A hydrodynamic approach to cosmology - Texture-seeded cold dark matter and hot dark matter cosmogonies

NASA Technical Reports Server (NTRS)

Cen, R. Y.; Ostriker, J. P.; Spergel, D. N.; Turok, N.

1991-01-01

Hydrodynamical simulations of galaxy formation in a texture-seeded cosmology are presented, with attention given to Omega = 1 galaxies dominated by both hot dark matter (HDM) and cold dark matter (CDM). The simulations include both gravitational and hydrodynamical physics with a detailed treatment of collisional and radiative thermal processes, and use a cooling criterion to estimate galaxy formation. Background radiation fields and Zel'dovich-Sunyaev fluctuations are explicitly computed. The derived galaxy mass function is well fitted by the observed Schechter luminosity function for a baryonic M/L of 3 and total M/L of 60 in galaxies. In both HDM and CDM texture scenarios, the 'galaxies' and 'clusters' are significantly more strongly correlated than the dark matter due to physical bias processes. The slope of the correlation function in both cases is consistent with observations. In contrast to Gaussian models, peaks in the dark matter density distributrion are less correlated than average.

Entanglement with negative Wigner function of three thousand atoms heralded by one photon

NASA Astrophysics Data System (ADS)

McConnell, Robert; Zhang, Hao; Hu, Jiazhong; Ćuk, Senka; Vuletić, Vladan

2016-06-01

Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11, 12], and very recently in large atomic ensembles [13, 14, 15]. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function, an important hallmark of nonclassicality, and verify an entanglement depth (minimum number of mutually entangled atoms) of 2910 ± 190 out of 3100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. While the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing.

Elegant Ince-Gaussian beams in a quadratic-index medium

NASA Astrophysics Data System (ADS)

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

2011-09-01

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

Dimension of quantum phase space measured by photon correlations

NASA Astrophysics Data System (ADS)

Leuchs, Gerd; Glauber, Roy J.; Schleich, Wolfgang P.

2015-06-01

We show that the different values 1, 2 and 3 of the normalized second-order correlation function {g}(2)(0) corresponding to a coherent state, a thermal state and a highly squeezed vacuum originate from the different dimensionality of these states in phase space. In particular, we derive an exact expression for {g}(2)(0) in terms of the ratio of the moments of the classical energy evaluated with the Wigner function of the quantum state of interest and corrections proportional to the reciprocal of powers of the average number of photons. In this way we establish a direct link between {g}(2)(0) and the shape of the state in phase space. Moreover, we illuminate this connection by demonstrating that in the semi-classical limit the familiar photon statistics of a thermal state arise from an area in phase space weighted by a two-dimensional Gaussian, whereas those of a highly squeezed state are governed by a line-integral of a one-dimensional Gaussian. We dedicate this article to Margarita and Vladimir Man’ko on the occasion of their birthdays. The topic of our contribution is deeply rooted in and motivated by their love for non-classical light, quantum mechanical phase space distribution functions and orthogonal polynomials. Indeed, through their articles, talks and most importantly by many stimulating discussions and intensive collaborations with us they have contributed much to our understanding of physics. Happy birthday to you both!

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

Smallwood, D.O.

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

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

NASA Astrophysics Data System (ADS)

Ben-Arie, Jezekiel; Rao, Raghunath K.

1991-10-01

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

An analysis of scatter decomposition

NASA Technical Reports Server (NTRS)

Nicol, David M.; Saltz, Joel H.

1990-01-01

A formal analysis of a powerful mapping technique known as scatter decomposition is presented. Scatter decomposition divides an irregular computational domain into a large number of equal sized pieces, and distributes them modularly among processors. A probabilistic model of workload in one dimension is used to formally explain why, and when scatter decomposition works. The first result is that if correlation in workload is a convex function of distance, then scattering a more finely decomposed domain yields a lower average processor workload variance. The second result shows that if the workload process is stationary Gaussian and the correlation function decreases linearly in distance until becoming zero and then remains zero, scattering a more finely decomposed domain yields a lower expected maximum processor workload. Finally it is shown that if the correlation function decreases linearly across the entire domain, then among all mappings that assign an equal number of domain pieces to each processor, scatter decomposition minimizes the average processor workload variance. The dependence of these results on the assumption of decreasing correlation is illustrated with situations where a coarser granularity actually achieves better load balance.

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

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

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

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

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

2013-06-01

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

Improved Discrete Approximation of Laplacian of Gaussian

NASA Technical Reports Server (NTRS)

Shuler, Robert L., Jr.

2004-01-01

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

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

PubMed

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

2017-01-21

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Loop corrections to primordial non-Gaussianity

NASA Astrophysics Data System (ADS)

Boran, Sibel; Kahya, E. O.

2018-02-01

We discuss quantum gravitational loop effects to observable quantities such as curvature power spectrum and primordial non-Gaussianity of cosmic microwave background (CMB) radiation. We first review the previously shown case where one gets a time dependence for zeta-zeta correlator due to loop corrections. Then we investigate the effect of loop corrections to primordial non-Gaussianity of CMB. We conclude that, even with a single scalar inflaton, one might get a huge value for non-Gaussianity which would exceed the observed value by at least 30 orders of magnitude. Finally we discuss the consequences of this result for scalar driven inflationary models.

On hierarchical solutions to the BBGKY hierarchy

NASA Technical Reports Server (NTRS)

Hamilton, A. J. S.

1988-01-01

It is thought that the gravitational clustering of galaxies in the universe may approach a scale-invariant, hierarchical form in the small separation, large-clustering regime. Past attempts to solve the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy in this regime have assumed a certain separable hierarchical form for the higher order correlation functions of galaxies in phase space. It is shown here that such separable solutions to the BBGKY equations must satisfy the condition that the clustered component of the solution has cluster-cluster correlations equal to galaxy-galaxy correlations to all orders. The solutions also admit the presence of an arbitrary unclustered component, which plays no dyamical role in the large-clustering regime. These results are a particular property of the specific separable model assumed for the correlation functions in phase space, not an intrinsic property of spatially hierarchical solutions to the BBGKY hierarchy. The observed distribution of galaxies does not satisfy the required conditions. The disagreement between theory and observation may be traced, at least in part, to initial conditions which, if Gaussian, already have cluster correlations greater than galaxy correlations.

Detection methods for non-Gaussian gravitational wave stochastic backgrounds

NASA Astrophysics Data System (ADS)

Drasco, Steve; Flanagan, Éanna É.

2003-04-01

A gravitational wave stochastic background can be produced by a collection of independent gravitational wave events. There are two classes of such backgrounds, one for which the ratio of the average time between events to the average duration of an event is small (i.e., many events are on at once), and one for which the ratio is large. In the first case the signal is continuous, sounds something like a constant hiss, and has a Gaussian probability distribution. In the second case, the discontinuous or intermittent signal sounds something like popcorn popping, and is described by a non-Gaussian probability distribution. In this paper we address the issue of finding an optimal detection method for such a non-Gaussian background. As a first step, we examine the idealized situation in which the event durations are short compared to the detector sampling time, so that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. For this situation we derive an appropriate version of the maximum likelihood detection statistic. We compare the performance of this statistic to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. In general the maximum likelihood statistic performs better than the cross-correlation statistic when the stochastic background is sufficiently non-Gaussian, resulting in a gain factor in the minimum gravitational-wave energy density necessary for detection. This gain factor ranges roughly between 1 and 3, depending on the duty cycle of the background, for realistic observing times and signal strengths for both ground and space based detectors. The computational cost of the statistic, although significantly greater than that of the cross-correlation statistic, is not unreasonable. Before the statistic can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned detectors with realistic, colored, non-Gaussian noise.

Density-dependent clustering: I. Pulling back the curtains on motions of the BAO peak

NASA Astrophysics Data System (ADS)

Neyrinck, Mark C.; Szapudi, István; McCullagh, Nuala; Szalay, Alexander S.; Falck, Bridget; Wang, Jie

2018-05-01

The most common statistic used to analyze large-scale structure surveys is the correlation function, or power spectrum. Here, we show how `slicing' the correlation function on local density brings sensitivity to interesting non-Gaussian features in the large-scale structure, such as the expansion or contraction of baryon acoustic oscillations (BAO) according to the local density. The sliced correlation function measures the large-scale flows that smear out the BAO, instead of just correcting them as reconstruction algorithms do. Thus, we expect the sliced correlation function to be useful in constraining the growth factor, and modified gravity theories that involve the local density. Out of the studied cases, we find that the run of the BAO peak location with density is best revealed when slicing on a ˜40 h-1 Mpc filtered density. But slicing on a ˜100 h-1 Mpc filtered density may be most useful in distinguishing between underdense and overdense regions, whose BAO peaks are separated by a substantial ˜5 h-1 Mpc at z = 0. We also introduce `curtain plots' showing how local densities drive particle motions toward or away from each other over the course of an N-body simulation.

One-electron reduced density matrices of strongly correlated harmonium atoms.

PubMed

Cioslowski, Jerzy

2015-03-21

Explicit asymptotic expressions are derived for the reduced one-electron density matrices (the 1-matrices) of strongly correlated two- and three-electron harmonium atoms in the ground and first excited states. These expressions, which are valid at the limit of small confinement strength ω, yield electron densities and kinetic energies in agreement with the published values. In addition, they reveal the ω(5/6) asymptotic scaling of the exchange components of the electron-electron repulsion energies that differs from the ω(2/3) scaling of their Coulomb and correlation counterparts. The natural orbitals of the totally symmetric ground state of the two-electron harmonium atom are found to possess collective occupancies that follow a mixed power/Gaussian dependence on the angular momentum in variance with the simple power-law prediction of Hill's asymptotics. Providing rigorous constraints on energies as functionals of 1-matrices, these results are expected to facilitate development of approximate implementations of the density matrix functional theory and ensure their proper description of strongly correlated systems.

Persistence of non-Markovian Gaussian stationary processes in discrete time

NASA Astrophysics Data System (ADS)

Nyberg, Markus; Lizana, Ludvig

2018-04-01

The persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval. Although persistence is a simple concept to understand, it is in general hard to calculate. Here we consider zero mean Gaussian stationary processes in discrete time n . Few results are known for the persistence P0(n ) in discrete time, except the large time behavior which is characterized by the nontrivial constant θ through P0(n ) ˜θn . Using a modified version of the independent interval approximation (IIA) that we developed before, we are able to calculate P0(n ) analytically in z -transform space in terms of the autocorrelation function A (n ) . If A (n )→0 as n →∞ , we extract θ numerically, while if A (n )=0 , for finite n >N , we find θ exactly (within the IIA). We apply our results to three special cases: the nearest-neighbor-correlated "first order moving average process", where A (n )=0 for n >1 , the double exponential-correlated "second order autoregressive process", where A (n ) =c1λ1n+c2λ2n , and power-law-correlated variables, where A (n ) ˜n-μ . Apart from the power-law case when μ <5 , we find excellent agreement with simulations.

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.

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

NASA Astrophysics Data System (ADS)

Selim, M. M.; Bezák, V.

2003-06-01

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

FIBER AND INTEGRAL OPTICS: Mode composition of radiation in graded-index waveguides with random microbending of the axis

NASA Astrophysics Data System (ADS)

Valyaev, A. B.; Krivoshlykov, S. G.

1989-06-01

It is shown that the problem of investigating the mode composition of a partly coherent radiation beam in a randomly inhomogeneous medium can be reduced to a study of evolution of the energy of individual modes and of the coefficients of correlations between the modes. General expressions are obtained for the coupling coefficients of modes in a parabolic waveguide with a random microbending of the axis and an analysis is made of their evolution as a function of the excitation conditions. An estimate is obtained of the distance in which a steady-state energy distribution between the modes is established. Explicit expressions are obtained for the correlation function in the case when a waveguide is excited by off-axial Gaussian beams or Gauss-Hermite modes.

A Concept for Measuring Electron Distribution Functions Using Collective Thomson Scattering

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence

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

Adesso, Gerardo; Centre for Quantum Computation, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA; Serafini, Alessio

2006-03-15

We present a complete analysis of the multipartite entanglement of three-mode Gaussian states of continuous-variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations can be quantified by a proper convex roof extension of the squared logarithmic negativity, the continuous-variable tangle, or contangle. We review and elucidate in detail the proof that in multimode Gaussian states the contangle satisfies a monogamy inequalitymore » constraint [G. Adesso and F. Illuminati, New J. Phys8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communications and defines a measure of genuine tripartite entanglements. We determine the analytical expression of the residual contangle for arbitrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such states. This analysis yields that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/W states of continuous-variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the W states of three qubits. We finally consider the effect of decoherence on three-mode Gaussian states, studying the decay of the residual contangle. The GHZ/W states are shown to be maximally robust against losses and thermal noise.« less

Density functional Gaussian-type-orbital approach to theoretical study of nitric oxide dimers

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

Jursic, B.S.; Zdravkovski, Z.

Structure and total energies of the cis NO dimer, the trans NO dimer, and the NO monomer were calculated by ab initio methods (UHF, UMP2, and MP3) and density functional theory methods (LSDA and BLYP) with different basis sets [from 3-21G* to 6-311++(3df,3pd)]. The system is especially hard to model because two NO molecules are weakly associated in a dimer that has very long N-N bond. The results obtained by different methods are compared and the necessity of correlational methods for studying these systems is discussed.

Scale-invariant curvature fluctuations from an extended semiclassical gravity

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

Pinamonti, Nicola, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it; INFN Sezione di Genova, Via Dodecaneso 33, 16146 Genova; Siemssen, Daniel, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it

2015-02-15

We present an extension of the semiclassical Einstein equations which couple n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. We apply this extension to calculate the quantum fluctuations during an inflationary period, where we take as a model a massive conformally coupled scalar field on a perturbed de Sitter space and describe how a renormalization independent, almost-scale-invariant power spectrum of the scalar metric perturbation is produced. Furthermore, we discuss how this model yields a natural basis for the calculation of non-Gaussianities of the considered metric fluctuations.

Pyrcca: Regularized Kernel Canonical Correlation Analysis in Python and Its Applications to Neuroimaging.

PubMed

Bilenko, Natalia Y; Gallant, Jack L

2016-01-01

In this article we introduce Pyrcca, an open-source Python package for performing canonical correlation analysis (CCA). CCA is a multivariate analysis method for identifying relationships between sets of variables. Pyrcca supports CCA with or without regularization, and with or without linear, polynomial, or Gaussian kernelization. We first use an abstract example to describe Pyrcca functionality. We then demonstrate how Pyrcca can be used to analyze neuroimaging data. Specifically, we use Pyrcca to implement cross-subject comparison in a natural movie functional magnetic resonance imaging (fMRI) experiment by finding a data-driven set of functional response patterns that are similar across individuals. We validate this cross-subject comparison method in Pyrcca by predicting responses to novel natural movies across subjects. Finally, we show how Pyrcca can reveal retinotopic organization in brain responses to natural movies without the need for an explicit model.

Pyrcca: Regularized Kernel Canonical Correlation Analysis in Python and Its Applications to Neuroimaging

PubMed Central

Bilenko, Natalia Y.; Gallant, Jack L.

2016-01-01

In this article we introduce Pyrcca, an open-source Python package for performing canonical correlation analysis (CCA). CCA is a multivariate analysis method for identifying relationships between sets of variables. Pyrcca supports CCA with or without regularization, and with or without linear, polynomial, or Gaussian kernelization. We first use an abstract example to describe Pyrcca functionality. We then demonstrate how Pyrcca can be used to analyze neuroimaging data. Specifically, we use Pyrcca to implement cross-subject comparison in a natural movie functional magnetic resonance imaging (fMRI) experiment by finding a data-driven set of functional response patterns that are similar across individuals. We validate this cross-subject comparison method in Pyrcca by predicting responses to novel natural movies across subjects. Finally, we show how Pyrcca can reveal retinotopic organization in brain responses to natural movies without the need for an explicit model. PMID:27920675

Blind channel estimation and deconvolution in colored noise using higher-order cumulants

NASA Astrophysics Data System (ADS)

Tugnait, Jitendra K.; Gummadavelli, Uma

1994-10-01

Existing approaches to blind channel estimation and deconvolution (equalization) focus exclusively on channel or inverse-channel impulse response estimation. It is well-known that the quality of the deconvolved output depends crucially upon the noise statistics also. Typically it is assumed that the noise is white and the signal-to-noise ratio is known. In this paper we remove these restrictions. Both the channel impulse response and the noise model are estimated from the higher-order (fourth, e.g.) cumulant function and the (second-order) correlation function of the received data via a least-squares cumulant/correlation matching criterion. It is assumed that the noise higher-order cumulant function vanishes (e.g., Gaussian noise, as is the case for digital communications). Consistency of the proposed approach is established under certain mild sufficient conditions. The approach is illustrated via simulation examples involving blind equalization of digital communications signals.

Partial removal of correlated noise in thermal imagery

NASA Astrophysics Data System (ADS)

Borel, Christoph C.; Cooke, Bradly J.; Laubscher, Bryan E.

1996-05-01

Correlated noise occurs in many imaging systems such as scanners and push-broom imagers. The sources of correlated noise can be from the detectors, pre-amplifiers and sampling circuits. Correlated noise appears as streaking along the scan direction of a scanner or in the along track direction of a push-broom imager. We have developed algorithms to simulate correlated noise and pre-filter to reduce the amount of streaking while not destroying the scene content. The pre-filter in the Fourier domain consists of the product of two filters. One filter models the correlated noise spectrum, the other is a windowing function, e.g. Gaussian or Hanning window with variable width to block high frequency noise away from the origin of the Fourier Transform of the image data. We have optimized the filter parameters for various scenes and find improvements of the RMS error of the original minus the pre-filtered noisy image.

The Non-Gaussian Nature of Prostate Motion Based on Real-Time Intrafraction Tracking

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

Lin, Yuting; Liu, Tian; Yang, Wells

2013-10-01

Purpose: The objective of this work is to test the validity of the Gaussian approximation for prostate motion through characterization of its spatial distribution. Methods and Materials: Real-time intrafraction prostate motion was observed using Calypso 4-dimensional (4D) nonradioactive electromagnetic tracking system. We report the results from a total of 1024 fractions from 31 prostate cancer patients. First, the correlation of prostate motion in right/left (RL), anteroposterior (AP), and superoinferior (SI) direction were determined using Pearson's correlation of coefficient. Then the spatial distribution of prostate motion was analyzed for individual fraction, individual patient including all fractions, and all patients including allmore » fractions. The displacement in RL, AP, SI, oblique, or total direction is fitted into a Gaussian distribution, and a Lilliefors test was used to evaluate the validity of the hypothesis that the displacement is normally distributed. Results: There is high correlation in AP/SI direction (61% of fractions with medium or strong correlation). This is consistent with the longitudinal oblique motion of the prostate, and likely the effect from respiration on an organ confined within the genitourinary diaphragm with the rectum sitting posteriorly and bladder sitting superiorly. In all directions, the non-Gaussian distribution is more common for individual fraction, individual patient including all fractions, and all patients including all fractions. The spatial distribution of prostate motion shows an elongated shape in oblique direction, indicating a higher range of motion in the AP and SI directions. Conclusions: Our results showed that the prostate motion is highly correlated in AP and SI direction, indicating an oblique motion preference. In addition, the spatial distribution of prostate motion is elongated in an oblique direction, indicating that the organ motion dosimetric modeling using Gaussian kernel may need to be modified to account for the particular organ motion character of prostate.« less

The non-Gaussian nature of prostate motion based on real-time intrafraction tracking.

PubMed

Lin, Yuting; Liu, Tian; Yang, Wells; Yang, Xiaofeng; Khan, Mohammad K

2013-10-01

The objective of this work is to test the validity of the Gaussian approximation for prostate motion through characterization of its spatial distribution. Real-time intrafraction prostate motion was observed using Calypso 4-dimensional (4D) nonradioactive electromagnetic tracking system. We report the results from a total of 1024 fractions from 31 prostate cancer patients. First, the correlation of prostate motion in right/left (RL), anteroposterior (AP), and superoinferior (SI) direction were determined using Pearson's correlation of coefficient. Then the spatial distribution of prostate motion was analyzed for individual fraction, individual patient including all fractions, and all patients including all fractions. The displacement in RL, AP, SI, oblique, or total direction is fitted into a Gaussian distribution, and a Lilliefors test was used to evaluate the validity of the hypothesis that the displacement is normally distributed. There is high correlation in AP/SI direction (61% of fractions with medium or strong correlation). This is consistent with the longitudinal oblique motion of the prostate, and likely the effect from respiration on an organ confined within the genitourinary diaphragm with the rectum sitting posteriorly and bladder sitting superiorly. In all directions, the non-Gaussian distribution is more common for individual fraction, individual patient including all fractions, and all patients including all fractions. The spatial distribution of prostate motion shows an elongated shape in oblique direction, indicating a higher range of motion in the AP and SI directions. Our results showed that the prostate motion is highly correlated in AP and SI direction, indicating an oblique motion preference. In addition, the spatial distribution of prostate motion is elongated in an oblique direction, indicating that the organ motion dosimetric modeling using Gaussian kernel may need to be modified to account for the particular organ motion character of prostate. Copyright © 2013 Elsevier Inc. All rights reserved.

Multifractal analysis of time series generated by discrete Ito equations

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

Telesca, Luciano; Czechowski, Zbigniew; Lovallo, Michele

2015-06-15

In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.

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.

Gaussian covariance graph models accounting for correlated marker effects in genome-wide prediction.

PubMed

Martínez, C A; Khare, K; Rahman, S; Elzo, M A

2017-10-01

Several statistical models used in genome-wide prediction assume uncorrelated marker allele substitution effects, but it is known that these effects may be correlated. In statistics, graphical models have been identified as a useful tool for covariance estimation in high-dimensional problems and it is an area that has recently experienced a great expansion. In Gaussian covariance graph models (GCovGM), the joint distribution of a set of random variables is assumed to be Gaussian and the pattern of zeros of the covariance matrix is encoded in terms of an undirected graph G. In this study, methods adapting the theory of GCovGM to genome-wide prediction were developed (Bayes GCov, Bayes GCov-KR and Bayes GCov-H). In simulated data sets, improvements in correlation between phenotypes and predicted breeding values and accuracies of predicted breeding values were found. Our models account for correlation of marker effects and permit to accommodate general structures as opposed to models proposed in previous studies, which consider spatial correlation only. In addition, they allow incorporation of biological information in the prediction process through its use when constructing graph G, and their extension to the multi-allelic loci case is straightforward. © 2017 Blackwell Verlag GmbH.

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

PubMed

Chen, Zhaoxue; Chen, Hao

2014-01-01

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

Theoretical investigation of gas-surface interactions

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1990-01-01

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

Gaussian entanglement generation from coherence using beam-splitters

PubMed Central

Wang, Zhong-Xiao; Wang, Shuhao; Ma, Teng; Wang, Tie-Jun; Wang, Chuan

2016-01-01

The generation and quantification of quantum entanglement is crucial for quantum information processing. Here we study the transition of Gaussian correlation under the effect of linear optical beam-splitters. We find the single-mode Gaussian coherence acts as the resource in generating Gaussian entanglement for two squeezed states as the input states. With the help of consecutive beam-splitters, single-mode coherence and quantum entanglement can be converted to each other. Our results reveal that by using finite number of beam-splitters, it is possible to extract all the entanglement from the single-mode coherence even if the entanglement is wiped out before each beam-splitter. PMID:27892537

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

PubMed

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

2018-06-01

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

Periodic boundary conditions for QM/MM calculations: Ewald summation for extended Gaussian basis sets

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

Holden, Zachary C.; Richard, Ryan M.; Herbert, John M., E-mail: herbert@chemistry.ohio-state.edu

2013-12-28

An implementation of Ewald summation for use in mixed quantum mechanics/molecular mechanics (QM/MM) calculations is presented, which builds upon previous work by others that was limited to semi-empirical electronic structure for the QM region. Unlike previous work, our implementation describes the wave function's periodic images using “ChElPG” atomic charges, which are determined by fitting to the QM electrostatic potential evaluated on a real-space grid. This implementation is stable even for large Gaussian basis sets with diffuse exponents, and is thus appropriate when the QM region is described by a correlated wave function. Derivatives of the ChElPG charges with respect tomore » the QM density matrix are a potentially serious bottleneck in this approach, so we introduce a ChElPG algorithm based on atom-centered Lebedev grids. The ChElPG charges thus obtained exhibit good rotational invariance even for sparse grids, enabling significant cost savings. Detailed analysis of the optimal choice of user-selected Ewald parameters, as well as timing breakdowns, is presented.« less

Application of Monte Carlo Method for Evaluation of Uncertainties of ITS-90 by Standard Platinum Resistance Thermometer

NASA Astrophysics Data System (ADS)

Palenčár, Rudolf; Sopkuliak, Peter; Palenčár, Jakub; Ďuriš, Stanislav; Suroviak, Emil; Halaj, Martin

2017-06-01

Evaluation of uncertainties of the temperature measurement by standard platinum resistance thermometer calibrated at the defining fixed points according to ITS-90 is a problem that can be solved in different ways. The paper presents a procedure based on the propagation of distributions using the Monte Carlo method. The procedure employs generation of pseudo-random numbers for the input variables of resistances at the defining fixed points, supposing the multivariate Gaussian distribution for input quantities. This allows taking into account the correlations among resistances at the defining fixed points. Assumption of Gaussian probability density function is acceptable, with respect to the several sources of uncertainties of resistances. In the case of uncorrelated resistances at the defining fixed points, the method is applicable to any probability density function. Validation of the law of propagation of uncertainty using the Monte Carlo method is presented on the example of specific data for 25 Ω standard platinum resistance thermometer in the temperature range from 0 to 660 °C. Using this example, we demonstrate suitability of the method by validation of its results.

Gaussian discriminating strength

NASA Astrophysics Data System (ADS)

Rigovacca, L.; Farace, A.; De Pasquale, A.; Giovannetti, V.

2015-10-01

We present a quantifier of nonclassical correlations for bipartite, multimode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in Farace et al., [New J. Phys. 16, 073010 (2014), 10.1088/1367-2630/16/7/073010]. As the latter the new measure exploits the quantum Chernoff bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam splitter a factorized two-mode thermal state. For these density matrices, we study how nonclassical correlations are related with the entanglement present in the system and with its total photon number.

A perturbative approach to the redshift space correlation function: beyond the Standard Model

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

Bose, Benjamin; Koyama, Kazuya, E-mail: benjamin.bose@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model whichmore » is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with ≤ 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpc h ≤ s ≤ 180Mpc/ h . Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.« less

Statistical analysis of Geopotential Height (GH) timeseries based on Tsallis non-extensive statistical mechanics

NASA Astrophysics Data System (ADS)

Karakatsanis, L. P.; Iliopoulos, A. C.; Pavlos, E. G.; Pavlos, G. P.

2018-02-01

In this paper, we perform statistical analysis of time series deriving from Earth's climate. The time series are concerned with Geopotential Height (GH) and correspond to temporal and spatial components of the global distribution of month average values, during the period (1948-2012). The analysis is based on Tsallis non-extensive statistical mechanics and in particular on the estimation of Tsallis' q-triplet, namely {qstat, qsens, qrel}, the reconstructed phase space and the estimation of correlation dimension and the Hurst exponent of rescaled range analysis (R/S). The deviation of Tsallis q-triplet from unity indicates non-Gaussian (Tsallis q-Gaussian) non-extensive character with heavy tails probability density functions (PDFs), multifractal behavior and long range dependences for all timeseries considered. Also noticeable differences of the q-triplet estimation found in the timeseries at distinct local or temporal regions. Moreover, in the reconstructive phase space revealed a lower-dimensional fractal set in the GH dynamical phase space (strong self-organization) and the estimation of Hurst exponent indicated multifractality, non-Gaussianity and persistence. The analysis is giving significant information identifying and characterizing the dynamical characteristics of the earth's climate.

Optimal Filter Estimation for Lucas-Kanade Optical Flow

PubMed Central

Sharmin, Nusrat; Brad, Remus

2012-01-01

Optical flow algorithms offer a way to estimate motion from a sequence of images. The computation of optical flow plays a key-role in several computer vision applications, including motion detection and segmentation, frame interpolation, three-dimensional scene reconstruction, robot navigation and video compression. In the case of gradient based optical flow implementation, the pre-filtering step plays a vital role, not only for accurate computation of optical flow, but also for the improvement of performance. Generally, in optical flow computation, filtering is used at the initial level on original input images and afterwards, the images are resized. In this paper, we propose an image filtering approach as a pre-processing step for the Lucas-Kanade pyramidal optical flow algorithm. Based on a study of different types of filtering methods and applied on the Iterative Refined Lucas-Kanade, we have concluded on the best filtering practice. As the Gaussian smoothing filter was selected, an empirical approach for the Gaussian variance estimation was introduced. Tested on the Middlebury image sequences, a correlation between the image intensity value and the standard deviation value of the Gaussian function was established. Finally, we have found that our selection method offers a better performance for the Lucas-Kanade optical flow algorithm.

Entanglement and purity of two-mode Gaussian states in noisy channels

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

Serafini, Alessio; Illuminati, Fabrizio; De Siena, Silvio

2004-02-01

We study the evolution of purity, entanglement, and total correlations of general two-mode continuous variable Gaussian states in arbitrary uncorrelated Gaussian environments. The time evolution of purity, von Neumann entropy, logarithmic negativity, and mutual information is analyzed for a wide range of initial conditions. In general, we find that a local squeezing of the bath leads to a faster degradation of purity and entanglement, while it can help to preserve the mutual information between the modes.

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

NASA Astrophysics Data System (ADS)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

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

A generalized non-Gaussian consistency relation for single field inflation

NASA Astrophysics Data System (ADS)

Bravo, Rafael; Mooij, Sander; Palma, Gonzalo A.; Pradenas, Bastián

2018-05-01

We show that a perturbed inflationary spacetime, driven by a canonical single scalar field, is invariant under a special class of coordinate transformations together with a field reparametrization of the curvature perturbation in co-moving gauge. This transformation may be used to derive the squeezed limit of the 3-point correlation function of the co-moving curvature perturbations valid in the case that these do not freeze after horizon crossing. This leads to a generalized version of Maldacena's non-Gaussian consistency relation in the sense that the bispectrum squeezed limit is completely determined by spacetime diffeomorphisms. Just as in the case of the standard consistency relation, this result may be understood as the consequence of how long-wavelength modes modulate those of shorter wavelengths. This relation allows one to derive the well known violation to the consistency relation encountered in ultra slow-roll, where curvature perturbations grow exponentially after horizon crossing.

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

PubMed

Reddy, Ch Sridhar; Prasad, M Durga

2016-04-28

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

GAUSSIAN 76: An ab initio Molecular Orbital Program

DOE R&D Accomplishments Database

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

1978-01-01

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

Large-deviation probabilities for correlated Gaussian processes and intermittent dynamical systems

NASA Astrophysics Data System (ADS)

Massah, Mozhdeh; Nicol, Matthew; Kantz, Holger

2018-05-01

In its classical version, the theory of large deviations makes quantitative statements about the probability of outliers when estimating time averages, if time series data are identically independently distributed. We study large-deviation probabilities (LDPs) for time averages in short- and long-range correlated Gaussian processes and show that long-range correlations lead to subexponential decay of LDPs. A particular deterministic intermittent map can, depending on a control parameter, also generate long-range correlated time series. We illustrate numerically, in agreement with the mathematical literature, that this type of intermittency leads to a power law decay of LDPs. The power law decay holds irrespective of whether the correlation time is finite or infinite, and hence irrespective of whether the central limit theorem applies or not.

Comparing the structure of an emerging market with a mature one under global perturbation

NASA Astrophysics Data System (ADS)

Namaki, A.; Jafari, G. R.; Raei, R.

2011-09-01

In this paper we investigate the Tehran stock exchange (TSE) and Dow Jones Industrial Average (DJIA) in terms of perturbed correlation matrices. To perturb a stock market, there are two methods, namely local and global perturbation. In the local method, we replace a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series, whereas in the global method, we reconstruct the correlation matrix after replacing the original return series with Gaussian-distributed time series. The local perturbation is just a technical study. We analyze these markets through two statistical approaches, random matrix theory (RMT) and the correlation coefficient distribution. By using RMT, we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks. We find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with Gaussian-distributed time series, the mean values of correlation coefficients, the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the RMT prediction fall sharply in both markets. By comparing these two markets, we can see that the DJIA is more sensitive to global perturbations. These findings are crucial for risk management and portfolio selection.

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

DTIC Science & Technology

1987-09-18

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

Selective Attention in Pigeon Temporal Discrimination.

PubMed

Subramaniam, Shrinidhi; Kyonka, Elizabeth

2017-07-27

Cues can vary in how informative they are about when specific outcomes, such as food availability, will occur. This study was an experimental investigation of the functional relation between cue informativeness and temporal discrimination in a peak-interval (PI) procedure. Each session consisted of fixed-interval (FI) 2-s and 4-s schedules of food and occasional, 12-s PI trials during which pecks had no programmed consequences. Across conditions, the phi (ϕ) correlation between key light color and FI schedule value was manipulated. Red and green key lights signaled the onset of either or both FI schedules. Different colors were either predictive (ϕ = 1), moderately predictive (ϕ = 0.2-0.8), or not predictive (ϕ = 0) of a specific FI schedule. This study tested the hypothesis that temporal discrimination is a function of the momentary conditional probability of food; that is, pigeons peck the most at either 2 s or 4 s when ϕ = 1 and peck at both intervals when ϕ < 1. Response distributions were bimodal Gaussian curves; distributions from red- and green-key PI trials converged when ϕ ≤ 0.6. Peak times estimated by summed Gaussian functions, averaged across conditions and pigeons, were 1.85 s and 3.87 s, however, pigeons did not always maximize the momentary probability of food. When key light color was highly correlated with FI schedules (ϕ ≥ 0.6), estimates of peak times indicated that temporal discrimination accuracy was reduced at the unlikely interval, but not the likely interval. The mechanism of this reduced temporal discrimination accuracy could be interpreted as an attentional process.

Correlation Between Analog Noise Measurements and the Expected Bit Error Rate of a Digital Signal Propagating Through Passive Components

NASA Technical Reports Server (NTRS)

Warner, Joseph D.; Theofylaktos, Onoufrios

2012-01-01

A method of determining the bit error rate (BER) of a digital circuit from the measurement of the analog S-parameters of the circuit has been developed. The method is based on the measurement of the noise and the standard deviation of the noise in the S-parameters. Once the standard deviation and the mean of the S-parameters are known, the BER of the circuit can be calculated using the normal Gaussian function.

Condensate statistics in interacting and ideal dilute bose gases

PubMed

Kocharovsky; Kocharovsky; Scully

2000-03-13

We obtain analytical formulas for the statistics, in particular, for the characteristic function and all cumulants, of the Bose-Einstein condensate in dilute weakly interacting and ideal equilibrium gases in the canonical ensemble via the particle-number-conserving operator formalism of Girardeau and Arnowitt. We prove that the ground-state occupation statistics is not Gaussian even in the thermodynamic limit. We calculate the effect of Bogoliubov coupling on suppression of ground-state occupation fluctuations and show that they are governed by a pair-correlation, squeezing mechanism.

Tsallis non-extensive statistics and solar wind plasma complexity

NASA Astrophysics Data System (ADS)

Pavlos, G. P.; Iliopoulos, A. C.; Zastenker, G. N.; Zelenyi, L. M.; Karakatsanis, L. P.; Riazantseva, M. O.; Xenakis, M. N.; Pavlos, E. G.

2015-03-01

This article presents novel results revealing non-equilibrium phase transition processes in the solar wind plasma during a strong shock event, which took place on 26th September 2011. Solar wind plasma is a typical case of stochastic spatiotemporal distribution of physical state variables such as force fields (B → , E →) and matter fields (particle and current densities or bulk plasma distributions). This study shows clearly the non-extensive and non-Gaussian character of the solar wind plasma and the existence of multi-scale strong correlations from the microscopic to the macroscopic level. It also underlines the inefficiency of classical magneto-hydro-dynamic (MHD) or plasma statistical theories, based on the classical central limit theorem (CLT), to explain the complexity of the solar wind dynamics, since these theories include smooth and differentiable spatial-temporal functions (MHD theory) or Gaussian statistics (Boltzmann-Maxwell statistical mechanics). On the contrary, the results of this study indicate the presence of non-Gaussian non-extensive statistics with heavy tails probability distribution functions, which are related to the q-extension of CLT. Finally, the results of this study can be understood in the framework of modern theoretical concepts such as non-extensive statistical mechanics (Tsallis, 2009), fractal topology (Zelenyi and Milovanov, 2004), turbulence theory (Frisch, 1996), strange dynamics (Zaslavsky, 2002), percolation theory (Milovanov, 1997), anomalous diffusion theory and anomalous transport theory (Milovanov, 2001), fractional dynamics (Tarasov, 2013) and non-equilibrium phase transition theory (Chang, 1992).

Nonperturbative-transverse-momentum effects and evolution in dihadron and direct photon-hadron angular correlations in p +p collisions at √{s } =510 GeV

NASA Astrophysics Data System (ADS)

Adare, A.; Aidala, C.; Ajitanand, N. N.; Akiba, Y.; Akimoto, R.; Alexander, J.; Alfred, M.; Andrieux, V.; Aoki, K.; Apadula, N.; Aramaki, Y.; Asano, H.; Atomssa, E. T.; Awes, T. C.; Ayuso, C.; Azmoun, B.; Babintsev, V.; Bai, M.; Bai, X.; Bandara, N. S.; Bannier, B.; Barish, K. N.; Bathe, S.; Baublis, V.; Baumann, C.; Baumgart, S.; Bazilevsky, A.; Beaumier, M.; Beckman, S.; Belmont, R.; Berdnikov, A.; Berdnikov, Y.; Black, D.; Blau, D. S.; Boer, M.; Bok, J. S.; Boyle, K.; Brooks, M. L.; Bryslawskyj, J.; Buesching, H.; Bumazhnov, V.; Butler, C.; Butsyk, S.; Campbell, S.; Canoa Roman, V.; Cervantes, R.; Chen, C.-H.; Chi, C. Y.; Chiu, M.; Choi, I. J.; Choi, J. B.; Choi, S.; Christiansen, P.; Chujo, T.; Cianciolo, V.; Citron, Z.; Cole, B. A.; Connors, M.; Cronin, N.; Crossette, N.; Csanád, M.; Csörgő, T.; Danley, T. W.; Datta, A.; Daugherity, M. S.; David, G.; Deblasio, K.; Dehmelt, K.; Denisov, A.; Deshpande, A.; Desmond, E. J.; Ding, L.; Dion, A.; Dixit, D.; Do, J. H.; D'Orazio, L.; Drapier, O.; Drees, A.; Drees, K. A.; Dumancic, M.; Durham, J. M.; Durum, A.; Elder, T.; Engelmore, T.; Enokizono, A.; En'yo, H.; Esumi, S.; Eyser, K. O.; Fadem, B.; Fan, W.; Feege, N.; Fields, D. E.; Finger, M.; Finger, M.; Fleuret, F.; Fokin, S. L.; Frantz, J. E.; Franz, A.; Frawley, A. D.; Fukao, Y.; Fukuda, Y.; Fusayasu, T.; Gainey, K.; Gal, C.; Gallus, P.; Garg, P.; Garishvili, A.; Garishvili, I.; Ge, H.; Giordano, F.; Glenn, A.; Gong, X.; Gonin, M.; Goto, Y.; Granier de Cassagnac, R.; Grau, N.; Greene, S. V.; Grosse Perdekamp, M.; Gu, Y.; Gunji, T.; Guragain, H.; Hachiya, T.; Haggerty, J. S.; Hahn, K. I.; Hamagaki, H.; Hamilton, H. F.; Han, S. Y.; Hanks, J.; Hasegawa, S.; Haseler, T. O. S.; Hashimoto, K.; Hayano, R.; He, X.; Hemmick, T. K.; Hester, T.; Hill, J. C.; Hill, K.; Hollis, R. S.; Homma, K.; Hong, B.; Hoshino, T.; Hotvedt, N.; Huang, J.; Huang, S.; Ichihara, T.; Ikeda, Y.; Imai, K.; Imazu, Y.; Imrek, J.; Inaba, M.; Iordanova, A.; Isenhower, D.; Isinhue, A.; Ito, Y.; Ivanishchev, D.; Jacak, B. V.; Jeon, S. J.; Jezghani, M.; Ji, Z.; Jia, J.; Jiang, X.; Johnson, B. M.; Joo, E.; Joo, K. S.; Jorjadze, V.; Jouan, D.; Jumper, D. S.; Kamin, J.; Kanda, S.; Kang, B. H.; Kang, J. H.; Kang, J. S.; Kapukchyan, D.; Kapustinsky, J.; Karthas, S.; Kawall, D.; Kazantsev, A. V.; Key, J. A.; Khachatryan, V.; Khandai, P. K.; Khanzadeev, A.; Kihara, K.; Kijima, K. M.; Kim, C.; Kim, D. H.; Kim, D. J.; Kim, E.-J.; Kim, H.-J.; Kim, M. H.; Kim, M.; Kim, Y.-J.; Kim, Y. K.; Kincses, D.; Kistenev, E.; Klatsky, J.; Kleinjan, D.; Kline, P.; Koblesky, T.; Kofarago, M.; Komkov, B.; Koster, J.; Kotchetkov, D.; Kotov, D.; Krizek, F.; Kudo, S.; Kurita, K.; Kurosawa, M.; Kwon, Y.; Lacey, R.; Lai, Y. S.; Lajoie, J. G.; Lallow, E. O.; Lebedev, A.; Lee, D. M.; Lee, G. H.; Lee, J.; Lee, K. B.; Lee, K. S.; Lee, S.; Lee, S. H.; Leitch, M. J.; Leitgab, M.; Leung, Y. H.; Lewis, B.; Lewis, N. A.; Li, X.; Li, X.; Lim, S. H.; Liu, L. D.; Liu, M. X.; Loggins, V.-R.; Loggins, V.-R.; Lovasz, K.; Lynch, D.; Maguire, C. F.; Majoros, T.; Makdisi, Y. I.; Makek, M.; Malaev, M.; Manion, A.; Manko, V. I.; Mannel, E.; Masuda, H.; McCumber, M.; McGaughey, P. L.; McGlinchey, D.; McKinney, C.; Meles, A.; Mendoza, M.; Meredith, B.; Miake, Y.; Mibe, T.; Mignerey, A. C.; Mihalik, D. E.; Miller, A. J.; Milov, A.; Mishra, D. K.; Mitchell, J. T.; Mitsuka, G.; Miyasaka, S.; Mizuno, S.; Mohanty, A. K.; Mohapatra, S.; Montuenga, P.; Moon, T.; Morrison, D. P.; Morrow, S. I. M.; Moskowitz, M.; Moukhanova, T. V.; Murakami, T.; Murata, J.; Mwai, A.; Nagae, T.; Nagai, K.; Nagamiya, S.; Nagashima, K.; Nagashima, T.; Nagle, J. L.; Nagy, M. I.; Nakagawa, I.; Nakagomi, H.; Nakamiya, Y.; Nakamura, K. R.; Nakamura, T.; Nakano, K.; Nattrass, C.; Netrakanti, P. K.; Nihashi, M.; Niida, T.; Nouicer, R.; Novák, T.; Novitzky, N.; Novotny, R.; Nyanin, A. S.; O'Brien, E.; Ogilvie, C. A.; Oide, H.; Okada, K.; Orjuela Koop, J. D.; Osborn, J. D.; Oskarsson, A.; Ottino, G. J.; Ozawa, K.; Pak, R.; Pantuev, V.; Papavassiliou, V.; Park, I. H.; Park, J. S.; Park, S.; Park, S. K.; Pate, S. F.; Patel, L.; Patel, M.; Peng, J.-C.; Peng, W.; Perepelitsa, D. V.; Perera, G. D. N.; Peressounko, D. Yu.; Perezlara, C. E.; Perry, J.; Petti, R.; Phipps, M.; Pinkenburg, C.; Pinson, R.; Pisani, R. P.; Pun, A.; Purschke, M. L.; Qu, H.; Rak, J.; Ravinovich, I.; Read, K. F.; Reynolds, D.; Riabov, V.; Riabov, Y.; Richardson, E.; Richford, D.; Rinn, T.; Riveli, N.; Roach, D.; Rolnick, S. D.; Rosati, M.; Rowan, Z.; Rubin, J. G.; Runchey, J.; Ryu, M. S.; Safonov, A. S.; Sahlmueller, B.; Saito, N.; Sakaguchi, T.; Sako, H.; Samsonov, V.; Sarsour, M.; Sato, K.; Sato, S.; Sawada, S.; Schaefer, B.; Schmoll, B. K.; Schmoll, B. K.; Sedgwick, K.; Seele, J.; Seidl, R.; Sekiguchi, Y.; Sen, A.; Seto, R.; Sett, P.; Sexton, A.; Sharma, D.; Shaver, A.; Shein, I.; Shibata, T.-A.; Shigaki, K.; Shimomura, M.; Shioya, T.; Shoji, K.; Shukla, P.; Sickles, A.; Silva, C. L.; Silvermyr, D.; Singh, B. K.; Singh, C. P.; Singh, V.; Skolnik, M.; Slunečka, M.; Smith, K. L.; Snowball, M.; Solano, S.; Soltz, R. A.; Sondheim, W. E.; Sorensen, S. P.; Sourikova, I. V.; Stankus, P. W.; Steinberg, P.; Stenlund, E.; Stepanov, M.; Ster, A.; Stoll, S. P.; Stone, M. R.; Sugitate, T.; Sukhanov, A.; Sumita, T.; Sun, J.; Syed, S.; Sziklai, J.; Takahara, A.; Takeda, A.; Taketani, A.; Tanaka, Y.; Tanida, K.; Tannenbaum, M. J.; Tarafdar, S.; Taranenko, A.; Tarnai, G.; Tennant, E.; Tieulent, R.; Timilsina, A.; Todoroki, T.; Tomášek, M.; Torii, H.; Towell, C. L.; Towell, M.; Towell, R.; Towell, R. S.; Tserruya, I.; Ueda, Y.; Ujvari, B.; van Hecke, H. W.; Vargyas, M.; Vazquez-Carson, S.; Vazquez-Zambrano, E.; Veicht, A.; Velkovska, J.; Vértesi, R.; Virius, M.; Vrba, V.; Vukman, N.; Vznuzdaev, E.; Wang, X. R.; Wang, Z.; Watanabe, D.; Watanabe, K.; Watanabe, Y.; Watanabe, Y. S.; Wei, F.; Whitaker, S.; Wolin, S.; Wong, C. P.; Woody, C. L.; Wysocki, M.; Xia, B.; Xu, C.; Xu, Q.; Xue, L.; Yalcin, S.; Yamaguchi, Y. L.; Yamamoto, H.; Yanovich, A.; Yin, P.; Yokkaichi, S.; Yoo, J. H.; Yoon, I.; You, Z.; Younus, I.; Yu, H.; Yushmanov, I. E.; Zajc, W. A.; Zelenski, A.; Zharko, S.; Zhou, S.; Zou, L.; Phenix Collaboration

2017-04-01

Dihadron and isolated direct photon-hadron angular correlations are measured in p +p collisions at √{s }=510 GeV . Correlations of charged hadrons of 0.7

Pairing versus quarteting coherence length

NASA Astrophysics Data System (ADS)

Delion, D. S.; Baran, V. V.

2015-02-01

We systematically analyze the coherence length in even-even nuclei. The pairing coherence length in the spin-singlet channel for the effective density-dependent delta (DDD) and Gaussian interaction is estimated. We consider in our calculations bound states as well as narrow resonances. It turns out that the pairing gaps given by the DDD interaction are similar to those of the Gaussian potential if one renormalizes the radial width to the nuclear radius. The correlations induced by the pairing interaction have, in all considered cases, a long-range character inside the nucleus and a decrease towards the surface. The mean coherence length is larger than the geometrical radius for light nuclei and approaches this value for heavy nuclei. The effect of the temperature and states in the continuum is investigated. Strong shell effects are put in evidence, especially for protons. We generalize this concept to quartets by considering similar relations, but between proton and neutron pairs. The quartet coherence length has a similar shape, but with larger values on the nuclear surface. We provide evidence of the important role of proton-neutron correlations by estimating the so-called alpha coherence length, which takes into account the overlap with the proton-neutron part of the α -particle wave function. It turns out that it does not depend on the nuclear size and has a value comparable to the free α -particle radius. We have shown that pairing correlations are mainly concentrated inside the nucleus, while quarteting correlations are connected to the nuclear surface.

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.

Multi-resolution analysis for region of interest extraction in thermographic nondestructive evaluation

NASA Astrophysics Data System (ADS)

Ortiz-Jaramillo, B.; Fandiño Toro, H. A.; Benitez-Restrepo, H. D.; Orjuela-Vargas, S. A.; Castellanos-Domínguez, G.; Philips, W.

2012-03-01

Infrared Non-Destructive Testing (INDT) is known as an effective and rapid method for nondestructive inspection. It can detect a broad range of near-surface structuring flaws in metallic and composite components. Those flaws are modeled as a smooth contour centered at peaks of stored thermal energy, termed Regions of Interest (ROI). Dedicated methodologies must detect the presence of those ROIs. In this paper, we present a methodology for ROI extraction in INDT tasks. The methodology deals with the difficulties due to the non-uniform heating. The non-uniform heating affects low spatial/frequencies and hinders the detection of relevant points in the image. In this paper, a methodology for ROI extraction in INDT using multi-resolution analysis is proposed, which is robust to ROI low contrast and non-uniform heating. The former methodology includes local correlation, Gaussian scale analysis and local edge detection. In this methodology local correlation between image and Gaussian window provides interest points related to ROIs. We use a Gaussian window because thermal behavior is well modeled by Gaussian smooth contours. Also, the Gaussian scale is used to analyze details in the image using multi-resolution analysis avoiding low contrast, non-uniform heating and selection of the Gaussian window size. Finally, local edge detection is used to provide a good estimation of the boundaries in the ROI. Thus, we provide a methodology for ROI extraction based on multi-resolution analysis that is better or equal compared with the other dedicate algorithms proposed in the state of art.

Dynamic Socialized Gaussian Process Models for Human Behavior Prediction in a Health Social Network

PubMed Central

Shen, Yelong; Phan, NhatHai; Xiao, Xiao; Jin, Ruoming; Sun, Junfeng; Piniewski, Brigitte; Kil, David; Dou, Dejing

2016-01-01

Modeling and predicting human behaviors, such as the level and intensity of physical activity, is a key to preventing the cascade of obesity and helping spread healthy behaviors in a social network. In our conference paper, we have developed a social influence model, named Socialized Gaussian Process (SGP), for socialized human behavior modeling. Instead of explicitly modeling social influence as individuals' behaviors influenced by their friends' previous behaviors, SGP models the dynamic social correlation as the result of social influence. The SGP model naturally incorporates personal behavior factor and social correlation factor (i.e., the homophily principle: Friends tend to perform similar behaviors) into a unified model. And it models the social influence factor (i.e., an individual's behavior can be affected by his/her friends) implicitly in dynamic social correlation schemes. The detailed experimental evaluation has shown the SGP model achieves better prediction accuracy compared with most of baseline methods. However, a Socialized Random Forest model may perform better at the beginning compared with the SGP model. One of the main reasons is the dynamic social correlation function is purely based on the users' sequential behaviors without considering other physical activity-related features. To address this issue, we further propose a novel “multi-feature SGP model” (mfSGP) which improves the SGP model by using multiple physical activity-related features in the dynamic social correlation learning. Extensive experimental results illustrate that the mfSGP model clearly outperforms all other models in terms of prediction accuracy and running time. PMID:27746515

BAO from Angular Clustering: Optimization and Mitigation of Theoretical Systematics

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

Crocce, M.; et al.

We study the theoretical systematics and optimize the methodology in Baryon Acoustic Oscillations (BAO) detections using the angular correlation function with tomographic bins. We calibrate and optimize the pipeline for the Dark Energy Survey Year 1 dataset using 1800 mocks. We compare the BAO fitting results obtained with three estimators: the Maximum Likelihood Estimator (MLE), Profile Likelihood, and Markov Chain Monte Carlo. The MLE method yields the least bias in the fit results (bias/spreadmore » $$\\sim 0.02$$) and the error bar derived is the closest to the Gaussian results (1% from 68% Gaussian expectation). When there is mismatch between the template and the data either due to incorrect fiducial cosmology or photo-$z$ error, the MLE again gives the least-biased results. The BAO angular shift that is estimated based on the sound horizon and the angular diameter distance agree with the numerical fit. Various analysis choices are further tested: the number of redshift bins, cross-correlations, and angular binning. We propose two methods to correct the mock covariance when the final sample properties are slightly different from those used to create the mock. We show that the sample changes can be accommodated with the help of the Gaussian covariance matrix or more effectively using the eigenmode expansion of the mock covariance. The eigenmode expansion is significantly less susceptible to statistical fluctuations relative to the direct measurements of the covariance matrix because the number of free parameters is substantially reduced [$p$ parameters versus $p(p+1)/2$ from direct measurement].« less

Genuine multipartite entanglement of symmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure

NASA Astrophysics Data System (ADS)

Adesso, Gerardo; Illuminati, Fabrizio

2008-10-01

We investigate the structural aspects of genuine multipartite entanglement in Gaussian states of continuous variable systems. Generalizing the results of Adesso and Illuminati [Phys. Rev. Lett. 99, 150501 (2007)], we analyze whether the entanglement shared by blocks of modes distributes according to a strong monogamy law. This property, once established, allows us to quantify the genuine N -partite entanglement not encoded into 2,…,K,…,(N-1) -partite quantum correlations. Strong monogamy is numerically verified, and the explicit expression of the measure of residual genuine multipartite entanglement is analytically derived, by a recursive formula, for a subclass of Gaussian states. These are fully symmetric (permutation-invariant) states that are multipartitioned into blocks, each consisting of an arbitrarily assigned number of modes. We compute the genuine multipartite entanglement shared by the blocks of modes and investigate its scaling properties with the number and size of the blocks, the total number of modes, the global mixedness of the state, and the squeezed resources needed for state engineering. To achieve the exact computation of the block entanglement, we introduce and prove a general result of symplectic analysis: Correlations among K blocks in N -mode multisymmetric and multipartite Gaussian states, which are locally invariant under permutation of modes within each block, can be transformed by a local (with respect to the partition) unitary operation into correlations shared by K single modes, one per block, in effective nonsymmetric states where N-K modes are completely uncorrelated. Due to this theorem, the above results, such as the derivation of the explicit expression for the residual multipartite entanglement, its nonnegativity, and its scaling properties, extend to the subclass of non-symmetric Gaussian states that are obtained by the unitary localization of the multipartite entanglement of symmetric states. These findings provide strong numerical evidence that the distributed Gaussian entanglement is strongly monogamous under and possibly beyond specific symmetry constraints, and that the residual continuous-variable tangle is a proper measure of genuine multipartite entanglement for permutation-invariant Gaussian states under any multipartition of the modes.

Matter bounce cosmology with a generalized single field: non-Gaussianity and an extended no-go theorem

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

Additivity of nonsimultaneous masking for short Gaussian-shaped sinusoids.

PubMed

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

2011-02-01

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

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

PubMed

Lin, Chuan-Kai; Wang, Sheng-De

2004-11-01

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

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

PubMed

Kang; Ih; Kim; Kim

2000-03-01

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

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.

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.

Effect of central obscuration on the LDR point spread function

NASA Technical Reports Server (NTRS)

Vanzyl, Jakob J.

1988-01-01

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

Estimation of the four-wave mixing noise probability-density function by the multicanonical Monte Carlo method.

PubMed

Neokosmidis, Ioannis; Kamalakis, Thomas; Chipouras, Aristides; Sphicopoulos, Thomas

2005-01-01

The performance of high-powered wavelength-division multiplexed (WDM) optical networks can be severely degraded by four-wave-mixing- (FWM-) induced distortion. The multicanonical Monte Carlo method (MCMC) is used to calculate the probability-density function (PDF) of the decision variable of a receiver, limited by FWM noise. Compared with the conventional Monte Carlo method previously used to estimate this PDF, the MCMC method is much faster and can accurately estimate smaller error probabilities. The method takes into account the correlation between the components of the FWM noise, unlike the Gaussian model, which is shown not to provide accurate results.

Digital image analysis of a turbulent flame

NASA Astrophysics Data System (ADS)

Zucherman, L.; Kawall, J. G.; Keffer, J. F.

1988-01-01

Digital image analysis of cine pictures of an unconfined rich premixed turbulent flame has been used to determine structural characteristics of the turbulent/non-turbulent interface of the flame. The results, comprising various moments of the interface position, probability density functions and correlation functions, establish that the instantaneous flame-interface position is essentially a Gaussian random variable with a superimposed quasi-periodical component. The latter is ascribable to a pulsation caused by the convection and the stretching of ring vortices present within the flame. To a first approximation, the flame can be considered similar to a three-dimensional axisymmetric turbulent jet, with superimposed ring vortices, in which combustion occurs.

Correlators in tensor models from character calculus

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2017-11-01

We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz) character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.

Geographically weighted regression model on poverty indicator

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

NASA Astrophysics Data System (ADS)

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

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

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

PubMed

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

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

Logarithmic violation of scaling in anisotropic kinematic dynamo model

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2016-01-01

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝δ (t -t')/k⊥d-1 +ξ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to the distinguished direction. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: instead of power-like corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L.

Gaussian basis functions for highly oscillatory scattering wavefunctions

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

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

NASA Astrophysics Data System (ADS)

Lasuik, J.; Shalchi, A.

2018-06-01

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

Pedagogical introduction to the entropy of entanglement for Gaussian states

NASA Astrophysics Data System (ADS)

Demarie, Tommaso F.

2018-05-01

In quantum information theory, the entropy of entanglement is a standard measure of bipartite entanglement between two partitions of a composite system. For a particular class of continuous variable quantum states, the Gaussian states, the entropy of entanglement can be expressed elegantly in terms of symplectic eigenvalues, elements that characterise a Gaussian state and depend on the correlations of the canonical variables. We give a rigorous step-by-step derivation of this result and provide physical insights, together with an example that can be useful in practice for calculations.

Hybrid [¹⁸F]-FDG PET/MRI including non-Gaussian diffusion-weighted imaging (DWI): preliminary results in non-small cell lung cancer (NSCLC).

PubMed

Heusch, Philipp; Köhler, Jens; Wittsack, Hans-Joerg; Heusner, Till A; Buchbender, Christian; Poeppel, Thorsten D; Nensa, Felix; Wetter, Axel; Gauler, Thomas; Hartung, Verena; Lanzman, Rotem S

2013-11-01

To assess the feasibility of non-Gaussian DWI as part of a FDG-PET/MRI protocol in patients with histologically proven non-small cell lung cancer. 15 consecutive patients with histologically proven NSCLC (mean age 61 ± 11 years) were included in this study and underwent whole-body FDG-PET/MRI following whole-body FDG-PET/CT. As part of the whole-body FDG-PET/MRI protocol, an EPI-sequence with 5 b-values (0, 100, 500, 1000 and 2000 s/mm(2)) was acquired for DWI of the thorax during free-breathing. Volume of interest (VOI) measurements were performed to determine the maximum and mean standardized uptake value (SUV(max); SUV(mean)). A region of interest (ROI) was manually drawn around the tumor on b=0 images and then transferred to the corresponding parameter maps to assess ADC(mono), D(app) and K(app). To assess the goodness of the mathematical fit R(2) was calculated for monoexponential and non-Gaussian analysis. Spearman's correlation coefficients were calculated to compare SUV values and diffusion coefficients. A Student's t-test was performed to compare the monoexponential and non-Gaussian diffusion fitting (R(2)). T staging was equal between FDG-PET/CT and FDG-PET/MRI in 12 of 15 patients. For NSCLC, mean ADC(mono) was 2.11 ± 1.24 × 10(-3) mm(2)/s, Dapp was 2.46 ± 1.29 × 10(-3) mm(2)/s and mean Kapp was 0.70 ± 0.21. The non-Gaussian diffusion analysis (R(2)=0.98) provided a significantly better mathematical fitting to the DWI signal decay than the monoexponetial analysis (R(2)=0.96) (p<0.001). SUV(max) and SUV(mean) of NSCLC was 13.5 ± 7.6 and 7.9 ± 4.3 for FDG-PET/MRI. ADC(mono) as well as Dapp exhibited a significant inverse correlation with the SUV(max) (ADC(mono): R=-0.67; p<0.01; Dapp: R=-0.69; p<0.01) as well as with SUV(mean) assessed by FDG-PET/MRI (ADC(mono): R=-0.66; p<0.01; Dapp: R=-0.69; p<0.01). Furthermore, Kapp exhibited a significant correlation with SUV(max) (R=0.72; p<0.05) and SUV(mean) as assessed by FDG-PET/MRI (R=0.71; p<0.005). Simultaneous PET and non-Gaussian diffusion acquisitions are feasible. Non-Gaussian diffusion parameters show a good correlation with SUV and might provide additional information beyond monoexponential ADC, especially as non-Gaussian diffusion exhibits better mathematical fitting to the decay of the diffusion signal than monoexponential DWI. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Halo correlations in nonlinear cosmic density fields

NASA Astrophysics Data System (ADS)

Bernardeau, F.; Schaeffer, R.

1999-09-01

The question we address in this paper is the determination of the correlation properties of the dark matter halos appearing in cosmic density fields once they underwent a strongly nonlinear evolution induced by gravitational dynamics. A series of previous works have given indications that kind of non-Gaussian features are induced by nonlinear evolution in term of the high-order correlation functions. Assuming such patterns for the matter field, i.e. that the high-order correlation functions behave as products of two-body correlation functions, we derive the correlation properties of the halos, that are assumed to represent the correlation properties of galaxies or clusters. The hierarchical pattern originally induced by gravity is shown to be conserved for the halos. The strength of their correlations at any order varies, however, but is found to depend only on their internal properties, namely on the parameter x~ m/r(3-gamma ) where m is the mass of the halo, r its size and gamma is the power law index of the two-body correlation function. This internal parameter is seen to be close to the depth of the internal potential well of virialized objects. We were able to derive the explicit form of the generating function of the moments of the halo counts probability distribution function. In particular we show explicitly that, generically, S_P(x)-> P(P-2) in the rare halo limit. Various illustrations of our general results are presented. As a function of the properties of the underlying matter field, we construct the count probabilities for halos and in particular discuss the halo void probability. We evaluate the dependence of the halo mass function on the environment: within clusters, hierarchical clustering implies the higher masses are favored. These properties solely arise from what is a natural bias (ie, naturally induced by gravity) between the observed objects and the unseen matter field, and how it manifests itself depending on which selection effects are imposed.

Truncated Gaussians as tolerance sets

NASA Technical Reports Server (NTRS)

Cozman, Fabio; Krotkov, Eric

1994-01-01

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

A path integral approach to the Hodgkin-Huxley model

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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.

Optimal modeling of 1D azimuth correlations in the context of Bayesian inference

NASA Astrophysics Data System (ADS)

De Kock, Michiel B.; Eggers, Hans C.; Trainor, Thomas A.

2015-09-01

Analysis and interpretation of spectrum and correlation data from high-energy nuclear collisions is currently controversial because two opposing physics narratives derive contradictory implications from the same data, one narrative claiming collision dynamics is dominated by dijet production and projectile-nucleon fragmentation, the other claiming collision dynamics is dominated by a dense, flowing QCD medium. Opposing interpretations seem to be supported by alternative data models, and current model-comparison schemes are unable to distinguish between them. There is clearly need for a convincing new methodology to break the deadlock. In this study we introduce Bayesian inference (BI) methods applied to angular correlation data as a basis to evaluate competing data models. For simplicity the data considered are projections of two-dimensional (2D) angular correlations onto a 1D azimuth from three centrality classes of 200-GeV Au-Au collisions. We consider several data models typical of current model choices, including Fourier series (FS) and a Gaussian plus various combinations of individual cosine components. We evaluate model performance with BI methods and with power-spectrum analysis. We find that FS-only models are rejected in all cases by Bayesian analysis, which always prefers a Gaussian. A cylindrical quadrupole cos(2 ϕ ) is required in some cases but rejected for 0%-5%-central Au-Au collisions. Given a Gaussian centered at the azimuth origin, "higher harmonics" cos(m ϕ ) for m >2 are rejected. A model consisting of Gaussian +dipole cos(ϕ )+quadrupole cos(2 ϕ ) provides good 1D data descriptions in all cases.

Stability of Ince-Gaussian beams in elliptical core few-mode fibers.

PubMed

Sakpal, Sahil; Milione, Giovanni; Li, Min-Jun; Nouri, Mehdi; Shahoei, Hiva; LaFave, Tim; Ashrafi, Solyman; MacFarlane, Duncan

2018-06-01

A comparative stability analysis of Ince-Gaussian and Hermite-Gaussian modes in elliptical core few-mode fibers is provided to inform the design of spatial division multiplexing systems. The correlation method is used to construct crosstalk matrices that characterize the spatial modes of the fiber. Up to six low-order modes are shown to exhibit about -20  dB crosstalk. The crosstalk performance of each mode set is found to be similar. However, a direct comparison between modes of equal Gouy phase shift, a parameter that ensures identical beam quality, and phase at the detector, demonstrates better relative power transmission for Ince-Gaussian beams. This result is consistent with the natural modes supported by a 100 m elliptical core fiber for which a mode ellipticity of ϵ=2 was found to be optimal. The relative power difference is expected to be magnified over longer fiber lengths in favor of Ince-Gaussian modes.

Optimization of spectroscopic surveys for testing non-Gaussianity

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

Raccanelli, Alvise; Doré, Olivier; Dalal, Neal, E-mail: alvise@caltech.edu, E-mail: Olivier.P.Dore@jpl.nasa.gov, E-mail: dalaln@illinois.edu

We investigate optimization strategies to measure primordial non-Gaussianity with future spectroscopic surveys. We forecast measurements coming from the 3D galaxy power spectrum and compute constraints on primordial non-Gaussianity parameters f{sub NL} and n{sub NG}. After studying the dependence on those parameters upon survey specifications such as redshift range, area, number density, we assume a reference mock survey and investigate the trade-off between number density and area surveyed. We then define the observational requirements to reach the detection of f{sub NL} of order 1. Our results show that power spectrum constraints on non-Gaussianity from future spectroscopic surveys can improve on currentmore » CMB limits, but the multi-tracer technique and higher order correlations will be needed in order to reach an even better precision in the measurements of the non-Gaussianity parameter f{sub NL}.« less

Approximate Bayesian computation in large-scale structure: constraining the galaxy-halo connection

NASA Astrophysics Data System (ADS)

Hahn, ChangHoon; Vakili, Mohammadjavad; Walsh, Kilian; Hearin, Andrew P.; Hogg, David W.; Campbell, Duncan

2017-08-01

Standard approaches to Bayesian parameter inference in large-scale structure assume a Gaussian functional form (chi-squared form) for the likelihood. This assumption, in detail, cannot be correct. Likelihood free inferences such as approximate Bayesian computation (ABC) relax these restrictions and make inference possible without making any assumptions on the likelihood. Instead ABC relies on a forward generative model of the data and a metric for measuring the distance between the model and data. In this work, we demonstrate that ABC is feasible for LSS parameter inference by using it to constrain parameters of the halo occupation distribution (HOD) model for populating dark matter haloes with galaxies. Using specific implementation of ABC supplemented with population Monte Carlo importance sampling, a generative forward model using HOD and a distance metric based on galaxy number density, two-point correlation function and galaxy group multiplicity function, we constrain the HOD parameters of mock observation generated from selected 'true' HOD parameters. The parameter constraints we obtain from ABC are consistent with the 'true' HOD parameters, demonstrating that ABC can be reliably used for parameter inference in LSS. Furthermore, we compare our ABC constraints to constraints we obtain using a pseudo-likelihood function of Gaussian form with MCMC and find consistent HOD parameter constraints. Ultimately, our results suggest that ABC can and should be applied in parameter inference for LSS analyses.

The impact of turbulent renewable energy production on power grid stability and quality

NASA Astrophysics Data System (ADS)

Schmietendorf, Katrin; Peinke, Joachim; Kamps, Oliver

2017-11-01

Feed-in fluctuations induced by renewables are one of the key challenges to the stability and quality of electrical power grids. In particular short-term fluctuations disturb the system on a time scale, on which load balancing does not operate yet and the system is intrinsically governed by self-organized synchronization. Wind and solar power are known to be strongly non-Gaussian with intermittent increment statistics in these time scales. We investigate the impact of short-term wind fluctuations on the basis of a Kuramoto-like power grid model considering stability in terms of desynchronization and frequency and voltage quality aspects. We present a procedure to generate realistic feed-in fluctuations with temporal correlations, Kolmogorov power spectrum and intermittent increments. By comparison to correlated Gaussian noise of the same spectrum and Gaussian white noise, we found out that while the correlations are essential to capture the likelihood of severe outages, the intermittent nature of wind power has significant consequences on power quality: intermittency is directly transferred into frequency and voltage fluctuations yielding a novel type of fluctuations, which is beyond engineering status of knowledge.

Statistics of a neuron model driven by asymmetric colored noise.

PubMed

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

2015-02-01

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

Gravitational Lensing Effect on the Two-Point Correlation of Hot Spots in the Cosmic Microwave Background.

PubMed

Takada; Komatsu; Futamase

2000-04-20

We investigate the weak gravitational lensing effect that is due to the large-scale structure of the universe on two-point correlations of local maxima (hot spots) in the two-dimensional sky map of the cosmic microwave background (CMB) anisotropy. According to the Gaussian random statistics, as most inflationary scenarios predict, the hot spots are discretely distributed, with some characteristic angular separations on the last scattering surface that are due to oscillations of the CMB angular power spectrum. The weak lensing then causes pairs of hot spots, which are separated with the characteristic scale, to be observed with various separations. We found that the lensing fairly smooths out the oscillatory features of the two-point correlation function of hot spots. This indicates that the hot spot correlations can be a new statistical tool for measuring the shape and normalization of the power spectrum of matter fluctuations from the lensing signatures.

Shape and energy consistent pseudopotentials for correlated electron systems

PubMed Central

Needs, R. J.

2017-01-01

A method is developed for generating pseudopotentials for use in correlated-electron calculations. The paradigms of shape and energy consistency are combined and defined in terms of correlated-electron wave-functions. The resulting energy consistent correlated electron pseudopotentials (eCEPPs) are constructed for H, Li–F, Sc–Fe, and Cu. Their accuracy is quantified by comparing the relaxed molecular geometries and dissociation energies which they provide with all electron results, with all quantities evaluated using coupled cluster singles, doubles, and triples calculations. Errors inherent in the pseudopotentials are also compared with those arising from a number of approximations commonly used with pseudopotentials. The eCEPPs provide a significant improvement in optimised geometries and dissociation energies for small molecules, with errors for the latter being an order-of-magnitude smaller than for Hartree-Fock-based pseudopotentials available in the literature. Gaussian basis sets are optimised for use with these pseudopotentials. PMID:28571391

Analysis of soft-decision FEC on non-AWGN channels.

PubMed

Cho, Junho; Xie, Chongjin; Winzer, Peter J

2012-03-26

Soft-decision forward error correction (SD-FEC) schemes are typically designed for additive white Gaussian noise (AWGN) channels. In a fiber-optic communication system, noise may be neither circularly symmetric nor Gaussian, thus violating an important assumption underlying SD-FEC design. This paper quantifies the impact of non-AWGN noise on SD-FEC performance for such optical channels. We use a conditionally bivariate Gaussian noise model (CBGN) to analyze the impact of correlations among the signal's two quadrature components, and assess the effect of CBGN on SD-FEC performance using the density evolution of low-density parity-check (LDPC) codes. On a CBGN channel generating severely elliptic noise clouds, it is shown that more than 3 dB of coding gain are attainable by utilizing correlation information. Our analyses also give insights into potential improvements of the detection performance for fiber-optic transmission systems assisted by SD-FEC.

Time since maximum of Brownian motion and asymmetric Lévy processes

NASA Astrophysics Data System (ADS)

Martin, R. J.; Kearney, M. J.

2018-07-01

Motivated by recent studies of record statistics in relation to strongly correlated time series, we consider explicitly the drawdown time of a Lévy process, which is defined as the time since it last achieved its running maximum when observed over a fixed time period . We show that the density function of this drawdown time, in the case of a completely asymmetric jump process, may be factored as a function of t multiplied by a function of T  ‑  t. This extends a known result for the case of pure Brownian motion. We state the factors explicitly for the cases of exponential down-jumps with drift, and for the downward inverse Gaussian Lévy process with drift.

Speckle-field propagation in 'frozen' turbulence: brightness function approach

NASA Astrophysics Data System (ADS)

Dudorov, Vadim V.; Vorontsov, Mikhail A.; Kolosov, Valeriy V.

2006-08-01

Speckle-field long- and short-exposure spatial correlation characteristics for target-in-the-loop (TIL) laser beam propagation and scattering in atmospheric turbulence are analyzed through the use of two different approaches: the conventional Monte Carlo (MC) technique and the recently developed brightness function (BF) method. Both the MC and the BF methods are applied to analysis of speckle-field characteristics averaged over target surface roughness realizations under conditions of 'frozen' turbulence. This corresponds to TIL applications where speckle-field fluctuations associated with target surface roughness realization updates occur within a time scale that can be significantly shorter than the characteristic atmospheric turbulence time. Computational efficiency and accuracy of both methods are compared on the basis of a known analytical solution for the long-exposure mutual correlation function. It is shown that in the TIL propagation scenarios considered the BF method provides improved accuracy and requires significantly less computational time than the conventional MC technique. For TIL geometry with a Gaussian outgoing beam and Lambertian target surface, both analytical and numerical estimations for the speckle-field long-exposure correlation length are obtained. Short-exposure speckle-field correlation characteristics corresponding to propagation in 'frozen' turbulence are estimated using the BF method. It is shown that atmospheric turbulence-induced static refractive index inhomogeneities do not significantly affect the characteristic correlation length of the speckle field, whereas long-exposure spatial correlation characteristics are strongly dependent on turbulence strength.

Speckle-field propagation in 'frozen' turbulence: brightness function approach.

PubMed

Dudorov, Vadim V; Vorontsov, Mikhail A; Kolosov, Valeriy V

2006-08-01

Speckle-field long- and short-exposure spatial correlation characteristics for target-in-the-loop (TIL) laser beam propagation and scattering in atmospheric turbulence are analyzed through the use of two different approaches: the conventional Monte Carlo (MC) technique and the recently developed brightness function (BF) method. Both the MC and the BF methods are applied to analysis of speckle-field characteristics averaged over target surface roughness realizations under conditions of 'frozen' turbulence. This corresponds to TIL applications where speckle-field fluctuations associated with target surface roughness realization updates occur within a time scale that can be significantly shorter than the characteristic atmospheric turbulence time. Computational efficiency and accuracy of both methods are compared on the basis of a known analytical solution for the long-exposure mutual correlation function. It is shown that in the TIL propagation scenarios considered the BF method provides improved accuracy and requires significantly less computational time than the conventional MC technique. For TIL geometry with a Gaussian outgoing beam and Lambertian target surface, both analytical and numerical estimations for the speckle-field long-exposure correlation length are obtained. Short-exposure speckle-field correlation characteristics corresponding to propagation in 'frozen' turbulence are estimated using the BF method. It is shown that atmospheric turbulence-induced static refractive index inhomogeneities do not significantly affect the characteristic correlation length of the speckle field, whereas long-exposure spatial correlation characteristics are strongly dependent on turbulence strength.

A Method for Approximating the Bivariate Normal Correlation Coefficient.

ERIC Educational Resources Information Center

Kirk, David B.

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

Spatial Copula Model for Imputing Traffic Flow Data from Remote Microwave Sensors.

PubMed

Ma, Xiaolei; Luan, Sen; Du, Bowen; Yu, Bin

2017-09-21

Issues of missing data have become increasingly serious with the rapid increase in usage of traffic sensors. Analyses of the Beijing ring expressway have showed that up to 50% of microwave sensors pose missing values. The imputation of missing traffic data must be urgently solved although a precise solution that cannot be easily achieved due to the significant number of missing portions. In this study, copula-based models are proposed for the spatial interpolation of traffic flow from remote traffic microwave sensors. Most existing interpolation methods only rely on covariance functions to depict spatial correlation and are unsuitable for coping with anomalies due to Gaussian consumption. Copula theory overcomes this issue and provides a connection between the correlation function and the marginal distribution function of traffic flow. To validate copula-based models, a comparison with three kriging methods is conducted. Results indicate that copula-based models outperform kriging methods, especially on roads with irregular traffic patterns. Copula-based models demonstrate significant potential to impute missing data in large-scale transportation networks.

Power-law decay of the spatial correlation function in exciton-polariton condensates

PubMed Central

Roumpos, Georgios; Lohse, Michael; Nitsche, Wolfgang H.; Keeling, Jonathan; Szymańska, Marzena Hanna; Littlewood, Peter B.; Löffler, Andreas; Höfling, Sven; Worschech, Lukas; Forchel, Alfred; Yamamoto, Yoshihisa

2012-01-01

We create a large exciton-polariton condensate and employ a Michelson interferometer setup to characterize the short- and long-distance behavior of the first order spatial correlation function. Our experimental results show distinct features of both the two-dimensional and nonequilibrium characters of the condensate. We find that the gaussian short-distance decay is followed by a power-law decay at longer distances, as expected for a two-dimensional condensate. The exponent of the power law is measured in the range 0.9–1.2, larger than is possible in equilibrium. We compare the experimental results to a theoretical model to understand the features required to observe a power law and to clarify the influence of external noise on spatial coherence in nonequilibrium phase transitions. Our results indicate that Berezinskii–Kosterlitz–Thouless-like phase order survives in open-dissipative systems. PMID:22496595

Probabilistic density function method for nonlinear dynamical systems driven by colored noise

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

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

PubMed

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

2016-01-01

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

On the streaming model for redshift-space distortions

NASA Astrophysics Data System (ADS)

Kuruvilla, Joseph; Porciani, Cristiano

2018-06-01

The streaming model describes the mapping between real and redshift space for 2-point clustering statistics. Its key element is the probability density function (PDF) of line-of-sight pairwise peculiar velocities. Following a kinetic-theory approach, we derive the fundamental equations of the streaming model for ordered and unordered pairs. In the first case, we recover the classic equation while we demonstrate that modifications are necessary for unordered pairs. We then discuss several statistical properties of the pairwise velocities for DM particles and haloes by using a suite of high-resolution N-body simulations. We test the often used Gaussian ansatz for the PDF of pairwise velocities and discuss its limitations. Finally, we introduce a mixture of Gaussians which is known in statistics as the generalised hyperbolic distribution and show that it provides an accurate fit to the PDF. Once inserted in the streaming equation, the fit yields an excellent description of redshift-space correlations at all scales that vastly outperforms the Gaussian and exponential approximations. Using a principal-component analysis, we reduce the complexity of our model for large redshift-space separations. Our results increase the robustness of studies of anisotropic galaxy clustering and are useful for extending them towards smaller scales in order to test theories of gravity and interacting dark-energy models.

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

PubMed

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

2015-03-01

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

Gaussian Boson Sampling.

PubMed

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

2017-10-27

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

Gaussian process regression for forecasting battery state of health

NASA Astrophysics Data System (ADS)

Richardson, Robert R.; Osborne, Michael A.; Howey, David A.

2017-07-01

Accurately predicting the future capacity and remaining useful life of batteries is necessary to ensure reliable system operation and to minimise maintenance costs. The complex nature of battery degradation has meant that mechanistic modelling of capacity fade has thus far remained intractable; however, with the advent of cloud-connected devices, data from cells in various applications is becoming increasingly available, and the feasibility of data-driven methods for battery prognostics is increasing. Here we propose Gaussian process (GP) regression for forecasting battery state of health, and highlight various advantages of GPs over other data-driven and mechanistic approaches. GPs are a type of Bayesian non-parametric method, and hence can model complex systems whilst handling uncertainty in a principled manner. Prior information can be exploited by GPs in a variety of ways: explicit mean functions can be used if the functional form of the underlying degradation model is available, and multiple-output GPs can effectively exploit correlations between data from different cells. We demonstrate the predictive capability of GPs for short-term and long-term (remaining useful life) forecasting on a selection of capacity vs. cycle datasets from lithium-ion cells.

Phase space methods for Majorana fermions

NASA Astrophysics Data System (ADS)

Rushin Joseph, Ria; Rosales-Zárate, Laura E. C.; Drummond, Peter D.

2018-06-01

Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The resulting phase-space of covariance matrices belongs to the symmetry class D, one of the non-standard symmetry classes. This was originally proposed to study mesoscopic normal-metal-superconducting hybrid structures, which is the type of structure that has led to recent experimental observations of Majorana fermions. Under a unitary transformation, it is possible to express these Gaussian operators using real anti-symmetric matrices and Majorana operators, which are much simpler mathematical objects. We derive differential identities involving Majorana fermion operators and an antisymmetric matrix which are relevant to the derivation of the corresponding Fokker–Planck equations on symmetric space. These enable stochastic simulations either in real or imaginary time. This formalism has direct relevance to the study of fermionic systems in which there are Majorana type excitations, and is an alternative to using expansions involving conventional Fermi operators. The approach is illustrated by showing how a linear coupled Hamiltonian as used to study topological excitations can be transformed to Fokker–Planck and stochastic equation form, including dissipation through particle losses.

Description of an α-cluster tail in 8Be and 20Ne: Delocalization of the α cluster by quantum penetration

NASA Astrophysics Data System (ADS)

Kanada-En'yo, Yoshiko

2014-10-01

We analyze the α-cluster wave functions in cluster states of ^8Be and ^{20}Ne by comparing the exact relative wave function obtained by the generator coordinate method (GCM) with various types of trial functions. For the trial functions, we adopt the fixed range shifted Gaussian of the Brink-Bloch (BB) wave function, the spherical Gaussian with the adjustable range parameter of the spherical Tohsaki-Horiuchi-Schuck-Röpke (sTHSR), the deformed Gaussian of the deformed THSR (dTHSR), and a function with the Yukawa tail (YT). The quality of the description of the exact wave function with a trial function is judged by the squared overlap between the trial function and the GCM wave function. A better result is obtained with the sTHSR wave function than the BB wave function, and further improvement can be made with the dTHSR wave function because these wave functions can describe the outer tail better. The YT wave function gives almost an equal quality to or even better quality than the dTHSR wave function, indicating that the outer tail of α-cluster states is characterized by the Yukawa-like tail rather than the Gaussian tail. In weakly bound α-cluster states with small α separation energy and the low centrifugal and Coulomb barriers, the outer tail part is the slowly damping function described well by the quantum penetration through the effective barrier. This outer tail characterizes the almost zero-energy free α gas behavior, i.e., the delocalization of the cluster.

Some Modified Integrated Squared Error Procedures for Multivariate Normal Data.

DTIC Science & Technology

1982-06-01

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

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

ERIC Educational Resources Information Center

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

2013-01-01

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

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon.

PubMed

McConnell, Robert; Zhang, Hao; Hu, Jiazhong; Ćuk, Senka; Vuletić, Vladan

2015-03-26

Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized, but these states display Gaussian spin distribution functions with a non-negative Wigner quasiprobability distribution function. Non-Gaussian entangled states have been produced in small ensembles of ions, and very recently in large atomic ensembles. Here we generate entanglement in a large atomic ensemble via an interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function--an important hallmark of non-classicality--and verify an entanglement depth (the minimum number of mutually entangled atoms) of 2,910 ± 190 out of 3,100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. Although the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing. More generally, our results demonstrate the power of heralded methods for entanglement generation, and illustrate how the information contained in a single photon can drastically alter the quantum state of a large system.

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

PubMed

Spiga, D

2018-01-01

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

Fidelity matters: the birth of entanglement in the mixing of Gaussian states.

PubMed

Olivares, Stefano; Paris, Matteo G A

2011-10-21

We address the interaction of two Gaussian states through bilinear exchange Hamiltonians and analyze the correlations exhibited by the resulting bipartite systems. We demonstrate that entanglement arises if and only if the fidelity between the two input Gaussian states falls under a threshold value depending only on their purities, first moments, and the strength of the coupling. Our result clarifies the role of quantum fluctuations (squeezing) as a prerequisite for entanglement generation and provides a tool to optimize the generation of entanglement in linear systems of interest for quantum technology. © 2011 American Physical Society

Model-independent test for scale-dependent non-Gaussianities in the cosmic microwave background.

PubMed

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.

Leading non-Gaussian corrections for diffusion orientation distribution function.

PubMed

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

2014-02-01

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

Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function

PubMed Central

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

2014-01-01

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

Elegant Gaussian beams for enhanced optical manipulation

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

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

2015-06-15

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

Whole-Volume Clustering of Time Series Data from Zebrafish Brain Calcium Images via Mixture Modeling.

PubMed

Nguyen, Hien D; Ullmann, Jeremy F P; McLachlan, Geoffrey J; Voleti, Venkatakaushik; Li, Wenze; Hillman, Elizabeth M C; Reutens, David C; Janke, Andrew L

2018-02-01

Calcium is a ubiquitous messenger in neural signaling events. An increasing number of techniques are enabling visualization of neurological activity in animal models via luminescent proteins that bind to calcium ions. These techniques generate large volumes of spatially correlated time series. A model-based functional data analysis methodology via Gaussian mixtures is suggested for the clustering of data from such visualizations is proposed. The methodology is theoretically justified and a computationally efficient approach to estimation is suggested. An example analysis of a zebrafish imaging experiment is presented.

Beam-width spreading of vortex beams in free space

NASA Astrophysics Data System (ADS)

Wang, Weiwei; Li, Jinhong; Duan, Meiling

2018-01-01

Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function, the analytical expression for the beam-width spreading of Gaussian Schell-model (GSM) vortex beams in free space are derived, and used to study the influence of beam parameters on the beam-width spreading of GSM vortex beams. With the increment of the propagation distance, the beam-width spreading of GSM vortex beams will increase; the bigger the topological charge, spatial correlation length, wavelength and waist width are, the smaller the beam-width spreading is.

Multipole Vectors: Decomposing Functions on a Sphere

NASA Astrophysics Data System (ADS)

Copi, C. J.; Huterer, D.; Starkman, G. D.

2011-09-01

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order l is represented by l unit vectors pointing in directions on the sky and an overall magnitude. These "multipole vectors and scalars" transform as vectors under rotations. Like the usual spherical harmonics, multipole vectors form an irreducible representation of the proper rotation group SO(3). However, they are related to the familiar spherical harmonic coefficients, alm, in a nonlinear way, and are therefore sensitive to different aspects of the CMB anisotropy. Nevertheless, it is straightforward to determine the multipole vectors for a given CMB map and we present an algorithm to compute them. Using the WMAP full-sky maps, we perform several tests of the hypothesis that the CMB anisotropy is statistically isotropic and Gaussian random. We find that the result from comparing the oriented area of planes defined by these vectors between multipole pairs 2<=l1!=l2<=8 is inconsistent with the isotropic Gaussian hypothesis at the 99.4% level for the ILC map and at 98.9% level for the cleaned map of Tegmark et al. A particular correlation is suggested between the l=3 and l=8 multipoles, as well as several other pairs. This effect is entirely different from the now familiar planarity and alignment of the quadrupole and octupole: while the aforementioned is fairly unlikely, the multipole vectors indicate correlations not expected in Gaussian random skies that make them unusually likely. The result persists after accounting for pixel noise and after assuming a residual 10% dust contamination in the cleaned WMAP map. While the definitive analysis of these results will require more work, we hope that multipole vectors will become a valuable tool for various cosmological tests, in particular those of cosmic isotropy.

Pollutant Plume Dispersion over Hypothetical Urban Areas based on Wind Tunnel Measurements

NASA Astrophysics Data System (ADS)

Mo, Ziwei; Liu, Chun-Ho

2017-04-01

Gaussian plume model is commonly adopted for pollutant concentration prediction in the atmospheric boundary layer (ABL). However, it has a number of limitations being applied to pollutant dispersion over complex land-surface morphology. In this study, the friction factor (f), as a measure of aerodynamic resistance induced by rough surfaces in the engineering community, was proposed to parameterize the vertical dispersion coefficient (σz) in the Gaussian model. A series of wind tunnel experiments were carried out to verify the mathematical hypothesis and to characterize plume dispersion as a function of surface roughness as well. Hypothetical urban areas, which were assembled in the form of idealized street canyons of different aspect (building-height-to-street-width) ratios (AR = 1/2, 1/4, 1/8 and 1/12), were fabricated by aligning identical square aluminum bars at different separation apart in cross flows. Pollutant emitted from a ground-level line source into the turbulent boundary layer (TBL) was simulated using water vapour generated by ultrasonic atomizer. The humidity and the velocity (mean and fluctuating components) were measured, respectively, by humidity sensors and hot-wire anemometry (HWA) with X-wire probes in streamwise and vertical directions. Wind tunnel results showed that the pollutant concentration exhibits the conventional Gaussian distribution, suggesting the feasibility of using water vapour as a passive scalar in wind tunnel experiments. The friction factor increased with decreasing aspect ratios (widening the building separation). It was peaked at AR = 1/8 and decreased thereafter. Besides, a positive correlation between σz/xn (x is the distance from the pollutant source) and f1/4 (correlation coefficient r2 = 0.61) was observed, formulating the basic parameterization of plume dispersion over urban areas.

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

PubMed

Brown, James; Carrington, Tucker

2015-07-28

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

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

PubMed

Yura, Harold T; Hanson, Steen G

2012-04-01

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

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

NASA Astrophysics Data System (ADS)

Shi, Shuyan; Ji, Ruirui; Zhang, Fan

2018-04-01

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

The trispectrum in the Effective Field Theory of Large Scale Structure

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

Bertolini, Daniele; Schutz, Katelin; Solon, Mikhail P.

2016-06-01

We compute the connected four point correlation function (the trispectrum in Fourier space) of cosmological density perturbations at one-loop order in Standard Perturbation Theory (SPT) and the Effective Field Theory of Large Scale Structure (EFT of LSS). This paper is a companion to our earlier work on the non-Gaussian covariance of the matter power spectrum, which corresponds to a particular wavenumber configuration of the trispectrum. In the present calculation, we highlight and clarify some of the subtle aspects of the EFT framework that arise at third order in perturbation theory for general wavenumber configurations of the trispectrum. We consistently incorporatemore » vorticity and non-locality in time into the EFT counterterms and lay out a complete basis of building blocks for the stress tensor. We show predictions for the one-loop SPT trispectrum and the EFT contributions, focusing on configurations which have particular relevance for using LSS to constrain primordial non-Gaussianity.« less

Stochastic bifurcation in a model of love with colored noise

NASA Astrophysics Data System (ADS)

Yue, Xiaokui; Dai, Honghua; Yuan, Jianping

2015-07-01

In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.

oGNM: online computation of structural dynamics using the Gaussian Network Model

PubMed Central

Yang, Lee-Wei; Rader, A. J.; Liu, Xiong; Jursa, Cristopher Jon; Chen, Shann Ching; Karimi, Hassan A.; Bahar, Ivet

2006-01-01

An assessment of the equilibrium dynamics of biomolecular systems, and in particular their most cooperative fluctuations accessible under native state conditions, is a first step towards understanding molecular mechanisms relevant to biological function. We present a web-based system, oGNM that enables users to calculate online the shape and dispersion of normal modes of motion for proteins, oligonucleotides and their complexes, or associated biological units, using the Gaussian Network Model (GNM). Computations with the new engine are 5–6 orders of magnitude faster than those using conventional normal mode analyses. Two cases studies illustrate the utility of oGNM. The first shows that the thermal fluctuations predicted for 1250 non-homologous proteins correlate well with X-ray crystallographic data over a broad range [7.3–15 Å] of inter-residue interaction cutoff distances and the correlations improve with increasing observation temperatures. The second study, focused on 64 oligonucleotides and oligonucleotide–protein complexes, shows that good agreement with experiments is achieved by representing each nucleotide by three GNM nodes (as opposed to one-node-per-residue in proteins) along with uniform interaction ranges for all components of the complexes. These results open the way to a rapid assessment of the dynamics of DNA/RNA-containing complexes. The server can be accessed at . PMID:16845002

Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: effects of strong compressibility and large-scale anisotropy.

PubMed

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.

Thermal noise in confined fluids.

PubMed

Sanghi, T; Aluru, N R

2014-11-07

In this work, we discuss a combined memory function equation (MFE) and generalized Langevin equation (GLE) approach (referred to as MFE/GLE formulation) to characterize thermal noise in confined fluids. Our study reveals that for fluids confined inside nanoscale geometries, the correlation time and the time decay of the autocorrelation function of the thermal noise are not significantly different across the confinement. We show that it is the strong cross-correlation of the mean force with the molecular velocity that gives rise to the spatial anisotropy in the velocity-autocorrelation function of the confined fluids. Further, we use the MFE/GLE formulation to extract the thermal force a fluid molecule experiences in a MD simulation. Noise extraction from MD simulation suggests that the frequency distribution of the thermal force is non-Gaussian. Also, the frequency distribution of the thermal force near the confining surface is found to be different in the direction parallel and perpendicular to the confinement. We also use the formulation to compute the noise correlation time of water confined inside a (6,6) carbon-nanotube (CNT). It is observed that inside the (6,6) CNT, in which water arranges itself in a highly concerted single-file arrangement, the correlation time of thermal noise is about an order of magnitude higher than that of bulk water.

Signatures of Hong-Ou-Mandel interference at microwave frequencies

NASA Astrophysics Data System (ADS)

Woolley, M. J.; Lang, C.; Eichler, C.; Wallraff, A.; Blais, A.

2013-10-01

Two-photon quantum interference at a beam splitter, commonly known as Hong-Ou-Mandel interference, is a fundamental demonstration of the quantum mechanical nature of electromagnetic fields and a key component of various quantum information processing protocols. The phenomenon was recently demonstrated with microwave-frequency photons by Lang et al (2013 Nature Phys. 9 345-8). This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter using linear detectors. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of pulsed Gaussian or Lorentzian single microwave photons and (ii) resonant fluorescent microwave fields from continuously driven circuit QED systems. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Lang et al (2013) was performed with trains of Lorentzian single photons, and very good agreement with experimental data is obtained. The results are relevant not only to interference experiments using circuit QED systems, but any such setup with highly controllable sources and time-resolved detection.

Thermal noise in confined fluids

NASA Astrophysics Data System (ADS)

Sanghi, T.; Aluru, N. R.

2014-11-01

In this work, we discuss a combined memory function equation (MFE) and generalized Langevin equation (GLE) approach (referred to as MFE/GLE formulation) to characterize thermal noise in confined fluids. Our study reveals that for fluids confined inside nanoscale geometries, the correlation time and the time decay of the autocorrelation function of the thermal noise are not significantly different across the confinement. We show that it is the strong cross-correlation of the mean force with the molecular velocity that gives rise to the spatial anisotropy in the velocity-autocorrelation function of the confined fluids. Further, we use the MFE/GLE formulation to extract the thermal force a fluid molecule experiences in a MD simulation. Noise extraction from MD simulation suggests that the frequency distribution of the thermal force is non-Gaussian. Also, the frequency distribution of the thermal force near the confining surface is found to be different in the direction parallel and perpendicular to the confinement. We also use the formulation to compute the noise correlation time of water confined inside a (6,6) carbon-nanotube (CNT). It is observed that inside the (6,6) CNT, in which water arranges itself in a highly concerted single-file arrangement, the correlation time of thermal noise is about an order of magnitude higher than that of bulk water.

Theoretical study of the NO gamma system

NASA Technical Reports Server (NTRS)

Langhoff, Stephen R.; Bauschlicher, Charles W., Jr.; Partridge, Harry

1988-01-01

A systematic study of the NO gamma system with level of correlation treatment was carried out using large Gaussian basis sets to determine the potential curves for the X2Pi and A2Sigma(+) states of NO. It is shown that the A2Sigma-X2Pi electronic transition moment (gamma system) increases monotonically with decreasing internuclear distance and that the increase in the moment as r decreases is correlated with the increasing degree of diffuse character in the X2Pi state. The results of a study of the X2Pi and A2Sigma(+) dipole moment functions showed that the X2Pi vibrationally averaged dipole moments and the (1-0) and (2-0) vibration-rotation band intensities agree well with experimental data.

Influence of local inhomogeneities induced in corneal ablation on the evolution of contrast sensitivity

NASA Astrophysics Data System (ADS)

Ortiz, Dolores; Saiz, Jose M.; González, Francisco

2004-04-01

The presence of local inhomogeneities in corneal tissue after refractive surgery has an influence on visual performance. Here we focus on the corneal ablation associated with Lasik surgery and its effect on the modulation transfer function (MTF) that we obtained by modifying a personalized Kooijman model. Inhomogeneities induced by the ablation occur in the form of Gaussian-distributed refractive-index variations of a given correlation length. We show how variation of refractive-index deviation and correlation length (size) of the inhomogeneities allows us to obtain pairs of values that are able to achieve a MTF evolution similar to that observed for contrast sensitivity in the same patients. An estimate of the characteristics of the local effects is obtained.

Passive advection of a vector field: Anisotropy, finite correlation time, exact solution, and logarithmic corrections to ordinary scaling

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2015-10-01

In this work we study the generalization of the problem considered in [Phys. Rev. E 91, 013002 (2015), 10.1103/PhysRevE.91.013002] to the case of finite correlation time of the environment (velocity) field. The model describes a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow. Inertial-range asymptotic behavior is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and preassigned pair correlation function. Due to the presence of distinguished direction n , all the multiloop diagrams in this model vanish, so that the results obtained are exact. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to the two nontrivial fixed points of the RG equations. Their stability depends on the relation between the exponents in the energy spectrum E ∝k⊥1 -ξ and the dispersion law ω ∝k⊥2 -η . In contrast to the well-known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the corrections to ordinary scaling are polynomials of logarithms of the integral turbulence scale L .

Tables Of Gaussian-Type Orbital Basis Functions

NASA Technical Reports Server (NTRS)

Partridge, Harry

1992-01-01

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

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

PubMed

Liu, Peng; Zeng, Zhigang; Wang, Jun

2017-01-01

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

Investigating the relation between the geometric properties of river basins and the filtering parameters for regional land hydrology applications using GRACE models

NASA Astrophysics Data System (ADS)

Piretzidis, Dimitrios; Sideris, Michael G.

2016-04-01

This study investigates the possibilities of local hydrology signal extraction using GRACE data and conventional filtering techniques. The impact of the basin shape has also been studied in order to derive empirical rules for tuning the GRACE filter parameters. GRACE CSR Release 05 monthly solutions were used from April 2002 to August 2015 (161 monthly solutions in total). SLR data were also used to replace the GRACE C2,0 coefficient, and a de-correlation filter with optimal parameters for CSR Release 05 data was applied to attenuate the correlation errors of monthly mass differences. For basins located at higher latitudes, the effect of Glacial Isostatic Adjustment (GIA) was taken into account using the ICE-6G model. The study focuses on three geometric properties, i.e., the area, the convexity and the width in the longitudinal direction, of 100 basins with global distribution. Two experiments have been performed. The first one deals with the determination of the Gaussian smoothing radius that minimizes the gaussianity of GRACE equivalent water height (EWH) over the selected basins. The EWH kurtosis was selected as a metric of gaussianity. The second experiment focuses on the derivation of the Gaussian smoothing radius that minimizes the RMS difference between GRACE data and a hydrology model. The GLDAS 1.0 Noah hydrology model was chosen, which shows good agreement with GRACE data according to previous studies. Early results show that there is an apparent relation between the geometric attributes of the basins examined and the Gaussian radius derived from the two experiments. The kurtosis analysis experiment tends to underestimate the optimal Gaussian radius, which is close to 200-300 km in many cases. Empirical rules for the selection of the Gaussian radius have been also developed for sub-regional scale basins.

Generalized Bootstrap Method for Assessment of Uncertainty in Semivariogram Inference

USGS Publications Warehouse

Olea, R.A.; Pardo-Iguzquiza, E.

2011-01-01

The semivariogram and its related function, the covariance, play a central role in classical geostatistics for modeling the average continuity of spatially correlated attributes. Whereas all methods are formulated in terms of the true semivariogram, in practice what can be used are estimated semivariograms and models based on samples. A generalized form of the bootstrap method to properly model spatially correlated data is used to advance knowledge about the reliability of empirical semivariograms and semivariogram models based on a single sample. Among several methods available to generate spatially correlated resamples, we selected a method based on the LU decomposition and used several examples to illustrate the approach. The first one is a synthetic, isotropic, exhaustive sample following a normal distribution, the second example is also a synthetic but following a non-Gaussian random field, and a third empirical sample consists of actual raingauge measurements. Results show wider confidence intervals than those found previously by others with inadequate application of the bootstrap. Also, even for the Gaussian example, distributions for estimated semivariogram values and model parameters are positively skewed. In this sense, bootstrap percentile confidence intervals, which are not centered around the empirical semivariogram and do not require distributional assumptions for its construction, provide an achieved coverage similar to the nominal coverage. The latter cannot be achieved by symmetrical confidence intervals based on the standard error, regardless if the standard error is estimated from a parametric equation or from bootstrap. ?? 2010 International Association for Mathematical Geosciences.

Gaussian Mixture Model of Heart Rate Variability

PubMed Central

Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

2012-01-01

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

A Bernoulli Gaussian Watermark for Detecting Integrity Attacks in Control Systems

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

Weerakkody, Sean; Ozel, Omur; Sinopoli, Bruno

We examine the merit of Bernoulli packet drops in actively detecting integrity attacks on control systems. The aim is to detect an adversary who delivers fake sensor measurements to a system operator in order to conceal their effect on the plant. Physical watermarks, or noisy additive Gaussian inputs, have been previously used to detect several classes of integrity attacks in control systems. In this paper, we consider the analysis and design of Gaussian physical watermarks in the presence of packet drops at the control input. On one hand, this enables analysis in a more general network setting. On the othermore » hand, we observe that in certain cases, Bernoulli packet drops can improve detection performance relative to a purely Gaussian watermark. This motivates the joint design of a Bernoulli-Gaussian watermark which incorporates both an additive Gaussian input and a Bernoulli drop process. We characterize the effect of such a watermark on system performance as well as attack detectability in two separate design scenarios. Here, we consider a correlation detector for attack recognition. We then propose efficiently solvable optimization problems to intelligently select parameters of the Gaussian input and the Bernoulli drop process while addressing security and performance trade-offs. Finally, we provide numerical results which illustrate that a watermark with packet drops can indeed outperform a Gaussian watermark.« less

Gaussian Finite Element Method for Description of Underwater Sound Diffraction

NASA Astrophysics Data System (ADS)

Huang, Dehua

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

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

PubMed

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

2016-09-01

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

Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors

PubMed Central

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

2015-01-01

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

'A device for being able to book P&L': the organizational embedding of the Gaussian copula.

PubMed

MacKenzie, Donald; Spears, Taylor

2014-06-01

This article, the second of two articles on the Gaussian copula family of models, discusses the attitude of 'quants' (modellers) to these models, showing that contrary to some accounts, those quants were not 'model dopes' who uncritically accepted the outputs of the models. Although sometimes highly critical of Gaussian copulas - even 'othering' them as not really being models --they nevertheless nearly all kept using them, an outcome we explain with reference to the embedding of these models in inter- and intra-organizational processes: communication, risk control and especially the setting of bonuses. The article also examines the role of Gaussian copula models in the 2007-2008 global crisis and in a 2005 episode known as 'the correlation crisis'. We end with the speculation that all widely used derivatives models (and indeed the evaluation culture in which they are embedded) help generate inter-organizational co-ordination, and all that is special in this respect about the Gaussian copula is that its status as 'other' makes this role evident.

Non-Markovian dynamics of single- and two-qubit systems interacting with Gaussian and non-Gaussian fluctuating transverse environments

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

Gaussian-Beam Laser-Resonator Program

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

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

NASA Astrophysics Data System (ADS)

Kumar, Santosh

2015-11-01

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

Tmd Factorization and Evolution for Tmd Correlation Functions

NASA Astrophysics Data System (ADS)

Mert Aybat, S.; Rogers, Ted C.

We discuss the application of transverse momentum dependent (TMD) factorization theorems to phenomenology. Our treatment relies on recent extensions of the Collins-Soper-Sterman (CSS) formalism. Emphasis is placed on the importance of using well-defined TMD parton distribution functions (PDFs) and fragmentation functions (FFs) in calculating the evolution of these objects. We explain how parametrizations of unpolarized TMDs can be obtained from currently existing fixed-scale Gaussian fits and previous implementations of the CSS formalism in the Drell-Yan process, and provide some examples. We also emphasize the importance of agreed-upon definitions for having an unambiguous prescription for calculating higher orders in the hard part, and provide examples of higher order calculations. We end with a discussion of strategies for extending the phenomenological applications of TMD factorization to situations beyond the unpolarized case.

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

Stress-induced electric current fluctuations in rocks: a superstatistical model

NASA Astrophysics Data System (ADS)

Cartwright-Taylor, Alexis; Vallianatos, Filippos; Sammonds, Peter

2017-04-01

We recorded spontaneous electric current flow in non-piezoelectric Carrara marble samples during triaxial deformation. Mechanical data, ultrasonic velocities and acoustic emissions were acquired simultaneously with electric current to constrain the relationship between electric current flow, differential stress and damage. Under strain-controlled loading, spontaneous electric current signals (nA) were generated and sustained under all conditions tested. In dry samples, a detectable electric current arises only during dilatancy and the overall signal is correlated with the damage induced by microcracking. Our results show that fracture plays a key role in the generation of electric currents in deforming rocks (Cartwright-Taylor et al., in prep). We also analysed the high-frequency fluctuations of these electric current signals and found that they are not normally distributed - they exhibit power-law tails (Cartwright-Taylor et al., 2014). We modelled these distributions with q-Gaussian statistics, derived by maximising the Tsallis entropy. This definition of entropy is particularly applicable to systems which are strongly correlated and far from equilibrium. Good agreement, at all experimental conditions, between the distributions of electric current fluctuations and the q-Gaussian function with q-values far from one, illustrates the highly correlated, fractal nature of the electric source network within the samples and provides further evidence that the source of the electric signals is the developing fractal network of cracks. It has been shown (Beck, 2001) that q-Gaussian distributions can arise from the superposition of local relaxations in the presence of a slowly varying driving force, thus providing a dynamic reason for the appearance of Tsallis statistics in systems with a fluctuating energy dissipation rate. So, the probability distribution for a dynamic variable, u under some external slow forcing, β, can be obtained as a superposition of temporary local equilibrium processes whose variance fluctuates over time. The appearance of q-Gaussian statistics are caused by the fluctuating β parameter, which effectively models the fluctuating energy dissipation rate in the system. This concept is known as superstatistics and is physically relevant for modelling driven non-equilibrium systems where the environmental conditions fluctuate on a large scale. The idea is that the environmental variable, such as temperature or pressure, changes so slowly that a rapidly fluctuating variable within that environment has time to relax back to equilibrium between each change in the environment. The application of superstatistical techniques to our experimental electric current fluctuations show that they can indeed be described, to good approximation, by the superposition of local Gaussian processes with fluctuating variance. We conclude, then, that the measured electric current fluctuates in response to intermittent energy dissipation and is driven to varying temporary local equilibria during deformation by the variations in stress intensity. The advantage of this technique is that, once the model has been established to be a good description of the system in question, the average β parameter (a measure of the average energy dissipation rate) for the system can be obtained simply from the macroscopic q-Gaussian distribution parameters.

Working covariance model selection for generalized estimating equations.

PubMed

Carey, Vincent J; Wang, You-Gan

2011-11-20

We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice. Copyright © 2011 John Wiley & Sons, Ltd.

Gaussian Elimination-Based Novel Canonical Correlation Analysis Method for EEG Motion Artifact Removal.

PubMed

Roy, Vandana; Shukla, Shailja; Shukla, Piyush Kumar; Rawat, Paresh

2017-01-01

The motion generated at the capturing time of electro-encephalography (EEG) signal leads to the artifacts, which may reduce the quality of obtained information. Existing artifact removal methods use canonical correlation analysis (CCA) for removing artifacts along with ensemble empirical mode decomposition (EEMD) and wavelet transform (WT). A new approach is proposed to further analyse and improve the filtering performance and reduce the filter computation time under highly noisy environment. This new approach of CCA is based on Gaussian elimination method which is used for calculating the correlation coefficients using backslash operation and is designed for EEG signal motion artifact removal. Gaussian elimination is used for solving linear equation to calculate Eigen values which reduces the computation cost of the CCA method. This novel proposed method is tested against currently available artifact removal techniques using EEMD-CCA and wavelet transform. The performance is tested on synthetic and real EEG signal data. The proposed artifact removal technique is evaluated using efficiency matrices such as del signal to noise ratio (DSNR), lambda ( λ ), root mean square error (RMSE), elapsed time, and ROC parameters. The results indicate suitablity of the proposed algorithm for use as a supplement to algorithms currently in use.

On an additive partial correlation operator and nonparametric estimation of graphical models.

PubMed

Lee, Kuang-Yao; Li, Bing; Zhao, Hongyu

2016-09-01

We introduce an additive partial correlation operator as an extension of partial correlation to the nonlinear setting, and use it to develop a new estimator for nonparametric graphical models. Our graphical models are based on additive conditional independence, a statistical relation that captures the spirit of conditional independence without having to resort to high-dimensional kernels for its estimation. The additive partial correlation operator completely characterizes additive conditional independence, and has the additional advantage of putting marginal variation on appropriate scales when evaluating interdependence, which leads to more accurate statistical inference. We establish the consistency of the proposed estimator. Through simulation experiments and analysis of the DREAM4 Challenge dataset, we demonstrate that our method performs better than existing methods in cases where the Gaussian or copula Gaussian assumption does not hold, and that a more appropriate scaling for our method further enhances its performance.

On an additive partial correlation operator and nonparametric estimation of graphical models

PubMed Central

Li, Bing; Zhao, Hongyu

2016-01-01

Abstract We introduce an additive partial correlation operator as an extension of partial correlation to the nonlinear setting, and use it to develop a new estimator for nonparametric graphical models. Our graphical models are based on additive conditional independence, a statistical relation that captures the spirit of conditional independence without having to resort to high-dimensional kernels for its estimation. The additive partial correlation operator completely characterizes additive conditional independence, and has the additional advantage of putting marginal variation on appropriate scales when evaluating interdependence, which leads to more accurate statistical inference. We establish the consistency of the proposed estimator. Through simulation experiments and analysis of the DREAM4 Challenge dataset, we demonstrate that our method performs better than existing methods in cases where the Gaussian or copula Gaussian assumption does not hold, and that a more appropriate scaling for our method further enhances its performance. PMID:29422689

Accurate Drift Time Determination by Traveling Wave Ion Mobility Spectrometry: The Concept of the Diffusion Calibration.

PubMed

Kune, Christopher; Far, Johann; De Pauw, Edwin

2016-12-06

Ion mobility spectrometry (IMS) is a gas phase separation technique, which relies on differences in collision cross section (CCS) of ions. Ionic clouds of unresolved conformers overlap if the CCS difference is below the instrumental resolution expressed as CCS/ΔCCS. The experimental arrival time distribution (ATD) peak is then a superimposition of the various contributions weighted by their relative intensities. This paper introduces a strategy for accurate drift time determination using traveling wave ion mobility spectrometry (TWIMS) of poorly resolved or unresolved conformers. This method implements through a calibration procedure the link between the peak full width at half-maximum (fwhm) and the drift time of model compounds for wide range of settings for wave heights and velocities. We modified a Gaussian equation, which achieves the deconvolution of ATD peaks where the fwhm is fixed according to our calibration procedure. The new fitting Gaussian equation only depends on two parameters: The apex of the peak (A) and the mean drift time value (μ). The standard deviation parameter (correlated to fwhm) becomes a function of the drift time. This correlation function between μ and fwhm is obtained using the TWIMS calibration procedure which determines the maximum instrumental ion beam diffusion under limited and controlled space charge effect using ionic compounds which are detected as single conformers in the gas phase. This deconvolution process has been used to highlight the presence of poorly resolved conformers of crown ether complexes and peptides leading to more accurate CCS determinations in better agreement with quantum chemistry predictions.

Precise Determination of the Absorption Maximum in Wide Bands

ERIC Educational Resources Information Center

Eriksson, Karl-Hugo; And Others

1977-01-01

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

A partial differential equation-based general framework adapted to Rayleigh's, Rician's and Gaussian's distributed noise for restoration and enhancement of magnetic resonance image.

PubMed

Yadav, Ram Bharos; Srivastava, Subodh; Srivastava, Rajeev

2016-01-01

The proposed framework is obtained by casting the noise removal problem into a variational framework. This framework automatically identifies the various types of noise present in the magnetic resonance image and filters them by choosing an appropriate filter. This filter includes two terms: the first term is a data likelihood term and the second term is a prior function. The first term is obtained by minimizing the negative log likelihood of the corresponding probability density functions: Gaussian or Rayleigh or Rician. Further, due to the ill-posedness of the likelihood term, a prior function is needed. This paper examines three partial differential equation based priors which include total variation based prior, anisotropic diffusion based prior, and a complex diffusion (CD) based prior. A regularization parameter is used to balance the trade-off between data fidelity term and prior. The finite difference scheme is used for discretization of the proposed method. The performance analysis and comparative study of the proposed method with other standard methods is presented for brain web dataset at varying noise levels in terms of peak signal-to-noise ratio, mean square error, structure similarity index map, and correlation parameter. From the simulation results, it is observed that the proposed framework with CD based prior is performing better in comparison to other priors in consideration.

Structure of gamma-ray burst jets: intrinsic versus apparent properties

NASA Astrophysics Data System (ADS)

Salafia, O. S.; Ghisellini, G.; Pescalli, A.; Ghirlanda, G.; Nappo, F.

2015-07-01

With this paper we introduce the concept of apparent structure of a gamma-ray burst (GRB) jet, as opposed to its intrinsic structure. The latter is customarily defined specifying the functions ɛ(θ) (the energy emitted per jet unit solid angle) and Γ(θ) (the Lorentz factor of the emitting material); the apparent structure is instead defined by us as the isotropic equivalent energy Eiso(θv) as a function of the viewing angle θv. We show how to predict the apparent structure of a jet given its intrinsic structure. We find that a Gaussian intrinsic structure yields a power-law apparent structure: this opens a new viewpoint on the Gaussian (which can be understood as a proxy for a realistic narrow, well-collimated jet structure) as a possible candidate for a quasi-universal GRB jet structure. We show that such a model (a) is consistent with recent constraints on the observed luminosity function of GRBs; (b) implies fewer orphan afterglows with respect to the standard uniform model; (c) can break out the progenitor star (in the collapsar scenario) without wasting an unreasonable amount of energy; (d) is compatible with the explanation of the Amati correlation as a viewing angle effect; (e) can be very standard in energy content, and still yield a very wide range of observed isotropic equivalent energies.

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.

Wilson loops and chiral correlators on squashed spheres

NASA Astrophysics Data System (ADS)

Fucito, F.; Morales, J. F.; Poghossian, R.

2015-11-01

We study chiral deformations of N=2 and N=4 supersymmetric gauge theories obtained by turning on τ J tr Φ J interactions with Φ the N=2 superfield. Using localization, we compute the deformed gauge theory partition function Z(overrightarrow{τ}|q) and the expectation value of circular Wilson loops W on a squashed four-sphere. In the case of the deformed {N}=4 theory, exact formulas for Z and W are derived in terms of an underlying U( N) interacting matrix model replacing the free Gaussian model describing the {N}=4 theory. Using the AGT correspondence, the τ J -deformations are related to the insertions of commuting integrals of motion in the four-point CFT correlator and chiral correlators are expressed as τ-derivatives of the gauge theory partition function on a finite Ω-background. In the so called Nekrasov-Shatashvili limit, the entire ring of chiral relations is extracted from the ɛ-deformed Seiberg-Witten curve. As a byproduct of our analysis we show that SU(2) gauge theories on rational Ω-backgrounds are dual to CFT minimal models.

Coupled-cluster based basis sets for valence correlation calculations

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

Claudino, Daniel; Bartlett, Rodney J., E-mail: bartlett@qtp.ufl.edu; Gargano, Ricardo

Novel basis sets are generated that target the description of valence correlation in atoms H through Ar. The new contraction coefficients are obtained according to the Atomic Natural Orbital (ANO) procedure from CCSD(T) (coupled-cluster singles and doubles with perturbative triples correction) density matrices starting from the primitive functions of Dunning et al. [J. Chem. Phys. 90, 1007 (1989); ibid. 98, 1358 (1993); ibid. 100, 2975 (1993)] (correlation consistent polarized valence X-tuple zeta, cc-pVXZ). The exponents of the primitive Gaussian functions are subject to uniform scaling in order to ensure satisfaction of the virial theorem for the corresponding atoms. These newmore » sets, named ANO-VT-XZ (Atomic Natural Orbital Virial Theorem X-tuple Zeta), have the same number of contracted functions as their cc-pVXZ counterparts in each subshell. The performance of these basis sets is assessed by the evaluation of the contraction errors in four distinct computations: correlation energies in atoms, probing the density in different regions of space via 〈r{sup n}〉 (−3 ≤ n ≤ 3) in atoms, correlation energies in diatomic molecules, and the quality of fitting potential energy curves as measured by spectroscopic constants. All energy calculations with ANO-VT-QZ have contraction errors within “chemical accuracy” of 1 kcal/mol, which is not true for cc-pVQZ, suggesting some improvement compared to the correlation consistent series of Dunning and co-workers.« less

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Weighted Feature Gaussian Kernel SVM for Emotion Recognition

PubMed Central

Jia, Qingxuan

2016-01-01

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

On Nonlinear Functionals of Random Spherical Eigenfunctions

NASA Astrophysics Data System (ADS)

Marinucci, Domenico; Wigman, Igor

2014-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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

NASA Astrophysics Data System (ADS)

Amiri, Ali; Fathy, Mahmood

2010-12-01

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

Persistence Probabilities of Two-Sided (Integrated) Sums of Correlated Stationary Gaussian Sequences

NASA Astrophysics Data System (ADS)

Aurzada, Frank; Buck, Micha

2018-02-01

We study the persistence probability for some two-sided, discrete-time Gaussian sequences that are discrete-time analogues of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in continuous time in Molchan (Commun Math Phys 205(1):97-111, 1999) and Molchan (J Stat Phys 167(6):1546-1554, 2017) to a wide class of discrete-time processes.

Non-Gaussian and Multivariate Noise Models for Signal Detection.

DTIC Science & Technology

1982-09-01

follow, some of the basic results of asymptotic "theory are presented. both to make the notation clear. and to give some i ~ background for the...densities are considered within a detection framework. The discussions include specific examples and also some general methods of density generation ...densities generated by a memoryless, nonlinear transformation of a correlated, Gaussian source is discussed in some detail. A member of this class has the

Normal form decomposition for Gaussian-to-Gaussian superoperators

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

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

2015-05-15

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

2dFLenS and KiDS: determining source redshift distributions with cross-correlations

NASA Astrophysics Data System (ADS)

Johnson, Andrew; Blake, Chris; Amon, Alexandra; Erben, Thomas; Glazebrook, Karl; Harnois-Deraps, Joachim; Heymans, Catherine; Hildebrandt, Hendrik; Joudaki, Shahab; Klaes, Dominik; Kuijken, Konrad; Lidman, Chris; Marin, Felipe A.; McFarland, John; Morrison, Christopher B.; Parkinson, David; Poole, Gregory B.; Radovich, Mario; Wolf, Christian

2017-03-01

We develop a statistical estimator to infer the redshift probability distribution of a photometric sample of galaxies from its angular cross-correlation in redshift bins with an overlapping spectroscopic sample. This estimator is a minimum-variance weighted quadratic function of the data: a quadratic estimator. This extends and modifies the methodology presented by McQuinn & White. The derived source redshift distribution is degenerate with the source galaxy bias, which must be constrained via additional assumptions. We apply this estimator to constrain source galaxy redshift distributions in the Kilo-Degree imaging survey through cross-correlation with the spectroscopic 2-degree Field Lensing Survey, presenting results first as a binned step-wise distribution in the range z < 0.8, and then building a continuous distribution using a Gaussian process model. We demonstrate the robustness of our methodology using mock catalogues constructed from N-body simulations, and comparisons with other techniques for inferring the redshift distribution.

Two-proton correlations in the target fragmentation region of nuclear collisions at 200 A GeV

NASA Astrophysics Data System (ADS)

Awes, T. C.; Barlag, C.; Berger, F.; Bloomer, M. A.; Blume, C.; Bock, D.; Bock, R.; Bohne, E.-M.; Bucher, D.; Claussen, A.; Clewing, G.; Dragon, L.; Eklund, A.; Garpman, S.; Glasow, R.; Gustafsson, H.; Gutbrod, H. H.; Hölker, G.; Idh, J.; Jacobs, P.; Kampert, K. H.; Kolb, B. W.; Löhner, H.; Lund, I.; Obenshain, F. E.; Oskarsson, A.; Otterlund, I.; Peitzmann, T.; Plasil, F.; Poskanzer, A. M.; Purschke, M.; Roters, B.; Saini, S.; Santo, R.; Schmidt, H. R.; Sørensen, S. P.; Steffens, K.; Steinhaeuser, P.; Stenlund, E.; Stüken, D.; Young, G. R.

1995-06-01

Correlations between protons are studied in the target fragmentation region of reactions of protons and16O with C, Cu, Ag, Au and of32S with Al and Au at 200 A GeV. The emitted protons were measured with the Plastic Ball detector in the WA80 experiment at the CERN SPS. The comparison of the correlation function with calculations, assuming a spherical, gaussian shaped source with a lifetime τ=0 fm/ c, allows the extraction of radius parameters. The values are very close to those expected from the geometry of the target nuclei and increase with the target mass as α A {Target/1/3}. Even in proton induced reactions the whole target nucleus is involved. The dependence of the radii on centrality, polar angle θ lab, and energy, and their relation to measured proton yields are presented.

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

Exploring super-Gaussianity toward robust information-theoretical time delay estimation.

PubMed

Petsatodis, Theodoros; Talantzis, Fotios; Boukis, Christos; Tan, Zheng-Hua; Prasad, Ramjee

2013-03-01

Time delay estimation (TDE) is a fundamental component of speaker localization and tracking algorithms. Most of the existing systems are based on the generalized cross-correlation method assuming gaussianity of the source. It has been shown that the distribution of speech, captured with far-field microphones, is highly varying, depending on the noise and reverberation conditions. Thus the performance of TDE is expected to fluctuate depending on the underlying assumption for the speech distribution, being also subject to multi-path reflections and competitive background noise. This paper investigates the effect upon TDE when modeling the source signal with different speech-based distributions. An information theoretical TDE method indirectly encapsulating higher order statistics (HOS) formed the basis of this work. The underlying assumption of Gaussian distributed source has been replaced by that of generalized Gaussian distribution that allows evaluating the problem under a larger set of speech-shaped distributions, ranging from Gaussian to Laplacian and Gamma. Closed forms of the univariate and multivariate entropy expressions of the generalized Gaussian distribution are derived to evaluate the TDE. The results indicate that TDE based on the specific criterion is independent of the underlying assumption for the distribution of the source, for the same covariance matrix.

A comparison of gantry-mounted x-ray-based real-time target tracking methods.

PubMed

Montanaro, Tim; Nguyen, Doan Trang; Keall, Paul J; Booth, Jeremy; Caillet, Vincent; Eade, Thomas; Haddad, Carol; Shieh, Chun-Chien

2018-03-01

Most modern radiotherapy machines are built with a 2D kV imaging system. Combining this imaging system with a 2D-3D inference method would allow for a ready-made option for real-time 3D tumor tracking. This work investigates and compares the accuracy of four existing 2D-3D inference methods using both motion traces inferred from external surrogates and measured internally from implanted beacons. Tumor motion data from 160 fractions (46 thoracic/abdominal patients) of Synchrony traces (inferred traces), and 28 fractions (7 lung patients) of Calypso traces (internal traces) from the LIGHT SABR trial (NCT02514512) were used in this study. The motion traces were used as the ground truth. The ground truth trajectories were used in silico to generate 2D positions projected on the kV detector. These 2D traces were then passed to the 2D-3D inference methods: interdimensional correlation, Gaussian probability density function (PDF), arbitrary-shape PDF, and the Kalman filter. The inferred 3D positions were compared with the ground truth to determine tracking errors. The relationships between tracking error and motion magnitude, interdimensional correlation, and breathing periodicity index (BPI) were also investigated. Larger tracking errors were observed from the Calypso traces, with RMS and 95th percentile 3D errors of 0.84-1.25 mm and 1.72-2.64 mm, compared to 0.45-0.68 mm and 0.74-1.13 mm from the Synchrony traces. The Gaussian PDF method was found to be the most accurate, followed by the Kalman filter, the interdimensional correlation method, and the arbitrary-shape PDF method. Tracking error was found to strongly and positively correlate with motion magnitude for both the Synchrony and Calypso traces and for all four methods. Interdimensional correlation and BPI were found to negatively correlate with tracking error only for the Synchrony traces. The Synchrony traces exhibited higher interdimensional correlation than the Calypso traces especially in the anterior-posterior direction. Inferred traces often exhibit higher interdimensional correlation, which are not true representation of thoracic/abdominal motion and may underestimate kV-based tracking errors. The use of internal traces acquired from systems such as Calypso is advised for future kV-based tracking studies. The Gaussian PDF method is the most accurate 2D-3D inference method for tracking thoracic/abdominal targets. Motion magnitude has significant impact on 2D-3D inference error, and should be considered when estimating kV-based tracking error. © 2018 American Association of Physicists in Medicine.

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

NASA Astrophysics Data System (ADS)

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

2010-02-01

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

Intra-Individual Response Variability Assessed by Ex-Gaussian Analysis may be a New Endophenotype for Attention-Deficit/Hyperactivity Disorder.

PubMed

Henríquez-Henríquez, Marcela Patricia; Billeke, Pablo; Henríquez, Hugo; Zamorano, Francisco Javier; Rothhammer, Francisco; Aboitiz, Francisco

2014-01-01

Intra-individual variability of response times (RTisv) is considered as potential endophenotype for attentional deficit/hyperactivity disorder (ADHD). Traditional methods for estimating RTisv lose information regarding response times (RTs) distribution along the task, with eventual effects on statistical power. Ex-Gaussian analysis captures the dynamic nature of RTisv, estimating normal and exponential components for RT distribution, with specific phenomenological correlates. Here, we applied ex-Gaussian analysis to explore whether intra-individual variability of RTs agrees with criteria proposed by Gottesman and Gould for endophenotypes. Specifically, we evaluated if normal and/or exponential components of RTs may (a) present the stair-like distribution expected for endophenotypes (ADHD > siblings > typically developing children (TD) without familiar history of ADHD) and (b) represent a phenotypic correlate for previously described genetic risk variants. This is a pilot study including 55 subjects (20 ADHD-discordant sibling-pairs and 15 TD children), all aged between 8 and 13 years. Participants resolved a visual Go/Nogo with 10% Nogo probability. Ex-Gaussian distributions were fitted to individual RT data and compared among the three samples. In order to test whether intra-individual variability may represent a correlate for previously described genetic risk variants, VNTRs at DRD4 and SLC6A3 were identified in all sibling-pairs following standard protocols. Groups were compared adjusting independent general linear models for the exponential and normal components from the ex-Gaussian analysis. Identified trends were confirmed by the non-parametric Jonckheere-Terpstra test. Stair-like distributions were observed for μ (p = 0.036) and σ (p = 0.009). An additional "DRD4-genotype" × "clinical status" interaction was present for τ (p = 0.014) reflecting a possible severity factor. Thus, normal and exponential RTisv components are suitable as ADHD endophenotypes.

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

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

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

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

PubMed

Wear, Keith A

2002-11-01

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

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

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

Aksenova, Olga A.; Khalidov, Iskander A.

2014-12-09

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

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

PubMed

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

2001-12-17

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

A Long-Lived Oscillatory Space-Time Correlation Function of Two Dimensional Colloids

NASA Astrophysics Data System (ADS)

Kim, Jeongmin; Sung, Bong June

2014-03-01

Diffusion of a colloid in solution has drawn significant attention for a century. A well-known behavior of the colloid is called Brownian motion : the particle displacement probability distribution (PDPD) is Gaussian and the mean-square displacement (MSD) is linear with time. However, recent simulation and experimental studies revealed the heterogeneous dynamics of colloids near glass transitions or in complex environments such as entangled actin, PDPD exhibited the exponential tail at a large length instead of being Gaussian at all length scales. More interestingly, PDPD is still exponential even when MSD was still linear with time. It requires a refreshing insight on the colloidal diffusion in the complex environments. In this work, we study heterogeneous dynamics of two dimensional (2D) colloids using molecular dynamics simulations. Unlike in three dimensions, 2D solids do not follow the Lindemann melting criterion. The Kosterlitz-Thouless-Halperin-Nelson-Young theory predicts two-step phase transitions with an intermediate phase, the hexatic phase between isotropic liquids and solids. Near solid-hexatic transition, PDPD shows interesting oscillatory behavior between a central Gaussian part and an exponential tail. Until 12 times longer than translational relaxation time, the oscillatory behavior still persists even after entering the Fickian regime. We also show that multi-layered kinetic clusters account for heterogeneous dynamics of 2D colloids with the long-lived anomalous oscillatory PDPD.

Thermodynamically consistent Langevin dynamics with spatially correlated noise predicting frictionless regime and transient attraction effect

NASA Astrophysics Data System (ADS)

Majka, M.; Góra, P. F.

2016-10-01

While the origins of temporal correlations in Langevin dynamics have been thoroughly researched, the understanding of spatially correlated noise (SCN) is rather incomplete. In particular, very little is known about the relation between friction and SCN. In this article, starting from the microscopic, deterministic model, we derive the analytical formula for the spatial correlation function in the particle-bath interactions. This expression shows that SCN is the inherent component of binary mixtures, originating from the effective (entropic) interactions. Further, employing this spatial correlation function, we postulate the thermodynamically consistent Langevin equation driven by the Gaussian SCN and calculate the adequate fluctuation-dissipation relation. The thermodynamical consistency is achieved by introducing the spatially variant friction coefficient, which can be also derived analytically. This coefficient exhibits a number of intriguing properties, e.g., the singular behavior for certain types of interactions. Eventually, we apply this new theory to the system of two charged particles in the presence of counter-ions. Such particles interact via the screened-charge Yukawa potential and the inclusion of SCN leads to the emergence of the anomalous frictionless regime. In this regime the particles can experience active propulsion leading to the transient attraction effect. This effect suggests a nonequilibrium mechanism facilitating the molecular binding of the like-charged particles.

Photocurrent spectroscopy of pentacene thin film transistors

NASA Astrophysics Data System (ADS)

Breban, Mihaela

We demonstrate the application of photocurrent modulation spectroscopy in characterizing the performance of organic thin-film transistors. A parallel analysis of the direct current and photocurrent voltage characteristics provides a model free determination of the field-effect mobility and the density of free carriers in the transistor channel as a function of the applied gate voltage. Applying this technique to pentacene thin-film transistors demonstrates that the mobility increases as V1/3g . The free-carrier density is approximately 1/10 of the expected capacitive charge, and the mobility increases monotonically with the free carrier density, consistent with the trap and release model of transport. Also, the modulated photocurrent spectroscopy can be used as a probe of defect states in pentacene thin film transistors, measuring simultaneously the magnitude and the phase of the photocurrent as a function of the modulation frequency. This is accomplished by modeling the photo-carrier generation process as exciton dissociation via interaction with localized traps. Experimental data reveal a Gaussian distribution of localized states centered around 0.3 eV above the highest occupied molecular orbital. We also investigated the effect of the gate dielectric material with our probe and found that the position of the extracted Gaussian slightly shifts, consistent with the expected image charge effect for Pn through the dielectric substrate. Also shifts in the Gaussian position for samples fabricated with variable deposition conditions are correlated with changes in Pn morphology. The morphological differences between Pn films were also detected in current-voltage characteristics and photocurrent spectra. However, the origin of the ubiquitous 0.3 eV defect in Pn seems to be unrelated to structural differences in Pn films.

Limitations of the clump-correlation theories of shear-induced turbulence suppression

NASA Astrophysics Data System (ADS)

Zhang, Y. Z.; Mahajan, S. M.

2017-05-01

The clump theory, primarily constructed by Dupree [Phys. Fluids 15, 334 (1972)] based on the moment approach and then generalized to the correlation theory [Y. Z. Zhang and S. M. Mahajan, Phys. Fluids B 5, 2000 (1993)], has long served as a basis for constructing theories of turbulence suppression by shear flow. In order to reveal the "intrinsic approximation" invoked in the clump-correlation theory, we examine a model based on two dimensional magnetized drift waves. After a rigorous derivation of the exact response function—a key to average the Green function of the system—we show that the Dupree, Zhang-Mahajan approach is recovered as the lowest order approximation in a small dimensionless parameter ϒ which is a triple product of the correlation time, wave number, and fluctuating drift velocity. The clump-correlation theory, thus, constitutes the Gaussian and lowest order non-Markovian process for a homogeneous stationary turbulence. We also provide, especially for the tokamak community, a readily usable formula to evaluate the effectiveness of shear-flow suppression; this formula pertains regardless of the specific model of correlation time.

Effects of scale-dependent non-Gaussianity on cosmological structures

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

LoVerde, Marilena; Miller, Amber; Shandera, Sarah

2008-04-15

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

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

PubMed

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

2006-04-01

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

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

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

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

Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

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

An estimation of distribution method for infrared target detection based on Copulas

NASA Astrophysics Data System (ADS)

Wang, Shuo; Zhang, Yiqun

2015-10-01

Track-before-detect (TBD) based target detection involves a hypothesis test of merit functions which measure each track as a possible target track. Its accuracy depends on the precision of the distribution of merit functions, which determines the threshold for a test. Generally, merit functions are regarded Gaussian, and on this basis the distribution is estimated, which is true for most methods such as the multiple hypothesis tracking (MHT). However, merit functions for some other methods such as the dynamic programming algorithm (DPA) are non-Guassian and cross-correlated. Since existing methods cannot reasonably measure the correlation, the exact distribution can hardly be estimated. If merit functions are assumed Guassian and independent, the error between an actual distribution and its approximation may occasionally over 30 percent, and is divergent by propagation. Hence, in this paper, we propose a novel estimation of distribution method based on Copulas, by which the distribution can be estimated precisely, where the error is less than 1 percent without propagation. Moreover, the estimation merely depends on the form of merit functions and the structure of a tracking algorithm, and is invariant to measurements. Thus, the distribution can be estimated in advance, greatly reducing the demand for real-time calculation of distribution functions.

Intensity-based masking: A tool to improve functional connectivity results of resting-state fMRI.

PubMed

Peer, Michael; Abboud, Sami; Hertz, Uri; Amedi, Amir; Arzy, Shahar

2016-07-01

Seed-based functional connectivity (FC) of resting-state functional MRI data is a widely used methodology, enabling the identification of functional brain networks in health and disease. Based on signal correlations across the brain, FC measures are highly sensitive to noise. A somewhat neglected source of noise is the fMRI signal attenuation found in cortical regions in close vicinity to sinuses and air cavities, mainly in the orbitofrontal, anterior frontal and inferior temporal cortices. BOLD signal recorded at these regions suffers from dropout due to susceptibility artifacts, resulting in an attenuated signal with reduced signal-to-noise ratio in as many as 10% of cortical voxels. Nevertheless, signal attenuation is largely overlooked during FC analysis. Here we first demonstrate that signal attenuation can significantly influence FC measures by introducing false functional correlations and diminishing existing correlations between brain regions. We then propose a method for the detection and removal of the attenuated signal ("intensity-based masking") by fitting a Gaussian-based model to the signal intensity distribution and calculating an intensity threshold tailored per subject. Finally, we apply our method on real-world data, showing that it diminishes false correlations caused by signal dropout, and significantly improves the ability to detect functional networks in single subjects. Furthermore, we show that our method increases inter-subject similarity in FC, enabling reliable distinction of different functional networks. We propose to include the intensity-based masking method as a common practice in the pre-processing of seed-based functional connectivity analysis, and provide software tools for the computation of intensity-based masks on fMRI data. Hum Brain Mapp 37:2407-2418, 2016. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Regulator dependence of fixed points in quantum Einstein gravity with R 2 truncation

NASA Astrophysics Data System (ADS)

Nagy, S.; Fazekas, B.; Peli, Z.; Sailer, K.; Steib, I.

2018-03-01

We performed a functional renormalization group analysis for the quantum Einstein gravity including a quadratic term in the curvature. The ultraviolet non-gaussian fixed point and its critical exponent for the correlation length are identified for different forms of regulators in case of dimension 3. We searched for that optimized regulator where the physical quantities show the least regulator parameter dependence. It is shown that the Litim regulator satisfies this condition. The infrared fixed point has also been investigated, it is found that the exponent is insensitive to the third coupling introduced by the R 2 term.

Precision measurements and computations of transition energies in rotationally cold triatomic hydrogen ions up to the midvisible spectral range.

PubMed

Pavanello, Michele; Adamowicz, Ludwik; Alijah, Alexander; Zobov, Nikolai F; Mizus, Irina I; Polyansky, Oleg L; Tennyson, Jonathan; Szidarovszky, Tamás; Császár, Attila G; Berg, Max; Petrignani, Annemieke; Wolf, Andreas

2012-01-13

First-principles computations and experimental measurements of transition energies are carried out for vibrational overtone lines of the triatomic hydrogen ion H(3)(+) corresponding to floppy vibrations high above the barrier to linearity. Action spectroscopy is improved to detect extremely weak visible-light spectral lines on cold trapped H(3)(+) ions. A highly accurate potential surface is obtained from variational calculations using explicitly correlated Gaussian wave function expansions. After nonadiabatic corrections, the floppy H(3)(+) vibrational spectrum is reproduced at the 0.1 cm(-1) level up to 16600 cm(-1).

Non-stationary pre-envelope covariances of non-classically damped systems

NASA Astrophysics Data System (ADS)

Muscolino, G.

1991-08-01

A new formulation is given to evaluate the stationary and non-stationary response of linear non-classically damped systems subjected to multi-correlated non-separable Gaussian input processes. This formulation is based on a new and more suitable definition of the impulse response function matrix for such systems. It is shown that, when using this definition, the stochastic response of non-classically damped systems involves the evaluation of quantities similar to those of classically damped ones. Furthermore, considerations about non-stationary cross-covariances, spectral moments and pre-envelope cross-covariances are presented for a monocorrelated input process.

PERIODIC AUTOREGRESSIVE-MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES.

USGS Publications Warehouse

Vecchia, A.V.

1985-01-01

Results involving correlation properties and parameter estimation for autogressive-moving average models with periodic parameters are presented. A multivariate representation of the PARMA model is used to derive parameter space restrictions and difference equations for the periodic autocorrelations. Close approximation to the likelihood function for Gaussian PARMA processes results in efficient maximum-likelihood estimation procedures. Terms in the Fourier expansion of the parameters are sequentially included, and a selection criterion is given for determining the optimal number of harmonics to be included. Application of the techniques is demonstrated through analysis of a monthly streamflow time series.

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

NASA Astrophysics Data System (ADS)

Zverev, V. V.; Rubinstein, B. Ya.

1991-04-01

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.

Coupled-cluster treatment of molecular strong-field ionization

NASA Astrophysics Data System (ADS)

Jagau, Thomas-C.

2018-05-01

Ionization rates and Stark shifts of H2, CO, O2, H2O, and CH4 in static electric fields have been computed with coupled-cluster methods in a basis set of atom-centered Gaussian functions with a complex-scaled exponent. Consideration of electron correlation is found to be of great importance even for a qualitatively correct description of the dependence of ionization rates and Stark shifts on the strength and orientation of the external field. The analysis of the second moments of the molecular charge distribution suggests a simple criterion for distinguishing tunnel and barrier suppression ionization in polyatomic molecules.

A Degree-Scale Measurement of the Anisotropy in the Cosmic Microwave Background

NASA Technical Reports Server (NTRS)

Wollack, Ed; Jarosik, Norm; Netterfield, Barth; Page, Lyman; Wilkinson, David

1995-01-01

We report the detection of anisotropy in the microwave sky at 3O GHz and at l deg angular scales. The most economical interpretation of the data is that the fluctuations are intrinsic to the cosmic microwave background. However, galactic free-free emission is ruled out with only 90% confidence. The most likely root-mean-squared amplitude of the fluctuations, assuming they are described by a Gaussian auto-correlation function with a coherence angle of 1.2 deg, is 41(+16/-13) (mu)K. We also present limits on the anisotropy of the polarization of the cosmic microwave background.

Molecular dynamics of liquid crystals

NASA Astrophysics Data System (ADS)

Sarman, Sten

1997-02-01

We derive Green-Kubo relations for the viscosities of a nematic liquid crystal. The derivation is based on the application of a Gaussian constraint algorithm that makes the director angular velocity of a liquid crystal a constant of motion. Setting this velocity equal to zero means that a director-based coordinate system becomes an inertial frame and that the constraint torques do not do any work on the system. The system consequently remains in equilibrium. However, one generates a different equilibrium ensemble. The great advantage of this ensemble is that the Green-Kubo relations for the viscosities become linear combinations of time correlation function integrals, whereas they are complicated rational functions in the conventional canonical ensemble. This facilitates the numerical evaluation of the viscosities by molecular dynamics simulations.

Correlated continuous time random walk and option pricing

NASA Astrophysics Data System (ADS)

Lv, Longjin; Xiao, Jianbin; Fan, Liangzhong; Ren, Fuyao

2016-04-01

In this paper, we study a correlated continuous time random walk (CCTRW) with averaged waiting time, whose probability density function (PDF) is proved to follow stretched Gaussian distribution. Then, we apply this process into option pricing problem. Supposing the price of the underlying is driven by this CCTRW, we find this model captures the subdiffusive characteristic of financial markets. By using the mean self-financing hedging strategy, we obtain the closed-form pricing formulas for a European option with and without transaction costs, respectively. At last, comparing the obtained model with the classical Black-Scholes model, we find the price obtained in this paper is higher than that obtained from the Black-Scholes model. A empirical analysis is also introduced to confirm the obtained results can fit the real data well.

Profiling and Quantification of Phenolics in Stevia rebaudiana Leaves.

PubMed

Karaköse, Hande; Müller, Anja; Kuhnert, Nikolai

2015-10-21

Stevia rebaudiana (Bertoni) is a plant from the Asteraceae family with significant economic value because of the steviol glycoside sweeteners in its leaves. Chlorogenic acids and flavonoid glycosides of S. rebaudiana from seven different botanical varieties cultivated over two years and harvested three times a year in eight European locations were profiled and quantified in a total of 166 samples. Compounds quantified include chlorogenic acids as well as flavonoid glycosides and aglycons. All phenolic concentration profiles show a perfect Gaussian distribution. Principal component analyses allow distinction between varieties of different geographical origin and distinction between different plant varieties. Although concentrations of all chlorogenic acids showed a positive correlation, no correlation was observed for flavonoid glycosides. Conclusions from these findings with respect to the biosynthesis and functional role of phenolics in S. rebaudiana are discussed.

Large Footprint LiDAR Data Processing for Ground Detection and Biomass Estimation

NASA Astrophysics Data System (ADS)

Zhuang, Wei

Ground detection in large footprint waveform Light Detection And Ranging (LiDAR) data is important in calculating and estimating downstream products, especially in forestry applications. For example, tree heights are calculated as the difference between the ground peak and first returned signal in a waveform. Forest attributes, such as aboveground biomass, are estimated based on the tree heights. This dissertation investigated new metrics and algorithms for estimating aboveground biomass and extracting ground peak location in large footprint waveform LiDAR data. In the first manuscript, an accurate and computationally efficient algorithm, named Filtering and Clustering Algorithm (FICA), was developed based on a set of multiscale second derivative filters for automatically detecting the ground peak in an waveform from Land, Vegetation and Ice Sensor. Compared to existing ground peak identification algorithms, FICA was tested in different land cover type plots and showed improved accuracy in ground detections of the vegetation plots and similar accuracy in developed area plots. Also, FICA adopted a peak identification strategy rather than following a curve-fitting process, and therefore, exhibited improved efficiency. In the second manuscript, an algorithm was developed specifically for shrub waveforms. The algorithm only partially fitted the shrub canopy reflection and detected the ground peak by investigating the residual signal, which was generated by deducting a Gaussian fitting function from the raw waveform. After the deduction, the overlapping ground peak was identified as the local maximum of the residual signal. In addition, an applicability model was built for determining waveforms where the proposed PCF algorithm should be applied. In the third manuscript, a new set of metrics was developed to increase accuracy in biomass estimation models. The metrics were based on the results of Gaussian decomposition. They incorporated both waveform intensity represented by the area covered by a Gaussian function and its associated heights, which was the centroid of the Gaussian function. By considering signal reflection of different vegetation layers, the developed metrics obtained better estimation accuracy in aboveground biomass when compared to existing metrics. In addition, the new developed metrics showed strong correlation with other forest structural attributes, such as mean Diameter at Breast Height (DBH) and stem density. In sum, the dissertation investigated the various techniques for large footprint waveform LiDAR processing for detecting the ground peak and estimating biomass. The novel techniques developed in this dissertation showed better performance than existing methods or metrics.

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

PubMed

Ginzburg, D; Mann, A

2014-03-10

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

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

NASA Astrophysics Data System (ADS)

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

2000-05-01

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

Linear Scaling Density Functional Calculations with Gaussian Orbitals

NASA Technical Reports Server (NTRS)

Scuseria, Gustavo E.

1999-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1974-01-01

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

CMB bispectrum, trispectrum, non-Gaussianity, and the Cramer-Rao bound

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

Kamionkowski, Marc; Smith, Tristan L.; Heavens, Alan

Minimum-variance estimators for the parameter f{sub nl} that quantifies local-model non-Gaussianity can be constructed from the cosmic microwave background (CMB) bispectrum (three-point function) and also from the trispectrum (four-point function). Some have suggested that a comparison between the estimates for the values of f{sub nl} from the bispectrum and trispectrum allow a consistency test for the model. But others argue that the saturation of the Cramer-Rao bound--which gives a lower limit to the variance of an estimator--by the bispectrum estimator implies that no further information on f{sub nl} can be obtained from the trispectrum. Here, we elaborate the nature ofmore » the correlation between the bispectrum and trispectrum estimators for f{sub nl}. We show that the two estimators become statistically independent in the limit of large number of CMB pixels, and thus that the trispectrum estimator does indeed provide additional information on f{sub nl} beyond that obtained from the bispectrum. We explain how this conclusion is consistent with the Cramer-Rao bound. Our discussion of the Cramer-Rao bound may be of interest to those doing Fisher-matrix parameter-estimation forecasts or data analysis in other areas of physics as well.« less

Joint resonant CMB power spectrum and bispectrum estimation

NASA Astrophysics Data System (ADS)

Meerburg, P. Daniel; Münchmeyer, Moritz; Wandelt, Benjamin

2016-02-01

We develop the tools necessary to assess the statistical significance of resonant features in the CMB correlation functions, combining power spectrum and bispectrum measurements. This significance is typically addressed by running a large number of simulations to derive the probability density function (PDF) of the feature-amplitude in the Gaussian case. Although these simulations are tractable for the power spectrum, for the bispectrum they require significant computational resources. We show that, by assuming that the PDF is given by a multivariate Gaussian where the covariance is determined by the Fisher matrix of the sine and cosine terms, we can efficiently produce spectra that are statistically close to those derived from full simulations. By drawing a large number of spectra from this PDF, both for the power spectrum and the bispectrum, we can quickly determine the statistical significance of candidate signatures in the CMB, considering both single frequency and multifrequency estimators. We show that for resonance models, cosmology and foreground parameters have little influence on the estimated amplitude, which allows us to simplify the analysis considerably. A more precise likelihood treatment can then be applied to candidate signatures only. We also discuss a modal expansion approach for the power spectrum, aimed at quickly scanning through large families of oscillating models.

Stochastic and Statistical Analysis of Utility Revenues and Weather Data Analysis for Consumer Demand Estimation in Smart Grids

PubMed Central

Ali, S. M.; Mehmood, C. A; Khan, B.; Jawad, M.; Farid, U; Jadoon, J. K.; Ali, M.; Tareen, N. K.; Usman, S.; Majid, M.; Anwar, S. M.

2016-01-01

In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion. PMID:27314229

Stochastic and Statistical Analysis of Utility Revenues and Weather Data Analysis for Consumer Demand Estimation in Smart Grids.

PubMed

Ali, S M; Mehmood, C A; Khan, B; Jawad, M; Farid, U; Jadoon, J K; Ali, M; Tareen, N K; Usman, S; Majid, M; Anwar, S M

2016-01-01

In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion.

Statistical theory for the Kardar-Parisi-Zhang equation in (1+1) dimensions.

PubMed

Masoudi, A A; Shahbazi, F; Davoudi, J; Tabar, M Reza Rahimi

2002-02-01

The Kardar-Parisi-Zhang (KPZ) equation in (1+1) dimensions dynamically develops sharply connected valley structures within which the height derivative is not continuous. We develop a statistical theory for the KPZ equation in (1+1) dimensions driven with a random forcing that is white in time and Gaussian-correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient P(h-h*, partial differential(x)h,t) when the forcing correlation length is much smaller than the system size and much larger than the typical sharp valley width. In the time scales before the creation of the sharp valleys, we find the exact generating function of h-h* and partial differential(x)h. The time scale of the sharp valley formation is expressed in terms of the force characteristics. In the stationary state, when the sharp valleys are fully developed, finite-size corrections to the scaling laws of the structure functions left angle bracket(h-h*)(n)(partial differential(x)h)(m)right angle bracket are also obtained.

Accurate B-spline-based 3-D interpolation scheme for digital volume correlation

NASA Astrophysics Data System (ADS)

Ren, Maodong; Liang, Jin; Wei, Bin

2016-12-01

An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

Spatial Copula Model for Imputing Traffic Flow Data from Remote Microwave Sensors

PubMed Central

Ma, Xiaolei; Du, Bowen; Yu, Bin

2017-01-01

Issues of missing data have become increasingly serious with the rapid increase in usage of traffic sensors. Analyses of the Beijing ring expressway have showed that up to 50% of microwave sensors pose missing values. The imputation of missing traffic data must be urgently solved although a precise solution that cannot be easily achieved due to the significant number of missing portions. In this study, copula-based models are proposed for the spatial interpolation of traffic flow from remote traffic microwave sensors. Most existing interpolation methods only rely on covariance functions to depict spatial correlation and are unsuitable for coping with anomalies due to Gaussian consumption. Copula theory overcomes this issue and provides a connection between the correlation function and the marginal distribution function of traffic flow. To validate copula-based models, a comparison with three kriging methods is conducted. Results indicate that copula-based models outperform kriging methods, especially on roads with irregular traffic patterns. Copula-based models demonstrate significant potential to impute missing data in large-scale transportation networks. PMID:28934164

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.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

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

PubMed

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-08-01

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

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

PubMed

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

2010-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2010-12-01

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

Time-frequency distributions for propulsion-system diagnostics

NASA Astrophysics Data System (ADS)

Griffin, Michael E.; Tulpule, Sharayu

1991-12-01

The Wigner distribution and its smoothed versions, i.e., Choi-Williams and Gaussian kernels, are evaluated for propulsion system diagnostics. The approach is intended for off-line kernel design by using the ambiguity domain to select the appropriate Gaussian kernel. The features produced by the Wigner distribution and its smoothed versions correlate remarkably well with documented failure indications. The selection of the kernel on the other hand is very subjective for our unstructured data.

Reliability Implications in Wood Systems of a Bivariate Gaussian-Weibull Distribution and the Associated Univariate Pseudo-truncated Weibull

Treesearch

Steve P. Verrill; James W. Evans; David E. Kretschmann; Cherilyn A. Hatfield

2014-01-01

Two important wood properties are the modulus of elasticity (MOE) and the modulus of rupture (MOR). In the past, the statistical distribution of the MOE has often been modeled as Gaussian, and that of the MOR as lognormal or as a two- or three-parameter Weibull distribution. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior...

Performance Evaluation of Satellite Communication Systems Operating in the Q/V/W Bands

DTIC Science & Technology

2013-06-30

cloud liquid water content (blue line = original MODIS data, red line = underlying Gaussian process) and of rainfall ( NIMROD rain rate data) .. 3-22...correlation of rainfall as obtained from an extensive set of rain field collected by the NIMROD weather radar network [Luini and Capsoni, 2012] has been...underlying Gaussian process) Rain ( NIMROD data) Figure 3-21. Decorrelation with distance of the cloud liquid water content (blue line = original

Maximum likelihood estimation of the parameters of a bivariate Gaussian-Weibull distribution from machine stress-rated data

Treesearch

Steve P. Verrill; David E. Kretschmann; James W. Evans

2016-01-01

Two important wood properties are stiffness (modulus of elasticity, MOE) and bending strength (modulus of rupture, MOR). In the past, MOE has often been modeled as a Gaussian and MOR as a lognormal or a two- or threeparameter Weibull. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior of MOE and MOR for the purposes of wood...

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

PubMed

Čársky, Petr; Čurík, Roman; Varga, Štefan

2012-03-21

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

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

PubMed

Kühn, Michael; Weigend, Florian

2013-12-10

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

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

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Anomalous transport in the crowded world of biological cells

NASA Astrophysics Data System (ADS)

Höfling, Felix; Franosch, Thomas

2013-04-01

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2015-01-01

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field-theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝δ (t -t') /k⊥d -1 +ξ , where k⊥=|k⊥| and k⊥ is the component of the wave vector, perpendicular to the distinguished direction ("direction of the flow")—the d -dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131, 381 (1990), 10.1007/BF02161420]. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well-known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: Instead of powerlike corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L . The key point is that the matrices of scaling dimensions of the relevant families of composite operators appear nilpotent and cannot be diagonalized. The detailed proof of this fact is given for the correlation functions of arbitrary order.

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

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

PubMed

Liu, Chengyu; Zhao, Lina; Liu, Changchun

2014-01-01

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

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

PubMed

Zhou, Nan; Wang, Jian

2018-05-23

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Non-Gaussianity in a quasiclassical electronic circuit

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi J.; Hayakawa, Hisao

2017-05-01

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

Second order Pseudo-gaussian shaper

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

Beche, Jean-Francois

2002-11-22

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

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

NASA Technical Reports Server (NTRS)

Steinwolf, Alexander; Rizzi, Stephen A.

2003-01-01

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

Quantum non-Gaussianity and quantification of nonclassicality

NASA Astrophysics Data System (ADS)

Kühn, B.; Vogel, W.

2018-05-01

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

On the analysis of very small samples of Gaussian repeated measurements: an alternative approach.

PubMed

Westgate, Philip M; Burchett, Woodrow W

2017-03-15

The analysis of very small samples of Gaussian repeated measurements can be challenging. First, due to a very small number of independent subjects contributing outcomes over time, statistical power can be quite small. Second, nuisance covariance parameters must be appropriately accounted for in the analysis in order to maintain the nominal test size. However, available statistical strategies that ensure valid statistical inference may lack power, whereas more powerful methods may have the potential for inflated test sizes. Therefore, we explore an alternative approach to the analysis of very small samples of Gaussian repeated measurements, with the goal of maintaining valid inference while also improving statistical power relative to other valid methods. This approach uses generalized estimating equations with a bias-corrected empirical covariance matrix that accounts for all small-sample aspects of nuisance correlation parameter estimation in order to maintain valid inference. Furthermore, the approach utilizes correlation selection strategies with the goal of choosing the working structure that will result in the greatest power. In our study, we show that when accurate modeling of the nuisance correlation structure impacts the efficiency of regression parameter estimation, this method can improve power relative to existing methods that yield valid inference. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Redshift Evolution of Non-Gaussianity in Cosmic Large-Scale Structure

NASA Astrophysics Data System (ADS)

Sullivan, James; Wiegand, Alexander; Eisenstein, Daniel

2018-01-01

We probe the higher-order galaxy clustering in the final data release (DR12) of the Sloan Digital Sky Survey using germ-grain Minkowski Functionals (MFs). Our data selection contains 979,430 BOSS galaxies from both the northern and southern galactic caps over the redshift range 0.2 - 0.6. We extract the higher-order parts of the MFs and find deviations from the case without higher order MFs with chi-squared values of order 1000 for 24 degrees of freedom across the entire data selection. We show the MFs to be sensitive to contributions up to the five-point correlation function across the entire data selection. We measure significant redshift evolution in the higher-order functionals for the first time, with a percentage growth between redshift bins of approximately 20 % in both galactic caps. This is a nearly a factor of 2 greater than similar growth in the two-point correlation function and will allow for tests of non-linear structure growth by comparing the three-point and higher-order parts to their expected theoretical values. The SAO REU program is funded by the National Science Foundation REU and Department of Defense ASSURE programs under NSF Grant AST-1659473, and by the Smithsonian Institution.

Schrödinger and Dirac solutions to few-body problems

NASA Astrophysics Data System (ADS)

Muolo, Andrea; Reiher, Markus

We elaborate on the variational solution of the Schrödinger and Dirac equations for small atomic and molecular systems without relying on the Born-Oppenheimer approximation. The all-particle equations of motion are solved in a numerical procedure that relies on the variational principle, Cartesian coordinates and parametrized explicitly correlated Gaussians functions. A stochastic optimization of the variational parameters allows the calculation of accurate wave functions for ground and excited states. Expectation values such as the radial and angular distribution functions or the dipole moment can be calculated. We developed a simple strategy for the elimination of the global translation that allows to generally adopt laboratory-fixed cartesian coordinates. Simple expressions for the coordinates and operators are then preserved throughout the formalism. For relativistic calculations we devised a kinetic-balance condition for explicitly correlated basis functions. We demonstrate that the kinetic-balance condition can be obtained from the row reduction process commonly applied to solve systems of linear equations. The resulting form of kinetic balance establishes a relation between all components of the spinor of an N-fermion system. ETH Zürich, Laboratorium für Physikalische Chemie, CH-8093 Zürich, Switzerland.