The Exponential and Gaussian semi-variograms are chosen as extreme-cases of correlation for short distances and statistical properties of the resulting porous media (indicator field) are described using the Matèrn covariance model, with characteristic lengths of spatial autocorrelation (pore size) varying from 2% to 13% of the linear domain. To consider the sensitivity of the modeling results to the geostatistical representativeness of the domain as well as to the adopted resolution, porous media have been generated repetitively with re-initialized random seeds and three different resolutions have been tested for each resulting realization. The main difference among results is observed between the two adopted semi-variograms, indicating that the roughness (short distances autocorrelation) is the property mainly affecting the flux. However, computed seepage velocities show additionally a wide variability (about three orders of magnitude) for each semi-variogram model in relation to the assigned correlation length, corresponding to pore sizes. The spatial resolution affects more the results for short correlation lengths (i.e., small pore sizes), resulting in an increasing underestimation of the seepage velocity with the decreasing correlation length. On the other hand, results show an increasing uncertainty as the correlation length approaches the domain size.
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Time reversibility of intracranial human EEG recordings in mesial temporal lobe epilepsy
NASA Astrophysics Data System (ADS)
van der Heyden, M. J.; Diks, C.; Pijn, J. P. M.; Velis, D. N.
1996-02-01
Intracranial electroencephalograms from patients suffering from mesial temporal lobe epilepsy were tested for time reversibility. If the recorded time series is irreversible, the input of the recording system cannot be a realisation of a linear Gaussian random process. We confirmed experimentally that the measurement equipment did not introduce irreversibility in the recorded output when the input was a realisation of a linear Gaussian random process. In general, the non-seizure recordings are reversible, whereas the seizure recordings are irreversible. These results suggest that time reversibility is a useful property for the characterisation of human intracranial EEG recordings in mesial temporal lobe epilepsy.
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An analytical approach to gravitational lensing by an ensemble of axisymmetric lenses
NASA Technical Reports Server (NTRS)
Lee, Man Hoi; Spergel, David N.
1990-01-01
The problem of gravitational lensing by an ensemble of identical axisymmetric lenses randomly distributed on a single lens plane is considered and a formal expression is derived for the joint probability density of finding shear and convergence at a random point on the plane. The amplification probability for a source can be accurately estimated from the distribution in shear and convergence. This method is applied to two cases: lensing by an ensemble of point masses and by an ensemble of objects with Gaussian surface mass density. There is no convergence for point masses whereas shear is negligible for wide Gaussian lenses.
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Tian, Yuzhen; Guo, Jin; Wang, Rui; Wang, Tingfeng
2011-09-12
In order to research the statistical properties of Gaussian beam propagation through an arbitrary thickness random phase screen for adaptive optics and laser communication application in the laboratory, we establish mathematic models of statistical quantities, which are based on the Rytov method and the thin phase screen model, involved in the propagation process. And the analytic results are developed for an arbitrary thickness phase screen based on the Kolmogorov power spectrum. The comparison between the arbitrary thickness phase screen and the thin phase screen shows that it is more suitable for our results to describe the generalized case, especially the scintillation index.
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NASA Technical Reports Server (NTRS)
Frehlich, Rod
1993-01-01
Calculations of the exact Cramer-Rao Bound (CRB) for unbiased estimates of the mean frequency, signal power, and spectral width of Doppler radar/lidar signals (a Gaussian random process) are presented. Approximate CRB's are derived using the Discrete Fourier Transform (DFT). These approximate results are equal to the exact CRB when the DFT coefficients are mutually uncorrelated. Previous high SNR limits for CRB's are shown to be inaccurate because the discrete summations cannot be approximated with integration. The performance of an approximate maximum likelihood estimator for mean frequency approaches the exact CRB for moderate signal to noise ratio and moderate spectral width.
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Light scattering from laser induced pit ensembles on high power laser optics
Feigenbaum, Eyal; Elhadj, Selim; Matthews, Manyalibo J.
2015-01-01
Far-field light scattering characteristics from randomly arranged shallow Gaussian-like shaped laser induced pits, found on optics exposed to high energy laser pulses, is studied. Closed-form expressions for the far-field intensity distribution and scattered power are derived for individual pits and validated using numerical calculations of both Fourier optics and FDTD solutions to Maxwell’s equations. It is found that the scattered power is proportional to the square of the pit width and approximately also to the square of the pit depth, with the proportionality factor scaling with pit depth. As a result, the power scattered from shallow pitted optics is expectedmore » to be substantially lower than assuming complete scattering from the total visible footprint of the pits.« less
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A curvature-corrected Kirchhoff formulation for radar sea-return from the near vertical
NASA Technical Reports Server (NTRS)
Jackson, F. C.
1974-01-01
A new theoretical treatment of the problem of electromagnetic wave scattering from a randomly rough surface is given. A high frequency correction to the Kirchhoff approximation is derived from a field integral equation for a perfectly conducting surface. The correction, which accounts for the effect of local surface curvature, is seen to be identical with an asymptotic form found by Fock (1945) for diffraction by a paraboloid. The corrected boundary values are substituted into the far field Stratton-Chu integral, and average backscattered powers are computed assuming the scattering surface is a homogeneous Gaussian process. Preliminary calculations for K(-4) ocean wave spectrum indicate a resonable modelling of polarization effects near the vertical, theta 45 deg. Correspondence with the results of small perturbation theory is shown.
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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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Heterodyne efficiency for a coherent laser radar with diffuse or aerosol targets
NASA Technical Reports Server (NTRS)
Frehlich, R. G.
1993-01-01
The performance of a Coherent Laser Radar is determined by the statistics of the coherent Doppler signal. The heterodyne efficiency is an excellent indication of performance because it is an absolute measure of beam alignment and is independent of the transmitter power, the target backscatter coefficient, the atmospheric attenuation, and the detector quantum efficiency and gain. The theoretical calculation of heterodyne efficiency for an optimal monostatic lidar with a circular aperture and Gaussian transmit laser is presented including beam misalignment in the far-field and near-field regimes. The statistical behavior of estimates of the heterodyne efficiency using a calibration hard target are considered. For space based applications, a biased estimate of heterodyne efficiency is proposed that removes the variability due to the random surface return but retains the sensitivity to misalignment. Physical insight is provided by simulation of the fields on the detector surface. The required detector calibration is also discussed.
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Model-independent test for scale-dependent non-Gaussianities in the cosmic microwave background.
Räth, C; Morfill, G E; Rossmanith, G; Banday, A J; Górski, K M
2009-04-03
We present a model-independent method to test for scale-dependent non-Gaussianities in combination with scaling indices as test statistics. Therefore, surrogate data sets are generated, in which the power spectrum of the original data is preserved, while the higher order correlations are partly randomized by applying a scale-dependent shuffling procedure to the Fourier phases. We apply this method to the Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background and find signatures for non-Gaussianities on large scales. Further tests are required to elucidate the origin of the detected anomalies.
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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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NASA Astrophysics Data System (ADS)
Delpueyo, D.; Balandraud, X.; Grédiac, M.
2013-09-01
The aim of this paper is to present a post-processing technique based on a derivative Gaussian filter to reconstruct heat source fields from temperature fields measured by infrared thermography. Heat sources can be deduced from temperature variations thanks to the heat diffusion equation. Filtering and differentiating are key-issues which are closely related here because the temperature fields which are processed are unavoidably noisy. We focus here only on the diffusion term because it is the most difficult term to estimate in the procedure, the reason being that it involves spatial second derivatives (a Laplacian for isotropic materials). This quantity can be reasonably estimated using a convolution of the temperature variation fields with second derivatives of a Gaussian function. The study is first based on synthetic temperature variation fields corrupted by added noise. The filter is optimised in order to reconstruct at best the heat source fields. The influence of both the dimension and the level of a localised heat source is discussed. Obtained results are also compared with another type of processing based on an averaging filter. The second part of this study presents an application to experimental temperature fields measured with an infrared camera on a thin plate in aluminium alloy. Heat sources are generated with an electric heating patch glued on the specimen surface. Heat source fields reconstructed from measured temperature fields are compared with the imposed heat sources. Obtained results illustrate the relevancy of the derivative Gaussian filter to reliably extract heat sources from noisy temperature fields for the experimental thermomechanics of materials.
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Entanglement dynamics in random media
NASA Astrophysics Data System (ADS)
Menezes, G.; Svaiter, N. F.; Zarro, C. A. D.
2017-12-01
We study how the entanglement dynamics between two-level atoms is impacted by random fluctuations of the light cone. In our model the two-atom system is envisaged as an open system coupled with an electromagnetic field in the vacuum state. We employ the quantum master equation in the Born-Markov approximation in order to describe the completely positive time evolution of the atomic system. We restrict our investigations to the situation in which the atoms are coupled individually to two spatially separated cavities, one of which displays the emergence of light-cone fluctuations. In such a disordered cavity, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that disorder has the effect of slowing down the entanglement decay. We conjecture that in a strong-disorder environment the mean life of entangled states can be enhanced in such a way as to almost completely suppress quantum nonlocal decoherence.
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Distribution law of the Dirac eigenmodes in QCD
NASA Astrophysics Data System (ADS)
Catillo, Marco; Glozman, Leonid Ya.
2018-04-01
The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS) via the Banks-Casher relation. At the same time, the distribution of the near-zero modes is well described by the Random Matrix Theory (RMT) with the Gaussian Unitary Ensemble (GUE). Then, it has become a standard lore that a randomness, as observed through distributions of the near-zero modes of the Dirac operator, is a consequence of SBCS. The higher-lying modes of the Dirac operator are not affected by SBCS and are sensitive to confinement physics and related SU(2)CS and SU(2NF) symmetries. We study the distribution of the near-zero and higher-lying eigenmodes of the overlap Dirac operator within NF = 2 dynamical simulations. We find that both the distributions of the near-zero and higher-lying modes are perfectly described by GUE of RMT. This means that randomness, while consistent with SBCS, is not a consequence of SBCS and is linked to the confining chromo-electric field.
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Ionospheric scintillation studies
NASA Technical Reports Server (NTRS)
Rino, C. L.; Freemouw, E. J.
1973-01-01
The diffracted field of a monochromatic plane wave was characterized by two complex correlation functions. For a Gaussian complex field, these quantities suffice to completely define the statistics of the field. Thus, one can in principle calculate the statistics of any measurable quantity in terms of the model parameters. The best data fits were achieved for intensity statistics derived under the Gaussian statistics hypothesis. The signal structure that achieved the best fit was nearly invariant with scintillation level and irregularity source (ionosphere or solar wind). It was characterized by the fact that more than 80% of the scattered signal power is in phase quadrature with the undeviated or coherent signal component. Thus, the Gaussian-statistics hypothesis is both convenient and accurate for channel modeling work.
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Cosmic microwave background trispectrum and primordial magnetic field limits.
Trivedi, Pranjal; Seshadri, T R; Subramanian, Kandaswamy
2012-06-08
Primordial magnetic fields will generate non-gaussian signals in the cosmic microwave background (CMB) as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. We compute a new measure of magnetic non-gaussianity, the CMB trispectrum, on large angular scales, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately a few times 10(-29) and 10(-19), respectively. Observational limits on CMB non-gaussianity from WMAP data allow us to conservatively set upper limits of a nG, and plausibly sub-nG, on the present value of the primordial cosmic magnetic field. This represents the tightest limit so far on the strength of primordial magnetic fields, on Mpc scales, and is better than limits from the CMB bispectrum and all modes in the CMB power spectrum. Thus, the CMB trispectrum is a new and more sensitive probe of primordial magnetic fields on large scales.
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Accelerating Sequential Gaussian Simulation with a constant path
NASA Astrophysics Data System (ADS)
Nussbaumer, Raphaël; Mariethoz, Grégoire; Gravey, Mathieu; Gloaguen, Erwan; Holliger, Klaus
2018-03-01
Sequential Gaussian Simulation (SGS) is a stochastic simulation technique commonly employed for generating realizations of Gaussian random fields. Arguably, the main limitation of this technique is the high computational cost associated with determining the kriging weights. This problem is compounded by the fact that often many realizations are required to allow for an adequate uncertainty assessment. A seemingly simple way to address this problem is to keep the same simulation path for all realizations. This results in identical neighbourhood configurations and hence the kriging weights only need to be determined once and can then be re-used in all subsequent realizations. This approach is generally not recommended because it is expected to result in correlation between the realizations. Here, we challenge this common preconception and make the case for the use of a constant path approach in SGS by systematically evaluating the associated benefits and limitations. We present a detailed implementation, particularly regarding parallelization and memory requirements. Extensive numerical tests demonstrate that using a constant path allows for substantial computational gains with very limited loss of simulation accuracy. This is especially the case for a constant multi-grid path. The computational savings can be used to increase the neighbourhood size, thus allowing for a better reproduction of the spatial statistics. The outcome of this study is a recommendation for an optimal implementation of SGS that maximizes accurate reproduction of the covariance structure as well as computational efficiency.
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NASA Astrophysics Data System (ADS)
Gharekhan, Anita H.; Biswal, Nrusingh C.; Gupta, Sharad; Pradhan, Asima; Sureshkumar, M. B.; Panigrahi, Prasanta K.
2008-02-01
The statistical and characteristic features of the polarized fluorescence spectra from cancer, normal and benign human breast tissues are studied through wavelet transform and singular value decomposition. The discrete wavelets enabled one to isolate high and low frequency spectral fluctuations, which revealed substantial randomization in the cancerous tissues, not present in the normal cases. In particular, the fluctuations fitted well with a Gaussian distribution for the cancerous tissues in the perpendicular component. One finds non-Gaussian behavior for normal and benign tissues' spectral variations. The study of the difference of intensities in parallel and perpendicular channels, which is free from the diffusive component, revealed weak fluorescence activity in the 630nm domain, for the cancerous tissues. This may be ascribable to porphyrin emission. The role of both scatterers and fluorophores in the observed minor intensity peak for the cancer case is experimentally confirmed through tissue-phantom experiments. Continuous Morlet wavelet also highlighted this domain for the cancerous tissue fluorescence spectra. Correlation in the spectral fluctuation is further studied in different tissue types through singular value decomposition. Apart from identifying different domains of spectral activity for diseased and non-diseased tissues, we found random matrix support for the spectral fluctuations. The small eigenvalues of the perpendicular polarized fluorescence spectra of cancerous tissues fitted remarkably well with random matrix prediction for Gaussian random variables, confirming our observations about spectral fluctuations in the wavelet domain.
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Analytical and numerical studies of photo-injected charge transport in molecularly-doped polymers
NASA Astrophysics Data System (ADS)
Roy Chowdhury, Amrita
The mobility of photo-injected charge carriers in molecularly-doped polymers (MDPs) exhibits a commonly observed, and nearly universal Poole-Frenkel field dependence, mu exp√(beta0E), that has been shown to arise from the correlated Gaussian energy distribution of transport sites encountered by charges undergoing hopping transport through the material. Analytical and numerical studies of photo-injected charge transport in these materials are presented here with an attempt to understand how specific features of the various models developed to describe these systems depend on the microscopic parameters that define them. Specifically, previously published time-of-flight mobility data for the molecularly doped polymer 30% DEH:PC (polycarbonate doped with 30 wt.% aromatic hydrazone DEH) is compared with direct analytical and numerical predictions of five disorder-based models, the Gaussian disorder model (GDM) of Bassler, and four correlated disorder models introduced by Novikov, et al., and by Parris, et al. In these numerical studies, disorder parameters describing each model were varied from reasonable starting conditions, in order to give the best overall fit. The uncorrelated GDM describes the Poole-Frenkel field dependence of the mobility only at very high fields, but fails for fields lower than about 64 V/mum. The correlated disorder models with small amounts of geometrical disorder do a good over-all job of reproducing a robust Poole-Frenkel field dependence, with correlated disorder theories that employ polaron transition rates showing qualitatively better agreement with experiment than those that employ Miller-Abrahams rates. In a separate study, the heuristic treatment of spatial or geometric disorder incorporated in existing theories is critiqued, and a randomly-diluted lattice gas model is developed to describe the spatial disorder of the transport sites in a more realistic way.
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Renyi entropy measures of heart rate Gaussianity.
Lake, Douglas E
2006-01-01
Sample entropy and approximate entropy are measures that have been successfully utilized to study the deterministic dynamics of heart rate (HR). A complementary stochastic point of view and a heuristic argument using the Central Limit Theorem suggests that the Gaussianity of HR is a complementary measure of the physiological complexity of the underlying signal transduction processes. Renyi entropy (or q-entropy) is a widely used measure of Gaussianity in many applications. Particularly important members of this family are differential (or Shannon) entropy (q = 1) and quadratic entropy (q = 2). We introduce the concepts of differential and conditional Renyi entropy rate and, in conjunction with Burg's theorem, develop a measure of the Gaussianity of a linear random process. Robust algorithms for estimating these quantities are presented along with estimates of their standard errors.
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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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NASA Astrophysics Data System (ADS)
Brekhna, Brekhna; Mahmood, Arif; Zhou, Yuanfeng; Zhang, Caiming
2017-11-01
Superpixels have gradually become popular in computer vision and image processing applications. However, no comprehensive study has been performed to evaluate the robustness of superpixel algorithms in regard to common forms of noise in natural images. We evaluated the robustness of 11 recently proposed algorithms to different types of noise. The images were corrupted with various degrees of Gaussian blur, additive white Gaussian noise, and impulse noise that either made the object boundaries weak or added extra information to it. We performed a robustness analysis of simple linear iterative clustering (SLIC), Voronoi Cells (VCells), flooding-based superpixel generation (FCCS), bilateral geodesic distance (Bilateral-G), superpixel via geodesic distance (SSS-G), manifold SLIC (M-SLIC), Turbopixels, superpixels extracted via energy-driven sampling (SEEDS), lazy random walk (LRW), real-time superpixel segmentation by DBSCAN clustering, and video supervoxels using partially absorbing random walks (PARW) algorithms. The evaluation process was carried out both qualitatively and quantitatively. For quantitative performance comparison, we used achievable segmentation accuracy (ASA), compactness, under-segmentation error (USE), and boundary recall (BR) on the Berkeley image database. The results demonstrated that all algorithms suffered performance degradation due to noise. For Gaussian blur, Bilateral-G exhibited optimal results for ASA and USE measures, SLIC yielded optimal compactness, whereas FCCS and DBSCAN remained optimal for BR. For the case of additive Gaussian and impulse noises, FCCS exhibited optimal results for ASA, USE, and BR, whereas Bilateral-G remained a close competitor in ASA and USE for Gaussian noise only. Additionally, Turbopixel demonstrated optimal performance for compactness for both types of noise. Thus, no single algorithm was able to yield optimal results for all three types of noise across all performance measures. Conclusively, to solve real-world problems effectively, more robust superpixel algorithms must be developed.
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Quasi-analytical treatment of spatially averaged radiation transfer in complex terrain
NASA Astrophysics Data System (ADS)
Löwe, H.; Helbig, N.
2012-04-01
We provide a new quasi-analytical method to compute the topographic influence on the effective albedo of complex topography as required for meteorological, land-surface or climate models. We investigate radiative transfer in complex terrain via the radiosity equation on isotropic Gaussian random fields. Under controlled approximations we derive expressions for domain averages of direct, diffuse and terrain radiation and the sky view factor. Domain averaged quantities are related to a type of level-crossing probability of the random field which is approximated by longstanding results developed for acoustic scattering at ocean boundaries. This allows us to express all non-local horizon effects in terms of a local terrain parameter, namely the mean squared slope. Emerging integrals are computed numerically and fit formulas are given for practical purposes. As an implication of our approach we provide an expression for the effective albedo of complex terrain in terms of the sun elevation angle, mean squared slope, the area averaged surface albedo, and the direct-to-diffuse ratio of solar radiation. As an application, we compute the effective albedo for the Swiss Alps and discuss possible generalizations of the method.
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On the theory of Brownian motion with the Alder-Wainwright effect
NASA Astrophysics Data System (ADS)
Okabe, Yasunori
1986-12-01
The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.
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A Comparison of Three Random Number Generators for Aircraft Dynamic Modeling Applications
NASA Technical Reports Server (NTRS)
Grauer, Jared A.
2017-01-01
Three random number generators, which produce Gaussian white noise sequences, were compared to assess their suitability in aircraft dynamic modeling applications. The first generator considered was the MATLAB (registered) implementation of the Mersenne-Twister algorithm. The second generator was a website called Random.org, which processes atmospheric noise measured using radios to create the random numbers. The third generator was based on synthesis of the Fourier series, where the random number sequences are constructed from prescribed amplitude and phase spectra. A total of 200 sequences, each having 601 random numbers, for each generator were collected and analyzed in terms of the mean, variance, normality, autocorrelation, and power spectral density. These sequences were then applied to two problems in aircraft dynamic modeling, namely estimating stability and control derivatives from simulated onboard sensor data, and simulating flight in atmospheric turbulence. In general, each random number generator had good performance and is well-suited for aircraft dynamic modeling applications. Specific strengths and weaknesses of each generator are discussed. For Monte Carlo simulation, the Fourier synthesis method is recommended because it most accurately and consistently approximated Gaussian white noise and can be implemented with reasonable computational effort.
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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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Self-accelerating Airy-Ince-Gaussian and Airy-Helical-Ince-Gaussian light bullets in free space.
Peng, Yulian; Chen, Bo; Peng, Xi; Zhou, Meiling; Zhang, Liping; Li, Dongdong; Deng, Dongmei
2016-08-22
The evolution of the three-dimensional (3D) self-accelerating Airy-Ince-Gaussian (AiIG) and Airy-Helical-Ince-Gaussian (AiHIG) light bullets is investigated by solving the (3+1)D linear spatiotemporal evolution equation of an optical field analytically. As far as we know, the numerical experimental demonstrations of the Ince-Gaussian (IG) and Helical-Ince-Gaussian (HIG) beams in various modes are first developed to study the evolution characteristics of the different 3D spatiotemporal light bullets. A conclusion can be drawn that the different photoelastics, pulse stacked, boundary, elliptical ring and physically separated in-line vortices can be achieved by adjusting the ellipticity, the evolution distance and the mode-number of light bullets.
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NASA Astrophysics Data System (ADS)
Kim, Ji Hye; Ahn, Il Jun; Nam, Woo Hyun; Ra, Jong Beom
2015-02-01
Positron emission tomography (PET) images usually suffer from a noticeable amount of statistical noise. In order to reduce this noise, a post-filtering process is usually adopted. However, the performance of this approach is limited because the denoising process is mostly performed on the basis of the Gaussian random noise. It has been reported that in a PET image reconstructed by the expectation-maximization (EM), the noise variance of each voxel depends on its mean value, unlike in the case of Gaussian noise. In addition, we observe that the variance also varies with the spatial sensitivity distribution in a PET system, which reflects both the solid angle determined by a given scanner geometry and the attenuation information of a scanned object. Thus, if a post-filtering process based on the Gaussian random noise is applied to PET images without consideration of the noise characteristics along with the spatial sensitivity distribution, the spatially variant non-Gaussian noise cannot be reduced effectively. In the proposed framework, to effectively reduce the noise in PET images reconstructed by the 3-D ordinary Poisson ordered subset EM (3-D OP-OSEM), we first denormalize an image according to the sensitivity of each voxel so that the voxel mean value can represent its statistical properties reliably. Based on our observation that each noisy denormalized voxel has a linear relationship between the mean and variance, we try to convert this non-Gaussian noise image to a Gaussian noise image. We then apply a block matching 4-D algorithm that is optimized for noise reduction of the Gaussian noise image, and reconvert and renormalize the result to obtain a final denoised image. Using simulated phantom data and clinical patient data, we demonstrate that the proposed framework can effectively suppress the noise over the whole region of a PET image while minimizing degradation of the image resolution.
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Perturbative Gaussianizing transforms for cosmological fields
NASA Astrophysics Data System (ADS)
Hall, Alex; Mead, Alexander
2018-01-01
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.
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Non-Gaussianities in a two-field generalization of natural inflation
NASA Astrophysics Data System (ADS)
Riquelme M., Simon
2018-04-01
We describe a two-field model that generalizes natural inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spontaneously broken, and the radial mode is dynamical. We analyze how the dynamics fundamentally depends on the mass of the radial mode and calculate/estimate the non-Gaussianities arising from such a scenario.
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NASA Astrophysics Data System (ADS)
Xin, Wei; Zhao, Yu-Wei; Sudu; Eerdunchaolu
2018-05-01
Considering Hydrogen-like impurity and the thickness effect, the eigenvalues and eigenfunctions of the electronic ground and first exited states in a quantum dot (QD) are derived by using the Lee-Low-Pins-Pekar variational method with the harmonic and Gaussian potentials as the transverse and longitudinal confinement potentials, respectively. A two-level system is constructed on the basis of those two states, and the electronic quantum transition affected by an electromagnetic field is discussed in terms of the two-level system theory. The results indicate the Gaussian potential reflects the real confinement potential more accurately than the parabolic one; the influence of the thickness of the QD on the electronic transition probability is interesting and significant, and cannot be ignored; the electronic transition probability Γ is influenced significantly by some physical quantities, such as the strength of the electron-phonon coupling α, the electric-field strength F, the magnetic-field cyclotron frequency ωc , the barrier height V0 and confinement range L of the asymmetric Gaussian potential, suggesting the transport and optical properties of the QD can be manipulated further though those physical quantities.
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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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Propagation properties of cylindrical sinc Gaussian beam
NASA Astrophysics Data System (ADS)
Eyyuboğlu, Halil T.; Bayraktar, Mert
2016-09-01
We investigate the propagation properties of cylindrical sinc Gaussian beam in turbulent atmosphere. Since an analytic solution is hardly derivable, the study is carried out with the aid of random phase screens. Evolutions of the beam intensity profile, beam size and kurtosis parameter are analysed. It is found that on the source plane, cylindrical sinc Gaussian beam has a dark hollow appearance, where the side lobes also start to emerge with increase in width parameter and Gaussian source size. During propagation, beams with small width and Gaussian source size exhibit off-axis behaviour, losing the dark hollow shape, accumulating the intensity asymmetrically on one side, whereas those with large width and Gaussian source size retain dark hollow appearance even at long propagation distances. It is seen that the beams with large widths expand more in beam size than the ones with small widths. The structure constant values chosen do not seem to alter this situation. The kurtosis parameters of the beams having small widths are seen to be larger than the ones with the small widths. Again the choice of the structure constant does not change this trend.
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Recovering dark-matter clustering from galaxies with Gaussianization
NASA Astrophysics Data System (ADS)
McCullagh, Nuala; Neyrinck, Mark; Norberg, Peder; Cole, Shaun
2016-04-01
The Gaussianization transform has been proposed as a method to remove the issues of scale-dependent galaxy bias and non-linearity from galaxy clustering statistics, but these benefits have yet to be thoroughly tested for realistic galaxy samples. In this paper, we test the effectiveness of the Gaussianization transform for different galaxy types by applying it to realistic simulated blue and red galaxy samples. We show that in real space, the shapes of the Gaussianized power spectra of both red and blue galaxies agree with that of the underlying dark matter, with the initial power spectrum, and with each other to smaller scales than do the statistics of the usual (untransformed) density field. However, we find that the agreement in the Gaussianized statistics breaks down in redshift space. We attribute this to the fact that red and blue galaxies exhibit very different fingers of god in redshift space. After applying a finger-of-god compression, the agreement on small scales between the Gaussianized power spectra is restored. We also compare the Gaussianization transform to the clipped galaxy density field and find that while both methods are effective in real space, they have more complicated behaviour in redshift space. Overall, we find that Gaussianization can be useful in recovering the shape of the underlying dark-matter power spectrum to k ˜ 0.5 h Mpc-1 and of the initial power spectrum to k ˜ 0.4 h Mpc-1 in certain cases at z = 0.
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Second harmonic sound field after insertion of a biological tissue sample
NASA Astrophysics Data System (ADS)
Zhang, Dong; Gong, Xiu-Fen; Zhang, Bo
2002-01-01
Second harmonic sound field after inserting a biological tissue sample is investigated by theory and experiment. The sample is inserted perpendicular to the sound axis, whose acoustical properties are different from those of surrounding medium (distilled water). By using the superposition of Gaussian beams and the KZK equation in quasilinear and parabolic approximations, the second harmonic field after insertion of the sample can be derived analytically and expressed as a linear combination of self- and cross-interaction of the Gaussian beams. Egg white, egg yolk, porcine liver, and porcine fat are used as the samples and inserted in the sound field radiated from a 2 MHz uniformly excited focusing source. Axial normalized sound pressure curves of the second harmonic wave before and after inserting the sample are measured and compared with the theoretical results calculated with 10 items of Gaussian beam functions.
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NASA Astrophysics Data System (ADS)
Safari, Samaneh; Niknam, Ali Reza; Jahangiri, Fazel; Jazi, Bahram
2018-04-01
The nonlinear interaction of Hermite-Gaussian and Laguerre-Gaussian (LG) laser beams with a collisional inhomogeneous plasma is studied, and the amplitude of the emitted terahertz (THz) electric field is evaluated. The effects of laser beams and plasma parameters, including the beams width, LG modes, the plasma collision frequency, and the amplitude of density ripple on the evolution of THz electric field amplitude, are examined. It is found that the shape of the generated THz radiation pattern can be tuned by the laser parameters. In addition, the optimum values of the effective parameters for achieving the maximum THz electric field amplitude are proposed. It is shown that a significant enhancement up to 4.5% can be obtained in our scheme, which is much greater than the maximum efficiency obtained for laser beams with the same profiles.
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Elegant Gaussian beams for enhanced optical manipulation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Alpmann, Christina, E-mail: c.alpmann@uni-muenster.de; Schöler, Christoph; Denz, Cornelia
2015-06-15
Generation of micro- and nanostructured complex light beams attains increasing impact in photonics and laser applications. In this contribution, we demonstrate the implementation and experimental realization of the relatively unknown, but highly versatile class of complex-valued Elegant Hermite- and Laguerre-Gaussian beams. These beams create higher trapping forces compared to standard Gaussian light fields due to their propagation changing properties. We demonstrate optical trapping and alignment of complex functional particles as nanocontainers with standard and Elegant Gaussian light beams. Elegant Gaussian beams will inspire manifold applications in optical manipulation, direct laser writing, or microscopy, where the design of the point-spread functionmore » is relevant.« less
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Infrared small target detection in heavy sky scene clutter based on sparse representation
NASA Astrophysics Data System (ADS)
Liu, Depeng; Li, Zhengzhou; Liu, Bing; Chen, Wenhao; Liu, Tianmei; Cao, Lei
2017-09-01
A novel infrared small target detection method based on sky clutter and target sparse representation is proposed in this paper to cope with the representing uncertainty of clutter and target. The sky scene background clutter is described by fractal random field, and it is perceived and eliminated via the sparse representation on fractal background over-complete dictionary (FBOD). The infrared small target signal is simulated by generalized Gaussian intensity model, and it is expressed by the generalized Gaussian target over-complete dictionary (GGTOD), which could describe small target more efficiently than traditional structured dictionaries. Infrared image is decomposed on the union of FBOD and GGTOD, and the sparse representation energy that target signal and background clutter decomposed on GGTOD differ so distinctly that it is adopted to distinguish target from clutter. Some experiments are induced and the experimental results show that the proposed approach could improve the small target detection performance especially under heavy clutter for background clutter could be efficiently perceived and suppressed by FBOD and the changing target could also be represented accurately by GGTOD.
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Space-time models based on random fields with local interactions
NASA Astrophysics Data System (ADS)
Hristopulos, Dionissios T.; Tsantili, Ivi C.
2016-08-01
The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.
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Electric Field Fluctuations in Water
NASA Astrophysics Data System (ADS)
Thorpe, Dayton; Limmer, David; Chandler, David
2013-03-01
Charge transfer in solution, such as autoionization and ion pair dissociation in water, is governed by rare electric field fluctuations of the solvent. Knowing the statistics of such fluctuations can help explain the dynamics of these rare events. Trajectories short enough to be tractable by computer simulation are virtually certain not to sample the large fluctuations that promote rare events. Here, we employ importance sampling techniques with classical molecular dynamics simulations of liquid water to study statistics of electric field fluctuations far from their means. We find that the distributions of electric fields located on individual water molecules are not in general gaussian. Near the mean this non-gaussianity is due to the internal charge distribution of the water molecule. Further from the mean, however, there is a previously unreported Bjerrum-like defect that stabilizes certain large fluctuations out of equilibrium. As expected, differences in electric fields acting between molecules are gaussian to a remarkable degree. By studying these differences, though, we are able to determine what configurations result not only in large electric fields, but also in electric fields with long spatial correlations that may be needed to promote charge separation.
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Impact of spurious shear on cosmological parameter estimates from weak lensing observables
Petri, Andrea; May, Morgan; Haiman, Zoltán; ...
2014-12-30
We research, residual errors in shear measurements, after corrections for instrument systematics and atmospheric effects, can impact cosmological parameters derived from weak lensing observations. Here we combine convergence maps from our suite of ray-tracing simulations with random realizations of spurious shear. This allows us to quantify the errors and biases of the triplet (Ω m,w,σ 8) derived from the power spectrum (PS), as well as from three different sets of non-Gaussian statistics of the lensing convergence field: Minkowski functionals (MFs), low-order moments (LMs), and peak counts (PKs). Our main results are as follows: (i) We find an order of magnitudemore » smaller biases from the PS than in previous work. (ii) The PS and LM yield biases much smaller than the morphological statistics (MF, PK). (iii) For strictly Gaussian spurious shear with integrated amplitude as low as its current estimate of σ sys 2 ≈ 10 -7, biases from the PS and LM would be unimportant even for a survey with the statistical power of Large Synoptic Survey Telescope. However, we find that for surveys larger than ≈ 100 deg 2, non-Gaussianity in the noise (not included in our analysis) will likely be important and must be quantified to assess the biases. (iv) The morphological statistics (MF, PK) introduce important biases even for Gaussian noise, which must be corrected in large surveys. The biases are in different directions in (Ωm,w,σ8) parameter space, allowing self-calibration by combining multiple statistics. Our results warrant follow-up studies with more extensive lensing simulations and more accurate spurious shear estimates.« less
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Signal-Preserving Erratic Noise Attenuation via Iterative Robust Sparsity-Promoting Filter
Zhao, Qiang; Du, Qizhen; Gong, Xufei; ...
2018-04-06
Sparse domain thresholding filters operating in a sparse domain are highly effective in removing Gaussian random noise under Gaussian distribution assumption. Erratic noise, which designates non-Gaussian noise that consists of large isolated events with known or unknown distribution, also needs to be explicitly taken into account. However, conventional sparse domain thresholding filters based on the least-squares (LS) criterion are severely sensitive to data with high-amplitude and non-Gaussian noise, i.e., the erratic noise, which makes the suppression of this type of noise extremely challenging. Here, in this paper, we present a robust sparsity-promoting denoising model, in which the LS criterion ismore » replaced by the Huber criterion to weaken the effects of erratic noise. The random and erratic noise is distinguished by using a data-adaptive parameter in the presented method, where random noise is described by mean square, while the erratic noise is downweighted through a damped weight. Different from conventional sparse domain thresholding filters, definition of the misfit between noisy data and recovered signal via the Huber criterion results in a nonlinear optimization problem. With the help of theoretical pseudoseismic data, an iterative robust sparsity-promoting filter is proposed to transform the nonlinear optimization problem into a linear LS problem through an iterative procedure. The main advantage of this transformation is that the nonlinear denoising filter can be solved by conventional LS solvers. Lastly, tests with several data sets demonstrate that the proposed denoising filter can successfully attenuate the erratic noise without damaging useful signal when compared with conventional denoising approaches based on the LS criterion.« less
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Signal-Preserving Erratic Noise Attenuation via Iterative Robust Sparsity-Promoting Filter
DOE Office of Scientific and Technical Information (OSTI.GOV)
Zhao, Qiang; Du, Qizhen; Gong, Xufei
Sparse domain thresholding filters operating in a sparse domain are highly effective in removing Gaussian random noise under Gaussian distribution assumption. Erratic noise, which designates non-Gaussian noise that consists of large isolated events with known or unknown distribution, also needs to be explicitly taken into account. However, conventional sparse domain thresholding filters based on the least-squares (LS) criterion are severely sensitive to data with high-amplitude and non-Gaussian noise, i.e., the erratic noise, which makes the suppression of this type of noise extremely challenging. Here, in this paper, we present a robust sparsity-promoting denoising model, in which the LS criterion ismore » replaced by the Huber criterion to weaken the effects of erratic noise. The random and erratic noise is distinguished by using a data-adaptive parameter in the presented method, where random noise is described by mean square, while the erratic noise is downweighted through a damped weight. Different from conventional sparse domain thresholding filters, definition of the misfit between noisy data and recovered signal via the Huber criterion results in a nonlinear optimization problem. With the help of theoretical pseudoseismic data, an iterative robust sparsity-promoting filter is proposed to transform the nonlinear optimization problem into a linear LS problem through an iterative procedure. The main advantage of this transformation is that the nonlinear denoising filter can be solved by conventional LS solvers. Lastly, tests with several data sets demonstrate that the proposed denoising filter can successfully attenuate the erratic noise without damaging useful signal when compared with conventional denoising approaches based on the LS criterion.« less
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EVOLUTION OF FAST MAGNETOACOUSTIC PULSES IN RANDOMLY STRUCTURED CORONAL PLASMAS
DOE Office of Scientific and Technical Information (OSTI.GOV)
Yuan, D.; Li, B.; Pascoe, D. J.
2015-02-01
We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in the context of large-scale propagating waves in the solar atmosphere. We perform one-dimensional numerical simulations of fast wave pulses propagating perpendicular to a constant magnetic field in a low-β plasma with a random density profile across the field. Both linear and nonlinear regimes are considered. We study how the evolution of the pulse amplitude and width depends on their initial values and the parameters of the random structuring. Acting as a dispersive medium, a randomly structured plasma causes amplitude attenuation and width broadening of the fast wavemore » pulses. After the passage of the main pulse, secondary propagating and standing fast waves appear. Width evolution of both linear and nonlinear pulses can be well approximated by linear functions; however, narrow pulses may have zero or negative broadening. This arises because narrow pulses are prone to splitting, while broad pulses usually deviate less from their initial Gaussian shape and form ripple structures on top of the main pulse. Linear pulses decay at an almost constant rate, while nonlinear pulses decay exponentially. A pulse interacts most efficiently with a random medium with a correlation length of about half of the initial pulse width. This detailed model of fast wave pulses propagating in highly structured media substantiates the interpretation of EIT waves as fast magnetoacoustic waves. Evolution of a fast pulse provides us with a novel method to diagnose the sub-resolution filamentation of the solar atmosphere.« less
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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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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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NASA Astrophysics Data System (ADS)
Hematizadeh, Ayoob; Jazayeri, Seyed Masud; Ghafary, Bijan
2018-02-01
A scheme for excitation of terahertz (THz) radiation is presented by photo mixing of two super-Gaussian laser beams in a rippled density collisional magnetized plasma. Lasers having different frequencies and wave numbers but the same electric fields create a ponderomotive force on the electrons of plasma in the beating frequency. Super-Gaussian laser beam has the exclusive features such as steep gradient in laser intensity distribution, wider cross-section in comparison with Gaussian profiles, which make stronger ponderomotive force and higher THz radiation. The magnetic field is considered oblique to laser beams propagation direction; in this case, depending on the phase matching conditions different mode waves can propagate in plasma. It is found that amplitude and efficiency of the emitted THz radiation not only are sensitive to the beating frequency, collision frequency, and magnetic field strength but to the angle between laser beams and static magnetic field. The efficiency of THz radiation can be optimized in a certain angle.
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Nonlinear scalar forcing based on a reaction analogy
NASA Astrophysics Data System (ADS)
Daniel, Don; Livescu, Daniel
2017-11-01
We present a novel reaction analogy (RA) based forcing method for generating stationary passive scalar fields in incompressible turbulence. The new method can produce more general scalar PDFs (e.g. double-delta) than current methods, while ensuring that scalar fields remain bounded, unlike existent forcing methodologies that can potentially violate naturally existing bounds. Such features are useful for generating initial fields in non-premixed combustion or for studying non-Gaussian scalar turbulence. The RA method mathematically models hypothetical chemical reactions that convert reactants in a mixed state back into its pure unmixed components. Various types of chemical reactions are formulated and the corresponding mathematical expressions derived. For large values of the scalar dissipation rate, the method produces statistically steady double-delta scalar PDFs. Gaussian scalar statistics are recovered for small values of the scalar dissipation rate. In contrast, classical forcing methods consistently produce unimodal Gaussian scalar fields. The ability of the new method to produce fully developed scalar fields is discussed using 2563, 5123, and 10243 periodic box simulations.
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μ SR study of NaCaNi2F7 in zero field and applied longitudinal magnetic field
NASA Astrophysics Data System (ADS)
Cai, Yipeng; Wilson, Murray; Hallas, Alannah; Liu, Lian; Frandsen, Benjamin; Dunsiger, Sarah; Krizan, Jason; Cava, Robert; Uemura, Yasutomo; Luke, Graeme
Rich physics of abundant magnetic ground states has been realized in the A2B2X7 geometrically frustrated magnetic pyrochlores. Recently, a new spin-1 Ni2+ pyrochlore, NaCaNi2F7, was synthesized and shown to have spin freezing at 3.6 K with a frustration index of f 36 and antiferromagnetic exchange interactions [1] . This structure has chemical disorder on the A site caused by randomly distributed Ca and Na ions, which causes bond disorder around the magnetic Ni sites. We present Zero Field (ZF) and Longitudinal Field (LF) muon spin rotation (μSR) measurements on this single crystal pyrochlore. Our data shows that the Ni2+ spins start freezing around 4 K giving a static local field of 140 G. The data show no oscillations down to 75 mK which indicates no long range magnetic order. They are well described by the dynamic Gaussian Kubo-Toyabe function with a non-zero hopping rate that is not easily decoupled with an applied longitudinal field, which implies persistent spin dynamics down to 75 mK.
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Common inputs in subthreshold membrane potential: The role of quiescent states in neuronal activity
NASA Astrophysics Data System (ADS)
Montangie, Lisandro; Montani, Fernando
2018-06-01
Experiments in certain regions of the cerebral cortex suggest that the spiking activity of neuronal populations is regulated by common non-Gaussian inputs across neurons. We model these deviations from random-walk processes with q -Gaussian distributions into simple threshold neurons, and investigate the scaling properties in large neural populations. We show that deviations from the Gaussian statistics provide a natural framework to regulate population statistics such as sparsity, entropy, and specific heat. This type of description allows us to provide an adequate strategy to explain the information encoding in the case of low neuronal activity and its possible implications on information transmission.
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NASA Astrophysics Data System (ADS)
Zhao, Leihong; Qu, Xiaolu; Lin, Hongjun; Yu, Genying; Liao, Bao-Qiang
2018-03-01
Simulation of randomly rough bioparticle surface is crucial to better understand and control interface behaviors and membrane fouling. Pursuing literature indicated a lack of effective method for simulating random rough bioparticle surface. In this study, a new method which combines Gaussian distribution, Fourier transform, spectrum method and coordinate transformation was proposed to simulate surface topography of foulant bioparticles in a membrane bioreactor (MBR). The natural surface of a foulant bioparticle was found to be irregular and randomly rough. The topography simulated by the new method was quite similar to that of real foulant bioparticles. Moreover, the simulated topography of foulant bioparticles was critically affected by parameters correlation length (l) and root mean square (σ). The new method proposed in this study shows notable superiority over the conventional methods for simulation of randomly rough foulant bioparticles. The ease, facility and fitness of the new method point towards potential applications in interface behaviors and membrane fouling research.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Müller, Florian, E-mail: florian.mueller@sam.math.ethz.ch; Jenny, Patrick, E-mail: jenny@ifd.mavt.ethz.ch; Meyer, Daniel W., E-mail: meyerda@ethz.ch
2013-10-01
Monte Carlo (MC) is a well known method for quantifying uncertainty arising for example in subsurface flow problems. Although robust and easy to implement, MC suffers from slow convergence. Extending MC by means of multigrid techniques yields the multilevel Monte Carlo (MLMC) method. MLMC has proven to greatly accelerate MC for several applications including stochastic ordinary differential equations in finance, elliptic stochastic partial differential equations and also hyperbolic problems. In this study, MLMC is combined with a streamline-based solver to assess uncertain two phase flow and Buckley–Leverett transport in random heterogeneous porous media. The performance of MLMC is compared tomore » MC for a two dimensional reservoir with a multi-point Gaussian logarithmic permeability field. The influence of the variance and the correlation length of the logarithmic permeability on the MLMC performance is studied.« less
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Radiation Transport in Random Media With Large Fluctuations
NASA Astrophysics Data System (ADS)
Olson, Aaron; Prinja, Anil; Franke, Brian
2017-09-01
Neutral particle transport in media exhibiting large and complex material property spatial variation is modeled by representing cross sections as lognormal random functions of space and generated through a nonlinear memory-less transformation of a Gaussian process with covariance uniquely determined by the covariance of the cross section. A Karhunen-Loève decomposition of the Gaussian process is implemented to effciently generate realizations of the random cross sections and Woodcock Monte Carlo used to transport particles on each realization and generate benchmark solutions for the mean and variance of the particle flux as well as probability densities of the particle reflectance and transmittance. A computationally effcient stochastic collocation method is implemented to directly compute the statistical moments such as the mean and variance, while a polynomial chaos expansion in conjunction with stochastic collocation provides a convenient surrogate model that also produces probability densities of output quantities of interest. Extensive numerical testing demonstrates that use of stochastic reduced-order modeling provides an accurate and cost-effective alternative to random sampling for particle transport in random media.
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Tight focusing of higher orders Laguerre-Gaussian modes
DOE Office of Scientific and Technical Information (OSTI.GOV)
Savelyev, Dmitry A., E-mail: dmitrey.savelyev@yandex.ru; Khonina, Svetlana N.; Samara State Aerospace University, 34 Moskovskoye Shosse, Samara 443086
2016-04-13
The spatial redistribution of the contribution of different electric field components provides a decrease in the size of the central focal spot for higher orders Laguerre-Gaussian modes. It was shown that when sharply focusing laser beams with vortex or special binary phase plate, a sub-wavelength light localization of separate vector field components is possible for any polarization type. This fact should be considered for the interaction of laser radiation with materials selectively sensitive to lateral and longitudinal components of the electromagnetic field.
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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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Pataky, Todd C; Vanrenterghem, Jos; Robinson, Mark A
2016-06-14
A false positive is the mistake of inferring an effect when none exists, and although α controls the false positive (Type I error) rate in classical hypothesis testing, a given α value is accurate only if the underlying model of randomness appropriately reflects experimentally observed variance. Hypotheses pertaining to one-dimensional (1D) (e.g. time-varying) biomechanical trajectories are most often tested using a traditional zero-dimensional (0D) Gaussian model of randomness, but variance in these datasets is clearly 1D. The purpose of this study was to determine the likelihood that analyzing smooth 1D data with a 0D model of variance will produce false positives. We first used random field theory (RFT) to predict the probability of false positives in 0D analyses. We then validated RFT predictions via numerical simulations of smooth Gaussian 1D trajectories. Results showed that, across a range of public kinematic, force/moment and EMG datasets, the median false positive rate was 0.382 and not the assumed α=0.05, even for a simple two-sample t test involving N=10 trajectories per group. The median false positive rate for experiments involving three-component vector trajectories was p=0.764. This rate increased to p=0.945 for two three-component vector trajectories, and to p=0.999 for six three-component vectors. This implies that experiments involving vector trajectories have a high probability of yielding 0D statistical significance when there is, in fact, no 1D effect. Either (a) explicit a priori identification of 0D variables or (b) adoption of 1D methods can more tightly control α. Copyright © 2016 Elsevier Ltd. All rights reserved.
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NASA Astrophysics Data System (ADS)
Fiori, A.; Zarlenga, A.; Jankovic, I.; Dagan, G.
2017-12-01
Natural gradient steady flow of mean velocity U takes place in heterogeneous aquifers of random logconductivity Y = lnK , characterized by the normal univariate PDF f(Y) and autocorrelation ρY, of variance σY2 and horizontal integral scale I. Solute transport is quantified by the Breakthrough Curve (BTC) M at planes at distance x from the injection plane. The study builds on the extensive 3D numerical simulations of flow and transport of Jankovic et al. (2017) for different conductivity structures. The present study further explores the predictive capabilities of the Advection Dispersion Equation (ADE), with macrodispersivity αL given by the First Order Approximation (FOA), by checking in a quantitative manner its applicability. After a discussion on the suitable boundary conditions for ADE, we find that the ADE-FOA solution is a sufficiently accurate predictor for applications, the many other sources of uncertainty prevailing in practice notwithstanding. We checked by least squares and by comparison of travel time of quantiles of M that indeed the analytical Inverse Gaussian M with αL =σY2 I , is able to fit well the bulk of the simulated BTCs. It tends to underestimate the late arrival time of the thin and persistent tail. The tail is better reproduced by the semi-analytical MIMSCA model, which also allows for a physical explanation of the success of the Inverse Gaussian solution. Examination of the pertinent longitudinal mass distribution shows that it is different from the commonly used Gaussian one in the analysis of field experiments, and it captures the main features of the plume measurements of the MADE experiment. The results strengthen the confidence in the applicability of the ADE and the FOA to predicting longitudinal spreading in solute transport through heterogeneous aquifers of stationary random structure.
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Improvements in GRACE Gravity Field Determination through Stochastic Observation Modeling
NASA Astrophysics Data System (ADS)
McCullough, C.; Bettadpur, S. V.
2016-12-01
Current unconstrained Release 05 GRACE gravity field solutions from the Center for Space Research (CSR RL05) assume random observation errors following an independent multivariate Gaussian distribution. This modeling of observations, a simplifying assumption, fails to account for long period, correlated errors arising from inadequacies in the background force models. Fully modeling the errors inherent in the observation equations, through the use of a full observation covariance (modeling colored noise), enables optimal combination of GPS and inter-satellite range-rate data and obviates the need for estimating kinematic empirical parameters during the solution process. Most importantly, fully modeling the observation errors drastically improves formal error estimates of the spherical harmonic coefficients, potentially enabling improved uncertainty quantification of scientific results derived from GRACE and optimizing combinations of GRACE with independent data sets and a priori constraints.
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Inference with minimal Gibbs free energy in information field theory.
Ensslin, Torsten A; Weig, Cornelius
2010-11-01
Non-linear and non-gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the gaussian approximation to the full posterior probability, which has maximal cross information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a gaussian signal with unknown spectrum, and (iii) inference of a poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-gaussian posterior.
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NASA Astrophysics Data System (ADS)
Pfeilsticker, K.; Davis, A.; Marshak, A.; Suszcynsky, D. M.; Buldryrev, S.; Barker, H.
2001-12-01
2-stream RT models, as used in all current GCMs, are mathematically equivalent to standard diffusion theory where the physical picture is a slow propagation of the diffuse radiation by Gaussian random walks. In other words, after the conventional van de Hulst rescaling by 1/(1-g) in R3 and also by (1-g) in t, solar photons follow convoluted fractal trajectories in the atmosphere. For instance, we know that transmitted light is typically scattered about (1-g)τ 2 times while reflected light is scattered on average about τ times, where τ is the optical depth of the column. The space/time spread of this diffusion process is described exactly by a Gaussian distribution; from the statistical physics viewpoint, this follows from the convergence of the sum of many (rescaled) steps between scattering events with a finite variance. This Gaussian picture follows from directly from first principles (the RT equation) under the assumptions of horizontal uniformity and large optical depth, i.e., there is a homogeneous plane-parallel cloud somewhere in the column. The first-order effect of 3D variability of cloudiness, the main source of scattering, is to perturb the distribution of single steps between scatterings which, modulo the '1-g' rescaling, can be assumed effectively isotropic. The most natural generalization of the Gaussian distribution is the 1-parameter family of symmetric Lévy-stable distributions because the sum of many zero-mean random variables with infinite variance, but finite moments of order q < α (0 < α < 2), converge to them. It has been shown on heuristic grounds that for these Lévy-based random walks the typical number of scatterings is now (1-g)τ α for transmitted light. The appearance of a non-rational exponent is why this is referred to as anomalous diffusion. Note that standard/Gaussian diffusion is retrieved in the limit α = 2-. Lévy transport theory has been successfully used in the statistical physics to investigate a wide variety of systems with strongly nonlinear dynamics; these applications range from random advection in turbulent fluids to the erratic behavior of financial time-series and, most recently, self-regulating ecological systems. We will briefly survey the state-of-the-art observations that offer compelling empirical support for the Lévy/anomalous diffusion model in atmospheric radiation: (1) high-resolution spectroscopy of differential absorption in the O2 A-band from ground; (2) temporal transient records of lightning strokes transmitted through clouds to a sensitive detector in space; and (3) the Gamma-distributions of optical depths derived from Landsat cloud scenes at 30-m resolution. We will then introduce a rigorous analytical formulation of anomalous transport through finite media based on fractional derivatives and Sonin calculus. A remarkable result from this new theoretical development is an extremal property of the α = 1+ case (divergent mean-free-path), as is observed in the cloudy atmosphere. Finally, we will discuss the implications of anomalous transport theory for bulk 3D effects on the current enhanced absorption problem as well as its role as the basis of a next-generation GCM RT parameterization.
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Optimal random search for a single hidden target.
Snider, Joseph
2011-01-01
A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the minimum number of trials. Here it will be shown that if the searcher must get very close to the target to find it, then the best search distribution is proportional to the square root of the target distribution regardless of dimension. For a Gaussian target distribution, the optimum search distribution is approximately a Gaussian with a standard deviation that varies inversely with how close the searcher must be to the target to find it. For a network where the searcher randomly samples nodes and looks for the fixed target along edges, the optimum is either to sample a node with probability proportional to the square root of the out-degree plus 1 or not to do so at all.
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NASA Astrophysics Data System (ADS)
Alimi, Jean-Michel; de Fromont, Paul
2018-04-01
The statistical properties of cosmic structures are well known to be strong probes for cosmology. In particular, several studies tried to use the cosmic void counting number to obtain tight constrains on dark energy. In this paper, we model the statistical properties of these regions using the CoSphere formalism (de Fromont & Alimi) in both primordial and non-linearly evolved Universe in the standard Λ cold dark matter model. This formalism applies similarly for minima (voids) and maxima (such as DM haloes), which are here considered symmetrically. We first derive the full joint Gaussian distribution of CoSphere's parameters in the Gaussian random field. We recover the results of Bardeen et al. only in the limit where the compensation radius becomes very large, i.e. when the central extremum decouples from its cosmic environment. We compute the probability distribution of the compensation size in this primordial field. We show that this distribution is redshift independent and can be used to model cosmic voids size distribution. We also derive the statistical distribution of the peak parameters introduced by Bardeen et al. and discuss their correlation with the cosmic environment. We show that small central extrema with low density are associated with narrow compensation regions with deep compensation density, while higher central extrema are preferentially located in larger but smoother over/under massive regions.
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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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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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Reversible wavefront shaping between Gaussian and Airy beams by mimicking gravitational field
NASA Astrophysics Data System (ADS)
Wang, Xiangyang; Liu, Hui; Sheng, Chong; Zhu, Shining
2018-02-01
In this paper, we experimentally demonstrate reversible wavefront shaping through mimicking gravitational field. A gradient-index micro-structured optical waveguide with special refractive index profile was constructed whose effective index satisfying a gravitational field profile. Inside the waveguide, an incident broad Gaussian beam is firstly transformed into an accelerating beam, and the generated accelerating beam is gradually changed back to a Gaussian beam afterwards. To validate our experiment, we performed full-wave continuum simulations that agree with the experimental results. Furthermore, a theoretical model was established to describe the evolution of the laser beam based on Landau’s method, showing that the accelerating beam behaves like the Airy beam in the small range in which the linear potential approaches zero. To our knowledge, such a reversible wavefront shaping technique has not been reported before.
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Linear Space-Variant Image Restoration of Photon-Limited Images
1978-03-01
levels of performance of the wavefront seisor. The parameter ^ represents the residual rms wavefront error ^measurement noise plus ♦ttting error...known to be optimum only when the signal and noise are uncorrelated stationary random processes «nd when the noise statistics are gaussian. In the...regime of photon-Iimited imaging, the noise is non-gaussian and signaI-dependent, and it is therefore reasonable to assume that tome form of linear
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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
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On the identification of Dragon Kings among extreme-valued outliers
NASA Astrophysics Data System (ADS)
Riva, M.; Neuman, S. P.; Guadagnini, A.
2013-07-01
Extreme values of earth, environmental, ecological, physical, biological, financial and other variables often form outliers to heavy tails of empirical frequency distributions. Quite commonly such tails are approximated by stretched exponential, log-normal or power functions. Recently there has been an interest in distinguishing between extreme-valued outliers that belong to the parent population of most data in a sample and those that do not. The first type, called Gray Swans by Nassim Nicholas Taleb (often confused in the literature with Taleb's totally unknowable Black Swans), is drawn from a known distribution of the tails which can thus be extrapolated beyond the range of sampled values. However, the magnitudes and/or space-time locations of unsampled Gray Swans cannot be foretold. The second type of extreme-valued outliers, termed Dragon Kings by Didier Sornette, may in his view be sometimes predicted based on how other data in the sample behave. This intriguing prospect has recently motivated some authors to propose statistical tests capable of identifying Dragon Kings in a given random sample. Here we apply three such tests to log air permeability data measured on the faces of a Berea sandstone block and to synthetic data generated in a manner statistically consistent with these measurements. We interpret the measurements to be, and generate synthetic data that are, samples from α-stable sub-Gaussian random fields subordinated to truncated fractional Gaussian noise (tfGn). All these data have frequency distributions characterized by power-law tails with extreme-valued outliers about the tail edges.
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New description of charged particle propagation in random magnetic fields
NASA Technical Reports Server (NTRS)
Earl, James A.
1994-01-01
When charged particles spiral along a large constant magnetic field, their trajectories are scattered by random components that are superposed on the guiding field. In the simplest analysis of this situation, scattering causes the particles to diffuse parallel to the guiding field. At the next level of approximation, moving pulses that correspond to a coherent mode of propagation are present, but they are represented by delta-functions whose infinitely narrow width makes no sense physically and is inconsistent with the finite duration of coherent pulses observed in solar energetic particle events. To derive a more realistic description, the transport problem is formulated in terms of 4 x 4 matrices, which derive from a representation of the particle distribution function in terms of eigenfunctions of the scattering operator, and which lead to useful approximations that give explicit predictions of the detailed evolution not only of the coherent pulses, but also of the diffusive wake. More specifically, the new description embodies a simple convolution of a narrow Gaussian with the solutions above that involve delta-functions, but with a slightly reduced coherent velocity. The validity of these approximations, which can easily be calculated on a desktop computer, has been exhaustively confirmed by comparison with results of Monte Carlo simulations which kept track of 50 million particles and which were carried out on the Maspar computer at Goddard Space Flight Center.
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Ray, J.; Lee, J.; Yadav, V.; ...
2015-04-29
Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) andmore » fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Ray, J.; Lee, J.; Yadav, V.
Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) andmore » fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less
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NASA Astrophysics Data System (ADS)
Aziz-Aghchegala, V. L.; Mughnetsyan, V. N.; Kirakosyan, A. A.
2018-02-01
The effect of interdiffusion and magnetic field on confined states of electron and heavy hole as well as on interband absorption spectrum in a Ga1-xAlxAs/GaAs Gaussian-shaped double quantum ring are investigated. It is shown that both interdiffusion and magnetic field lead to the change of the charge carriers' quantum states arrangement by their energies. The oscillating behavior of the electron ground state energy as a function of magnetic field induction gradually disappears with the increase of diffusion parameter due to the enhanced tunneling of electron to the central region of the ring. For the heavy hole the ground state energy oscillations are not observable in the region of the values of magnetic field induction B = 0 - 10 T . For considered transitions both the magnetic field and the interdiffusion lead to a blue-shift of the absorption spectrum and to decreasing of the absorption intensity. The obtained results indicate on the opportunity of purposeful manipulation of energy states and absorption spectrum of a Gaussian-shaped double quantum ring by means of the post growth annealing and the external magnetic field.
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Robust Tracking of Small Displacements with a Bayesian Estimator
Dumont, Douglas M.; Byram, Brett C.
2016-01-01
Radiation-force-based elasticity imaging describes a group of techniques that use acoustic radiation force (ARF) to displace tissue in order to obtain qualitative or quantitative measurements of tissue properties. Because ARF-induced displacements are on the order of micrometers, tracking these displacements in vivo can be challenging. Previously, it has been shown that Bayesian-based estimation can overcome some of the limitations of a traditional displacement estimator like normalized cross-correlation (NCC). In this work, we describe a Bayesian framework that combines a generalized Gaussian-Markov random field (GGMRF) prior with an automated method for selecting the prior’s width. We then evaluate its performance in the context of tracking the micrometer-order displacements encountered in an ARF-based method like acoustic radiation force impulse (ARFI) imaging. The results show that bias, variance, and mean-square error performance vary with prior shape and width, and that an almost one order-of-magnitude reduction in mean-square error can be achieved by the estimator at the automatically-selected prior width. Lesion simulations show that the proposed estimator has a higher contrast-to-noise ratio but lower contrast than NCC, median-filtered NCC, and the previous Bayesian estimator, with a non-Gaussian prior shape having better lesion-edge resolution than a Gaussian prior. In vivo results from a cardiac, radiofrequency ablation ARFI imaging dataset show quantitative improvements in lesion contrast-to-noise ratio over NCC as well as the previous Bayesian estimator. PMID:26529761
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Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model
NASA Astrophysics Data System (ADS)
Kanazawa, Takuya; Kieburg, Mario
2018-06-01
We consider a random matrix model which interpolates between the chiral Gaussian unitary ensemble and the Gaussian unitary ensemble while preserving chiral symmetry. This ensemble describes flavor symmetry breaking for staggered fermions in 3D QCD as well as in 4D QCD at high temperature or in 3D QCD at a finite isospin chemical potential. Our model is an Osborn-type two-matrix model which is equivalent to the elliptic ensemble but we consider the singular value statistics rather than the complex eigenvalue statistics. We report on exact results for the partition function and the microscopic level density of the Dirac operator in the ɛ regime of QCD. We compare these analytical results with Monte Carlo simulations of the matrix model.
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Controllable gaussian-qubit interface for extremal quantum state engineering.
Adesso, Gerardo; Campbell, Steve; Illuminati, Fabrizio; Paternostro, Mauro
2010-06-18
We study state engineering through bilinear interactions between two remote qubits and two-mode gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.
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Dynamic heterogeneity and non-Gaussian statistics for acetylcholine receptors on live cell membrane
NASA Astrophysics Data System (ADS)
He, W.; Song, H.; Su, Y.; Geng, L.; Ackerson, B. J.; Peng, H. B.; Tong, P.
2016-05-01
The Brownian motion of molecules at thermal equilibrium usually has a finite correlation time and will eventually be randomized after a long delay time, so that their displacement follows the Gaussian statistics. This is true even when the molecules have experienced a complex environment with a finite correlation time. Here, we report that the lateral motion of the acetylcholine receptors on live muscle cell membranes does not follow the Gaussian statistics for normal Brownian diffusion. From a careful analysis of a large volume of the protein trajectories obtained over a wide range of sampling rates and long durations, we find that the normalized histogram of the protein displacements shows an exponential tail, which is robust and universal for cells under different conditions. The experiment indicates that the observed non-Gaussian statistics and dynamic heterogeneity are inherently linked to the slow-active remodelling of the underlying cortical actin network.
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Recurrence plots of discrete-time Gaussian stochastic processes
NASA Astrophysics Data System (ADS)
Ramdani, Sofiane; Bouchara, Frédéric; Lagarde, Julien; Lesne, Annick
2016-09-01
We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1. These results allow us to obtain theoretical values of three measures: (i) the recurrence rate (REC) (ii) the percent determinism (DET) and (iii) RP-based estimation of the ε-entropy κ(ε) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.
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NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Behnke, marlana N.; Przekop, Adam
2010-01-01
High-cycle fatigue of an elastic-plastic beam structure under the combined action of thermal and high-intensity non-Gaussian acoustic loadings is considered. Such loadings can be highly damaging when snap-through motion occurs between thermally post-buckled equilibria. The simulated non-Gaussian loadings investigated have a range of skewness and kurtosis typical of turbulent boundary layer pressure fluctuations in the vicinity of forward facing steps. Further, the duration and steadiness of high excursion peaks is comparable to that found in such turbulent boundary layer data. Response and fatigue life estimates are found to be insensitive to the loading distribution, with the minor exception of cases involving plastic deformation. In contrast, the fatigue life estimate was found to be highly affected by a different type of non-Gaussian loading having bursts of high excursion peaks.
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Gaussian effective potential: Quantum mechanics
NASA Astrophysics Data System (ADS)
Stevenson, P. M.
1984-10-01
We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.
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Scaling properties of the two-dimensional randomly stirred Navier-Stokes equation.
Mazzino, Andrea; Muratore-Ginanneschi, Paolo; Musacchio, Stefano
2007-10-05
We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree 2 - 2 epsilon. This is at variance with the setting usually assumed to derive Kraichnan's classical theory. We contrast accurate numerical experiments with the different predictions provided for the small epsilon regime by Kraichnan's double cascade theory and by renormalization group analysis. We give clear evidence that for all epsilon, Kraichnan's theory is consistent with the observed phenomenology. Our results call for a revision in the renormalization group analysis of (2D) fully developed turbulence.
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Qi, Hong; Qiao, Yao-Bin; Ren, Ya-Tao; Shi, Jing-Wen; Zhang, Ze-Yu; Ruan, Li-Ming
2016-10-17
Sequential quadratic programming (SQP) is used as an optimization algorithm to reconstruct the optical parameters based on the time-domain radiative transfer equation (TD-RTE). Numerous time-resolved measurement signals are obtained using the TD-RTE as forward model. For a high computational efficiency, the gradient of objective function is calculated using an adjoint equation technique. SQP algorithm is employed to solve the inverse problem and the regularization term based on the generalized Gaussian Markov random field (GGMRF) model is used to overcome the ill-posed problem. Simulated results show that the proposed reconstruction scheme performs efficiently and accurately.
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NASA Astrophysics Data System (ADS)
Šantić, Neven; Fusaro, Adrien; Salem, Sabeur; Garnier, Josselin; Picozzi, Antonio; Kaiser, Robin
2018-02-01
The nonlinear Schrödinger equation, used to describe the dynamics of quantum fluids, is known to be valid not only for massive particles but also for the propagation of light in a nonlinear medium, predicting condensation of classical waves. Here we report on the initial evolution of random waves with Gaussian statistics using atomic vapors as an efficient two dimensional nonlinear medium. Experimental and theoretical analysis of near field images reveal a phenomenon of nonequilibrium precondensation, characterized by a fast relaxation towards a precondensate fraction of up to 75%. Such precondensation is in contrast to complete thermalization to the Rayleigh-Jeans equilibrium distribution, requiring prohibitive long interaction lengths.
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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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Ensemble Solute Transport in 2-D Operator-Stable Random Fields
NASA Astrophysics Data System (ADS)
Monnig, N. D.; Benson, D. A.
2006-12-01
The heterogeneous velocity field that exists at many scales in an aquifer will typically cause a dissolved solute plume to grow at a rate faster than Fick's Law predicts. Some statistical model must be adopted to account for the aquifer structure that engenders the velocity heterogeneity. A fractional Brownian motion (fBm) model has been shown to create the long-range correlation that can produce continually faster-than-Fickian plume growth. Previous fBm models have assumed isotropic scaling (defined here by a scalar Hurst coefficient). Motivated by field measurements of aquifer hydraulic conductivity, recent techniques were developed to construct random fields with anisotropic scaling with a self-similarity parameter that is defined by a matrix. The growth of ensemble plumes is analyzed for transport through 2-D "operator- stable" fBm hydraulic conductivity (K) fields. Both the longitudinal and transverse Hurst coefficients are important to both plume growth rates and the timing and duration of breakthrough. Smaller Hurst coefficients in the transverse direction lead to more "continuity" or stratification in the direction of transport. The result is continually faster-than-Fickian growth rates, highly non-Gaussian ensemble plumes, and a longer tail early in the breakthrough curve. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rate never exceeds Mercado's [1967] purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent super-Mercado growth must be the result of other factors, such as larger plumes corresponding to either a larger initial plume size or greater variance of the ln(K) field.
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Yu, Wenxi; Liu, Yang; Ma, Zongwei; Bi, Jun
2017-08-01
Using satellite-based aerosol optical depth (AOD) measurements and statistical models to estimate ground-level PM 2.5 is a promising way to fill the areas that are not covered by ground PM 2.5 monitors. The statistical models used in previous studies are primarily Linear Mixed Effects (LME) and Geographically Weighted Regression (GWR) models. In this study, we developed a new regression model between PM 2.5 and AOD using Gaussian processes in a Bayesian hierarchical setting. Gaussian processes model the stochastic nature of the spatial random effects, where the mean surface and the covariance function is specified. The spatial stochastic process is incorporated under the Bayesian hierarchical framework to explain the variation of PM 2.5 concentrations together with other factors, such as AOD, spatial and non-spatial random effects. We evaluate the results of our model and compare them with those of other, conventional statistical models (GWR and LME) by within-sample model fitting and out-of-sample validation (cross validation, CV). The results show that our model possesses a CV result (R 2 = 0.81) that reflects higher accuracy than that of GWR and LME (0.74 and 0.48, respectively). Our results indicate that Gaussian process models have the potential to improve the accuracy of satellite-based PM 2.5 estimates.
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NASA Astrophysics Data System (ADS)
Yao, Weiguang; Merchant, Thomas E.; Farr, Jonathan B.
2016-10-01
The lateral homogeneity assumption is used in most analytical algorithms for proton dose, such as the pencil-beam algorithms and our simplified analytical random walk model. To improve the dose calculation in the distal fall-off region in heterogeneous media, we analyzed primary proton fluence near heterogeneous media and propose to calculate the lateral fluence with voxel-specific Gaussian distributions. The lateral fluence from a beamlet is no longer expressed by a single Gaussian for all the lateral voxels, but by a specific Gaussian for each lateral voxel. The voxel-specific Gaussian for the beamlet of interest is calculated by re-initializing the fluence deviation on an effective surface where the proton energies of the beamlet of interest and the beamlet passing the voxel are the same. The dose improvement from the correction scheme was demonstrated by the dose distributions in two sets of heterogeneous phantoms consisting of cortical bone, lung, and water and by evaluating distributions in example patients with a head-and-neck tumor and metal spinal implants. The dose distributions from Monte Carlo simulations were used as the reference. The correction scheme effectively improved the dose calculation accuracy in the distal fall-off region and increased the gamma test pass rate. The extra computation for the correction was about 20% of that for the original algorithm but is dependent upon patient geometry.
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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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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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Interpretation of Extinction in Gaussian-Beam Scattering
NASA Technical Reports Server (NTRS)
Lock, James A.
1995-01-01
The extinction efficiency for the interaction of a plane wave with a large nonabsorbing spherical particle is approximately 2.0. When a Gaussian beam of half-width w(sub 0) is incident upon a spherical particle of radius a with w(sub 0)/a less than 1, the extinction efficiency attains unexpectedly high or low values, contrary to intuitive expectations. The reason for this is associated with the so-called compensating term in the scattered field, which cancels the field of the Gaussian beam behind the particle, thereby producing the particle's shadow. I introduce a decomposition of the total exterior field into incoming and outgoing portions that are free of compensating terms. It is then shown that a suitably defined interaction efficiency has the intuitively expected asymptotic values of 2.0 for w(sub 0)/a much greater than 1 and 1.0 for w(sub 0)/a much less than 1.
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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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Axial acoustic radiation force on a sphere in Gaussian field
DOE Office of Scientific and Technical Information (OSTI.GOV)
Wu, Rongrong; Liu, Xiaozhou, E-mail: xzliu@nju.edu.cn; Gong, Xiufen
2015-10-28
Based on the finite series method, the acoustical radiation force resulting from a Gaussian beam incident on a spherical object is investigated analytically. When the position of the particles deviating from the center of the beam, the Gaussian beam is expanded as a spherical function at the center of the particles and the expanded coefficients of the Gaussian beam is calculated. The analytical expression of the acoustic radiation force on spherical particles deviating from the Gaussian beam center is deduced. The acoustic radiation force affected by the acoustic frequency and the offset distance from the Gaussian beam center is investigated.more » Results have been presented for Gaussian beams with different wavelengths and it has been shown that the interaction of a Gaussian beam with a sphere can result in attractive axial force under specific operational conditions. Results indicate the capability of manipulating and separating spherical spheres based on their mechanical and acoustical properties, the results provided here may provide a theoretical basis for development of single-beam acoustical tweezers.« less
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NASA Astrophysics Data System (ADS)
Libera, Arianna; de Barros, Felipe P. J.; Riva, Monica; Guadagnini, Alberto
2017-10-01
Our study is keyed to the analysis of the interplay between engineering factors (i.e., transient pumping rates versus less realistic but commonly analyzed uniform extraction rates) and the heterogeneous structure of the aquifer (as expressed by the probability distribution characterizing transmissivity) on contaminant transport. We explore the joint influence of diverse (a) groundwater pumping schedules (constant and variable in time) and (b) representations of the stochastic heterogeneous transmissivity (T) field on temporal histories of solute concentrations observed at an extraction well. The stochastic nature of T is rendered by modeling its natural logarithm, Y = ln T, through a typical Gaussian representation and the recently introduced Generalized sub-Gaussian (GSG) model. The latter has the unique property to embed scale-dependent non-Gaussian features of the main statistics of Y and its (spatial) increments, which have been documented in a variety of studies. We rely on numerical Monte Carlo simulations and compute the temporal evolution at the well of low order moments of the solute concentration (C), as well as statistics of the peak concentration (Cp), identified as the environmental performance metric of interest in this study. We show that the pumping schedule strongly affects the pattern of the temporal evolution of the first two statistical moments of C, regardless the nature (Gaussian or non-Gaussian) of the underlying Y field, whereas the latter quantitatively influences their magnitude. Our results show that uncertainty associated with C and Cp estimates is larger when operating under a transient extraction scheme than under the action of a uniform withdrawal schedule. The probability density function (PDF) of Cp displays a long positive tail in the presence of time-varying pumping schedule. All these aspects are magnified in the presence of non-Gaussian Y fields. Additionally, the PDF of Cp displays a bimodal shape for all types of pumping schemes analyzed, independent of the type of heterogeneity considered.
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NASA Astrophysics Data System (ADS)
Zhou, GuoQuan; Cai, YangJian; Dai, ChaoQing
2013-05-01
A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular momentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respectively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter γ, and transfer matrix elements A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in optical micromanipulation.
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Some error bounds for K-iterated Gaussian recursive filters
NASA Astrophysics Data System (ADS)
Cuomo, Salvatore; Galletti, Ardelio; Giunta, Giulio; Marcellino, Livia
2016-10-01
Recursive filters (RFs) have achieved a central role in several research fields over the last few years. For example, they are used in image processing, in data assimilation and in electrocardiogram denoising. More in particular, among RFs, the Gaussian RFs are an efficient computational tool for approximating Gaussian-based convolutions and are suitable for digital image processing and applications of the scale-space theory. As is a common knowledge, the Gaussian RFs, applied to signals with support in a finite domain, generate distortions and artifacts, mostly localized at the boundaries. Heuristic and theoretical improvements have been proposed in literature to deal with this issue (namely boundary conditions). They include the case in which a Gaussian RF is applied more than once, i.e. the so called K-iterated Gaussian RFs. In this paper, starting from a summary of the comprehensive mathematical background, we consider the case of the K-iterated first-order Gaussian RF and provide the study of its numerical stability and some component-wise theoretical error bounds.
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A Novel Weighted Kernel PCA-Based Method for Optimization and Uncertainty Quantification
NASA Astrophysics Data System (ADS)
Thimmisetty, C.; Talbot, C.; Chen, X.; Tong, C. H.
2016-12-01
It has been demonstrated that machine learning methods can be successfully applied to uncertainty quantification for geophysical systems through the use of the adjoint method coupled with kernel PCA-based optimization. In addition, it has been shown through weighted linear PCA how optimization with respect to both observation weights and feature space control variables can accelerate convergence of such methods. Linear machine learning methods, however, are inherently limited in their ability to represent features of non-Gaussian stochastic random fields, as they are based on only the first two statistical moments of the original data. Nonlinear spatial relationships and multipoint statistics leading to the tortuosity characteristic of channelized media, for example, are captured only to a limited extent by linear PCA. With the aim of coupling the kernel-based and weighted methods discussed, we present a novel mathematical formulation of kernel PCA, Weighted Kernel Principal Component Analysis (WKPCA), that both captures nonlinear relationships and incorporates the attribution of significance levels to different realizations of the stochastic random field of interest. We also demonstrate how new instantiations retaining defining characteristics of the random field can be generated using Bayesian methods. In particular, we present a novel WKPCA-based optimization method that minimizes a given objective function with respect to both feature space random variables and observation weights through which optimal snapshot significance levels and optimal features are learned. We showcase how WKPCA can be applied to nonlinear optimal control problems involving channelized media, and in particular demonstrate an application of the method to learning the spatial distribution of material parameter values in the context of linear elasticity, and discuss further extensions of the method to stochastic inversion.
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Encoding Gaussian curvature in glassy and elastomeric liquid crystal solids
Mostajeran, Cyrus; Ware, Taylor H.; White, Timothy J.
2016-01-01
We describe shape transitions of thin, solid nematic sheets with smooth, preprogrammed, in-plane director fields patterned across the surface causing spatially inhomogeneous local deformations. A metric description of the local deformations is used to study the intrinsic geometry of the resulting surfaces upon exposure to stimuli such as light and heat. We highlight specific patterns that encode constant Gaussian curvature of prescribed sign and magnitude. We present the first experimental results for such programmed solids, and they qualitatively support theory for both positive and negative Gaussian curvature morphing from flat sheets on stimulation by light or heat. We review logarithmic spiral patterns that generate cone/anti-cone surfaces, and introduce spiral director fields that encode non-localized positive and negative Gaussian curvature on punctured discs, including spherical caps and spherical spindles. Conditions are derived where these cap-like, photomechanically responsive regions can be anchored in inert substrates by designing solutions that ensure compatibility with the geometric constraints imposed by the surrounding media. This integration of such materials is a precondition for their exploitation in new devices. Finally, we consider the radial extension of such director fields to larger sheets using nematic textures defined on annular domains. PMID:27279777
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Effects of scale-dependent non-Gaussianity on cosmological structures
DOE Office of Scientific and Technical Information (OSTI.GOV)
LoVerde, Marilena; Miller, Amber; Shandera, Sarah
2008-04-15
The detection of primordial non-Gaussianity could provide a powerful means to test various inflationary scenarios. Although scale-invariant non-Gaussianity (often described by the f{sub NL} formalism) is currently best constrained by the CMB, single-field models with changing sound speed can have strongly scale-dependent non-Gaussianity. Such models could evade the CMB constraints but still have important effects at scales responsible for the formation of cosmological objects such as clusters and galaxies. We compute the effect of scale-dependent primordial non-Gaussianity on cluster number counts as a function of redshift, using a simple ansatz to model scale-dependent features. We forecast constraints on these modelsmore » achievable with forthcoming datasets. We also examine consequences for the galaxy bispectrum. Our results are relevant for the Dirac-Born-Infeld model of brane inflation, where the scale dependence of the non-Gaussianity is directly related to the geometry of the extra dimensions.« less
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Anomalous and non-Gaussian diffusion in Hertzian spheres
NASA Astrophysics Data System (ADS)
Ouyang, Wenze; Sun, Bin; Sun, Zhiwei; Xu, Shenghua
2018-09-01
By means of molecular dynamics simulations, we study the non-Gaussian diffusion in the fluid of Hertzian spheres. The time dependent non-Gaussian parameter, as an indicator of the dynamic heterogeneity, is increased with the increasing of temperature. When the temperature is high enough, the dynamic heterogeneity becomes very significant, and it seems counterintuitive that the maximum of non-Gaussian parameter and the position of its peak decrease monotonically with the increasing of density. By fitting the curves of self intermediate scattering function, we find that the character relaxation time τα is surprisingly not coupled with the time τmax where the non-Gaussian parameter reaches to a maximum. The intriguing features of non-Gaussian diffusion at high enough temperatures can be associated with the weakly correlated mean-field behavior of Hertzian spheres. Especially the time τmax is nearly inversely proportional to the density at extremely high temperatures.
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Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere
NASA Astrophysics Data System (ADS)
Lukin, Igor P.
2017-11-01
In this paper the theoretical research of coherent properties of the vortex Bessel-Gaussian optical beams propagating in turbulent atmosphere are developed. The approach to the analysis of this problem is based on the analytical solution of the equation for the transverse second-order mutual coherence function of a field of optical radiation. The behavior of integral scale of coherence degree of vortex Bessel-Gaussian optical beams depending on parameters of an optical beam and characteristics of turbulent atmosphere is particularly considered. It is shown that the integral scale of coherence degree of a vortex Bessel-Gaussian optical beam essentially depends on value of a topological charge of a vortex optical beam. With increase in a topological charge of a vortex Bessel-Gaussian optical beam the value of integral scale of coherence degree of a vortex Bessel-Gaussian optical beam are decreased.
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Continuous-variable phase estimation with unitary and random linear disturbance
NASA Astrophysics Data System (ADS)
Delgado de Souza, Douglas; Genoni, Marco G.; Kim, M. S.
2014-10-01
We address the problem of continuous-variable quantum phase estimation in the presence of linear disturbance at the Hamiltonian level by means of Gaussian probe states. In particular we discuss both unitary and random disturbance by considering the parameter which characterizes the unwanted linear term present in the Hamiltonian as fixed (unitary disturbance) or random with a given probability distribution (random disturbance). We derive the optimal input Gaussian states at fixed energy, maximizing the quantum Fisher information over the squeezing angle and the squeezing energy fraction, and we discuss the scaling of the quantum Fisher information in terms of the output number of photons, nout. We observe that, in the case of unitary disturbance, the optimal state is a squeezed vacuum state and the quadratic scaling is conserved. As regards the random disturbance, we observe that the optimal squeezing fraction may not be equal to one and, for any nonzero value of the noise parameter, the quantum Fisher information scales linearly with the average number of photons. Finally, we discuss the performance of homodyne measurement by comparing the achievable precision with the ultimate limit imposed by the quantum Cramér-Rao bound.
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Sassani, Farrokh
2014-01-01
The simulation results for electromagnetic energy harvesters (EMEHs) under broad band stationary Gaussian random excitations indicate the importance of both a high transformation factor and a high mechanical quality factor to achieve favourable mean power, mean square load voltage, and output spectral density. The optimum load is different for random vibrations and for sinusoidal vibration. Reducing the total damping ratio under band-limited random excitation yields a higher mean square load voltage. Reduced bandwidth resulting from decreased mechanical damping can be compensated by increasing the electrical damping (transformation factor) leading to a higher mean square load voltage and power. Nonlinear EMEHs with a Duffing spring and with linear plus cubic damping are modeled using the method of statistical linearization. These nonlinear EMEHs exhibit approximately linear behaviour under low levels of broadband stationary Gaussian random vibration; however, at higher levels of such excitation the central (resonant) frequency of the spectral density of the output voltage shifts due to the increased nonlinear stiffness and the bandwidth broadens slightly. Nonlinear EMEHs exhibit lower maximum output voltage and central frequency of the spectral density with nonlinear damping compared to linear damping. Stronger nonlinear damping yields broader bandwidths at stable resonant frequency. PMID:24605063
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A Gaussian beam method for ultrasonic non-destructive evaluation modeling
NASA Astrophysics Data System (ADS)
Jacquet, O.; Leymarie, N.; Cassereau, D.
2018-05-01
The propagation of high-frequency ultrasonic body waves can be efficiently estimated with a semi-analytic Dynamic Ray Tracing approach using paraxial approximation. Although this asymptotic field estimation avoids the computational cost of numerical methods, it may encounter several limitations in reproducing identified highly interferential features. Nevertheless, some can be managed by allowing paraxial quantities to be complex-valued. This gives rise to localized solutions, known as paraxial Gaussian beams. Whereas their propagation and transmission/reflection laws are well-defined, the fact remains that the adopted complexification introduces additional initial conditions. While their choice is usually performed according to strategies specifically tailored to limited applications, a Gabor frame method has been implemented to indiscriminately initialize a reasonable number of paraxial Gaussian beams. Since this method can be applied for an usefully wide range of ultrasonic transducers, the typical case of the time-harmonic piston radiator is investigated. Compared to the commonly used Multi-Gaussian Beam model [1], a better agreement is obtained throughout the radiated field between the results of numerical integration (or analytical on-axis solution) and the resulting Gaussian beam superposition. Sparsity of the proposed solution is also discussed.
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Bilateral filter regularized accelerated Demons for improved discontinuity preserving registration.
Demirović, D; Šerifović-Trbalić, A; Prljača, N; Cattin, Ph C
2015-03-01
The classical accelerated Demons algorithm uses Gaussian smoothing to penalize oscillatory motion in the displacement fields during registration. This well known method uses the L2 norm for regularization. Whereas the L2 norm is known for producing well behaving smooth deformation fields it cannot properly deal with discontinuities often seen in the deformation field as the regularizer cannot differentiate between discontinuities and smooth part of motion field. In this paper we propose replacement the Gaussian filter of the accelerated Demons with a bilateral filter. In contrast the bilateral filter not only uses information from displacement field but also from the image intensities. In this way we can smooth the motion field depending on image content as opposed to the classical Gaussian filtering. By proper adjustment of two tunable parameters one can obtain more realistic deformations in a case of discontinuity. The proposed approach was tested on 2D and 3D datasets and showed significant improvements in the Target Registration Error (TRE) for the well known POPI dataset. Despite the increased computational complexity, the improved registration result is justified in particular abdominal data sets where discontinuities often appear due to sliding organ motion. Copyright © 2014 Elsevier Ltd. All rights reserved.
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Photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Karbstein, Felix; Mosman, Elena A.
2017-12-01
In this article, we provide analytical expressions for the photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams. Our results are based on a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics. Hence, by construction they are limited to slowly varying electromagnetic fields, varying on spatial and temporal scales significantly larger than the Compton wavelength/time of the electron. The latter criterion is fulfilled by all laser beams currently available in the laboratory. Our findings will, e.g., be relevant for the study of vacuum birefringence experienced by probe photons brought into collision with a high-intensity laser pulse which can be represented as a superposition of either Hermite- or Laguerre-Gaussian modes.
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Caustics and Rogue Waves in an Optical Sea.
Mathis, Amaury; Froehly, Luc; Toenger, Shanti; Dias, Frédéric; Genty, Goëry; Dudley, John M
2015-08-06
There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an "optical sea" with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.
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Caustics and Rogue Waves in an Optical Sea
Mathis, Amaury; Froehly, Luc; Toenger, Shanti; Dias, Frédéric; Genty, Goëry; Dudley, John M.
2015-01-01
There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an “optical sea” with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed. PMID:26245864
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Turbulent mixing of a critical fluid: The non-perturbative renormalization
NASA Astrophysics Data System (ADS)
Hnatič, M.; Kalagov, G.; Nalimov, M.
2018-01-01
Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi 〉 ∼ (Pji⊥ + αPji∥) /k d + ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d = 3, ζ = 4 / 3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α ≲ 2.26. Otherwise, in the case of "strong compressibility" α ≳ 2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.
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Chialvo, Ariel A.; Vlcek, Lukas
2014-11-01
We present a detailed derivation of the complete set of expressions required for the implementation of an Ewald summation approach to handle the long-range electrostatic interactions of polar and ionic model systems involving Gaussian charges and induced dipole moments with a particular application to the isobaricisothermal molecular dynamics simulation of our Gaussian Charge Polarizable (GCP) water model and its extension to aqueous electrolytes solutions. The set comprises the individual components of the potential energy, electrostatic potential, electrostatic field and gradient, the electrostatic force and the corresponding virial. Moreover, we show how the derived expressions converge to known point-based electrostatic counterpartsmore » when the parameters, defining the Gaussian charge and induced-dipole distributions, are extrapolated to their limiting point values. Finally, we illustrate the Ewald implementation against the current reaction field approach by isothermal-isobaric molecular dynamics of ambient GCP water for which we compared the outcomes of the thermodynamic, microstructural, and polarization behavior.« less
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NASA Astrophysics Data System (ADS)
Shemer, L.; Sergeeva, A.
2009-12-01
The statistics of random water wave field determines the probability of appearance of extremely high (freak) waves. This probability is strongly related to the spectral wave field characteristics. Laboratory investigation of the spatial variation of the random wave-field statistics for various initial conditions is thus of substantial practical importance. Unidirectional nonlinear random wave groups are investigated experimentally in the 300 m long Large Wave Channel (GWK) in Hannover, Germany, which is the biggest facility of its kind in Europe. Numerous realizations of a wave field with the prescribed frequency power spectrum, yet randomly-distributed initial phases of each harmonic, were generated by a computer-controlled piston-type wavemaker. Several initial spectral shapes with identical dominant wave length but different width were considered. For each spectral shape, the total duration of sampling in all realizations was long enough to yield sufficient sample size for reliable statistics. Through all experiments, an effort had been made to retain the characteristic wave height value and thus the degree of nonlinearity of the wave field. Spatial evolution of numerous statistical wave field parameters (skewness, kurtosis and probability distributions) is studied using about 25 wave gauges distributed along the tank. It is found that, depending on the initial spectral shape, the frequency spectrum of the wave field may undergo significant modification in the course of its evolution along the tank; the values of all statistical wave parameters are strongly related to the local spectral width. A sample of the measured wave height probability functions (scaled by the variance of surface elevation) is plotted in Fig. 1 for the initially narrow rectangular spectrum. The results in Fig. 1 resemble findings obtained in [1] for the initial Gaussian spectral shape. The probability of large waves notably surpasses that predicted by the Rayleigh distribution and is the highest at the distance of about 100 m. Acknowledgement This study is carried out in the framework of the EC supported project "Transnational access to large-scale tests in the Large Wave Channel (GWK) of Forschungszentrum Küste (Contract HYDRALAB III - No. 022441). [1] L. Shemer and A. Sergeeva, J. Geophys. Res. Oceans 114, C01015 (2009). Figure 1. Variation along the tank of the measured wave height distribution for rectangular initial spectral shape, the carrier wave period T0=1.5 s.
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Galaxy bias and primordial non-Gaussianity
DOE Office of Scientific and Technical Information (OSTI.GOV)
Assassi, Valentin; Baumann, Daniel; Schmidt, Fabian, E-mail: assassi@ias.edu, E-mail: D.D.Baumann@uva.nl, E-mail: fabians@MPA-Garching.MPG.DE
2015-12-01
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin ofmore » any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation.« less
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Gaussian mixture models as flux prediction method for central receivers
NASA Astrophysics Data System (ADS)
Grobler, Annemarie; Gauché, Paul; Smit, Willie
2016-05-01
Flux prediction methods are crucial to the design and operation of central receiver systems. Current methods such as the circular and elliptical (bivariate) Gaussian prediction methods are often used in field layout design and aiming strategies. For experimental or small central receiver systems, the flux profile of a single heliostat often deviates significantly from the circular and elliptical Gaussian models. Therefore a novel method of flux prediction was developed by incorporating the fitting of Gaussian mixture models onto flux profiles produced by flux measurement or ray tracing. A method was also developed to predict the Gaussian mixture model parameters of a single heliostat for a given time using image processing. Recording the predicted parameters in a database ensures that more accurate predictions are made in a shorter time frame.
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Adaptive hierarchical grid model of water-borne pollutant dispersion
NASA Astrophysics Data System (ADS)
Borthwick, A. G. L.; Marchant, R. D.; Copeland, G. J. M.
Water pollution by industrial and agricultural waste is an increasingly major public health issue. It is therefore important for water engineers and managers to be able to predict accurately the local behaviour of water-borne pollutants. This paper describes the novel and efficient coupling of dynamically adaptive hierarchical grids with standard solvers of the advection-diffusion equation. Adaptive quadtree grids are able to focus on regions of interest such as pollutant fronts, while retaining economy in the total number of grid elements through selective grid refinement. Advection is treated using Lagrangian particle tracking. Diffusion is solved separately using two grid-based methods; one is by explicit finite differences, the other a diffusion-velocity approach. Results are given in two dimensions for pure diffusion of an initially Gaussian plume, advection-diffusion of the Gaussian plume in the rotating flow field of a forced vortex, and the transport of species in a rectangular channel with side wall boundary layers. Close agreement is achieved with analytical solutions of the advection-diffusion equation and simulations from a Lagrangian random walk model. An application to Sepetiba Bay, Brazil is included to demonstrate the method with complex flows and topography.
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Statistical segmentation of multidimensional brain datasets
NASA Astrophysics Data System (ADS)
Desco, Manuel; Gispert, Juan D.; Reig, Santiago; Santos, Andres; Pascau, Javier; Malpica, Norberto; Garcia-Barreno, Pedro
2001-07-01
This paper presents an automatic segmentation procedure for MRI neuroimages that overcomes part of the problems involved in multidimensional clustering techniques like partial volume effects (PVE), processing speed and difficulty of incorporating a priori knowledge. The method is a three-stage procedure: 1) Exclusion of background and skull voxels using threshold-based region growing techniques with fully automated seed selection. 2) Expectation Maximization algorithms are used to estimate the probability density function (PDF) of the remaining pixels, which are assumed to be mixtures of gaussians. These pixels can then be classified into cerebrospinal fluid (CSF), white matter and grey matter. Using this procedure, our method takes advantage of using the full covariance matrix (instead of the diagonal) for the joint PDF estimation. On the other hand, logistic discrimination techniques are more robust against violation of multi-gaussian assumptions. 3) A priori knowledge is added using Markov Random Field techniques. The algorithm has been tested with a dataset of 30 brain MRI studies (co-registered T1 and T2 MRI). Our method was compared with clustering techniques and with template-based statistical segmentation, using manual segmentation as a gold-standard. Our results were more robust and closer to the gold-standard.
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Quantifying the non-Gaussianity in the EoR 21-cm signal through bispectrum
NASA Astrophysics Data System (ADS)
Majumdar, Suman; Pritchard, Jonathan R.; Mondal, Rajesh; Watkinson, Catherine A.; Bharadwaj, Somnath; Mellema, Garrelt
2018-05-01
The epoch of reionization (EoR) 21-cm signal is expected to be highly non-Gaussian in nature and this non-Gaussianity is also expected to evolve with the progressing state of reionization. Therefore the signal will be correlated between different Fourier modes (k). The power spectrum will not be able capture this correlation in the signal. We use a higher order estimator - the bispectrum - to quantify this evolving non-Gaussianity. We study the bispectrum using an ensemble of simulated 21-cm signal and with a large variety of k triangles. We observe two competing sources driving the non-Gaussianity in the signal: fluctuations in the neutral fraction (x_{H I}) field and fluctuations in the matter density field. We find that the non-Gaussian contribution from these two sources varies, depending on the stage of reionization and on which k modes are being studied. We show that the sign of the bispectrum works as a unique marker to identify which among these two components is driving the non-Gaussianity. We propose that the sign change in the bispectrum, when plotted as a function of triangle configuration cos θ and at a certain stage of the EoR can be used as a confirmative test for the detection of the 21-cm signal. We also propose a new consolidated way to visualize the signal evolution (with evolving \\bar{x}_{H I} or redshift), through the trajectories of the signal in a power spectrum and equilateral bispectrum i.e. P(k) - B(k, k, k) space.
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Random matrix theory for transition strengths: Applications and open questions
NASA Astrophysics Data System (ADS)
Kota, V. K. B.
2017-12-01
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different) and so on. Using embedded ensembles (EE), there are efforts to derive a good statistical theory for transition strengths. With m fermions (or bosons) in N mean-field single particle levels and interacting via two-body forces, we have with GOE embedding, the so called EGOE(1+2). Now, the transition strength density (transition strength multiplied by the density of states at the initial and final energies) is a convolution of the density generated by the mean-field one-body part with a bivariate spreading function due to the two-body interaction. Using the embedding U(N) algebra, it is established, for a variety of transition operators, that the spreading function, for sufficiently strong interactions, is close to a bivariate Gaussian. Also, as the interaction strength increases, the spreading function exhibits a transition from bivariate Breit-Wigner to bivariate Gaussian form. In appropriate limits, this EE theory reduces to the polynomial theory of Draayer, French and Wong on one hand and to the theory due to Flambaum and Izrailev for one-body transition operators on the other. Using spin-cutoff factors for projecting angular momentum, the theory is applied to nuclear matrix elements for neutrinoless double beta decay (NDBD). In this paper we will describe: (i) various developments in the EE theory for transition strengths; (ii) results for nuclear matrix elements for 130Te and 136Xe NDBD; (iii) important open questions in the current form of the EE theory.
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Bayesian ionospheric multi-instrument 3D tomography
NASA Astrophysics Data System (ADS)
Norberg, Johannes; Vierinen, Juha; Roininen, Lassi
2017-04-01
The tomographic reconstruction of ionospheric electron densities is an inverse problem that cannot be solved without relatively strong regularising additional information. % Especially the vertical electron density profile is determined predominantly by the regularisation. % %Often utilised regularisations in ionospheric tomography include smoothness constraints and iterative methods with initial ionospheric models. % Despite its crucial role, the regularisation is often hidden in the algorithm as a numerical procedure without physical understanding. % % The Bayesian methodology provides an interpretative approach for the problem, as the regularisation can be given in a physically meaningful and quantifiable prior probability distribution. % The prior distribution can be based on ionospheric physics, other available ionospheric measurements and their statistics. % Updating the prior with measurements results as the posterior distribution that carries all the available information combined. % From the posterior distribution, the most probable state of the ionosphere can then be solved with the corresponding probability intervals. % Altogether, the Bayesian methodology provides understanding on how strong the given regularisation is, what is the information gained with the measurements and how reliable the final result is. % In addition, the combination of different measurements and temporal development can be taken into account in a very intuitive way. However, a direct implementation of the Bayesian approach requires inversion of large covariance matrices resulting in computational infeasibility. % In the presented method, Gaussian Markov random fields are used to form a sparse matrix approximations for the covariances. % The approach makes the problem computationally feasible while retaining the probabilistic and physical interpretation. Here, the Bayesian method with Gaussian Markov random fields is applied for ionospheric 3D tomography over Northern Europe. % Multi-instrument measurements are utilised from TomoScand receiver network for Low Earth orbit beacon satellite signals, GNSS receiver networks, as well as from EISCAT ionosondes and incoherent scatter radars. % %The performance is demonstrated in three-dimensional spatial domain with temporal development also taken into account.
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Parameter estimation for slit-type scanning sensors
NASA Technical Reports Server (NTRS)
Fowler, J. W.; Rolfe, E. G.
1981-01-01
The Infrared Astronomical Satellite, scheduled for launch into a 900 km near-polar orbit in August 1982, will perform an infrared point source survey by scanning the sky with slit-type sensors. The description of position information is shown to require the use of a non-Gaussian random variable. Methods are described for deciding whether separate detections stem from a single common source, and a formulism is developed for the scan-to-scan problems of identifying multiple sightings of inertially fixed point sources for combining their individual measurements into a refined estimate. Several cases are given where the general theory yields results which are quite different from the corresponding Gaussian applications, showing that argument by Gaussian analogy would lead to error.
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Classical and quantum stability in putative landscapes
Dine, Michael
2017-01-18
Landscape analyses often assume the existence of large numbers of fields, N, with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N, eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N; scaling of couplings with N may also be necessary for perturbativity.more » We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. Finally, we consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.« less
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Classical and quantum stability in putative landscapes
NASA Astrophysics Data System (ADS)
Dine, Michael
2017-01-01
Landscape analyses often assume the existence of large numbers of fields, N , with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N , eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N ; scaling of couplings with N may also be necessary for perturbativity. We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. We consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.
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Numeric Solutions of Dirac-Gursey Spinor Field Equation Under External Gaussian White Noise
NASA Astrophysics Data System (ADS)
Aydogmus, Fatma
2016-06-01
In this paper, we consider the Dirac-Gursey spinor field equation that has particle-like solutions derived classical field equations so-called instantons, formed by using Heisenberg ansatz, under the effect of an additional Gaussian white noise term. Our purpose is to understand how the behavior of spinor-type excited instantons in four dimensions can be affected by noise. Thus, we simulate the phase portraits and Poincaré sections of the obtained system numerically both with and without noise. Recurrence plots are also given for more detailed information regarding the system.
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Monte Carlo based toy model for fission process
NASA Astrophysics Data System (ADS)
Kurniadi, R.; Waris, A.; Viridi, S.
2014-09-01
There are many models and calculation techniques to obtain visible image of fission yield process. In particular, fission yield can be calculated by using two calculations approach, namely macroscopic approach and microscopic approach. This work proposes another calculation approach in which the nucleus is treated as a toy model. Hence, the fission process does not represent real fission process in nature completely. The toy model is formed by Gaussian distribution of random number that randomizes distance likesthe distance between particle and central point. The scission process is started by smashing compound nucleus central point into two parts that are left central and right central points. These three points have different Gaussian distribution parameters such as mean (μCN, μL, μR), and standard deviation (σCN, σL, σR). By overlaying of three distributions, the number of particles (NL, NR) that are trapped by central points can be obtained. This process is iterated until (NL, NR) become constant numbers. Smashing process is repeated by changing σL and σR, randomly.
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Nicolas, F; Coëtmellec, S; Brunel, M; Allano, D; Lebrun, D; Janssen, A J E M
2005-11-01
The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by a collimated plane wave [J. Opt. Soc. Am A 19, 1537 (2002)], but also by an elliptic and astigmatic Gaussian beam when two different fractional orders are considered. Simulations and experimental results are presented.
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Geostatistical Sampling Methods for Efficient Uncertainty Analysis in Flow and Transport Problems
NASA Astrophysics Data System (ADS)
Liodakis, Stylianos; Kyriakidis, Phaedon; Gaganis, Petros
2015-04-01
In hydrogeological applications involving flow and transport of in heterogeneous porous media the spatial distribution of hydraulic conductivity is often parameterized in terms of a lognormal random field based on a histogram and variogram model inferred from data and/or synthesized from relevant knowledge. Realizations of simulated conductivity fields are then generated using geostatistical simulation involving simple random (SR) sampling and are subsequently used as inputs to physically-based simulators of flow and transport in a Monte Carlo framework for evaluating the uncertainty in the spatial distribution of solute concentration due to the uncertainty in the spatial distribution of hydraulic con- ductivity [1]. Realistic uncertainty analysis, however, calls for a large number of simulated concentration fields; hence, can become expensive in terms of both time and computer re- sources. A more efficient alternative to SR sampling is Latin hypercube (LH) sampling, a special case of stratified random sampling, which yields a more representative distribution of simulated attribute values with fewer realizations [2]. Here, term representative implies realizations spanning efficiently the range of possible conductivity values corresponding to the lognormal random field. In this work we investigate the efficiency of alternative methods to classical LH sampling within the context of simulation of flow and transport in a heterogeneous porous medium. More precisely, we consider the stratified likelihood (SL) sampling method of [3], in which attribute realizations are generated using the polar simulation method by exploring the geometrical properties of the multivariate Gaussian distribution function. In addition, we propose a more efficient version of the above method, here termed minimum energy (ME) sampling, whereby a set of N representative conductivity realizations at M locations is constructed by: (i) generating a representative set of N points distributed on the surface of a M-dimensional, unit radius hyper-sphere, (ii) relocating the N points on a representative set of N hyper-spheres of different radii, and (iii) transforming the coordinates of those points to lie on N different hyper-ellipsoids spanning the multivariate Gaussian distribution. The above method is applied in a dimensionality reduction context by defining flow-controlling points over which representative sampling of hydraulic conductivity is performed, thus also accounting for the sensitivity of the flow and transport model to the input hydraulic conductivity field. The performance of the various stratified sampling methods, LH, SL, and ME, is compared to that of SR sampling in terms of reproduction of ensemble statistics of hydraulic conductivity and solute concentration for different sample sizes N (numbers of realizations). The results indicate that ME sampling constitutes an equally if not more efficient simulation method than LH and SL sampling, as it can reproduce to a similar extent statistics of the conductivity and concentration fields, yet with smaller sampling variability than SR sampling. References [1] Gutjahr A.L. and Bras R.L. Spatial variability in subsurface flow and transport: A review. Reliability Engineering & System Safety, 42, 293-316, (1993). [2] Helton J.C. and Davis F.J. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliability Engineering & System Safety, 81, 23-69, (2003). [3] Switzer P. Multiple simulation of spatial fields. In: Heuvelink G, Lemmens M (eds) Proceedings of the 4th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, Coronet Books Inc., pp 629?635 (2000).
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Coherent states field theory in supramolecular polymer physics
NASA Astrophysics Data System (ADS)
Fredrickson, Glenn H.; Delaney, Kris T.
2018-05-01
In 1970, Edwards and Freed presented an elegant representation of interacting branched polymers that resembles the coherent states (CS) formulation of second-quantized field theory. This CS polymer field theory has been largely overlooked during the intervening period in favor of more conventional "auxiliary field" (AF) interacting polymer representations that form the basis of modern self-consistent field theory (SCFT) and field-theoretic simulation approaches. Here we argue that the CS representation provides a simpler and computationally more efficient framework than the AF approach for broad classes of reversibly bonding polymers encountered in supramolecular polymer science. The CS formalism is reviewed, initially for a simple homopolymer solution, and then extended to supramolecular polymers capable of forming reversible linkages and networks. In the context of the Edwards model of a non-reacting homopolymer solution and one and two-component models of telechelic reacting polymers, we discuss the structure of CS mean-field theory, including the equivalence to SCFT, and show how weak-amplitude expansions (random phase approximations) can be readily developed without explicit enumeration of all reaction products in a mixture. We further illustrate how to analyze CS field theories beyond SCFT at the level of Gaussian field fluctuations and provide a perspective on direct numerical simulations using a recently developed complex Langevin technique.
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Random Wiring, Ganglion Cell Mosaics, and the Functional Architecture of the Visual Cortex
Coppola, David; White, Leonard E.; Wolf, Fred
2015-01-01
The architecture of iso-orientation domains in the primary visual cortex (V1) of placental carnivores and primates apparently follows species invariant quantitative laws. Dynamical optimization models assuming that neurons coordinate their stimulus preferences throughout cortical circuits linking millions of cells specifically predict these invariants. This might indicate that V1’s intrinsic connectome and its functional architecture adhere to a single optimization principle with high precision and robustness. To validate this hypothesis, it is critical to closely examine the quantitative predictions of alternative candidate theories. Random feedforward wiring within the retino-cortical pathway represents a conceptually appealing alternative to dynamical circuit optimization because random dimension-expanding projections are believed to generically exhibit computationally favorable properties for stimulus representations. Here, we ask whether the quantitative invariants of V1 architecture can be explained as a generic emergent property of random wiring. We generalize and examine the stochastic wiring model proposed by Ringach and coworkers, in which iso-orientation domains in the visual cortex arise through random feedforward connections between semi-regular mosaics of retinal ganglion cells (RGCs) and visual cortical neurons. We derive closed-form expressions for cortical receptive fields and domain layouts predicted by the model for perfectly hexagonal RGC mosaics. Including spatial disorder in the RGC positions considerably changes the domain layout properties as a function of disorder parameters such as position scatter and its correlations across the retina. However, independent of parameter choice, we find that the model predictions substantially deviate from the layout laws of iso-orientation domains observed experimentally. Considering random wiring with the currently most realistic model of RGC mosaic layouts, a pairwise interacting point process, the predicted layouts remain distinct from experimental observations and resemble Gaussian random fields. We conclude that V1 layout invariants are specific quantitative signatures of visual cortical optimization, which cannot be explained by generic random feedforward-wiring models. PMID:26575467
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Chaos and random matrices in supersymmetric SYK
NASA Astrophysics Data System (ADS)
Hunter-Jones, Nicholas; Liu, Junyu
2018-05-01
We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.
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Scale-invariant fluctuations from Galilean genesis
DOE Office of Scientific and Technical Information (OSTI.GOV)
Wang, Yi; Brandenberger, Robert, E-mail: wangyi@physics.mcgill.ca, E-mail: rhb@physics.mcgill.ca
2012-10-01
We study the spectrum of cosmological fluctuations in scenarios such as Galilean Genesis \\cite(Nicolis) in which a spectator scalar field acquires a scale-invariant spectrum of perturbations during an early phase which asymptotes in the far past to Minkowski space-time. In the case of minimal coupling to gravity and standard scalar field Lagrangian, the induced curvature fluctuations depend quadratically on the spectator field and are hence non-scale-invariant and highly non-Gaussian. We show that if higher dimensional operators (the same operators that lead to the η-problem for inflation) are considered, a linear coupling between background and spectator field fluctuations is induced whichmore » leads to scale-invariant and Gaussian curvature fluctuations.« 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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Spectral statistics and scattering resonances of complex primes arrays
NASA Astrophysics Data System (ADS)
Wang, Ren; Pinheiro, Felipe A.; Dal Negro, Luca
2018-01-01
We introduce a class of aperiodic arrays of electric dipoles generated from the distribution of prime numbers in complex quadratic fields (Eisenstein and Gaussian primes) as well as quaternion primes (Hurwitz and Lifschitz primes), and study the nature of their scattering resonances using the vectorial Green's matrix method. In these systems we demonstrate several distinctive spectral properties, such as the absence of level repulsion in the strongly scattering regime, critical statistics of level spacings, and the existence of critical modes, which are extended fractal modes with long lifetimes not supported by either random or periodic systems. Moreover, we show that one can predict important physical properties, such as the existence spectral gaps, by analyzing the eigenvalue distribution of the Green's matrix of the arrays in the complex plane. Our results unveil the importance of aperiodic correlations in prime number arrays for the engineering of gapped photonic media that support far richer mode localization and spectral properties compared to usual periodic and random media.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Petukhov, B. V., E-mail: petukhov@ns.crys.ras.r
2010-01-15
A model has been proposed for describing the influence of impurities adsorbed by dislocation cores on the mobility of dislocation kinks in materials with a high crystalline relief (Peierls barriers). The delay time spectrum of kinks at statistical fluctuations of the impurity density has been calculated for a sufficiently high energy of interaction between impurities and dislocations when the migration potential is not reduced to a random Gaussian potential. It has been shown that fluctuations in the impurity distribution substantially change the character of the migration of dislocation kinks due to the slow decrease in the probability of long delaymore » times. The dependences of the position of the boundary of the dynamic phase transition to a sublinear drift of kinks x {proportional_to} t{sup {delta}} ({delta} {sigma} 1) and the characteristics of the anomalous mobility on the physical parameters (stress, impurity concentration, experimental temperature, etc.) have been calculated.« less
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General immunity and superadditivity of two-way Gaussian quantum cryptography.
Ottaviani, Carlo; Pirandola, Stefano
2016-03-01
We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks.
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General immunity and superadditivity of two-way Gaussian quantum cryptography
Ottaviani, Carlo; Pirandola, Stefano
2016-01-01
We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks. PMID:26928053
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Computational algorithms for simulations in atmospheric optics.
Konyaev, P A; Lukin, V P
2016-04-20
A computer simulation technique for atmospheric and adaptive optics based on parallel programing is discussed. A parallel propagation algorithm is designed and a modified spectral-phase method for computer generation of 2D time-variant random fields is developed. Temporal power spectra of Laguerre-Gaussian beam fluctuations are considered as an example to illustrate the applications discussed. Implementation of the proposed algorithms using Intel MKL and IPP libraries and NVIDIA CUDA technology is shown to be very fast and accurate. The hardware system for the computer simulation is an off-the-shelf desktop with an Intel Core i7-4790K CPU operating at a turbo-speed frequency up to 5 GHz and an NVIDIA GeForce GTX-960 graphics accelerator with 1024 1.5 GHz processors.
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Ionospheric scintillation by a random phase screen Spectral approach
NASA Technical Reports Server (NTRS)
Rufenach, C. L.
1975-01-01
The theory developed by Briggs and Parkin, given in terms of an anisotropic gaussian correlation function, is extended to a spectral description specified as a continuous function of spatial wavenumber with an intrinsic outer scale as would be expected from a turbulent medium. Two spectral forms were selected for comparison: (1) a power-law variation in wavenumber with a constant three-dimensional index equal to 4, and (2) Gaussian spectral variation. The results are applied to the F-region ionosphere with an outer-scale wavenumber of 2 per km (approximately equal to the Fresnel wavenumber) for the power-law variation, and 0.2 per km for the Gaussian spectral variation. The power-law form with a small outer-scale wavenumber is consistent with recent F-region in-situ measurements, whereas the gaussian form is mathematically convenient and, hence, mostly used in the previous developments before the recent in-situ measurements. Some comparison with microwave scintillation in equatorial areas is made.
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Jitter Reduces Response-Time Variability in ADHD: An Ex-Gaussian Analysis.
Lee, Ryan W Y; Jacobson, Lisa A; Pritchard, Alison E; Ryan, Matthew S; Yu, Qilu; Denckla, Martha B; Mostofsky, Stewart; Mahone, E Mark
2015-09-01
"Jitter" involves randomization of intervals between stimulus events. Compared with controls, individuals with ADHD demonstrate greater intrasubject variability (ISV) performing tasks with fixed interstimulus intervals (ISIs). Because Gaussian curves mask the effect of extremely slow or fast response times (RTs), ex-Gaussian approaches have been applied to study ISV. This study applied ex-Gaussian analysis to examine the effects of jitter on RT variability in children with and without ADHD. A total of 75 children, aged 9 to 14 years (44 ADHD, 31 controls), completed a go/no-go test with two conditions: fixed ISI and jittered ISI. ADHD children showed greater variability, driven by elevations in exponential (tau), but not normal (sigma) components of the RT distribution. Jitter decreased tau in ADHD to levels not statistically different than controls, reducing lapses in performance characteristic of impaired response control. Jitter may provide a nonpharmacologic mechanism to facilitate readiness to respond and reduce lapses from sustained (controlled) performance. © 2012 SAGE Publications.
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Simultaneous Gaussian and exponential inversion for improved analysis of shales by NMR relaxometry
Washburn, Kathryn E.; Anderssen, Endre; Vogt, Sarah J.; Seymour, Joseph D.; Birdwell, Justin E.; Kirkland, Catherine M.; Codd, Sarah L.
2014-01-01
Nuclear magnetic resonance (NMR) relaxometry is commonly used to provide lithology-independent porosity and pore-size estimates for petroleum resource evaluation based on fluid-phase signals. However in shales, substantial hydrogen content is associated with solid and fluid signals and both may be detected. Depending on the motional regime, the signal from the solids may be best described using either exponential or Gaussian decay functions. When the inverse Laplace transform, the standard method for analysis of NMR relaxometry results, is applied to data containing Gaussian decays, this can lead to physically unrealistic responses such as signal or porosity overcall and relaxation times that are too short to be determined using the applied instrument settings. We apply a new simultaneous Gaussian-Exponential (SGE) inversion method to simulated data and measured results obtained on a variety of oil shale samples. The SGE inversion produces more physically realistic results than the inverse Laplace transform and displays more consistent relaxation behavior at high magnetic field strengths. Residuals for the SGE inversion are consistently lower than for the inverse Laplace method and signal overcall at short T2 times is mitigated. Beyond geological samples, the method can also be applied in other fields where the sample relaxation consists of both Gaussian and exponential decays, for example in material, medical and food sciences.
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Invariant domain watermarking using heaviside function of order alpha and fractional Gaussian field.
Abbasi, Almas; Woo, Chaw Seng; Ibrahim, Rabha Waell; Islam, Saeed
2015-01-01
Digital image watermarking is an important technique for the authentication of multimedia content and copyright protection. Conventional digital image watermarking techniques are often vulnerable to geometric distortions such as Rotation, Scaling, and Translation (RST). These distortions desynchronize the watermark information embedded in an image and thus disable watermark detection. To solve this problem, we propose an RST invariant domain watermarking technique based on fractional calculus. We have constructed a domain using Heaviside function of order alpha (HFOA). The HFOA models the signal as a polynomial for watermark embedding. The watermark is embedded in all the coefficients of the image. We have also constructed a fractional variance formula using fractional Gaussian field. A cross correlation method based on the fractional Gaussian field is used for watermark detection. Furthermore the proposed method enables blind watermark detection where the original image is not required during the watermark detection thereby making it more practical than non-blind watermarking techniques. Experimental results confirmed that the proposed technique has a high level of robustness.
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Invariant Domain Watermarking Using Heaviside Function of Order Alpha and Fractional Gaussian Field
Abbasi, Almas; Woo, Chaw Seng; Ibrahim, Rabha Waell; Islam, Saeed
2015-01-01
Digital image watermarking is an important technique for the authentication of multimedia content and copyright protection. Conventional digital image watermarking techniques are often vulnerable to geometric distortions such as Rotation, Scaling, and Translation (RST). These distortions desynchronize the watermark information embedded in an image and thus disable watermark detection. To solve this problem, we propose an RST invariant domain watermarking technique based on fractional calculus. We have constructed a domain using Heaviside function of order alpha (HFOA). The HFOA models the signal as a polynomial for watermark embedding. The watermark is embedded in all the coefficients of the image. We have also constructed a fractional variance formula using fractional Gaussian field. A cross correlation method based on the fractional Gaussian field is used for watermark detection. Furthermore the proposed method enables blind watermark detection where the original image is not required during the watermark detection thereby making it more practical than non-blind watermarking techniques. Experimental results confirmed that the proposed technique has a high level of robustness. PMID:25884854
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Annular wave packets at Dirac points in graphene and their probability-density oscillation.
Luo, Ji; Valencia, Daniel; Lu, Junqiang
2011-12-14
Wave packets in graphene whose central wave vector is at Dirac points are investigated by numerical calculations. Starting from an initial Gaussian function, these wave packets form into annular peaks that propagate to all directions like ripple-rings on water surface. At the beginning, electronic probability alternates between the central peak and the ripple-rings and transient oscillation occurs at the center. As time increases, the ripple-rings propagate at the fixed Fermi speed, and their widths remain unchanged. The axial symmetry of the energy dispersion leads to the circular symmetry of the wave packets. The fixed speed and widths, however, are attributed to the linearity of the energy dispersion. Interference between states that, respectively, belong to two branches of the energy dispersion leads to multiple ripple-rings and the probability-density oscillation. In a magnetic field, annular wave packets become confined and no longer propagate to infinity. If the initial Gaussian width differs greatly from the magnetic length, expanding and shrinking ripple-rings form and disappear alternatively in a limited spread, and the wave packet resumes the Gaussian form frequently. The probability thus oscillates persistently between the central peak and the ripple-rings. If the initial Gaussian width is close to the magnetic length, the wave packet retains the Gaussian form and its height and width oscillate with a period determined by the first Landau energy. The wave-packet evolution is determined jointly by the initial state and the magnetic field, through the electronic structure of graphene in a magnetic field. © 2011 American Institute of Physics
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Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
DOE Office of Scientific and Technical Information (OSTI.GOV)
Monras, Alex; Illuminati, Fabrizio
2011-01-15
We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than coherent, thermal, or single-mode squeezed states. This suggests that at high-energy regimes, two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result indicates a stronger form ofmore » compatibility for the estimation of the two parameters. Indeed, not only the minimum variance can be achieved at fixed probe states, but also the optimal state is common to both parameters. Additionally, we explore numerically the performance of non-Gaussian states for particular parameter values to find that maximally entangled states within d-dimensional cutoff subspaces (d{<=}6) perform better than any randomly sampled states with similar energy. However, we also find that states with very similar performance and energy exist with much less entanglement than the maximally entangled ones.« less
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NASA Astrophysics Data System (ADS)
Hu, D. L.; Liu, X. B.
Both periodic loading and random forces commonly co-exist in real engineering applications. However, the dynamic behavior, especially dynamic stability of systems under parametric periodic and random excitations has been reported little in the literature. In this study, the moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and non-Gaussian colored noise excitations are investigated. The noise is simplified to an Ornstein-Uhlenbeck process by applying the path-integral method. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, the effects of the noise and parametric resonance (such as subharmonic resonance and combination additive resonance) on the stochastic stability of the binary airfoil system are discussed.
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NASA Astrophysics Data System (ADS)
Dean, David S.; Majumdar, Satya N.
2002-08-01
We study a fragmentation problem where an initial object of size x is broken into m random pieces provided x > x0 where x0 is an atomic cut-off. Subsequently, the fragmentation process continues for each of those daughter pieces whose sizes are bigger than x0. The process stops when all the fragments have sizes smaller than x0. We show that the fluctuation of the total number of splitting events, characterized by the variance, generically undergoes a nontrivial phase transition as one tunes the branching number m through a critical value m = mc. For m < mc, the fluctuations are Gaussian where as for m > mc they are anomalously large and non-Gaussian. We apply this general result to analyse two different search algorithms in computer science.
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Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon
2017-12-01
Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.
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Addendum to foundations of multidimensional wave field signal theory: Gaussian source function
NASA Astrophysics Data System (ADS)
Baddour, Natalie
2018-02-01
Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011)], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Shlivinski, A., E-mail: amirshli@ee.bgu.ac.il; Lomakin, V., E-mail: vlomakin@eng.ucsd.edu
2016-03-01
Scattering or coupling of electromagnetic beam-field at a surface discontinuity separating two homogeneous or inhomogeneous media with different propagation characteristics is formulated using surface integral equation, which are solved by the Method of Moments with the aid of the Gabor-based Gaussian window frame set of basis and testing functions. The application of the Gaussian window frame provides (i) a mathematically exact and robust tool for spatial-spectral phase-space formulation and analysis of the problem; (ii) a system of linear equations in a transmission-line like form relating mode-like wave objects of one medium with mode-like wave objects of the second medium; (iii)more » furthermore, an appropriate setting of the frame parameters yields mode-like wave objects that blend plane wave properties (as if solving in the spectral domain) with Green's function properties (as if solving in the spatial domain); and (iv) a representation of the scattered field with Gaussian-beam propagators that may be used in many large (in terms of wavelengths) systems.« less
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SU-E-T-558: Assessing the Effect of Inter-Fractional Motion in Esophageal Sparing Plans.
Williamson, R; Bluett, J; Niedzielski, J; Liao, Z; Gomez, D; Court, L
2012-06-01
To compare esophageal dose distributions in esophageal sparing IMRT plans with predicted dose distributions which include the effect of inter-fraction motion. Seven lung cancer patients were used, each with a standard and an esophageal sparing plan (74Gy, 2Gy fractions). The average max dose to esophagus was 8351cGy and 7758cGy for the standard and sparing plans, respectively. The average length of esophagus for which the total circumference was treated above 60Gy (LETT60) was 9.4cm in the standard plans and 5.8cm in the sparing plans. In order to simulate inter-fractional motion, a three-dimensional rigid shift was applied to the calculated dose field. A simulated course of treatment consisted of a single systematic shift applied throughout the treatment as well a random shift for each of the 37 fractions. Both systematic and random shifts were generated from Gaussian distributions of 3mm and 5mm standard deviation. Each treatment course was simulated 1000 times to obtain an expected distribution of the delivered dose. Simulated treatment dose received by the esophagus was less than dose seen in the treatment plan. The average reduction in maximum esophageal dose for the standard plans was 234cGy and 386cGY for the 3mm and 5mm Gaussian distributions, respectively. The average reduction in LETT60 was 0.6cm and 1.7cm, for the 3mm and 5mm distributions respectively. For the esophageal sparing plans, the average reduction in maximum esophageal dose was 94cGy and 202cGy for 3mm and 5mm Gaussian distributions, respectively. The average change in LETT60 for the esophageal sparing plans was smaller, at 0.1cm (increase) and 0.6cm (reduction), for the 3mm and 5mm distributions, respectively. Interfraction motion consistently reduced the maximum doses to the esophagus for both standard and esophageal sparing plans. © 2012 American Association of Physicists in Medicine.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Eley, John G.; Hogstrom, Kenneth R.; Matthews, Kenneth L.
2011-12-15
Purpose: The purpose of this work was to investigate the potential of discrete Gaussian edge feathering of the higher energy electron fields for improving abutment dosimetry in the planning volume when using an electron multileaf collimator (eMLC) to deliver segmented-field electron conformal therapy (ECT). Methods: A discrete (five-step) Gaussian edge spread function was used to match dose penumbras of differing beam energies (6-20 MeV) at a specified depth in a water phantom. Software was developed to define the leaf eMLC positions of an eMLC that most closely fit each electron field shape. The effect of 1D edge feathering of themore » higher energy field on dose homogeneity was computed and measured for segmented-field ECT treatment plans for three 2D PTVs in a water phantom, i.e., depth from the water surface to the distal PTV surface varied as a function of the x-axis (parallel to leaf motion) and remained constant along the y-axis (perpendicular to leaf motion). Additionally, the effect of 2D edge feathering was computed and measured for one radially symmetric, 3D PTV in a water phantom, i.e., depth from the water surface to the distal PTV surface varied as a function of both axes. For the 3D PTV, the feathering scheme was evaluated for 0.1-1.0-cm leaf widths. Dose calculations were performed using the pencil beam dose algorithm in the Pinnacle{sup 3} treatment planning system. Dose verification measurements were made using a prototype eMLC (1-cm leaf width). Results: 1D discrete Gaussian edge feathering reduced the standard deviation of dose in the 2D PTVs by 34, 34, and 39%. In the 3D PTV, the broad leaf width (1 cm) of the eMLC hindered the 2D application of the feathering solution to the 3D PTV, and the standard deviation of dose increased by 10%. However, 2D discrete Gaussian edge feathering with simulated eMLC leaf widths of 0.1-0.5 cm reduced the standard deviation of dose in the 3D PTV by 33-28%, respectively. Conclusions: A five-step discrete Gaussian edge spread function applied in 2D improves the abutment dosimetry but requires an eMLC leaf resolution better than 1 cm.« less
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Dynamic laser speckle analyzed considering inhomogeneities in the biological sample
NASA Astrophysics Data System (ADS)
Braga, Roberto A.; González-Peña, Rolando J.; Viana, Dimitri Campos; Rivera, Fernando Pujaico
2017-04-01
Dynamic laser speckle phenomenon allows a contactless and nondestructive way to monitor biological changes that are quantified by second-order statistics applied in the images in time using a secondary matrix known as time history of the speckle pattern (THSP). To avoid being time consuming, the traditional way to build the THSP restricts the data to a line or column. Our hypothesis is that the spatial restriction of the information could compromise the results, particularly when undesirable and unexpected optical inhomogeneities occur, such as in cell culture media. It tested a spatial random approach to collect the points to form a THSP. Cells in a culture medium and in drying paint, representing homogeneous samples in different levels, were tested, and a comparison with the traditional method was carried out. An alternative random selection based on a Gaussian distribution around a desired position was also presented. The results showed that the traditional protocol presented higher variation than the outcomes using the random method. The higher the inhomogeneity of the activity map, the higher the efficiency of the proposed method using random points. The Gaussian distribution proved to be useful when there was a well-defined area to monitor.
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On chemical distances and shape theorems in percolation models with long-range correlations
NASA Astrophysics Data System (ADS)
Drewitz, Alexander; Ráth, Balázs; Sapozhnikov, Artëm
2014-08-01
In this paper, we provide general conditions on a one parameter family of random infinite subsets of {{Z}}^d to contain a unique infinite connected component for which the chemical distances are comparable to the Euclidean distance. In addition, we show that these conditions also imply a shape theorem for the corresponding infinite connected component. By verifying these conditions for specific models, we obtain novel results about the structure of the infinite connected component of the vacant set of random interlacements and the level sets of the Gaussian free field. As a byproduct, we obtain alternative proofs to the corresponding results for random interlacements in the work of Černý and Popov ["On the internal distance in the interlacement set," Electron. J. Probab. 17(29), 1-25 (2012)], and while our main interest is in percolation models with long-range correlations, we also recover results in the spirit of the work of Antal and Pisztora ["On the chemical distance for supercritical Bernoulli percolation," Ann Probab. 24(2), 1036-1048 (1996)] for Bernoulli percolation. Finally, as a corollary, we derive new results about the (chemical) diameter of the largest connected component in the complement of the trace of the random walk on the torus.
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Hopping Conduction in Polymers
NASA Astrophysics Data System (ADS)
Bässler, Heinz
The concept of hopping within a Gaussian density of localized states introduced earlier to rationalize charge transport in random organic photoconductors is developed further to account for temporal features of time of flight (TOF) signals. At moderate degree of energetic disorder (σ/kT~3.5…4.5) there is a transport regime intermediate between dispersive and quasi-Gaussian type whose signatures are (i) universal TOF signals that can appear weakly dispersive despite yielding a well defined carrier mobility and (ii) an asymmetric propagator of the carrier packet yielding a time dependent diffusivity.
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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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The effects of induced heat loads on the propagation of Ince-Gaussian beams
NASA Astrophysics Data System (ADS)
Nadgaran, H.; Servatkhah, M.
2011-10-01
Thermal effects are very much influential in high power beam generators. Their impacts on special types of beams such as Helmholtz-Gauss beams have attracted special attentions. This work reports thermal effects on the generation and propagation of Ince-Gaussian beams. The results show considerable beam spot size variations for near fields under various induced heat loads. As Ince-Gaussian beams are directly related to cavity symmetry breaking, the results can greatly help system designers for circumventing these types of symmetry breaks usually encountered in high power lasers.
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Electrical source of pseudothermal light
NASA Astrophysics Data System (ADS)
Kuusela, Tom A.
2018-06-01
We describe a simple and compact electrical version of a pseudothermal light source. The source is based on electrical white noise whose spectral properties are tailored by analog filters. This signal is used to drive a light-emitting diode. The type of second-order coherence of the output light can be either Gaussian or Lorentzian, and the intensity distribution can be either Gaussian or non-Gaussian. The output light field is similar in all viewing angles, and thus, there is no need for a small aperture or optical fiber in temporal coherence analysis.
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Chialvo, Ariel A.; Moucka, Filip; Vlcek, Lukas; ...
2015-03-24
Here we implemented the Gaussian charge-on-spring (GCOS) version of the original self-consistent field implementation of the Gaussian Charge Polarizable water model and test its accuracy to represent the polarization behavior of the original model involving smeared charges and induced dipole moments. Moreover, for that purpose we adapted the recently developed multiple-particle-move (MPM) within the Gibbs and isochoric-isothermal ensembles Monte Carlo methods for the efficient simulation of polarizable fluids. We also assessed the accuracy of the GCOS representation by a direct comparison of the resulting vapor-liquid phase envelope, microstructure, and relevant microscopic descriptors of water polarization along the orthobaric curve againstmore » the corresponding quantities from the actual GCP water model.« less
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Antibunching and unconventional photon blockade with Gaussian squeezed states
NASA Astrophysics Data System (ADS)
Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.
2014-12-01
Photon antibunching is a quantum phenomenon typically observed in strongly nonlinear systems where photon blockade suppresses the probability of detecting two photons at the same time. Antibunching has also been reported with Gaussian states, where optimized amplitude squeezing yields classically forbidden values of the intensity correlation, g(2 )(0 ) <1 . As a consequence, observation of antibunching is not necessarily a signature of photon-photon interactions. To clarify the significance of the intensity correlations, we derive a sufficient condition for deducing whether a field is non-Gaussian based on a g(2 )(0 ) measurement. We then show that the Gaussian antibunching obtained with a degenerate parametric amplifier is close to the ideal case reached using dissipative squeezing protocols. We finally shed light on the so-called unconventional photon blockade effect predicted in a driven two-cavity setup with surprisingly weak Kerr nonlinearities, stressing that it is a particular realization of optimized Gaussian amplitude squeezing.
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Multifractality and freezing phenomena in random energy landscapes: An introduction
NASA Astrophysics Data System (ADS)
Fyodorov, Yan V.
2010-10-01
We start our lectures with introducing and discussing the general notion of multifractality spectrum for random measures on lattices, and how it can be probed using moments of that measure. Then we show that the Boltzmann-Gibbs probability distributions generated by logarithmically correlated random potentials provide a simple yet non-trivial example of disorder-induced multifractal measures. The typical values of the multifractality exponents can be extracted from calculating the free energy of the associated Statistical Mechanics problem. To succeed in such a calculation we introduce and discuss in some detail two analytically tractable models for logarithmically correlated potentials. The first model uses a special definition of distances between points in space and is based on the idea of multiplicative cascades which originated in theory of turbulent motion. It is essentially equivalent to statistical mechanics of directed polymers on disordered trees studied long ago by Derrida and Spohn (1988) in Ref. [12]. In this way we introduce the notion of the freezing transition which is identified with an abrupt change in the multifractality spectrum. Second model which allows for explicit analytical evaluation of the free energy is the infinite-dimensional version of the problem which can be solved by employing the replica trick. In particular, the latter version allows one to identify the freezing phenomenon with a mechanism of the replica symmetry breaking (RSB) and to elucidate its physical meaning. The corresponding one-step RSB solution turns out to be marginally stable everywhere in the low-temperature phase. We finish with a short discussion of recent developments and extensions of models with logarithmic correlations, in particular in the context of extreme value statistics. The first appendix summarizes the standard elementary information about Gaussian integrals and related subjects, and introduces the notion of the Gaussian free field characterized by logarithmic correlations. Three other appendices provide the detailed exposition of a few technical details underlying the replica analysis of the model discussed in the lectures.
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Higher-order correlations for fluctuations in the presence of fields.
Boer, A; Dumitru, S
2002-10-01
The higher-order moments of the fluctuations for thermodynamic systems in the presence of fields are investigated in the framework of a theoretical method. The method uses a generalized statistical ensemble consistent with an adequate expression for the internal energy. The applications refer to the case of a system in a magnetoquasistatic field. In the case of linear magnetic media, one finds that, for the description of the magnetic induction fluctuations, the Gaussian approximation is satisfactory. For nonlinear media, the corresponding fluctuations are non-Gaussian, having a non-null asymmetry. Furthermore, the respective fluctuations have characteristics of leptokurtic, mesokurtic and platykurtic type, depending on the value of the magnetic field strength as compared with a scaling factor of the magnetization curve.
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Stochastic Modeling of CO2 Migrations and Chemical Reactions in Deep Saline Formations
NASA Astrophysics Data System (ADS)
Ni, C.; Lee, I.; Lin, C.
2013-12-01
Carbon capture and storage (CCS) has been recognized the feasible technology that can significant reduce the anthropogenic CO2 emissions from large point sources. The CO2 injection in geological formations is one of the options to permanently store the captured CO2. Based on this concept a large number of target formations have been identified and intensively investigated with different types of techniques such as the hydrogeophysical experiments or numerical simulations. The numerical simulations of CO2 migrations in saline formations recently gather much attention because a number of models are available for this purpose and there are potential sites existing in many countries. The lower part of Cholan Formation (CF) near Changhua Coastal Industrial Park (CCIP) in west central Taiwan was identified the largest potential site for CO2 sequestration. The top elevations of the KF in this area varies from 1300 to 1700m below the sea level. Laboratory experiment showed that the permeability of CF is 10-14 to 10-12 m2. Over the years the offshore seismic survey and limited onshore borehole logs have provided information for the simulation of CO2 migration in the CF although the original investigations might not focus on the purpose of CO2 sequestration. In this study we modify the TOUGHREACT model to consider the small-scale heterogeneity in target formation and the cap rock of upper CF. A Monte Carlo Simulation (MCS) approach based on the TOUGHREACT model is employed to quantify the effect of small-scale heterogeneity on the CO2 migrations and hydrochemical reactions in the CF. We assume that the small-scale variability of permeability in KF can be described with a known Gaussian distribution. Therefore, the Gaussian type random field generator such as Sequential Gaussian Simulation (SGSIM) in Geostatistical Software Library (GSLIB) can be used to provide the random permeability realizations for the MCS. A variety of statistical parameters such as the variances and correlation lengths in a Gaussian covariance model are varied in the MCS and the uncertainty of the CO2 and other chemical concentrations are evaluated based on 144 random realizations. In this study a constant injection rate of100Mt/year supercritical CO2 is applied in the bottom of CF. The continuous injection time is 20 years and the uncertainty results are evaluated at 100 years. By comparing with the case without small-scale variability simulation results show that the CO2 plume sizes in the horizontal direction increase from tens of meters to hundreds of meters when the variances of small-scale variability are varied from 1.0 to 4.0. The changes of correlation lengths (i.e., from 100m, 200m, to 400m) show small contribution on the size increases of CO2 plumes. Other uncertainties of chemical concentrations show behaviors similar to the CO2 plume patterns.
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NASA Astrophysics Data System (ADS)
Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki
2018-03-01
We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2}). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3}) and the level sets of the Gaussian free field ({d≥ 3}). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.
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NASA Astrophysics Data System (ADS)
Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki
2017-12-01
We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2} ). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3} ) and the level sets of the Gaussian free field ({d≥ 3} ). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.
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On fatigue crack growth under random loading
NASA Astrophysics Data System (ADS)
Zhu, W. Q.; Lin, Y. K.; Lei, Y.
1992-09-01
A probabilistic analysis of the fatigue crack growth, fatigue life and reliability of a structural or mechanical component is presented on the basis of fracture mechanics and theory of random processes. The material resistance to fatigue crack growth and the time-history of the stress are assumed to be random. Analytical expressions are obtained for the special case in which the random stress is a stationary narrow-band Gaussian random process, and a randomized Paris-Erdogan law is applicable. As an example, the analytical method is applied to a plate with a central crack, and the results are compared with those obtained from digital Monte Carlo simulations.
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Non-Gaussianities in multifield DBI inflation with a waterfall phase transition
NASA Astrophysics Data System (ADS)
Kidani, Taichi; Koyama, Kazuya; Mizuno, Shuntaro
2012-10-01
We study multifield Dirac-Born-Infeld (DBI) inflation models with a waterfall phase transition. This transition happens for a D3 brane moving in the warped conifold if there is an instability along angular directions. The transition converts the angular perturbations into the curvature perturbation. Thanks to this conversion, multifield models can evade the stringent constraints that strongly disfavor single field ultraviolet (UV) DBI inflation models in string theory. We explicitly demonstrate that our model satisfies current observational constraints on the spectral index and equilateral non-Gaussianity as well as the bound on the tensor to scalar ratio imposed in string theory models. In addition, we show that large local type non-Gaussianity is generated together with equilateral non-Gaussianity in this model.
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Classification of echolocation clicks from odontocetes in the Southern California Bight.
Roch, Marie A; Klinck, Holger; Baumann-Pickering, Simone; Mellinger, David K; Qui, Simon; Soldevilla, Melissa S; Hildebrand, John A
2011-01-01
This study presents a system for classifying echolocation clicks of six species of odontocetes in the Southern California Bight: Visually confirmed bottlenose dolphins, short- and long-beaked common dolphins, Pacific white-sided dolphins, Risso's dolphins, and presumed Cuvier's beaked whales. Echolocation clicks are represented by cepstral feature vectors that are classified by Gaussian mixture models. A randomized cross-validation experiment is designed to provide conditions similar to those found in a field-deployed system. To prevent matched conditions from inappropriately lowering the error rate, echolocation clicks associated with a single sighting are never split across the training and test data. Sightings are randomly permuted before assignment to folds in the experiment. This allows different combinations of the training and test data to be used while keeping data from each sighting entirely in the training or test set. The system achieves a mean error rate of 22% across 100 randomized three-fold cross-validation experiments. Four of the six species had mean error rates lower than the overall mean, with the presumed Cuvier's beaked whale clicks showing the best performance (<2% error rate). Long-beaked common and bottlenose dolphins proved the most difficult to classify, with mean error rates of 53% and 68%, respectively.
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Continuous time quantum random walks in free space
NASA Astrophysics Data System (ADS)
Eichelkraut, Toni; Vetter, Christian; Perez-Leija, Armando; Christodoulides, Demetrios; Szameit, Alexander
2014-05-01
We show theoretically and experimentally that two-dimensional continuous time coherent random walks are possible in free space, that is, in the absence of any external potential, by properly tailoring the associated initial wave function. These effects are experimentally demonstrated using classical paraxial light. Evidently, the usage of classical beams to explore the dynamics of point-like quantum particles is possible since both phenomena are mathematically equivalent. This in turn makes our approach suitable for the realization of random walks using different quantum particles, including electrons and photons. To study the spatial evolution of a wavefunction theoretically, we consider the one-dimensional paraxial wave equation (i∂z +1/2 ∂x2) Ψ = 0 . Starting with the initially localized wavefunction Ψ (x , 0) = exp [ -x2 / 2σ2 ] J0 (αx) , one can show that the evolution of such Gaussian-apodized Bessel envelopes within a region of validity resembles the probability pattern of a quantum walker traversing a uniform lattice. In order to generate the desired input-field in our experimental setting we shape the amplitude and phase of a collimated light beam originating from a classical HeNe-Laser (633 nm) utilizing a spatial light modulator.
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Remote sensing of Earth terrain
NASA Technical Reports Server (NTRS)
Kong, Jin AU; Shin, Robert T.; Nghiem, Son V.; Yueh, Herng-Aung; Han, Hsiu C.; Lim, Harold H.; Arnold, David V.
1990-01-01
Remote sensing of earth terrain is examined. The layered random medium model is used to investigate the fully polarimetric scattering of electromagnetic waves from vegetation. The model is used to interpret the measured data for vegetation fields such as rice, wheat, or soybean over water or soil. Accurate calibration of polarimetric radar systems is essential for the polarimetric remote sensing of earth terrain. A polarimetric calibration algorithm using three arbitrary in-scene reflectors is developed. In the interpretation of active and passive microwave remote sensing data from the earth terrain, the random medium model was shown to be quite successful. A multivariate K-distribution is proposed to model the statistics of fully polarimetric radar returns from earth terrain. In the terrain cover classification using the synthetic aperture radar (SAR) images, the applications of the K-distribution model will provide better performance than the conventional Gaussian classifiers. The layered random medium model is used to study the polarimetric response of sea ice. Supervised and unsupervised classification procedures are also developed and applied to synthetic aperture radar polarimetric images in order to identify their various earth terrain components for more than two classes. These classification procedures were applied to San Francisco Bay and Traverse City SAR images.
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How Many Separable Sources? Model Selection In Independent Components Analysis
Woods, Roger P.; Hansen, Lars Kai; Strother, Stephen
2015-01-01
Unlike mixtures consisting solely of non-Gaussian sources, mixtures including two or more Gaussian components cannot be separated using standard independent components analysis methods that are based on higher order statistics and independent observations. The mixed Independent Components Analysis/Principal Components Analysis (mixed ICA/PCA) model described here accommodates one or more Gaussian components in the independent components analysis model and uses principal components analysis to characterize contributions from this inseparable Gaussian subspace. Information theory can then be used to select from among potential model categories with differing numbers of Gaussian components. Based on simulation studies, the assumptions and approximations underlying the Akaike Information Criterion do not hold in this setting, even with a very large number of observations. Cross-validation is a suitable, though computationally intensive alternative for model selection. Application of the algorithm is illustrated using Fisher's iris data set and Howells' craniometric data set. Mixed ICA/PCA is of potential interest in any field of scientific investigation where the authenticity of blindly separated non-Gaussian sources might otherwise be questionable. Failure of the Akaike Information Criterion in model selection also has relevance in traditional independent components analysis where all sources are assumed non-Gaussian. PMID:25811988
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Radiating pattern of surge-current-induced THz light in near-field and far-field zone.
Han, J W; Choi, Y G; Lee, J S
2018-04-25
We generate the THz wave on the surface of an unbiased GaAs crystal by illuminating femtosecond laser pulses with a 45° incidence angle, and investigate its propagation properties comprehensively both in a near-field and in a far-field zone by performing a knife-edge scan measurement. In the near-field zone, i.e. 540 μm away from the generation point, we found that the beam simply takes a Gaussian shape of which width follows well a behavior predicted by a paraxial wave equation. In the far-field zone, on the other hand, it takes a highly anisotropic shape; whereas the beam profile maintains a Gaussian shape along the normal to the plane of incidence, it takes satellite peak structures along the direction in parallel to the plane of incidence. From the comparison with simulation results obtained by using a dipole radiation model, we demonstrated that this irregular beam pattern is attributed to the combined effect of the position-dependent phase retardation of the THz waves and the diffraction-limited size of the initial beam which lead to the interference of the waves in the far-field zone. Also, we found that this consideration accounting for a crossover of THz beam profile to the anisotropic non-Gaussian beam in the far-field zone can be applied for a comprehensive understanding of several other THz beam profiles obtained previously in different configurations.
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Non-Gaussianity from self-ordering scalar fields
DOE Office of Scientific and Technical Information (OSTI.GOV)
Figueroa, Daniel G.; Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, 28049 Madrid; Caldwell, Robert R.
The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and providemore » a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges k{sub 1{approx_equal}}2k{sub 2{approx_equal}}2k{sub 3}) as opposed to the local-model bispectrum, which peaks for squeezed triangles (k{sub 1{approx_equal}}k{sub 2}>>k{sub 3}), and the equilateral bispectrum, which peaks at k{sub 1{approx_equal}}k{sub 2{approx_equal}}k{sub 3}. We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit.« less
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Anisotropic CMB distortions from non-Gaussian isocurvature perturbations
DOE Office of Scientific and Technical Information (OSTI.GOV)
Ota, Atsuhisa; Sekiguchi, Toyokazu; Tada, Yuichiro
2015-03-01
We calculate the CMB μ-distortion, (μ), and the angular power spectrum of its cross-correlation with the temperature anisotropy, (μT), in the presence of the non-Gaussian neutrino isocurvature density (NID) mode. While the pure Gaussian NID perturbations give merely subdominant contributions to (μ) and do not create (μT), we show large (μT) can be realized in case where, especially, the NID perturbations S(x) are proportional to the square of a Gaussian field g(x), i.e. S(x)∝ g{sup 2}(x). Such Gaussian-squared perturbations contribute to not only the power spectrum, but also the bispectrum of CMB anisotropies. The constraints from the power spectrum ismore » given by P{sub SS}(k{sub 0})∼P{sub g}{sup 2}(k{sub 0})∼<10{sup −10} at k{sub 0}=0.05 Mpc{sup −1}. We also forecast constraints from the CMB temperature and E-mode polarisation bispectra, and show that P{sub g}(k{sub 0})∼<10{sup −5} would be allowed from the Planck data. We find that (μ) and |l(l+1)C{sup μT}{sub l}| can respectively be as large as 10{sup −9} and 10{sup −14} with uncorrelated scale-invariant NID perturbations for P{sub g}(k{sub 0})=10{sup −5}. When the spectrum of the Gaussian field is blue-tilted (with spectral index n{sub g}≅1.5), (μT) can be enhanced by an order of magnitude.« less
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Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions
DOE Office of Scientific and Technical Information (OSTI.GOV)
Kawasaki, Masahiro; Yamada, Masaki; ICRR, University of Tokyo, Kashiwa, 277-8582
2014-02-03
I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper,more » we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles.« less
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Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions
DOE Office of Scientific and Technical Information (OSTI.GOV)
Kawasaki, Masahiro; Yamada, Masaki, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: yamadam@icrr.u-tokyo.ac.jp
2014-02-01
I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper,more » we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles.« less
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Chimera states in Gaussian coupled map lattices
NASA Astrophysics Data System (ADS)
Li, Xiao-Wen; Bi, Ran; Sun, Yue-Xiang; Zhang, Shuo; Song, Qian-Qian
2018-04-01
We study chimera states in one-dimensional and two-dimensional Gaussian coupled map lattices through simulations and experiments. Similar to the case of global coupling oscillators, individual lattices can be regarded as being controlled by a common mean field. A space-dependent order parameter is derived from a self-consistency condition in order to represent the collective state.
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NASA Astrophysics Data System (ADS)
Jones, A. W.; Bland-Hawthorn, J.; Kaiser, N.
1994-12-01
In the first half of 1995, the Anglo-Australian Observatory is due to commission a wide field (2.1(deg) ), 400-fiber, double spectrograph system (2dF) at the f/3.3 prime focus of the AAT 3.9m bi-national facility. The instrument should be able to measure ~ 4000 galaxy redshifts (assuming a magnitude limit of b_J ~\\ 20) in a single dark night and is therefore ideally suited to studies of large-scale structure. We have carried out simple 3D numerical simulations to judge the relative merits of sparse surveys and contiguous surveys. We generate a survey volume and fill it randomly with particles according to a selection function which mimics a magnitude-limited survey at b_J = 19.7. Each of the particles is perturbed by a gaussian random field according to the dimensionless power spectrum k(3) P(k) / 2pi (2) determined by Feldman, Kaiser & Peacock (1994) from the IRAS QDOT survey. We introduce some redshift-space distortion as described by Kaiser (1987), a `thermal' component measured from pairwise velocities (Davis & Peebles 1983), and `fingers of god' due to rich clusters at random density enhancements. Our particular concern is to understand how the window function W(2(k)) of the survey geometry compromises the accuracy of statistical measures [e.g., P(k), xi (r), xi (r_sigma ,r_pi )] commonly used in the study of large-scale structure. We also examine the reliability of various tools (e.g. genus) for describing the topological structure within a contiguous region of the survey.
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A mathematical study of a random process proposed as an atmospheric turbulence model
NASA Technical Reports Server (NTRS)
Sidwell, K.
1977-01-01
A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.
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Circuit theory and model-based inference for landscape connectivity
Hanks, Ephraim M.; Hooten, Mevin B.
2013-01-01
Circuit theory has seen extensive recent use in the field of ecology, where it is often applied to study functional connectivity. The landscape is typically represented by a network of nodes and resistors, with the resistance between nodes a function of landscape characteristics. The effective distance between two locations on a landscape is represented by the resistance distance between the nodes in the network. Circuit theory has been applied to many other scientific fields for exploratory analyses, but parametric models for circuits are not common in the scientific literature. To model circuits explicitly, we demonstrate a link between Gaussian Markov random fields and contemporary circuit theory using a covariance structure that induces the necessary resistance distance. This provides a parametric model for second-order observations from such a system. In the landscape ecology setting, the proposed model provides a simple framework where inference can be obtained for effects that landscape features have on functional connectivity. We illustrate the approach through a landscape genetics study linking gene flow in alpine chamois (Rupicapra rupicapra) to the underlying landscape.
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NASA Astrophysics Data System (ADS)
Stilgoe, Alexander B.; Nieminen, Timo A.; Rubinsztein-Dunlop, Halina
2015-12-01
Non-paraxial theories of wave propagation are essential to model the interaction of highly focused light with matter. Here we investigate the energy, momentum and propagation of the Laguerre-, Hermite- and Ince-Gaussian solutions (LG, HG, and IG) of the paraxial wave equation in an apertured non-paraxial regime. We investigate the far-field relationships between the LG, HG, and IG solutions and the vector spherical wave function (VSWF) solutions of the vector Helmholtz wave equation. We investigate the convergence of the VSWF and the various Gaussian solutions in the presence of an aperture. Finally, we investigate the differences in linear and angular momentum evaluated in the paraxial and non-paraxial regimes. The non-paraxial model we develop can be applied to calculations of the focusing of high-order Gaussian modes in high-resolution microscopes. We find that the addition of an aperture in high numerical aperture optical systems does not greatly affect far-field properties except when the beam is significantly clipped by an aperture. Diffraction from apertures causes large distortions in the near-field and will influence light-matter interactions. The method is not limited to a particular solution of the paraxial wave equation. Our model is constructed in a formalism that is commonly used in scattering calculations. It is thus applicable to optical trapping and other optical investigations of matter.
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Shaping propagation invariant laser beams
NASA Astrophysics Data System (ADS)
Soskind, Michael; Soskind, Rose; Soskind, Yakov
2015-11-01
Propagation-invariant structured laser beams possess several unique properties and play an important role in various photonics applications. The majority of propagation invariant beams are produced in the form of laser modes emanating from stable laser cavities. Therefore, their spatial structure is limited by the intracavity mode formation. We show that several types of anamorphic optical systems (AOSs) can be effectively employed to shape laser beams into a variety of propagation invariant structured fields with different shapes and phase distributions. We present a propagation matrix approach for designing AOSs and defining mode-matching conditions required for preserving propagation invariance of the output shaped fields. The propagation matrix approach was selected, as it provides a more straightforward approach in designing AOSs for shaping propagation-invariant laser beams than the alternative technique based on the Gouy phase evolution, especially in the case of multielement AOSs. Several practical configurations of optical systems that are suitable for shaping input laser beams into a diverse variety of structured propagation invariant laser beams are also presented. The laser beam shaping approach was applied by modeling propagation characteristics of several input laser beam types, including Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian structured field distributions. The influence of the Ince-Gaussian beam semifocal separation parameter and the azimuthal orientation between the input laser beams and the AOSs onto the resulting shape of the propagation invariant laser beams is presented as well.
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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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Automatic lung tumor segmentation on PET/CT images using fuzzy Markov random field model.
Guo, Yu; Feng, Yuanming; Sun, Jian; Zhang, Ning; Lin, Wang; Sa, Yu; Wang, Ping
2014-01-01
The combination of positron emission tomography (PET) and CT images provides complementary functional and anatomical information of human tissues and it has been used for better tumor volume definition of lung cancer. This paper proposed a robust method for automatic lung tumor segmentation on PET/CT images. The new method is based on fuzzy Markov random field (MRF) model. The combination of PET and CT image information is achieved by using a proper joint posterior probability distribution of observed features in the fuzzy MRF model which performs better than the commonly used Gaussian joint distribution. In this study, the PET and CT simulation images of 7 non-small cell lung cancer (NSCLC) patients were used to evaluate the proposed method. Tumor segmentations with the proposed method and manual method by an experienced radiation oncologist on the fused images were performed, respectively. Segmentation results obtained with the two methods were similar and Dice's similarity coefficient (DSC) was 0.85 ± 0.013. It has been shown that effective and automatic segmentations can be achieved with this method for lung tumors which locate near other organs with similar intensities in PET and CT images, such as when the tumors extend into chest wall or mediastinum.
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Semantic Building FAÇADE Segmentation from Airborne Oblique Images
NASA Astrophysics Data System (ADS)
Lin, Y.; Nex, F.; Yang, M. Y.
2018-05-01
With the introduction of airborne oblique camera systems and the improvement of photogrammetric techniques, high-resolution 2D and 3D data can be acquired in urban areas. This high-resolution data allows us to perform detailed investigations on building roofs and façades which can contribute to LoD3 city modeling. Normally, façade segmentation is achieved from terrestrial views. In this paper, we address the problem from aerial views by using high resolution oblique aerial images as the data source in urban areas. In addition to traditional image features, such as RGB and SIFT, normal vector and planarity are also extracted from dense matching point clouds. Then, these 3D geometrical features are projected back to 2D space to assist façade interpretation. Random forest is trained and applied to label façade pixels. Fully connected conditional random field (CRF), capturing long-range spatial interactions, is used as a post-processing to refine our classification results. Its pairwise potential is defined by a linear combination of Gaussian kernels and the CRF model is efficiently solved by mean field approximation. Experiments show that 3D features can significantly improve classification results. Also, fully connected CRF performs well in correcting noisy pixels.
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Estimating the State of Aerodynamic Flows in the Presence of Modeling Errors
NASA Astrophysics Data System (ADS)
da Silva, Andre F. C.; Colonius, Tim
2017-11-01
The ensemble Kalman filter (EnKF) has been proven to be successful in fields such as meteorology, in which high-dimensional nonlinear systems render classical estimation techniques impractical. When the model used to forecast state evolution misrepresents important aspects of the true dynamics, estimator performance may degrade. In this work, parametrization and state augmentation are used to track misspecified boundary conditions (e.g., free stream perturbations). The resolution error is modeled as a Gaussian-distributed random variable with the mean (bias) and variance to be determined. The dynamics of the flow past a NACA 0009 airfoil at high angles of attack and moderate Reynolds number is represented by a Navier-Stokes equations solver with immersed boundaries capabilities. The pressure distribution on the airfoil or the velocity field in the wake, both randomized by synthetic noise, are sampled as measurement data and incorporated into the estimated state and bias following Kalman's analysis scheme. Insights about how to specify the modeling error covariance matrix and its impact on the estimator performance are conveyed. This work has been supported in part by a Grant from AFOSR (FA9550-14-1-0328) with Dr. Douglas Smith as program manager, and by a Science without Borders scholarship from the Ministry of Education of Brazil (Capes Foundation - BEX 12966/13-4).
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Gravitational lensing by eigenvalue distributions of random matrix models
NASA Astrophysics Data System (ADS)
Martínez Alonso, Luis; Medina, Elena
2018-05-01
We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We prove that these models can be applied to describe lensing by systems of edge-on galaxies. We illustrate our analysis with the Gaussian and the quartic unitary matrix ensembles.
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Symmetry Breaking in a random passive scalar
NASA Astrophysics Data System (ADS)
Kilic, Zeliha; McLaughlin, Richard; Camassa, Roberto
2017-11-01
We consider the evolution of a decaying passive scalar in the presence of a gaussian white noise fluctuating shear flow. We focus on deterministic initial data and establish the short, intermediate, and long time symmetry properties of the evolving point wise probability measure for the random passive scalar. Analytical results are compared directly to Monte Carlo simulations. Time permitting we will compare the predictions to experimental observations.
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On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis.
Li, Bing; Chun, Hyonho; Zhao, Hongyu
2014-09-01
We introduce a nonparametric method for estimating non-gaussian graphical models based on a new statistical relation called additive conditional independence, which is a three-way relation among random vectors that resembles the logical structure of conditional independence. Additive conditional independence allows us to use one-dimensional kernel regardless of the dimension of the graph, which not only avoids the curse of dimensionality but also simplifies computation. It also gives rise to a parallel structure to the gaussian graphical model that replaces the precision matrix by an additive precision operator. The estimators derived from additive conditional independence cover the recently introduced nonparanormal graphical model as a special case, but outperform it when the gaussian copula assumption is violated. We compare the new method with existing ones by simulations and in genetic pathway analysis.
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NASA Astrophysics Data System (ADS)
Bauer, Sebastian; Mathias, Gerald; Tavan, Paul
2014-03-01
We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ɛ(r) is close to one everywhere inside the protein. The Gaussian widths σi of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σi. A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua.
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Bauer, Sebastian; Mathias, Gerald; Tavan, Paul
2014-03-14
We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ(i) of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ(i). A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua.
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Spectra of empirical autocorrelation matrices: A random-matrix-theory-inspired perspective
NASA Astrophysics Data System (ADS)
Jamali, Tayeb; Jafari, G. R.
2015-07-01
We construct an autocorrelation matrix of a time series and analyze it based on the random-matrix theory (RMT) approach. The autocorrelation matrix is capable of extracting information which is not easily accessible by the direct analysis of the autocorrelation function. In order to provide a precise conclusion based on the information extracted from the autocorrelation matrix, the results must be first evaluated. In other words they need to be compared with some sort of criterion to provide a basis for the most suitable and applicable conclusions. In the context of the present study, the criterion is selected to be the well-known fractional Gaussian noise (fGn). We illustrate the applicability of our method in the context of stock markets. For the former, despite the non-Gaussianity in returns of the stock markets, a remarkable agreement with the fGn is achieved.
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Molecules with an induced dipole moment in a stochastic electric field.
Band, Y B; Ben-Shimol, Y
2013-10-01
The mean-field dynamics of a molecule with an induced dipole moment (e.g., a homonuclear diatomic molecule) in a deterministic and a stochastic (fluctuating) electric field is solved to obtain the decoherence properties of the system. The average (over fluctuations) electric dipole moment and average angular momentum as a function of time for a Gaussian white noise electric field are determined via perturbative and nonperturbative solutions in the fluctuating field. In the perturbative solution, the components of the average electric dipole moment and the average angular momentum along the deterministic electric field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a Gaussian white noise magnetic field. In the nonperturbative solution, the component of the average electric dipole moment and the average angular momentum in the deterministic electric field direction also decay to zero.
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The 6dFGS Peculiar Velocity Field
NASA Astrophysics Data System (ADS)
Springob, Chris M.; Magoulas, C.; Colless, M.; Mould, J.; Erdogdu, P.; Jones, D. H.; Lucey, J.; Campbell, L.; Merson, A.; Jarrett, T.
2012-01-01
The 6dF Galaxy Survey (6dFGS) is an all southern sky galaxy survey, including 125,000 redshifts and a Fundamental Plane (FP) subsample of 10,000 peculiar velocities, making it the largest peculiar velocity sample to date. We have fit the FP using a maximum likelihood fit to a tri-variate Gaussian. We subsequently compute a Bayesian probability distribution for every possible peculiar velocity for each of the 10,000 galaxies, derived from the tri-variate Gaussian probability density distribution, accounting for our selection effects and measurement errors. We construct a predicted peculiar velocity field from the 2MASS redshift survey, and compare our observed 6dFGS velocity field to the predicted field. We discuss the resulting agreement between the observed and predicted fields, and the implications for measurements of the bias parameter and bulk flow.
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Quantum and classical dissipation of charged particles
DOE Office of Scientific and Technical Information (OSTI.GOV)
Ibarra-Sierra, V.G.; Anzaldo-Meneses, A.; Cardoso, J.L.
2013-08-15
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail. -- Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle.more » •Classical and quantum dynamics of a damped electric charge.« less
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Cigar-shaped quarkonia under strong magnetic field
NASA Astrophysics Data System (ADS)
Suzuki, Kei; Yoshida, Tetsuya
2016-03-01
Heavy quarkonia in a homogeneous magnetic field are analyzed by using a potential model with constituent quarks. To obtain anisotropic wave functions and corresponding eigenvalues, the cylindrical Gaussian expansion method is applied, where the anisotropic wave functions are expanded by a Gaussian basis in the cylindrical coordinates. Deformation of the wave functions and the mass shifts of the S-wave heavy quarkonia (ηc, J /ψ , ηc(2 S ), ψ (2 S ) and bottomonia) are examined for the wide range of external magnetic field. The spatial structure of the wave functions changes drastically as adjacent energy levels cross each other. Possible observables in heavy-ion collision experiments and future lattice QCD simulations are also discussed.
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CMB constraints on running non-Gaussianity
NASA Astrophysics Data System (ADS)
Oppizzi, F.; Liguori, M.; Renzi, A.; Arroja, F.; Bartolo, N.
2018-05-01
We develop a complete set of tools for CMB forecasting, simulation and estimation of primordial running bispectra, arising from a variety of curvaton and single-field (DBI) models of Inflation. We validate our pipeline using mock CMB running non-Gaussianity realizations and test it on real data by obtaining experimental constraints on the fNL running spectral index, nNG, using WMAP 9-year data. Our final bounds (68% C.L.) read ‑0.6< nNG<1.4}, ‑0.3< nNG<1.2, ‑1.1
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Realistic continuous-variable quantum teleportation with non-Gaussian resources
DOE Office of Scientific and Technical Information (OSTI.GOV)
Dell'Anno, F.; De Siena, S.; CNR-INFM Coherentia, Napoli, Italy, and CNISM and INFN Sezione di Napoli, Gruppo Collegato di Salerno, Baronissi, SA
2010-01-15
We present a comprehensive investigation of nonideal continuous-variable quantum teleportation implemented with entangled non-Gaussian resources. We discuss in a unified framework the main decoherence mechanisms, including imperfect Bell measurements and propagation of optical fields in lossy fibers, applying the formalism of the characteristic function. By exploiting appropriate displacement strategies, we compute analytically the success probability of teleportation for input coherent states and two classes of non-Gaussian entangled resources: two-mode squeezed Bell-like states (that include as particular cases photon-added and photon-subtracted de-Gaussified states), and two-mode squeezed catlike states. We discuss the optimization procedure on the free parameters of the non-Gaussian resourcesmore » at fixed values of the squeezing and of the experimental quantities determining the inefficiencies of the nonideal protocol. It is found that non-Gaussian resources enhance significantly the efficiency of teleportation and are more robust against decoherence than the corresponding Gaussian ones. Partial information on the alphabet of input states allows further significant improvement in the performance of the nonideal teleportation protocol.« less
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Effect of lensing non-Gaussianity on the CMB power spectra
DOE Office of Scientific and Technical Information (OSTI.GOV)
Lewis, Antony; Pratten, Geraint, E-mail: antony@cosmologist.info, E-mail: geraint.pratten@gmail.com
2016-12-01
Observed CMB anisotropies are lensed, and the lensed power spectra can be calculated accurately assuming the lensing deflections are Gaussian. However, the lensing deflections are actually slightly non-Gaussian due to both non-linear large-scale structure growth and post-Born corrections. We calculate the leading correction to the lensed CMB power spectra from the non-Gaussianity, which is determined by the lensing bispectrum. Assuming no primordial non-Gaussianity, the lowest-order result gives ∼ 0.3% corrections to the BB and EE polarization spectra on small-scales. However we show that the effect on EE is reduced by about a factor of two by higher-order Gaussian lensing smoothing,more » rendering the total effect safely negligible for the foreseeable future. We give a simple analytic model for the signal expected from skewness of the large-scale lensing field; the effect is similar to a net demagnification and hence a small change in acoustic scale (and therefore out of phase with the dominant lensing smoothing that predominantly affects the peaks and troughs of the power spectrum).« less
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Non-Gaussian Methods for Causal Structure Learning.
Shimizu, Shohei
2018-05-22
Causal structure learning is one of the most exciting new topics in the fields of machine learning and statistics. In many empirical sciences including prevention science, the causal mechanisms underlying various phenomena need to be studied. Nevertheless, in many cases, classical methods for causal structure learning are not capable of estimating the causal structure of variables. This is because it explicitly or implicitly assumes Gaussianity of data and typically utilizes only the covariance structure. In many applications, however, non-Gaussian data are often obtained, which means that more information may be contained in the data distribution than the covariance matrix is capable of containing. Thus, many new methods have recently been proposed for using the non-Gaussian structure of data and inferring the causal structure of variables. This paper introduces prevention scientists to such causal structure learning methods, particularly those based on the linear, non-Gaussian, acyclic model known as LiNGAM. These non-Gaussian data analysis tools can fully estimate the underlying causal structures of variables under assumptions even in the presence of unobserved common causes. This feature is in contrast to other approaches. A simulated example is also provided.
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Inference for dynamics of continuous variables: the extended Plefka expansion with hidden nodes
NASA Astrophysics Data System (ADS)
Bravi, B.; Sollich, P.
2017-06-01
We consider the problem of a subnetwork of observed nodes embedded into a larger bulk of unknown (i.e. hidden) nodes, where the aim is to infer these hidden states given information about the subnetwork dynamics. The biochemical networks underlying many cellular and metabolic processes are important realizations of such a scenario as typically one is interested in reconstructing the time evolution of unobserved chemical concentrations starting from the experimentally more accessible ones. We present an application to this problem of a novel dynamical mean field approximation, the extended Plefka expansion, which is based on a path integral description of the stochastic dynamics. As a paradigmatic model we study the stochastic linear dynamics of continuous degrees of freedom interacting via random Gaussian couplings. The resulting joint distribution is known to be Gaussian and this allows us to fully characterize the posterior statistics of the hidden nodes. In particular the equal-time hidden-to-hidden variance—conditioned on observations—gives the expected error at each node when the hidden time courses are predicted based on the observations. We assess the accuracy of the extended Plefka expansion in predicting these single node variances as well as error correlations over time, focussing on the role of the system size and the number of observed nodes.
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Hyper-Spectral Image Analysis With Partially Latent Regression and Spatial Markov Dependencies
NASA Astrophysics Data System (ADS)
Deleforge, Antoine; Forbes, Florence; Ba, Sileye; Horaud, Radu
2015-09-01
Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between physical parameters and spectra has been established in a data-driven fashion, the learned relationship can be used to estimate physical parameters for new hyper-spectral observations. Within this framework, we propose a spatially-constrained and partially-latent regression method which maps high-dimensional inputs (hyper-spectral images) onto low-dimensional responses (physical parameters such as the local chemical composition of the soil). The proposed regression model comprises two key features. Firstly, it combines a Gaussian mixture of locally-linear mappings (GLLiM) with a partially-latent response model. While the former makes high-dimensional regression tractable, the latter enables to deal with physical parameters that cannot be observed or, more generally, with data contaminated by experimental artifacts that cannot be explained with noise models. Secondly, spatial constraints are introduced in the model through a Markov random field (MRF) prior which provides a spatial structure to the Gaussian-mixture hidden variables. Experiments conducted on a database composed of remotely sensed observations collected from the Mars planet by the Mars Express orbiter demonstrate the effectiveness of the proposed model.
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NASA Astrophysics Data System (ADS)
Hunziker, Jürg; Laloy, Eric; Linde, Niklas
2016-04-01
Deterministic inversion procedures can often explain field data, but they only deliver one final subsurface model that depends on the initial model and regularization constraints. This leads to poor insights about the uncertainties associated with the inferred model properties. In contrast, probabilistic inversions can provide an ensemble of model realizations that accurately span the range of possible models that honor the available calibration data and prior information allowing a quantitative description of model uncertainties. We reconsider the problem of inferring the dielectric permittivity (directly related to radar velocity) structure of the subsurface by inversion of first-arrival travel times from crosshole ground penetrating radar (GPR) measurements. We rely on the DREAM_(ZS) algorithm that is a state-of-the-art Markov chain Monte Carlo (MCMC) algorithm. Such algorithms need several orders of magnitude more forward simulations than deterministic algorithms and often become infeasible in high parameter dimensions. To enable high-resolution imaging with MCMC, we use a recently proposed dimensionality reduction approach that allows reproducing 2D multi-Gaussian fields with far fewer parameters than a classical grid discretization. We consider herein a dimensionality reduction from 5000 to 257 unknowns. The first 250 parameters correspond to a spectral representation of random and uncorrelated spatial fluctuations while the remaining seven geostatistical parameters are (1) the standard deviation of the data error, (2) the mean and (3) the variance of the relative electric permittivity, (4) the integral scale along the major axis of anisotropy, (5) the anisotropy angle, (6) the ratio of the integral scale along the minor axis of anisotropy to the integral scale along the major axis of anisotropy and (7) the shape parameter of the Matérn function. The latter essentially defines the type of covariance function (e.g., exponential, Whittle, Gaussian). We present an improved formulation of the dimensionality reduction, and numerically show how it reduces artifacts in the generated models and provides better posterior estimation of the subsurface geostatistical structure. We next show that the results of the method compare very favorably against previous deterministic and stochastic inversion results obtained at the South Oyster Bacterial Transport Site in Virginia, USA. The long-term goal of this work is to enable MCMC-based full waveform inversion of crosshole GPR data.
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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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Renormalization group fixed points of foliated gravity-matter systems
NASA Astrophysics Data System (ADS)
Biemans, Jorn; Platania, Alessia; Saueressig, Frank
2017-05-01
We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) "time"- direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton's constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d g d λ . We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.
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Gaussian content as a laser beam quality parameter.
Ruschin, Shlomo; Yaakobi, Elad; Shekel, Eyal
2011-08-01
We propose the Gaussian content (GC) as an optional quality parameter for the characterization of laser beams. It is defined as the overlap integral of a given field with an optimally defined Gaussian. The definition is especially suited for applications where coherence properties are targeted. Mathematical definitions and basic calculation procedures are given along with results for basic beam profiles. The coherent combination of an array of laser beams and the optimal coupling between a diode laser and a single-mode fiber are elaborated as application examples. The measurement of the GC and its conservation upon propagation are experimentally confirmed.
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NASA Astrophysics Data System (ADS)
Belov, A. V.; Kurkov, Andrei S.; Chikolini, A. V.
1990-08-01
An offset method is modified to allow an analysis of the distribution of fields in a single-mode fiber waveguide without recourse to the Gaussian approximation. A new approximation for the field is obtained for fiber waveguides with a step refractive index profile and a special analysis employing the Hankel transformation is applied to waveguides with a distributed refractive index. The field distributions determined by this method are compared with the corresponding distributions calculated from the refractive index of a preform from which the fibers are drawn. It is shown that these new approaches can be used to determine the dimensions of a mode spot defined in different ways and to forecast the dispersion characteristics of single-mode fiber waveguides.
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Flat-fielding of Solar Hα Observations Based on the Maximum Correntropy Criterion
NASA Astrophysics Data System (ADS)
Xu, Gao-Gui; Zheng, Sheng; Lin, Gang-Hua; Wang, Xiao-Fan
2016-08-01
The flat-field CCD calibration method of Kuhn et al. (KLL) is an efficient method for flat-fielding. However, since it depends on the minimum of the sum of squares error (SSE), its solution is sensitive to noise, especially non-Gaussian noise. In this paper, a new algorithm is proposed to determine the flat field. The idea is to change the criterion of gain estimate from SSE to the maximum correntropy. The result of a test on simulated data demonstrates that our method has a higher accuracy and a faster convergence than KLL’s and Chae’s. It has been found that the method effectively suppresses noise, especially in the case of typical non-Gaussian noise. And the computing time of our algorithm is the shortest.
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Smooth Scalar-on-Image Regression via Spatial Bayesian Variable Selection
Goldsmith, Jeff; Huang, Lei; Crainiceanu, Ciprian M.
2013-01-01
We develop scalar-on-image regression models when images are registered multidimensional manifolds. We propose a fast and scalable Bayes inferential procedure to estimate the image coefficient. The central idea is the combination of an Ising prior distribution, which controls a latent binary indicator map, and an intrinsic Gaussian Markov random field, which controls the smoothness of the nonzero coefficients. The model is fit using a single-site Gibbs sampler, which allows fitting within minutes for hundreds of subjects with predictor images containing thousands of locations. The code is simple and is provided in less than one page in the Appendix. We apply this method to a neuroimaging study where cognitive outcomes are regressed on measures of white matter microstructure at every voxel of the corpus callosum for hundreds of subjects. PMID:24729670
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Reaction-diffusion on the fully-connected lattice: A+A\\rightarrow A
NASA Astrophysics Data System (ADS)
Turban, Loïc; Fortin, Jean-Yves
2018-04-01
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular, we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.
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Large Scale Gaussian Processes for Atmospheric Parameter Retrieval and Cloud Screening
NASA Astrophysics Data System (ADS)
Camps-Valls, G.; Gomez-Chova, L.; Mateo, G.; Laparra, V.; Perez-Suay, A.; Munoz-Mari, J.
2017-12-01
Current Earth-observation (EO) applications for image classification have to deal with an unprecedented big amount of heterogeneous and complex data sources. Spatio-temporally explicit classification methods are a requirement in a variety of Earth system data processing applications. Upcoming missions such as the super-spectral Copernicus Sentinels EnMAP and FLEX will soon provide unprecedented data streams. Very high resolution (VHR) sensors like Worldview-3 also pose big challenges to data processing. The challenge is not only attached to optical sensors but also to infrared sounders and radar images which increased in spectral, spatial and temporal resolution. Besides, we should not forget the availability of the extremely large remote sensing data archives already collected by several past missions, such ENVISAT, Cosmo-SkyMED, Landsat, SPOT, or Seviri/MSG. These large-scale data problems require enhanced processing techniques that should be accurate, robust and fast. Standard parameter retrieval and classification algorithms cannot cope with this new scenario efficiently. In this work, we review the field of large scale kernel methods for both atmospheric parameter retrieval and cloud detection using infrared sounding IASI data and optical Seviri/MSG imagery. We propose novel Gaussian Processes (GPs) to train problems with millions of instances and high number of input features. Algorithms can cope with non-linearities efficiently, accommodate multi-output problems, and provide confidence intervals for the predictions. Several strategies to speed up algorithms are devised: random Fourier features and variational approaches for cloud classification using IASI data and Seviri/MSG, and engineered randomized kernel functions and emulation in temperature, moisture and ozone atmospheric profile retrieval from IASI as a proxy to the upcoming MTG-IRS sensor. Excellent compromise between accuracy and scalability are obtained in all applications.
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NASA Astrophysics Data System (ADS)
Oroza, C.; Zheng, Z.; Glaser, S. D.; Bales, R. C.; Conklin, M. H.
2016-12-01
We present a structured, analytical approach to optimize ground-sensor placements based on time-series remotely sensed (LiDAR) data and machine-learning algorithms. We focused on catchments within the Merced and Tuolumne river basins, covered by the JPL Airborne Snow Observatory LiDAR program. First, we used a Gaussian mixture model to identify representative sensor locations in the space of independent variables for each catchment. Multiple independent variables that govern the distribution of snow depth were used, including elevation, slope, and aspect. Second, we used a Gaussian process to estimate the areal distribution of snow depth from the initial set of measurements. This is a covariance-based model that also estimates the areal distribution of model uncertainty based on the independent variable weights and autocorrelation. The uncertainty raster was used to strategically add sensors to minimize model uncertainty. We assessed the temporal accuracy of the method using LiDAR-derived snow-depth rasters collected in water-year 2014. In each area, optimal sensor placements were determined using the first available snow raster for the year. The accuracy in the remaining LiDAR surveys was compared to 100 configurations of sensors selected at random. We found the accuracy of the model from the proposed placements to be higher and more consistent in each remaining survey than the average random configuration. We found that a relatively small number of sensors can be used to accurately reproduce the spatial patterns of snow depth across the basins, when placed using spatial snow data. Our approach also simplifies sensor placement. At present, field surveys are required to identify representative locations for such networks, a process that is labor intensive and provides limited guarantees on the networks' representation of catchment independent variables.
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Fixing convergence of Gaussian belief propagation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Johnson, Jason K; Bickson, Danny; Dolev, Danny
Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm ismore » linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanari's linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.« less
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Eberhard, Wynn L
2017-04-01
The maximum likelihood estimator (MLE) is derived for retrieving the extinction coefficient and zero-range intercept in the lidar slope method in the presence of random and independent Gaussian noise. Least-squares fitting, weighted by the inverse of the noise variance, is equivalent to the MLE. Monte Carlo simulations demonstrate that two traditional least-squares fitting schemes, which use different weights, are less accurate. Alternative fitting schemes that have some positive attributes are introduced and evaluated. The principal factors governing accuracy of all these schemes are elucidated. Applying these schemes to data with Poisson rather than Gaussian noise alters accuracy little, even when the signal-to-noise ratio is low. Methods to estimate optimum weighting factors in actual data are presented. Even when the weighting estimates are coarse, retrieval accuracy declines only modestly. Mathematical tools are described for predicting retrieval accuracy. Least-squares fitting with inverse variance weighting has optimum accuracy for retrieval of parameters from single-wavelength lidar measurements when noise, errors, and uncertainties are Gaussian distributed, or close to optimum when only approximately Gaussian.
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Planck 2015 results. XVI. Isotropy and statistics of the CMB
NASA Astrophysics Data System (ADS)
Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Akrami, Y.; Aluri, P. K.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartolo, N.; Basak, S.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bock, J. J.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; Cardoso, J.-F.; Casaponsa, B.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H. C.; Christensen, P. R.; Church, S.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Combet, C.; Contreras, D.; Couchot, F.; Coulais, A.; Crill, B. P.; Cruz, M.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Désert, F.-X.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T. A.; Eriksen, H. K.; Fantaye, Y.; Fergusson, J.; Fernandez-Cobos, R.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A. A.; Franceschi, E.; Frejsel, A.; Frolov, A.; Galeotta, S.; Galli, S.; Ganga, K.; Gauthier, C.; Ghosh, T.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J. E.; Hansen, F. K.; Hanson, D.; Harrison, D. L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huang, Z.; Huffenberger, K. M.; Hurier, G.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kim, J.; Kisner, T. S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C. R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; Liu, H.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Marinucci, D.; Maris, M.; Martin, P. G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McGehee, P.; Meinhold, P. R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mikkelsen, K.; Mitra, S.; Miville-Deschênes, M.-A.; Molinari, D.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Pant, N.; Paoletti, D.; Pasian, F.; Patanchon, G.; Pearson, T. J.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Rotti, A.; Roudier, G.; Rubiño-Martín, J. A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Souradeep, T.; Spencer, L. D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Trombetti, T.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Wade, L. A.; Wandelt, B. D.; Wehus, I. K.; Yvon, D.; Zacchei, A.; Zibin, J. P.; Zonca, A.
2016-09-01
We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect our studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The "Cold Spot" is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.
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Planck 2015 results: XVI. Isotropy and statistics of the CMB
Ade, P. A. R.; Aghanim, N.; Akrami, Y.; ...
2016-09-20
In this paper, we test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect ourmore » studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The “Cold Spot” is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Finally, where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.« less
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Ade, P. A. R.; Aghanim, N.; Akrami, Y.
In this paper, we test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect ourmore » studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The “Cold Spot” is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Finally, where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.« less
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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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Plasma oscillations in spherical Gaussian shaped ultracold neutral plasma
DOE Office of Scientific and Technical Information (OSTI.GOV)
Chen, Tianxing; Lu, Ronghua, E-mail: lurh@siom.ac.cn; Guo, Li
2016-04-15
The collective plasma oscillations are investigated in ultracold neutral plasma with a non-uniform density profile. Instead of the plane configuration widely used, we derive the plasma oscillation equations with spherically symmetric distribution and Gaussian density profile. The damping of radial oscillation is found. The Tonks–Dattner resonances of the ultracold neutral plasma with an applied RF field are also calculated.
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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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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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NASA Astrophysics Data System (ADS)
Avendaño-Valencia, Luis David; Fassois, Spilios D.
2017-07-01
The study focuses on vibration response based health monitoring for an operating wind turbine, which features time-dependent dynamics under environmental and operational uncertainty. A Gaussian Mixture Model Random Coefficient (GMM-RC) model based Structural Health Monitoring framework postulated in a companion paper is adopted and assessed. The assessment is based on vibration response signals obtained from a simulated offshore 5 MW wind turbine. The non-stationarity in the vibration signals originates from the continually evolving, due to blade rotation, inertial properties, as well as the wind characteristics, while uncertainty is introduced by random variations of the wind speed within the range of 10-20 m/s. Monte Carlo simulations are performed using six distinct structural states, including the healthy state and five types of damage/fault in the tower, the blades, and the transmission, with each one of them characterized by four distinct levels. Random vibration response modeling and damage diagnosis are illustrated, along with pertinent comparisons with state-of-the-art diagnosis methods. The results demonstrate consistently good performance of the GMM-RC model based framework, offering significant performance improvements over state-of-the-art methods. Most damage types and levels are shown to be properly diagnosed using a single vibration sensor.
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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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A method for selective excitation of Ince-Gaussian modes in an end-pumped solid-state laser
NASA Astrophysics Data System (ADS)
Lei, J.; Hu, A.; Wang, Y.; Chen, P.
2014-12-01
A method for selective excitation of Ince-Gaussian modes is presented. The method is based on the spatial distributions of Ince-Gaussian modes as well as the transverse mode selection theory. Significant diffraction loss is introduced in a resonator by using opaque lines at zero-intensity positions, and this loss allows to excite a specific mode; we call this method "loss control." We study the method by means of numerical simulation of a half-symmetric laser resonator. The simulated field is represented by angular spectrum of the plane waves representation, and its changes are calculated by the two-dimensional fast Fourier transform algorithm when it passes through the optical elements and propagates back and forth in the resonator. The output lasing modes of our method have an overlap of over 90 % with the target Ince-Gaussian modes. The method will be beneficial to the further study of properties and potential applications of Ince-Gaussian modes.
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Study on the mapping of dark matter clustering from real space to redshift space
NASA Astrophysics Data System (ADS)
Zheng, Yi; Song, Yong-Seon
2016-08-01
The mapping of dark matter clustering from real space to redshift space introduces the anisotropic property to the measured density power spectrum in redshift space, known as the redshift space distortion effect. The mapping formula is intrinsically non-linear, which is complicated by the higher order polynomials due to indefinite cross correlations between the density and velocity fields, and the Finger-of-God effect due to the randomness of the peculiar velocity field. Whilst the full higher order polynomials remain unknown, the other systematics can be controlled consistently within the same order truncation in the expansion of the mapping formula, as shown in this paper. The systematic due to the unknown non-linear density and velocity fields is removed by separately measuring all terms in the expansion directly using simulations. The uncertainty caused by the velocity randomness is controlled by splitting the FoG term into two pieces, 1) the ``one-point" FoG term being independent of the separation vector between two different points, and 2) the ``correlated" FoG term appearing as an indefinite polynomials which is expanded in the same order as all other perturbative polynomials. Using 100 realizations of simulations, we find that the Gaussian FoG function with only one scale-independent free parameter works quite well, and that our new mapping formulation accurately reproduces the observed 2-dimensional density power spectrum in redshift space at the smallest scales by far, up to k~ 0.2 Mpc-1, considering the resolution of future experiments.
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Calculation of exchange interaction for modified Gaussian coupled quantum dots
NASA Astrophysics Data System (ADS)
Khordad, R.
2017-08-01
A system of two laterally coupled quantum dots with modified Gaussian potential has been considered. Each quantum dot has an electron under electric and magnetic field. The quantum dots have been considered as hydrogen-like atoms. The physical picture has translated into the Heisenberg spin Hamiltonian. The Schrödinger equation using finite element method has been numerically solved. The exchange energy factor has been calculated as a functions of electric field, magnetic field, and the separation distance between the centers of the dots ( d). According to the results, it is found that there is the transition from anti-ferromagnetic to ferromagnetic for constant electric field. Also, the transition occurs from ferromagnetic to anti-ferromagnetic for constant magnetic field (B>1 T). With decreasing the distance between the centers of the dots and increasing magnetic field, the transition occurs from anti-ferromagnetic to ferromagnetic. It is found that a switching of exchange energy factor is presented without canceling the interactions of the electric and magnetic fields on the system.
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Identifying the Tunneling Site in Strong-Field Ionization of H_{2}^{+}.
Liu, Kunlong; Barth, Ingo
2017-12-15
The tunneling site of the electron in a molecule exposed to a strong laser field determines the initial position of the ionizing electron and, as a result, has a large impact on the subsequent ultrafast electron dynamics on the polyatomic Coulomb potential. Here, the tunneling site of the electron of H_{2}^{+} ionized by a strong circularly polarized (CP) laser pulse is studied by numerically solving the time-dependent Schrödinger equation. We show that the electron removed from the down-field site is directly driven away by the CP field and the lateral photoelectron momentum distribution (LPMD) exhibits a Gaussian-like distribution, whereas the corresponding LPMD of the electron removed from the up-field site differs from the Gaussian shape due to the Coulomb focusing and scattering by the down-field core. Our current study presents the direct evidence clarifying a long-standing controversy over the tunneling site in H_{2}^{+} and raises the important role of the tunneling site in strong-field molecular ionization.
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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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FEL amplifier performance in the Compton regime
NASA Astrophysics Data System (ADS)
Cover, R. A.; Bhowmik, A.
1984-01-01
The Kroll-Morton-Rosenbluth equations of motion for electrons in a linearly polarized, tapered wiggler are utilized to describe gain in free-electron laser amplifiers. The three-dimensional amplifier model includes the effects of density variation in the electron beam, off-axis variations in the wiggler magnetic field, and betatron oscillations. The input electromagnetic field is injected and subsequently propagated within the wiggler by computing the Fresnel-Kirchhoff diffraction integral using the Gardner-Fresnel-Kirchhoff algorithm. The injected optical beam used in evaluating amplifier performance is initially a Gaussian which in general may be astigmatic. The importance of the above effects on extraction efficiency is computed both with rigorous three-dimensional electromagnetic wave propagation and a Gaussian treatment of the field.
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NASA Technical Reports Server (NTRS)
Huang, N. E.; Long, S. R.; Bliven, L. F.; Tung, C.-C.
1984-01-01
On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared with a series of carefully controlled laboratory observations, and good agreement is noted. Furthermore, the laboratory wind wave field observations indicate that the capillary or capillary-gravity waves may not be the dominant components in determining the total roughness of the wave field. Thus, the analytic results, though derived specifically for the gravity waves, may have more general applications.
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Li, Yu-Bin; Cai, Yi-Fu; Quintin, Jerome
We extend the matter bounce scenario to a more general theory in which the background dynamics and cosmological perturbations are generated by a k -essence scalar field with an arbitrary sound speed. When the sound speed is small, the curvature perturbation is enhanced, and the tensor-to-scalar ratio, which is excessively large in the original model, can be sufficiently suppressed to be consistent with observational bounds. Then, we study the primordial three-point correlation function generated during the matter-dominated contraction stage and find that it only depends on the sound speed parameter. Similar to the canonical case, the shape of the bispectrummore » is mainly dominated by a local form, though for some specific sound speed values a new shape emerges and the scaling behaviour changes. Meanwhile, a small sound speed also results in a large amplitude of non-Gaussianities, which is disfavored by current observations. As a result, it does not seem possible to suppress the tensor-to-scalar ratio without amplifying the production of non-Gaussianities beyond current observational constraints (and vice versa). This suggests an extension of the previously conjectured no-go theorem in single field nonsingular matter bounce cosmologies, which rules out a large class of models. However, the non-Gaussianity results remain as a distinguishable signature of matter bounce cosmology and have the potential to be detected by observations in the near future.« less
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Productive interactions: heavy particles and non-Gaussianity
DOE Office of Scientific and Technical Information (OSTI.GOV)
Flauger, Raphael; Mirbabayi, Mehrdad; Senatore, Leonardo
We analyze the shape and amplitude of oscillatory features in the primordial power spectrum and non-Gaussianity induced by periodic production of heavy degrees of freedom coupled to the inflaton Φ. We find that non-adiabatic production of particles can contribute effects which are detectable or constrainable using cosmological data even if their time-dependent masses are always heavier than the scale Φ 1/2, much larger than the Hubble scale. This provides a new role for UV completion, consistent with the criteria from effective field theory for when heavy fields cannot be integrated out. This analysis is motivated in part by the structuremore » of axion monodromy, and leads to an additional oscillatory signature in a subset of its parameter space. At the level of a quantum field theory model that we analyze in detail, the effect arises consistently with radiative stability for an interesting window of couplings up to of order ≲ 1. The amplitude of the bispectrum and higher-point functions can be larger than that for Resonant Non-Gaussianity, and its signal/noise may be comparable to that of the corresponding oscillations in the power spectrum (and even somewhat larger within a controlled regime of parameters). Its shape is distinct from previously analyzed templates, but was partly motivated by the oscillatory equilateral searches performed recently by the Planck collaboration. As a result, we also make some general comments about the challenges involved in making a systematic study of primordial non-Gaussianity.« less
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Productive interactions: heavy particles and non-Gaussianity
DOE Office of Scientific and Technical Information (OSTI.GOV)
Flauger, Raphael; Mirbabayi, Mehrdad; Senatore, Leonardo
We analyze the shape and amplitude of oscillatory features in the primordial power spectrum and non-Gaussianity induced by periodic production of heavy degrees of freedom coupled to the inflaton φ. We find that non-adiabatic production of particles can contribute effects which are detectable or constrainable using cosmological data even if their time-dependent masses are always heavier than the scale φ̇{sup 1/2}, much larger than the Hubble scale. This provides a new role for UV completion, consistent with the criteria from effective field theory for when heavy fields cannot be integrated out. This analysis is motivated in part by the structuremore » of axion monodromy, and leads to an additional oscillatory signature in a subset of its parameter space. At the level of a quantum field theory model that we analyze in detail, the effect arises consistently with radiative stability for an interesting window of couplings up to of order ∼< 1. The amplitude of the bispectrum and higher-point functions can be larger than that for Resonant Non-Gaussianity, and its signal/noise may be comparable to that of the corresponding oscillations in the power spectrum (and even somewhat larger within a controlled regime of parameters). Its shape is distinct from previously analyzed templates, but was partly motivated by the oscillatory equilateral searches performed recently by the Planck collaboration. We also make some general comments about the challenges involved in making a systematic study of primordial non-Gaussianity.« less
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Productive interactions: heavy particles and non-Gaussianity
Flauger, Raphael; Mirbabayi, Mehrdad; Senatore, Leonardo; ...
2017-10-31
We analyze the shape and amplitude of oscillatory features in the primordial power spectrum and non-Gaussianity induced by periodic production of heavy degrees of freedom coupled to the inflaton Φ. We find that non-adiabatic production of particles can contribute effects which are detectable or constrainable using cosmological data even if their time-dependent masses are always heavier than the scale Φ 1/2, much larger than the Hubble scale. This provides a new role for UV completion, consistent with the criteria from effective field theory for when heavy fields cannot be integrated out. This analysis is motivated in part by the structuremore » of axion monodromy, and leads to an additional oscillatory signature in a subset of its parameter space. At the level of a quantum field theory model that we analyze in detail, the effect arises consistently with radiative stability for an interesting window of couplings up to of order ≲ 1. The amplitude of the bispectrum and higher-point functions can be larger than that for Resonant Non-Gaussianity, and its signal/noise may be comparable to that of the corresponding oscillations in the power spectrum (and even somewhat larger within a controlled regime of parameters). Its shape is distinct from previously analyzed templates, but was partly motivated by the oscillatory equilateral searches performed recently by the Planck collaboration. As a result, we also make some general comments about the challenges involved in making a systematic study of primordial non-Gaussianity.« less
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Statistical Analyses of Brain Surfaces Using Gaussian Random Fields on 2-D Manifolds
Staib, Lawrence H.; Xu, Dongrong; Zhu, Hongtu; Peterson, Bradley S.
2008-01-01
Interest in the morphometric analysis of the brain and its subregions has recently intensified because growth or degeneration of the brain in health or illness affects not only the volume but also the shape of cortical and subcortical brain regions, and new image processing techniques permit detection of small and highly localized perturbations in shape or localized volume, with remarkable precision. An appropriate statistical representation of the shape of a brain region is essential, however, for detecting, localizing, and interpreting variability in its surface contour and for identifying differences in volume of the underlying tissue that produce that variability across individuals and groups of individuals. Our statistical representation of the shape of a brain region is defined by a reference region for that region and by a Gaussian random field (GRF) that is defined across the entire surface of the region. We first select a reference region from a set of segmented brain images of healthy individuals. The GRF is then estimated as the signed Euclidean distances between points on the surface of the reference region and the corresponding points on the corresponding region in images of brains that have been coregistered to the reference. Correspondences between points on these surfaces are defined through deformations of each region of a brain into the coordinate space of the reference region using the principles of fluid dynamics. The warped, coregistered region of each subject is then unwarped into its native space, simultaneously bringing into that space the map of corresponding points that was established when the surfaces of the subject and reference regions were tightly coregistered. The proposed statistical description of the shape of surface contours makes no assumptions, other than smoothness, about the shape of the region or its GRF. The description also allows for the detection and localization of statistically significant differences in the shapes of the surfaces across groups of subjects at both a fine and coarse scale. We demonstrate the effectiveness of these statistical methods by applying them to study differences in shape of the amygdala and hippocampus in a large sample of normal subjects and in subjects with attention deficit/hyperactivity disorder (ADHD). PMID:17243583
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DOE Office of Scientific and Technical Information (OSTI.GOV)
Zhang, G; Xing, L
2016-06-15
Purpose: Cone beam X-ray luminescence computed tomography (CB-XLCT), which aims to achieve molecular and functional imaging by X-rays, has recently been proposed as a new imaging modality. However, the inverse problem of CB-XLCT is seriously ill-conditioned, hindering us to achieve good image quality. In this work, a novel reconstruction method based on Bayesian theory is proposed to tackle this problem Methods: Bayesian theory provides a natural framework for utilizing various kinds of available prior information to improve the reconstruction image quality. A generalized Gaussian Markov random field (GGMRF) model is proposed here to construct the prior model of the Bayesianmore » theory. The most important feature of GGMRF model is the adjustable shape parameter p, which can be continuously adjusted from 1 to 2. The reconstruction image tends to have more edge-preserving property when p is slide to 1, while having more noise tolerance property when p is slide to 2, just like the behavior of L1 and L2 regularization methods, respectively. The proposed method provides a flexible regularization framework to adapt to a wide range of applications. Results: Numerical simulations were implemented to test the performance of the proposed method. The Digimouse atlas were employed to construct a three-dimensional mouse model, and two small cylinders were placed inside to serve as the targets. Reconstruction results show that the proposed method tends to obtain better spatial resolution with a smaller shape parameter, while better signal-to-noise image with a larger shape parameter. Quantitative indexes, contrast-to-noise ratio (CNR) and full-width at half-maximum (FWHM), were used to assess the performance of the proposed method, and confirmed its effectiveness in CB-XLCT reconstruction. Conclusion: A novel reconstruction method for CB-XLCT is proposed based on GGMRF model, which enables an adjustable performance tradeoff between L1 and L2 regularization methods. Numerical simulations were conducted to demonstrate its performance.« less
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Fisher information as a generalized measure of coherence in classical and quantum optics.
Luis, Alfredo
2012-10-22
We show that metrological resolution in the detection of small phase shifts provides a suitable generalization of the degrees of coherence and polarization. Resolution is estimated via Fisher information. Besides the standard two-beam Gaussian case, this approach provides also good results for multiple field components and nonGaussian statistics. This works equally well in quantum and classical optics.
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Revisiting non-Gaussianity from non-attractor inflation models
NASA Astrophysics Data System (ADS)
Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei
2018-05-01
Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition—such as in the case of smooth transition or some sharp transition scenarios—the Script O(1) local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.