Simultaneous Gaussian and exponential inversion for improved analysis of shales by NMR relaxometry

Science.gov (United States)

Washburn, Kathryn E.; Anderssen, Endre; Vogt, Sarah J.; Seymour, Joseph D.; Birdwell, Justin E.; Kirkland, Catherine M.; Codd, Sarah L.

2014-01-01

Nuclear magnetic resonance (NMR) relaxometry is commonly used to provide lithology-independent porosity and pore-size estimates for petroleum resource evaluation based on fluid-phase signals. However in shales, substantial hydrogen content is associated with solid and fluid signals and both may be detected. Depending on the motional regime, the signal from the solids may be best described using either exponential or Gaussian decay functions. When the inverse Laplace transform, the standard method for analysis of NMR relaxometry results, is applied to data containing Gaussian decays, this can lead to physically unrealistic responses such as signal or porosity overcall and relaxation times that are too short to be determined using the applied instrument settings. We apply a new simultaneous Gaussian-Exponential (SGE) inversion method to simulated data and measured results obtained on a variety of oil shale samples. The SGE inversion produces more physically realistic results than the inverse Laplace transform and displays more consistent relaxation behavior at high magnetic field strengths. Residuals for the SGE inversion are consistently lower than for the inverse Laplace method and signal overcall at short T2 times is mitigated. Beyond geological samples, the method can also be applied in other fields where the sample relaxation consists of both Gaussian and exponential decays, for example in material, medical and food sciences.

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

DEFF Research Database (Denmark)

Berg, Jacob; Natarajan, Anand; Mann, Jakob

2016-01-01

taking into account the safety factor for extreme moments. Other extreme load moments as well as the fatigue loads are not affected because of the use of non-Gaussian turbulent inflow. It is suggested that the turbine thus acts like a low-pass filter that averages out the non-Gaussian behaviour, which......From large-eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non-Gaussian counterpart. Time series from the two...

Moderately nonlinear ultrasound propagation in blood-mimicking fluid.

Science.gov (United States)

Kharin, Nikolay A; Vince, D Geoffrey

2004-04-01

In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading.

Gaussian entanglement revisited

Science.gov (United States)

Lami, Ludovico; Serafini, Alessio; Adesso, Gerardo

2018-02-01

We present a novel approach to the separability problem for Gaussian quantum states of bosonic continuous variable systems. We derive a simplified necessary and sufficient separability criterion for arbitrary Gaussian states of m versus n modes, which relies on convex optimisation over marginal covariance matrices on one subsystem only. We further revisit the currently known results stating the equivalence between separability and positive partial transposition (PPT) for specific classes of Gaussian states. Using techniques based on matrix analysis, such as Schur complements and matrix means, we then provide a unified treatment and compact proofs of all these results. In particular, we recover the PPT-separability equivalence for: (i) Gaussian states of 1 versus n modes; and (ii) isotropic Gaussian states. In passing, we also retrieve (iii) the recently established equivalence between separability of a Gaussian state and and its complete Gaussian extendability. Our techniques are then applied to progress beyond the state of the art. We prove that: (iv) Gaussian states that are invariant under partial transposition are necessarily separable; (v) the PPT criterion is necessary and sufficient for separability for Gaussian states of m versus n modes that are symmetric under the exchange of any two modes belonging to one of the parties; and (vi) Gaussian states which remain PPT under passive optical operations can not be entangled by them either. This is not a foregone conclusion per se (since Gaussian bound entangled states do exist) and settles a question that had been left unanswered in the existing literature on the subject. This paper, enjoyable by both the quantum optics and the matrix analysis communities, overall delivers technical and conceptual advances which are likely to be useful for further applications in continuous variable quantum information theory, beyond the separability problem.

Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states

International Nuclear Information System (INIS)

Adesso, Gerardo; Illuminati, Fabrizio

2005-01-01

We study the entanglement of general (pure or mixed) two-mode Gaussian states of continuous-variable systems by comparing the two available classes of computable measures of entanglement: entropy-inspired Gaussian convex-roof measures and positive partial transposition-inspired measures (negativity and logarithmic negativity). We first review the formalism of Gaussian measures of entanglement, adopting the framework introduced in M. M. Wolf et al., Phys. Rev. A 69, 052320 (2004), where the Gaussian entanglement of formation was defined. We compute explicitly Gaussian measures of entanglement for two important families of nonsymmetric two-mode Gaussian state: namely, the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in G. Adesso et al., Phys. Rev. Lett. 92, 087901 (2004). This analysis allows us to compare the different orderings induced on the set of entangled two-mode Gaussian states by the negativities and by the Gaussian measures of entanglement. We find that in a certain range of values of the global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement of formation than states of maximum negativity. Consequently, Gaussian measures and negativities are definitely inequivalent measures of entanglement on nonsymmetric two-mode Gaussian states, even when restricted to a class of extremal states. On the other hand, the two families of entanglement measures are completely equivalent on symmetric states, for which the Gaussian entanglement of formation coincides with the true entanglement of formation. Finally, we show that the inequivalence between the two families of continuous-variable entanglement measures is somehow limited. Namely, we rigorously prove that, at fixed negativities, the Gaussian measures of entanglement are bounded from below. Moreover, we provide some strong evidence suggesting that they

Sums and Gaussian vectors

CERN Document Server

Yurinsky, Vadim Vladimirovich

1995-01-01

Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.

Osmotic Suppression of Positional Fluctuation of a Trapped Particle in a Near-Critical Binary Fluid Mixture in the Regime of the Gaussian Model

Science.gov (United States)

Fujitani, Youhei

2017-11-01

Suppose a spherical colloidal particle surrounded by a near-critical binary fluid mixture in the homogeneous phase. The particle surface usually preferentially attracts one component of the mixture, and the resultant concentration gradient, which causes the osmotic pressure, becomes significant in the ambient near-criticality. The concentration profile is deformed by the particle motion, and can generate a nonzero force exerted on the moving particle. This link was previously shown to slightly suppress the positional equal-time correlation of a particle trapped by a harmonic potential. This previous study presupposed a small fluctuation amplitude of a particle much larger than the correlation length, a weak preferential attraction, and the Gaussian model for the free-energy functional of the mixture. In the present study, we calculate the equal-time correlation without assuming the weak preferential attraction and show that the suppression becomes much more distinct in some range of the trap stiffness because of the increased induced mass. This suggests the possible experimental usage of a trapped particle as a probe for local environments of a near-critical binary fluid mixture.

Nonlinear Bayesian Estimation of BOLD Signal under Non-Gaussian Noise

Directory of Open Access Journals (Sweden)

Ali Fahim Khan

2015-01-01

Full Text Available Modeling the blood oxygenation level dependent (BOLD signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF.

Resampling methods in Microsoft Excel® for estimating reference intervals.

Science.gov (United States)

Theodorsson, Elvar

2015-01-01

Computer-intensive resampling/bootstrap methods are feasible when calculating reference intervals from non-Gaussian or small reference samples. Microsoft Excel® in version 2010 or later includes natural functions, which lend themselves well to this purpose including recommended interpolation procedures for estimating 2.5 and 97.5 percentiles. 
The purpose of this paper is to introduce the reader to resampling estimation techniques in general and in using Microsoft Excel® 2010 for the purpose of estimating reference intervals in particular.
 Parametric methods are preferable to resampling methods when the distributions of observations in the reference samples is Gaussian or can transformed to that distribution even when the number of reference samples is less than 120. Resampling methods are appropriate when the distribution of data from the reference samples is non-Gaussian and in case the number of reference individuals and corresponding samples are in the order of 40. At least 500-1000 random samples with replacement should be taken from the results of measurement of the reference samples.

Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.

Science.gov (United States)

Cagniot, Emmanuel; Fromager, Michael; Ait-Ameur, Kamel

2009-11-01

A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.

Resource theory of non-Gaussian operations

Science.gov (United States)

Zhuang, Quntao; Shor, Peter W.; Shapiro, Jeffrey H.

2018-05-01

Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.

Cerebrospinal fluid glucose and lactate: age-specific reference values and implications for clinical practice.

NARCIS (Netherlands)

Leen, W.G.; Willemsen, M.A.A.P.; Wevers, R.A.; Verbeek, M.M.

2012-01-01

Cerebrospinal fluid (CSF) analysis is an important tool in the diagnostic work-up of many neurological disorders, but reference ranges for CSF glucose, CSF/plasma glucose ratio and CSF lactate based on studies with large numbers of CSF samples are not available. Our aim was to define age-specific

Extended q -Gaussian and q -exponential distributions from gamma random variables

Science.gov (United States)

Budini, Adrián A.

2015-05-01

The family of q -Gaussian and q -exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q -Gaussian and q -exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q -Gaussian and modified q -exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.

A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families

KAUST Repository

Dutta, Subhajit

2014-07-28

Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.

A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families

KAUST Repository

Dutta, Subhajit; Genton, Marc G.

2014-01-01

Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.

Vibronic Boson Sampling: Generalized Gaussian Boson Sampling for Molecular Vibronic Spectra at Finite Temperature.

Science.gov (United States)

Huh, Joonsuk; Yung, Man-Hong

2017-08-07

Molecular vibroic spectroscopy, where the transitions involve non-trivial Bosonic correlation due to the Duschinsky Rotation, is strongly believed to be in a similar complexity class as Boson Sampling. At finite temperature, the problem is represented as a Boson Sampling experiment with correlated Gaussian input states. This molecular problem with temperature effect is intimately related to the various versions of Boson Sampling sharing the similar computational complexity. Here we provide a full description to this relation in the context of Gaussian Boson Sampling. We find a hierarchical structure, which illustrates the relationship among various Boson Sampling schemes. Specifically, we show that every instance of Gaussian Boson Sampling with an initial correlation can be simulated by an instance of Gaussian Boson Sampling without initial correlation, with only a polynomial overhead. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes. We refer such a generalized Gaussian Boson Sampling motivated by the molecular sampling problem as Vibronic Boson Sampling.

Quantum information with Gaussian states

International Nuclear Information System (INIS)

Wang Xiangbin; Hiroshima, Tohya; Tomita, Akihisa; Hayashi, Masahito

2007-01-01

Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright Gaussian light and weak Gaussian light. Extending the existing results of quantum information with discrete quantum states to the case of continuous variable quantum states is an interesting theoretical job. The quantum Gaussian states play a central role in such a case. We review the properties and applications of Gaussian states in quantum information with emphasis on the fundamental concepts, the calculation techniques and the effects of imperfections of the real-life experimental setups. Topics here include the elementary properties of Gaussian states and relevant quantum information device, entanglement-based quantum tasks such as quantum teleportation, quantum cryptography with weak and strong Gaussian states and the quantum channel capacity, mathematical theory of quantum entanglement and state estimation for Gaussian states

Noise Estimation and Quality Assessment of Gaussian Noise Corrupted Images

Science.gov (United States)

Kamble, V. M.; Bhurchandi, K.

2018-03-01

Evaluating the exact quantity of noise present in an image and quality of an image in the absence of reference image is a challenging task. We propose a near perfect noise estimation method and a no reference image quality assessment method for images corrupted by Gaussian noise. The proposed methods obtain initial estimate of noise standard deviation present in an image using the median of wavelet transform coefficients and then obtains a near to exact estimate using curve fitting. The proposed noise estimation method provides the estimate of noise within average error of +/-4%. For quality assessment, this noise estimate is mapped to fit the Differential Mean Opinion Score (DMOS) using a nonlinear function. The proposed methods require minimum training and yields the noise estimate and image quality score. Images from Laboratory for image and Video Processing (LIVE) database and Computational Perception and Image Quality (CSIQ) database are used for validation of the proposed quality assessment method. Experimental results show that the performance of proposed quality assessment method is at par with the existing no reference image quality assessment metric for Gaussian noise corrupted images.

Fluid Dynamic Models for Bhattacharyya-Based Discriminant Analysis.

Science.gov (United States)

Noh, Yung-Kyun; Hamm, Jihun; Park, Frank Chongwoo; Zhang, Byoung-Tak; Lee, Daniel D

2018-01-01

Classical discriminant analysis attempts to discover a low-dimensional subspace where class label information is maximally preserved under projection. Canonical methods for estimating the subspace optimize an information-theoretic criterion that measures the separation between the class-conditional distributions. Unfortunately, direct optimization of the information-theoretic criteria is generally non-convex and intractable in high-dimensional spaces. In this work, we propose a novel, tractable algorithm for discriminant analysis that considers the class-conditional densities as interacting fluids in the high-dimensional embedding space. We use the Bhattacharyya criterion as a potential function that generates forces between the interacting fluids, and derive a computationally tractable method for finding the low-dimensional subspace that optimally constrains the resulting fluid flow. We show that this model properly reduces to the optimal solution for homoscedastic data as well as for heteroscedastic Gaussian distributions with equal means. We also extend this model to discover optimal filters for discriminating Gaussian processes and provide experimental results and comparisons on a number of datasets.

The Research of Indoor Positioning Based on Double-peak Gaussian Model

Directory of Open Access Journals (Sweden)

Lina Chen

2014-04-01

Full Text Available Location fingerprinting using Wi-Fi signals has been very popular and is a well accepted indoor positioning method. The key issue of the fingerprinting approach is generating the fingerprint radio map. Limited by the practical workload, only a few samples of the received signal strength are collected at each reference point. Unfortunately, fewer samples cannot accurately represent the actual distribution of the signal strength from each access point. This study finds most Wi- Fi signals have two peaks. According to the new finding, a double-peak Gaussian arithmetic is proposed to generate a fingerprint radio map. This approach requires little time to receive WiFi signals and it easy to estimate the parameters of the double-peak Gaussian function. Compared to the Gaussian function and histogram method to generate a fingerprint radio map, this method better approximates the occurrence signal distribution. This paper also compared the positioning accuracy using K-Nearest Neighbour theory for three radio maps, the test results show that the positioning distance error utilizing the double-peak Gaussian function is better than the other two methods.

When non-Gaussian states are Gaussian: Generalization of nonseparability criterion for continuous variables

International Nuclear Information System (INIS)

McHugh, Derek; Buzek, Vladimir; Ziman, Mario

2006-01-01

We present a class of non-Gaussian two-mode continuous-variable states for which the separability criterion for Gaussian states can be employed to detect whether they are separable or not. These states reduce to the two-mode Gaussian states as a special case

Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models

NARCIS (Netherlands)

Koopman, S.J.; Lucas, A.; Scharth, M.

2015-01-01

We propose a general likelihood evaluation method for nonlinear non-Gaussian state-space models using the simulation-based method of efficient importance sampling. We minimize the simulation effort by replacing some key steps of the likelihood estimation procedure by numerical integration. We refer

A Monte Carlo simulation model for stationary non-Gaussian processes

DEFF Research Database (Denmark)

Grigoriu, M.; Ditlevsen, Ove Dalager; Arwade, S. R.

2003-01-01

includes translation processes and is useful for both Monte Carlo simulation and analytical studies. As for translation processes, the mixture of translation processes can have a wide range of marginal distributions and correlation functions. Moreover, these processes can match a broader range of second...... athe proposed Monte Carlo algorithm and compare features of translation processes and mixture of translation processes. Keywords: Monte Carlo simulation, non-Gaussian processes, sampling theorem, stochastic processes, translation processes......A class of stationary non-Gaussian processes, referred to as the class of mixtures of translation processes, is defined by their finite dimensional distributions consisting of mixtures of finite dimensional distributions of translation processes. The class of mixtures of translation processes...

Statistics of peaks of Gaussian random fields

International Nuclear Information System (INIS)

Bardeen, J.M.; Bond, J.R.; Kaiser, N.; Szalay, A.S.; Stanford Univ., CA; California Univ., Berkeley; Cambridge Univ., England; Fermi National Accelerator Lab., Batavia, IL)

1986-01-01

A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of upcrossing points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima. 67 references

Aperture averaging and BER for Gaussian beam in underwater oceanic turbulence

Science.gov (United States)

Gökçe, Muhsin Caner; Baykal, Yahya

2018-03-01

In an underwater wireless optical communication (UWOC) link, power fluctuations over finite-sized collecting lens are investigated for a horizontally propagating Gaussian beam wave. The power scintillation index, also known as the irradiance flux variance, for the received irradiance is evaluated in weak oceanic turbulence by using the Rytov method. This lets us further quantify the associated performance indicators, namely, the aperture averaging factor and the average bit-error rate (). The effects on the UWOC link performance of the oceanic turbulence parameters, i.e., the rate of dissipation of kinetic energy per unit mass of fluid, the rate of dissipation of mean-squared temperature, Kolmogorov microscale, the ratio of temperature to salinity contributions to the refractive index spectrum as well as system parameters, i.e., the receiver aperture diameter, Gaussian source size, laser wavelength and the link distance are investigated.

Control method for multi-input multi-output non-Gaussian random vibration test with cross spectra consideration

Directory of Open Access Journals (Sweden)

Ronghui ZHENG

2017-12-01

Full Text Available A control method for Multi-Input Multi-Output (MIMO non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multi-output kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well. Keywords: Cross spectra, Kurtosis control, Multi-input multi-output, Non-Gaussian, Random vibration test

Vortices in Gaussian beams

CSIR Research Space (South Africa)

Roux, FS

2009-01-01

Full Text Available , t0)} = P(du, dv) {FR{g(u, v, t0)}} Replacement: u→ du = t− t0 i2 ∂ ∂u′ v → dv = t− t0 i2 ∂ ∂v′ CSIR National Laser Centre – p.13/30 Differentiation i.s.o integration Evaluate the integral over the Gaussian beam (once and for all). Then, instead... . Gaussian beams with vortex dipoles CSIR National Laser Centre – p.2/30 Gaussian beam notation Gaussian beam in normalised coordinates: g(u, v, t) = exp ( −u 2 + v2 1− it ) u = xω0 v = yω0 t = zρ ρ = piω20 λ ω0 — 1/e2 beam waist radius; ρ— Rayleigh range ω ω...

Valid analytical performance specifications for combined analytical bias and imprecision for the use of common reference intervals.

Science.gov (United States)

Hyltoft Petersen, Per; Lund, Flemming; Fraser, Callum G; Sandberg, Sverre; Sölétormos, György

2018-01-01

Background Many clinical decisions are based on comparison of patient results with reference intervals. Therefore, an estimation of the analytical performance specifications for the quality that would be required to allow sharing common reference intervals is needed. The International Federation of Clinical Chemistry (IFCC) recommended a minimum of 120 reference individuals to establish reference intervals. This number implies a certain level of quality, which could then be used for defining analytical performance specifications as the maximum combination of analytical bias and imprecision required for sharing common reference intervals, the aim of this investigation. Methods Two methods were investigated for defining the maximum combination of analytical bias and imprecision that would give the same quality of common reference intervals as the IFCC recommendation. Method 1 is based on a formula for the combination of analytical bias and imprecision and Method 2 is based on the Microsoft Excel formula NORMINV including the fractional probability of reference individuals outside each limit and the Gaussian variables of mean and standard deviation. The combinations of normalized bias and imprecision are illustrated for both methods. The formulae are identical for Gaussian and log-Gaussian distributions. Results Method 2 gives the correct results with a constant percentage of 4.4% for all combinations of bias and imprecision. Conclusion The Microsoft Excel formula NORMINV is useful for the estimation of analytical performance specifications for both Gaussian and log-Gaussian distributions of reference intervals.

Entropy of level-cut random Gaussian structures at different volume fractions.

Science.gov (United States)

Marčelja, Stjepan

2017-10-01

Cutting random Gaussian fields at a given level can create a variety of morphologically different two- or several-phase structures that have often been used to describe physical systems. The entropy of such structures depends on the covariance function of the generating Gaussian random field, which in turn depends on its spectral density. But the entropy of level-cut structures also depends on the volume fractions of different phases, which is determined by the selection of the cutting level. This dependence has been neglected in earlier work. We evaluate the entropy of several lattice models to show that, even in the cases of strongly coupled systems, the dependence of the entropy of level-cut structures on molar fractions of the constituents scales with the simple ideal noninteracting system formula. In the last section, we discuss the application of the results to binary or ternary fluids and microemulsions.

Entropy of level-cut random Gaussian structures at different volume fractions

Science.gov (United States)

Marčelja, Stjepan

2017-10-01

Cutting random Gaussian fields at a given level can create a variety of morphologically different two- or several-phase structures that have often been used to describe physical systems. The entropy of such structures depends on the covariance function of the generating Gaussian random field, which in turn depends on its spectral density. But the entropy of level-cut structures also depends on the volume fractions of different phases, which is determined by the selection of the cutting level. This dependence has been neglected in earlier work. We evaluate the entropy of several lattice models to show that, even in the cases of strongly coupled systems, the dependence of the entropy of level-cut structures on molar fractions of the constituents scales with the simple ideal noninteracting system formula. In the last section, we discuss the application of the results to binary or ternary fluids and microemulsions.

AUTONOMOUS GAUSSIAN DECOMPOSITION

International Nuclear Information System (INIS)

Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John

2015-01-01

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

AUTONOMOUS GAUSSIAN DECOMPOSITION

Energy Technology Data Exchange (ETDEWEB)

Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Heiles, Carl [Radio Astronomy Lab, UC Berkeley, 601 Campbell Hall, Berkeley, CA 94720 (United States); Hennebelle, Patrick [Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp-CNRS-Université Paris Diderot, F-91191 Gif-sur Yvette Cedex (France); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville, Socorro, NM 87801 (United States); Dickey, John, E-mail: rlindner@astro.wisc.edu [University of Tasmania, School of Maths and Physics, Private Bag 37, Hobart, TAS 7001 (Australia)

2015-04-15

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

Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function

KAUST Repository

Yan, Yuan; Genton, Marc G.

2017-01-01

Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.

Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function

KAUST Repository

Yan, Yuan

2017-07-13

Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.

Thermodynamics and structure of liquid alkali metals from the charged-hard-sphere reference fluid

International Nuclear Information System (INIS)

Lai, S.K.; Akinlade, O.; Tosi, M.P.

1989-12-01

The evaluation of thermodynamic properties of liquid alkali metals is re-examined in the approach based on the Gibbs-Bogoliubov inequality and using the fluid of charged hard spheres in the mean spherical approximation as reference system, with a view to achieving consistency with the liquid structure factor. The perturbative variational calculation of the Helmholtz free energy is based on an ab initio and highly reliable nonlocal pseudopotential. Only limited improvement is found in the calculated thermodynamic functions, even when full advantage is taken of the two variational parameters inherent in this approach. The role of thermodynamic self-consistency between the equations of state of the reference fluid derived from the routes of the internal energy and of the virial theorem is then discussed, using previous results by Hoye and Stell. An approximate evaluation of the corresponding contribution to the free energy of liquid alkali metals yields appreciable improvements in both the thermodynamic functions and the liquid structure factor. It thus appears that an accurate treatment of thermodynamic self-consistency in the charged-hard-sphere system may help to resolve some of the difficulties that are commonly met in the evaluation of thermodynamic and structural properties of liquid metals. (author). 55 refs, 4 figs, 4 tabs

Detecting the presence of a magnetic field under Gaussian and non-Gaussian noise by adaptive measurement

Energy Technology Data Exchange (ETDEWEB)

Wang, Yuan-Mei; Li, Jun-Gang, E-mail: jungl@bit.edu.cn; Zou, Jian

2017-06-15

Highlights: • Adaptive measurement strategy is used to detect the presence of a magnetic field. • Gaussian Ornstein–Uhlenbeck noise and non-Gaussian noise have been considered. • Weaker magnetic fields may be more easily detected than some stronger ones. - Abstract: By using the adaptive measurement method we study how to detect whether a weak magnetic field is actually present or not under Gaussian noise and non-Gaussian noise. We find that the adaptive measurement method can effectively improve the detection accuracy. For the case of Gaussian noise, we find the stronger the magnetic field strength, the easier for us to detect the magnetic field. Counterintuitively, for non-Gaussian noise, some weaker magnetic fields are more likely to be detected rather than some stronger ones. Finally, we give a reasonable physical interpretation.

Geometry of Gaussian quantum states

International Nuclear Information System (INIS)

Link, Valentin; Strunz, Walter T

2015-01-01

We study the Hilbert–Schmidt measure on the manifold of mixed Gaussian states in multi-mode continuous variable quantum systems. An analytical expression for the Hilbert–Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert–Schmidt measure. (paper)

A Digital Image Denoising Algorithm Based on Gaussian Filtering and Bilateral Filtering

Directory of Open Access Journals (Sweden)

Piao Weiying

2018-01-01

Full Text Available Bilateral filtering has been applied in the area of digital image processing widely, but in the high gradient region of the image, bilateral filtering may generate staircase effect. Bilateral filtering can be regarded as one particular form of local mode filtering, according to above analysis, an mixed image de-noising algorithm is proposed based on Gaussian filter and bilateral filtering. First of all, it uses Gaussian filter to filtrate the noise image and get the reference image, then to take both the reference image and noise image as the input for range kernel function of bilateral filter. The reference image can provide the image’s low frequency information, and noise image can provide image’s high frequency information. Through the competitive experiment on both the method in this paper and traditional bilateral filtering, the experimental result showed that the mixed de-noising algorithm can effectively overcome staircase effect, and the filtrated image was more smooth, its textural features was also more close to the original image, and it can achieve higher PSNR value, but the amount of calculation of above two algorithms are basically the same.

Versatile Gaussian probes for squeezing estimation

Science.gov (United States)

Rigovacca, Luca; Farace, Alessandro; Souza, Leonardo A. M.; De Pasquale, Antonella; Giovannetti, Vittorio; Adesso, Gerardo

2017-05-01

We consider an instance of "black-box" quantum metrology in the Gaussian framework, where we aim to estimate the amount of squeezing applied on an input probe, without previous knowledge on the phase of the applied squeezing. By taking the quantum Fisher information (QFI) as the figure of merit, we evaluate its average and variance with respect to this phase in order to identify probe states that yield good precision for many different squeezing directions. We first consider the case of single-mode Gaussian probes with the same energy, and find that pure squeezed states maximize the average quantum Fisher information (AvQFI) at the cost of a performance that oscillates strongly as the squeezing direction is changed. Although the variance can be brought to zero by correlating the probing system with a reference mode, the maximum AvQFI cannot be increased in the same way. A different scenario opens if one takes into account the effects of photon losses: coherent states represent the optimal single-mode choice when losses exceed a certain threshold and, moreover, correlated probes can now yield larger AvQFI values than all single-mode states, on top of having zero variance.

Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture

International Nuclear Information System (INIS)

Ji, Se-Wan; Nha, Hyunchul; Kim, M S

2015-01-01

It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous manner is relevant to study it under certain circumstances and here we address quantum steerability of Gaussian states to this aim. In particular, we attempt to reformulate the criterion for Gaussian steering in terms of local and global purities and show that it is sufficient and necessary for the case of steering a 1-mode system by an N-mode system. It subsequently enables us to reinforce a strong monogamy relation under which only one party can steer a local system of 1-mode. Moreover, we show that only a negative partial-transpose state can manifest quantum steerability by Gaussian measurements in relation to the Peres conjecture. We also discuss our formulation for the case of distributing a two-mode squeezed state via one-way quantum channels making dissipation and amplification effects, respectively. Finally, we extend our approach to include non-Gaussian measurements, more precisely, all orders of higher-order squeezing measurements, and find that this broad set of non-Gaussian measurements is not useful to demonstrate steering for Gaussian states beyond Gaussian measurements. (paper)

Super-Gaussian transport theory and the field-generating thermal instability in laser–plasmas

International Nuclear Information System (INIS)

Bissell, J J; Ridgers, C P; Kingham, R J

2013-01-01

Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser–plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal (anomalous Nernst) magnetic field advection up gradients in the electron number density n e , which we associate with a novel heat-flow q n ∝∇n e . Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ, in which case the Nernst effect is reduced by a factor of five, the ∇T e × ∇n e field generation mechanism by ∼30% (where T e is the electron temperature), and the diffusive and Righi–Leduc heat-flows by ∼80 and ∼90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux q n are checked against kinetic simulation using the Vlasov–Fokker–Planck code impact, and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic analysis. Given such strong inhibition of transport at low χ, we consider the impact of IB on the seeding and evolution of magnetic fields (in otherwise un-magnetized conditions) by examining the well-known field-generating thermal instability in the light of super-Gaussian transport theory (Tidman and Shanny 1974 Phys. Fluids 12 1207). Estimates based on conditions in an inertial confinement fusion (ICF) hohlraum suggest that super-Gaussian effects can reduce the growth-rate of the instability by ≳80%. This result may be important for ICF experiments, since by increasing the strength of IB heating it would appear possible to inhibit the spontaneous generation of large magnetic fields. (paper)

Super-Gaussian transport theory and the field-generating thermal instability in laser-plasmas

Science.gov (United States)

Bissell, J. J.; Ridgers, C. P.; Kingham, R. J.

2013-02-01

Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser-plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal (anomalous Nernst) magnetic field advection up gradients in the electron number density ne, which we associate with a novel heat-flow qn∝∇ne. Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ, in which case the Nernst effect is reduced by a factor of five, the ∇Te × ∇ne field generation mechanism by ˜30% (where Te is the electron temperature), and the diffusive and Righi-Leduc heat-flows by ˜80 and ˜90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux qn are checked against kinetic simulation using the Vlasov-Fokker-Planck code impact, and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic analysis. Given such strong inhibition of transport at low χ, we consider the impact of IB on the seeding and evolution of magnetic fields (in otherwise un-magnetized conditions) by examining the well-known field-generating thermal instability in the light of super-Gaussian transport theory (Tidman and Shanny 1974 Phys. Fluids 12 1207). Estimates based on conditions in an inertial confinement fusion (ICF) hohlraum suggest that super-Gaussian effects can reduce the growth-rate of the instability by ≳80%. This result may be important for ICF experiments, since by increasing the strength of IB heating it would appear possible to inhibit the spontaneous generation of large magnetic fields.

Fecal electrolyte testing for evaluation of unexplained diarrhea: Validation of body fluid test accuracy in the absence of a reference method.

Science.gov (United States)

Voskoboev, Nikolay V; Cambern, Sarah J; Hanley, Matthew M; Giesen, Callen D; Schilling, Jason J; Jannetto, Paul J; Lieske, John C; Block, Darci R

2015-11-01

Validation of tests performed on body fluids other than blood or urine can be challenging due to the lack of a reference method to confirm accuracy. The aim of this study was to evaluate alternate assessments of accuracy that laboratories can rely on to validate body fluid tests in the absence of a reference method using the example of sodium (Na(+)), potassium (K(+)), and magnesium (Mg(2+)) testing in stool fluid. Validations of fecal Na(+), K(+), and Mg(2+) were performed on the Roche cobas 6000 c501 (Roche Diagnostics) using residual stool specimens submitted for clinical testing. Spiked recovery, mixing studies, and serial dilutions were performed and % recovery of each analyte was calculated to assess accuracy. Results were confirmed by comparison to a reference method (ICP-OES, PerkinElmer). Mean recoveries for fecal electrolytes were Na(+) upon spiking=92%, mixing=104%, and dilution=105%; K(+) upon spiking=94%, mixing=96%, and dilution=100%; and Mg(2+) upon spiking=93%, mixing=98%, and dilution=100%. When autoanalyzer results were compared to reference ICP-OES results, Na(+) had a slope=0.94, intercept=4.1, and R(2)=0.99; K(+) had a slope=0.99, intercept=0.7, and R(2)=0.99; and Mg(2+) had a slope=0.91, intercept=-4.6, and R(2)=0.91. Calculated osmotic gap using both methods were highly correlated with slope=0.95, intercept=4.5, and R(2)=0.97. Acid pretreatment increased magnesium recovery from a subset of clinical specimens. A combination of mixing, spiking, and dilution recovery experiments are an acceptable surrogate for assessing accuracy in body fluid validations in the absence of a reference method. Copyright © 2015 The Canadian Society of Clinical Chemists. Published by Elsevier Inc. All rights reserved.

Treatment of non-Gaussian tails of multiple Coulomb scattering in track fitting with a Gaussian-sum filter

International Nuclear Information System (INIS)

Strandlie, A.; Wroldsen, J.

2006-01-01

If any of the probability densities involved in track fitting deviate from the Gaussian assumption, it is plausible that a non-linear estimator which better takes the actual shape of the distribution into account can do better. One such non-linear estimator is the Gaussian-sum filter, which is adequate if the distributions under consideration can be approximated by Gaussian mixtures. The main purpose of this paper is to present a Gaussian-sum filter for track fitting, based on a two-component approximation of the distribution of angular deflections due to multiple scattering. In a simulation study within a linear track model the Gaussian-sum filter is shown to be a competitive alternative to the Kalman filter. Scenarios at various momenta and with various maximum number of components in the Gaussian-sum filter are considered. Particularly at low momenta the Gaussian-sum filter yields a better estimate of the uncertainties than the Kalman filter, and it is also slightly more precise than the latter

Palm distributions for log Gaussian Cox processes

DEFF Research Database (Denmark)

Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus Plenge

2017-01-01

This paper establishes a remarkable result regarding Palm distributions for a log Gaussian Cox process: the reduced Palm distribution for a log Gaussian Cox process is itself a log Gaussian Cox process that only differs from the original log Gaussian Cox process in the intensity function. This new...... result is used to study functional summaries for log Gaussian Cox processes....

High-Order Local Pooling and Encoding Gaussians Over a Dictionary of Gaussians.

Science.gov (United States)

Li, Peihua; Zeng, Hui; Wang, Qilong; Shiu, Simon C K; Zhang, Lei

2017-07-01

Local pooling (LP) in configuration (feature) space proposed by Boureau et al. explicitly restricts similar features to be aggregated, which can preserve as much discriminative information as possible. At the time it appeared, this method combined with sparse coding achieved competitive classification results with only a small dictionary. However, its performance lags far behind the state-of-the-art results as only the zero-order information is exploited. Inspired by the success of high-order statistical information in existing advanced feature coding or pooling methods, we make an attempt to address the limitation of LP. To this end, we present a novel method called high-order LP (HO-LP) to leverage the information higher than the zero-order one. Our idea is intuitively simple: we compute the first- and second-order statistics per configuration bin and model them as a Gaussian. Accordingly, we employ a collection of Gaussians as visual words to represent the universal probability distribution of features from all classes. Our problem is naturally formulated as encoding Gaussians over a dictionary of Gaussians as visual words. This problem, however, is challenging since the space of Gaussians is not a Euclidean space but forms a Riemannian manifold. We address this challenge by mapping Gaussians into the Euclidean space, which enables us to perform coding with common Euclidean operations rather than complex and often expensive Riemannian operations. Our HO-LP preserves the advantages of the original LP: pooling only similar features and using a small dictionary. Meanwhile, it achieves very promising performance on standard benchmarks, with either conventional, hand-engineered features or deep learning-based features.

Detecting impact signal in mechanical fault diagnosis under chaotic and Gaussian background noise

Science.gov (United States)

Hu, Jinfeng; Duan, Jie; Chen, Zhuo; Li, Huiyong; Xie, Julan; Chen, Hanwen

2018-01-01

In actual fault diagnosis, useful information is often submerged in heavy noise, and the feature information is difficult to extract. Traditional methods, such like stochastic resonance (SR), which using noise to enhance weak signals instead of suppressing noise, failed in chaotic background. Neural network, which use reference sequence to estimate and reconstruct the background noise, failed in white Gaussian noise. To solve these problems, a novel weak signal detection method aimed at the problem of detecting impact signal buried under heavy chaotic and Gaussian background noise is proposed. First, the proposed method obtains the virtual reference sequence by constructing the Hankel data matrix. Then an M-order optimal FIR filter is designed, which can minimize the output power of background noise and pass the weak periodic signal undistorted. Finally, detection and reconstruction of the weak periodic signal are achieved from the output SBNR (signal to background noise ratio). The simulation shows, compared with the stochastic resonance (SR) method, the proposed method can detect the weak periodic signal in chaotic noise background while stochastic resonance (SR) method cannot. Compared with the neural network method, (a) the proposed method does not need a reference sequence while neural network method needs one; (b) the proposed method can detect the weak periodic signal in white Gaussian noise background while the neural network method fails, in chaotic noise background, the proposed method can detect the weak periodic signal under a lower SBNR (about 8-17 dB lower) than the neural network method; (c) the proposed method can reconstruct the weak periodic signal precisely.

The force distribution probability function for simple fluids by density functional theory.

Science.gov (United States)

Rickayzen, G; Heyes, D M

2013-02-28

Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.

Breaking Gaussian incompatibility on continuous variable quantum systems

Energy Technology Data Exchange (ETDEWEB)

Heinosaari, Teiko, E-mail: teiko.heinosaari@utu.fi [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Kiukas, Jukka, E-mail: jukka.kiukas@aber.ac.uk [Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, SY23 3BZ (United Kingdom); Schultz, Jussi, E-mail: jussi.schultz@gmail.com [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy)

2015-08-15

We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.

Learning non-Gaussian Time Series using the Box-Cox Gaussian Process

OpenAIRE

Rios, Gonzalo; Tobar, Felipe

2018-01-01

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model general non-Gaussian data with complex correlation structure, GPs can be paired with an expressive covariance kernel and then fed into a nonlinear transformation (or warping). However, overparametrising the kernel and the warping is known to, respectively, hin...

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

Science.gov (United States)

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

1998-03-01

The macrodispersion of an inert solute in a 2-D heterogeneous porous media is estimated numerically in a series of fields of varying heterogeneity. Four different random function (RF) models are used to model log-transmissivity (ln T) spatial variability, and for each of these models, ln T variance is varied from 0.1 to 2.0. The four RF models share the same univariate Gaussian histogram and the same isotropic covariance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme values (both high and low) are spatially uncorrelated. The other three models are non-multi-Gaussian: model B with high connectivity of high extreme values, model C with high connectivity of low extreme values, and model D with high connectivities of both high and low extreme values. Residence time distributions (RTDs) and macrodispersivities (longitudinal and transverse) are computed on ln T fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RTDs and macrodispersivities for the multi-Gaussian model are in good agreement with analytically derived values using first-order theories for log-transmissivity variance up to 2.0. The results from the non-multi-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when ln T variance is small. RTDs in non-multi-Gaussian realizations with high connectivity at high extreme values display earlier breakthrough than in multi-Gaussian realizations, whereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian realizations are, in general, larger than

Non-Gaussian halo assembly bias

International Nuclear Information System (INIS)

Reid, Beth A.; Verde, Licia; Dolag, Klaus; Matarrese, Sabino; Moscardini, Lauro

2010-01-01

The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f NL , offers a promising avenue towards constraining primordial non-Gaussianity with large-scale structure surveys. In this paper, we present the first detection of the dependence of the non-Gaussian halo bias on halo formation history using N-body simulations. We also present an analytic derivation of the expected signal based on the extended Press-Schechter formalism. In excellent agreement with our analytic prediction, we find that the halo formation history-dependent contribution to the non-Gaussian halo bias (which we call non-Gaussian halo assembly bias) can be factorized in a form approximately independent of redshift and halo mass. The correction to the non-Gaussian halo bias due to the halo formation history can be as large as 100%, with a suppression of the signal for recently formed halos and enhancement for old halos. This could in principle be a problem for realistic galaxy surveys if observational selection effects were to pick galaxies occupying only recently formed halos. Current semi-analytic galaxy formation models, for example, imply an enhancement in the expected signal of ∼ 23% and ∼ 48% for galaxies at z = 1 selected by stellar mass and star formation rate, respectively

Thermodynamics of mixtures of patchy and spherical colloids of different sizes: A multi-body association theory with complete reference fluid information

Science.gov (United States)

Bansal, Artee; Valiya Parambathu, Arjun; Asthagiri, D.; Cox, Kenneth R.; Chapman, Walter G.

2017-04-01

We present a theory to predict the structure and thermodynamics of mixtures of colloids of different diameters, building on our earlier work [A. Bansal et al., J. Chem. Phys. 145, 074904 (2016)] that considered mixtures with all particles constrained to have the same size. The patchy, solvent particles have short-range directional interactions, while the solute particles have short-range isotropic interactions. The hard-sphere mixture without any association site forms the reference fluid. An important ingredient within the multi-body association theory is the description of clustering of the reference solvent around the reference solute. Here we account for the physical, multi-body clusters of the reference solvent around the reference solute in terms of occupancy statistics in a defined observation volume. These occupancy probabilities are obtained from enhanced sampling simulations, but we also present statistical mechanical models to estimate these probabilities with limited simulation data. Relative to an approach that describes only up to three-body correlations in the reference, incorporating the complete reference information better predicts the bonding state and thermodynamics of the physical solute for a wide range of system conditions. Importantly, analysis of the residual chemical potential of the infinitely dilute solute from molecular simulation and theory shows that whereas the chemical potential is somewhat insensitive to the description of the structure of the reference fluid, the energetic and entropic contributions are not, with the results from the complete reference approach being in better agreement with particle simulations.

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

Science.gov (United States)

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.

Determination of Cross-Sectional Area of Focused Picosecond Gaussian Laser Beam

Science.gov (United States)

Ledesma, Rodolfo; Fitz-Gerald, James; Palmieri, Frank; Connell, John

2018-01-01

Measurement of the waist diameter of a focused Gaussian-beam at the 1/e(sup 2) intensity, also referred to as spot size, is key to determining the fluence in laser processing experiments. Spot size measurements are also helpful to calculate the threshold energy and threshold fluence of a given material. This work reports an application of a conventional method, by analyzing single laser ablated spots for different laser pulse energies, to determine the cross-sectional area of a focused Gaussian-beam, which has a nominal pulse width of approx. 10 ps. Polished tungsten was used as the target material, due to its low surface roughness and low ablation threshold, to measure the beam waist diameter. From the ablative spot measurements, the ablation threshold fluence of the tungsten substrate was also calculated.

Gaussian-2 theory using reduced Moller--Plesset orders

International Nuclear Information System (INIS)

Curtiss, L.A.; Raghavachari, K.; Pople, J.A.

1993-01-01

Two variations of Gaussian-2 (G2) theory are presented. In the first, referred to as G2 (MP2) theory, the basis-set-extension energy corrections are obtained at the 2nd order Moller--Plesset (MP2) level and in the second, referred to as G2(MP3) theory, they are obtained at the MP3 level. The methods are tested out on the set of 125 systems used for validation of G2 theory [J. Chem Phys. 94, 7221 (1991)]. The average absolute deviation of the G2(MP2) and G2(MP3) theories from experiment are 1.58 and 1.52 kcal/mol, respectively, compared to 1.21 kcal/mol for G2 theory. The new methods provide significant savings in computational time and disk storage

Response moments of dynamic systems under non-Gaussian random excitation by the equivalent non-Gaussian excitation method

International Nuclear Information System (INIS)

Tsuchida, Takahiro; Kimura, Koji

2016-01-01

Equivalent non-Gaussian excitation method is proposed to obtain the response moments up to the 4th order of dynamic systems under non-Gaussian random excitation. The non-Gaussian excitation is prescribed by the probability density and the power spectrum, and is described by an Ito stochastic differential equation. Generally, moment equations for the response, which are derived from the governing equations for the excitation and the system, are not closed due to the nonlinearity of the diffusion coefficient in the equation for the excitation even though the system is linear. In the equivalent non-Gaussian excitation method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by a quadratic polynomial. In numerical examples, a linear system subjected to nonGaussian excitations with bimodal and Rayleigh distributions is analyzed by using the present method. The results show that the method yields the variance, skewness and kurtosis of the response with high accuracy for non-Gaussian excitation with the widely different probability densities and bandwidth. The statistical moments of the equivalent non-Gaussian excitation are also investigated to describe the feature of the method. (paper)

Emergence of Multiscaling in a Random-Force Stirred Fluid

Science.gov (United States)

Yakhot, Victor; Donzis, Diego

2017-07-01

We consider the transition to strong turbulence in an infinite fluid stirred by a Gaussian random force. The transition is defined as a first appearance of anomalous scaling of normalized moments of velocity derivatives (dissipation rates) emerging from the low-Reynolds-number Gaussian background. It is shown that, due to multiscaling, strongly intermittent rare events can be quantitatively described in terms of an infinite number of different "Reynolds numbers" reflecting a multitude of anomalous scaling exponents. The theoretically predicted transition disappears at Rλ≤3 . The developed theory is in quantitative agreement with the outcome of large-scale numerical simulations.

Analytic matrix elements with shifted correlated Gaussians

DEFF Research Database (Denmark)

Fedorov, D. V.

2017-01-01

Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.......Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics....

Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data

DEFF Research Database (Denmark)

Bennedsen, Mikkel

Using theory on (conditionally) Gaussian processes with stationary increments developed in Barndorff-Nielsen et al. (2009, 2011), this paper presents a general semiparametric approach to conducting inference on the fractal index, α, of a time series. Our setup encompasses a large class of Gaussian...

A Gaussian mixture copula model based localized Gaussian process regression approach for long-term wind speed prediction

International Nuclear Information System (INIS)

Yu, Jie; Chen, Kuilin; Mori, Junichi; Rashid, Mudassir M.

2013-01-01

Optimizing wind power generation and controlling the operation of wind turbines to efficiently harness the renewable wind energy is a challenging task due to the intermittency and unpredictable nature of wind speed, which has significant influence on wind power production. A new approach for long-term wind speed forecasting is developed in this study by integrating GMCM (Gaussian mixture copula model) and localized GPR (Gaussian process regression). The time series of wind speed is first classified into multiple non-Gaussian components through the Gaussian mixture copula model and then Bayesian inference strategy is employed to incorporate the various non-Gaussian components using the posterior probabilities. Further, the localized Gaussian process regression models corresponding to different non-Gaussian components are built to characterize the stochastic uncertainty and non-stationary seasonality of the wind speed data. The various localized GPR models are integrated through the posterior probabilities as the weightings so that a global predictive model is developed for the prediction of wind speed. The proposed GMCM–GPR approach is demonstrated using wind speed data from various wind farm locations and compared against the GMCM-based ARIMA (auto-regressive integrated moving average) and SVR (support vector regression) methods. In contrast to GMCM–ARIMA and GMCM–SVR methods, the proposed GMCM–GPR model is able to well characterize the multi-seasonality and uncertainty of wind speed series for accurate long-term prediction. - Highlights: • A novel predictive modeling method is proposed for long-term wind speed forecasting. • Gaussian mixture copula model is estimated to characterize the multi-seasonality. • Localized Gaussian process regression models can deal with the random uncertainty. • Multiple GPR models are integrated through Bayesian inference strategy. • The proposed approach shows higher prediction accuracy and reliability

Equivalent non-Gaussian excitation method for response moment calculation of systems under non-Gaussian random excitation

International Nuclear Information System (INIS)

Tsuchida, Takahiro; Kimura, Koji

2015-01-01

Equivalent non-Gaussian excitation method is proposed to obtain the moments up to the fourth order of the response of systems under non-Gaussian random excitation. The excitation is prescribed by the probability density and power spectrum. Moment equations for the response can be derived from the stochastic differential equations for the excitation and the system. However, the moment equations are not closed due to the nonlinearity of the diffusion coefficient in the equation for the excitation. In the proposed method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by the second-order polynomial. In order to demonstrate the validity of the method, a linear system to non-Gaussian excitation with generalized Gaussian distribution is analyzed. The results show the method is applicable to non-Gaussian excitation with the widely different kurtosis and bandwidth. (author)

Entanglement in Gaussian matrix-product states

International Nuclear Information System (INIS)

Adesso, Gerardo; Ericsson, Marie

2006-01-01

Gaussian matrix-product states are obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of N sites of a harmonic chain. Replacing the projections by associated Gaussian states, the building blocks, we show that the entanglement range in translationally invariant Gaussian matrix-product states depends on how entangled the building blocks are. In particular, infinite entanglement in the building blocks produces fully symmetric Gaussian states with maximum entanglement range. From their peculiar properties of entanglement sharing, a basic difference with spin chains is revealed: Gaussian matrix-product states can possess unlimited, long-range entanglement even with minimum number of ancillary bonds (M=1). Finally we discuss how these states can be experimentally engineered from N copies of a three-mode building block and N two-mode finitely squeezed states

Nonlinear wave breaking in self-gravitating viscoelastic quantum fluid

Energy Technology Data Exchange (ETDEWEB)

Mitra, Aniruddha, E-mail: anibabun@gmail.com [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India); Roychoudhury, Rajkumar, E-mail: rajdaju@rediffmail.com [Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata 700075 (India); Department of Mathematics, Bethune College, Kolkata 700006 (India); Bhar, Radhaballav [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India); Khan, Manoranjan, E-mail: mkhan.ju@gmail.com [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India)

2017-02-12

The stability of a viscoelastic self-gravitating quantum fluid has been studied. Symmetry breaking instability of solitary wave has been observed through ‘viscosity modified Ostrovsky equation’ in weak gravity limit. In presence of strong gravitational field, the solitary wave breaks into shock waves. Response to a Gaussian perturbation, the system produces quasi-periodic short waves, which in terns predicts the existence of gravito-acoustic quasi-periodic short waves in lower solar corona region. Stability analysis of this dynamical system predicts gravity has the most prominent effect on the phase portraits, therefore, on the stability of the system. The non-existence of chaotic solution has also been observed at long wavelength perturbation through index value theorem. - Highlights: • In weak gravitational field, viscoelastic quantum fluid exhibits symmetry breaking instability. • Gaussian perturbation produces quasi-periodic gravito-acoustic waves into the system. • There exists no chaotic state of the system against long wavelength perturbations.

Path integral methods for primordial density perturbations - sampling of constrained Gaussian random fields

International Nuclear Information System (INIS)

Bertschinger, E.

1987-01-01

Path integrals may be used to describe the statistical properties of a random field such as the primordial density perturbation field. In this framework the probability distribution is given for a Gaussian random field subjected to constraints such as the presence of a protovoid or supercluster at a specific location in the initial conditions. An algorithm has been constructed for generating samples of a constrained Gaussian random field on a lattice using Monte Carlo techniques. The method makes possible a systematic study of the density field around peaks or other constrained regions in the biased galaxy formation scenario, and it is effective for generating initial conditions for N-body simulations with rare objects in the computational volume. 21 references

Non-Gaussianity from isocurvature perturbations

Energy Technology Data Exchange (ETDEWEB)

Kawasaki, Masahiro; Nakayama, Kazunori; Sekiguchi, Toyokazu; Suyama, Teruaki [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582 (Japan); Takahashi, Fuminobu, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: nakayama@icrr.u-tokyo.ac.jp, E-mail: sekiguti@icrr.u-tokyo.ac.jp, E-mail: suyama@icrr.u-tokyo.ac.jp, E-mail: fuminobu.takahashi@ipmu.jp [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan)

2008-11-15

We develop a formalism for studying non-Gaussianity in both curvature and isocurvature perturbations. It is shown that non-Gaussianity in the isocurvature perturbation between dark matter and photons leaves distinct signatures in the cosmic microwave background temperature fluctuations, which may be confirmed in future experiments, or possibly even in the currently available observational data. As an explicit example, we consider the quantum chromodynamics axion and show that it can actually induce sizable non-Gaussianity for the inflationary scale, H{sub inf} = O(10{sup 9}-10{sup 11}) GeV.

Handbook of Gaussian basis sets

International Nuclear Information System (INIS)

Poirier, R.; Kari, R.; Csizmadia, I.G.

1985-01-01

A collection of a large body of information is presented useful for chemists involved in molecular Gaussian computations. Every effort has been made by the authors to collect all available data for cartesian Gaussian as found in the literature up to July of 1984. The data in this text includes a large collection of polarization function exponents but in this case the collection is not complete. Exponents for Slater type orbitals (STO) were included for completeness. This text offers a collection of Gaussian exponents primarily without criticism. (Auth.)

Gaussian capacity of the quantum bosonic memory channel with additive correlated Gaussian noise

International Nuclear Information System (INIS)

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

2011-01-01

We present an algorithm for calculation of the Gaussian classical capacity of a quantum bosonic memory channel with additive Gaussian noise. The algorithm, restricted to Gaussian input states, is applicable to all channels with noise correlations obeying certain conditions and works in the full input energy domain, beyond previous treatments of this problem. As an illustration, we study the optimal input states and capacity of a quantum memory channel with Gauss-Markov noise [J. Schaefer, Phys. Rev. A 80, 062313 (2009)]. We evaluate the enhancement of the transmission rate when using these optimal entangled input states by comparison with a product coherent-state encoding and find out that such a simple coherent-state encoding achieves not less than 90% of the capacity.

Acoustic radiation force on a multilayered sphere in a Gaussian standing field

Science.gov (United States)

Wang, Haibin; Liu, Xiaozhou; Gao, Sha; Cui, Jun; Liu, Jiehui; He, Aijun; Zhang, Gutian

2018-03-01

We develop a model for calculating the radiation force on spherically symmetric multilayered particles based on the acoustic scattering approach. An expression is derived for the radiation force on a multilayered sphere centered on the axis of a Gaussian standing wave propagating in an ideal fluid. The effects of the sound absorption of the materials and sound wave on acoustic radiation force of a multilayered sphere immersed in water are analyzed, with particular emphasis on the shell thickness of every layer, and the width of the Gaussian beam. The results reveal that the existence of particle trapping behavior depends on the choice of the non-dimensional frequency ka, as well as the shell thickness of each layer. This study provides a theoretical basis for the development of acoustical tweezers in a Gaussian standing wave, which may benefit the improvement and development of acoustic control technology, such as trapping, sorting, and assembling a cell, and drug delivery applications. Project supported by National Key R&D Program (Grant No. 2016YFF0203000), the National Natural Science Foundation of China (Grant Nos. 11774167 and 61571222), the Fundamental Research Funds for the Central Universities of China (Grant No. 020414380001), the Key Laboratory of Underwater Acoustic Environment, Institute of Acoustics, Chinese Academy of Sciences (Grant No. SSHJ-KFKT-1701), and the AQSIQ Technology R&D Program of China (Grant No. 2017QK125).

Searching for non-Gaussianity in the WMAP data

International Nuclear Information System (INIS)

Bernui, A.; Reboucas, M. J.

2009-01-01

Some analyses of recent cosmic microwave background (CMB) data have provided hints that there are deviations from Gaussianity in the WMAP CMB temperature fluctuations. Given the far-reaching consequences of such a non-Gaussianity for our understanding of the physics of the early universe, it is important to employ alternative indicators in order to determine whether the reported non-Gaussianity is of cosmological origin, and/or extract further information that may be helpful for identifying its causes. We propose two new non-Gaussianity indicators, based on skewness and kurtosis of large-angle patches of CMB maps, which provide a measure of departure from Gaussianity on large angular scales. A distinctive feature of these indicators is that they provide sky maps of non-Gaussianity of the CMB temperature data, thus allowing a possible additional window into their origins. Using these indicators, we find no significant deviation from Gaussianity in the three and five-year WMAP Internal Linear Combination (ILC) map with KQ75 mask, while the ILC unmasked map exhibits deviation from Gaussianity, quantifying therefore the WMAP team recommendation to employ the new mask KQ75 for tests of Gaussianity. We also use our indicators to test for Gaussianity the single frequency foreground unremoved WMAP three and five-year maps, and show that the K and Ka maps exhibit a clear indication of deviation from Gaussianity even with the KQ75 mask. We show that our findings are robust with respect to the details of the method.

Reproducing kernel Hilbert spaces of Gaussian priors

NARCIS (Netherlands)

Vaart, van der A.W.; Zanten, van J.H.; Clarke, B.; Ghosal, S.

2008-01-01

We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described

Gaussian process regression analysis for functional data

CERN Document Server

Shi, Jian Qing

2011-01-01

Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dime

Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute

Science.gov (United States)

Bansal, Artee; Chapman, Walter G.; Asthagiri, D.

2017-09-01

We derive an expression for the chemical potential of an associating solute in a solvent relative to the value in a reference fluid using the quasichemical organization of the potential distribution theorem. The fraction of times the solute is not associated with the solvent, the monomer fraction, is expressed in terms of (a) the statistics of occupancy of the solvent around the solute in the reference fluid and (b) the Widom factors that arise because of turning on solute-solvent association. Assuming pair-additivity, we expand the Widom factor into a product of Mayer f-functions and the resulting expression is rearranged to reveal a form of the monomer fraction that is analogous to that used within the statistical associating fluid theory (SAFT). The present formulation avoids all graph-theoretic arguments and provides a fresh, more intuitive, perspective on Wertheim's theory and SAFT. Importantly, multi-body effects are transparently incorporated into the very foundations of the theory. We illustrate the generality of the present approach by considering examples of multiple solvent association to a colloid solute with bonding domains that range from a small patch on the sphere to a Janus particle to a solute whose entire surface is available for association.

Comparison of Gaussian and non-Gaussian Atmospheric Profile Retrievals from Satellite Microwave Data

Science.gov (United States)

Kliewer, A.; Forsythe, J. M.; Fletcher, S. J.; Jones, A. S.

2017-12-01

The Cooperative Institute for Research in the Atmosphere at Colorado State University has recently developed two different versions of a mixed-distribution (lognormal combined with a Gaussian) based microwave temperature and mixing ratio retrieval system as well as the original Gaussian-based approach. These retrieval systems are based upon 1DVAR theory but have been adapted to use different descriptive statistics of the lognormal distribution to minimize the background errors. The input radiance data is from the AMSU-A and MHS instruments on the NOAA series of spacecraft. To help illustrate how the three retrievals are affected by the change in the distribution we are in the process of creating a new website to show the output from the different retrievals. Here we present initial results from different dynamical situations to show how the tool could be used by forecasters as well as for educators. However, as the new retrieved values are from a non-Gaussian based 1DVAR then they will display non-Gaussian behaviors that need to pass a quality control measure that is consistent with this distribution, and these new measures are presented here along with initial results for checking the retrievals.

Gaussian operations and privacy

International Nuclear Information System (INIS)

Navascues, Miguel; Acin, Antonio

2005-01-01

We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in [Navascues et al. Phys. Rev. Lett. 94, 010502 (2005)]. Then, we prove that a generalized version of this protocol does not allow one to distill a secret key out of bound entangled Gaussian states

On the thermodynamic properties of the generalized Gaussian core model

Directory of Open Access Journals (Sweden)

B.M.Mladek

2005-01-01

Full Text Available We present results of a systematic investigation of the properties of the generalized Gaussian core model of index n. The potential of this system interpolates via the index n between the potential of the Gaussian core model and the penetrable sphere system, thereby varying the steepness of the repulsion. We have used both conventional and self-consistent liquid state theories to calculate the structural and thermodynamic properties of the system; reference data are provided by computer simulations. The results indicate that the concept of self-consistency becomes indispensable to guarantee excellent agreement with simulation data; in particular, structural consistency (in our approach taken into account via the zero separation theorem is obviously a very important requirement. Simulation results for the dimensionless equation of state, β P / ρ, indicate that for an index-value of 4, a clustering transition, possibly into a structurally ordered phase might set in as the system is compressed.

Geometry of perturbed Gaussian states and quantum estimation

International Nuclear Information System (INIS)

Genoni, Marco G; Giorda, Paolo; Paris, Matteo G A

2011-01-01

We address the non-Gaussianity (nG) of states obtained by weakly perturbing a Gaussian state and investigate the relationships with quantum estimation. For classical perturbations, i.e. perturbations to eigenvalues, we found that the nG of the perturbed state may be written as the quantum Fisher information (QFI) distance minus a term depending on the infinitesimal energy change, i.e. it provides a lower bound to statistical distinguishability. Upon moving on isoenergetic surfaces in a neighbourhood of a Gaussian state, nG thus coincides with a proper distance in the Hilbert space and exactly quantifies the statistical distinguishability of the perturbations. On the other hand, for perturbations leaving the covariance matrix unperturbed, we show that nG provides an upper bound to the QFI. Our results show that the geometry of non-Gaussian states in the neighbourhood of a Gaussian state is definitely not trivial and cannot be subsumed by a differential structure. Nevertheless, the analysis of perturbations to a Gaussian state reveals that nG may be a resource for quantum estimation. The nG of specific families of perturbed Gaussian states is analysed in some detail with the aim of finding the maximally non-Gaussian state obtainable from a given Gaussian one. (fast track communication)

Non-Gaussianity in island cosmology

International Nuclear Information System (INIS)

Piao Yunsong

2009-01-01

In this paper we fully calculate the non-Gaussianity of primordial curvature perturbation of the island universe by using the second order perturbation equation. We find that for the spectral index n s ≅0.96, which is favored by current observations, the non-Gaussianity level f NL seen in an island will generally lie between 30 and 60, which may be tested by the coming observations. In the landscape, the island universe is one of anthropically acceptable cosmological histories. Thus the results obtained in some sense mean the coming observations, especially the measurement of non-Gaussianity, will be significant to clarify how our position in the landscape is populated.

Cerebrospinal fluid culture

Science.gov (United States)

... Alternative Names Culture - CSF; Spinal fluid culture; CSF culture Images Pneumococci organism References Karcher DS, McPherson RA. Cerebrospinal, synovial, serous body fluids, and alternative specimens. In: McPherson RA, Pincus ...

Monogamy inequality for distributed gaussian entanglement.

Science.gov (United States)

Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio

2007-02-02

We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.

Non-Gaussianity from inflation: theory and observations

Science.gov (United States)

Bartolo, N.; Komatsu, E.; Matarrese, S.; Riotto, A.

2004-11-01

This is a review of models of inflation and of their predictions for the primordial non-Gaussianity in the density perturbations which are thought to be at the origin of structures in the Universe. Non-Gaussianity emerges as a key observable to discriminate among competing scenarios for the generation of cosmological perturbations and is one of the primary targets of present and future Cosmic Microwave Background satellite missions. We give a detailed presentation of the state-of-the-art of the subject of non-Gaussianity, both from the theoretical and the observational point of view, and provide all the tools necessary to compute at second order in perturbation theory the level of non-Gaussianity in any model of cosmological perturbations. We discuss the new wave of models of inflation, which are firmly rooted in modern particle physics theory and predict a significant amount of non-Gaussianity. The review is addressed to both astrophysicists and particle physicists and contains useful tables which summarize the theoretical and observational results regarding non-Gaussianity.

Effect of reference conditions on flow rate, modifier fraction and retention in supercritical fluid chromatography.

Science.gov (United States)

De Pauw, Ruben; Shoykhet Choikhet, Konstantin; Desmet, Gert; Broeckhoven, Ken

2016-08-12

When using compressible mobile phases such as fluidic CO2, the density, the volumetric flow rates and volumetric fractions are pressure dependent. The pressure and temperature definition of these volumetric parameters (referred to as the reference conditions) may alter between systems, manufacturers and operating conditions. A supercritical fluid chromatography system was modified to operate in two modes with different definition of the eluent delivery parameters, referred to as fixed and variable mode. For the variable mode, the volumetric parameters are defined with reference to the pump operating pressure and actual pump head temperature. These conditions may vary when, e.g. changing the column length, permeability, flow rate, etc. and are thus variable reference conditions. For the fixed mode, the reference conditions were set at 150bar and 30°C, resulting in a mass flow rate and mass fraction of modifier definition which is independent of the operation conditions. For the variable mode, the mass flow rate of carbon dioxide increases with system pump operating pressure, decreasing the fraction of modifier. Comparing the void times and retention factor shows that the deviation between the two modes is almost independent of modifier percentage, but depends on the operating pressure. Recalculating the set volumetric fraction of modifier to the mass fraction results in the same retention behaviour for both modes. This shows that retention in SFC can be best modelled using the mass fraction of modifier. The fixed mode also simplifies method scaling as it only requires matching average column pressure. Copyright © 2016 Elsevier B.V. All rights reserved.

Non-gaussianity versus nonlinearity of cosmological perturbations.

Science.gov (United States)

Verde, L

2001-06-01

Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

Galaxy bias and primordial non-Gaussianity

Energy Technology Data Exchange (ETDEWEB)

Assassi, Valentin; Baumann, Daniel [DAMTP, Cambridge University, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Schmidt, Fabian, E-mail: assassi@ias.edu, E-mail: D.D.Baumann@uva.nl, E-mail: fabians@MPA-Garching.MPG.DE [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching (Germany)

2015-12-01

We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation.

Optimal cloning of mixed Gaussian states

International Nuclear Information System (INIS)

Guta, Madalin; Matsumoto, Keiji

2006-01-01

We construct the optimal one to two cloning transformation for the family of displaced thermal equilibrium states of a harmonic oscillator, with a fixed and known temperature. The transformation is Gaussian and it is optimal with respect to the figure of merit based on the joint output state and norm distance. The proof of the result is based on the equivalence between the optimal cloning problem and that of optimal amplification of Gaussian states which is then reduced to an optimization problem for diagonal states of a quantum oscillator. A key concept in finding the optimum is that of stochastic ordering which plays a similar role in the purely classical problem of Gaussian cloning. The result is then extended to the case of n to m cloning of mixed Gaussian states

Galaxy bias and primordial non-Gaussianity

International Nuclear Information System (INIS)

Assassi, Valentin; Baumann, Daniel; Schmidt, Fabian

2015-01-01

We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation

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

Science.gov (United States)

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.

Information geometry of Gaussian channels

International Nuclear Information System (INIS)

Monras, Alex; Illuminati, Fabrizio

2010-01-01

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).

Laguerre Gaussian beam multiplexing through turbulence

CSIR Research Space (South Africa)

Trichili, A

2014-08-17

Full Text Available We analyze the effect of atmospheric turbulence on the propagation of multiplexed Laguerre Gaussian modes. We present a method to multiplex Laguerre Gaussian modes using digital holograms and decompose the resulting field after encountering a...

Phase statistics in non-Gaussian scattering

International Nuclear Information System (INIS)

Watson, Stephen M; Jakeman, Eric; Ridley, Kevin D

2006-01-01

Amplitude weighting can improve the accuracy of frequency measurements in signals corrupted by multiplicative speckle noise. When the speckle field constitutes a circular complex Gaussian process, the optimal function of amplitude weighting is provided by the field intensity, corresponding to the intensity-weighted phase derivative statistic. In this paper, we investigate the phase derivative and intensity-weighted phase derivative returned from a two-dimensional random walk, which constitutes a generic scattering model capable of producing both Gaussian and non-Gaussian fluctuations. Analytical results are developed for the correlation properties of the intensity-weighted phase derivative, as well as limiting probability densities of the scattered field. Numerical simulation is used to generate further probability densities and determine optimal weighting criteria from non-Gaussian fields. The results are relevant to frequency retrieval in radiation scattered from random media

Generalized Gaussian Error Calculus

CERN Document Server

Grabe, Michael

2010-01-01

For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...

MCEM algorithm for the log-Gaussian Cox process

OpenAIRE

Delmas, Celine; Dubois-Peyrard, Nathalie; Sabbadin, Regis

2014-01-01

Log-Gaussian Cox processes are an important class of models for aggregated point patterns. They have been largely used in spatial epidemiology (Diggle et al., 2005), in agronomy (Bourgeois et al., 2012), in forestry (Moller et al.), in ecology (sightings of wild animals) or in environmental sciences (radioactivity counts). A log-Gaussian Cox process is a Poisson process with a stochastic intensity depending on a Gaussian random eld. We consider the case where this Gaussian random eld is ...

Linking network usage patterns to traffic Gaussianity fit

NARCIS (Netherlands)

de Oliveira Schmidt, R.; Sadre, R.; Melnikov, Nikolay; Schönwälder, Jürgen; Pras, Aiko

Gaussian traffic models are widely used in the domain of network traffic modeling. The central assumption is that traffic aggregates are Gaussian distributed. Due to its importance, the Gaussian character of network traffic has been extensively assessed by researchers in the past years. In 2001,

Characterisation of random Gaussian and non-Gaussian stress processes in terms of extreme responses

Directory of Open Access Journals (Sweden)

Colin Bruno

2015-01-01

Full Text Available In the field of military land vehicles, random vibration processes generated by all-terrain wheeled vehicles in motion are not classical stochastic processes with a stationary and Gaussian nature. Non-stationarity of processes induced by the variability of the vehicle speed does not form a major difficulty because the designer can have good control over the vehicle speed by characterising the histogram of instantaneous speed of the vehicle during an operational situation. Beyond this non-stationarity problem, the hard point clearly lies in the fact that the random processes are not Gaussian and are generated mainly by the non-linear behaviour of the undercarriage and the strong occurrence of shocks generated by roughness of the terrain. This non-Gaussian nature is expressed particularly by very high flattening levels that can affect the design of structures under extreme stresses conventionally acquired by spectral approaches, inherent to Gaussian processes and based essentially on spectral moments of stress processes. Due to these technical considerations, techniques for characterisation of random excitation processes generated by this type of carrier need to be changed, by proposing innovative characterisation methods based on time domain approaches as described in the body of the text rather than spectral domain approaches.

Stochastic differential calculus for Gaussian and non-Gaussian noises: A critical review

Science.gov (United States)

Falsone, G.

2018-03-01

In this paper a review of the literature works devoted to the study of stochastic differential equations (SDEs) subjected to Gaussian and non-Gaussian white noises and to fractional Brownian noises is given. In these cases, particular attention must be paid in treating the SDEs because the classical rules of the differential calculus, as the Newton-Leibnitz one, cannot be applied or are applicable with many difficulties. Here all the principal approaches solving the SDEs are reported for any kind of noise, highlighting the negative and positive properties of each one and making the comparisons, where it is possible.

Gaussian maximally multipartite-entangled states

Science.gov (United States)

Facchi, Paolo; Florio, Giuseppe; Lupo, Cosmo; Mancini, Stefano; Pascazio, Saverio

2009-12-01

We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n≤7 .

Gaussian maximally multipartite-entangled states

International Nuclear Information System (INIS)

Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Lupo, Cosmo; Mancini, Stefano

2009-01-01

We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n≤7.

Loop corrections to primordial non-Gaussianity

Science.gov (United States)

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.

Variational Gaussian approximation for Poisson data

Science.gov (United States)

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

2018-02-01

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

Phase space structure of generalized Gaussian cat states

International Nuclear Information System (INIS)

Nicacio, Fernando; Maia, Raphael N.P.; Toscano, Fabricio; Vallejos, Raul O.

2010-01-01

We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states. The structure of the interference term of the Wigner function is always hyperbolic, surviving the action of a thermal reservoir. We also consider certain superpositions of mixed Gaussian states. An application to semiclassical dynamics is discussed.

Prediction and retrodiction with continuously monitored Gaussian states

DEFF Research Database (Denmark)

Zhang, Jinglei; Mølmer, Klaus

2017-01-01

Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and continuous probing which maintain their Gaussian state property......(t)$ to Gaussian states implies that the matrix $E(t)$ is also fully characterized by a vector of mean values and a covariance matrix. We derive the dynamical equations for these quantities and we illustrate their use in the retrodiction of measurements on Gaussian systems....

Description of the nucleon wave function as a sum of well-chosen Gaussian functions

International Nuclear Information System (INIS)

Roux, C.; Silvestre-Brac, B.

1995-01-01

We study in detail the possibility of describing the nucleon (three quark-system) wave function as a superposition of Gaussian functions. A Faddeev treatment including 8 amplitudes is performed and taken as reference for the exact values. Several approximations are proposed and compared carefully to the exact solutions. Three different potentials have been tested and several observables are considered. (author)

Fast uncertainty reduction strategies relying on Gaussian process models

International Nuclear Information System (INIS)

Chevalier, Clement

2013-01-01

This work deals with sequential and batch-sequential evaluation strategies of real-valued functions under limited evaluation budget, using Gaussian process models. Optimal Stepwise Uncertainty Reduction (SUR) strategies are investigated for two different problems, motivated by real test cases in nuclear safety. First we consider the problem of identifying the excursion set above a given threshold T of a real-valued function f. Then we study the question of finding the set of 'safe controlled configurations', i.e. the set of controlled inputs where the function remains below T, whatever the value of some others non-controlled inputs. New SUR strategies are presented, together with efficient procedures and formulas to compute and use them in real world applications. The use of fast formulas to recalculate quickly the posterior mean or covariance function of a Gaussian process (referred to as the 'kriging update formulas') does not only provide substantial computational savings. It is also one of the key tools to derive closed form formulas enabling a practical use of computationally-intensive sampling strategies. A contribution in batch-sequential optimization (with the multi-points Expected Improvement) is also presented. (author)

Super-resolving random-Gaussian apodized photon sieve.

Science.gov (United States)

Sabatyan, Arash; Roshaninejad, Parisa

2012-09-10

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

Some continual integrals from gaussian forms

International Nuclear Information System (INIS)

Mazmanishvili, A.S.

1985-01-01

The result summary of continual integration of gaussian functional type is given. The summary contains 124 continual integrals which are the mathematical expectation of the corresponding gaussian form by the continuum of random trajectories of four types: real-valued Ornstein-Uhlenbeck process, Wiener process, complex-valued Ornstein-Uhlenbeck process and the stochastic harmonic one. The summary includes both the known continual integrals and the unpublished before integrals. Mathematical results of the continual integration carried in the work may be applied in the problem of the theory of stochastic process, approaching to the finding of mean from gaussian forms by measures generated by the pointed stochastic processes

Current inversion induced by colored non-Gaussian noise

International Nuclear Information System (INIS)

Bag, Bidhan Chandra; Hu, Chin-Kung

2009-01-01

We study a stochastic process driven by colored non-Gaussian noises. For the flashing ratchet model we find that there is a current inversion in the variation of the current with the half-cycle period which accounts for the potential on–off operation. The current inversion almost disappears if one switches from non-Gaussian (NG) to Gaussian (G) noise. We also find that at low value of the asymmetry parameter of the potential the mobility controlled current is more negative for NG noise as compared to G noise. But at large magnitude of the parameter the diffusion controlled positive current is higher for the former than for the latter. On increasing the noise correlation time (τ), keeping the noise strength fixed, the mean velocity of a particle first increases and then decreases after passing through a maximum if the noise is non-Gaussian. For Gaussian noise, the current monotonically decreases. The current increases with the noise parameter p, 0< p<5/3, which is 1 for Gaussian noise

Passivity and practical work extraction using Gaussian operations

International Nuclear Information System (INIS)

Brown, Eric G; Huber, Marcus; Friis, Nicolai

2016-01-01

Quantum states that can yield work in a cyclical Hamiltonian process form one of the primary resources in the context of quantum thermodynamics. Conversely, states whose average energy cannot be lowered by unitary transformations are called passive. However, while work may be extracted from non-passive states using arbitrary unitaries, the latter may be hard to realize in practice. It is therefore pertinent to consider the passivity of states under restricted classes of operations that can be feasibly implemented. Here, we ask how restrictive the class of Gaussian unitaries is for the task of work extraction. We investigate the notion of Gaussian passivity, that is, we present necessary and sufficient criteria identifying all states whose energy cannot be lowered by Gaussian unitaries. For all other states we give a prescription for the Gaussian operations that extract the maximal amount of energy. Finally, we show that the gap between passivity and Gaussian passivity is maximal, i.e., Gaussian-passive states may still have a maximal amount of energy that is extractable by arbitrary unitaries, even under entropy constraints. (paper)

Tachyon mediated non-Gaussianity

International Nuclear Information System (INIS)

Dutta, Bhaskar; Leblond, Louis; Kumar, Jason

2008-01-01

We describe a general scenario where primordial non-Gaussian curvature perturbations are generated in models with extra scalar fields. The extra scalars communicate to the inflaton sector mainly through the tachyonic (waterfall) field condensing at the end of hybrid inflation. These models can yield significant non-Gaussianity of the local shape, and both signs of the bispectrum can be obtained. These models have cosmic strings and a nearly flat power spectrum, which together have been recently shown to be a good fit to WMAP data. We illustrate with a model of inflation inspired from intersecting brane models.

Large deviations for Gaussian processes in Hoelder norm

International Nuclear Information System (INIS)

Fatalov, V R

2003-01-01

Some results are proved on the exact asymptotic representation of large deviation probabilities for Gaussian processes in the Hoeder norm. The following classes of processes are considered: the Wiener process, the Brownian bridge, fractional Brownian motion, and stationary Gaussian processes with power-law covariance function. The investigation uses the method of double sums for Gaussian fields

Increasing Entanglement between Gaussian States by Coherent Photon Subtraction

DEFF Research Database (Denmark)

Ourjoumtsev, Alexei; Dantan, Aurelien Romain; Tualle Brouri, Rosa

2007-01-01

We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states...

New gaussian points for the solution of first order ordinary ...

African Journals Online (AJOL)

Numerical experiments carried out using the new Gaussian points revealed there efficiency on stiff differential equations. The results also reveal that methods using the new Gaussian points are more accurate than those using the standard Gaussian points on non-stiff initial value problems. Keywords: Gaussian points ...

Gaussian entanglement distribution via satellite

Science.gov (United States)

Hosseinidehaj, Nedasadat; Malaney, Robert

2015-02-01

In this work we analyze three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme, the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the tradeoff between space-based engineering complexity and the rate of ground-station entanglement generation.

Revisiting non-Gaussianity from non-attractor inflation models

Science.gov (United States)

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

2018-05-01

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

Gaussian limit of compact spin systems

International Nuclear Information System (INIS)

Bellissard, J.; Angelis, G.F. de

1981-01-01

It is shown that the Wilson and Wilson-Villain U(1) models reproduce, in the low coupling limit, the gaussian lattice approximation of the Euclidean electromagnetic field. By the same methods it is also possible to prove that the plane rotator and the Villain model share a common gaussian behaviour in the low temperature limit. (Auth.)

Gaussian cloning of coherent states with known phases

International Nuclear Information System (INIS)

Alexanian, Moorad

2006-01-01

The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of 2/3. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of 4/5. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier

Non-Gaussian Methods for Causal Structure Learning.

Science.gov (United States)

Shimizu, Shohei

2018-05-22

Causal structure learning is one of the most exciting new topics in the fields of machine learning and statistics. In many empirical sciences including prevention science, the causal mechanisms underlying various phenomena need to be studied. Nevertheless, in many cases, classical methods for causal structure learning are not capable of estimating the causal structure of variables. This is because it explicitly or implicitly assumes Gaussianity of data and typically utilizes only the covariance structure. In many applications, however, non-Gaussian data are often obtained, which means that more information may be contained in the data distribution than the covariance matrix is capable of containing. Thus, many new methods have recently been proposed for using the non-Gaussian structure of data and inferring the causal structure of variables. This paper introduces prevention scientists to such causal structure learning methods, particularly those based on the linear, non-Gaussian, acyclic model known as LiNGAM. These non-Gaussian data analysis tools can fully estimate the underlying causal structures of variables under assumptions even in the presence of unobserved common causes. This feature is in contrast to other approaches. A simulated example is also provided.

Gaussian polynomials and content ideal in trivial extensions

International Nuclear Information System (INIS)

Bakkari, C.; Mahdou, N.

2006-12-01

The goal of this paper is to exhibit a class of Gaussian non-coherent rings R (with zero-divisors) such that wdim(R) = ∞ and fPdim(R) is always at most one and also exhibits a new class of rings (with zerodivisors) which are neither locally Noetherian nor locally domain where Gaussian polynomials have a locally principal content. For this purpose, we study the possible transfer of the 'Gaussian' property and the property 'the content ideal of a Gaussian polynomial is locally principal' to various trivial extension contexts. This article includes a brief discussion of the scopes and limits of our result. (author)

Quantifying entanglement in two-mode Gaussian states

Science.gov (United States)

Tserkis, Spyros; Ralph, Timothy C.

2017-12-01

Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography, and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure that is straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.

Optimal unitary dilation for bosonic Gaussian channels

International Nuclear Information System (INIS)

Caruso, Filippo; Eisert, Jens; Giovannetti, Vittorio; Holevo, Alexander S.

2011-01-01

A general quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. In this paper the minimal number of quantum Gaussian environmental modes required to provide a unitary dilation of a multimode bosonic Gaussian channel is analyzed for both pure and mixed environments. We compute this quantity in the case of pure environment corresponding to the Stinespring representation and give an improved estimate in the case of mixed environment. The computations rely, on one hand, on the properties of the generalized Choi-Jamiolkowski state and, on the other hand, on an explicit construction of the minimal dilation for arbitrary bosonic Gaussian channel. These results introduce a new quantity reflecting ''noisiness'' of bosonic Gaussian channels and can be applied to address some issues concerning transmission of information in continuous variables systems.

Graphical calculus for Gaussian pure states

International Nuclear Information System (INIS)

Menicucci, Nicolas C.; Flammia, Steven T.; Loock, Peter van

2011-01-01

We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.

Mode entanglement of Gaussian fermionic states

Science.gov (United States)

Spee, C.; Schwaiger, K.; Giedke, G.; Kraus, B.

2018-04-01

We investigate the entanglement of n -mode n -partite Gaussian fermionic states (GFS). First, we identify a reasonable definition of separability for GFS and derive a standard form for mixed states, to which any state can be mapped via Gaussian local unitaries (GLU). As the standard form is unique, two GFS are equivalent under GLU if and only if their standard forms coincide. Then, we investigate the important class of local operations assisted by classical communication (LOCC). These are central in entanglement theory as they allow one to partially order the entanglement contained in states. We show, however, that there are no nontrivial Gaussian LOCC (GLOCC) among pure n -partite (fully entangled) states. That is, any such GLOCC transformation can also be accomplished via GLU. To obtain further insight into the entanglement properties of such GFS, we investigate the richer class of Gaussian stochastic local operations assisted by classical communication (SLOCC). We characterize Gaussian SLOCC classes of pure n -mode n -partite states and derive them explicitly for few-mode states. Furthermore, we consider certain fermionic LOCC and show how to identify the maximally entangled set of pure n -mode n -partite GFS, i.e., the minimal set of states having the property that any other state can be obtained from one state inside this set via fermionic LOCC. We generalize these findings also to the pure m -mode n -partite (for m >n ) case.

Gaussian Mixture Model of Heart Rate Variability

Science.gov (United States)

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

Learning conditional Gaussian networks

DEFF Research Database (Denmark)

Bøttcher, Susanne Gammelgaard

This paper considers conditional Gaussian networks. The parameters in the network are learned by using conjugate Bayesian analysis. As conjugate local priors, we apply the Dirichlet distribution for discrete variables and the Gaussian-inverse gamma distribution for continuous variables, given...... a configuration of the discrete parents. We assume parameter independence and complete data. Further, to learn the structure of the network, the network score is deduced. We then develop a local master prior procedure, for deriving parameter priors in these networks. This procedure satisfies parameter...... independence, parameter modularity and likelihood equivalence. Bayes factors to be used in model search are introduced. Finally the methods derived are illustrated by a simple example....

Theoretical Fluid Dynamics

CERN Document Server

Shivamoggi, Bhimsen K

1998-01-01

"Although there are many texts and monographs on fluid dynamics, I do not know of any which is as comprehensive as the present book. It surveys nearly the entire field of classical fluid dynamics in an advanced, compact, and clear manner, and discusses the various conceptual and analytical models of fluid flow." - Foundations of Physics on the first edition. Theoretical Fluid Dynamics functions equally well as a graduate-level text and a professional reference. Steering a middle course between the empiricism of engineering and the abstractions of pure mathematics, the author focuses

Two-photon optics of Bessel-Gaussian modes

CSIR Research Space (South Africa)

McLaren, M

2013-09-01

Full Text Available In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum...

Gaussian discriminating strength

Science.gov (United States)

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.

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

Science.gov (United States)

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.

Functional Dual Adaptive Control with Recursive Gaussian Process Model

International Nuclear Information System (INIS)

Prüher, Jakub; Král, Ladislav

2015-01-01

The paper deals with dual adaptive control problem, where the functional uncertainties in the system description are modelled by a non-parametric Gaussian process regression model. Current approaches to adaptive control based on Gaussian process models are severely limited in their practical applicability, because the model is re-adjusted using all the currently available data, which keeps growing with every time step. We propose the use of recursive Gaussian process regression algorithm for significant reduction in computational requirements, thus bringing the Gaussian process-based adaptive controllers closer to their practical applicability. In this work, we design a bi-criterial dual controller based on recursive Gaussian process model for discrete-time stochastic dynamic systems given in an affine-in-control form. Using Monte Carlo simulations, we show that the proposed controller achieves comparable performance with the full Gaussian process-based controller in terms of control quality while keeping the computational demands bounded. (paper)

Back to Normal! Gaussianizing posterior distributions for cosmological probes

Science.gov (United States)

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

2014-05-01

We present a method to map multivariate non-Gaussian posterior probability densities into Gaussian ones via nonlinear Box-Cox transformations, and generalizations thereof. This is analogous to the search for normal parameters in the CMB, but can in principle be applied to any probability density that is continuous and unimodal. The search for the optimally Gaussianizing transformation amongst the Box-Cox family is performed via a maximum likelihood formalism. We can judge the quality of the found transformation a posteriori: qualitatively via statistical tests of Gaussianity, and more illustratively by how well it reproduces the credible regions. The method permits an analytical reconstruction of the posterior from a sample, e.g. a Markov chain, and simplifies the subsequent joint analysis with other experiments. Furthermore, it permits the characterization of a non-Gaussian posterior in a compact and efficient way. The expression for the non-Gaussian posterior can be employed to find analytic formulae for the Bayesian evidence, and consequently be used for model comparison.

On the Shaker Simulation of Wind-Induced Non-Gaussian Random Vibration

Directory of Open Access Journals (Sweden)

Fei Xu

2016-01-01

Full Text Available Gaussian signal is produced by ordinary random vibration controllers to test the products in the laboratory, while the field data is usually non-Gaussian. Two methodologies are presented in this paper for shaker simulation of wind-induced non-Gaussian vibration. The first methodology synthesizes the non-Gaussian signal offline and replicates it on the shaker in the Time Waveform Replication (TWR mode. A new synthesis method is used to model the non-Gaussian signal as a Gaussian signal multiplied by an amplitude modulation function (AMF. A case study is presented to show that the synthesized non-Gaussian signal has the same power spectral density (PSD, probability density function (PDF, and loading cycle distribution (LCD as the field data. The second methodology derives a damage equivalent Gaussian signal from the non-Gaussian signal based on the fatigue damage spectrum (FDS and the extreme response spectrum (ERS and reproduces it on the shaker in the closed-loop frequency domain control mode. The PSD level and the duration time of the derived Gaussian signal can be manipulated for accelerated testing purpose. A case study is presented to show that the derived PSD matches the damage potential of the non-Gaussian environment for both fatigue and peak response.

Optimal multicopy asymmetric Gaussian cloning of coherent states

International Nuclear Information System (INIS)

Fiurasek, Jaromir; Cerf, Nicolas J.

2007-01-01

We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward

Optimal multicopy asymmetric Gaussian cloning of coherent states

Science.gov (United States)

Fiurášek, Jaromír; Cerf, Nicolas J.

2007-05-01

We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward.

How Gaussian can our Universe be?

Energy Technology Data Exchange (ETDEWEB)

Cabass, G. [Physics Department and INFN, Università di Roma ' ' La Sapienza' ' , P.le Aldo Moro 2, 00185, Rome (Italy); Pajer, E. [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); Schmidt, F., E-mail: giovanni.cabass@roma1.infn.it, E-mail: e.pajer@uu.nl, E-mail: fabians@mpa-garching.mpg.de [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)

2017-01-01

Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of k {sub ℓ}{sup 2}/ k {sub s} {sup 2}, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × ( n {sub s}−1).

How Gaussian can our Universe be?

Science.gov (United States)

Cabass, G.; Pajer, E.; Schmidt, F.

2017-01-01

Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of kl2/ks2, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × (ns-1).

Boltzmann-Gaussian transition under specific noise effect

International Nuclear Information System (INIS)

Anh, Chu Thuy; Lan, Nguyen Tri; Viet, Nguyen Ai

2014-01-01

It is observed that a short time data set of market returns presents almost symmetric Boltzmann distribution whereas a long time data set tends to show a Gaussian distribution. To understand this universal phenomenon, many hypotheses which are spreading in a wide range of interdisciplinary research were proposed. In current work, the effects of background fluctuations on symmetric Boltzmann distribution is investigated. The numerical calculation is performed to show that the Gaussian noise may cause the transition from initial Boltzmann distribution to Gaussian one. The obtained results would reflect non-dynamic nature of the transition under consideration.

Gaussian sum rules for optical functions

International Nuclear Information System (INIS)

Kimel, I.

1981-12-01

A new (Gaussian) type of sum rules (GSR) for several optical functions, is presented. The functions considered are: dielectric permeability, refractive index, energy loss function, rotatory power and ellipticity (circular dichroism). While reducing to the usual type of sum rules in a certain limit, the GSR contain in general, a Gaussian factor that serves to improve convergence. GSR might be useful in analysing experimental data. (Author) [pt

Approximation problems with the divergence criterion for Gaussian variablesand Gaussian processes

NARCIS (Netherlands)

A.A. Stoorvogel; J.H. van Schuppen (Jan)

1996-01-01

textabstractSystem identification for stationary Gaussian processes includes an approximation problem. Currently the subspace algorithm for this problem enjoys much attention. This algorithm is based on a transformation of a finite time series to canonical variable form followed by a truncation.

Palm distributions for log Gaussian Cox processes

DEFF Research Database (Denmark)

Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus

This paper reviews useful results related to Palm distributions of spatial point processes and provides a new result regarding the characterization of Palm distributions for the class of log Gaussian Cox processes. This result is used to study functional summary statistics for a log Gaussian Cox...

Stochastic characteristics and Second Law violations of atomic fluids in Couette flow

Science.gov (United States)

Raghavan, Bharath V.; Karimi, Pouyan; Ostoja-Starzewski, Martin

2018-04-01

Using Non-equilibrium Molecular Dynamics (NEMD) simulations, we study the statistical properties of an atomic fluid undergoing planar Couette flow, in which particles interact via a Lennard-Jones potential. We draw a connection between local density contrast and temporal fluctuations in the shear stress, which arise naturally through the equivalence between the dissipation function and entropy production according to the fluctuation theorem. We focus on the shear stress and the spatio-temporal density fluctuations and study the autocorrelations and spectral densities of the shear stress. The bispectral density of the shear stress is used to measure the degree of departure from a Gaussian model and the degree of nonlinearity induced in the system owing to the applied strain rate. More evidence is provided by the probability density function of the shear stress. We use the Information Theory to account for the departure from Gaussian statistics and to develop a more general probability distribution function that captures this broad range of effects. By accounting for negative shear stress increments, we show how this distribution preserves the violations of the Second Law of Thermodynamics observed in planar Couette flow of atomic fluids, and also how it captures the non-Gaussian nature of the system by allowing for non-zero higher moments. We also demonstrate how the temperature affects the band-width of the shear-stress and how the density affects its Power Spectral Density, thus determining the conditions under which the shear-stress acts is a narrow-band or wide-band random process. We show that changes in the statistical characteristics of the parameters of interest occur at a critical strain rate at which an ordering transition occurs in the fluid causing shear thinning and affecting its stability. A critical strain rate of this kind is also predicted by the Loose-Hess stability criterion.

Making tensor factorizations robust to non-gaussian noise.

Energy Technology Data Exchange (ETDEWEB)

Chi, Eric C. (Rice University, Houston, TX); Kolda, Tamara Gibson

2011-03-01

Tensors are multi-way arrays, and the CANDECOMP/PARAFAC (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of independent and identically distributed (i.i.d.) Gaussian noise. We demonstrate that this loss function can be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization (MM) algorithm for fitting a CP model using our proposed loss function (CPAL1) and compare its performance to the workhorse algorithm for fitting CP models, CP alternating least squares (CPALS).

Integration of non-Gaussian fields

DEFF Research Database (Denmark)

Ditlevsen, Ove Dalager; Mohr, Gunnar; Hoffmeyer, Pernille

1996-01-01

The limitations of the validity of the central limit theorem argument as applied to definite integrals of non-Gaussian random fields are empirically explored by way of examples. The purpose is to investigate in specific cases whether the asymptotic convergence to the Gaussian distribution is fast....... and Randrup-Thomsen, S. Reliability of silo ring under lognormal stochastic pressure using stochastic interpolation. Proc. IUTAM Symp., Probabilistic Structural Mechanics: Advances in Structural Reliability Methods, San Antonio, TX, USA, June 1993 (eds.: P. D. Spanos & Y.-T. Wu) pp. 134-162. Springer, Berlin...

Estimators for local non-Gaussianities

International Nuclear Information System (INIS)

Creminelli, P.; Senatore, L.; Zaldarriaga, M.

2006-05-01

We study the Likelihood function of data given f NL for the so-called local type of non-Gaussianity. In this case the curvature perturbation is a non-linear function, local in real space, of a Gaussian random field. We compute the Cramer-Rao bound for f NL and show that for small values of f NL the 3- point function estimator saturates the bound and is equivalent to calculating the full Likelihood of the data. However, for sufficiently large f NL , the naive 3-point function estimator has a much larger variance than previously thought. In the limit in which the departure from Gaussianity is detected with high confidence, error bars on f NL only decrease as 1/ln N pix rather than N pix -1/2 as the size of the data set increases. We identify the physical origin of this behavior and explain why it only affects the local type of non- Gaussianity, where the contribution of the first multipoles is always relevant. We find a simple improvement to the 3-point function estimator that makes the square root of its variance decrease as N pix -1/2 even for large f NL , asymptotically approaching the Cramer-Rao bound. We show that using the modified estimator is practically equivalent to computing the full Likelihood of f NL given the data. Thus other statistics of the data, such as the 4-point function and Minkowski functionals, contain no additional information on f NL . In particular, we explicitly show that the recent claims about the relevance of the 4-point function are not correct. By direct inspection of the Likelihood, we show that the data do not contain enough information for any statistic to be able to constrain higher order terms in the relation between the Gaussian field and the curvature perturbation, unless these are orders of magnitude larger than the size suggested by the current limits on f NL . (author)

A comparison on the propagation characteristics of focused Gaussian beam and fundamental Gaussian beam in vacuum

International Nuclear Information System (INIS)

Liu Shixiong; Guo Hong; Liu Mingwei; Wu Guohua

2004-01-01

Propagation characteristics of focused Gaussian beam (FoGB) and fundamental Gaussian beam (FuGB) propagating in vacuum are investigated. Based on the Fourier transform and the angular spectral analysis, the transverse component and the second-order approximate longitudinal component of the electric field are obtained in the paraxial approximation. The electric field components, the phase velocity and the group velocity of FoGB are compared with those of FuGB. The spot size of FoGB is also discussed

Valid analytical performance specifications for combined analytical bias and imprecision for the use of common reference intervals

DEFF Research Database (Denmark)

Hyltoft Petersen, Per; Lund, Flemming; Fraser, Callum G

2018-01-01

for the combination of analytical bias and imprecision and Method 2 is based on the Microsoft Excel formula NORMINV including the fractional probability of reference individuals outside each limit and the Gaussian variables of mean and standard deviation. The combinations of normalized bias and imprecision...... are illustrated for both methods. The formulae are identical for Gaussian and log-Gaussian distributions. Results Method 2 gives the correct results with a constant percentage of 4.4% for all combinations of bias and imprecision. Conclusion The Microsoft Excel formula NORMINV is useful for the estimation...

Calculating emittance for Gaussian and Non-Gaussian distributions by the method of correlations for slits

International Nuclear Information System (INIS)

Tan, Cheng-Yang; Fermilab

2006-01-01

One common way for measuring the emittance of an electron beam is with the slits method. The usual approach for analyzing the data is to calculate an emittance that is a subset of the parent emittance. This paper shows an alternative way by using the method of correlations which ties the parameters derived from the beamlets to the actual parameters of the parent emittance. For parent distributions that are Gaussian, this method yields exact results. For non-Gaussian beam distributions, this method yields an effective emittance that can serve as a yardstick for emittance comparisons

Non-Gaussianity in a quasiclassical electronic circuit

Science.gov (United States)

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.

Emergence of multi-scaling in fluid turbulence

Science.gov (United States)

Donzis, Diego; Yakhot, Victor

2017-11-01

We present new theoretical and numerical results on the transition to strong turbulence in an infinite fluid stirred by a Gaussian random force. The transition is defined as a first appearance of anomalous scaling of normalized moments of velocity derivatives (or dissipation rates) emerging from the low-Reynolds-number Gaussian background. It is shown that due to multi-scaling, strongly intermittent rare events can be quantitatively described in terms of an infinite number of different ``Reynolds numbers'' reflecting a multitude of anomalous scaling exponents. We found that anomalous scaling for high order moments emerges at very low Reynolds numbers implying that intense dissipative-range fluctuations are established at even lower Reynolds number than that required for an inertial range. Thus, our results suggest that information about inertial range dynamics can be obtained from dissipative scales even when the former does not exit. We discuss our further prediction that transition to fully anomalous turbulence disappears at Rλ < 3 . Support from NSF is acknowledged.

A fast Gaussian filtering algorithm for three-dimensional surface roughness measurements

International Nuclear Information System (INIS)

Yuan, Y B; Piao, W Y; Xu, J B

2007-01-01

The two-dimensional (2-D) Gaussian filter can be separated into two one-dimensional (1-D) Gaussian filters. The 1-D Gaussian filter can be implemented approximately by the cascaded Butterworth filters. The approximation accuracy will be improved with the increase of the number of the cascaded filters. A recursive algorithm for Gaussian filtering requires a relatively small number of simple mathematical operations such as addition, subtraction, multiplication, or division, so that it has considerable computational efficiency and it is very useful for three-dimensional (3-D) surface roughness measurements. The zero-phase-filtering technique is used in this algorithm, so there is no phase distortion in the Gaussian filtered mean surface. High-order approximation Gaussian filters are proposed for practical use to assure high accuracy of Gaussian filtering of 3-D surface roughness measurements

A fast Gaussian filtering algorithm for three-dimensional surface roughness measurements

Science.gov (United States)

Yuan, Y. B.; Piao, W. Y.; Xu, J. B.

2007-07-01

The two-dimensional (2-D) Gaussian filter can be separated into two one-dimensional (1-D) Gaussian filters. The 1-D Gaussian filter can be implemented approximately by the cascaded Butterworth filters. The approximation accuracy will be improved with the increase of the number of the cascaded filters. A recursive algorithm for Gaussian filtering requires a relatively small number of simple mathematical operations such as addition, subtraction, multiplication, or division, so that it has considerable computational efficiency and it is very useful for three-dimensional (3-D) surface roughness measurements. The zero-phase-filtering technique is used in this algorithm, so there is no phase distortion in the Gaussian filtered mean surface. High-order approximation Gaussian filters are proposed for practical use to assure high accuracy of Gaussian filtering of 3-D surface roughness measurements.

Imprint of primordial non-Gaussianity on dark matter halo profiles

Energy Technology Data Exchange (ETDEWEB)

Dizgah, Azadeh Moradinezhad; Dodelson, Scott; Riotto, Antonio

2013-09-01

We study the impact of primordial non-Gaussianity on the density profile of dark matter halos by using the semi-analytical model introduced recently by Dalal {\\it et al.} which relates the peaks of the initial linear density field to the final density profile of dark matter halos. Models with primordial non-Gaussianity typically produce an initial density field that differs from that produced in Gaussian models. We use the path-integral formulation of excursion set theory to calculate the non-Gaussian corrections to the peak profile and derive the statistics of the peaks of non-Gaussian density field. In the context of the semi-analytic model for halo profiles, currently allowed values for primordial non-Gaussianity would increase the shapes of the inner dark matter profiles, but only at the sub-percent level except in the very innermost regions.

On the dependence structure of Gaussian queues

NARCIS (Netherlands)

Es-Saghouani, A.; Mandjes, M.R.H.

2009-01-01

In this article we study Gaussian queues (that is, queues fed by Gaussian processes, such as fractional Brownian motion (fBm) and the integrated Ornstein-Uhlenbeck (iOU) process), with a focus on the dependence structure of the workload process. The main question is to what extent does the workload

Shedding new light on Gaussian harmonic analysis

NARCIS (Netherlands)

Teuwen, J.J.B.

2016-01-01

This dissertation consists out of two rather disjoint parts. One part concerns some results on Gaussian harmonic analysis and the other on an optimization problem in optics. In the first part we study the Ornstein–Uhlenbeck process with respect to the Gaussian measure. We focus on two areas. One is

Divergence of relative difference in Gaussian distribution function and stochastic resonance in a bistable system with frictionless state transition

Science.gov (United States)

Kasai, Seiya; Ichiki, Akihisa; Tadokoro, Yukihiro

2018-03-01

A bistable system efficiently detects a weak signal by adding noise, which is referred to as stochastic resonance. A previous theory deals with friction in state transition; however, this hypothesis is inadequate when friction force is negligible such as in nano- and molecular-scale systems. We show that, when the transition occurs without friction, the sensitivity of the bistable system to a Gaussian-noise-imposed weak signal becomes significantly high. The sensitivity is determined by the relative difference in noise distribution function. We find that the relative difference in Gaussian distribution function diverges in its tail edge, resulting in a high sensitivity in the present system.

Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models.

Directory of Open Access Journals (Sweden)

Georgios C Manikis

Full Text Available The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer.Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2 at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG and non-Gaussian (MNG and BNG were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE. To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC and F-ratio.All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area.No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.

Representation of Gaussian semimartingales with applications to the covariance function

DEFF Research Database (Denmark)

Basse-O'Connor, Andreas

2010-01-01

stationary Gaussian semimartingales and their canonical decomposition. Thirdly, we give a new characterization of the covariance function of Gaussian semimartingales, which enable us to characterize the class of martingales and the processes of bounded variation among the Gaussian semimartingales. We...

On a Generalized Squared Gaussian Diffusion Model for Option Valuation

Directory of Open Access Journals (Sweden)

Edeki S.O.

2017-01-01

Full Text Available In financial mathematics, option pricing models are vital tools whose usefulness cannot be overemphasized. Modern approaches and modelling of financial derivatives are therefore required in option pricing and valuation settings. In this paper, we derive via the application of Ito lemma, a pricing model referred to as Generalized Squared Gaussian Diffusion Model (GSGDM for option pricing and valuation. Same approach can be considered via Stratonovich stochastic dynamics. We also show that the classical Black-Scholes, and the square root constant elasticity of variance models are special cases of the GSGDM. In addition, general solution of the GSGDM is obtained using modified variational iterative method (MVIM.

Scaled unscented transform Gaussian sum filter: Theory and application

KAUST Repository

Luo, Xiaodong

2010-05-01

In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]). In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel. As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to

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

Science.gov (United States)

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

2007-04-01

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

Limit theorems for functionals of Gaussian vectors

Institute of Scientific and Technical Information of China (English)

Hongshuai DAI; Guangjun SHEN; Lingtao KONG

2017-01-01

Operator self-similar processes,as an extension of self-similar processes,have been studied extensively.In this work,we study limit theorems for functionals of Gaussian vectors.Under some conditions,we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.

Gaussian statistics for palaeomagnetic vectors

Science.gov (United States)

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

2003-01-01

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to

Gaussian statistics for palaeomagnetic vectors

Science.gov (United States)

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

2003-03-01

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimodal) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to

Consistency relations for sharp inflationary non-Gaussian features

Energy Technology Data Exchange (ETDEWEB)

Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Blanco Encalada 2008, Santiago (Chile); Soto, Alex, E-mail: sander.mooij@ing.uchile.cl, E-mail: gpalmaquilod@ing.uchile.cl, E-mail: gpanotop@ing.uchile.cl, E-mail: gatogeno@gmail.com [Departamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago (Chile)

2016-09-01

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

Consistency relations for sharp inflationary non-Gaussian features

International Nuclear Information System (INIS)

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

2016-01-01

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

Comparing Fixed and Variable-Width Gaussian Networks

Czech Academy of Sciences Publication Activity Database

Kůrková, Věra; Kainen, P.C.

2014-01-01

Roč. 57, September (2014), s. 23-28 ISSN 0893-6080 R&D Projects: GA MŠk(CZ) LD13002 Institutional support: RVO:67985807 Keywords : Gaussian radial and kernel networks * Functionally equivalent networks * Universal approximators * Stabilizers defined by Gaussian kernels * Argminima of error functionals Subject RIV: IN - Informatics, Computer Science Impact factor: 2.708, year: 2014

Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids

International Nuclear Information System (INIS)

Holm, D.D.

1976-07-01

The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented

Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids

Energy Technology Data Exchange (ETDEWEB)

Holm, D.D.

1976-07-01

The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented.

Covariance-Based Measurement Selection Criterion for Gaussian-Based Algorithms

Directory of Open Access Journals (Sweden)

Fernando A. Auat Cheein

2013-01-01

Full Text Available Process modeling by means of Gaussian-based algorithms often suffers from redundant information which usually increases the estimation computational complexity without significantly improving the estimation performance. In this article, a non-arbitrary measurement selection criterion for Gaussian-based algorithms is proposed. The measurement selection criterion is based on the determination of the most significant measurement from both an estimation convergence perspective and the covariance matrix associated with the measurement. The selection criterion is independent from the nature of the measured variable. This criterion is used in conjunction with three Gaussian-based algorithms: the EIF (Extended Information Filter, the EKF (Extended Kalman Filter and the UKF (Unscented Kalman Filter. Nevertheless, the measurement selection criterion shown herein can also be applied to other Gaussian-based algorithms. Although this work is focused on environment modeling, the results shown herein can be applied to other Gaussian-based algorithm implementations. Mathematical descriptions and implementation results that validate the proposal are also included in this work.

Gaussian Process-Mixture Conditional Heteroscedasticity.

Science.gov (United States)

Platanios, Emmanouil A; Chatzis, Sotirios P

2014-05-01

Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an alternative approach based on methodologies widely used in the field of statistical machine learning. Specifically, we propose a novel nonparametric Bayesian mixture of Gaussian process regression models, each component of which models the noise variance process that contaminates the observed data as a separate latent Gaussian process driven by the observed data. This way, we essentially obtain a Gaussian process-mixture conditional heteroscedasticity (GPMCH) model for volatility modeling in financial return series. We impose a nonparametric prior with power-law nature over the distribution of the model mixture components, namely the Pitman-Yor process prior, to allow for better capturing modeled data distributions with heavy tails and skewness. Finally, we provide a copula-based approach for obtaining a predictive posterior for the covariances over the asset returns modeled by means of a postulated GPMCH model. We evaluate the efficacy of our approach in a number of benchmark scenarios, and compare its performance to state-of-the-art methodologies.

Resonant non-Gaussianity with equilateral properties

International Nuclear Information System (INIS)

Gwyn, Rhiannon; Rummel, Markus

2012-11-01

We discuss the effect of superimposing multiple sources of resonant non-Gaussianity, which arise for instance in models of axion inflation. The resulting sum of oscillating shape contributions can be used to ''Fourier synthesize'' different non-oscillating shapes in the bispectrum. As an example we reproduce an approximately equilateral shape from the superposition of O(10) oscillatory contributions with resonant shape. This implies a possible degeneracy between the equilateral-type non-Gaussianity typical of models with non-canonical kinetic terms, such as DBI inflation, and an equilateral-type shape arising from a superposition of resonant-type contributions in theories with canonical kinetic terms. The absence of oscillations in the 2-point function together with the structure of the resonant N-point functions, imply that detection of equilateral non-Gaussianity at a level greater than the PLANCK sensitivity of f NL ∝O(5) will rule out a resonant origin. We comment on the questions arising from possible embeddings of this idea in a string theory setting.

Non-Gaussian conductivity fluctuations in semiconductors

International Nuclear Information System (INIS)

Melkonyan, S.V.

2010-01-01

A theoretical study is presented on the statistical properties of conductivity fluctuations caused by concentration and mobility fluctuations of the current carriers. It is established that mobility fluctuations result from random deviations in the thermal equilibrium distribution of the carriers. It is shown that mobility fluctuations have generation-recombination and shot components which do not satisfy the requirements of the central limit theorem, in contrast to the current carrier's concentration fluctuation and intraband component of the mobility fluctuation. It is shown that in general the mobility fluctuation consist of thermal (or intraband) Gaussian and non-thermal (or generation-recombination, shot, etc.) non-Gaussian components. The analyses of theoretical results and experimental data from literature show that the statistical properties of mobility fluctuation and of 1/f-noise fully coincide. The deviation from Gaussian statistics of the mobility or 1/f fluctuations goes hand in hand with the magnitude of non-thermal noise (generation-recombination, shot, burst, pulse noises, etc.).

Legendre Duality of Spherical and Gaussian Spin Glasses

Energy Technology Data Exchange (ETDEWEB)

Genovese, Giuseppe, E-mail: giuseppe.genovese@math.uzh.ch [Universität Zürich, Institut für Mathematik (Switzerland); Tantari, Daniele, E-mail: daniele.tantari@sns.it [Scuola Normale Superiore di Pisa, Centro Ennio de Giorgi (Italy)

2015-12-15

The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.

Legendre Duality of Spherical and Gaussian Spin Glasses

International Nuclear Information System (INIS)

Genovese, Giuseppe; Tantari, Daniele

2015-01-01

The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model

Methods to characterize non-Gaussian noise in TAMA

International Nuclear Information System (INIS)

Ando, Masaki; Arai, K; Takahashi, R; Tatsumi, D; Beyersdorf, P; Kawamura, S; Miyoki, S; Mio, N; Moriwaki, S; Numata, K; Kanda, N; Aso, Y; Fujimoto, M-K; Tsubono, K; Kuroda, K

2003-01-01

We present a data characterization method for the main output signal of the interferometric gravitational-wave detector, in particular targeting at effective detection of burst gravitational waves from stellar core collapse. The time scale of non-Gaussian events is evaluated in this method, and events with longer time scale than real signals are rejected as non-Gaussian noises. As a result of data analysis using 1000 h of real data with the interferometric gravitational-wave detector TAMA300, the false-alarm rate was improved 10 3 times with this non-Gaussian noise evaluation and rejection method

Comparison of non-Gaussian and Gaussian diffusion models of diffusion weighted imaging of rectal cancer at 3.0 T MRI.

Science.gov (United States)

Zhang, Guangwen; Wang, Shuangshuang; Wen, Didi; Zhang, Jing; Wei, Xiaocheng; Ma, Wanling; Zhao, Weiwei; Wang, Mian; Wu, Guosheng; Zhang, Jinsong

2016-12-09

Water molecular diffusion in vivo tissue is much more complicated. We aimed to compare non-Gaussian diffusion models of diffusion-weighted imaging (DWI) including intra-voxel incoherent motion (IVIM), stretched-exponential model (SEM) and Gaussian diffusion model at 3.0 T MRI in patients with rectal cancer, and to determine the optimal model for investigating the water diffusion properties and characterization of rectal carcinoma. Fifty-nine consecutive patients with pathologically confirmed rectal adenocarcinoma underwent DWI with 16 b-values at a 3.0 T MRI system. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models (IVIM-mono, IVIM-bi and SEM) on primary tumor and adjacent normal rectal tissue. Parameters of standard apparent diffusion coefficient (ADC), slow- and fast-ADC, fraction of fast ADC (f), α value and distributed diffusion coefficient (DDC) were generated and compared between the tumor and normal tissues. The SEM exhibited the best fitting results of actual DWI signal in rectal cancer and the normal rectal wall (R 2  = 0.998, 0.999 respectively). The DDC achieved relatively high area under the curve (AUC = 0.980) in differentiating tumor from normal rectal wall. Non-Gaussian diffusion models could assess tissue properties more accurately than the ADC derived Gaussian diffusion model. SEM may be used as a potential optimal model for characterization of rectal cancer.

Influence of particle size distributions on magnetorheological fluid performances

International Nuclear Information System (INIS)

Chiriac, H; Stoian, G

2010-01-01

In this paper we investigate the influence that size distributions of the magnetic particles might have on the magnetorheological fluid performances. In our study, several size distributions have been tailored first by sieving a micrometric Fe powder in order to obtain narrow distribution powders and then by recomposing the new size distributions (different from Gaussian). We used spherical Fe particles (mesh -325) commercially available. The powder was sieved by means of a sieve shaker using a series of sieves with the following mesh size: 20, 32, 40, 50, 63, 80 micrometers. All magnetic powders were characterized through Vibrating Sample Magnetometer (VSM) measurements, particle size analysis and also Scanning Electron Microscope (SEM) images were taken. Magnetorheological (MR) fluids based on the resulted magnetic powders were prepared and studied by means of a rheometer with a magnetorheological module. The MR fluids were measured in magnetic field and in zero magnetic field as well. As we noticed in our previous experiments particles size distribution can also influence the MR fluids performances.

Scalable Gaussian Processes and the search for exoplanets

CERN Multimedia

CERN. Geneva

2015-01-01

Gaussian Processes are a class of non-parametric models that are often used to model stochastic behavior in time series or spatial data. A major limitation for the application of these models to large datasets is the computational cost. The cost of a single evaluation of the model likelihood scales as the third power of the number of data points. In the search for transiting exoplanets, the datasets of interest have tens of thousands to millions of measurements with uneven sampling, rendering naive application of a Gaussian Process model impractical. To attack this problem, we have developed robust approximate methods for Gaussian Process regression that can be applied at this scale. I will describe the general problem of Gaussian Process regression and offer several applicable use cases. Finally, I will present our work on scaling this model to the exciting field of exoplanet discovery and introduce a well-tested open source implementation of these new methods.

Isostructural solid-solid transition of (colloidal) simple fluids

International Nuclear Information System (INIS)

Tejero, C.F.; Daanoun, A.; Lakkerkerker, H.N.W.; Baus, M.

1995-01-01

A variational approach based on the Gibbs-Bogoliubov inequality is used in order to evaluate the free energy of simple fluids described by a double-Yukawa pair potential. A hard-sphere reference fluid is used to describe the fluid phases, and an Einstein reference crystal to describe the solid phases. Apart from the usual type of phase diagram, typical of atomic simple fluids with long-ranged attractions, we find two types of phase diagrams, specific to colloidal systems with intermediate and short-ranged attractions. One of the latter phase diagrams exhibits an isostructural solid-solid transition, which has not yet been observed experimentally

Realistic continuous-variable quantum teleportation with non-Gaussian resources

International Nuclear Information System (INIS)

Dell'Anno, F.; De Siena, S.; Illuminati, F.

2010-01-01

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

Generation of Quasi-Gaussian Pulses Based on Correlation Techniques

Directory of Open Access Journals (Sweden)

POHOATA, S.

2012-02-01

Full Text Available The Gaussian pulses have been mostly used within communications, where some applications can be emphasized: mobile telephony (GSM, where GMSK signals are used, as well as the UWB communications, where short-period pulses based on Gaussian waveform are generated. Since the Gaussian function signifies a theoretical concept, which cannot be accomplished from the physical point of view, this should be expressed by using various functions, able to determine physical implementations. New techniques of generating the Gaussian pulse responses of good precision are approached, proposed and researched in this paper. The second and third order derivatives with regard to the Gaussian pulse response are accurately generated. The third order derivates is composed of four individual rectangular pulses of fixed amplitudes, being easily to be generated by standard techniques. In order to generate pulses able to satisfy the spectral mask requirements, an adequate filter is necessary to be applied. This paper emphasizes a comparative analysis based on the relative error and the energy spectra of the proposed pulses.

The Gaussian radial basis function method for plasma kinetic theory

Energy Technology Data Exchange (ETDEWEB)

Hirvijoki, E., E-mail: eero.hirvijoki@chalmers.se [Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg (Sweden); Candy, J.; Belli, E. [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); Embréus, O. [Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg (Sweden)

2015-10-30

Description of a magnetized plasma involves the Vlasov equation supplemented with the non-linear Fokker–Planck collision operator. For non-Maxwellian distributions, the collision operator, however, is difficult to compute. In this Letter, we introduce Gaussian Radial Basis Functions (RBFs) to discretize the velocity space of the entire kinetic system, and give the corresponding analytical expressions for the Vlasov and collision operator. Outlining the general theory, we also highlight the connection to plasma fluid theories, and give 2D and 3D numerical solutions of the non-linear Fokker–Planck equation. Applications are anticipated in both astrophysical and laboratory plasmas. - Highlights: • A radically new method to address the velocity space discretization of the non-linear kinetic equation of plasmas. • Elegant and physically intuitive, flexible and mesh-free. • Demonstration of numerical solution of both 2-D and 3-D non-linear Fokker–Planck relaxation problem.

Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere

Science.gov (United States)

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.

Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data

Directory of Open Access Journals (Sweden)

Ji Hoon Ryoo

2017-08-01

Full Text Available As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet growth modeling with non-Gaussian data is somewhat limited when considering the transformed expectation of the response via a linear predictor as a functional form of explanatory variables. In this study, we introduce a fractional polynomial model (FPM that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. The results clearly show the efficiency and flexibility of the FPM for such applications.

GaussianCpG: a Gaussian model for detection of CpG island in human genome sequences.

Science.gov (United States)

Yu, Ning; Guo, Xuan; Zelikovsky, Alexander; Pan, Yi

2017-05-24

As crucial markers in identifying biological elements and processes in mammalian genomes, CpG islands (CGI) play important roles in DNA methylation, gene regulation, epigenetic inheritance, gene mutation, chromosome inactivation and nuclesome retention. The generally accepted criteria of CGI rely on: (a) %G+C content is ≥ 50%, (b) the ratio of the observed CpG content and the expected CpG content is ≥ 0.6, and (c) the general length of CGI is greater than 200 nucleotides. Most existing computational methods for the prediction of CpG island are programmed on these rules. However, many experimentally verified CpG islands deviate from these artificial criteria. Experiments indicate that in many cases %G+C is human genome. We analyze the energy distribution over genomic primary structure for each CpG site and adopt the parameters from statistics of Human genome. The evaluation results show that the new model can predict CpG islands efficiently by balancing both sensitivity and specificity over known human CGI data sets. Compared with other models, GaussianCpG can achieve better performance in CGI detection. Our Gaussian model aims to simplify the complex interaction between nucleotides. The model is computed not by the linear statistical method but by the Gaussian energy distribution and accumulation. The parameters of Gaussian function are not arbitrarily designated but deliberately chosen by optimizing the biological statistics. By using the pseudopotential analysis on CpG islands, the novel model is validated on both the real and artificial data sets.

Transient Properties of a Bistable System with Delay Time Driven by Non-Gaussian and Gaussian Noises: Mean First-Passage Time

International Nuclear Information System (INIS)

Li Dongxi; Xu Wei; Guo Yongfeng; Li Gaojie

2008-01-01

The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter (measures deviation from Gaussian character) r, the delay time τ, the noise correlation time τ 0 , the intensities D and α of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ 0 , or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system

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

Science.gov (United States)

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%.

Coincidence Imaging and interference with coherent Gaussian beams

Institute of Scientific and Technical Information of China (English)

CAI Yang-jian; ZHU Shi-yao

2006-01-01

we present a theoretical study of coincidence imaging and interference with coherent Gaussian beams The equations for the coincidence image formation and interference fringes are derived,from which it is clear that the imaging is due to the corresponding focusing in the two paths .The quality and visibility of the images and fringes can be high simultaneously.The nature of the coincidence imaging and interference between quantum entangled photon pairs and coherent Gaussian beams are different .The coincidence image with coherent Gaussian beams is due to intensity-intensity correspondence,a classical nature,while that with entangled photon pairs is due to the amplitude correlation a quantum nature.

EDITORIAL: Non-linear and non-Gaussian cosmological perturbations Non-linear and non-Gaussian cosmological perturbations

Science.gov (United States)

Sasaki, Misao; Wands, David

2010-06-01

In recent years there has been a resurgence of interest in the study of non-linear perturbations of cosmological models. This has been the result of both theoretical developments and observational advances. New theoretical challenges arise at second and higher order due to mode coupling and the need to develop new gauge-invariant variables beyond first order. In particular, non-linear interactions lead to deviations from a Gaussian distribution of primordial perturbations even if initial vacuum fluctuations are exactly Gaussian. These non-Gaussianities provide an important probe of models for the origin of structure in the very early universe. We now have a detailed picture of the primordial distribution of matter from surveys of the cosmic microwave background, notably NASA's WMAP satellite. The situation will continue to improve with future data from the ESA Planck satellite launched in 2009. To fully exploit these data cosmologists need to extend non-linear cosmological perturbation theory beyond the linear theory that has previously been sufficient on cosmological scales. Another recent development has been the realization that large-scale structure, revealed in high-redshift galaxy surveys, could also be sensitive to non-linearities in the primordial curvature perturbation. This focus section brings together a collection of invited papers which explore several topical issues in this subject. We hope it will be of interest to theoretical physicists and astrophysicists alike interested in understanding and interpreting recent developments in cosmological perturbation theory and models of the early universe. Of course it is only an incomplete snapshot of a rapidly developing field and we hope the reader will be inspired to read further work on the subject and, perhaps, fill in some of the missing pieces. This focus section is dedicated to the memory of Lev Kofman (1957-2009), an enthusiastic pioneer of inflationary cosmology and non-Gaussian perturbations.

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

Science.gov (United States)

Lukin, Igor P

2016-04-20

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

Ultrawide Bandwidth Receiver Based on a Multivariate Generalized Gaussian Distribution

KAUST Repository

Ahmed, Qasim Zeeshan

2015-04-01

Multivariate generalized Gaussian density (MGGD) is used to approximate the multiple access interference (MAI) and additive white Gaussian noise in pulse-based ultrawide bandwidth (UWB) system. The MGGD probability density function (pdf) is shown to be a better approximation of a UWB system as compared to multivariate Gaussian, multivariate Laplacian and multivariate Gaussian-Laplacian mixture (GLM). The similarity between the simulated and the approximated pdf is measured with the help of modified Kullback-Leibler distance (KLD). It is also shown that MGGD has the smallest KLD as compared to Gaussian, Laplacian and GLM densities. A receiver based on the principles of minimum bit error rate is designed for the MGGD pdf. As the requirement is stringent, the adaptive implementation of the receiver is also carried out in this paper. Training sequence of the desired user is the only requirement when implementing the detector adaptively. © 2002-2012 IEEE.

Relative entropy as a measure of entanglement for Gaussian states

Institute of Scientific and Technical Information of China (English)

Lu Huai-Xin; Zhao Bo

2006-01-01

In this paper, we derive an explicit analytic expression of the relative entropy between two general Gaussian states. In the restriction of the set for Gaussian states and with the help of relative entropy formula and Peres-Simon separability criterion, one can conveniently obtain the relative entropy entanglement for Gaussian states. As an example,the relative entanglement for a two-mode squeezed thermal state has been obtained.

Resonant non-Gaussianity with equilateral properties

Energy Technology Data Exchange (ETDEWEB)

Gwyn, Rhiannon [Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut), Potsdam (Germany); Rummel, Markus [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2012-11-15

We discuss the effect of superimposing multiple sources of resonant non-Gaussianity, which arise for instance in models of axion inflation. The resulting sum of oscillating shape contributions can be used to ''Fourier synthesize'' different non-oscillating shapes in the bispectrum. As an example we reproduce an approximately equilateral shape from the superposition of O(10) oscillatory contributions with resonant shape. This implies a possible degeneracy between the equilateral-type non-Gaussianity typical of models with non-canonical kinetic terms, such as DBI inflation, and an equilateral-type shape arising from a superposition of resonant-type contributions in theories with canonical kinetic terms. The absence of oscillations in the 2-point function together with the structure of the resonant N-point functions, imply that detection of equilateral non-Gaussianity at a level greater than the PLANCK sensitivity of f{sub NL} {proportional_to}O(5) will rule out a resonant origin. We comment on the questions arising from possible embeddings of this idea in a string theory setting.

Unitarily localizable entanglement of Gaussian states

International Nuclear Information System (INIS)

Serafini, Alessio; Adesso, Gerardo; Illuminati, Fabrizio

2005-01-01

We consider generic (mxn)-mode bipartitions of continuous-variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as (m+n)-mode Gaussian states invariant under local mode permutations on the m-mode and n-mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of m+n-2 uncorrelated single-mode states. The entanglement between the m-mode and the n-mode blocks can then be completely concentrated on a single pair of modes by means of local unitary operations alone. This result allows us to prove that the PPT (positivity of the partial transpose) condition is necessary and sufficient for the separability of (m+n)-mode bisymmetric Gaussian states. We determine exactly their negativity and identify a subset of bisymmetric states whose multimode entanglement of formation can be computed analytically. We consider explicit examples of pure and mixed bisymmetric states and study their entanglement scaling with the number of modes

Bayes factor between Student t and Gaussian mixed models within an animal breeding context

Directory of Open Access Journals (Sweden)

García-Cortés Luis

2008-07-01

Full Text Available Abstract The implementation of Student t mixed models in animal breeding has been suggested as a useful statistical tool to effectively mute the impact of preferential treatment or other sources of outliers in field data. Nevertheless, these additional sources of variation are undeclared and we do not know whether a Student t mixed model is required or if a standard, and less parameterized, Gaussian mixed model would be sufficient to serve the intended purpose. Within this context, our aim was to develop the Bayes factor between two nested models that only differed in a bounded variable in order to easily compare a Student t and a Gaussian mixed model. It is important to highlight that the Student t density converges to a Gaussian process when degrees of freedom tend to infinity. The twomodels can then be viewed as nested models that differ in terms of degrees of freedom. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling of the complex model (Student t mixed model. The performance of this Bayes factor was tested under simulation and on a real dataset, using the deviation information criterion (DIC as the standard reference criterion. The two statistical tools showed similar trends along the parameter space, although the Bayes factor appeared to be the more conservative. There was considerable evidence favoring the Student t mixed model for data sets simulated under Student t processes with limited degrees of freedom, and moderate advantages associated with using the Gaussian mixed model when working with datasets simulated with 50 or more degrees of freedom. For the analysis of real data (weight of Pietrain pigs at six months, both the Bayes factor and DIC slightly favored the Student t mixed model, with there being a reduced incidence of outlier individuals in this population.

A wavelet-based Gaussian method for energy dispersive X-ray fluorescence spectrum

Directory of Open Access Journals (Sweden)

Pan Liu

2017-05-01

Full Text Available This paper presents a wavelet-based Gaussian method (WGM for the peak intensity estimation of energy dispersive X-ray fluorescence (EDXRF. The relationship between the parameters of Gaussian curve and the wavelet coefficients of Gaussian peak point is firstly established based on the Mexican hat wavelet. It is found that the Gaussian parameters can be accurately calculated by any two wavelet coefficients at the peak point which has to be known. This fact leads to a local Gaussian estimation method for spectral peaks, which estimates the Gaussian parameters based on the detail wavelet coefficients of Gaussian peak point. The proposed method is tested via simulated and measured spectra from an energy X-ray spectrometer, and compared with some existing methods. The results prove that the proposed method can directly estimate the peak intensity of EDXRF free from the background information, and also effectively distinguish overlap peaks in EDXRF spectrum.

Stable Lévy motion with inverse Gaussian subordinator

Science.gov (United States)

Kumar, A.; Wyłomańska, A.; Gajda, J.

2017-09-01

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

Quantum Teamwork for Unconditional Multiparty Communication with Gaussian States

Science.gov (United States)

Zhang, Jing; Adesso, Gerardo; Xie, Changde; Peng, Kunchi

2009-08-01

We demonstrate the capability of continuous variable Gaussian states to communicate multipartite quantum information. A quantum teamwork protocol is presented according to which an arbitrary possibly entangled multimode state can be faithfully teleported between two teams each comprising many cooperative users. We prove that N-mode Gaussian weighted graph states exist for arbitrary N that enable unconditional quantum teamwork implementations for any arrangement of the teams. These perfect continuous variable maximally multipartite entangled resources are typical among pure Gaussian states and are unaffected by the entanglement frustration occurring in multiqubit states.

Controllable gaussian-qubit interface for extremal quantum state engineering.

Science.gov (United States)

Adesso, Gerardo; Campbell, Steve; Illuminati, Fabrizio; Paternostro, Mauro

2010-06-18

We study state engineering through bilinear interactions between two remote qubits and two-mode gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.

Primordial non-Gaussian features from DBI Galileon inflation

International Nuclear Information System (INIS)

Choudhury, Sayantan; Pal, Supratik

2015-01-01

We have studied primordial non-Gaussian features of a model of potential-driven single field DBI Galileon inflation. We have computed the bispectrum from the three-point correlation function considering all possible cross correlations between the scalar and tensor modes of the proposed setup. Further, we have computed the trispectrum from a four-point correlation function considering the contribution from contact interaction, and scalar and graviton exchange diagrams in the in-in picture. Finally we have obtained the non-Gaussian consistency conditions from the four-point correlator, which results in partial violation of the Suyama-Yamaguchi four-point consistency relation. This further leads to the conclusion that sufficient primordial non-Gaussianities can be obtained from DBI Galileon inflation. (orig.)

PHYSICS OF NON-GAUSSIAN FIELDS AND THE COSMOLOGICAL GENUS STATISTIC

International Nuclear Information System (INIS)

James, J. Berian

2012-01-01

We report a technique to calculate the impact of distinct physical processes inducing non-Gaussianity on the cosmological density field. A natural decomposition of the cosmic genus statistic into an orthogonal polynomial sequence allows complete expression of the scale-dependent evolution of the topology of large-scale structure, in which effects including galaxy bias, nonlinear gravitational evolution, and primordial non-Gaussianity may be delineated. The relationship of this decomposition to previous methods for analyzing the genus statistic is briefly considered and the following applications are made: (1) the expression of certain systematics affecting topological measurements, (2) the quantification of broad deformations from Gaussianity that appear in the genus statistic as measured in the Horizon Run simulation, and (3) the study of the evolution of the genus curve for simulations with primordial non-Gaussianity. These advances improve the treatment of flux-limited galaxy catalogs for use with this measurement and further the use of the genus statistic as a tool for exploring non-Gaussianity.

The properties of the dark matter halo distribution in non-Gaussian scenarios

International Nuclear Information System (INIS)

Carbone, C.; Branchini, E.; Dolag, K.; Grossi, M.; Iannuzzi, F.; Matarrese, S.; Moscardini, L.; Verde, L.

2009-01-01

The description of halo abundance and clustering for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys, which can potentially detect primordial non-Gaussianity of the local form with a non-Gaussianity parameter |f NL | of order unity. This is particularly exciting because, while the simplest single-field slow-roll models of inflation predict a primordial |f NL | NL of large-scale structures that are expected to be above the predicted detection threshold [C. Carbone, L. Verde, and S. Matarrese, ApJL 684 (2008) L1]. We present tests on N-body simulations of analytical formulae describing the halo abundance and clustering for non-Gaussian initial conditions. In particular, when we calibrate the analytic non-Gaussian mass function of [S. Matarrese, L. Verde, L. and R. Jimenez, ApJL 541 (2000) 10] and [M. LoVerde, A. Miller, S. Shandera and L. Verde, JCAP 04 (2008) 014] and the analytic description of halo clustering for non-Gaussian initial conditions on N-body simulations, we find excellent agreement between the simulations and the analytic predictions if we make the substitutions δ c →δ c x√(q) and δ c →δ c xq where q≅0.75, in the density threshold for gravitational collapse and in the non-Gaussian fractional correction to the halo bias, respectively. We discuss the implications of these corrections on present and forecasted primordial non-Gaussianity constraints. We confirm that the non-Gaussian halo bias offers a robust and highly competitive test of primordial non-Gaussianity.

Inflation in random Gaussian landscapes

Energy Technology Data Exchange (ETDEWEB)

Masoumi, Ali; Vilenkin, Alexander; Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

2017-05-01

We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations n {sub s} and its running α {sub s} . These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.

Investigation of non-Gaussian effects in the Brazilian option market

Science.gov (United States)

Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.

2018-04-01

An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.

Detectability of the effect of Inflationary non-Gaussianity on halo bias

CERN Document Server

Verde, Licia

2009-01-01

We consider the description of the clustering of halos for physically-motivated types of non-Gaussian initial conditions. In particular we include non-Gaussianity of the type arising from single field slow-roll, multi fields, curvaton (local type), higher-order derivative-type (equilateral), vacuum-state modifications (enfolded-type) and horizon-scale GR corrections type. We show that large-scale halo bias is a very sensitive tool to probe non-Gaussianity, potentially leading, for some planned surveys, to a detection of non-Gaussianity arising from horizon-scale GR corrections.

Off-Axis Gaussian Beams with Random Displacement in Atmospheric Turbulence

Directory of Open Access Journals (Sweden)

Yahya Baykal

2006-10-01

Full Text Available Our recent work in which we study the propagation of the general Hermite-sinusoidal-Gaussian laser beams in wireless broadband access telecommunication systems is elaborated in this paper to cover the special case of an off-axis Gaussian beam. We mainly investigate the propagation characteristics in atmospheric turbulence of an off-axis Gaussian beam possessing Gaussian distributed random displacement parameters. Our interest is to search for different types of laser beams that will improve the performance of a wireless broadband access system when atmospheric turbulence is considered. Our formulation is based on the basic solution of the second order mutual coherence function evaluated at the receiver plane. For fixed turbulence strength, the coherence length calculated at the receiver plane is found to decrease as the variance of the random displacement is increased. It is shown that as the turbulence becomes stronger, coherence lengths due to off-axis Gaussian beams tend to approach the same value, irrespective of the variance of the random displacement. As expected, the beam spreading is found to be pronounced for larger variance of displacement parameter. Average intensity profiles when atmospheric turbulence is present are plotted for different values of the variance of the random displacement parameter of the off-axis Gaussian beam.

Skewness and kurtosis analysis for non-Gaussian distributions

Science.gov (United States)

Celikoglu, Ahmet; Tirnakli, Ugur

2018-06-01

In this paper we address a number of pitfalls regarding the use of kurtosis as a measure of deviations from the Gaussian. We treat kurtosis in both its standard definition and that which arises in q-statistics, namely q-kurtosis. We have recently shown that the relation proposed by Cristelli et al. (2012) between skewness and kurtosis can only be verified for relatively small data sets, independently of the type of statistics chosen; however it fails for sufficiently large data sets, if the fourth moment of the distribution is finite. For infinite fourth moments, kurtosis is not defined as the size of the data set tends to infinity. For distributions with finite fourth moments, the size, N, of the data set for which the standard kurtosis saturates to a fixed value, depends on the deviation of the original distribution from the Gaussian. Nevertheless, using kurtosis as a criterion for deciding which distribution deviates further from the Gaussian can be misleading for small data sets, even for finite fourth moment distributions. Going over to q-statistics, we find that although the value of q-kurtosis is finite in the range of 0 < q < 3, this quantity is not useful for comparing different non-Gaussian distributed data sets, unless the appropriate q value, which truly characterizes the data set of interest, is chosen. Finally, we propose a method to determine the correct q value and thereby to compute the q-kurtosis of q-Gaussian distributed data sets.

Fluid dynamics theoretical and computational approaches

CERN Document Server

Warsi, ZUA

2005-01-01

Important Nomenclature Kinematics of Fluid Motion Introduction to Continuum Motion Fluid Particles Inertial Coordinate Frames Motion of a Continuum The Time Derivatives Velocity and Acceleration Steady and Nonsteady Flow Trajectories of Fluid Particles and Streamlines Material Volume and Surface Relation between Elemental Volumes Kinematic Formulas of Euler and Reynolds Control Volume and Surface Kinematics of Deformation Kinematics of Vorticity and Circulation References Problems The Conservation Laws and the Kinetics of Flow Fluid Density and the Conservation of Mass Prin

Entanglement negativity bounds for fermionic Gaussian states

Science.gov (United States)

Eisert, Jens; Eisler, Viktor; Zimborás, Zoltán

2018-04-01

The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for noninteracting bosonic systems, one can compute the negativity efficiently in the number of modes. However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian. To provide a remedy for this state of affairs, in this work, we introduce efficiently computable and rigorous upper and lower bounds to the negativity, making use of techniques of semidefinite programming, building upon the Lagrangian formulation of fermionic linear optics, and exploiting suitable products of Gaussian operators. We discuss examples in quantum many-body theory and hint at applications in the study of topological properties at finite temperature.

Non-Gaussian diffusion in static disordered media

Science.gov (United States)

Luo, Liang; Yi, Ming

2018-04-01

Non-Gaussian diffusion is commonly considered as a result of fluctuating diffusivity, which is correlated in time or in space or both. In this work, we investigate the non-Gaussian diffusion in static disordered media via a quenched trap model, where the diffusivity is spatially correlated. Several unique effects due to quenched disorder are reported. We analytically estimate the diffusion coefficient Ddis and its fluctuation over samples of finite size. We show a mechanism of population splitting in the non-Gaussian diffusion. It results in a sharp peak in the distribution of displacement P (x ,t ) around x =0 , that has frequently been observed in experiments. We examine the fidelity of the coarse-grained diffusion map, which is reconstructed from particle trajectories. Finally, we propose a procedure to estimate the correlation length in static disordered environments, where the information stored in the sample-to-sample fluctuation has been utilized.

Occupational Hearing Loss from Non-Gaussian Noise.

Science.gov (United States)

Suter, Alice H

2017-08-01

Noise levels are truly continuous in relatively few occupations, with some degree of intermittency the most common condition. The sound levels of intermittent noise are often referred to as non-Gaussian in that they are not normally distributed in the time domain. In some conditions, intermittent noise affects the ear differently from continuous noise, and it is this assumption that underlies the selection of the 5-dB exchange rate (ER). The scientific and professional communities have debated this assumption over recent decades. This monograph explores the effect of non-Gaussian noise on the auditory system. It begins by summarizing an earlier report by the same author concentrating on the subject of the ER. The conclusions of the earlier report supported the more conservative 3-dB ER with possible adjustments to the permissible exposure limit for certain working conditions. The current document has expanded on the earlier report in light of the relevant research accomplished in the intervening decades. Although some of the animal research has supported the mitigating effect of intermittency, a closer look at many of these studies reveals certain weaknesses, along with the fact that these noise exposures were not usually representative of the conditions under which people actually work. The more recent animal research on complex noise shows that intermittencies do not protect the cochlea and that many of the previous assumptions about the ameliorative effect of intermittencies are no longer valid, lending further support to the 3-dB ER. The neurologic effects of noise on hearing have gained increasing attention in recent years because of improvements in microscopy and immunostaining techniques. Animal experiments showing damage to auditory synapses from noise exposures previously considered harmless may signify the need for a more conservative approach to the assessment of noise-induced hearing loss and consequently the practice of hearing conservation programs.

Effect of Asymmetric Potential and Gaussian Colored Noise on Stochastic Resonance

International Nuclear Information System (INIS)

Han Yinxia; Li Jinghui; Chen Shigang

2005-01-01

The phenomenon of stochastic resonance (SR) in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio (SNR) is calculated according to the generalized two-state theory (shown in [H.S. Wio and S. Bouzat, Brazilian J. Phys. 29 (1999) 136]). We find that the SNR increases with the proximity of a to zero. In addition, the correlation time τ between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time τ between the Gaussian additive colored noise is, the higher of the peak value of SNR.

Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic.

Science.gov (United States)

Yokoyama, Jun'ichi

2014-01-01

After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student's t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case.

Searching for primordial non-Gaussianity in Planck CMB maps using a combined estimator

Energy Technology Data Exchange (ETDEWEB)

Novaes, C.P.; Wuensche, C.A. [Divisão de Astrofísica, Instituto Nacional de Pesquisas Espaciais, Av. dos Astronautas 1758, São José dos Campos 12227-010, SP (Brazil); Bernui, A. [Observatório Nacional, Rua General José Cristino 77, São Cristóvão, 20921-400, Rio de Janeiro, RJ (Brazil); Ferreira, I.S., E-mail: camilapnovaes@gmail.com, E-mail: bernui@on.br, E-mail: ivan@fis.unb.br, E-mail: ca.wuensche@inpe.br [Instituto de Física, Universidade de Brasília, Campus Universitário Darcy Ribeiro, Asa Norte, 70919-970, Brasília, DF (Brazil)

2014-01-01

The extensive search for deviations from Gaussianity in cosmic microwave background radiation (CMB) data is very important due to the information about the very early moments of the universe encoded there. Recent analyses from Planck CMB data do not exclude the presence of non-Gaussianity of small amplitude, although they are consistent with the Gaussian hypothesis. The use of different techniques is essential to provide information about types and amplitudes of non-Gaussianities in the CMB data. In particular, we find interesting to construct an estimator based upon the combination of two powerful statistical tools that appears to be sensitive enough to detect tiny deviations from Gaussianity in CMB maps. This estimator combines the Minkowski functionals with a Neural Network, maximizing a tool widely used to study non-Gaussian signals with a reinforcement of another tool designed to identify patterns in a data set. We test our estimator by analyzing simulated CMB maps contaminated with different amounts of local primordial non-Gaussianity quantified by the dimensionless parameter f{sub  NL}. We apply it to these sets of CMB maps and find ∼> 98% of chance of positive detection, even for small intensity local non-Gaussianity like f{sub  NL} = 38±18, the current limit from Planck data for large angular scales. Additionally, we test the suitability to distinguish between primary and secondary non-Gaussianities: first we train the Neural Network with two sets, one of nearly Gaussian CMB maps (|f{sub  NL}| ≤ 10) but contaminated with realistic inhomogeneous Planck noise (i.e., secondary non-Gaussianity) and the other of non-Gaussian CMB maps, that is, maps endowed with weak primordial non-Gaussianity (28 ≤ f{sub  NL} ≤ 48); after that we test an ensemble composed of CMB maps either with one of these non-Gaussian contaminations, and find out that our method successfully classifies ∼ 95% of the tested maps as being CMB maps containing primordial or

Bounded Gaussian process regression

DEFF Research Database (Denmark)

Jensen, Bjørn Sand; Nielsen, Jens Brehm; Larsen, Jan

2013-01-01

We extend the Gaussian process (GP) framework for bounded regression by introducing two bounded likelihood functions that model the noise on the dependent variable explicitly. This is fundamentally different from the implicit noise assumption in the previously suggested warped GP framework. We...... with the proposed explicit noise-model extension....

Degeneracy of energy levels of pseudo-Gaussian oscillators

International Nuclear Information System (INIS)

Iacob, Theodor-Felix; Iacob, Felix; Lute, Marina

2015-01-01

We study the main features of the isotropic radial pseudo-Gaussian oscillators spectral properties. This study is made upon the energy levels degeneracy with respect to orbital angular momentum quantum number. In a previous work [6] we have shown that the pseudo-Gaussian oscillators belong to the class of quasi-exactly solvable models and an exact solution has been found

Non-Gaussianity from tachyonic preheating in hybrid inflation

International Nuclear Information System (INIS)

Barnaby, Neil; Cline, James M.

2007-01-01

In a previous work we showed that large non-Gaussianities and nonscale-invariant distortions in the cosmic microwave background power spectrum can be generated in hybrid inflation models, due to the contributions of the tachyon (waterfall) field to the second order curvature perturbation. Here we clarify, correct, and extend those results. We show that large non-Gaussianity occurs only when the tachyon remains light throughout inflation, whereas n=4 contamination to the spectrum is the dominant effect when the tachyon is heavy. We find constraints on the parameters of warped-throat brane-antibrane inflation from non-Gaussianity. For F-term and D-term inflation models from supergravity, we obtain nontrivial constraints from the spectral distortion effect. We also establish that our analysis applies to complex tachyon fields

Study of atmospheric stratification influence on pollutants dispersion using a numerical fluid mechanics model. Code-Saturne validation with the Prairie Grass experiment/Study of atmospheric stratification influence on pollutants dispersion using a numerical fluid mechanics software

International Nuclear Information System (INIS)

Coulon, Fanny

2010-09-01

A validation of Code-Saturne, a computational fluids dynamics model developed by EDF, is proposed for stable conditions. The goal is to guarantee the performance of the model in order to use it for impacts study. A comparison with the Prairie Grass data field experiment and with two Gaussian plume models will be done [fr

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States

Science.gov (United States)

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

2017-11-01

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

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

Science.gov (United States)

Mitri, Farid G

2015-10-01

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

Core-shell particles at fluid interfaces

NARCIS (Netherlands)

Buchcic, C.

2016-01-01

There is a growing interest in the use of particles as stabilizers for foams and emulsions. Applying hard particles for stabilization of fluid interface is referred to as Pickering stabilization. By using hard particles instead of surfactants and polymers, fluid interfaces can be effectively

A Bernoulli Gaussian Watermark for Detecting Integrity Attacks in Control Systems

Energy Technology Data Exchange (ETDEWEB)

Weerakkody, Sean [Carnegie Mellon Univ., Pittsburgh, PA (United States); Ozel, Omur [Carnegie Mellon Univ., Pittsburgh, PA (United States); Sinopoli, Bruno [Carnegie Mellon Univ., Pittsburgh, PA (United States)

2017-11-02

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 other 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.

Quantum information theory with Gaussian systems

Energy Technology Data Exchange (ETDEWEB)

Krueger, O.

2006-04-06

This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)

Quantum information theory with Gaussian systems

International Nuclear Information System (INIS)

Krueger, O.

2006-01-01

This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)

Supercritical fluid chromatography

Science.gov (United States)

Vigdergauz, M. S.; Lobachev, A. L.; Lobacheva, I. V.; Platonov, I. A.

1992-03-01

The characteristic features of supercritical fluid chromatography (SCFC) are examined and there is a brief historical note concerning the development of the method. Information concerning the use of supercritical fluid chromatography in the analysis of objects of different nature is presented in the form of a table. The roles of the mobile and stationary phases in the separation process and the characteristic features of the apparatus and of the use of the method in physicochemical research are discussed. The bibliography includes 364 references.

Application Of Shared Gamma And Inverse-Gaussian Frailty Models ...

African Journals Online (AJOL)

Shared Gamma and Inverse-Gaussian Frailty models are used to analyze the survival times of patients who are clustered according to cancer/tumor types under Parametric Proportional Hazard framework. The result of the ... However, no evidence is strong enough for preference of either Gamma or Inverse Gaussian Frailty.

Core temperature in super-Gaussian pumped air-clad photonic ...

Indian Academy of Sciences (India)

In this paper we investigate the core temperature of air-clad photonic crystal fiber (PCF) lasers pumped by a super-Gaussian (SG) source of order four. The results are compared with conventional double-clad fiber (DCF) lasers pumped by the same super-Gaussian and by top-hat pump profiles.

Standard sirens and dark sector with Gaussian process*

Directory of Open Access Journals (Sweden)

Cai Rong-Gen

2018-01-01

Full Text Available The gravitational waves from compact binary systems are viewed as a standard siren to probe the evolution of the universe. This paper summarizes the potential and ability to use the gravitational waves to constrain the cosmological parameters and the dark sector interaction in the Gaussian process methodology. After briefly introducing the method to reconstruct the dark sector interaction by the Gaussian process, the concept of standard sirens and the analysis of reconstructing the dark sector interaction with LISA are outlined. Furthermore, we estimate the constraint ability of the gravitational waves on cosmological parameters with ET. The numerical methods we use are Gaussian process and the Markov-Chain Monte-Carlo. Finally, we also forecast the improvements of the abilities to constrain the cosmological parameters with ET and LISA combined with the Planck.

Nonlinear dynamics in a trapped atomic Bose-Einstein condensate induced by an oscillating Gaussian potential

International Nuclear Information System (INIS)

Fujimoto, Kazuya; Tsubota, Makoto

2011-01-01

We consider a trapped atomic Bose-Einstein condensate penetrated by a repulsive Gaussian potential and theoretically investigate the dynamics induced by oscillating the Gaussian potential. Our study is based on the numerical calculation of the two-dimensional Gross-Pitaevskii equation. Our calculation reveals the dependence of the characteristic behavior of the condensate on the amplitude and frequency of the oscillating potential. These dynamics are deeply related to the nucleation and dynamics of quantized vortices and solitons. When the potential oscillates with a large amplitude, it nucleates many vortex pairs that move away from the potential. When the amplitude of the oscillation is small, it nucleates solitons through an annihilation of vortex pairs. We discuss three issues concerning the nucleation of vortices. The first is the phase diagram for the nucleation of vortices and solitons near the oscillating potential. The second is the mechanism and critical velocity of the nucleation. The critical velocity of the nucleation is an important issue in quantum fluids, and we propose an expression for the velocity containing both the coherence length and the size of the potential. The third is the divergence of the nucleation time, which is the time it takes for the potential to nucleate vortices, near the critical parameters for vortex nucleation.

Gaussian random-matrix process and universal parametric correlations in complex systems

International Nuclear Information System (INIS)

Attias, H.; Alhassid, Y.

1995-01-01

We introduce the framework of the Gaussian random-matrix process as an extension of Dyson's Gaussian ensembles and use it to discuss the statistical properties of complex quantum systems that depend on an external parameter. We classify the Gaussian processes according to the short-distance diffusive behavior of their energy levels and demonstrate that all parametric correlation functions become universal upon the appropriate scaling of the parameter. The class of differentiable Gaussian processes is identified as the relevant one for most physical systems. We reproduce the known spectral correlators and compute eigenfunction correlators in their universal form. Numerical evidence from both a chaotic model and weakly disordered model confirms our predictions

A new method used to evaluate organic working fluids

International Nuclear Information System (INIS)

Zhang, Xinxin; He, Maogang; Wang, Jingfu

2014-01-01

In this paper, we propose a method named “Weight Classification-Hasse Dominance” to evaluate organic working fluids. This new method combines the advantages of both the method of weight determination and the Hasse Diagram Technique (HDT). It can be used to evaluate the thermodynamic performance, environmental protection indicator, and safety requirement of organic working fluid simultaneously. This evaluation method can offer good reference for working fluid selection. Using this method, the organic working fluids which have been phased out and will be phased out by the Montreal Protocol including CFCs (chlorofluorocarbons), HCFCs (hydrochlorofluorocarbons), and HFCs (hydrofluorocarbons) were evaluated. Moreover, HCs (hydrocarbons) can be considered as a completely different kind of organic working fluid from CFCs, HCFCs, and HFCs according to the comparison based on this new evaluation method. - Highlights: • We propose a new method used to evaluate organic working fluids. • This evaluation method can offer good reference for working fluid selection. • CFC, HCFC, and HFC working fluids were evaluated using this evaluation method. • HC can be considered as a totally different working fluid from CFC, HCFC, and HFC

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

CERN Document Server

Verde, Licia; Heavens, Alan F; Jimenez, Raul; Matarrese, Sabino

2013-01-01

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 7{\\sigma} for fNL values (both true and sampled) not ruled 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.

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

Science.gov (United States)

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

2017-10-01

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

Non-Gaussian signatures arising from warm inflation driven by geometric tachyon

International Nuclear Information System (INIS)

Bhattacharjee, Anindita; Deshamukhya, Atri

2014-01-01

In a warm inflationary scenario, the initial seeds of density perturbation arise from thermal fluctuations of the inflaton field. These fluctuations in principle have Gaussian distribution. In a Gaussian distribution the density perturbation can be expressed as the two point correlation function. Thus if in an inflationary model the density perturbation is expressed as correlation function of order higher than two, these fluctuations are non-Gaussian in nature. A simple inflationary model containing single scalar field, slow roll, canonical kinetic term and vacuum initial state can produce a tiny amount of non-Gaussianity which are very small to be detected by any experiment. Non-Gaussianity can also arise in inflationary models containing multiple scalar fields. For an inflationary scenario with single scalar field, non-Gaussianity can be expressed in terms of bi-spectrum however for multi field Inflation, it is expressed in terms of trispectrum etc. In this piece of work, the warm inflationary scenario, driven by a D3 brane due to the presence of a stack of k coincident NS 5 branes is considered and the non-Gaussian effects in such an inflationary scenario has been analysed by measuring the bispectrum of the gravitational field fluctuations generated during the warm inflation in strong dissipative regime. The bi-spectrum of the Inflation is expressed in terms of the parameter f NL and it is seen that the value of f NL parameter lies well within the limit observed by WMAP7

Higher-Order Hybrid Gaussian Kernel in Meshsize Boosting Algorithm

African Journals Online (AJOL)

In this paper, we shall use higher-order hybrid Gaussian kernel in a meshsize boosting algorithm in kernel density estimation. Bias reduction is guaranteed in this scheme like other existing schemes but uses the higher-order hybrid Gaussian kernel instead of the regular fixed kernels. A numerical verification of this scheme ...

Rotating quantum Gaussian packets

International Nuclear Information System (INIS)

Dodonov, V V

2015-01-01

We study two-dimensional quantum Gaussian packets with a fixed value of mean angular momentum. This value is the sum of two independent parts: the ‘external’ momentum related to the motion of the packet center and the ‘internal’ momentum due to quantum fluctuations. The packets minimizing the mean energy of an isotropic oscillator with the fixed mean angular momentum are found. They exist for ‘co-rotating’ external and internal motions, and they have nonzero correlation coefficients between coordinates and momenta, together with some (moderate) amount of quadrature squeezing. Variances of angular momentum and energy are calculated, too. Differences in the behavior of ‘co-rotating’ and ‘anti-rotating’ packets are shown. The time evolution of rotating Gaussian packets is analyzed, including the cases of a charge in a homogeneous magnetic field and a free particle. In the latter case, the effect of initial shrinking of packets with big enough coordinate-momentum correlation coefficients (followed by the well known expansion) is discovered. This happens due to a competition of ‘focusing’ and ‘de-focusing’ in the orthogonal directions. (paper)

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

Science.gov (United States)

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.

Partial summations of stationary sequences of non-Gaussian random variables

DEFF Research Database (Denmark)

Mohr, Gunnar; Ditlevsen, Ove Dalager

1996-01-01

The distribution of the sum of a finite number of identically distributed random variables is in many cases easily determined given that the variables are independent. The moments of any order of the sum can always be expressed by the moments of the single term without computational problems...... of convergence of the distribution of a sum (or an integral) of mutually dependent random variables to the Gaussian distribution. The paper is closely related to the work in Ditlevsen el al. [Ditlevsen, O., Mohr, G. & Hoffmeyer, P. Integration of non-Gaussian fields. Prob. Engng Mech 11 (1996) 15-23](2)....... lognormal variables or polynomials of standard Gaussian variables. The dependency structure is induced by specifying the autocorrelation structure of the sequence of standard Gaussian variables. Particularly useful polynomials are the Winterstein approximations that distributionally fit with non...

Cosmological information in Gaussianized weak lensing signals

Science.gov (United States)

Joachimi, B.; Taylor, A. N.; Kiessling, A.

2011-11-01

Gaussianizing the one-point distribution of the weak gravitational lensing convergence has recently been shown to increase the signal-to-noise ratio contained in two-point statistics. We investigate the information on cosmology that can be extracted from the transformed convergence fields. Employing Box-Cox transformations to determine optimal transformations to Gaussianity, we develop analytical models for the transformed power spectrum, including effects of noise and smoothing. We find that optimized Box-Cox transformations perform substantially better than an offset logarithmic transformation in Gaussianizing the convergence, but both yield very similar results for the signal-to-noise ratio. None of the transformations is capable of eliminating correlations of the power spectra between different angular frequencies, which we demonstrate to have a significant impact on the errors in cosmology. Analytic models of the Gaussianized power spectrum yield good fits to the simulations and produce unbiased parameter estimates in the majority of cases, where the exceptions can be traced back to the limitations in modelling the higher order correlations of the original convergence. In the ideal case, without galaxy shape noise, we find an increase in the cumulative signal-to-noise ratio by a factor of 2.6 for angular frequencies up to ℓ= 1500, and a decrease in the area of the confidence region in the Ωm-σ8 plane, measured in terms of q-values, by a factor of 4.4 for the best performing transformation. When adding a realistic level of shape noise, all transformations perform poorly with little decorrelation of angular frequencies, a maximum increase in signal-to-noise ratio of 34 per cent, and even slightly degraded errors on cosmological parameters. We argue that to find Gaussianizing transformations of practical use, it will be necessary to go beyond transformations of the one-point distribution of the convergence, extend the analysis deeper into the non

Fractional Diffusion in Gaussian Noisy Environment

Directory of Open Access Journals (Sweden)

Guannan Hu

2015-03-01

Full Text Available We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: \\(D_t^{(\\alpha} u(t, x=\\textit{B}u+u\\cdot \\dot W^H\\, where \\(D_t^{(\\alpha}\\ is the Caputo fractional derivative of order \\(\\alpha\\in (0,1\\ with respect to the time variable \\(t\\, \\(\\textit{B}\\ is a second order elliptic operator with respect to the space variable \\(x\\in\\mathbb{R}^d\\ and \\(\\dot W^H\\ a time homogeneous fractional Gaussian noise of Hurst parameter \\(H=(H_1, \\cdots, H_d\\. We obtain conditions satisfied by \\(\\alpha\\ and \\(H\\, so that the square integrable solution \\(u\\ exists uniquely.

Quantum hall fluid on fuzzy two dimensional sphere

International Nuclear Information System (INIS)

Luo Xudong; Peng Dantao

2004-01-01

After reviewing the Haldane's description about the quantum Hall effect on the fuzzy two-sphere S 2 , authors construct the noncommutative algebra on the fuzzy sphere S 2 and the Moyal structure of the Hilbert space. By constructing noncommutative Chern-Simons theory of the incompressible Hall fluid on the fuzzy sphere and solving the Gaussian constraint with quasiparticle source, authors find the Calogero matrix on S 2 and the complete set of the Laughlin wave function for the lowest Landau level, and this wave function is expressed by the generalized Jack polynomials in terms of spinor coordinates. (author)

Prediction and retrodiction with continuously monitored Gaussian states

Science.gov (United States)

Zhang, Jinglei; Mølmer, Klaus

2017-12-01

Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and continuous probing which maintain their Gaussian state property. Such dynamics is found in many physical systems that can therefore be efficiently described by the ensuing effective representation of the density matrix ρ (t ) . Our probabilistic knowledge about the outcome of measurements on a quantum system at time t is not only governed by ρ (t ) conditioned on the evolution and measurement outcomes obtained until time t but is also modified by any information acquired after t . It was shown [S. Gammelmark, B. Julsgaard, and K. Mølmer, Phys. Rev. Lett. 111, 160401 (2013), 10.1103/PhysRevLett.111.160401] that this information is represented by a supplementary matrix, E (t ) . We show here that the restriction of the dynamics of ρ (t ) to Gaussian states implies that the matrix E (t ) is also fully characterized by a vector of mean values and a covariance matrix. We derive the dynamical equations for these quantities and we illustrate their use in the retrodiction of measurements on Gaussian systems.

Optimality of Gaussian attacks in continuous-variable quantum cryptography.

Science.gov (United States)

Navascués, Miguel; Grosshans, Frédéric; Acín, Antonio

2006-11-10

We analyze the asymptotic security of the family of Gaussian modulated quantum key distribution protocols for continuous-variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.

Continuous-variable quantum teleportation with non-Gaussian resources

International Nuclear Information System (INIS)

Dell'Anno, F.; De Siena, S.; Albano, L.; Illuminati, F.

2007-01-01

We investigate continuous variable quantum teleportation using non-Gaussian states of the radiation field as entangled resources. We compare the performance of different classes of degaussified resources, including two-mode photon-added and two-mode photon-subtracted squeezed states. We then introduce a class of two-mode squeezed Bell-like states with one-parameter dependence for optimization. These states interpolate between and include as subcases different classes of degaussified resources. We show that optimized squeezed Bell-like resources yield a remarkable improvement in the fidelity of teleportation both for coherent and nonclassical input states. The investigation reveals that the optimal non-Gaussian resources for continuous variable teleportation are those that most closely realize the simultaneous maximization of the content of entanglement, the degree of affinity with the two-mode squeezed vacuum, and the, suitably measured, amount of non-Gaussianity

MEASURING PRIMORDIAL NON-GAUSSIANITY THROUGH WEAK-LENSING PEAK COUNTS

International Nuclear Information System (INIS)

Marian, Laura; Hilbert, Stefan; Smith, Robert E.; Schneider, Peter; Desjacques, Vincent

2011-01-01

We explore the possibility of detecting primordial non-Gaussianity of the local type using weak-lensing peak counts. We measure the peak abundance in sets of simulated weak-lensing maps corresponding to three models f NL = 0, - 100, and 100. Using survey specifications similar to those of EUCLID and without assuming any knowledge of the lens and source redshifts, we find the peak functions of the non-Gaussian models with f NL = ±100 to differ by up to 15% from the Gaussian peak function at the high-mass end. For the assumed survey parameters, the probability of fitting an f NL = 0 peak function to the f NL = ±100 peak functions is less than 0.1%. Assuming the other cosmological parameters are known, f NL can be measured with an error Δf NL ∼ 13. It is therefore possible that future weak-lensing surveys like EUCLID and LSST may detect primordial non-Gaussianity from the abundance of peak counts, and provide information complementary to that obtained from the cosmic microwave background.

Gaussian Process Regression for WDM System Performance Prediction

DEFF Research Database (Denmark)

Wass, Jesper; Thrane, Jakob; Piels, Molly

2017-01-01

Gaussian process regression is numerically and experimentally investigated to predict the bit error rate of a 24 x 28 CiBd QPSK WDM system. The proposed method produces accurate predictions from multi-dimensional and sparse measurement data.......Gaussian process regression is numerically and experimentally investigated to predict the bit error rate of a 24 x 28 CiBd QPSK WDM system. The proposed method produces accurate predictions from multi-dimensional and sparse measurement data....

A new birthweight reference in Guangzhou, southern China, and its comparison with the global reference.

Science.gov (United States)

He, Jian-Rong; Xia, Hui-Min; Liu, Yu; Xia, Xiao-Yan; Mo, Wei-Jian; Wang, Ping; Cheng, Kar Keung; Leung, Gabriel M; Feng, Qiong; Schooling, C Mary; Qiu, Xiu

2014-12-01

To formulate a new birthweight reference for different gestational ages in Guangzhou, southern China, and compare it with the currently used reference in China and the global reference. All singleton live births of more than 26 weeks' gestational age recorded in the Guangzhou Perinatal Health Care and Delivery Surveillance System for the years 2009, 2010 and 2011 (n=510 837) were retrospectively included in the study. In addition, the study sample was supplemented by all singleton live births (n=3538) at gestational ages 26-33 weeks from 2007 and 2008. We used Gaussian mixture models and robust regression to exclude outliers of birth weight and then applied Generalized Additive Models for Location, Scale, and Shape (GAMLSS) to generate smoothed percentile curves separately for gender and parity. Of infants defined as small for gestational age (SGA) in the new reference, 15.3-47.7% (depending on gestational age) were considered appropriate for gestational age (AGA) by the currently used reference of China. Of the infants defined as SGA by the new reference, 9.2% with gestational ages 34-36 weeks and 14.3% with 37-41 weeks were considered AGA by the global reference. At the 50th centile line, the new reference curve was similar to that of the global reference for gestational ages 26-33 weeks and above the global reference for 34-40 weeks. The new birthweight reference based on birthweight data for neonates in Guangzhou, China, differs from the reference currently used in China and the global reference, and appears to be more relevant to the local population. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

Colored non-gaussian noise driven open systems: generalization of Kramers' theory with a unified approach.

Science.gov (United States)

Baura, Alendu; Sen, Monoj Kumar; Goswami, Gurupada; Bag, Bidhan Chandra

2011-01-28

In this paper we have calculated escape rate from a meta stable state in the presence of both colored internal thermal and external nonthermal noises. For the internal noise we have considered usual gaussian distribution but the external noise may be gaussian or non-gaussian in characteristic. The calculated rate is valid for low noise strength of non-gaussian noise such that an effective gaussian approximation of non-gaussian noise wherein the higher order even cumulants of order "4" and higher are neglected. The rate expression we derived here reduces to the known results of the literature, as well as for purely external noise driven activated rate process. The latter exhibits how the rate changes if one switches from non-gaussian to gaussian character of the external noise.

Gaussianization for fast and accurate inference from cosmological data

Science.gov (United States)

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

2016-06-01

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

Gaussian-log-Gaussian wavelet trees, frequentist and Bayesian inference, and statistical signal processing applications

DEFF Research Database (Denmark)

Møller, Jesper; Jacobsen, Robert Dahl

We introduce a promising alternative to the usual hidden Markov tree model for Gaussian wavelet coefficients, where their variances are specified by the hidden states and take values in a finite set. In our new model, the hidden states have a similar dependence structure but they are jointly Gaus...

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

GAUSSIAN 76: an ab initio molecular orbital program

International Nuclear Information System (INIS)

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

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

Gaussian processes and constructive scalar field theory

International Nuclear Information System (INIS)

Benfatto, G.; Nicolo, F.

1981-01-01

The last years have seen a very deep progress of constructive euclidean field theory, with many implications in the area of the random fields theory. The authors discuss an approach to super-renormalizable scalar field theories, which puts in particular evidence the connections with the theory of the Gaussian processes associated to the elliptic operators. The paper consists of two parts. Part I treats some problems in the theory of Gaussian processes which arise in the approach to the PHI 3 4 theory. Part II is devoted to the discussion of the ultraviolet stability in the PHI 3 4 theory. (Auth.)

Model selection for Gaussian kernel PCA denoising

DEFF Research Database (Denmark)

Jørgensen, Kasper Winther; Hansen, Lars Kai

2012-01-01

We propose kernel Parallel Analysis (kPA) for automatic kernel scale and model order selection in Gaussian kernel PCA. Parallel Analysis [1] is based on a permutation test for covariance and has previously been applied for model order selection in linear PCA, we here augment the procedure to also...... tune the Gaussian kernel scale of radial basis function based kernel PCA.We evaluate kPA for denoising of simulated data and the US Postal data set of handwritten digits. We find that kPA outperforms other heuristics to choose the model order and kernel scale in terms of signal-to-noise ratio (SNR...

Dynamic analysis of structures with solid-fluid interaction

International Nuclear Information System (INIS)

Nahavandi, A.N.; Pedrido, R.R.; Cloud, R.L.

1977-01-01

This study develops a finite element model for interaction between an elastic solid and fluid medium (flow-induced vibrations in nuclear reactor components). Plane triangular finite elements have been used separately for fluid, solid, and solid-fluid continuua and the equivalent mass, damping, and stiffness matrices and interaction load arrays for all elements are derived and assembled into global matrices. The global matrix differential equation of motion developed is solved in time to obtain the pressure and velocity distributions in the fluid, as well as the displacements in the solid. Two independent computer programs are used to obtain the dynamic solution. The first program is a finite element program developed for solid-fluid interaction studies. This program uses the modal superposition technique in which the eigenvalues and eigenvectors for the system are found and used to uncouple the equations. This approach allows an analytic solution in each integration time step. The second program is WECAN finite element program in which a new element library subroutine for solid-fluid interaction was incorporated. This program can employ a NASTRAN direct integration scheme based on a central difference formula for the acceleration and velocity terms and an implicit representation of the displacement term. This reduces the problem to a matrix equation whose right hand side is updated in every time step and is solved by a variation of the Gaussian elimination method known as the wave front technique. Results have been obtained for the case of water, between two flat elastic parallel plates, initially at rest and accelerated suddenly by applying a step pressure. The results obtained from the above-mentioned two independent finite element programs are in full agreement. This verification provides the confidence needed to initiate parametric studies. Both rigid wall (no solid-fluid interaction) and flexible wall (including solid-fluid interaction) cases were examined

Extension of filament propagation in water with Bessel-Gaussian beams

Energy Technology Data Exchange (ETDEWEB)

Kaya, G.; Sayrac, M.; Boran, Y.; Kolomenskii, A. A. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Kaya, N.; Schuessler, H. A. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Science and Petroleum, Texas A& M University at Qatar, Doha 23874 (Qatar); Strohaber, J. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Department of Physics, Florida A& M University, Tallahassee, Florida 32307 (United States); Amani, M. [Science and Petroleum, Texas A& M University at Qatar, Doha 23874 (Qatar)

2016-03-15

We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.

A note on moving average models for Gaussian random fields

DEFF Research Database (Denmark)

Hansen, Linda Vadgård; Thorarinsdottir, Thordis L.

The class of moving average models offers a flexible modeling framework for Gaussian random fields with many well known models such as the Matérn covariance family and the Gaussian covariance falling under this framework. Moving average models may also be viewed as a kernel smoothing of a Lévy...... basis, a general modeling framework which includes several types of non-Gaussian models. We propose a new one-parameter spatial correlation model which arises from a power kernel and show that the associated Hausdorff dimension of the sample paths can take any value between 2 and 3. As a result...

Frequentist and Bayesian inference for Gaussian-log-Gaussian wavelet trees and statistical signal processing applications

DEFF Research Database (Denmark)

Jacobsen, Christian Robert Dahl; Møller, Jesper

2017-01-01

We introduce new estimation methods for a subclass of the Gaussian scale mixture models for wavelet trees by Wainwright, Simoncelli and Willsky that rely on modern results for composite likelihoods and approximate Bayesian inference. Our methodology is illustrated for denoising and edge detection...

Standard forms and entanglement engineering of multimode Gaussian states under local operations

International Nuclear Information System (INIS)

Serafini, Alessio; Adesso, Gerardo

2007-01-01

We investigate the action of local unitary operations on multimode (pure or mixed) Gaussian states and single out the minimal number of locally invariant parameters which completely characterize the covariance matrix of such states. For pure Gaussian states, central resources for continuous-variable quantum information, we investigate separately the parameter reduction due to the additional constraint of global purity, and the one following by the local-unitary freedom. Counting arguments and insights from the phase-space Schmidt decomposition and in general from the framework of symplectic analysis, accompany our description of the standard form of pure n-mode Gaussian states. In particular, we clarify why only in pure states with n ≤ 3 modes all the direct correlations between position and momentum operators can be set to zero by local unitary operations. For any n, the emerging minimal set of parameters contains complete information about all forms of entanglement in the corresponding states. An efficient state engineering scheme (able to encode direct correlations between position and momentum operators as well) is proposed to produce entangled multimode Gaussian resources, its number of optical elements matching the minimal number of locally invariant degrees of freedom of general pure n-mode Gaussian states. Finally, we demonstrate that so-called 'block-diagonal' Gaussian states, without direct correlations between position and momentum, are systematically less entangled, on average, than arbitrary pure Gaussian states

Convergence of posteriors for discretized log Gaussian Cox processes

DEFF Research Database (Denmark)

Waagepetersen, Rasmus Plenge

2004-01-01

In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations...... when the cell sizes of the discretization tends to zero. The effect of discretization is studied in a data example....

Gaussian Process Interpolation for Uncertainty Estimation in Image Registration

Science.gov (United States)

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

2014-01-01

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

Non-Gaussianity and cross-scale coupling in interplanetary magnetic field turbulence during a rope-rope magnetic reconnection event

Science.gov (United States)

Miranda, Rodrigo A.; Schelin, Adriane B.; Chian, Abraham C.-L.; Ferreira, José L.

2018-03-01

In a recent paper (Chian et al., 2016) it was shown that magnetic reconnection at the interface region between two magnetic flux ropes is responsible for the genesis of interplanetary intermittent turbulence. The normalized third-order moment (skewness) and the normalized fourth-order moment (kurtosis) display a quadratic relation with a parabolic shape that is commonly observed in observational data from turbulence in fluids and plasmas, and is linked to non-Gaussian fluctuations due to coherent structures. In this paper we perform a detailed study of the relation between the skewness and the kurtosis of the modulus of the magnetic field |B| during a triple interplanetary magnetic flux rope event. In addition, we investigate the skewness-kurtosis relation of two-point differences of |B| for the same event. The parabolic relation displays scale dependence and is found to be enhanced during magnetic reconnection, rendering support for the generation of non-Gaussian coherent structures via rope-rope magnetic reconnection. Our results also indicate that a direct coupling between the scales of magnetic flux ropes and the scales within the inertial subrange occurs in the solar wind.

Analog model for quantum gravity effects: phonons in random fluids.

Science.gov (United States)

Krein, G; Menezes, G; Svaiter, N F

2010-09-24

We describe an analog model for quantum gravity effects in condensed matter physics. The situation discussed is that of phonons propagating in a fluid with a random velocity wave equation. We consider that there are random fluctuations in the reciprocal of the bulk modulus of the system and study free phonons in the presence of Gaussian colored noise with zero mean. We show that, in this model, after performing the random averages over the noise function a free conventional scalar quantum field theory describing free phonons becomes a self-interacting model.

Statistical tests for the Gaussian nature of primordial fluctuations through CBR experiments

International Nuclear Information System (INIS)

Luo, X.

1994-01-01

Information about the physical processes that generate the primordial fluctuations in the early Universe can be gained by testing the Gaussian nature of the fluctuations through cosmic microwave background radiation (CBR) temperature anisotropy experiments. One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian, whereas seeds produced by topological defects left over from an early cosmic phase transition tend to be non-Gaussian. To carry out this test, sophisticated statistical tools are required. In this paper, we will discuss several such statistical tools, including multivariant skewness and kurtosis, Euler-Poincare characteristics, the three-point temperature correlation function, and Hotelling's T 2 statistic defined through bispectral estimates of a one-dimensional data set. The effect of noise present in the current data is discussed in detail and the COBE 53 GHz data set is analyzed. Our analysis shows that, on the large angular scale to which COBE is sensitive, the statistics are probably Gaussian. On the small angular scales, the importance of Hotelling's T 2 statistic is stressed, and the minimum sample size required to test Gaussianity is estimated. Although the current data set available from various experiments at half-degree scales is still too small, improvement of the data set by roughly a factor of 2 will be enough to test the Gaussianity statistically. On the arc min scale, we analyze the recent RING data through bispectral analysis, and the result indicates possible deviation from Gaussianity. Effects of point sources are also discussed. It is pointed out that the Gaussianity problem can be resolved in the near future by ground-based or balloon-borne experiments

Generation of singular optical beams from fundamental Gaussian beam using Sagnac interferometer

Science.gov (United States)

Naik, Dinesh N.; Viswanathan, Nirmal K.

2016-09-01

We propose a simple free-space optics recipe for the controlled generation of optical vortex beams with a vortex dipole or a single charge vortex, using an inherently stable Sagnac interferometer. We investigate the role played by the amplitude and phase differences in generating higher-order Gaussian beams from the fundamental Gaussian mode. Our simulation results reveal how important the control of both the amplitude and the phase difference between superposing beams is to achieving optical vortex beams. The creation of a vortex dipole from null interference is unveiled through the introduction of a lateral shear and a radial phase difference between two out-of-phase Gaussian beams. A stable and high quality optical vortex beam, equivalent to the first-order Laguerre-Gaussian beam, is synthesized by coupling lateral shear with linear phase difference, introduced orthogonal to the shear between two out-of-phase Gaussian beams.

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

Science.gov (United States)

Filip, Radim; Rakhubovsky, Andrey A.

2015-11-01

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

Neutron inverse kinetics via Gaussian Processes

International Nuclear Information System (INIS)

Picca, Paolo; Furfaro, Roberto

2012-01-01

Highlights: ► A novel technique for the interpretation of experiments in ADS is presented. ► The technique is based on Bayesian regression, implemented via Gaussian Processes. ► GPs overcome the limits of classical methods, based on PK approximation. ► Results compares GPs and ANN performance, underlining similarities and differences. - Abstract: The paper introduces the application of Gaussian Processes (GPs) to determine the subcriticality level in accelerator-driven systems (ADSs) through the interpretation of pulsed experiment data. ADSs have peculiar kinetic properties due to their special core design. For this reason, classical – inversion techniques based on point kinetic (PK) generally fail to generate an accurate estimate of reactor subcriticality. Similarly to Artificial Neural Networks (ANNs), Gaussian Processes can be successfully trained to learn the underlying inverse neutron kinetic model and, as such, they are not limited to the model choice. Importantly, GPs are strongly rooted into the Bayes’ theorem which makes them a powerful tool for statistical inference. Here, GPs have been designed and trained on a set of kinetics models (e.g. point kinetics and multi-point kinetics) for homogeneous and heterogeneous settings. The results presented in the paper show that GPs are very efficient and accurate in predicting the reactivity for ADS-like systems. The variance computed via GPs may provide an indication on how to generate additional data as function of the desired accuracy.

Gaussian Hypothesis Testing and Quantum Illumination.

Science.gov (United States)

Wilde, Mark M; Tomamichel, Marco; Lloyd, Seth; Berta, Mario

2017-09-22

Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of the minimal type-II error probability in a quantum hypothesis test of two Gaussian states given a fixed constraint on the type-I error probability. This formula is a direct function of the mean vectors and covariance matrices of the quantum Gaussian states in question. We give an application to quantum illumination, which is the task of determining whether there is a low-reflectivity object embedded in a target region with a bright thermal-noise bath. For the asymmetric-error setting, we find that a quantum illumination transmitter can achieve an error probability exponent stronger than a coherent-state transmitter of the same mean photon number, and furthermore, that it requires far fewer trials to do so. This occurs when the background thermal noise is either low or bright, which means that a quantum advantage is even easier to witness than in the symmetric-error setting because it occurs for a larger range of parameters. Going forward from here, we expect our formula to have applications in settings well beyond those considered in this paper, especially to quantum communication tasks involving quantum Gaussian channels.

Perturbative Gaussianizing transforms for cosmological fields

Science.gov (United States)

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.

Detecting periodicities with Gaussian processes

Directory of Open Access Journals (Sweden)

Nicolas Durrande

2016-04-01

Full Text Available We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression, which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in the arabidopsis genome.

Time-optimal thermalization of single-mode Gaussian states

Science.gov (United States)

Carlini, Alberto; Mari, Andrea; Giovannetti, Vittorio

2014-11-01

We consider the problem of time-optimal control of a continuous bosonic quantum system subject to the action of a Markovian dissipation. In particular, we consider the case of a one-mode Gaussian quantum system prepared in an arbitrary initial state and which relaxes to the steady state due to the action of the dissipative channel. We assume that the unitary part of the dynamics is represented by Gaussian operations which preserve the Gaussian nature of the quantum state, i.e., arbitrary phase rotations, bounded squeezing, and unlimited displacements. In the ideal ansatz of unconstrained quantum control (i.e., when the unitary phase rotations, squeezing, and displacement of the mode can be performed instantaneously), we study how control can be optimized for speeding up the relaxation towards the fixed point of the dynamics and we analytically derive the optimal relaxation time. Our model has potential and interesting applications to the control of modes of electromagnetic radiation and of trapped levitated nanospheres.

Non-Gaussian bias: insights from discrete density peaks

CERN Document Server

Desjacques, Vincent; Riotto, Antonio

2013-01-01

Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastly simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out tha...

Extension of filament propagation in water with Bessel-Gaussian beams

Directory of Open Access Journals (Sweden)

G. Kaya

2016-03-01

Full Text Available We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.

Quantum error correction of continuous-variable states against Gaussian noise

Energy Technology Data Exchange (ETDEWEB)

Ralph, T. C. [Centre for Quantum Computation and Communication Technology, School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072 (Australia)

2011-08-15

We describe a continuous-variable error correction protocol that can correct the Gaussian noise induced by linear loss on Gaussian states. The protocol can be implemented using linear optics and photon counting. We explore the theoretical bounds of the protocol as well as the expected performance given current knowledge and technology.

Cosmic microwave background power asymmetry from non-Gaussian modulation.

Science.gov (United States)

Schmidt, Fabian; Hui, Lam

2013-01-04

Non-Gaussianity in the inflationary perturbations can couple observable scales to modes of much longer wavelength (even superhorizon), leaving as a signature a large-angle modulation of the observed cosmic microwave background power spectrum. This provides an alternative origin for a power asymmetry that is otherwise often ascribed to a breaking of statistical isotropy. The non-Gaussian modulation effect can be significant even for typical ~10(-5) perturbations while respecting current constraints on non-Gaussianity if the squeezed limit of the bispectrum is sufficiently infrared divergent. Just such a strongly infrared-divergent bispectrum has been claimed for inflation models with a non-Bunch-Davies initial state, for instance. Upper limits on the observed cosmic microwave background power asymmetry place stringent constraints on the duration of inflation in such models.

Generalization of the Gaussian electrostatic model: Extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods

Science.gov (United States)

Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.

2006-11-01

The simulation of biological systems by means of current empirical force fields presents shortcomings due to their lack of accuracy, especially in the description of the nonbonded terms. We have previously introduced a force field based on density fitting termed the Gaussian electrostatic model-0 (GEM-0) J.-P. Piquemal et al. [J. Chem. Phys. 124, 104101 (2006)] that improves the description of the nonbonded interactions. GEM-0 relies on density fitting methodology to reproduce each contribution of the constrained space orbital variation (CSOV) energy decomposition scheme, by expanding the electronic density of the molecule in s-type Gaussian functions centered at specific sites. In the present contribution we extend the Coulomb and exchange components of the force field to auxiliary basis sets of arbitrary angular momentum. Since the basis functions with higher angular momentum have directionality, a reference molecular frame (local frame) formalism is employed for the rotation of the fitted expansion coefficients. In all cases the intermolecular interaction energies are calculated by means of Hermite Gaussian functions using the McMurchie-Davidson [J. Comput. Phys. 26, 218 (1978)] recursion to calculate all the required integrals. Furthermore, the use of Hermite Gaussian functions allows a point multipole decomposition determination at each expansion site. Additionally, the issue of computational speed is investigated by reciprocal space based formalisms which include the particle mesh Ewald (PME) and fast Fourier-Poisson (FFP) methods. Frozen-core (Coulomb and exchange-repulsion) intermolecular interaction results for ten stationary points on the water dimer potential-energy surface, as well as a one-dimensional surface scan for the canonical water dimer, formamide, stacked benzene, and benzene water dimers, are presented. All results show reasonable agreement with the corresponding CSOV calculated reference contributions, around 0.1 and 0.15kcal/mol error for

Polarization coupling of vector Bessel–Gaussian beams

International Nuclear Information System (INIS)

Takeuchi, Ryushi; Kozawa, Yuichi; Sato, Shunichi

2013-01-01

We report polarization coupling of radial and azimuthal electric field components of a vector light beam as predicted by the fact that the vector Helmholtz equation is expressed as coupled differential equations in cylindrical coordinates. To clearly observe the polarization variation of a beam as it propagates, higher order transverse modes of a vector Bessel–Gaussian beam were generated by a gain distribution modulation technique, which created a narrow ring-shaped gain region in a Nd:YVO 4 crystal. The polarization coupling was confirmed by the observation that the major polarization component of a vector Bessel–Gaussian beam alternates between radial and azimuthal components along with the propagation. (paper)

Construction of Capacity Achieving Lattice Gaussian Codes

KAUST Repository

Alghamdi, Wael

2016-04-01

We propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3].

Invariant measures on multimode quantum Gaussian states

Science.gov (United States)

Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.

2012-12-01

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Invariant measures on multimode quantum Gaussian states

International Nuclear Information System (INIS)

Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.

2012-01-01

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Invariant measures on multimode quantum Gaussian states

Energy Technology Data Exchange (ETDEWEB)

Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)

2012-12-15

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Gaussian-state entanglement in a quantum beat laser

International Nuclear Information System (INIS)

Tahira, Rabia; Ikram, Manzoor; Nha, Hyunchul; Zubairy, M. Suhail

2011-01-01

Recently quantum beat lasers have been considered as a source of entangled radiation [S. Qamar, F. Ghafoor, M. Hillery, and M. S. Zubairy, Phys. Rev. A 77, 062308 (2008)]. We investigate and quantify the entanglement of this system when the initial cavity modes are prepared in a Gaussian two-mode state, one being a nonclassical state and the other a thermal state. It is investigated how the output entanglement varies with the nonclassicality of the input Gaussian state, thermal noise, and the strength of the driving field.

Gauge freedom in perfect fluid spatially homogeneous spacetimes

International Nuclear Information System (INIS)

Jantzen, R.T.

1983-01-01

The class of reference systems compatible with the symmetry of a spatially homogeneous perfect fluid spacetime is discussed together with the associated class of symmetry adapted comoving ADM frames (or computational frames). The fluid equations of motion are related to the four functions on the space of fluid flow lines discovered by Taub and which characterize an isentropic flow. (Auth.)

The halo bispectrum in N-body simulations with non-Gaussian initial conditions

Science.gov (United States)

Sefusatti, E.; Crocce, M.; Desjacques, V.

2012-10-01

We present measurements of the bispectrum of dark matter haloes in numerical simulations with non-Gaussian initial conditions of local type. We show, in the first place, that the overall effect of primordial non-Gaussianity on the halo bispectrum is larger than on the halo power spectrum when all measurable configurations are taken into account. We then compare our measurements with a tree-level perturbative prediction, finding good agreement at large scales when the constant Gaussian bias parameter, both linear and quadratic, and their constant non-Gaussian corrections are fitted for. The best-fitting values of the Gaussian bias factors and their non-Gaussian, scale-independent corrections are in qualitative agreement with the peak-background split expectations. In particular, we show that the effect of non-Gaussian initial conditions on squeezed configurations is fairly large (up to 30 per cent for fNL = 100 at redshift z = 0.5) and results from contributions of similar amplitude induced by the initial matter bispectrum, scale-dependent bias corrections as well as from non-linear matter bispectrum corrections. We show, in addition, that effects at second order in fNL are irrelevant for the range of values allowed by cosmic microwave background and galaxy power spectrum measurements, at least on the scales probed by our simulations (k > 0.01 h Mpc-1). Finally, we present a Fisher matrix analysis to assess the possibility of constraining primordial non-Gaussianity with future measurements of the galaxy bispectrum. We find that a survey with a volume of about 10 h-3 Gpc3 at mean redshift z ≃ 1 could provide an error on fNL of the order of a few. This shows the relevance of a joint analysis of galaxy power spectrum and bispectrum in future redshift surveys.

Capacity and optimal collusion attack channels for Gaussian fingerprinting games

Science.gov (United States)

Wang, Ying; Moulin, Pierre

2007-02-01

In content fingerprinting, the same media covertext - image, video, audio, or text - is distributed to many users. A fingerprint, a mark unique to each user, is embedded into each copy of the distributed covertext. In a collusion attack, two or more users may combine their copies in an attempt to "remove" their fingerprints and forge a pirated copy. To trace the forgery back to members of the coalition, we need fingerprinting codes that can reliably identify the fingerprints of those members. Researchers have been focusing on designing or testing fingerprints for Gaussian host signals and the mean square error (MSE) distortion under some classes of collusion attacks, in terms of the detector's error probability in detecting collusion members. For example, under the assumptions of Gaussian fingerprints and Gaussian attacks (the fingerprinted signals are averaged and then the result is passed through a Gaussian test channel), Moulin and Briassouli1 derived optimal strategies in a game-theoretic framework that uses the detector's error probability as the performance measure for a binary decision problem (whether a user participates in the collusion attack or not); Stone2 and Zhao et al. 3 studied average and other non-linear collusion attacks for Gaussian-like fingerprints; Wang et al. 4 stated that the average collusion attack is the most efficient one for orthogonal fingerprints; Kiyavash and Moulin 5 derived a mathematical proof of the optimality of the average collusion attack under some assumptions. In this paper, we also consider Gaussian cover signals, the MSE distortion, and memoryless collusion attacks. We do not make any assumption about the fingerprinting codes used other than an embedding distortion constraint. Also, our only assumptions about the attack channel are an expected distortion constraint, a memoryless constraint, and a fairness constraint. That is, the colluders are allowed to use any arbitrary nonlinear strategy subject to the above

Performance of BICM-T transceivers over Gaussian mixture noise channels

KAUST Repository

Malik, Muhammad Talha; Hossain, Md Jahangir; Alouini, Mohamed-Slim

2014-01-01

in the Gaussian mixture. The results presented for 16-QAM show that the BICM-T can result in gains up to 1.5 dB for a target BER of 10-6 if the impulsive noise in the Gaussian mixture is below a certain threshold level. The simulation results verify the tightness

Bootstrapping realized volatility and realized beta under a local Gaussianity assumption

DEFF Research Database (Denmark)

Hounyo, Ulrich

The main contribution of this paper is to propose a new bootstrap method for statistics based on high frequency returns. The new method exploits the local Gaussianity and the local constancy of volatility of high frequency returns, two assumptions that can simplify inference in the high frequency...... context, as recently explained by Mykland and Zhang (2009). Our main contributions are as follows. First, we show that the local Gaussian bootstrap is firstorder consistent when used to estimate the distributions of realized volatility and ealized betas. Second, we show that the local Gaussian bootstrap...... matches accurately the first four cumulants of realized volatility, implying that this method provides third-order refinements. This is in contrast with the wild bootstrap of Gonçalves and Meddahi (2009), which is only second-order correct. Third, we show that the local Gaussian bootstrap is able...

Encoding information using laguerre gaussian modes

CSIR Research Space (South Africa)

Trichili, A

2015-08-01

Full Text Available The authors experimentally demonstrate an information encoding protocol using the two degrees of freedom of Laguerre Gaussian modes having different radial and azimuthal components. A novel method, based on digital holography, for information...

Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures

KAUST Repository

Huser, Raphaël

2017-06-23

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.

Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures

KAUST Repository

Huser, Raphaë l; Opitz, Thomas; Thibaud, Emeric

2017-01-01

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.

Beam shape coefficients of the most general focused Gaussian laser beam for light scattering applications

International Nuclear Information System (INIS)

Lock, James A.

2013-01-01

The vector wave equation for electromagnetic waves, when subject to a number of constraints corresponding to propagation of a monochromatic beam, reduces to a pair of inhomogeneous differential equations describing the transverse electric and transverse magnetic polarized beam components. These differential equations are solved analytically to obtain the most general focused Gaussian beam to order s 4 , where s is the beam confinement parameter, and various properties of the most general Gaussian beam are then discussed. The radial fields of the most general Gaussian beam are integrated to obtain the on-axis beam shape coefficients of the generalized Lorenz–Mie theory formalism of light scattering. The beam shape coefficients are then compared with those of the localized Gaussian beam model and the Davis–Barton fifth-order symmetrized beam. -- Highlights: ► Derive the differential equation for the most general Gaussian beam. ► Solve the differential equation for the most general Gaussian beam. ► Determine the properties of the most general Gaussian beam. ► Determine the beam shape coefficients of the most general Gaussian beam

Generating higher-order radial Laguerre-Gaussian modes using a digital laser

CSIR Research Space (South Africa)

Bell, Teboho

2015-07-01

Full Text Available Using the digital laser one can generate various types of modes, like, Laguerre-Gaussian modes. The digital laser was forced to generate high-order radial Laguerre-Gaussian modes, LGp , with zero azimuthal order, by loading a digital hologram...

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene.

Science.gov (United States)

Oettinger, D; Mendoza, M; Herrmann, H J

2013-07-01

We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as the weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, which satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential the electronic fluid behaves as if it increases its effective viscosity.

Linear quadratic Gaussian controller design for plasma current, position and shape control system in ITER

International Nuclear Information System (INIS)

Belyakov, V.; Kavin, A.; Rumyantsev, E.; Kharitonov, V.; Misenov, B.; Ovsyannikov, A.; Ovsyannikov, D.; Veremei, E.; Zhabko, A.; Mitrishkin, Y.

1999-01-01

This paper is focused on the linear quadratic Gaussian (LQG) controller synthesis methodology for the ITER plasma current, position and shape control system as well as power derivative management system. It has been shown that some poloidal field (PF) coils have less influence on reference plasma-wall gaps control during plasma disturbances and hence they have been used to reduce total control power derivative by means of the additional non-linear feedback. The design has been done on the basis of linear models. Simulation was provided for non-linear model and results are presented and discussed. (orig.)

Coulomb Final State Interactions for Gaussian Wave Packets

CERN Document Server

Wiedemann, Urs Achim; Heinz, Ulrich W

1999-01-01

Two-particle like-sign and unlike-sign correlations including Coulomb final state interactions are calculated for Gaussian wave packets emitted from a Gaussian source. We show that the width of the wave packets can be fully absorbed into the spatial and momentum space widths of an effective emission function for plane wave states, and that Coulomb final state interaction effects are sensitive only to the latter, but not to the wave packet width itself. Results from analytical and numerical calculations are compared with recently published work by other authors.

Propagation of Gaussian Beams through Active GRIN Materials

International Nuclear Information System (INIS)

Gomez-Varela, A I; Flores-Arias, M T; Bao-Varela, C; Gomez-Reino, C; De la Fuente, X

2011-01-01

We discussed light propagation through an active GRIN material that exhibits loss or gain. Effects of gain or loss in GRIN materials can be phenomenologically taken into account by using a complex refractive index in the wave equation. This work examines the implication of using a complex refractive index on light propagation in an active GRIN material illuminated by a non-uniform monochromatic wave described by a Gaussian beam. We analyze how a Gaussian beam is propagated through the active material in order to characterize it by the beam parameters and the transverse irradiance distribution.

Performance of BICM-T transceivers over Gaussian mixture noise channels

KAUST Repository

Malik, Muhammad Talha

2014-04-01

Experimental measurements have shown that the noise in many communication channels is non-Gaussian. Bit interleaved coded modulation (BICM) is very popular for spectrally efficient transmission. Recent results have shown that the performance of BICM using convolutional codes in non-fading channels can be significantly improved if the coded bits are not interleaved at all. This particular BICM design is called BICM trivial (BICM-T). In this paper, we analyze the performance of a generalized BICM-T design for communication over Gaussian mixture noise (GMN) channels. The results disclose that for an optimal bit error rate (BER) performance, the use of an interleaver in BICM for GMN channels depends upon the strength of the impulsive noise components in the Gaussian mixture. The results presented for 16-QAM show that the BICM-T can result in gains up to 1.5 dB for a target BER of 10-6 if the impulsive noise in the Gaussian mixture is below a certain threshold level. The simulation results verify the tightness of developed union bound (UB) on BER performance.

Relativistic effects and primordial non-Gaussianity in the galaxy bias

International Nuclear Information System (INIS)

Bartolo, Nicola; Matarrese, Sabino; Riotto, Antonio

2011-01-01

When dealing with observables, one needs to generalize the bias relation between the observed galaxy fluctuation field to the underlying matter distribution in a gauge-invariant way. We provide such relation at second-order in perturbation theory adopting the local Eulerian bias model and starting from the observationally motivated uniform-redshift gauge. Our computation includes the presence of primordial non-Gaussianity. We show that large scale-dependent relativistic effects in the Eulerian bias arise independently from the presence of some primordial non-Gaussianity. Furthermore, the Eulerian bias inherits from the primordial non-Gaussianity not only a scale-dependence, but also a modulation with the angle of observation when sources with different biases are correlated

Outage performance of cognitive radio systems with Improper Gaussian signaling

KAUST Repository

Amin, Osama

2015-06-14

Improper Gaussian signaling has proved its ability to improve the achievable rate of the systems that suffer from interference compared with proper Gaussian signaling. In this paper, we first study impact of improper Gaussian signaling on the performance of the cognitive radio system by analyzing the outage probability of both the primary user (PU) and the secondary user (SU). We derive exact expression of the SU outage probability and upper and lower bounds for the PU outage probability. Then, we design the SU signal by adjusting its transmitted power and the circularity coefficient to minimize the SU outage probability while maintaining a certain PU quality-of-service. Finally, we evaluate the proposed bounds and adaptive algorithms by numerical results.

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

International Nuclear Information System (INIS)

Booth, George H.; Tsatsoulis, Theodoros; Grüneis, Andreas; Chan, Garnet Kin-Lic

2016-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Booth, George H., E-mail: george.booth@kcl.ac.uk [Department of Physics, King’s College London, Strand, London WC2R 2LS (United Kingdom); Tsatsoulis, Theodoros; Grüneis, Andreas, E-mail: a.grueneis@fkf.mpg.de [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Chan, Garnet Kin-Lic [Frick Laboratory, Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States)

2016-08-28

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

Topological recursion for Gaussian means and cohomological field theories

Science.gov (United States)

Andersen, J. E.; Chekhov, L. O.; Norbury, P.; Penner, R. C.

2015-12-01

We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich-Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M g,s disc (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M g,1 for all g in three ways: using the refined Harer-Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.

Gaussian white noise as a resource for work extraction.

Science.gov (United States)

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

2017-03-01

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

Bayesian nonparametric adaptive control using Gaussian processes.

Science.gov (United States)

Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A

2015-03-01

Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.

Linear velocity fields in non-Gaussian models for large-scale structure

Science.gov (United States)

Scherrer, Robert J.

1992-01-01

Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.

Efficient Hardware Implementation For Fingerprint Image Enhancement Using Anisotropic Gaussian Filter.

Science.gov (United States)

Khan, Tariq Mahmood; Bailey, Donald G; Khan, Mohammad A U; Kong, Yinan

2017-05-01

A real-time image filtering technique is proposed which could result in faster implementation for fingerprint image enhancement. One major hurdle associated with fingerprint filtering techniques is the expensive nature of their hardware implementations. To circumvent this, a modified anisotropic Gaussian filter is efficiently adopted in hardware by decomposing the filter into two orthogonal Gaussians and an oriented line Gaussian. An architecture is developed for dynamically controlling the orientation of the line Gaussian filter. To further improve the performance of the filter, the input image is homogenized by a local image normalization. In the proposed structure, for a middle-range reconfigurable FPGA, both parallel compute-intensive and real-time demands were achieved. We manage to efficiently speed up the image-processing time and improve the resource utilization of the FPGA. Test results show an improved speed for its hardware architecture while maintaining reasonable enhancement benchmarks.

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

Science.gov (United States)

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

2015-01-01

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating

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

Science.gov (United States)

Sellentin, Elena; Heavens, Alan F.

2018-01-01

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

Reference Ellipsoid and Geoid in Chronometric Geodesy

Science.gov (United States)

Kopeikin, Sergei M.

2016-02-01

Chronometric geodesy applies general relativity to study the problem of the shape of celestial bodies including the earth, and their gravitational field. The present paper discusses the relativistic problem of construction of a background geometric manifold that is used for describing a reference ellipsoid, geoid, the normal gravity field of the earth and for calculating geoid's undulation (height). We choose the perfect fluid with an ellipsoidal mass distribution uniformly rotating around a fixed axis as a source of matter generating the geometry of the background manifold through the Einstein equations. We formulate the post-Newtonian hydrodynamic equations of the rotating fluid to find out the set of algebraic equations defining the equipotential surface of the gravity field. In order to solve these equations we explicitly perform all integrals characterizing the interior gravitational potentials in terms of elementary functions depending on the parameters defining the shape of the body and the mass distribution. We employ the coordinate freedom of the equations to choose these parameters to make the shape of the rotating fluid configuration to be an ellipsoid of rotation. We derive expressions of the post-Newtonian mass and angular momentum of the rotating fluid as functions of the rotational velocity and the parameters of the ellipsoid including its bare density, eccentricity and semi-major axes. We formulate the post-Newtonian Pizzetti and Clairaut theorems that are used in geodesy to connect the parameters of the reference ellipsoid to the polar and equatorial values of force of gravity. We expand the post-Newtonian geodetic equations characterizing the reference ellipsoid into the Taylor series with respect to the eccentricity of the ellipsoid, and discuss the small-eccentricity approximation. Finally, we introduce the concept of relativistic geoid and its undulation with respect to the reference ellipsoid, and discuss how to calculate it in chronometric

s -wave scattering length of a Gaussian potential

Science.gov (United States)

Jeszenszki, Peter; Cherny, Alexander Yu.; Brand, Joachim

2018-04-01

We provide accurate expressions for the s -wave scattering length for a Gaussian potential well in one, two, and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of ultracold-atomic gases, where the s -wave scattering length is a physically relevant parameter. We first describe a numerical procedure to compute the value of the s -wave scattering length from the parameters of the Gaussian, but find that its accuracy is limited in the vicinity of singularities that result from the formation of new bound states. We then derive simple analytical expressions that capture the correct asymptotic behavior of the s -wave scattering length near the bound states. Expressions that are increasingly accurate in wide parameter regimes are found by a hierarchy of approximations that capture an increasing number of bound states. The small number of numerical coefficients that enter these expressions is determined from accurate numerical calculations. The approximate formulas combine the advantages of the numerical and approximate expressions, yielding an accurate and simple description from the weakly to the strongly interacting limit.

Gaussian density matrices: Quantum analogs of classical states

International Nuclear Information System (INIS)

Mann, A.; Revzen, M.

1993-01-01

We study quantum analogs of clasical situations, i.e. quantum states possessing some specific classical attribute(s). These states seem quite generally, to have the form of gaussian density matrices. Such states can always be parametrized as thermal squeezed states (TSS). We consider the following specific cases: (a) Two beams that are built from initial beams which passed through a beam splitter cannot, classically, be distinguished from (appropriately prepared) two independent beams that did not go through a splitter. The only quantum states possessing this classical attribute are TSS. (b) The classical Cramer's theorem was shown to have a quantum version (Hegerfeldt). Again, the states here are Gaussian density matrices. (c) The special case in the study of the quantum version of Cramer's theorem, viz. when the state obtained after partial tracing is a pure state, leads to the conclusion that all states involved are zero temperature limit TSS. The classical analog here are gaussians of zero width, i.e. all distributions are δ functions in phase space. (orig.)

Interaction of Airy–Gaussian beams in saturable media

International Nuclear Information System (INIS)

Zhou Meiling; Peng Yulian; Chen Chidao; Chen Bo; Peng Xi; Deng Dongmei

2016-01-01

Based on the nonlinear Schrödinger equation, the interactions of the two Airy–Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy–Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy–Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. (paper)

Intra-cavity metamorphosis of a Gaussian beam to flat-top distribution

CSIR Research Space (South Africa)

Naidoo, Darryl

2014-02-01

Full Text Available We explore an intra-cavity beam shaping approach to generate a Gaussian distribution by the metamorphosis of a Gaussian beam into a flat-top distribution on opposing mirrors. The concept is tested external to the cavity through the use of two...

A Novel Bearing Fault Diagnosis Method Based on Gaussian Restricted Boltzmann Machine

Directory of Open Access Journals (Sweden)

Xiao-hui He

2016-01-01

Full Text Available To realize the fault diagnosis of bearing effectively, this paper presents a novel bearing fault diagnosis method based on Gaussian restricted Boltzmann machine (Gaussian RBM. Vibration signals are firstly resampled to the same equivalent speed. Subsequently, the envelope spectrums of the resampled data are used directly as the feature vectors to represent the fault types of bearing. Finally, in order to deal with the high-dimensional feature vectors based on envelope spectrum, a classifier model based on Gaussian RBM is applied. Gaussian RBM has the ability to provide a closed-form representation of the distribution underlying the training data, and it is very convenient for modeling high-dimensional real-valued data. Experiments on 10 different data sets verify the performance of the proposed method. The superiority of Gaussian RBM classifier is also confirmed by comparing with other classifiers, such as extreme learning machine, support vector machine, and deep belief network. The robustness of the proposed method is also studied in this paper. It can be concluded that the proposed method can realize the bearing fault diagnosis accurately and effectively.

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

Energy Technology Data Exchange (ETDEWEB)

Gleyzes, Jérôme; De Putter, Roland; Doré, Olivier [California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125 (United States); Green, Daniel, E-mail: jerome.l.gleyzes@jpl.nasa.gov, E-mail: rdputter@caltech.edu, E-mail: drgreen@cita.utoronto.ca, E-mail: olivier.p.dore@jpl.nasa.gov [Department of Physics, University of California, 366 LeConte hall, Berkeley, CA 94720 (United States)

2017-04-01

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

On Gaussian conditional independence structures

Czech Academy of Sciences Publication Activity Database

Lněnička, Radim; Matúš, František

2007-01-01

Roč. 43, č. 3 (2007), s. 327-342 ISSN 0023-5954 R&D Projects: GA AV ČR IAA100750603 Institutional research plan: CEZ:AV0Z10750506 Keywords : multivariate Gaussian distribution * positive definite matrices * determinants * gaussoids * covariance selection models * Markov perfectness Subject RIV: BA - General Mathematics Impact factor: 0.552, year: 2007

Operator-sum representation for bosonic Gaussian channels

International Nuclear Information System (INIS)

Ivan, J. Solomon; Sabapathy, Krishna Kumar; Simon, R.

2011-01-01

Operator-sum or Kraus representations for single-mode bosonic Gaussian channels are developed, and several of their consequences explored. The fact that the two-mode metaplectic operators acting as unitary purification of these channels do not, in their canonical form, mix the position and momentum variables is exploited to present a procedure which applies uniformly to all families in the Holevo classification. In this procedure the Kraus operators of every quantum-limited Gaussian channel can be simply read off from the matrix elements of a corresponding metaplectic operator. Kraus operators are employed to bring out, in the Fock basis, the manner in which the antilinear, unphysical matrix transposition map when accompanied by injection of a threshold classical noise becomes a physical channel, denoted D(κ) in the Holevo classification. The matrix transposition channels D(κ), D(κ -1 ) turn out to be a dual pair in the sense that their Kraus operators are related by the adjoint operation. The amplifier channel with amplification factor κ and the beam-splitter channel with attenuation factor κ -1 turn out to be mutually dual in the same sense. The action of the quantum-limited attenuator and amplifier channels as simply scaling maps on suitable quasiprobabilities in phase space is examined in the Kraus picture. Consideration of cumulants is used to examine the issue of fixed points. The semigroup property of the amplifier and attenuator families leads in both cases to a Zeno-like effect arising as a consequence of interrupted evolution. In the cases of entanglement-breaking channels a description in terms of rank 1 Kraus operators is shown to emerge quite simply. In contradistinction, it is shown that there is not even one finite rank operator in the entire linear span of Kraus operators of the quantum-limited amplifier or attenuator families, an assertion far stronger than the statement that these are not entanglement breaking channels. A characterization of

Effects of relativistic and channel focusing on q-Gaussian laser beam propagating in a preformed parabolic plasma channel

Energy Technology Data Exchange (ETDEWEB)

Wang, Li; Hong, Xue-Ren, E-mail: hxr_nwnu@163.com; Sun, Jian-An, E-mail: sunja@nwnu.edu.cn; Tang, Rong-An; Yang, Yang; Zhou, Wei-Jun; Tian, Jian-Min; Duan, Wen-Shan

2017-07-12

The propagation of q-Gaussian laser beam in a preformed plasma channel is investigated by means of the variational method. A differential equation for the spot size has been obtained by including the effects of relativistic self-focusing, ponderomotive self-channeling and preformed channel focusing. The propagation behaviors and their corresponding physical conditions are identified. The comparison of the propagation between q-Gaussian and Gaussian laser beams is done by theoretical and numerical analysis. It is shown that, in the same channel, the focusing power of q-Gaussian laser beam is lower than that of Gaussian laser beam, i.e., the q-Gaussian laser beam is easier to focus than Gaussian laser beam. - Highlights: • Some behaviors for Gaussian laser are also found for q-Gaussian one. • The parameter regions corresponding to different laser behaviors are given. • Influence of q on the laser propagation behavior is obvious. • The q-Gaussian laser beam is easier to focus than the Gaussian one.

Effects of relativistic and channel focusing on q-Gaussian laser beam propagating in a preformed parabolic plasma channel

International Nuclear Information System (INIS)

Wang, Li; Hong, Xue-Ren; Sun, Jian-An; Tang, Rong-An; Yang, Yang; Zhou, Wei-Jun; Tian, Jian-Min; Duan, Wen-Shan

2017-01-01

The propagation of q-Gaussian laser beam in a preformed plasma channel is investigated by means of the variational method. A differential equation for the spot size has been obtained by including the effects of relativistic self-focusing, ponderomotive self-channeling and preformed channel focusing. The propagation behaviors and their corresponding physical conditions are identified. The comparison of the propagation between q-Gaussian and Gaussian laser beams is done by theoretical and numerical analysis. It is shown that, in the same channel, the focusing power of q-Gaussian laser beam is lower than that of Gaussian laser beam, i.e., the q-Gaussian laser beam is easier to focus than Gaussian laser beam. - Highlights: • Some behaviors for Gaussian laser are also found for q-Gaussian one. • The parameter regions corresponding to different laser behaviors are given. • Influence of q on the laser propagation behavior is obvious. • The q-Gaussian laser beam is easier to focus than the Gaussian one.

Identification and estimation of non-Gaussian structural vector autoregressions

DEFF Research Database (Denmark)

Lanne, Markku; Meitz, Mika; Saikkonen, Pentti

-Gaussian components is, without any additional restrictions, identified and leads to (essentially) unique impulse responses. We also introduce an identification scheme under which the maximum likelihood estimator of the non-Gaussian SVAR model is consistent and asymptotically normally distributed. As a consequence......, additional economic identifying restrictions can be tested. In an empirical application, we find a negative impact of a contractionary monetary policy shock on financial markets, and clearly reject the commonly employed recursive identifying restrictions....

An R Package for a General Class of Inverse Gaussian Distributions

Directory of Open Access Journals (Sweden)

Victor Leiva

2007-03-01

Full Text Available The inverse Gaussian distribution is a positively skewed probability model that has received great attention in the last 20 years. Recently, a family that generalizes this model called inverse Gaussian type distributions has been developed. The new R package named ig has been designed to analyze data from inverse Gaussian type distributions. This package contains basic probabilistic functions, lifetime indicators and a random number generator from this model. Also, parameter estimates and diagnostics analysis can be obtained using likelihood methods by means of this package. In addition, goodness-of-fit methods are implemented in order to detect the suitability of the model to the data. The capabilities and features of the ig package are illustrated using simulated and real data sets. Furthermore, some new results related to the inverse Gaussian type distribution are also obtained. Moreover, a simulation study is conducted for evaluating the estimation method implemented in the ig package.

Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

Science.gov (United States)

Arzani, Francesco; Treps, Nicolas; Ferrini, Giulia

2017-05-01

In quantum computation with continuous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the laboratory. We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state. Our protocols use as a primary non-Gaussian resource a single-photon counter. We use the fidelity of the transformation with the target one on Fock and coherent states to assess the quality of the approximate gate.

Power variation for Gaussian processes with stationary increments

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Corcuera, J.M.; Podolskij, Mark

2009-01-01

We develop the asymptotic theory for the realised power variation of the processes X=•G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity conditions on the path of the pr......We develop the asymptotic theory for the realised power variation of the processes X=•G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity conditions on the path...... a chaos representation....

Full-Duplex Relaying with Improper Gaussian Signaling over Nakagami-m Fading Channels

KAUST Repository

Gaafar, Mohamed; Khafagy, Mohammad Galal; Amin, Osama; Schaefer, Rafael F.; Alouini, Mohamed-Slim

2017-01-01

We study the potential employment of improper Gaussian signaling (IGS) in full-duplex relaying (FDR) with non-negligible residual self-interference (RSI) under Nakagami- m fading. IGS is recently shown to outperform traditional proper Gaussian

A Gaussian beam method for ultrasonic non-destructive evaluation modeling

Science.gov (United States)

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

2018-05-01

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

Extended Linear Models with Gaussian Priors

DEFF Research Database (Denmark)

Quinonero, Joaquin

2002-01-01

In extended linear models the input space is projected onto a feature space by means of an arbitrary non-linear transformation. A linear model is then applied to the feature space to construct the model output. The dimension of the feature space can be very large, or even infinite, giving the model...... a very big flexibility. Support Vector Machines (SVM's) and Gaussian processes are two examples of such models. In this technical report I present a model in which the dimension of the feature space remains finite, and where a Bayesian approach is used to train the model with Gaussian priors...... on the parameters. The Relevance Vector Machine, introduced by Tipping, is a particular case of such a model. I give the detailed derivations of the expectation-maximisation (EM) algorithm used in the training. These derivations are not found in the literature, and might be helpful for newcomers....

Image reconstruction under non-Gaussian noise

DEFF Research Database (Denmark)

Sciacchitano, Federica

During acquisition and transmission, images are often blurred and corrupted by noise. One of the fundamental tasks of image processing is to reconstruct the clean image from a degraded version. The process of recovering the original image from the data is an example of inverse problem. Due...... to the ill-posedness of the problem, the simple inversion of the degradation model does not give any good reconstructions. Therefore, to deal with the ill-posedness it is necessary to use some prior information on the solution or the model and the Bayesian approach. Additive Gaussian noise has been......D thesis intends to solve some of the many open questions for image restoration under non-Gaussian noise. The two main kinds of noise studied in this PhD project are the impulse noise and the Cauchy noise. Impulse noise is due to for instance the malfunctioning pixel elements in the camera sensors, errors...

Propagation of truncated modified Laguerre-Gaussian beams

Science.gov (United States)

Deng, D.; Li, J.; Guo, Q.

2010-01-01

By expanding the circ function into a finite sum of complex Gaussian functions and applying the Collins formula, the propagation of hard-edge diffracted modified Laguerre-Gaussian beams (MLGBs) through a paraxial ABCD system is studied, and the approximate closed-form propagation expression of hard-edge diffracted MLGBs is obtained. The transverse intensity distribution of the MLGB carrying finite power can be characterized by a single bright and symmetric ring during propagation when the aperture radius is very large. Starting from the definition of the generalized truncated second-order moments, the beam quality factor of MLGBs through a hard-edged circular aperture is investigated in a cylindrical coordinate system, which turns out to be dependent on the truncated radius and the beam orders.

Direct Importance Estimation with Gaussian Mixture Models

Science.gov (United States)

Yamada, Makoto; Sugiyama, Masashi

The ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extention of the Kullback-Leibler importance estimation procedure (KLIEP), an importance estimation method using linear or kernel models. An advantage of GMMs is that covariance matrices can also be learned through an expectation-maximization procedure, so the proposed method — which we call the Gaussian mixture KLIEP (GM-KLIEP) — is expected to work well when the true importance function has high correlation. Through experiments, we show the validity of the proposed approach.

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

Science.gov (United States)

Steely, Sidney L.

1993-01-01

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

Image interpolation and denoising for division of focal plane sensors using Gaussian processes.

Science.gov (United States)

Gilboa, Elad; Cunningham, John P; Nehorai, Arye; Gruev, Viktor

2014-06-16

Image interpolation and denoising are important techniques in image processing. These methods are inherent to digital image acquisition as most digital cameras are composed of a 2D grid of heterogeneous imaging sensors. Current polarization imaging employ four different pixelated polarization filters, commonly referred to as division of focal plane polarization sensors. The sensors capture only partial information of the true scene, leading to a loss of spatial resolution as well as inaccuracy of the captured polarization information. Interpolation is a standard technique to recover the missing information and increase the accuracy of the captured polarization information. Here we focus specifically on Gaussian process regression as a way to perform a statistical image interpolation, where estimates of sensor noise are used to improve the accuracy of the estimated pixel information. We further exploit the inherent grid structure of this data to create a fast exact algorithm that operates in ����(N(3/2)) (vs. the naive ���� (N³)), thus making the Gaussian process method computationally tractable for image data. This modeling advance and the enabling computational advance combine to produce significant improvements over previously published interpolation methods for polarimeters, which is most pronounced in cases of low signal-to-noise ratio (SNR). We provide the comprehensive mathematical model as well as experimental results of the GP interpolation performance for division of focal plane polarimeter.

Modeling text with generalizable Gaussian mixtures

DEFF Research Database (Denmark)

Hansen, Lars Kai; Sigurdsson, Sigurdur; Kolenda, Thomas

2000-01-01

We apply and discuss generalizable Gaussian mixture (GGM) models for text mining. The model automatically adapts model complexity for a given text representation. We show that the generalizability of these models depends on the dimensionality of the representation and the sample size. We discuss...

Perfusion Quantification Using Gaussian Process Deconvolution

DEFF Research Database (Denmark)

Andersen, Irene Klærke; Have, Anna Szynkowiak; Rasmussen, Carl Edward

2002-01-01

The quantification of perfusion using dynamic susceptibility contrast MRI (DSC-MRI) requires deconvolution to obtain the residual impulse response function (IRF). In this work, a method using the Gaussian process for deconvolution (GPD) is proposed. The fact that the IRF is smooth is incorporated...

Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity

CERN Document Server

Ade, P.A.R.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R.C.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, L.Y.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Desert, F.X.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Ducout, A.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Elsner, F.; Ensslin, T.A.; Eriksen, H.K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Galeotta, S.; Ganga, K.; Giard, M.; Giraud-Heraud, Y.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F.K.; Hanson, D.; Harrison, D.; Heavens, A.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Jaffe, T.R.; Jaffe, A.H.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lacasa, F.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Laureijs, R.J.; Lawrence, C.R.; Leahy, J.P.; Leonardi, R.; Lesgourgues, J.; Lewis, A.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maffei, B.; Maino, D.; Mandolesi, N.; Mangilli, A.; Marinucci, D.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Naselsky, P.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Osborne, S.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H.V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Racine, B.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rubino-Martin, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Smith, K.; Spencer, L.D.; Starck, J.L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L.A.; Wandelt, B.D.; White, M.; White, S.D.M.; Yvon, D.; Zacchei, A.; Zonca, A.

2014-01-01

The Planck nominal mission cosmic microwave background (CMB) maps yield unprecedented constraints on primordial non-Gaussianity (NG). Using three optimal bispectrum estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result fNL^local= 2.7+/-5.8, fNL^equil= -42+/-75, and fNL^ortho= -25+\\-39 (68% CL statistical). NG is detected in the data; using skew-C_l statistics we find a nonzero bispectrum from residual point sources, and the ISW-lensing bispectrum at a level expected in the LambdaCDM scenario. The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are confirmed by skew-C_l, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, 3-dimensional...

Simulation of ultrasonic surface waves with multi-Gaussian and point source beam models

International Nuclear Information System (INIS)

Zhao, Xinyu; Schmerr, Lester W. Jr.; Li, Xiongbing; Sedov, Alexander

2014-01-01

In the past decade, multi-Gaussian beam models have been developed to solve many complicated bulk wave propagation problems. However, to date those models have not been extended to simulate the generation of Rayleigh waves. Here we will combine Gaussian beams with an explicit high frequency expression for the Rayleigh wave Green function to produce a three-dimensional multi-Gaussian beam model for the fields radiated from an angle beam transducer mounted on a solid wedge. Simulation results obtained with this model are compared to those of a point source model. It is shown that the multi-Gaussian surface wave beam model agrees well with the point source model while being computationally much more efficient

Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing.

Science.gov (United States)

Mitri, F G; Fellah, Z E A

2014-01-01

The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z(R). Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere's resonance frequencies for kw₀≤1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force. Copyright © 2013 Elsevier B.V. All rights reserved.

Detection Performance of Signals in Dependent Noise From a Gaussian Mixture Uncertainty Class

National Research Council Canada - National Science Library

Gerlach, K

1998-01-01

... (correlated) multivariate noise from a Gaussian mixture uncertainty class. This uncertainty class is defined using upper and lower bounding functions on the univariate Gaussian mixing distribution function...

Full Life Wind Turbine Gearbox Lubricating Fluids

Energy Technology Data Exchange (ETDEWEB)

Lutz, Glenn A.; Jungk, Manfred; Bryant, Jonathan J.; Lauer, Rebecca S.; Chobot, Anthony; Mayer, Tyler; Palmer, Shane; Kauffman, Robert E.

2012-02-28

Industrial gear box lubricants typically are hydrocarbon based mineral oils with considerable amounts of additives to overcome the lack of base fluid properties like wear protection, oxidation stability, load carrying capacity, low temperature solidification and drop of viscosity at higher temperatures. For today's wind turbine gearboxes, the requirements are more severe and synthetic hydrocarbon oils are used to improve on this, but all such hydrocarbon based lubricants require significant amounts of Extreme Pressure (EP) additives to meet performance requirements. Perfluoropolyether (PFPE) fluids provide load carrying capacity as an inherent property. During the course of the project with the main tasks of 'Establish a Benchmark', 'Lubricant Evaluation', 'Full Scale Gearbox Trial' and 'Economic Evaluation', the PAO Reference oil exhibited significant changes after laboratory gear testing, in service operation in the field and full scale gearbox trial. Four hydrocarbon base oils were selected for comparison in the benchmarking exercise and showed variation with respect to meeting the requirements for the laboratory micro-pitting tests, while the PFPE fluid exceeded the requirements even with the material taken after the full scale gear box trial. This is remarkable for a lubricant without EP additives. Laboratory bearing tests performed on the PFPE fluids before and after the full scale gear box trial showed the results met requirements for the industry standard. The PFPE fluid successfully completed the full scale gear box test program which included baseline and progressive staged load testing. The evaluation of gears showed no micro-pitting or objectionable wear. By the final stage, lubricant film thickness had been reduced to just 21% of its original value, this was by design and resulted in a lambda ratio of well below 1. This test design scenario of a low lambda ratio is a very undesirable lubrication condition

Behaviour of Lagrangian triangular mixed fluid finite elements

Indian Academy of Sciences (India)

The behaviour of mixed fluid finite elements, formulated based on the Lagrangian frame of reference, is investigated to understand the effects of locking due to incompressibility and irrotational constraints. For this purpose, both linear and quadratic mixed triangular fluid elements are formulated. It is found that there exists a ...

Multipoint propagators for non-Gaussian initial conditions

International Nuclear Information System (INIS)

Bernardeau, Francis; Sefusatti, Emiliano; Crocce, Martin

2010-01-01

We show here how renormalized perturbation theory calculations applied to the quasilinear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions. It is explicitly demonstrated that the series reordering scheme proposed in Bernardeau, Crocce, and Scoccimarro [Phys. Rev. D 78, 103521 (2008)] is preserved for non-Gaussian initial conditions. This scheme applies to the power spectrum and higher-order spectra and is based on a reorganization of the contributing terms into the sum of products of multipoint propagators. In case of PNG, new contributing terms appear, the importance of which is discussed in the context of current PNG models. The properties of the building blocks of such resummation schemes, the multipoint propagators, are then investigated. It is first remarked that their expressions are left unchanged at one-loop order irrespective of statistical properties of the initial field. We furthermore show that the high-momentum limit of each of these propagators can be explicitly computed even for arbitrary initial conditions. They are found to be damped by an exponential cutoff whose expression is directly related to the moment generating function of the one-dimensional displacement field. This extends what had been established for multipoint propagators for Gaussian initial conditions. Numerical forms of the cutoff are shown for the so-called local model of PNG.

Modeling of Video Sequences by Gaussian Mixture: Application in Motion Estimation by Block Matching Method

Directory of Open Access Journals (Sweden)

Abdenaceur Boudlal

2010-01-01

Full Text Available This article investigates a new method of motion estimation based on block matching criterion through the modeling of image blocks by a mixture of two and three Gaussian distributions. Mixture parameters (weights, means vectors, and covariance matrices are estimated by the Expectation Maximization algorithm (EM which maximizes the log-likelihood criterion. The similarity between a block in the current image and the more resembling one in a search window on the reference image is measured by the minimization of Extended Mahalanobis distance between the clusters of mixture. Performed experiments on sequences of real images have given good results, and PSNR reached 3 dB.

SWIFT, 3-D Fluid Flow, Heat Transfer, Decay Chain Transport in Geological Media

International Nuclear Information System (INIS)

Cranwell, R.M.; Reeves, M.

2003-01-01

1 - Description of problem or function: SWIFT solves the coupled or individual equations governing fluid flow, heat transport, brine displacement, and radionuclide displacement in geologic media. Fluid flow may be transient or steady-state. One, two, or three dimensions are available and transport of radionuclides chains is possible. 4. Method of solution: Finite differencing is used to discretize the partial differential equations in space and time. The user may choose centered or backward spatial differencing, coupled with either central or backward temporal differencing. The matrix equations may be solved iteratively (two line successive-over-relaxation) or directly (special matrix banding and Gaussian elimination). 5. Restrictions on the complexity of the problem: On the CDC7600 in direct solution mode, the maximum number of grid blocks allowed is approximately 1400

Gaussian vector fields on triangulated surfaces

DEFF Research Database (Denmark)

Ipsen, John H

2016-01-01

proven to be very useful to resolve the complex interplay between in-plane ordering of membranes and membrane conformations. In the present work we have developed a procedure for realistic representations of Gaussian models with in-plane vector degrees of freedoms on a triangulated surface. The method...

Modulation depth of Michelson interferometer with Gaussian beam.

Science.gov (United States)

Välikylä, Tuomas; Kauppinen, Jyrki

2011-12-20

Mirror misalignment or the tilt angle of the Michelson interferometer can be estimated from the modulation depth measured with collimated monochromatic light. The intensity of the light beam is usually assumed to be uniform, but, for example, with gas lasers it generally has a Gaussian distribution, which makes the modulation depth less sensitive to the tilt angle. With this assumption, the tilt angle may be underestimated by about 50%. We have derived a mathematical model for modulation depth with a circular aperture and Gaussian beam. The model reduces the error of the tilt angle estimate to below 1%. The results of the model have been verified experimentally.

Gaussian basis functions for highly oscillatory scattering wavefunctions

Science.gov (United States)

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.

Finite Range Decomposition of Gaussian Processes

CERN Document Server

Brydges, C D; Mitter, P K

2003-01-01

Let $D$ be the finite difference Laplacian associated to the lattice $bZ^{d}$. For dimension $dge 3$, $age 0$ and $L$ a sufficiently large positive dyadic integer, we prove that the integral kernel of the resolvent $G^{a}:=(a-D)^{-1}$ can be decomposed as an infinite sum of positive semi-definite functions $ V_{n} $ of finite range, $ V_{n} (x-y) = 0$ for $|x-y|ge O(L)^{n}$. Equivalently, the Gaussian process on the lattice with covariance $G^{a}$ admits a decomposition into independent Gaussian processes with finite range covariances. For $a=0$, $ V_{n} $ has a limiting scaling form $L^{-n(d-2)}Gamma_{ c,ast }{bigl (frac{x-y}{ L^{n}}bigr )}$ as $nrightarrow infty$. As a corollary, such decompositions also exist for fractional powers $(-D)^{-alpha/2}$, $0

Experimental Results and Numerical Simulation of the Target RCS using Gaussian Beam Summation Method

Directory of Open Access Journals (Sweden)

Ghanmi Helmi

2018-05-01

Full Text Available This paper presents a numerical and experimental study of Radar Cross Section (RCS of radar targets using Gaussian Beam Summation (GBS method. The purpose GBS method has several advantages over ray method, mainly on the caustic problem. To evaluate the performance of the chosen method, we started the analysis of the RCS using Gaussian Beam Summation (GBS and Gaussian Beam Launching (GBL, the asymptotic models Physical Optic (PO, Geometrical Theory of Diffraction (GTD and the rigorous Method of Moment (MoM. Then, we showed the experimental validation of the numerical results using experimental measurements which have been executed in the anechoic chamber of Lab-STICC at ENSTA Bretagne. The numerical and experimental results of the RCS are studied and given as a function of various parameters: polarization type, target size, Gaussian beams number and Gaussian beams width.

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

Science.gov (United States)

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

2018-04-01

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

On Alternate Relaying with Improper Gaussian Signaling

KAUST Repository

Gaafar, Mohamed; Amin, Osama; Ikhlef, Aissa; Chaaban, Anas; Alouini, Mohamed-Slim

2016-01-01

In this letter, we investigate the potential benefits of adopting improper Gaussian signaling (IGS) in a two-hop alternate relaying (AR) system. Given the known benefits of using IGS in interference-limited networks, we propose to use IGS to relieve the inter-relay interference (IRI) impact on the AR system assuming no channel state information is available at the source. In this regard, we assume that the two relays use IGS and the source uses proper Gaussian signaling (PGS). Then, we optimize the degree of impropriety of the relays signal, measured by the circularity coefficient, to maximize the total achievable rate. Simulation results show that using IGS yields a significant performance improvement over PGS, especially when the first hop is a bottleneck due to weak source-relay channel gains and/or strong IRI.

On Alternate Relaying with Improper Gaussian Signaling

KAUST Repository

Gaafar, Mohamed

2016-06-06

In this letter, we investigate the potential benefits of adopting improper Gaussian signaling (IGS) in a two-hop alternate relaying (AR) system. Given the known benefits of using IGS in interference-limited networks, we propose to use IGS to relieve the inter-relay interference (IRI) impact on the AR system assuming no channel state information is available at the source. In this regard, we assume that the two relays use IGS and the source uses proper Gaussian signaling (PGS). Then, we optimize the degree of impropriety of the relays signal, measured by the circularity coefficient, to maximize the total achievable rate. Simulation results show that using IGS yields a significant performance improvement over PGS, especially when the first hop is a bottleneck due to weak source-relay channel gains and/or strong IRI.

Crossover between the Gaussian orthogonal ensemble, the Gaussian unitary ensemble, and Poissonian statistics.

Science.gov (United States)

Schweiner, Frank; Laturner, Jeanine; Main, Jörg; Wunner, Günter

2017-11-01

Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) have analytical formulas for the level spacing distribution function been derived within random matrix theory. We investigate arbitrary crossovers in the triangle between all three statistics. To this aim we propose an according formula for the level spacing distribution function depending on two parameters. Comparing the behavior of our formula for the special cases of P→GUE, P→GOE, and GOE→GUE with the results from random matrix theory, we prove that these crossovers are described reasonably. Recent investigations by F. Schweiner et al. [Phys. Rev. E 95, 062205 (2017)2470-004510.1103/PhysRevE.95.062205] have shown that the Hamiltonian of magnetoexcitons in cubic semiconductors can exhibit all three statistics in dependence on the system parameters. Evaluating the numerical results for magnetoexcitons in dependence on the excitation energy and on a parameter connected with the cubic valence band structure and comparing the results with the formula proposed allows us to distinguish between regular and chaotic behavior as well as between existent or broken antiunitary symmetries. Increasing one of the two parameters, transitions between different crossovers, e.g., from the P→GOE to the P→GUE crossover, are observed and discussed.

Scale-dependent bias from the reconstruction of non-Gaussian distributions

International Nuclear Information System (INIS)

Chongchitnan, Sirichai; Silk, Joseph

2011-01-01

Primordial non-Gaussianity introduces a scale-dependent variation in the clustering of density peaks corresponding to rare objects. This variation, parametrized by the bias, is investigated on scales where a linear perturbation theory is sufficiently accurate. The bias is obtained directly in real space by comparing the one- and two-point probability distributions of density fluctuations. We show that these distributions can be reconstructed using a bivariate Edgeworth series, presented here up to an arbitrarily high order. The Edgeworth formalism is shown to be well-suited for ''local'' cubic-order non-Gaussianity parametrized by g NL . We show that a strong scale dependence in the bias can be produced by g NL of order 10 5 , consistent with cosmic microwave background constraints. On a separation length of ∼100 Mpc, current constraints on g NL still allow the bias for the most massive clusters to be enhanced by 20-30% of the Gaussian value. We further examine the bias as a function of mass scale, and also explore the relationship between the clustering and the abundance of massive clusters in the presence of g NL . We explain why the Edgeworth formalism, though technically challenging, is a very powerful technique for constraining high-order non-Gaussianity with large-scale structures.

Neutron study of non-Gaussian self dynamics in liquid parahydrogen

International Nuclear Information System (INIS)

Bafile, Ubaldo; Celli, Milva; Colognesi, Daniele; Zoppi, Marco; Guarini, Eleonora; De Francesco, Alessio; Formisano, Ferdinando; Neumann, Martin

2012-01-01

A time-honoured approach to single-molecule, or self, dynamics of liquids is based on the so-called Gaussian approximation (GA), where it is assumed that, in the whole dynamical range between hydrodynamic diffusion and free-particle streaming, the motion of a particle is fully determined by a unique function of time directly related to the velocity autocorrelation function. An evident support to the GA is offered by the fact that the approximation becomes exact in both above limit conditions. Yet, experimental inquiries into the presence of non-Gaussian dynamics are very scarce, particularly in liquid parahydrogen in spite of its importance as the prototype of a 'quantum Boltzmann liquid' which has also served as a benchmark for the development of quantum dynamics simulation algorithms. Though experimental evidence of the breakdown of the GA was obtained by some of the authors a few years ago, the localization in Q space of non-Gaussian behaviour was still undetermined, and no quantitative assessment of the effect was ever obtained. These issues have been tackled and solved by a new neutron investigation, which provides the first determination of non-Gaussian behaviour in the framework of the well-known theoretical approach by Rahman, Singwi and Sjölander.

Interweave Cognitive Radio with Improper Gaussian Signaling

KAUST Repository

Hedhly, Wafa; Amin, Osama; Alouini, Mohamed-Slim

2018-01-01

Improper Gaussian signaling (IGS) has proven its ability in improving the performance of underlay and overlay cognitive radio paradigms. In this paper, the interweave cognitive radio paradigm is studied when the cognitive user employs IGS

The Wehrl entropy has Gaussian optimizers

DEFF Research Database (Denmark)

De Palma, Giacomo

2018-01-01

We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel...

Fluid bilayer structure determination: Joint refinement in composition space using X-ray and neutron diffraction data

Energy Technology Data Exchange (ETDEWEB)

White, S.H. [Univ. of California, Irvine, CA (United States); Wiener, M.C. [Univ. of California, San Francisco, CA (United States)

1994-12-31

Experimentally-determined structural models of fluid lipid bilayers are essential for verifying molecular dynamics simulations of bilayers and for understanding the structural consequences of peptide interactions. The extreme thermal motion of bilayers precludes the possibility of atomic-level structural models. Defining {open_quote}the structure{close_quote} of a bilayer as the time-averaged transbilayer distribution of the water and the principal lipid structural groups such as the carbonyls and double-bonds (quasimolecular fragments), one can represent the bilayer structure as a sum of Gaussian functions referred to collectively as the quasimolecular structure. One method of determining the structure is by neutron diffraction combined with exhaustive specific deuteration. This method is impractical because of the expense of the chemical syntheses and the limited amount of neutron beam time currently available. We have therefore developed the composition space refinement method for combining X-ray and minimal neutron diffraction data to arrive at remarkably detailed and accurate structures of fluid bilayers. The composition space representation of the bilayer describes the probability of occupancy per unit length across the width of the bilayer of each quasimolecular component and permits the joint refinement of X-ray and neutron lamellar diffraction data by means of a single quasimolecular structure that is fitted simultaneously to both data sets. Scaling of each component by the appropriate neutron or X-ray scattering length maps the composition-space profile to the appropriate scattering length space for comparison to experimental data. The difficulty with the method is that fluid bilayer structures are generally only marginally determined by the experimental data. This means that the space of possible solutions must be extensively explored in conjunction with a thorough analysis of errors.

Fluid bilayer structure determination: Joint refinement in composition space using X-ray and neutron diffraction data

International Nuclear Information System (INIS)

White, S.H.; Wiener, M.C.

1994-01-01

Experimentally-determined structural models of fluid lipid bilayers are essential for verifying molecular dynamics simulations of bilayers and for understanding the structural consequences of peptide interactions. The extreme thermal motion of bilayers precludes the possibility of atomic-level structural models. Defining open-quote the structure close-quote of a bilayer as the time-averaged transbilayer distribution of the water and the principal lipid structural groups such as the carbonyls and double-bonds (quasimolecular fragments), one can represent the bilayer structure as a sum of Gaussian functions referred to collectively as the quasimolecular structure. One method of determining the structure is by neutron diffraction combined with exhaustive specific deuteration. This method is impractical because of the expense of the chemical syntheses and the limited amount of neutron beam time currently available. We have therefore developed the composition space refinement method for combining X-ray and minimal neutron diffraction data to arrive at remarkably detailed and accurate structures of fluid bilayers. The composition space representation of the bilayer describes the probability of occupancy per unit length across the width of the bilayer of each quasimolecular component and permits the joint refinement of X-ray and neutron lamellar diffraction data by means of a single quasimolecular structure that is fitted simultaneously to both data sets. Scaling of each component by the appropriate neutron or X-ray scattering length maps the composition-space profile to the appropriate scattering length space for comparison to experimental data. The difficulty with the method is that fluid bilayer structures are generally only marginally determined by the experimental data. This means that the space of possible solutions must be extensively explored in conjunction with a thorough analysis of errors

American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution

DEFF Research Database (Denmark)

Stentoft, Lars Peter

In this paper we propose a feasible way to price American options in a model with time varying volatility and conditional skewness and leptokurtosis using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk neutral dynamics can be obtained in this model, we interpret...... properties shows that there are important option pricing differences compared to the Gaussian case as well as to the symmetric special case. A large scale empirical examination shows that our model outperforms the Gaussian case for pricing options on three large US stocks as well as a major index...

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

Science.gov (United States)

Mao, Tianqi; Wang, Zhaocheng; Wang, Qi

2017-01-23

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

Probabilistic wind power forecasting with online model selection and warped gaussian process

International Nuclear Information System (INIS)

Kou, Peng; Liang, Deliang; Gao, Feng; Gao, Lin

2014-01-01

Highlights: • A new online ensemble model for the probabilistic wind power forecasting. • Quantifying the non-Gaussian uncertainties in wind power. • Online model selection that tracks the time-varying characteristic of wind generation. • Dynamically altering the input features. • Recursive update of base models. - Abstract: Based on the online model selection and the warped Gaussian process (WGP), this paper presents an ensemble model for the probabilistic wind power forecasting. This model provides the non-Gaussian predictive distributions, which quantify the non-Gaussian uncertainties associated with wind power. In order to follow the time-varying characteristics of wind generation, multiple time dependent base forecasting models and an online model selection strategy are established, thus adaptively selecting the most probable base model for each prediction. WGP is employed as the base model, which handles the non-Gaussian uncertainties in wind power series. Furthermore, a regime switch strategy is designed to modify the input feature set dynamically, thereby enhancing the adaptiveness of the model. In an online learning framework, the base models should also be time adaptive. To achieve this, a recursive algorithm is introduced, thus permitting the online updating of WGP base models. The proposed model has been tested on the actual data collected from both single and aggregated wind farms

Statistically tuned Gaussian background subtraction technique for ...

Indian Academy of Sciences (India)

temporal median method and mixture of Gaussian model and performance evaluation ... to process the videos captured by unmanned aerial vehicle (UAV). ..... The output is obtained by simulation using MATLAB 2010 in a standalone PC with ...

Decoherence and tripartite entanglement dynamics in the presence of Gaussian and non-Gaussian classical noise

Energy Technology Data Exchange (ETDEWEB)

Kenfack, Lionel Tenemeza, E-mail: kenfacklionel300@gmail.com [Mesoscopic and Multilayer Structure Laboratory, Department of Physics, Faculty of Science, University of Dschang, PO Box: 67 Dschang (Cameroon); Tchoffo, Martin; Fai, Lukong Cornelius [Mesoscopic and Multilayer Structure Laboratory, Department of Physics, Faculty of Science, University of Dschang, PO Box: 67 Dschang (Cameroon); Fouokeng, Georges Collince [Mesoscopic and Multilayer Structure Laboratory, Department of Physics, Faculty of Science, University of Dschang, PO Box: 67 Dschang (Cameroon); Laboratoire de Génie des Matériaux, Pôle Recherche-Innovation-Entrepreneuriat (PRIE), Institut Universitaire de la Côte, BP 3001 Douala (Cameroon)

2017-04-15

We address the entanglement dynamics of a three-qubit system interacting with a classical fluctuating environment described either by a Gaussian or non-Gaussian noise in three different configurations namely: common, independent and mixed environments. Specifically, we focus on the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise (RTN). The qubits are prepared in a state composed of a Greenberger-Horne-Zeilinger (GHZ) and a W state. With the help of the tripartite negativity, we show that the entanglement evolution is not only affected by the type of system-environment coupling but also by the kind and the memory properties of the considered noise. We also compared the dynamics induced by the two kinds of noise and we find that even if both noises have a Lorentzian spectrum, the effects of the OU noise cannot be in a simple way deduced from those of the RTN and vice-versa. In addition, we show that the entanglement can be indefinitely preserved when the qubits are coupled to the environmental noise in a common environment (CE). Finally, the presence or absence of peculiar phenomena such as entanglement revivals (ER) and entanglement sudden death (ESD) is observed.

Decoherence and tripartite entanglement dynamics in the presence of Gaussian and non-Gaussian classical noise

International Nuclear Information System (INIS)

Kenfack, Lionel Tenemeza; Tchoffo, Martin; Fai, Lukong Cornelius; Fouokeng, Georges Collince

2017-01-01

We address the entanglement dynamics of a three-qubit system interacting with a classical fluctuating environment described either by a Gaussian or non-Gaussian noise in three different configurations namely: common, independent and mixed environments. Specifically, we focus on the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise (RTN). The qubits are prepared in a state composed of a Greenberger-Horne-Zeilinger (GHZ) and a W state. With the help of the tripartite negativity, we show that the entanglement evolution is not only affected by the type of system-environment coupling but also by the kind and the memory properties of the considered noise. We also compared the dynamics induced by the two kinds of noise and we find that even if both noises have a Lorentzian spectrum, the effects of the OU noise cannot be in a simple way deduced from those of the RTN and vice-versa. In addition, we show that the entanglement can be indefinitely preserved when the qubits are coupled to the environmental noise in a common environment (CE). Finally, the presence or absence of peculiar phenomena such as entanglement revivals (ER) and entanglement sudden death (ESD) is observed.

Rotating fluid models in classical and quantum mechanics

International Nuclear Information System (INIS)

Arvieu, R.; Troudet, T.

1979-01-01

To describe the behavior of high-spin nuclei it is necessary to refer back to the classical mechanics of fluids in rotation where some results are general enough to apply to the rotational nuclear fluid. It is then shown that the quantum model of rotational oscillator gives a simple classification of rotating configurations [fr

Post-Newtonian reference ellipsoid for relativistic geodesy

Science.gov (United States)

Kopeikin, Sergei; Han, Wenbiao; Mazurova, Elena

2016-02-01

We apply general relativity to construct the post-Newtonian background manifold that serves as a reference spacetime in relativistic geodesy for conducting a relativistic calculation of the geoid's undulation and the deflection of the plumb line from the vertical. We chose an axisymmetric ellipsoidal body made up of a perfect homogeneous fluid uniformly rotating around a fixed axis, as a source generating the reference geometry of the background manifold through Einstein's equations. We then reformulate and extend hydrodynamic calculations of rotating fluids done by a number of previous researchers for astrophysical applications to the realm of relativistic geodesy to set up algebraic equations defining the shape of the post-Newtonian reference ellipsoid. To complete this task, we explicitly perform all integrals characterizing gravitational field potentials inside the fluid body and represent them in terms of the elementary functions depending on the eccentricity of the ellipsoid. We fully explore the coordinate (gauge) freedom of the equations describing the post-Newtonian ellipsoid and demonstrate that the fractional deviation of the post-Newtonian level surface from the Maclaurin ellipsoid can be made much smaller than the previously anticipated estimate based on the astrophysical application of the coordinate gauge advocated by Bardeen and Chandrasekhar. We also derive the gauge-invariant relations of the post-Newtonian mass and the constant angular velocity of the rotating fluid with the parameters characterizing the shape of the post-Newtonian ellipsoid including its eccentricity, a semiminor axis, and a semimajor axis. We formulate the post-Newtonian theorems of Pizzetti and Clairaut that are used in geodesy to connect the geometric parameters of the reference ellipsoid to the physically measurable force of gravity at the pole and equator of the ellipsoid. Finally, we expand the post-Newtonian geodetic equations describing the post-Newtonian ellipsoid to

Reference ellipsoid and geoid in chronometric geodesy

Directory of Open Access Journals (Sweden)

Sergei M Kopeikin

2016-02-01

Full Text Available Chronometric geodesy applies general relativity to study the problem of the shape of celestial bodies including the earth, and their gravitational field. The present paper discusses the relativistic problem of construction of a background geometric manifold that is used for describing a reference ellipsoid, geoid, the normal gravity field of the earth and for calculating geoid's undulation (height. We choose the perfect fluid with an ellipsoidal mass distribution uniformly rotating around a fixed axis as a source of matter generating the geometry of the background manifold through the Einstein equations. We formulate the post-Newtonian hydrodynamic equations of the rotating fluid to find out the set of algebraic equations defining the equipotential surface of the gravity field. In order to solve these equations we explicitly perform all integrals characterizing the interior gravitational potentials in terms of elementary functions depending on the parameters defining the shape of the body and the mass distribution. We employ the coordinate freedom of the equations to choose these parameters to make the shape of the rotating fluid configuration to be an ellipsoid of rotation. We derive expressions of the post-Newtonian mass and angular momentum of the rotating fluid as functions of the rotational velocity and the parameters of the ellipsoid including its bare density, eccentricity and semi-major axes. We formulate the post-Newtonian Pizzetti and Clairaut theorems that are used in geodesy to connect the parameters of the reference ellipsoid to the polar and equatorial values of force of gravity. We expand the post-Newtonian geodetic equations characterizing the reference ellipsoid into the Taylor series with respect to the eccentricity of the ellipsoid, and discuss the small-eccentricity approximation. Finally, we introduce the concept of relativistic geoid and its undulation with respect to the reference ellipsoid, and discuss how to calculate it

Reference Ellipsoid and Geoid in Chronometric Geodesy

Energy Technology Data Exchange (ETDEWEB)

Kopeikin, Sergei M., E-mail: kopeikins@missouri.edu [Department of Physics and Astronomy, University of Missouri, Columbia, MO (United States); Department of Physical Geodesy and Remote Sensing, Siberian State University of Geosystems and Technologies, Novosibirsk (Russian Federation)

2016-02-25

Chronometric geodesy applies general relativity to study the problem of the shape of celestial bodies including the earth, and their gravitational field. The present paper discusses the relativistic problem of construction of a background geometric manifold that is used for describing a reference ellipsoid, geoid, the normal gravity field of the earth and for calculating geoid's undulation (height). We choose the perfect fluid with an ellipsoidal mass distribution uniformly rotating around a fixed axis as a source of matter generating the geometry of the background manifold through the Einstein equations. We formulate the post-Newtonian hydrodynamic equations of the rotating fluid to find out the set of algebraic equations defining the equipotential surface of the gravity field. In order to solve these equations we explicitly perform all integrals characterizing the interior gravitational potentials in terms of elementary functions depending on the parameters defining the shape of the body and the mass distribution. We employ the coordinate freedom of the equations to choose these parameters to make the shape of the rotating fluid configuration to be an ellipsoid of rotation. We derive expressions of the post-Newtonian mass and angular momentum of the rotating fluid as functions of the rotational velocity and the parameters of the ellipsoid including its bare density, eccentricity and semi-major axes. We formulate the post-Newtonian Pizzetti and Clairaut theorems that are used in geodesy to connect the parameters of the reference ellipsoid to the polar and equatorial values of force of gravity. We expand the post-Newtonian geodetic equations characterizing the reference ellipsoid into the Taylor series with respect to the eccentricity of the ellipsoid, and discuss the small-eccentricity approximation. Finally, we introduce the concept of relativistic geoid and its undulation with respect to the reference ellipsoid, and discuss how to calculate it in

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

Science.gov (United States)

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

2018-02-01

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

Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere.

Science.gov (United States)

Eyyuboğlu, Halil Tanyer

2005-08-01

Hermite-cosine-Gaussian (HcosG) laser beams are studied. The source plane intensity of the HcosG beam is introduced and its dependence on the source parameters is examined. By application of the Fresnel diffraction integral, the average receiver intensity of HcosG beam is formulated for the case of propagation in turbulent atmosphere. The average receiver intensity is seen to reduce appropriately to various special cases. When traveling in turbulence, the HcosG beam initially experiences the merging of neighboring beam lobes, and then a TEM-type cosh-Gaussian beam is formed, temporarily leading to a plain cosh-Gaussian beam. Eventually a pure Gaussian beam results. The numerical evaluation of the normalized beam size along the propagation axis at selected mode indices indicates that relative spreading of higher-order HcosG beam modes is less than that of the lower-order counterparts. Consequently, it is possible at some propagation distances to capture more power by using higher-mode-indexed HcosG beams.

Improved Expectation Maximization Algorithm for Gaussian Mixed Model Using the Kernel Method

Directory of Open Access Journals (Sweden)

Mohd Izhan Mohd Yusoff

2013-01-01

Full Text Available Fraud activities have contributed to heavy losses suffered by telecommunication companies. In this paper, we attempt to use Gaussian mixed model, which is a probabilistic model normally used in speech recognition to identify fraud calls in the telecommunication industry. We look at several issues encountered when calculating the maximum likelihood estimates of the Gaussian mixed model using an Expectation Maximization algorithm. Firstly, we look at a mechanism for the determination of the initial number of Gaussian components and the choice of the initial values of the algorithm using the kernel method. We show via simulation that the technique improves the performance of the algorithm. Secondly, we developed a procedure for determining the order of the Gaussian mixed model using the log-likelihood function and the Akaike information criteria. Finally, for illustration, we apply the improved algorithm to real telecommunication data. The modified method will pave the way to introduce a comprehensive method for detecting fraud calls in future work.

RISM theory distribution functions for Lennard--Jones interaction site fluids

International Nuclear Information System (INIS)

Johnson, E.; Hazoume, R.P.

1978-01-01

Reference interaction site model (RISM) theory distribution functions for Lennard-Jones interaction site fluids are discussed. The comparison with computer simulation results suggests that these distribution functions are as accurate as RISM distribution functions for fused hard sphere molecular fluids

Calculations of Sobol indices for the Gaussian process metamodel

Energy Technology Data Exchange (ETDEWEB)

Marrel, Amandine [CEA, DEN, DTN/SMTM/LMTE, F-13108 Saint Paul lez Durance (France)], E-mail: amandine.marrel@cea.fr; Iooss, Bertrand [CEA, DEN, DER/SESI/LCFR, F-13108 Saint Paul lez Durance (France); Laurent, Beatrice [Institut de Mathematiques, Universite de Toulouse (UMR 5219) (France); Roustant, Olivier [Ecole des Mines de Saint-Etienne (France)

2009-03-15

Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes. A well-known and widely used decision consists in replacing the computer code by a metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices. In this paper, we discuss about the Gaussian process model which gives analytical expressions of Sobol indices. Two approaches are studied to compute the Sobol indices: the first based on the predictor of the Gaussian process model and the second based on the global stochastic process model. Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness. Moreover, the second approach allows to integrate the modeling error of the Gaussian process model by directly giving some confidence intervals on the Sobol indices. These techniques are finally applied to a real case of hydrogeological modeling.

Calculations of Sobol indices for the Gaussian process metamodel

International Nuclear Information System (INIS)

Marrel, Amandine; Iooss, Bertrand; Laurent, Beatrice; Roustant, Olivier

2009-01-01

Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes. A well-known and widely used decision consists in replacing the computer code by a metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices. In this paper, we discuss about the Gaussian process model which gives analytical expressions of Sobol indices. Two approaches are studied to compute the Sobol indices: the first based on the predictor of the Gaussian process model and the second based on the global stochastic process model. Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness. Moreover, the second approach allows to integrate the modeling error of the Gaussian process model by directly giving some confidence intervals on the Sobol indices. These techniques are finally applied to a real case of hydrogeological modeling

An approximate fractional Gaussian noise model with computational cost

KAUST Repository

Sørbye, Sigrunn H.

2017-09-18

Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.

Blind signal processing algorithms under DC biased Gaussian noise

Science.gov (United States)

Kim, Namyong; Byun, Hyung-Gi; Lim, Jeong-Ok

2013-05-01

Distortions caused by the DC-biased laser input can be modeled as DC biased Gaussian noise and removing DC bias is important in the demodulation process of the electrical signal in most optical communications. In this paper, a new performance criterion and a related algorithm for unsupervised equalization are proposed for communication systems in the environment of channel distortions and DC biased Gaussian noise. The proposed criterion utilizes the Euclidean distance between the Dirac-delta function located at zero on the error axis and a probability density function of biased constant modulus errors, where constant modulus error is defined by the difference between the system out and a constant modulus calculated from the transmitted symbol points. From the results obtained from the simulation under channel models with fading and DC bias noise abruptly added to background Gaussian noise, the proposed algorithm converges rapidly even after the interruption of DC bias proving that the proposed criterion can be effectively applied to optical communication systems corrupted by channel distortions and DC bias noise.

Statistical nature of non-Gaussianity from cubic order primordial perturbations: CMB map simulations and genus statistic

International Nuclear Information System (INIS)

Chingangbam, Pravabati; Park, Changbom

2009-01-01

We simulate CMB maps including non-Gaussianity arising from cubic order perturbations of the primordial gravitational potential, characterized by the non-linearity parameter g NL . The maps are used to study the characteristic nature of the resulting non-Gaussian temperature fluctuations. We measure the genus and investigate how it deviates from Gaussian shape as a function of g NL and smoothing scale. We find that the deviation of the non-Gaussian genus curve from the Gaussian one has an antisymmetric, sine function like shape, implying more hot and more cold spots for g NL > 0 and less of both for g NL NL and also exhibits mild increase as the smoothing scale increases. We further study other statistics derived from the genus, namely, the number of hot spots, the number of cold spots, combined number of hot and cold spots and the slope of the genus curve at mean temperature fluctuation. We find that these observables carry signatures of g NL that are clearly distinct from the quadratic order perturbations, encoded in the parameter f NL . Hence they can be very useful tools for distinguishing not only between non-Gaussian temperature fluctuations and Gaussian ones but also between g NL and f NL type non-Gaussianities

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

Energy Technology Data Exchange (ETDEWEB)

Stein, Michael [Univ. of Chicago, IL (United States)

2017-03-13

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

Non-Gaussianities in multifield DBI inflation with a waterfall phase transition

Science.gov (United States)

Kidani, Taichi; Koyama, Kazuya; Mizuno, Shuntaro

2012-10-01

We study multifield Dirac-Born-Infeld (DBI) inflation models with a waterfall phase transition. This transition happens for a D3 brane moving in the warped conifold if there is an instability along angular directions. The transition converts the angular perturbations into the curvature perturbation. Thanks to this conversion, multifield models can evade the stringent constraints that strongly disfavor single field ultraviolet (UV) DBI inflation models in string theory. We explicitly demonstrate that our model satisfies current observational constraints on the spectral index and equilateral non-Gaussianity as well as the bound on the tensor to scalar ratio imposed in string theory models. In addition, we show that large local type non-Gaussianity is generated together with equilateral non-Gaussianity in this model.

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

Science.gov (United States)

Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

2016-09-01

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

A Note on Functional Averages over Gaussian Ensembles

Directory of Open Access Journals (Sweden)

Gabriel H. Tucci

2013-01-01

Full Text Available We find a new formula for matrix averages over the Gaussian ensemble. Let H be an n×n Gaussian random matrix with complex, independent, and identically distributed entries of zero mean and unit variance. Given an n×n positive definite matrix A and a continuous function f:ℝ+→ℝ such that ∫0∞‍e-αt|f(t|2dt0, we find a new formula for the expectation [Tr(f(HAH*]. Taking f(x=log(1+x gives another formula for the capacity of the MIMO communication channel, and taking f(x=(1+x-1 gives the MMSE achieved by a linear receiver.

Pseudo inputs for pairwise learning with Gaussian processes

DEFF Research Database (Denmark)

Nielsen, Jens Brehm; Jensen, Bjørn Sand; Larsen, Jan

2012-01-01

We consider learning and prediction of pairwise comparisons between instances. The problem is motivated from a perceptual view point, where pairwise comparisons serve as an effective and extensively used paradigm. A state-of-the-art method for modeling pairwise data in high dimensional domains...... is based on a classical pairwise probit likelihood imposed with a Gaussian process prior. While extremely flexible, this non-parametric method struggles with an inconvenient O(n3) scaling in terms of the n input instances which limits the method only to smaller problems. To overcome this, we derive...... to other similar approximations that have been applied in standard Gaussian process regression and classification problems such as FI(T)C and PI(T)C....

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

Science.gov (United States)

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

2017-04-01

Much of the stochastic groundwater literature is devoted to the analysis of flow and transport in Gaussian or multi-Gaussian log hydraulic conductivity (or transmissivity) fields, Y(x)=ln\\func K(x) (x being a position vector), characterized by one or (less frequently) a multiplicity of spatial correlation scales. Yet Y and many other variables and their (spatial or temporal) increments, ΔY, are known to be generally non-Gaussian. One common manifestation of non-Gaussianity is that whereas frequency distributions of Y often exhibit mild peaks and light tails, those of increments ΔY are generally symmetric with peaks that grow sharper, and tails that become heavier, as separation scale or lag between pairs of Y values decreases. A statistical model that captures these disparate, scale-dependent distributions of Y and ΔY in a unified and consistent manner has been recently proposed by us. This new "generalized sub-Gaussian (GSG)" model has the form Y(x)=U(x)G(x) where G(x) is (generally, but not necessarily) a multiscale Gaussian random field and U(x) is a nonnegative subordinator independent of G. The purpose of this paper is to explore analytically, in an elementary manner, lead-order effects that non-Gaussian heterogeneity described by the GSG model have on the stochastic description of flow and transport. Recognizing that perturbation expansion of hydraulic conductivity K=eY diverges when Y is sub-Gaussian, we render the expansion convergent by truncating Y's domain of definition. We then demonstrate theoretically and illustrate by way of numerical examples that, as the domain of truncation expands, (a) the variance of truncated Y (denoted by Yt) approaches that of Y and (b) the pdf (and thereby moments) of Yt increments approach those of Y increments and, as a consequence, the variogram of Yt approaches that of Y. This in turn guarantees that perturbing Kt=etY to second order in σYt (the standard deviation of Yt) yields results which approach those we obtain

Productive interactions: heavy particles and non-Gaussianity

International Nuclear Information System (INIS)

Flauger, Raphael; Mirbabayi, Mehrdad; Senatore, Leonardo; Silverstein, Eva

2017-01-01

We analyze the shape and amplitude of oscillatory features in the primordial power spectrum and non-Gaussianity induced by periodic production of heavy degrees of freedom coupled to the inflaton φ. We find that non-adiabatic production of particles can contribute effects which are detectable or constrainable using cosmological data even if their time-dependent masses are always heavier than the scale φ̇ 1/2 , much larger than the Hubble scale. This provides a new role for UV completion, consistent with the criteria from effective field theory for when heavy fields cannot be integrated out. This analysis is motivated in part by the structure of axion monodromy, and leads to an additional oscillatory signature in a subset of its parameter space. At the level of a quantum field theory model that we analyze in detail, the effect arises consistently with radiative stability for an interesting window of couplings up to of order ∼< 1. The amplitude of the bispectrum and higher-point functions can be larger than that for Resonant Non-Gaussianity, and its signal/noise may be comparable to that of the corresponding oscillations in the power spectrum (and even somewhat larger within a controlled regime of parameters). Its shape is distinct from previously analyzed templates, but was partly motivated by the oscillatory equilateral searches performed recently by the Planck collaboration. We also make some general comments about the challenges involved in making a systematic study of primordial non-Gaussianity.

Productive interactions: heavy particles and non-Gaussianity

Energy Technology Data Exchange (ETDEWEB)

Flauger, Raphael [Department of Physics, The University of Texas at Austin, Austin, TX, 78712 (United States); Mirbabayi, Mehrdad [Institute for Advanced Study, Princeton, NJ 08540 (United States); Senatore, Leonardo; Silverstein, Eva, E-mail: flauger@physics.ucsd.edu, E-mail: mehrdadm@ias.edu, E-mail: senatore@stanford.edu, E-mail: evas@slac.stanford.edu [Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305 (United States)

2017-10-01

We analyze the shape and amplitude of oscillatory features in the primordial power spectrum and non-Gaussianity induced by periodic production of heavy degrees of freedom coupled to the inflaton φ. We find that non-adiabatic production of particles can contribute effects which are detectable or constrainable using cosmological data even if their time-dependent masses are always heavier than the scale φ̇{sup 1/2}, much larger than the Hubble scale. This provides a new role for UV completion, consistent with the criteria from effective field theory for when heavy fields cannot be integrated out. This analysis is motivated in part by the structure of axion monodromy, and leads to an additional oscillatory signature in a subset of its parameter space. At the level of a quantum field theory model that we analyze in detail, the effect arises consistently with radiative stability for an interesting window of couplings up to of order ∼< 1. The amplitude of the bispectrum and higher-point functions can be larger than that for Resonant Non-Gaussianity, and its signal/noise may be comparable to that of the corresponding oscillations in the power spectrum (and even somewhat larger within a controlled regime of parameters). Its shape is distinct from previously analyzed templates, but was partly motivated by the oscillatory equilateral searches performed recently by the Planck collaboration. We also make some general comments about the challenges involved in making a systematic study of primordial non-Gaussianity.

Thermodynamic properties of cryogenic fluids

CERN Document Server

Leachman, Jacob; Lemmon, Eric; Penoncello, Steven

2017-01-01

This update to a classic reference text provides practising engineers and scientists with accurate thermophysical property data for cryogenic fluids. The equations for fifteen important cryogenic fluids are presented in a basic format, accompanied by pressure-enthalpy and temperature-entropy charts and tables of thermodynamic properties. It begins with a chapter introducing the thermodynamic relations and functional forms for equations of state, and goes on to describe the requirements for thermodynamic property formulations, needed for the complete definition of the thermodynamic properties of a fluid. The core of the book comprises extensive data tables and charts for the most commonly-encountered cryogenic fluids. This new edition sees significant updates to the data presented for air, argon, carbon monoxide, deuterium, ethane, helium, hydrogen, krypton, nitrogen and xenon. The book supports and complements NIST’s REFPROP - an interactive database and tool for the calculation of thermodynamic propertie...

Evolution of super-Gaussian pulses in a nonlinear optical fiber

Science.gov (United States)

Bugay, Aleksandr N.; Khalyapin, Vyacheslav A.

2018-04-01

An analytic and numerical study is carried out of the dynamics of parameters of a super-Gaussian pulse whose spectrum can fit both in the region of normal and anomalous dispersion of the group velocity. An analytical solution is found for the parameter characterizing the evolution of the degree of the super-Gaussian momentum. The loss of profile rectangularity is shown to be much faster than the pulse dispersion broadening, and corresponding characteristic length is determined by explicit formula.

Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

Science.gov (United States)

Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

2016-06-27

We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

A non-Gaussian approach to risk measures

Science.gov (United States)

Bormetti, Giacomo; Cisana, Enrica; Montagna, Guido; Nicrosini, Oreste

2007-03-01

Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modelling the power-law tails of the returns distribution in terms of a Student- t distribution. Non-Gaussian closed-form solutions for value-at-risk and expected shortfall are obtained and standard formulae known in the literature under the normality assumption are recovered as a special case. The implications of the approach for risk management are demonstrated through an empirical analysis of financial time series from the Italian stock market and in comparison with the results of the most widely used procedures of quantitative finance. Particular attention is paid to quantify the size of the errors affecting the market risk measures obtained according to different methodologies, by employing a bootstrap technique.

Teleportation of squeezing: Optimization using non-Gaussian resources

International Nuclear Information System (INIS)

Dell'Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio; Adesso, Gerardo

2010-01-01

We study the continuous-variable quantum teleportation of states, statistical moments of observables, and scale parameters such as squeezing. We investigate the problem both in ideal and imperfect Vaidman-Braunstein-Kimble protocol setups. We show how the teleportation fidelity is maximized and the difference between output and input variances is minimized by using suitably optimized entangled resources. Specifically, we consider the teleportation of coherent squeezed states, exploiting squeezed Bell states as entangled resources. This class of non-Gaussian states, introduced by Illuminati and co-workers [F. Dell'Anno, S. De Siena, L. Albano, and F. Illuminati, Phys. Rev. A 76, 022301 (2007); F. Dell'Anno, S. De Siena, and F. Illuminati, ibid. 81, 012333 (2010)], includes photon-added and photon-subtracted squeezed states as special cases. At variance with the case of entangled Gaussian resources, the use of entangled non-Gaussian squeezed Bell resources allows one to choose different optimization procedures that lead to inequivalent results. Performing two independent optimization procedures, one can either maximize the state teleportation fidelity, or minimize the difference between input and output quadrature variances. The two different procedures are compared depending on the degrees of displacement and squeezing of the input states and on the working conditions in ideal and nonideal setups.

Reconstruction of electrons with the Gaussian-sum filter in the CMS tracker at the LHC

International Nuclear Information System (INIS)

Adam, W; Fruehwirth, R; Strandlie, A; Todorov, T

2005-01-01

The bremsstrahlung energy loss distribution of electrons propagating in matter is highly non-Gaussian. Because the Kalman filter relies solely on Gaussian probability density functions, it is not necessarily the optimal reconstruction algorithm for electron tracks. A Gaussian-sum filter (GSF) algorithm for electron reconstruction in the CMS tracker has therefore been developed and implemented. The basic idea is to model the bremsstrahlung energy loss distribution by a Gaussian mixture rather than by a single Gaussian. It is shown that the GSF is able to improve the momentum resolution of electrons compared to the standard Kalman filter. The momentum resolution and the quality of the error estimate are studied both with a fast simulation, modelling the radiative energy loss in a simplified detector, and the full CMS tracker simulation. (research note from collaboration)

Reconstruction of Electrons with the Gaussian-Sum Filter in the CMS Tracker at the LHC

CERN Document Server

Adam, Wolfgang; Strandlie, Are; Todor, T

2005-01-01

The bremsstrahlung energy loss distribution of electrons propagating in matter is highly non-Gaussian. Because the Kalman filter relies solely on Gaussian probability density functions, it is not necessarily the optimal reconstruction algorithm for electron tracks. A Gaussian-sum filter (GSF) algorithm for electron reconstruction in the CMS tracker has therefore been developed and implemented. The basic idea is to model the bremsstrahlung energy loss distribution by a Gaussian mixture rather than by a single Gaussian. It is shown that the GSF is able to improve the momentum resolution of electrons compared to the standard Kalman filter. The momentum resolution and the quality of he error estimate are studied both with a fast simulation, modelling the radiative energy loss in a simplified detector, and the full CMS tracker simulation.

Hybrid algorithm of ensemble transform and importance sampling for assimilation of non-Gaussian observations

Directory of Open Access Journals (Sweden)

Shin'ya Nakano

2014-05-01

Full Text Available A hybrid algorithm that combines the ensemble transform Kalman filter (ETKF and the importance sampling approach is proposed. Since the ETKF assumes a linear Gaussian observation model, the estimate obtained by the ETKF can be biased in cases with nonlinear or non-Gaussian observations. The particle filter (PF is based on the importance sampling technique, and is applicable to problems with nonlinear or non-Gaussian observations. However, the PF usually requires an unrealistically large sample size in order to achieve a good estimation, and thus it is computationally prohibitive. In the proposed hybrid algorithm, we obtain a proposal distribution similar to the posterior distribution by using the ETKF. A large number of samples are then drawn from the proposal distribution, and these samples are weighted to approximate the posterior distribution according to the importance sampling principle. Since the importance sampling provides an estimate of the probability density function (PDF without assuming linearity or Gaussianity, we can resolve the bias due to the nonlinear or non-Gaussian observations. Finally, in the next forecast step, we reduce the sample size to achieve computational efficiency based on the Gaussian assumption, while we use a relatively large number of samples in the importance sampling in order to consider the non-Gaussian features of the posterior PDF. The use of the ETKF is also beneficial in terms of the computational simplicity of generating a number of random samples from the proposal distribution and in weighting each of the samples. The proposed algorithm is not necessarily effective in case that the ensemble is located distant from the true state. However, monitoring the effective sample size and tuning the factor for covariance inflation could resolve this problem. In this paper, the proposed hybrid algorithm is introduced and its performance is evaluated through experiments with non-Gaussian observations.

Gaussian curvature on hyperelliptic Riemann surfaces

Indian Academy of Sciences (India)

Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 2, May 2014, pp. 155–167. c Indian Academy of Sciences. Gaussian curvature on hyperelliptic Riemann surfaces. ABEL CASTORENA. Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México,. Campus Morelia) Apdo. Postal 61-3 Xangari, C.P. 58089 Morelia,.

Discretisation Schemes for Level Sets of Planar Gaussian Fields

Science.gov (United States)

Beliaev, D.; Muirhead, S.

2018-01-01

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

Computational fluid dynamics incompressible turbulent flows

CERN Document Server

Kajishima, Takeo

2017-01-01

This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications. • Introduces CFD techniques for incompressible flow and turbulence with a comprehensive approach; • Enr...

Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels

International Nuclear Information System (INIS)

Monras, Alex; Illuminati, Fabrizio

2011-01-01

We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than coherent, thermal, or single-mode squeezed states. This suggests that at high-energy regimes, two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result indicates a stronger form of compatibility for the estimation of the two parameters. Indeed, not only the minimum variance can be achieved at fixed probe states, but also the optimal state is common to both parameters. Additionally, we explore numerically the performance of non-Gaussian states for particular parameter values to find that maximally entangled states within d-dimensional cutoff subspaces (d≤6) perform better than any randomly sampled states with similar energy. However, we also find that states with very similar performance and energy exist with much less entanglement than the maximally entangled ones.

Gaussian solitary waves for the logarithmic-KdV and the logarithmic-KP equations

International Nuclear Information System (INIS)

Wazwaz, Abdul-Majid

2014-01-01

We investigate the logarithmic-KdV equation for more Gaussian solitary waves. We extend this work to derive the logarithmic-KP (Kadomtsev–Petviashvili) equation. We show that both logarithmic models are characterized by their Gaussian solitons. (paper)

Color Texture Segmentation by Decomposition of Gaussian Mixture Model

Czech Academy of Sciences Publication Activity Database

Grim, Jiří; Somol, Petr; Haindl, Michal; Pudil, Pavel

2006-01-01

Roč. 19, č. 4225 (2006), s. 287-296 ISSN 0302-9743. [Iberoamerican Congress on Pattern Recognition. CIARP 2006 /11./. Cancun, 14.11.2006-17.11.2006] R&D Projects: GA AV ČR 1ET400750407; GA MŠk 1M0572; GA MŠk 2C06019 EU Projects: European Commission(XE) 507752 - MUSCLE Institutional research plan: CEZ:AV0Z10750506 Keywords : texture segmentation * gaussian mixture model * EM algorithm Subject RIV: IN - Informatics, Computer Science Impact factor: 0.402, year: 2005 http://library.utia.cas.cz/separaty/historie/grim-color texture segmentation by decomposition of gaussian mixture model.pdf

An optical tweezer in asymmetrical vortex Bessel-Gaussian beams

Energy Technology Data Exchange (ETDEWEB)

Kotlyar, V. V.; Kovalev, A. A., E-mail: alexeysmr@mail.ru; Porfirev, A. P. [Image Processing Systems Institute, 151 Molodogvardeiskaya St., 443001 Samara (Russian Federation); Department of Technical cybernetics, Samara State Aerospace University, Samara 443086 (Russian Federation)

2016-07-14

We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.

Non-Gaussianities due to relativistic corrections to the observed galaxy bispectrum

International Nuclear Information System (INIS)

Dio, E. Di; Perrier, H.; Durrer, R.; Dizgah, A. Moradinezhad; Riotto, A.; Marozzi, G.; Noreña, J.

2017-01-01

High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for relativistic corrections to the clustering statistics is particularly important for the upcoming galaxy surveys covering progressively larger fraction of the sky. We focus on relativistic projection effects due to the fact that we observe the galaxies through the light that reaches the telescope on perturbed geodesics. These projection effects can give rise to an effective f NL that can be misinterpreted as the primordial non-Gaussianity signal and hence is a systematic to be carefully computed and accounted for in modelling of the bispectrum. We develop the technique to properly account for relativistic effects in terms of purely observable quantities, namely angles and redshifts. We give some examples by applying this approach to a subset of the contributions to the tree-level bispectrum of the observed galaxy number counts calculated within perturbation theory and estimate the corresponding non-Gaussianity parameter, f NL , for the local, equilateral and orthogonal shapes. For the local shape, we also compute the local non-Gaussianity resulting from terms obtained using the consistency relation for observed number counts. Our goal here is not to give a precise estimate of f NL for each shape but rather we aim to provide a scheme to compute the non-Gaussian contamination due to relativistic projection effects. For the terms considered in this work, we obtain contamination of f NL loc ∼ O(1).

Validity of the assumption of Gaussian turbulence; Gyldighed af antagelsen om Gaussisk turbulence

Energy Technology Data Exchange (ETDEWEB)

Nielsen, M.; Hansen, K.S.; Juul Pedersen, B.

2000-07-01

Wind turbines are designed to withstand the impact of turbulent winds, which fluctuations usually are assumed of Gaussian probability distribution. Based on a large number of measurements from many sites, this seems a reasonable assumption in flat homogeneous terrain whereas it may fail in complex terrain. At these sites the wind speed often has a skew distribution with more frequent lulls than gusts. In order to simulate aerodynamic loads, a numerical turbulence simulation method was developed and implemented. This method may simulate multiple time series of variable not necessarily Gaussian distribution without distortion of the spectral distribution or spatial coherence. The simulated time series were used as input to the dynamic-response simulation program Vestas Turbine Simulator (VTS). In this way we simulated the dynamic response of systems exposed to turbulence of either Gaussian or extreme, yet realistic, non-Gaussian probability distribution. Certain loads on turbines with active pitch regulation were enhanced by up to 15% compared to pure Gaussian turbulence. It should, however, be said that the undesired effect depends on the dynamic system, and it might be mitigated by optimisation of the wind turbine regulation system after local turbulence characteristics. (au)

Analytical performance specifications for changes in assay bias (Δbias) for data with logarithmic distributions as assessed by effects on reference change values

DEFF Research Database (Denmark)

Hyltoft Petersen, Per; Lund, Flemming; Fraser, Callum G

2016-01-01

BACKGROUND: The distributions of within-subject biological variation are usually described as coefficients of variation, as are analytical performance specifications for bias, imprecision and other characteristics. Estimation of specifications required for reference change values is traditionally...... done using relationship between the batch-related changes during routine performance, described as Δbias, and the coefficients of variation for analytical imprecision (CVA): the original theory is based on standard deviations or coefficients of variation calculated as if distributions were Gaussian....... METHODS: The distribution of between-subject biological variation can generally be described as log-Gaussian. Moreover, recent analyses of within-subject biological variation suggest that many measurands have log-Gaussian distributions. In consequence, we generated a model for the estimation of analytical...

Sensitivity and specificity of normality tests and consequences on reference interval accuracy at small sample size: a computer-simulation study.

Science.gov (United States)

Le Boedec, Kevin

2016-12-01

According to international guidelines, parametric methods must be chosen for RI construction when the sample size is small and the distribution is Gaussian. However, normality tests may not be accurate at small sample size. The purpose of the study was to evaluate normality test performance to properly identify samples extracted from a Gaussian population at small sample sizes, and assess the consequences on RI accuracy of applying parametric methods to samples that falsely identified the parent population as Gaussian. Samples of n = 60 and n = 30 values were randomly selected 100 times from simulated Gaussian, lognormal, and asymmetric populations of 10,000 values. The sensitivity and specificity of 4 normality tests were compared. Reference intervals were calculated using 6 different statistical methods from samples that falsely identified the parent population as Gaussian, and their accuracy was compared. Shapiro-Wilk and D'Agostino-Pearson tests were the best performing normality tests. However, their specificity was poor at sample size n = 30 (specificity for P Box-Cox transformation) on all samples regardless of their distribution or adjusting, the significance level of normality tests depending on sample size would limit the risk of constructing inaccurate RI. © 2016 American Society for Veterinary Clinical Pathology.

Generation of Laguerre-Gaussian Beams Using a Diode Pumped Solid-State Digital Laser

CSIR Research Space (South Africa)

Bell, Teboho

2015-10-01

Full Text Available The solid state digital laser was used in generation of Laguerre-Gaussian modes, LGpl, of different orders. This work demonstrates that we can generate high-order Laguerre-Gaussian modes with high purity using a digital laser....

Simple approximation for estimating centerline gamma absorbed dose rates due to a continuous Gaussian plume

International Nuclear Information System (INIS)

Overcamp, T.J.; Fjeld, R.A.

1987-01-01

A simple approximation for estimating the centerline gamma absorbed dose rates due to a continuous Gaussian plume was developed. To simplify the integration of the dose integral, this approach makes use of the Gaussian cloud concentration distribution. The solution is expressed in terms of the I1 and I2 integrals which were developed for estimating long-term dose due to a sector-averaged Gaussian plume. Estimates of tissue absorbed dose rates for the new approach and for the uniform cloud model were compared to numerical integration of the dose integral over a Gaussian plume distribution

The 1H NMR profile of healthy dog cerebrospinal fluid.

Directory of Open Access Journals (Sweden)

Mihai Musteata

Full Text Available The availability of data for reference values in cerebrospinal fluid for healthy humans is limited due to obvious practical and ethical issues. The variability of reported values for metabolites in human cerebrospinal fluid is quite large. Dogs present great similarities with humans, including in cases of central nervous system pathologies. The paper presents the first study on healthy dog cerebrospinal fluid metabolomic profile using (1H NMR spectroscopy. A number of 13 metabolites have been identified and quantified from cerebrospinal fluid collected from a group of 10 mix breed healthy dogs. The biological variability as resulting from the relative standard deviation of the physiological concentrations of the identified metabolites had a mean of 18.20% (range between 9.3% and 44.8%. The reported concentrations for metabolites may be used as normal reference values. The homogeneity of the obtained results and the low biologic variability show that the (1H NMR analysis of the dog's cerebrospinal fluid is reliable in designing and interpreting clinical and therapeutic trials in dogs with central nervous system pathologies.

Dynamics of Gaussian Wigner functions derived from a time-dependent variational principle

Directory of Open Access Journals (Sweden)

Jens Aage Poulsen

2017-11-01

Full Text Available By using a time-dependent variational principle formulated for Wigner phase-space functions, we obtain the optimal time-evolution for two classes of Gaussian Wigner functions, namely those of either thawed real-valued or frozen but complex Gaussians. It is shown that tunneling effects are approximately included in both schemes.

Gaussian elimination in split unitary groups with an application to public-key cryptography

Directory of Open Access Journals (Sweden)

Ayan Mahalanobis

2017-07-01

Full Text Available Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to split unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate that.

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

Science.gov (United States)

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

2017-08-01

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

Generation of correlated finite alphabet waveforms using gaussian random variables

KAUST Repository

Ahmed, Sajid

2016-01-13

Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.

Gaussian variable neighborhood search for the file transfer scheduling problem

Directory of Open Access Journals (Sweden)

Dražić Zorica

2016-01-01

Full Text Available This paper presents new modifications of Variable Neighborhood Search approach for solving the file transfer scheduling problem. To obtain better solutions in a small neighborhood of a current solution, we implement two new local search procedures. As Gaussian Variable Neighborhood Search showed promising results when solving continuous optimization problems, its implementation in solving the discrete file transfer scheduling problem is also presented. In order to apply this continuous optimization method to solve the discrete problem, mapping of uncountable set of feasible solutions into a finite set is performed. Both local search modifications gave better results for the large size instances, as well as better average performance for medium and large size instances. One local search modification achieved significant acceleration of the algorithm. The numerical experiments showed that the results obtained by Gaussian modifications are comparable with the results obtained by standard VNS based algorithms, developed for combinatorial optimization. In some cases Gaussian modifications gave even better results. [Projekat Ministarstava nauke Republike Srbije, br. 174010

Generation of correlated finite alphabet waveforms using gaussian random variables

KAUST Repository

Ahmed, Sajid; Alouini, Mohamed-Slim; Jardak, Seifallah

2016-01-01

Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.

Application of Gaussian cubature to model two-dimensional population balances

Directory of Open Access Journals (Sweden)

Bałdyga Jerzy

2017-09-01

Full Text Available In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations.

Weighted Feature Gaussian Kernel SVM for Emotion Recognition.

Science.gov (United States)

Wei, Wei; 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.

Non-Markovianity of Gaussian Channels.

Science.gov (United States)

Torre, G; Roga, W; Illuminati, F

2015-08-14

We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.

Fluid flow distribution optimization for minimizing the peak temperature of a tubular solar receiver

International Nuclear Information System (INIS)

Wei, Min; Fan, Yilin; Luo, Lingai; Flamant, Gilles

2015-01-01

High temperature solar receiver is a core component of solar thermal power plants. However, non-uniform solar irradiation on the receiver walls and flow maldistribution of heat transfer fluid inside the tubes may cause the excessive peak temperature, consequently leading to the reduced lifetime. This paper presents an original CFD (computational fluid dynamics)-based evolutionary algorithm to determine the optimal fluid distribution in a tubular solar receiver for the minimization of its peak temperature. A pressurized-air solar receiver comprising of 45 parallel tubes subjected to a Gaussian-shape net heat flux absorbed by the receiver is used for study. Two optimality criteria are used for the algorithm: identical outlet fluid temperatures and identical temperatures on the centerline of the heated surface. The influences of different filling materials and thermal contact resistances on the optimal fluid distribution and on the peak temperature reduction are also evaluated and discussed. Results show that the fluid distribution optimization using the algorithm could minimize the peak temperature of the receiver under the optimality criterion of identical temperatures on the centerline. Different shapes of optimal fluid distribution are determined for various filling materials. Cheap material with low thermal conductivity can also meet the peak temperature threshold through optimizing the fluid distribution. - Highlights: • A 3D pressurized-air solar receiver based on the tube-in-matrix concept is studied. • An original evolutionary algorithm is developed for fluid distribution optimization. • A new optimality criterion is proposed for minimizing the receiver peak temperature. • Different optimal fluid distributions are determined for various filling materials. • Filling material with high thermal conductivity is more favorable in practical use.

Gaussian shaping filter for nuclear spectrometry

International Nuclear Information System (INIS)

Menezes, A.S.C. de.

1980-01-01

A theorical study of a gaussian shaping filter, using Pade approximation, for using in gamma spectroscopy is presented. This approximation has proved superior to the classical cascade RC integrators approximation in therms of signal-to-noise ratio and pulse simmetry. An experimental filter was designed, simulated in computer, constructed, and tested in the laboratory. (author) [pt

Additivity properties of a Gaussian channel

International Nuclear Information System (INIS)

Giovannetti, Vittorio; Lloyd, Seth

2004-01-01

The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Renyi entropies at the output of a channel. The conjecture is proven true for all Renyi entropies of integer order greater than two in a class of Gaussian bosonic channel where the input signal is randomly displaced or where it is coupled linearly to an external environment

Interweave Cognitive Radio with Improper Gaussian Signaling

KAUST Repository

Hedhly, Wafa

2018-01-15

Improper Gaussian signaling (IGS) has proven its ability in improving the performance of underlay and overlay cognitive radio paradigms. In this paper, the interweave cognitive radio paradigm is studied when the cognitive user employs IGS. The instantaneous achievable rate performance of both the primary and secondary users are analyzed for specific secondary user sensing and detection capabilities. Next, the IGS scheme is optimized to maximize the achievable rate secondary user while satisfying a target minimum rate requirement for the primary user. Proper Gaussian signaling (PGS) scheme design is also derived to be used as benchmark of the IGS scheme design. Finally, different numerical results are introduced to show the gain reaped from adopting IGS over PGS under different system parameters. The main advantage of employing IGS is observed at low sensing and detection capabilities of the SU, lower PU direct link and higher SU interference on the PU side.

Perturbative corrections for approximate inference in gaussian latent variable models

DEFF Research Database (Denmark)

Opper, Manfred; Paquet, Ulrich; Winther, Ole

2013-01-01

Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact b...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....

Enhancement of force patterns classification based on Gaussian distributions.

Science.gov (United States)

Ertelt, Thomas; Solomonovs, Ilja; Gronwald, Thomas

2018-01-23

Description of the patterns of ground reaction force is a standard method in areas such as medicine, biomechanics and robotics. The fundamental parameter is the time course of the force, which is classified visually in particular in the field of clinical diagnostics. Here, the knowledge and experience of the diagnostician is relevant for its assessment. For an objective and valid discrimination of the ground reaction force pattern, a generic method, especially in the medical field, is absolutely necessary to describe the qualities of the time-course. The aim of the presented method was to combine the approaches of two existing procedures from the fields of machine learning and the Gauss approximation in order to take advantages of both methods for the classification of ground reaction force patterns. The current limitations of both methods could be eliminated by an overarching method. Twenty-nine male athletes from different sports were examined. Each participant was given the task of performing a one-legged stopping maneuver on a force plate from the maximum possible starting speed. The individual time course of the ground reaction force of each subject was registered and approximated on the basis of eight Gaussian distributions. The descriptive coefficients were then classified using Bayesian regulated neural networks. The different sports served as the distinguishing feature. Although the athletes were all given the same task, all sports referred to a different quality in the time course of ground reaction force. Meanwhile within each sport, the athletes were homogeneous. With an overall prediction (R = 0.938) all subjects/sports were classified correctly with 94.29% accuracy. The combination of the two methods: the mathematical description of the time course of ground reaction forces on the basis of Gaussian distributions and their classification by means of Bayesian regulated neural networks, seems an adequate and promising method to discriminate the

Topology optimization of fluid mechanics problems

DEFF Research Database (Denmark)

Gersborg-Hansen, Allan

While topology optimization for solid continuum structures have been studied for about 20 years and for the special case of trusses for many more years, topology optimization of fluid mechanics problems is more recent. Borrvall and Petersson [1] is the seminal reference for topology optimization......D Navier-Stokes equation as well as an example with convection dominated transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the present work gives a proof-of-concept for the application of the method within fluid mechanics problems and it remains...... processing tool. Prior to design manufacturing this allows the engineer to quantify the performance of the computed topology design using standard, credible analysis tools with a body-fitted mesh. [1] Borrvall and Petersson (2003) "Topology optimization of fluids in Stokes flow", Int. J. Num. Meth. Fluids...

Quantifying the non-Gaussianity in the EoR 21-cm signal through bispectrum

Science.gov (United States)

Majumdar, Suman; Pritchard, Jonathan R.; Mondal, Rajesh; Watkinson, Catherine A.; Bharadwaj, Somnath; Mellema, Garrelt

2018-05-01

The epoch of reionization (EoR) 21-cm signal is expected to be highly non-Gaussian in nature and this non-Gaussianity is also expected to evolve with the progressing state of reionization. Therefore the signal will be correlated between different Fourier modes (k). The power spectrum will not be able capture this correlation in the signal. We use a higher order estimator - the bispectrum - to quantify this evolving non-Gaussianity. We study the bispectrum using an ensemble of simulated 21-cm signal and with a large variety of k triangles. We observe two competing sources driving the non-Gaussianity in the signal: fluctuations in the neutral fraction (x_{H I}) field and fluctuations in the matter density field. We find that the non-Gaussian contribution from these two sources varies, depending on the stage of reionization and on which k modes are being studied. We show that the sign of the bispectrum works as a unique marker to identify which among these two components is driving the non-Gaussianity. We propose that the sign change in the bispectrum, when plotted as a function of triangle configuration cos θ and at a certain stage of the EoR can be used as a confirmative test for the detection of the 21-cm signal. We also propose a new consolidated way to visualize the signal evolution (with evolving \\bar{x}_{H I} or redshift), through the trajectories of the signal in a power spectrum and equilateral bispectrum i.e. P(k) - B(k, k, k) space.

Lifting Primordial Non-Gaussianity Above the Noise

NARCIS (Netherlands)

Welling, Yvette; Woude, Drian van der; Pajer, Enrico

2016-01-01

Primordial non-Gaussianity (PNG) in Large Scale Structures is obfuscated by the many additional sources of non-linearity. Within the Effective Field Theory approach to Standard Perturbation Theory, we show that matter non-linearities in the bispectrum can be modeled sufficiently well to strengthen

Non-Gaussianities due to relativistic corrections to the observed galaxy bispectrum

Energy Technology Data Exchange (ETDEWEB)

Dio, E. Di [INAF—Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, I-34143 Italy (Italy); Perrier, H.; Durrer, R.; Dizgah, A. Moradinezhad; Riotto, A. [University of Geneva, Department of Theoretical Physics and Center for Astroparticle Physics (CAP), 24 quai E. Ansermet, Geneva 4, CH-1211 Switzerland (Switzerland); Marozzi, G. [Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Urca, Rio de Janeiro, CEP 22290-180 Brazil (Brazil); Noreña, J., E-mail: Enea.DiDio@oats.inaf.it, E-mail: Hideki.Perrier@unige.ch, E-mail: Ruth.Durrer@unige.ch, E-mail: Marozzi@cbpf.br, E-mail: amoradinejad@physics.harvard.edu, E-mail: jorge.norena@pucv.cl, E-mail: Antonio.Riotto@unige.ch [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla, Valparaíso, 4059 Chile (Chile)

2017-03-01

High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for relativistic corrections to the clustering statistics is particularly important for the upcoming galaxy surveys covering progressively larger fraction of the sky. We focus on relativistic projection effects due to the fact that we observe the galaxies through the light that reaches the telescope on perturbed geodesics. These projection effects can give rise to an effective f {sub NL} that can be misinterpreted as the primordial non-Gaussianity signal and hence is a systematic to be carefully computed and accounted for in modelling of the bispectrum. We develop the technique to properly account for relativistic effects in terms of purely observable quantities, namely angles and redshifts. We give some examples by applying this approach to a subset of the contributions to the tree-level bispectrum of the observed galaxy number counts calculated within perturbation theory and estimate the corresponding non-Gaussianity parameter, f {sub NL}, for the local, equilateral and orthogonal shapes. For the local shape, we also compute the local non-Gaussianity resulting from terms obtained using the consistency relation for observed number counts. Our goal here is not to give a precise estimate of f {sub NL} for each shape but rather we aim to provide a scheme to compute the non-Gaussian contamination due to relativistic projection effects. For the terms considered in this work, we obtain contamination of f {sub NL}{sup loc} ∼ O(1).

Epileptic Seizure Detection with Log-Euclidean Gaussian Kernel-Based Sparse Representation.

Science.gov (United States)

Yuan, Shasha; Zhou, Weidong; Wu, Qi; Zhang, Yanli

2016-05-01

Epileptic seizure detection plays an important role in the diagnosis of epilepsy and reducing the massive workload of reviewing electroencephalography (EEG) recordings. In this work, a novel algorithm is developed to detect seizures employing log-Euclidean Gaussian kernel-based sparse representation (SR) in long-term EEG recordings. Unlike the traditional SR for vector data in Euclidean space, the log-Euclidean Gaussian kernel-based SR framework is proposed for seizure detection in the space of the symmetric positive definite (SPD) matrices, which form a Riemannian manifold. Since the Riemannian manifold is nonlinear, the log-Euclidean Gaussian kernel function is applied to embed it into a reproducing kernel Hilbert space (RKHS) for performing SR. The EEG signals of all channels are divided into epochs and the SPD matrices representing EEG epochs are generated by covariance descriptors. Then, the testing samples are sparsely coded over the dictionary composed by training samples utilizing log-Euclidean Gaussian kernel-based SR. The classification of testing samples is achieved by computing the minimal reconstructed residuals. The proposed method is evaluated on the Freiburg EEG dataset of 21 patients and shows its notable performance on both epoch-based and event-based assessments. Moreover, this method handles multiple channels of EEG recordings synchronously which is more speedy and efficient than traditional seizure detection methods.

Teleportation of squeezing: Optimization using non-Gaussian resources

Science.gov (United States)

Dell'Anno, Fabio; de Siena, Silvio; Adesso, Gerardo; Illuminati, Fabrizio

2010-12-01

We study the continuous-variable quantum teleportation of states, statistical moments of observables, and scale parameters such as squeezing. We investigate the problem both in ideal and imperfect Vaidman-Braunstein-Kimble protocol setups. We show how the teleportation fidelity is maximized and the difference between output and input variances is minimized by using suitably optimized entangled resources. Specifically, we consider the teleportation of coherent squeezed states, exploiting squeezed Bell states as entangled resources. This class of non-Gaussian states, introduced by Illuminati and co-workers [F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.76.022301 76, 022301 (2007); F. Dell’Anno, S. De Siena, and F. Illuminati, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.81.012333 81, 012333 (2010)], includes photon-added and photon-subtracted squeezed states as special cases. At variance with the case of entangled Gaussian resources, the use of entangled non-Gaussian squeezed Bell resources allows one to choose different optimization procedures that lead to inequivalent results. Performing two independent optimization procedures, one can either maximize the state teleportation fidelity, or minimize the difference between input and output quadrature variances. The two different procedures are compared depending on the degrees of displacement and squeezing of the input states and on the working conditions in ideal and nonideal setups.

Local features with large spiky non-Gaussianities during inflation

International Nuclear Information System (INIS)

Abolhasani, Ali Akbar; Firouzjahi, Hassan; Khosravi, Shahram; Sasaki, Misao

2012-01-01

We provide a dynamical mechanism to generate localized features during inflation. The local feature is due to a sharp waterfall phase transition which is coupled to the inflaton field. The key effect is the contributions of waterfall quantum fluctuations which induce a sharp peak on the curvature perturbation which can be as large as the background curvature perturbation from inflaton field. Due to non-Gaussian nature of waterfall quantum fluctuations a large spike non-Gaussianity is produced which is narrowly peaked at modes which leave the Hubble radius at the time of phase transition. The large localized peaks in power spectrum and bispectrum can have interesting consequences on CMB anisotropies

On the construction of capacity-achieving lattice Gaussian codes

KAUST Repository

Alghamdi, Wael Mohammed Abdullah

2016-08-15

In this paper, we propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3]. © 2016 IEEE.

Pulsed homodyne Gaussian quantum tomography with low detection efficiency

Science.gov (United States)

Esposito, M.; Benatti, F.; Floreanini, R.; Olivares, S.; Randi, F.; Titimbo, K.; Pividori, M.; Novelli, F.; Cilento, F.; Parmigiani, F.; Fausti, D.

2014-04-01

Pulsed homodyne quantum tomography usually requires a high detection efficiency, limiting its applicability in quantum optics. Here, it is shown that the presence of low detection efficiency (<50%) does not prevent the tomographic reconstruction of quantum states of light, specifically, of Gaussian states. This result is obtained by applying the so-called ‘minimax’ adaptive reconstruction of the Wigner function to pulsed homodyne detection. In particular, we prove, by both numerical and real experiments, that an effective discrimination of different Gaussian quantum states can be achieved. Our finding paves the way to a more extensive use of quantum tomographic methods, even in physical situations in which high detection efficiency is unattainable.

Pulsed homodyne Gaussian quantum tomography with low detection efficiency

International Nuclear Information System (INIS)

Esposito, M; Benatti, F; Randi, F; Titimbo, K; Pividori, M; Parmigiani, F; Fausti, D; Floreanini, R; Olivares, S; Novelli, F; Cilento, F

2014-01-01

Pulsed homodyne quantum tomography usually requires a high detection efficiency, limiting its applicability in quantum optics. Here, it is shown that the presence of low detection efficiency (<50) does not prevent the tomographic reconstruction of quantum states of light, specifically, of Gaussian states. This result is obtained by applying the so-called ‘minimax’ adaptive reconstruction of the Wigner function to pulsed homodyne detection. In particular, we prove, by both numerical and real experiments, that an effective discrimination of different Gaussian quantum states can be achieved. Our finding paves the way to a more extensive use of quantum tomographic methods, even in physical situations in which high detection efficiency is unattainable

On the construction of capacity-achieving lattice Gaussian codes

KAUST Repository

Alghamdi, Wael; Abediseid, Walid; Alouini, Mohamed-Slim

2016-01-01

In this paper, we propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3]. © 2016 IEEE.

Constraining primordial non-Gaussianity with cosmological weak lensing: shear and flexion

International Nuclear Information System (INIS)

Fedeli, C.; Bartelmann, M.; Moscardini, L.

2012-01-01

We examine the cosmological constraining power of future large-scale weak lensing surveys on the model of the ESA planned mission Euclid, with particular reference to primordial non-Gaussianity. Our analysis considers several different estimators of the projected matter power spectrum, based on both shear and flexion. We review the covariance and Fisher matrix for cosmic shear and evaluate those for cosmic flexion and for the cross-correlation between the two. The bounds provided by cosmic shear alone are looser than previously estimated, mainly due to the reduced sky coverage and background number density of sources for the latest Euclid specifications. New constraints for the local bispectrum shape, marginalized over σ 8 , are at the level of Δf NL ∼ 100, with the precise value depending on the exact multipole range that is considered in the analysis. We consider three additional bispectrum shapes, for which the cosmic shear constraints range from Δf NL ∼ 340 (equilateral shape) up to Δf NL ∼ 500 (orthogonal shape). Also, constraints on the level of non-Gaussianity and on the amplitude of the matter power spectrum σ 8 are almost perfectly anti-correlated, except for the orthogonal bispectrum shape for which they are correlated. The competitiveness of cosmic flexion constraints against cosmic shear ones depends by and large on the galaxy intrinsic flexion noise, that is still virtually unconstrained. Adopting the very high value that has been occasionally used in the literature results in the flexion contribution being basically negligible with respect to the shear one, and for realistic configurations the former does not improve significantly the constraining power of the latter. Since the shear shot noise is white, while the flexion one decreases with decreasing scale, by considering high enough multipoles the two contributions have to become comparable. Extending the analysis up to l max = 20,000 cosmic flexion, while being still subdominant

On Sparse Multi-Task Gaussian Process Priors for Music Preference Learning

DEFF Research Database (Denmark)

Nielsen, Jens Brehm; Jensen, Bjørn Sand; Larsen, Jan

In this paper we study pairwise preference learning in a music setting with multitask Gaussian processes and examine the effect of sparsity in the input space as well as in the actual judgments. To introduce sparsity in the inputs, we extend a classic pairwise likelihood model to support sparse...... simulation shows the performance on a real-world music preference dataset which motivates and demonstrates the potential of the sparse Gaussian process formulation for pairwise likelihoods....

Permutation entropy of fractional Brownian motion and fractional Gaussian noise

International Nuclear Information System (INIS)

Zunino, L.; Perez, D.G.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.

2008-01-01

We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays

Pedagogical introduction to the entropy of entanglement for Gaussian states

Science.gov (United States)

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.

General Galilei Covariant Gaussian Maps

Science.gov (United States)

Gasbarri, Giulio; Toroš, Marko; Bassi, Angelo

2017-09-01

We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we consider translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined by Nimmrichter and Hornberger [Phys. Rev. Lett. 110, 16 (2013)].

Gaussian Embeddings for Collaborative Filtering

OpenAIRE

Dos Santos , Ludovic; Piwowarski , Benjamin; Gallinari , Patrick

2017-01-01

International audience; Most collaborative ltering systems, such as matrix factorization, use vector representations for items and users. Those representations are deterministic, and do not allow modeling the uncertainty of the learned representation, which can be useful when a user has a small number of rated items (cold start), or when there is connict-ing information about the behavior of a user or the ratings of an item. In this paper, we leverage recent works in learning Gaussian embeddi...

Evaluation of Cutting Fluids in Multiple Reaming of Stainless Steel

DEFF Research Database (Denmark)

Belluco, Walter; Zeng, Z.; De Chiffre, Leonardo

2001-01-01

subsequent reaming operations were carried out on austenitic stainless steel using high-speed-steel and solid carbide tools. The tested fluids were all significantly different from the reference fluid in at least some of the tested conditions. Significant differences down to 2 percent in cutting forces and 6...

Improving the gaussian effective potential: quantum mechanics

International Nuclear Information System (INIS)

Eboli, O.J.P.; Thomaz, M.T.; Lemos, N.A.

1990-08-01

In order to gain intuition for variational problems in field theory, we analyze variationally the quantum-mechanical anharmonic oscillator [(V(x)sup(k) - sub(2) x sup(2) + sup(λ) - sub(4) λ sup(4)]. Special attention is paid to improvements to the Gaussian effective potential. (author)

Use of δN formalism-difficulties in generating large local-type non-Gaussianity during inflation

International Nuclear Information System (INIS)

Tanaka, Takahiro; Suyama, Teruaki; Yokoyama, Shuichiro

2010-01-01

We discuss the generation of non-Gaussianity in density perturbation through the super-horizon evolution during inflation by using the so-called δN formalism. We first provide a general formula for the nonlinearity parameter generated during inflation. We find that it is proportional to the slow-roll parameters, multiplied by the model-dependent factors that may enhance non-Gaussianity to the observable ranges. Then we discuss three typical examples to illustrate how difficult it is to generate sizable non-Gaussianity through the super-horizon evolution during inflation. The first example is the double inflation model, which shows that temporal violation of slow-roll conditions is not enough for the generation of non-Gaussianity. The second example is the ordinary hybrid inflation model, which illustrates the importance of taking into account perturbations on small scales. Finally, we discuss the Kadota-Stewart model. This model gives an example in which we have to choose rather unnatural initial conditions even if large non-Gaussianity can be generated.

Predictive Active Set Selection Methods for Gaussian Processes

DEFF Research Database (Denmark)

Henao, Ricardo; Winther, Ole

2012-01-01

We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal...... high impact to the classifier decision process while removing those that are less relevant. We introduce two active set rules based on different criteria, the first one prefers a model with interpretable active set parameters whereas the second puts computational complexity first, thus a model...... with active set parameters that directly control its complexity. We also provide both theoretical and empirical support for our active set selection strategy being a good approximation of a full Gaussian process classifier. Our extensive experiments show that our approach can compete with state...

Time-frequency analysis and harmonic Gaussian functions

International Nuclear Information System (INIS)

Ranaivoson, R.T.R; Raoelina Andriambololona; Hanitriarivo, R.

2013-01-01

A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called Harmonic Gaussian Functions. Then these functions are used to define a set of transformations, noted Τ n , which associate to a function ψ, of the time variable t, a set of functions Ψ n which depend on time, frequency and frequency (or time) standard deviation. Some properties of the transformations Τ n and the functions Ψ n are given. It is proved in particular that the square of the modulus of each function Ψ n can be interpreted as a representation of the energy distribution of the signal, represented by the function ψ, in the time-frequency plane for a given value of the frequency (or time) standard deviation. It is also shown that the function ψ can be recovered from the functions Ψ n .

Stochastic dynamic analysis of marine risers considering Gaussian system uncertainties

Science.gov (United States)

Ni, Pinghe; Li, Jun; Hao, Hong; Xia, Yong

2018-03-01

This paper performs the stochastic dynamic response analysis of marine risers with material uncertainties, i.e. in the mass density and elastic modulus, by using Stochastic Finite Element Method (SFEM) and model reduction technique. These uncertainties are assumed having Gaussian distributions. The random mass density and elastic modulus are represented by using the Karhunen-Loève (KL) expansion. The Polynomial Chaos (PC) expansion is adopted to represent the vibration response because the covariance of the output is unknown. Model reduction based on the Iterated Improved Reduced System (IIRS) technique is applied to eliminate the PC coefficients of the slave degrees of freedom to reduce the dimension of the stochastic system. Monte Carlo Simulation (MCS) is conducted to obtain the reference response statistics. Two numerical examples are studied in this paper. The response statistics from the proposed approach are compared with those from MCS. It is noted that the computational time is significantly reduced while the accuracy is kept. The results demonstrate the efficiency of the proposed approach for stochastic dynamic response analysis of marine risers.

Reference intervals for N-terminal pro-B-type natriuretic peptide in amniotic fluid between 10 and 34 weeks of gestation.

Directory of Open Access Journals (Sweden)

Waltraut M Merz

Full Text Available BACKGROUND: In adult and pediatric cardiology, n-terminal pro-B-type natriuretic peptide (nt-proBNP serves as biomarker in the diagnosis and management of cardiovascular dysfunction. Elevated levels of circulating nt-proBNP are present in fetal conditions associated with myocardial pressure or volume load. Compared to fetal blood sampling, amniocentesis is technically easier and can be performed from early pregnancy onwards. We aimed to investigate amniotic fluid (AF nt-proBNP concentrations in normal pregnancies between 10 and 34 weeks of gestation. METHODS: Nt-proBNP and total protein (TP was measured in AF by chemiluminescence assay (photometry, respectively. To adjust for a potential dilutional effect, the AF-nt-proBNP/AF-TP ratio was analyzed. Reference intervals were constructed by regression modeling across gestational age. RESULTS: 132 samples were analyzed. A negative correlation between AF-nt-proBNP/AF-TP ratio and gestational age was observed. Curves for the mean and the 5% and 95% reference interval between 10 and 34 weeks of gestation were established. CONCLUSION: In normal pregnancy, nt-proBNP is present in AF and decreases during gestation. Our data provide the basis for research on AF-nt-proBNP as biomarker in fetal medicine.

Fluid Dynamics Theory, Computation, and Numerical Simulation

CERN Document Server

Pozrikidis, Constantine

2009-01-01

Fluid Dynamics: Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner. The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming. This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice. There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes. Two distinguishing features of the discourse are: solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty. Matlab codes are presented and discussed for ...

Suitability of cerebrospinal fluid as a signal-intensity reference on MRI: evaluation of signal-intensity variations in the lumbosacral dural sac

International Nuclear Information System (INIS)

Luoma, E.K.; Luukkonen, R.; Riihimaeki, H.A.; Raininko, R.; Manninen, H.I.; Nummi, P.J.

1997-01-01

The suitability of the cerebrospinal fluid (CSF) in the lumbosacral dural sac as an internal signal-intensity reference was studied on magnetic resonance imaging (MRI) of the lumbar spine using a surface coil and motion artefact suppression technique. A signal-intensity reference is needed when signal is compared between images, studies or subjects. Homogeneity of the CSF was estimated visually on T2-weighted images of 60 subjects at 1.5 T and of another 60 subjects at 0.1 T. Spines with a severely narrowed dural sac or marked scoliosis were excluded from the study to avoid partial volume effect. CSF was homogeneous in 82% and 73% of the examinations at 1.5 T and 0.1 T, respectively. The type and location of the local inhomogeneities did not relate to local narrowings of the dural sac. The signal intensity of CSF was measured in 108 examinations at 0.1 T after correcting the spatially-dependent signal-intensity nonuniformities with a phantom-based method. The signal-intensity difference between the CSF in the upper and lower lumbar dural sac was less than 10% in 73% of the examinations. The CSF in the lumbosacral dural sac can be a useful signal-intensity reference for estimation of the signal of the adjacent structures in patients without severe narrowing of the dural sac or marked scoliosis. It may contribute to assessing spinal disease processes. (orig.). With 1 fig., 3 tabs

Comment on “Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma” [Phys. Plasmas 20, 072703 (2013)

International Nuclear Information System (INIS)

Habibi, M.; Ghamari, F.

2014-01-01

Patil and Takale in their recent article [Phys. Plasmas 20, 072703 (2013)], by evaluating the quantum dielectric response in thermal quantum plasma, have modeled the relativistic self-focusing of Gaussian laser beam in a plasma. We have found that there are some important shortcomings and fundamental mistakes in Patil and Takale [Phys. Plasmas 20, 072703 (2013)] that we give a brief description about them and refer readers to important misconception about the use of the Fermi temperature in quantum plasmas, appearing in Patil and Takale [Phys. Plasmas 20, 072703 (2013)

A self-reference PRF-shift MR thermometry method utilizing the phase gradient

International Nuclear Information System (INIS)

Langley, Jason; Potter, William; Phipps, Corey; Zhao Qun; Huang Feng

2011-01-01

In magnetic resonance (MR) imaging, the most widely used and accurate method for measuring temperature is based on the shift in proton resonance frequency (PRF). However, inter-scan motion and bulk magnetic field shifts can lead to inaccurate temperature measurements in the PRF-shift MR thermometry method. The self-reference PRF-shift MR thermometry method was introduced to overcome such problems by deriving a reference image from the heated or treated image, and approximates the reference phase map with low-order polynomial functions. In this note, a new approach is presented to calculate the baseline phase map in self-reference PRF-shift MR thermometry. The proposed method utilizes the phase gradient to remove the phase unwrapping step inherent to other self-reference PRF-shift MR thermometry methods. The performance of the proposed method was evaluated using numerical simulations with temperature distributions following a two-dimensional Gaussian function as well as phantom and in vivo experimental data sets. The results from both the numerical simulations and experimental data show that the proposed method is a promising technique for measuring temperature. (note)

Operation of a quasi-optical gyrotron with a gaussian output coupler

Energy Technology Data Exchange (ETDEWEB)

Hogge, J.P.; Tran, T.M.; Paris, P.J.; Tran, M.Q. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)

1996-03-01

The operation of a 92 GHz quasi-optical gyrotron (QOG) having a resonator formed by a spherical mirror and a diffraction grating placed in -1 order Littrow mount is presented. A power of 150 kW with a gaussian output pattern was measured. The gaussian content in the output was 98% with less than 1% of depolarization. By optimizing the magnetic field at fixed frequency, a maximum efficiency of 15% was reached. (author) 12 figs., 2 tabs., 22 refs.

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

International Nuclear Information System (INIS)

Serafini, Alessio; Illuminati, Fabrizio; De Siena, Silvio; Paris, Matteo G.A.

2004-01-01

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

Gaussian particle filter based pose and motion estimation

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

Determination of relative three-dimensional (3D) position, orientation, and relative motion between two reference frames is an important problem in robotic guidance, manipulation, and assembly as well as in other fields such as photogrammetry.A solution to pose and motion estimation problem that uses two-dimensional (2D) intensity images from a single camera is desirable for real-time applications. The difficulty in performing this measurement is that the process of projecting 3D object features to 2D images is a nonlinear transformation. In this paper, the 3D transformation is modeled as a nonlinear stochastic system with the state estimation providing six degrees-of-freedom motion and position values, using line features in image plane as measuring inputs and dual quaternion to represent both rotation and translation in a unified notation. A filtering method called the Gaussian particle filter (GPF) based on the particle filtering concept is presented for 3D pose and motion estimation of a moving target from monocular image sequences. The method has been implemented with simulated data, and simulation results are provided along with comparisons to the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) to show the relative advantages of the GPF. Simulation results showed that GPF is a superior alternative to EKF and UKF.

Global sensitivity analysis using a Gaussian Radial Basis Function metamodel

International Nuclear Information System (INIS)

Wu, Zeping; Wang, Donghui; Okolo N, Patrick; Hu, Fan; Zhang, Weihua

2016-01-01

Sensitivity analysis plays an important role in exploring the actual impact of adjustable parameters on response variables. Amongst the wide range of documented studies on sensitivity measures and analysis, Sobol' indices have received greater portion of attention due to the fact that they can provide accurate information for most models. In this paper, a novel analytical expression to compute the Sobol' indices is derived by introducing a method which uses the Gaussian Radial Basis Function to build metamodels of computationally expensive computer codes. Performance of the proposed method is validated against various analytical functions and also a structural simulation scenario. Results demonstrate that the proposed method is an efficient approach, requiring a computational cost of one to two orders of magnitude less when compared to the traditional Quasi Monte Carlo-based evaluation of Sobol' indices. - Highlights: • RBF based sensitivity analysis method is proposed. • Sobol' decomposition of Gaussian RBF metamodel is obtained. • Sobol' indices of Gaussian RBF metamodel are derived based on the decomposition. • The efficiency of proposed method is validated by some numerical examples.

Underlay Cognitive Radio Systems with Improper Gaussian Signaling: Outage Performance Analysis

KAUST Repository

Amin, Osama

2016-03-29

Improper Gaussian signaling has the ability over proper (conventional) Gaussian signaling to improve the achievable rate of systems that suffer from interference. In this paper, we study the impact of using improper Gaussian signaling on the performance limits of the underlay cognitive radio system by analyzing the achievable outage probability of both the primary user (PU) and secondary user (SU). We derive the exact outage probability expression of the SU and construct upper and lower bounds of the PU outage probability which results in formulating an approximate expression of the PU outage probability. This allows us to design the SU signal by adjusting its transmitted power and the circularity coefficient to minimize the SU outage probability while maintaining a certain PU quality-of-service. Finally, we evaluate the derived expressions for both the SU and the PU and the corresponding adaptive algorithms by numerical results.

Underlay Cognitive Radio Systems with Improper Gaussian Signaling: Outage Performance Analysis

KAUST Repository

Amin, Osama; Abediseid, Walid; Alouini, Mohamed-Slim

2016-01-01

Improper Gaussian signaling has the ability over proper (conventional) Gaussian signaling to improve the achievable rate of systems that suffer from interference. In this paper, we study the impact of using improper Gaussian signaling on the performance limits of the underlay cognitive radio system by analyzing the achievable outage probability of both the primary user (PU) and secondary user (SU). We derive the exact outage probability expression of the SU and construct upper and lower bounds of the PU outage probability which results in formulating an approximate expression of the PU outage probability. This allows us to design the SU signal by adjusting its transmitted power and the circularity coefficient to minimize the SU outage probability while maintaining a certain PU quality-of-service. Finally, we evaluate the derived expressions for both the SU and the PU and the corresponding adaptive algorithms by numerical results.

Underlay Spectrum Sharing Techniques with In-Band Full-Duplex Systems using Improper Gaussian Signaling

KAUST Repository

Gaafar, Mohamed

2016-10-26

Sharing the spectrum with in-band full-duplex (FD) primary users (PUs) is a challenging and interesting problem in the underlay cognitive radio (CR) systems. The self-interference introduced at the primary network may dramatically impede the secondary user (SU) opportunity to access the spectrum. To tackle this problem, we use the so-called improper Gaussian signaling. Particularly, we assume the downlink transmission of a SU that uses improper Gaussian signaling while the FD PU pair implements the regular proper Gaussian signaling. First, we derive a closed form expression and an upper bound for the SU and PUs outage probabilities, respectively. Second, we optimize the SU signal parameters to minimize its outage probability while maintaining the required PUs quality-of-service based on the average channel state information (CSI). Moreover, we provide the conditions to reap merits from employing improper Gaussian signaling at the SU. Third, we design the SU signal parameters based on perfect knowledge of its direct link instantaneous CSI and investigate all benefits that can be achieved at both the SU and PUs. Finally, we provide some numerical results that demonstrate the advantages of using improper Gaussian signaling to access the spectrum of the FD PUs.

Application of the RISM theory to Lennard-Jones interaction site molecular fluids

International Nuclear Information System (INIS)

Johnson, E.; Hazoume, R.P.

1979-01-01

It seems that reference interaction site model (RISM) theory atom--atom distribution functions have been obtained directly from the RISM equations only for fused hard sphere molecular fluids. RISM distribution functions for Lennard-Jones interaction site fluids are presented. Results presented suggest that these distribution functions are as accurate as RISM distribution functions for fused hard sphere molecular fluids

Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices

Science.gov (United States)

Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan; Gross, Sam; Hills, Gage; Hornstein, Michael; Lakkam, Milinda; Lee, Jason; Li, Jian; Liu, Linxi; Sing-Long, Carlos; Marx, Mike; Mittal, Akshay; Monajemi, Hatef; No, Albert; Omrani, Reza; Pekelis, Leonid; Qin, Junjie; Raines, Kevin; Ryu, Ernest; Saxe, Andrew; Shi, Dai; Siilats, Keith; Strauss, David; Tang, Gary; Wang, Chaojun; Zhou, Zoey; Zhu, Zhen

2013-01-01

In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions. PMID:23277588

Sharing the Licensed Spectrum of Full-Duplex Systems Using Improper Gaussian Signaling

KAUST Repository

Gaafar, Mohamed

2015-12-01

Sharing the spectrum with in-band full-duplex (FD) primary users (PU) is a challenging and interesting problem in the underlay cognitive radio (CR) systems. The self-interference introduced at the primary network may dramatically impede the secondary user (SU) opportunity to access the spectrum. In this work, we attempt to tackle this problem through the use of the so-called improper Gaussian signaling. Such a signaling technique has demonstrated its superiority in improving the overall performance in interference limited networks. Particularly, we assume a system with a SU pair working in half-duplex mode that uses improper Gaussian signaling while the FD PU pair implements the regular proper Gaussian signaling techniques. First, we derive a closed form expression for the SU outage probability and an upper bound for the PU outage probability. Then, we optimize the SU signal parameters to minimize its outage probability while maintaining the required PU quality-of-service based on the average channel state information. Finally, we provide some numerical results that validate the tightness of the PU outage probability bound and demonstrate the advantage of employing the improper Gaussian signaling to the SU in order to access the spectrum of the FD PU.

Verification of Eulerian-Eulerian and Eulerian-Lagrangian simulations for fluid-particle flows

Science.gov (United States)

Kong, Bo; Patel, Ravi G.; Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney O.

2017-11-01

In this work, we study the performance of three simulation techniques for fluid-particle flows: (1) a volume-filtered Euler-Lagrange approach (EL), (2) a quadrature-based moment method using the anisotropic Gaussian closure (AG), and (3) a traditional two-fluid model. By simulating two problems: particles in frozen homogeneous isotropic turbulence (HIT), and cluster-induced turbulence (CIT), the convergence of the methods under grid refinement is found to depend on the simulation method and the specific problem, with CIT simulations facing fewer difficulties than HIT. Although EL converges under refinement for both HIT and CIT, its statistical results exhibit dependence on the techniques used to extract statistics for the particle phase. For HIT, converging both EE methods (TFM and AG) poses challenges, while for CIT, AG and EL produce similar results. Overall, all three methods face challenges when trying to extract converged, parameter-independent statistics due to the presence of shocks in the particle phase. National Science Foundation and National Energy Technology Laboratory.

Non-Gaussianity from Broken Symmetries

CERN Document Server

Kolb, Edward W; Vallinotto, A; Kolb, Edward W.; Riotto, Antonio; Vallinotto, Alberto

2006-01-01

Recently we studied inflation models in which the inflaton potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, $f_{NL}$, can be as large as 10^2.

Non-gaussianity from the trispectrum and vector field perturbations

International Nuclear Information System (INIS)

Valenzuela-Toledo, Cesar A.; Rodriguez, Yeinzon

2010-01-01

We use the δN formalism to study the trispectrum T ζ of the primordial curvature perturbation ζ when the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, τ NL , is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f NL , and the level of statistical anisotropy in the power spectrum, g ζ . Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on τ NL from WMAP, for generic inflationary models, is done.

46 CFR 162.050-20 - Separator and bilge alarm test fluids.

Science.gov (United States)

2010-10-01

... residual fuel oil in accordance with ISO 8217 (incorporated by reference, see § 162.050-4), type RMG 380... water; (ii) 25.0 g of Test Fluid A; (iii) 25.0 g of Test Fluid B; (iv) 0.5 g of surfactant (sodium salt...

Fluid Shifts

Science.gov (United States)

Stenger, M. B.; Hargens, A. R.; Dulchavsky, S. A.; Arbeille, P.; Danielson, R. W.; Ebert, D. J.; Garcia, K. M.; Johnston, S. L.; Laurie, S. S.; Lee, S. M. C.;

Kinect Posture Reconstruction Based on a Local Mixture of Gaussian Process Models.

Science.gov (United States)

Liu, Zhiguang; Zhou, Liuyang; Leung, Howard; Shum, Hubert P H

2016-11-01

Depth sensor based 3D human motion estimation hardware such as Kinect has made interactive applications more popular recently. However, it is still challenging to accurately recognize postures from a single depth camera due to the inherently noisy data derived from depth images and self-occluding action performed by the user. In this paper, we propose a new real-time probabilistic framework to enhance the accuracy of live captured postures that belong to one of the action classes in the database. We adopt the Gaussian Process model as a prior to leverage the position data obtained from Kinect and marker-based motion capture system. We also incorporate a temporal consistency term into the optimization framework to constrain the velocity variations between successive frames. To ensure that the reconstructed posture resembles the accurate parts of the observed posture, we embed a set of joint reliability measurements into the optimization framework. A major drawback of Gaussian Process is its cubic learning complexity when dealing with a large database due to the inverse of a covariance matrix. To solve the problem, we propose a new method based on a local mixture of Gaussian Processes, in which Gaussian Processes are defined in local regions of the state space. Due to the significantly decreased sample size in each local Gaussian Process, the learning time is greatly reduced. At the same time, the prediction speed is enhanced as the weighted mean prediction for a given sample is determined by the nearby local models only. Our system also allows incrementally updating a specific local Gaussian Process in real time, which enhances the likelihood of adapting to run-time postures that are different from those in the database. Experimental results demonstrate that our system can generate high quality postures even under severe self-occlusion situations, which is beneficial for real-time applications such as motion-based gaming and sport training.

Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.

Science.gov (United States)

Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi

2015-02-01

We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.

Interaction of Airy-Gaussian beams in saturable media

Science.gov (United States)

Zhou, Meiling; Peng, Yulian; Chen, Chidao; Chen, Bo; Peng, Xi; Deng, Dongmei

2016-08-01

Based on the nonlinear Schrödinger equation, the interactions of the two Airy-Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy-Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy-Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108 and 10904041), the Foundation for the Author of Guangdong Province Excellent Doctoral Dissertation (Grant No. SYBZZXM201227), and the Foundation of Cultivating Outstanding Young Scholars (“Thousand, Hundred, Ten” Program) of Guangdong Province, China. CAS Key Laboratory of Geospace Environment, University of Science and Technology of China.

Neural pulse frequency modulation of an exponentially correlated Gaussian process

Science.gov (United States)

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

1976-01-01

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

Non-Gaussian Autoregressive Processes with Tukey g-and-h Transformations

KAUST Repository

Yan, Yuan

2017-11-20

When performing a time series analysis of continuous data, for example from climate or environmental problems, the assumption that the process is Gaussian is often violated. Therefore, we introduce two non-Gaussian autoregressive time series models that are able to fit skewed and heavy-tailed time series data. Our two models are based on the Tukey g-and-h transformation. We discuss parameter estimation, order selection, and forecasting procedures for our models and examine their performances in a simulation study. We demonstrate the usefulness of our models by applying them to two sets of wind speed data.

Bayesian analysis of log Gaussian Cox processes for disease mapping

DEFF Research Database (Denmark)

Benes, Viktor; Bodlák, Karel; Møller, Jesper

We consider a data set of locations where people in Central Bohemia have been infected by tick-borne encephalitis, and where population census data and covariates concerning vegetation and altitude are available. The aims are to estimate the risk map of the disease and to study the dependence...... of the risk on the covariates. Instead of using the common area level approaches we consider a Bayesian analysis for a log Gaussian Cox point process with covariates. Posterior characteristics for a discretized version of the log Gaussian Cox process are computed using markov chain Monte Carlo methods...

Non-Gaussian Autoregressive Processes with Tukey g-and-h Transformations

KAUST Repository

Yan, Yuan; Genton, Marc G.

2017-01-01

When performing a time series analysis of continuous data, for example from climate or environmental problems, the assumption that the process is Gaussian is often violated. Therefore, we introduce two non-Gaussian autoregressive time series models that are able to fit skewed and heavy-tailed time series data. Our two models are based on the Tukey g-and-h transformation. We discuss parameter estimation, order selection, and forecasting procedures for our models and examine their performances in a simulation study. We demonstrate the usefulness of our models by applying them to two sets of wind speed data.

A comparison of the Gaussian Plume models of Pasquill and Smith

International Nuclear Information System (INIS)

Barker, C.D.

1978-03-01

The Gaussian Plume models of Pasquill and Smith are compared over the full range of atmospheric stability for both short and continuous releases of material. For low level releases the two models compare well (to within a factor of approximately 2) except for very unstable conditions. The agreement between the two models for high level sources is not so good. It is concluded that the two Gaussian models are cheap and simple to use, but may require experimental verification in specific applications. (author)

Scattering and Gaussian Fluctuation Theory for Semiflexible Polymers

Directory of Open Access Journals (Sweden)

Xiangyu Bu

2016-09-01

Full Text Available The worm-like chain is one of the best theoretical models of the semiflexible polymer. The structure factor, which can be obtained by scattering experiment, characterizes the density correlation in different length scales. In the present review, the numerical method to compute the static structure factor of the worm-like chain model and its general properties are demonstrated. Especially, the chain length and persistence length involved multi-scale nature of the worm-like chain model are well discussed. Using the numerical structure factor, Gaussian fluctuation theory of the worm-like chain model can be developed, which is a powerful tool to analyze the structure stability and to predict the spinodal line of the system. The microphase separation of the worm-like diblock copolymer is considered as an example to demonstrate the usage of Gaussian fluctuation theory.

Nonlinear and non-Gaussian Bayesian based handwriting beautification

Science.gov (United States)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

Fluid flows due to earthquakes with reference to Yucca Mountain, Nevada

International Nuclear Information System (INIS)