Cosmic Microwave Background Likelihood Approximation by a Gaussianized Blackwell-Rao Estimator
NASA Astrophysics Data System (ADS)
Rudjord, Ø.; Groeneboom, N. E.; Eriksen, H. K.; Huey, Greg; Górski, K. M.; Jewell, J. B.
2009-02-01
We introduce a new cosmic microwave background (CMB) temperature likelihood approximation called the Gaussianized Blackwell-Rao estimator. This estimator is derived by transforming the observed marginal power spectrum distributions obtained by the CMB Gibbs sampler into standard univariate Gaussians, and then approximating their joint transformed distribution by a multivariate Gaussian. The method is exact for full-sky coverage and uniform noise and an excellent approximation for sky cuts and scanning patterns relevant for modern satellite experiments such as the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck. The result is a stable, accurate, and computationally very efficient CMB temperature likelihood representation that allows the user to exploit the unique error propagation capabilities of the Gibbs sampler to high ells. A single evaluation of this estimator between ell = 2 and 200 takes ~0.2 CPU milliseconds, while for comparison, a singe pixel space likelihood evaluation between ell = 2 and 30 for a map with ~2500 pixels requires ~20 s. We apply this tool to the five-year WMAP temperature data, and re-estimate the angular temperature power spectrum, C ell, and likelihood, L(C_{ℓ}), for ell <= 200, and derive new cosmological parameters for the standard six-parameter ΛCDM model. Our spectrum is in excellent agreement with the official WMAP spectrum, but we find slight differences in the derived cosmological parameters. Most importantly, the spectral index of scalar perturbations is ns = 0.973 ± 0.014, 1.9σ away from unity and 0.6σ higher than the official WMAP result, ns = 0.965 ± 0.014. This suggests that an exact likelihood treatment is required to higher ells than previously believed, reinforcing and extending our conclusions from the three-year WMAP analysis. In that case, we found that the suboptimal likelihood approximation adopted between ell = 12 and 30 by the WMAP team biased ns low by 0.4σ, while here we find that the same
Cosmological parameter constraints via Gibbs sampling and the Blackwell-Rao estimator
NASA Astrophysics Data System (ADS)
Chu, I.-Wen Mike
We study the Blackwell-Rao (BR) estimator of the probability distribution of the angular power spectrum, P ( C [cursive l] | d ), generated via Gibbs sampling of the Cosmic Microwave Background (CMB) data. From simulated samples of full-sky no-noise CMB maps, we find the estimator to be very fast and also highly accurate. We also find that the number of samples required for convergence of the BR estimate rises rapidly with increasing [cursive l], at least at low [cursive l]. Our existing sample chains as applied to the Wilkinson Microwave Anistropy Probe (WMAP) data are only long enough to achieve convergence at [cursive l] [Special characters omitted.] 40. In comparison with P ( C [cursive l] | d ) as reported by the WMAP team we find significant differences at these low [cursive l] values. These differences lead to up to ~ 0.5 s shifts in the estimates of parameters in a 7-parameter LCDM model with non-zero d n s /d ln k , the running in the spectral index. Fixing d n s /dln k = 0 makes these shifts much less significant. Unlike existing analytic approximations, the BR estimator can be straightforwardly extended for the case of power spectra from correlated fields, such as temperature and polarization. We discuss challenges to extending the procedure to higher [cursive l] and provide some solutions.
Gaussian systems for quantum-enhanced multiple phase estimation
NASA Astrophysics Data System (ADS)
Gagatsos, Christos N.; Branford, Dominic; Datta, Animesh
2016-10-01
For a fixed average energy, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We show this for a multimode interferometer with a phase in each mode, using Gaussian inputs and passive elements, by calculating the covariance matrix. The quantum Cramér-Rao bound provides a lower bound to the covariance matrix via the quantum Fisher information matrix, whose elements we derive to be the covariances of the photon numbers across the modes. We prove that this bound can be saturated. In spite of the Gaussian nature of the problem, the calculation of non-Gaussian integrals is required, which we accomplish analytically. We find our simultaneous strategy to yield no more than a factor-of-2 improvement in total precision, possibly because of a fundamental performance limitation of Gaussian states. Our work shows that no modal entanglement is necessary for simultaneous quantum-enhanced estimation of multiple phases.
Image estimation using doubly stochastic gaussian random field models.
Woods, J W; Dravida, S; Mediavilla, R
1987-02-01
The two-dimensional (2-D) doubly stochastic Gaussian (DSG) model was introduced by one of the authors to provide a complete model for spatial filters which adapt to the local structure in an image signal. Here we present the optimal estimator and 2-D fixed-lag smoother for this DSG model extending earlier work of Ackerson and Fu. As the optimal estimator has an exponentially growing state space, we investigate suboptimal estimators using both a tree and a decision-directed method. Experimental results are presented.
Estimation of nonclassical independent Gaussian processes by classical interferometry
Ruppert, László; Filip, Radim
2017-01-01
We propose classical interferometry with low-intensity thermal radiation for the estimation of nonclassical independent Gaussian processes in material samples. We generally determine the mean square error of the phase-independent parameters of an unknown Gaussian process, considering a noisy source of radiation the phase of which is not locked to the pump of the process. We verify the sufficiency of passive optical elements in the interferometer, active optical elements do not improve the quality of the estimation. We also prove the robustness of the method against the noise and loss in both interferometric channels and the sample. The proposed method is suitable even for the case when a source of radiation sufficient for homodyne detection is not available. PMID:28051094
Nonparametric autocovariance estimation from censored time series by Gaussian imputation.
Park, Jung Wook; Genton, Marc G; Ghosh, Sujit K
2009-02-01
One of the most frequently used methods to model the autocovariance function of a second-order stationary time series is to use the parametric framework of autoregressive and moving average models developed by Box and Jenkins. However, such parametric models, though very flexible, may not always be adequate to model autocovariance functions with sharp changes. Furthermore, if the data do not follow the parametric model and are censored at a certain value, the estimation results may not be reliable. We develop a Gaussian imputation method to estimate an autocovariance structure via nonparametric estimation of the autocovariance function in order to address both censoring and incorrect model specification. We demonstrate the effectiveness of the technique in terms of bias and efficiency with simulations under various rates of censoring and underlying models. We describe its application to a time series of silicon concentrations in the Arctic.
pyGMMis: Mixtures-of-Gaussians density estimation method
NASA Astrophysics Data System (ADS)
Melchior, Peter; Goulding, Andy D.
2016-11-01
pyGMMis is a mixtures-of-Gaussians density estimation method that accounts for arbitrary incompleteness in the process that creates the samples as long as the incompleteness is known over the entire feature space and does not depend on the sample density (missing at random). pyGMMis uses the Expectation-Maximization procedure and generates its best guess of the unobserved samples on the fly. It can also incorporate an uniform "background" distribution as well as independent multivariate normal measurement errors for each of the observed samples, and then recovers an estimate of the error-free distribution from which both observed and unobserved samples are drawn. The code automatically segments the data into localized neighborhoods, and is capable of performing density estimation with millions of samples and thousands of model components on machines with sufficient memory.
Spectrum-based kernel length estimation for Gaussian process classification.
Wang, Liang; Li, Chuan
2014-06-01
Recent studies have shown that Gaussian process (GP) classification, a discriminative supervised learning approach, has achieved competitive performance in real applications compared with most state-of-the-art supervised learning methods. However, the problem of automatic model selection in GP classification, involving the kernel function form and the corresponding parameter values (which are unknown in advance), remains a challenge. To make GP classification a more practical tool, this paper presents a novel spectrum analysis-based approach for model selection by refining the GP kernel function to match the given input data. Specifically, we target the problem of GP kernel length scale estimation. Spectrums are first calculated analytically from the kernel function itself using the autocorrelation theorem as well as being estimated numerically from the training data themselves. Then, the kernel length scale is automatically estimated by equating the two spectrum values, i.e., the kernel function spectrum equals to the estimated training data spectrum. Compared with the classical Bayesian method for kernel length scale estimation via maximizing the marginal likelihood (which is time consuming and could suffer from multiple local optima), extensive experimental results on various data sets show that our proposed method is both efficient and accurate.
Gaussian Process Regression for Uncertainty Estimation on Ecosystem Data
NASA Astrophysics Data System (ADS)
Menzer, O.; Moffat, A.; Lasslop, G.; Reichstein, M.
2011-12-01
The flow of carbon between terrestrial ecosystems and the atmosphere is mainly driven by nonlinear, complex and time-lagged processes. Understanding the associated ecosystem responses and climatic feedbacks is a key challenge regarding climate change questions such as increasing atmospheric CO2 levels. Usually, the underlying relationships are implemented in models as prescribed functions which interlink numerous meteorological, radiative and gas exchange variables. In contrast, supervised Machine Learning algorithms, such as Artificial Neural Networks or Gaussian Processes, allow for an insight into the relationships directly from a data perspective. Micrometeorological, high resolution measurements at flux towers of the FLUXNET observational network are an essential tool for obtaining quantifications of the ecosystem variables, as they continuously record e.g. CO2 exchange, solar radiation and air temperature. In order to facilitate the investigation of the interactions and feedbacks between these variables, several challenging data properties need to be taken into account: noisy, multidimensional and incomplete (Moffat, Accepted). The task of estimating uncertainties in such micrometeorological measurements can be addressed by Gaussian Processes (GPs), a modern nonparametric method for nonlinear regression. The GP approach has recently been shown to be a powerful modeling tool, regardless of the input dimensionality, the degree of nonlinearity and the noise level (Rasmussen and Williams, 2006). Heteroscedastic Gaussian Processes (HGPs) are a specialized GP method for data with a varying, inhomogeneous noise variance (Goldberg et al., 1998; Kersting et al., 2007), as usually observed in CO2 flux measurements (Richardson et al., 2006). Here, we showed by an evaluation of the HGP performance in several artificial experiments and a comparison to existing nonlinear regression methods, that their outstanding ability is to capture measurement noise levels, concurrently
A sparse Gaussian process framework for photometric redshift estimation
NASA Astrophysics Data System (ADS)
Almosallam, Ibrahim A.; Lindsay, Sam N.; Jarvis, Matt J.; Roberts, Stephen J.
2016-01-01
Accurate photometric redshifts are a lynchpin for many future experiments to pin down the cosmological model and for studies of galaxy evolution. In this study, a novel sparse regression framework for photometric redshift estimation is presented. Synthetic data set simulating the Euclid survey and real data from SDSS DR12 are used to train and test the proposed models. We show that approaches which include careful data preparation and model design offer a significant improvement in comparison with several competing machine learning algorithms. Standard implementations of most regression algorithms use the minimization of the sum of squared errors as the objective function. For redshift inference, this induces a bias in the posterior mean of the output distribution, which can be problematic. In this paper, we directly minimize the target metric Δz = (zs - zp)/(1 + zs) and address the bias problem via a distribution-based weighting scheme, incorporated as part of the optimization objective. The results are compared with other machine learning algorithms in the field such as artificial neural networks (ANN), Gaussian processes (GPs) and sparse GPs. The proposed framework reaches a mean absolute Δz = 0.0026(1 + zs), over the redshift range of 0 ≤ zs ≤ 2 on the simulated data, and Δz = 0.0178(1 + zs) over the entire redshift range on the SDSS DR12 survey, outperforming the standard ANNz used in the literature. We also investigate how the relative size of the training sample affects the photometric redshift accuracy. We find that a training sample of >30 per cent of total sample size, provides little additional constraint on the photometric redshifts, and note that our GP formalism strongly outperforms ANNz in the sparse data regime for the simulated data set.
Searching for primordial non-Gaussianity in Planck CMB maps using a combined estimator
Novaes, C.P.; Wuensche, C.A.; Bernui, A.; Ferreira, I.S. E-mail: bernui@on.br E-mail: ca.wuensche@inpe.br
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
Estimating Cortical Feature Maps with Dependent Gaussian Processes.
Hughes, Nicholas J; Goodhill, Geoffrey J
2016-11-02
A striking example of brain organisation is the stereotyped arrangement of cell preferences in the visual cortex for edges of particular orientations in the visual image. These "orientation preference maps" appear to have remarkably consistent statistical properties across many species. However fine scale analysis of these properties requires the accurate reconstruction of maps from imaging data which is highly noisy. A new approach for solving this reconstruction problem is to use Bayesian Gaussian process methods, which produce more accurate results than classical techniques. However, so far this work has not considered the fact that maps for several other features of visual input coexist with the orientation preference map and that these maps have mutually dependent spatial arrangements. Here we extend the Gaussian process framework to the multiple output case, so that we can consider multiple maps simultaneously. We demonstrate that this improves reconstruction of multiple maps compared to both classical techniques and the single output approach, can encode the empirically observed relationships, and is easily extendible. This provides the first principled approach for studying the spatial relationships between feature maps in visual cortex.
Parameter estimation in the presence of the most general Gaussian dissipative reservoir
NASA Astrophysics Data System (ADS)
Jarzyna, Marcin; Zwierz, Marcin
2017-01-01
We analyze the performance of quantum parameter estimation in the presence of the most general Gaussian dissipative reservoir. We derive lower bounds on the precision of phase estimation and a closely related problem of frequency estimation. For both problems we show that it is impossible to achieve the Heisenberg limit asymptotically in the presence of such a reservoir. However, we also find that for any fixed number of probes used in the setup there exists a Gaussian dissipative reservoir, which, in principle, allows for the Heisenberg-limited performance for that number of probes. We discuss a realistic implementation of a frequency estimation scheme in the presence of a Gaussian dissipative reservoir in a cavity system.
Gaussian estimation for discretely observed Cox-Ingersoll-Ross model
NASA Astrophysics Data System (ADS)
Wei, Chao; Shu, Huisheng; Liu, Yurong
2016-07-01
This paper is concerned with the parameter estimation problem for Cox-Ingersoll-Ross model based on discrete observation. First, a new discretized process is built based on the Euler-Maruyama scheme. Then, the parameter estimators are obtained by employing the maximum likelihood method and the explicit expressions of the error of estimation are given. Subsequently, the consistency property of all parameter estimators are proved by applying the law of large numbers for martingales, Holder's inequality, B-D-G inequality and Cauchy-Schwarz inequality. Finally, a numerical simulation example for estimators and the absolute error between estimators and true values is presented to demonstrate the effectiveness of the estimation approach used in this paper.
Stellar atmospheric parameter estimation using Gaussian process regression
NASA Astrophysics Data System (ADS)
Bu, Yude; Pan, Jingchang
2015-02-01
As is well known, it is necessary to derive stellar parameters from massive amounts of spectral data automatically and efficiently. However, in traditional automatic methods such as artificial neural networks (ANNs) and kernel regression (KR), it is often difficult to optimize the algorithm structure and determine the optimal algorithm parameters. Gaussian process regression (GPR) is a recently developed method that has been proven to be capable of overcoming these difficulties. Here we apply GPR to derive stellar atmospheric parameters from spectra. Through evaluating the performance of GPR on Sloan Digital Sky Survey (SDSS) spectra, Medium resolution Isaac Newton Telescope Library of Empirical Spectra (MILES) spectra, ELODIE spectra and the spectra of member stars of galactic globular clusters, we conclude that GPR can derive stellar parameters accurately and precisely, especially when we use data preprocessed with principal component analysis (PCA). We then compare the performance of GPR with that of several widely used regression methods (ANNs, support-vector regression and KR) and find that with GPR it is easier to optimize structures and parameters and more efficient and accurate to extract atmospheric parameters.
Parametric Estimation from Approximate Data: Non-Gaussian Diffusions
NASA Astrophysics Data System (ADS)
Azencott, Robert; Ren, Peng; Timofeyev, Ilya
2015-12-01
We study the problem of parameters estimation in indirect observability contexts, where X_t in R^r is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an approximating process Y^{\\varepsilon }_t which is close to X_t in L^4 norm.We construct consistent parameter estimators which are smooth functions of the sub-sampled empirical mean and empirical lagged covariance matrices computed from the observable data. We derive explicit optimal sub-sampling schemes specifying the best paired choices of sub-sampling time-step and number of observations. We show that these choices ensure that our parameter estimators reach optimized asymptotic L^2-convergence rates, which are constant multiples of the L^4 norm || Y^{\\varepsilon }_t - X_t ||.
EXACT MINIMAX ESTIMATION OF THE PREDICTIVE DENSITY IN SPARSE GAUSSIAN MODELS1
Mukherjee, Gourab; Johnstone, Iain M.
2015-01-01
We consider estimating the predictive density under Kullback–Leibler loss in an ℓ0 sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable priors and optimal predictive density estimates are derived. Compared to the sparse recovery results involving point estimation of the normal mean, new decision theoretic phenomena are seen. Suboptimal performance of the class of plug-in density estimates reflects the predictive nature of the problem and optimal strategies need diversification of the future risk. We find that minimax optimal strategies lie outside the Gaussian family but can be constructed with threshold predictive density estimates. Novel minimax techniques involving simultaneous calibration of the sparsity adjustment and the risk diversification mechanisms are used to design optimal predictive density estimates. PMID:26448678
Yu, Guoshen; Sapiro, Guillermo; Mallat, Stéphane
2012-05-01
A general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper. The approach is based on Gaussian mixture models, which are estimated via a maximum a posteriori expectation-maximization algorithm. A dual mathematical interpretation of the proposed framework with a structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques. We demonstrate that, in a number of image inverse problems, including interpolation, zooming, and deblurring of narrow kernels, the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art.
Weak measurement-based state estimation of Gaussian states of one-variable quantum systems
NASA Astrophysics Data System (ADS)
Das, Debmalya; Arvind
2017-04-01
We present a scheme to estimate Gaussian states of one-dimensional continuous variable systems, based on weak (unsharp) quantum measurements. The estimation of a Gaussian state requires us to find position (q), momentum (p) and their second order moments. We measure q weakly and follow it up with a projective measurement of p on half of the ensemble, and on the other half we measure p weakly followed by a projective measurement of q. In each case we use the state twice before discarding it. We compare our results with projective measurements and demonstrate that under certain conditions such weak measurement-based estimation schemes, where recycling of the states is possible, can outperform projective measurement-based state estimation schemes. We establish beyond statistical fluctuations that our method works better for small ensemble sizes.
On estimating the phase of a periodic waveform in additive Gaussian noise, part 3
NASA Technical Reports Server (NTRS)
Rauch, L. L.
1991-01-01
Motivated by advances in signal processing technology that support more complex algorithms, researchers have taken a new look at the problem of estimating the phase and other parameters of a nearly periodic waveform in additive Gaussian noise, based on observation during a given time interval. Parts 1 and 2 are very briefly reviewed. In part 3, the actual performances of some of the highly nonlinear estimation algorithms of parts 1 and 2 are evaluated by numerical simulation using Monte Carlo techniques.
An unbiased risk estimator for image denoising in the presence of mixed poisson-gaussian noise.
Le Montagner, Yoann; Angelini, Elsa D; Olivo-Marin, Jean-Christophe
2014-03-01
The behavior and performance of denoising algorithms are governed by one or several parameters, whose optimal settings depend on the content of the processed image and the characteristics of the noise, and are generally designed to minimize the mean squared error (MSE) between the denoised image returned by the algorithm and a virtual ground truth. In this paper, we introduce a new Poisson-Gaussian unbiased risk estimator (PG-URE) of the MSE applicable to a mixed Poisson-Gaussian noise model that unifies the widely used Gaussian and Poisson noise models in fluorescence bioimaging applications. We propose a stochastic methodology to evaluate this estimator in the case when little is known about the internal machinery of the considered denoising algorithm, and we analyze both theoretically and empirically the characteristics of the PG-URE estimator. Finally, we evaluate the PG-URE-driven parametrization for three standard denoising algorithms, with and without variance stabilizing transforms, and different characteristics of the Poisson-Gaussian noise mixture.
Nonlinear Bayesian Estimation of BOLD Signal under Non-Gaussian Noise
Khan, Ali Fahim; Younis, Muhammad Shahzad; Bajwa, Khalid Bashir
2015-01-01
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. PMID:25691911
Measuring the mass of Kepler-78b using nonparametric Gaussian process estimation
NASA Astrophysics Data System (ADS)
Grunblatt, Samuel K.; Howard, Andrew W.; Haywood, Raphaëlle D.
2016-10-01
Measuring the masses of rocky planets is quite difficult, as the relevant signal produced by such planets is often dwarfed by stellar activity by an order of magnitude or more. Developing a more robust way to isolate the stellar activity in these measurements is crucial to the search for Earth-like planets. We estimate the mass of Earth-size planet Kepler-78b using a Gaussian process estimator to describe the stellar activity in both photometric and radial velocity (RV) data, confirming previous results with a more robust technique that can be extended toward Earth analogues.
A Fast Elitism Gaussian Estimation of Distribution Algorithm and Application for PID Optimization
Xu, Qingyang; Zhang, Chengjin; Zhang, Li
2014-01-01
Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA. PMID:24892059
Robustness of Estimators of Long-Range Dependence and Self-Similarity under non-Gaussianity
NASA Astrophysics Data System (ADS)
Franzke, C.; Watkins, N. W.; Graves, T.; Gramacy, R.; Hughes, C.
2011-12-01
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that self-similarity in a system can be a superposition of both phenomena. These features, which are common in complex systems, impact the attribution of trends and the occurrence and clustering of extremes. The risk assessment of systems with these properties will lead to different outcomes (e.g. return periods) than the more common assumption of independence of extremes. Two paradigmatic models are discussed which can simultaneously account for long-range dependence and non-Gaussianity: Autoregressive Fractional Integrated Moving Average (ARFIMA) and Linear Fractional Stable Motion (LFSM). Statistical properties of estimators for long-range dependence and self-similarity are critically assessed. It is found that the most popular estimators can be biased in the presence of important features of many natural systems like trends and multiplicative noise. Also the long-range dependence and non-Gaussianity of two typical natural time series are discussed.
Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures
NASA Astrophysics Data System (ADS)
Procacci, Piero
2015-04-01
In this paper, we present an improved method for obtaining unbiased estimates of the free energy difference between two thermodynamic states using the work distribution measured in nonequilibrium driven experiments connecting these states. The method is based on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, whose normal components are identical in either direction of the nonequilibrium process, with weights regulated by the Crooks theorem. Using the prototypical example for the driven unfolding/folding of deca-alanine, we show that the predicted behavior of the forward and reverse work distributions, assuming a combination of only two Gaussian components with Crooks derived weights, explains surprisingly well the striking asymmetry in the observed distributions at fast pulling speeds. The proposed methodology opens the way for a perfectly parallel implementation of Jarzynski-based free energy calculations in complex systems.
Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures
Procacci, Piero
2015-04-21
In this paper, we present an improved method for obtaining unbiased estimates of the free energy difference between two thermodynamic states using the work distribution measured in nonequilibrium driven experiments connecting these states. The method is based on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, whose normal components are identical in either direction of the nonequilibrium process, with weights regulated by the Crooks theorem. Using the prototypical example for the driven unfolding/folding of deca-alanine, we show that the predicted behavior of the forward and reverse work distributions, assuming a combination of only two Gaussian components with Crooks derived weights, explains surprisingly well the striking asymmetry in the observed distributions at fast pulling speeds. The proposed methodology opens the way for a perfectly parallel implementation of Jarzynski-based free energy calculations in complex systems.
Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures.
Procacci, Piero
2015-04-21
In this paper, we present an improved method for obtaining unbiased estimates of the free energy difference between two thermodynamic states using the work distribution measured in nonequilibrium driven experiments connecting these states. The method is based on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, whose normal components are identical in either direction of the nonequilibrium process, with weights regulated by the Crooks theorem. Using the prototypical example for the driven unfolding/folding of deca-alanine, we show that the predicted behavior of the forward and reverse work distributions, assuming a combination of only two Gaussian components with Crooks derived weights, explains surprisingly well the striking asymmetry in the observed distributions at fast pulling speeds. The proposed methodology opens the way for a perfectly parallel implementation of Jarzynski-based free energy calculations in complex systems.
Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models
NASA Astrophysics Data System (ADS)
Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael
2016-06-01
We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.
Asymptotically Normal and Efficient Estimation of Covariate-Adjusted Gaussian Graphical Model
Chen, Mengjie; Ren, Zhao; Zhao, Hongyu; Zhou, Harrison
2015-01-01
A tuning-free procedure is proposed to estimate the covariate-adjusted Gaussian graphical model. For each finite subgraph, this estimator is asymptotically normal and efficient. As a consequence, a confidence interval can be obtained for each edge. The procedure enjoys easy implementation and efficient computation through parallel estimation on subgraphs or edges. We further apply the asymptotic normality result to perform support recovery through edge-wise adaptive thresholding. This support recovery procedure is called ANTAC, standing for Asymptotically Normal estimation with Thresholding after Adjusting Covariates. ANTAC outperforms other methodologies in the literature in a range of simulation studies. We apply ANTAC to identify gene-gene interactions using an eQTL dataset. Our result achieves better interpretability and accuracy in comparison with CAMPE. PMID:27499564
mclust 5: Clustering, Classification and Density Estimation Using Gaussian Finite Mixture Models
Scrucca, Luca; Fop, Michael; Murphy, T. Brendan; Raftery, Adrian E.
2016-01-01
Finite mixture models are being used increasingly to model a wide variety of random phenomena for clustering, classification and density estimation. mclust is a powerful and popular package which allows modelling of data as a Gaussian finite mixture with different covariance structures and different numbers of mixture components, for a variety of purposes of analysis. Recently, version 5 of the package has been made available on CRAN. This updated version adds new covariance structures, dimension reduction capabilities for visualisation, model selection criteria, initialisation strategies for the EM algorithm, and bootstrap-based inference, making it a full-featured R package for data analysis via finite mixture modelling. PMID:27818791
On estimating the phase of periodic waveform in additive Gaussian noise, part 2
NASA Astrophysics Data System (ADS)
Rauch, L. L.
1984-11-01
Motivated by advances in signal processing technology that support more complex algorithms, a new look is taken at the problem of estimating the phase and other parameters of a periodic waveform in additive Gaussian noise. The general problem was introduced and the maximum a posteriori probability criterion with signal space interpretation was used to obtain the structures of optimum and some suboptimum phase estimators for known constant frequency and unknown constant phase with an a priori distribution. Optimal algorithms are obtained for some cases where the frequency is a parameterized function of time with the unknown parameters and phase having a joint a priori distribution. In the last section, the intrinsic and extrinsic geometry of hypersurfaces is introduced to provide insight to the estimation problem for the small noise and large noise cases.
Bayesian estimation of airborne fugitive emissions using a Gaussian plume model
NASA Astrophysics Data System (ADS)
Hosseini, Bamdad; Stockie, John M.
2016-09-01
A new method is proposed for estimating the rate of fugitive emissions of particulate matter from multiple time-dependent sources via measurements of deposition and concentration. We cast this source inversion problem within the Bayesian framework, and use a forward model based on a Gaussian plume solution. We present three alternate models for constructing the prior distribution on the emission rates as functions of time. Next, we present an industrial case study in which our framework is applied to estimate the rate of fugitive emissions of lead particulates from a smelter in Trail, British Columbia, Canada. The Bayesian framework not only provides an approximate solution to the inverse problem, but also quantifies the uncertainty in the solution. Using this information we perform an uncertainty propagation study in order to assess the impact of the estimated sources on the area surrounding the industrial site.
Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise.
Liu, Yingjun; Liu, Yong; Wang, Kun; Jiang, Tianzi; Yang, Lihua
2009-12-01
Fractional Gaussian noise (fGn) is an important and widely used self-similar process, which is mainly parametrized by its Hurst exponent (H) . Many researchers have proposed methods for estimating the Hurst exponent of fGn. In this paper we put forward a modified periodogram method for estimating the Hurst exponent based on a refined approximation of the spectral density function. Generalizing the spectral exponent from a linear function to a piecewise polynomial, we obtained a closer approximation of the fGn's spectral density function. This procedure is significant because it reduced the bias in the estimation of H . Furthermore, the averaging technique that we used markedly reduced the variance of estimates. We also considered the asymptotical unbiasedness of the method and derived the upper bound of its variance and confidence interval. Monte Carlo simulations showed that the proposed estimator was superior to a wavelet maximum likelihood estimator in terms of mean-squared error and was comparable to Whittle's estimator. In addition, a real data set of Nile river minima was employed to evaluate the efficiency of our proposed method. These tests confirmed that our proposed method was computationally simpler and faster than Whittle's estimator.
Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise
NASA Astrophysics Data System (ADS)
Liu, Yingjun; Liu, Yong; Wang, Kun; Jiang, Tianzi; Yang, Lihua
2009-12-01
Fractional Gaussian noise (fGn) is an important and widely used self-similar process, which is mainly parametrized by its Hurst exponent (H) . Many researchers have proposed methods for estimating the Hurst exponent of fGn. In this paper we put forward a modified periodogram method for estimating the Hurst exponent based on a refined approximation of the spectral density function. Generalizing the spectral exponent from a linear function to a piecewise polynomial, we obtained a closer approximation of the fGn’s spectral density function. This procedure is significant because it reduced the bias in the estimation of H . Furthermore, the averaging technique that we used markedly reduced the variance of estimates. We also considered the asymptotical unbiasedness of the method and derived the upper bound of its variance and confidence interval. Monte Carlo simulations showed that the proposed estimator was superior to a wavelet maximum likelihood estimator in terms of mean-squared error and was comparable to Whittle’s estimator. In addition, a real data set of Nile river minima was employed to evaluate the efficiency of our proposed method. These tests confirmed that our proposed method was computationally simpler and faster than Whittle’s estimator.
Using Monte Carlo/Gaussian Based Small Area Estimates to Predict Where Medicaid Patients Reside
Behrens, Jess J.; Wen, Xuejin; Goel, Satyender; Zhou, Jing; Fu, Lina; Kho, Abel N.
2016-01-01
Electronic Health Records (EHR) are rapidly becoming accepted as tools for planning and population health1,2. With the national dialogue around Medicaid expansion12, the role of EHR data has become even more important. For their potential to be fully realized and contribute to these discussions, techniques for creating accurate small area estimates is vital. As such, we examined the efficacy of developing small area estimates for Medicaid patients in two locations, Albuquerque and Chicago, by using a Monte Carlo/Gaussian technique that has worked in accurately locating registered voters in North Carolina11. The Albuquerque data, which includes patient address, will first be used to assess the accuracy of the methodology. Subsequently, it will be combined with the EHR data from Chicago to develop a regression that predicts Medicaid patients by US Block Group. We seek to create a tool that is effective in translating EHR data’s potential for population health studies. PMID:28269824
Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M.; Derocher, Andrew E.; Lewis, Mark A.; Jonsen, Ian D.; Mills Flemming, Joanna
2016-01-01
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results. PMID:27220686
NASA Astrophysics Data System (ADS)
Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M.; Derocher, Andrew E.; Lewis, Mark A.; Jonsen, Ian D.; Mills Flemming, Joanna
2016-05-01
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.
Additive white Gaussian noise level estimation in SVD domain for images.
Liu, Wei; Lin, Weisi
2013-03-01
Accurate estimation of Gaussian noise level is of fundamental interest in a wide variety of vision and image processing applications as it is critical to the processing techniques that follow. In this paper, a new effective noise level estimation method is proposed on the basis of the study of singular values of noise-corrupted images. Two novel aspects of this paper address the major challenges in noise estimation: 1) the use of the tail of singular values for noise estimation to alleviate the influence of the signal on the data basis for the noise estimation process and 2) the addition of known noise to estimate the content-dependent parameter, so that the proposed scheme is adaptive to visual signals, thereby enabling a wider application scope of the proposed scheme. The analysis and experiment results demonstrate that the proposed algorithm can reliably infer noise levels and show robust behavior over a wide range of visual content and noise conditions, and that is outperforms relevant existing methods.
Building unbiased estimators from non-gaussian likelihoods with application to shear estimation
Madhavacheril, Mathew S.; McDonald, Patrick; Sehgal, Neelima; Slosar, Anze
2015-01-15
We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next we apply the approach to estimation of shear lensing, closely following the work of Bernstein and Armstrong (2014). Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods. Both our first-order estimator and Bernstein and Armstrong’s estimator exhibit a bias which is quadratic in true shear. Our third-order estimator is, at least in the realm of the toy problem of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors Δg/g for shears up to |g| = 0.2.
Building unbiased estimators from non-gaussian likelihoods with application to shear estimation
Madhavacheril, Mathew S.; McDonald, Patrick; Sehgal, Neelima; ...
2015-01-15
We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next we apply the approach to estimation of shear lensing, closely following the workmore » of Bernstein and Armstrong (2014). Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods. Both our first-order estimator and Bernstein and Armstrong’s estimator exhibit a bias which is quadratic in true shear. Our third-order estimator is, at least in the realm of the toy problem of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors Δg/g for shears up to |g| = 0.2.« less
Ma, Denglong; Zhang, Zaoxiao
2016-07-05
Gas dispersion model is important for predicting the gas concentrations when contaminant gas leakage occurs. Intelligent network models such as radial basis function (RBF), back propagation (BP) neural network and support vector machine (SVM) model can be used for gas dispersion prediction. However, the prediction results from these network models with too many inputs based on original monitoring parameters are not in good agreement with the experimental data. Then, a new series of machine learning algorithms (MLA) models combined classic Gaussian model with MLA algorithm has been presented. The prediction results from new models are improved greatly. Among these models, Gaussian-SVM model performs best and its computation time is close to that of classic Gaussian dispersion model. Finally, Gaussian-MLA models were applied to identifying the emission source parameters with the particle swarm optimization (PSO) method. The estimation performance of PSO with Gaussian-MLA is better than that with Gaussian, Lagrangian stochastic (LS) dispersion model and network models based on original monitoring parameters. Hence, the new prediction model based on Gaussian-MLA is potentially a good method to predict contaminant gas dispersion as well as a good forward model in emission source parameters identification problem.
Non-stationary noise estimation using dictionary learning and Gaussian mixture models
NASA Astrophysics Data System (ADS)
Hughes, James M.; Rockmore, Daniel N.; Wang, Yang
2014-02-01
Stationarity of the noise distribution is a common assumption in image processing. This assumption greatly simplifies denoising estimators and other model parameters and consequently assuming stationarity is often a matter of convenience rather than an accurate model of noise characteristics. The problematic nature of this assumption is exacerbated in real-world contexts, where noise is often highly non-stationary and can possess time- and space-varying characteristics. Regardless of model complexity, estimating the parameters of noise dis- tributions in digital images is a difficult task, and estimates are often based on heuristic assumptions. Recently, sparse Bayesian dictionary learning methods were shown to produce accurate estimates of the level of additive white Gaussian noise in images with minimal assumptions. We show that a similar model is capable of accu- rately modeling certain kinds of non-stationary noise processes, allowing for space-varying noise in images to be estimated, detected, and removed. We apply this modeling concept to several types of non-stationary noise and demonstrate the model's effectiveness on real-world problems, including denoising and segmentation of images according to noise characteristics, which has applications in image forensics.
Wavelet and Gaussian Approaches for Estimation of Groundwater Variations Using GRACE Data.
Fatolazadeh, Farzam; Voosoghi, Behzad; Naeeni, Mehdi Raoofian
2016-01-01
In this study, a scheme is presented to estimate groundwater storage variations in Iran. The variations are estimated using 11 years of Gravity Recovery and Climate Experiments (GRACE) observations from period of 2003 to April 2014 in combination with the outputs of Global Land Data Assimilation Systems (GLDAS) model including soil moisture, snow water equivalent, and total canopy water storage. To do so, the sums of GLDAS outputs are subtracted from terrestrial water storage variations determined by GRACE observations. Because of stripping errors in the GRACE data, two methodologies based on wavelet analysis and Gaussian filtering are applied to refine the GRACE data. It is shown that the wavelet approach could better localize the desired signal and increase the signal-to-noise ratio and thus results in more accurate estimation of groundwater storage variations. To validate the results of our procedure in estimation of ground water storage variations, they are compared with the measurements of pisometric wells data near the Urmia Lake which shows favorable agreements with our results.
Trispectrum estimation in various models of equilateral type non-Gaussianity
NASA Astrophysics Data System (ADS)
Izumi, Keisuke; Mizuno, Shuntaro; Koyama, Kazuya
2012-01-01
We calculate the shape correlations between trispectra in various equilateral non-Gaussian models, including Dirac-Born-Infeld inflation, ghost inflation and Lifshitz scalars, using the full trispectrum as well as the reduced trispectrum. We find that most theoretical models are distinguishable from the shapes of primordial trispectra except for several exceptions where it is difficult to discriminate between the models, such as single field Dirac-Born-Infeld inflation and a Lifshitz scalar model. We introduce an estimator for the amplitude of the trispectrum, gNLequil and relate it to model parameters in various models. Using constraints on gNLequil from WMAP5, we give constraints on the model parameters.
Jirapatnakul, Artit C; Fotin, Sergei V; Reeves, Anthony P; Biancardi, Alberto M; Yankelevitz, David F; Henschke, Claudia I
2009-01-01
Estimation of nodule location and size is an important pre-processing step in some nodule segmentation algorithms to determine the size and location of the region of interest. Ideally, such estimation methods will consistently find the same nodule location regardless of where the the seed point (provided either manually or by a nodule detection algorithm) is placed relative to the "true" center of the nodule, and the size should be a reasonable estimate of the true nodule size. We developed a method that estimates nodule location and size using multi-scale Laplacian of Gaussian (LoG) filtering. Nodule candidates near a given seed point are found by searching for blob-like regions with high filter response. The candidates are then pruned according to filter response and location, and the remaining candidates are sorted by size and the largest candidate selected. This method was compared to a previously published template-based method. The methods were evaluated on the basis of stability of the estimated nodule location to changes in the initial seed point and how well the size estimates agreed with volumes determined by a semi-automated nodule segmentation method. The LoG method exhibited better stability to changes in the seed point, with 93% of nodules having the same estimated location even when the seed point was altered, compared to only 52% of nodules for the template-based method. Both methods also showed good agreement with sizes determined by a nodule segmentation method, with an average relative size difference of 5% and -5% for the LoG and template-based methods respectively.
Ince, Robin A A; Giordano, Bruno L; Kayser, Christoph; Rousselet, Guillaume A; Gross, Joachim; Schyns, Philippe G
2017-03-01
We begin by reviewing the statistical framework of information theory as applicable to neuroimaging data analysis. A major factor hindering wider adoption of this framework in neuroimaging is the difficulty of estimating information theoretic quantities in practice. We present a novel estimation technique that combines the statistical theory of copulas with the closed form solution for the entropy of Gaussian variables. This results in a general, computationally efficient, flexible, and robust multivariate statistical framework that provides effect sizes on a common meaningful scale, allows for unified treatment of discrete, continuous, unidimensional and multidimensional variables, and enables direct comparisons of representations from behavioral and brain responses across any recording modality. We validate the use of this estimate as a statistical test within a neuroimaging context, considering both discrete stimulus classes and continuous stimulus features. We also present examples of analyses facilitated by these developments, including application of multivariate analyses to MEG planar magnetic field gradients, and pairwise temporal interactions in evoked EEG responses. We show the benefit of considering the instantaneous temporal derivative together with the raw values of M/EEG signals as a multivariate response, how we can separately quantify modulations of amplitude and direction for vector quantities, and how we can measure the emergence of novel information over time in evoked responses. Open-source Matlab and Python code implementing the new methods accompanies this article. Hum Brain Mapp 38:1541-1573, 2017. © 2016 Wiley Periodicals, Inc.
Giordano, Bruno L.; Kayser, Christoph; Rousselet, Guillaume A.; Gross, Joachim; Schyns, Philippe G.
2016-01-01
Abstract We begin by reviewing the statistical framework of information theory as applicable to neuroimaging data analysis. A major factor hindering wider adoption of this framework in neuroimaging is the difficulty of estimating information theoretic quantities in practice. We present a novel estimation technique that combines the statistical theory of copulas with the closed form solution for the entropy of Gaussian variables. This results in a general, computationally efficient, flexible, and robust multivariate statistical framework that provides effect sizes on a common meaningful scale, allows for unified treatment of discrete, continuous, unidimensional and multidimensional variables, and enables direct comparisons of representations from behavioral and brain responses across any recording modality. We validate the use of this estimate as a statistical test within a neuroimaging context, considering both discrete stimulus classes and continuous stimulus features. We also present examples of analyses facilitated by these developments, including application of multivariate analyses to MEG planar magnetic field gradients, and pairwise temporal interactions in evoked EEG responses. We show the benefit of considering the instantaneous temporal derivative together with the raw values of M/EEG signals as a multivariate response, how we can separately quantify modulations of amplitude and direction for vector quantities, and how we can measure the emergence of novel information over time in evoked responses. Open‐source Matlab and Python code implementing the new methods accompanies this article. Hum Brain Mapp 38:1541–1573, 2017. © 2016 Wiley Periodicals, Inc. PMID:27860095
SAR amplitude probability density function estimation based on a generalized Gaussian model.
Moser, Gabriele; Zerubia, Josiane; Serpico, Sebastiano B
2006-06-01
In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed "method-of-log-cumulants" (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena.
The binned bispectrum estimator: template-based and non-parametric CMB non-Gaussianity searches
NASA Astrophysics Data System (ADS)
Bucher, Martin; Racine, Benjamin; van Tent, Bartjan
2016-05-01
We describe the details of the binned bispectrum estimator as used for the official 2013 and 2015 analyses of the temperature and polarization CMB maps from the ESA Planck satellite. The defining aspect of this estimator is the determination of a map bispectrum (3-point correlation function) that has been binned in harmonic space. For a parametric determination of the non-Gaussianity in the map (the so-called fNL parameters), one takes the inner product of this binned bispectrum with theoretically motivated templates. However, as a complementary approach one can also smooth the binned bispectrum using a variable smoothing scale in order to suppress noise and make coherent features stand out above the noise. This allows one to look in a model-independent way for any statistically significant bispectral signal. This approach is useful for characterizing the bispectral shape of the galactic foreground emission, for which a theoretical prediction of the bispectral anisotropy is lacking, and for detecting a serendipitous primordial signal, for which a theoretical template has not yet been put forth. Both the template-based and the non-parametric approaches are described in this paper.
Long, Chengjiang; Hua, Gang; Kapoor, Ashish
2015-01-01
We present a noise resilient probabilistic model for active learning of a Gaussian process classifier from crowds, i.e., a set of noisy labelers. It explicitly models both the overall label noise and the expertise level of each individual labeler with two levels of flip models. Expectation propagation is adopted for efficient approximate Bayesian inference of our probabilistic model for classification, based on which, a generalized EM algorithm is derived to estimate both the global label noise and the expertise of each individual labeler. The probabilistic nature of our model immediately allows the adoption of the prediction entropy for active selection of data samples to be labeled, and active selection of high quality labelers based on their estimated expertise to label the data. We apply the proposed model for four visual recognition tasks, i.e., object category recognition, multi-modal activity recognition, gender recognition, and fine-grained classification, on four datasets with real crowd-sourced labels from the Amazon Mechanical Turk. The experiments clearly demonstrate the efficacy of the proposed model. In addition, we extend the proposed model with the Predictive Active Set Selection Method to speed up the active learning system, whose efficacy is verified by conducting experiments on the first three datasets. The results show our extended model can not only preserve a higher accuracy, but also achieve a higher efficiency. PMID:26924892
NASA Astrophysics Data System (ADS)
Reddy, K. S.; Somasundharam, S.
2016-09-01
In this work, inverse heat conduction problem (IHCP) involving the simultaneous estimation of principal thermal conductivities (kxx,kyy,kzz ) and specific heat capacity of orthotropic materials is solved by using surrogate forward model. Uniformly distributed random samples for each unknown parameter is generated from the prior knowledge about these parameters and Finite Volume Method (FVM) is employed to solve the forward problem for temperature distribution with space and time. A supervised machine learning technique- Gaussian Process Regression (GPR) is used to construct the surrogate forward model with the available temperature solution and randomly generated unknown parameter data. The statistical and machine learning toolbox available in MATLAB R2015b is used for this purpose. The robustness of the surrogate model constructed using GPR is examined by carrying out the parameter estimation for 100 new randomly generated test samples at a measurement error of ±0.3K. The temperature measurement is obtained by adding random noise with the mean at zero and known standard deviation (σ = 0.1) to the FVM solution of the forward problem. The test results show that Mean Percentage Deviation (MPD) of all test samples for all parameters is < 10%.
A Gaussian mixture model based cost function for parameter estimation of chaotic biological systems
NASA Astrophysics Data System (ADS)
Shekofteh, Yasser; Jafari, Sajad; Sprott, Julien Clinton; Hashemi Golpayegani, S. Mohammad Reza; Almasganj, Farshad
2015-02-01
As we know, many biological systems such as neurons or the heart can exhibit chaotic behavior. Conventional methods for parameter estimation in models of these systems have some limitations caused by sensitivity to initial conditions. In this paper, a novel cost function is proposed to overcome those limitations by building a statistical model on the distribution of the real system attractor in state space. This cost function is defined by the use of a likelihood score in a Gaussian mixture model (GMM) which is fitted to the observed attractor generated by the real system. Using that learned GMM, a similarity score can be defined by the computed likelihood score of the model time series. We have applied the proposed method to the parameter estimation of two important biological systems, a neuron and a cardiac pacemaker, which show chaotic behavior. Some simulated experiments are given to verify the usefulness of the proposed approach in clean and noisy conditions. The results show the adequacy of the proposed cost function.
NASA Astrophysics Data System (ADS)
Mangilli, A.; Wandelt, B.; Elsner, F.; Liguori, M.
2013-07-01
We present the tools to optimally extract the lensing-integrated Sachs Wolfe (L-ISW) bispectrum signal from future cosmic microwave background (CMB) data. We implemented two different methods to simulate the non-Gaussian CMB maps with the L-ISW signal: a non-perturbative method based on the FLINTS lensing code and the separable mode-expansion method. We implemented the Komatsu, Spergel, and Wandelt (KSW) optimal estimator analysis for the L-ISW bispectrum and tested it on the non-Gaussian simulations for realistic CMB experimental settings with an inhomogeneous sky coverage. We show that the estimator approaches the Cramer-Rao bound and that Wiener filtering the L-ISW simulations slightly improves the estimate of fNLL-ISW by ≤ 10%. For a realistic CMB experimental setting that accounts for anisotropic noise and masked sky, we show that the linear term of the estimator is highly correlated to the cubic term and it is necessary to recover the signal and the optimal error bars. We also show that the L-ISW bispectrum, if not correctly accounted for, yields an underestimation of the fNLlocal error bars of ≃ 4%. A joint analysis of the non-Gaussian shapes and/or L-ISW template subtraction is needed to recover unbiased results of the primordial non-Gaussian signal from ongoing and future CMB experiments.
NASA Astrophysics Data System (ADS)
Stamenkovic, J.; Notarnicola, C.; Spindler, N.; Cuozzo, G.; Bertoldi, G.; Della Chiesa, S.; Niedrist, G.; Greifeneder, F.; Tuia, D.; Borgeaud, M.; Thiran, J.-Ph.
2014-10-01
In this work we address the synergy of optical, SAR (Synthetic Aperture Radar) and topographic data in soil moisture retrieval over an Alpine area. As estimation technique, we consider Gaussian Process Regression (GPR). The test area is located in South Tyrol, Italy where the main land types are meadows and pastures. Time series of ASAR Wide Swath - SAR, optical, topographic and ancillary data (meteorological information and snow cover maps) acquired repetitively in 2010 were examined. Regarding optical data, we used both, daily MODIS reflectances, and daily NDVI, interpolated from the 16-day MODIS composite. Slope, elevation and aspect were extracted from a 2.5 m DEM (Digital Elevation Model) and resampled to 10 m. Daily soil moisture measurements were collected in the three fixed stations (two located in meadows and one located in pasture). The snow maps were used to mask the points covered by snow. The best performance was obtained by adding MODIS band 6 at 1640 nm to SAR and DEM features. The corresponding coefficient of determination, R2, was equal to 0.848, and the root mean square error, RMSE, to 5.4 % Vol. Compared to the case when no optical data were considered, there was an increase of ca. 0.05 in R2 and a decrease in RMSE of ca. 0.7 % Vol. This work showed that the joint use of NDVI or water absorption reflectance with SAR and topographic data can improve the estimation of soil moisture in specific Alpine area and that GPR is an effective method for estimation.
NASA Astrophysics Data System (ADS)
Almosallam, Ibrahim A.; Jarvis, Matt J.; Roberts, Stephen J.
2016-10-01
The next generation of cosmology experiments will be required to use photometric redshifts rather than spectroscopic redshifts. Obtaining accurate and well-characterized photometric redshift distributions is therefore critical for Euclid, the Large Synoptic Survey Telescope and the Square Kilometre Array. However, determining accurate variance predictions alongside single point estimates is crucial, as they can be used to optimize the sample of galaxies for the specific experiment (e.g. weak lensing, baryon acoustic oscillations, supernovae), trading off between completeness and reliability in the galaxy sample. The various sources of uncertainty in measurements of the photometry and redshifts put a lower bound on the accuracy that any model can hope to achieve. The intrinsic uncertainty associated with estimates is often non-uniform and input-dependent, commonly known in statistics as heteroscedastic noise. However, existing approaches are susceptible to outliers and do not take into account variance induced by non-uniform data density and in most cases require manual tuning of many parameters. In this paper, we present a Bayesian machine learning approach that jointly optimizes the model with respect to both the predictive mean and variance we refer to as Gaussian processes for photometric redshifts (GPZ). The predictive variance of the model takes into account both the variance due to data density and photometric noise. Using the Sloan Digital Sky Survey (SDSS) DR12 data, we show that our approach substantially outperforms other machine learning methods for photo-z estimation and their associated variance, such as TPZ and ANNZ2. We provide a MATLAB and PYTHON implementations that are available to download at https://github.com/OxfordML/GPz.
NASA Astrophysics Data System (ADS)
Ryu, Ji-Woo; Lee, Seon-Oh; Sim, Dong-Gyu; Han, Jong-Ki
2012-02-01
We present a no-reference peak signal to noise ratio (PSNR) estimation algorithm based on discrete cosine transform (DCT) coefficient distributions from H.264/MPEG-4 part 10 advanced video codec (H.264/AVC) bitstreams. To estimate the PSNR of a compressed picture without the original picture on the decoder side, it is important to model the distribution of transform coefficients obtained from quantized coefficients accurately. Whereas several conventional algorithms use the Laplacian or Cauchy distribution to model the DCT coefficient distribution, the proposed algorithm uses a generalized Gaussian distribution. Pearson's χ2 (chi-square) test was applied to show that the generalized Gaussian distribution is more appropriate than the other models for modeling the transform coefficients. The χ2 test was also used to find optimum parameters for the generalized Gaussian model. It was found that the generalized Gaussian model improves the accuracy of the DCT coefficient distribution, thus reducing the mean squared error between the real and the estimated PSNR.
Online Estimation and Prediction for a Non-Gaussian Orbital Propagation Model
NASA Astrophysics Data System (ADS)
Godinez, H. C.; Morzfeld, M.
2013-12-01
Accurate estimation and prediction of orbital trajectories of space objects has become an important problem due to the dramatic increase in the number of space debris and the resulting higher risk of collisions. In this work we present a series of assimilation experiments with a two-dimensional orbital propagation model to study the efficiency and applicability of three types of data assimilation methods to this problem. In particular, we consider the ensemble Kalman filter (EnKF), Monte Carlo (MC) sampling, and variational data assimilation (4D-Var). A series of experiments are performed were a number of conditions are tested, including the frequency of assimilation, and number of particles/ensemble members. The assimilation is performed under the twin-experiment framework, where the observations are sampled from a reference run and assimilated into a control run. The assimilation experiments show that the EnKF suffers from filter divergence when the observations are infrequently measured. In fact, the EnKF becomes unstable unless the assimilation is performed at least every 15 minutes approximately. This is mainly due to the strong non-linearity of the orbital propagation model, which results in a non-Gaussian posterior. In contrast, both 4D-Var and MC sampling performance is stable and reliable, and provide accurate estimates of positions and velocities, even if only the positions of the space objects are measured infrequently. While 4D-Var is computationally the most efficient method, MC sampling provides an accurate quantitative assessment of the uncertainty of the position and velocity of the space object. In particular, we found that implicit sampling, which can be thought of as a randomized variational sampling scheme, gave the best performance in terms of reliability, accuracy, and computation time.
Determining the Mass of Kepler-78b with Nonparametric Gaussian Process Estimation
NASA Astrophysics Data System (ADS)
Grunblatt, Samuel K.; Howard, Andrew W.; Haywood, Raphaëlle D.
2015-08-01
Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hr. The mass of Kepler-78b has been independently reported by two teams based on radial velocity (RV) measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in RV data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the RV data sets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV data sets, giving a Doppler amplitude of 1.86 ± 0.25 m s-1 and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of {1.87}-0.26+0.27 {M}\\oplus is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of {6.0}-1.4+1.9 g cm-3. We estimate that Kepler-78b is 32% ± 26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.
Determining the Mass of Kepler-78b with Nonparametric Gaussian Process Estimation
NASA Astrophysics Data System (ADS)
Grunblatt, Samuel Kai; Howard, Andrew; Haywood, Raphaëlle
2016-01-01
Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hr. The mass of Kepler-78b has been independently reported by two teams based on radial velocity (RV) measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in RV data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the RV data sets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV data sets, giving a Doppler amplitude of 1.86 ± 0.25 m s-1 and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87-0.26+0.27 ME is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0-1.4+1.9 g cm-3. We estimate that Kepler-78b is 32% ± 26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.
Determining the Mass of Kepler-78b With Nonparametric Gaussian Process Estimation
NASA Astrophysics Data System (ADS)
Grunblatt, Samuel K.; Howard, Andrew; Haywood, Raphaëlle
2015-12-01
Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hours. The mass of Kepler-78b has been independently reported by two teams based on radial velocity measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in radial velocity data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the radial velocity datasets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV datasets, giving a Doppler amplitude of 1.86 ± 0.25 m s-1 and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87 +0.27-0.26 M⊕ is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0+1.9-1.4 g cm-3. We estimate that Kepler-78b is 32±26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.
Removing the ISW-lensing bias from the local-form primordial non-Gaussianity estimation
Kim, Jaiseung; Komatsu, Eiichiro; Rotti, Aditya E-mail: aditya@iucaa.ernet.in
2013-04-01
The Integrated Sachs-Wolfe (ISW) effect produces a secondary temperature aniso\\-tropy of the cosmic microwave background (CMB), as CMB photons travel through time-varying potentials along the line-of-sight. The main contribution comes from redshifts z∼<2, where dark energy leads to a decay of potentials. As the same photons are gravitationally lensed by these decaying potentials, there exists a high degree of correlation between the ISW effect and CMB lensing, leading to a non-zero three-point correlation (bispectrum) of the observed temperature anisotropy. This ISW-lensing bispectrum, whose shape resembles that of the so-called ''local-form'' primordial bispectrum parametrized by f{sub NL}, is known to be the largest contamination of f{sub NL}. In order to avoid a spurious detection of primordial non-Gaussianity, we need to remove the ISW-lensing bias. In this work, we investigate three debiasing methods: (I) subtraction of an expected, ensemble average of the ISW-lensing bispectrum; (II) subtraction of a measured ISW-lensing bispectrum; and (III) direct subtraction of an estimated ISW signal from an observed temperature map. One may use an estimation of the ISW map from external non-CMB data or that from the CMB data themselves. As the methods II and III are based on fewer assumptions about the nature of dark energy, they are preferred over the method I. While the methods I and II yield unbiased estimates of f{sub NL} with comparable error bars, the method III yields a biased result when the underlying primordial f{sub NL} is non-zero and the ISW map is estimated from a lensing potential reconstructed from the observed temperature map. One of the sources of the bias is a lensing reconstruction noise bias which is independent of f{sub NL} and can be calculated precisely, but other f{sub NL}-dependent terms are difficult to compute reliably. We thus conclude that the method II is the best, model-independent way to remove the ISW-lensing bias of f{sub NL
A neural-network based estimator to search for primordial non-Gaussianity in Planck CMB maps
Novaes, C.P.; Bernui, A.; Ferreira, I.S.; Wuensche, C.A. E-mail: bernui@on.br E-mail: ca.wuensche@inpe.br
2015-09-01
We present an upgraded combined estimator, based on Minkowski Functionals and Neural Networks, with excellent performance in detecting primordial non-Gaussianity in simulated maps that also contain a weighted mixture of Galactic contaminations, besides real pixel's noise from Planck cosmic microwave background radiation data. We rigorously test the efficiency of our estimator considering several plausible scenarios for residual non-Gaussianities in the foreground-cleaned Planck maps, with the intuition to optimize the training procedure of the Neural Network to discriminate between contaminations with primordial and secondary non-Gaussian signatures. We look for constraints of primordial local non-Gaussianity at large angular scales in the foreground-cleaned Planck maps. For the SMICA map we found f{sub NL} = 33 ± 23, at 1σ confidence level, in excellent agreement with the WMAP-9yr and Planck results. In addition, for the other three Planck maps we obtain similar constraints with values in the interval f{sub NL} element of [33, 41], concomitant with the fact that these maps manifest distinct features in reported analyses, like having different pixel's noise intensities.
A new method based on the subpixel Gaussian model for accurate estimation of asteroid coordinates
NASA Astrophysics Data System (ADS)
Savanevych, V. E.; Briukhovetskyi, O. B.; Sokovikova, N. S.; Bezkrovny, M. M.; Vavilova, I. B.; Ivashchenko, Yu. M.; Elenin, L. V.; Khlamov, S. V.; Movsesian, Ia. S.; Dashkova, A. M.; Pogorelov, A. V.
2015-08-01
We describe a new iteration method to estimate asteroid coordinates, based on a subpixel Gaussian model of the discrete object image. The method operates by continuous parameters (asteroid coordinates) in a discrete observational space (the set of pixel potentials) of the CCD frame. In this model, the kind of coordinate distribution of the photons hitting a pixel of the CCD frame is known a priori, while the associated parameters are determined from a real digital object image. The method that is developed, which is flexible in adapting to any form of object image, has a high measurement accuracy along with a low calculating complexity, due to the maximum-likelihood procedure that is implemented to obtain the best fit instead of a least-squares method and Levenberg-Marquardt algorithm for minimization of the quadratic form. Since 2010, the method has been tested as the basis of our Collection Light Technology (COLITEC) software, which has been installed at several observatories across the world with the aim of the automatic discovery of asteroids and comets in sets of CCD frames. As a result, four comets (C/2010 X1 (Elenin), P/2011 NO1(Elenin), C/2012 S1 (ISON) and P/2013 V3 (Nevski)) as well as more than 1500 small Solar system bodies (including five near-Earth objects (NEOs), 21 Trojan asteroids of Jupiter and one Centaur object) have been discovered. We discuss these results, which allowed us to compare the accuracy parameters of the new method and confirm its efficiency. In 2014, the COLITEC software was recommended to all members of the Gaia-FUN-SSO network for analysing observations as a tool to detect faint moving objects in frames.
NASA Astrophysics Data System (ADS)
Varouchakis, Emmanouil; Hristopulos, Dionissios
2015-04-01
Space-time geostatistical approaches can improve the reliability of dynamic groundwater level models in areas with limited spatial and temporal data. Space-time residual Kriging (STRK) is a reliable method for spatiotemporal interpolation that can incorporate auxiliary information. The method usually leads to an underestimation of the prediction uncertainty. The uncertainty of spatiotemporal models is usually estimated by determining the space-time Kriging variance or by means of cross validation analysis. For de-trended data the former is not usually applied when complex spatiotemporal trend functions are assigned. A Bayesian approach based on the bootstrap idea and sequential Gaussian simulation are employed to determine the uncertainty of the spatiotemporal model (trend and covariance) parameters. These stochastic modelling approaches produce multiple realizations, rank the prediction results on the basis of specified criteria and capture the range of the uncertainty. The correlation of the spatiotemporal residuals is modeled using a non-separable space-time variogram based on the Spartan covariance family (Hristopulos and Elogne 2007, Varouchakis and Hristopulos 2013). We apply these simulation methods to investigate the uncertainty of groundwater level variations. The available dataset consists of bi-annual (dry and wet hydrological period) groundwater level measurements in 15 monitoring locations for the time period 1981 to 2010. The space-time trend function is approximated using a physical law that governs the groundwater flow in the aquifer in the presence of pumping. The main objective of this research is to compare the performance of two simulation methods for prediction uncertainty estimation. In addition, we investigate the performance of the Spartan spatiotemporal covariance function for spatiotemporal geostatistical analysis. Hristopulos, D.T. and Elogne, S.N. 2007. Analytic properties and covariance functions for a new class of generalized Gibbs
Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation
NASA Technical Reports Server (NTRS)
Mcreynolds, S. R.
1975-01-01
A simplified technique is proposed for calculating multidimensional Hermite-Gaussian quadratures that involves taking the square root of a matrix by the Cholesky algorithm rather than computation of the eigenvectors of the matrix. Ways of reducing the dimension, number, and order of the quadratures are set forth. If the function f(x) under the integral sign is not well approximated by a low-order algebraic expression, the order of the quadrature may be reduced by factoring f(x) into an expression that is nearly algebraic and one that is Gaussian.
Anai, Shigeo; Arimura, Hidetaka; Nakamura, Katsumasa; Araki, Fujio; Matsuki, Takaomi; Yoshikawa, Hideki; Yoshidome, Satoshi; Shioyama, Yoshiyuki; Honda, Hiroshi; Ikeda, Nobuo
2011-07-01
The X-ray source or focal radiation is one of the factors that can degrade the conformal field edge in stereotactic body radiotherapy. For that reason, it is very important to estimate the total focal radiation profiles of linear accelerators, which consists of X-ray focal-spot radiation and extra-focal radiation profiles. Our purpose in this study was to propose an experimental method for estimating the focal-spot and extra-focal radiation profiles of linear accelerators based on triple Gaussian functions. We measured the total X-ray focal radiation profiles of the accelerators by moving a slit in conjunction with a photon field p-type silicon diode. The slit width was changed so that the extra-focal radiation could be optimally included in the total focal radiation. The total focal radiation profiles of an accelerator at 4-MV and 10-MV energies were approximated with a combination of triple Gaussian functions, which correspond to the focal-spot radiation, extra-focal radiation, and radiation transmitted through the slit assembly. As a result, the ratios of the Gaussian peak value of the extra-focal radiation to that of the focal spot for 4 and 10 MV were 0.077 and 0.159, respectively. The peak widths of the focal-spot and extra-focal radiation profiles were 0.57 and 25.0 mm for 4 MV, respectively, and 0.60 and 22.0 mm for 10 MV, respectively. We concluded that the proposed focal radiation profile model based on the triple Gaussian functions may be feasible for estimating the X-ray focal-spot and extra-focal radiation profiles.
Non-Gaussian methods and high-pass filters in the estimation of effective connections.
Ramsey, Joseph D; Sanchez-Romero, Ruben; Glymour, Clark
2014-01-01
We consider several alternative ways of exploiting non-Gaussian distributional features, including some that can in principle identify direct, positive feedback relations (graphically, 2-cycles) and combinations of methods that can identify high dimensional graphs. All of the procedures are implemented in the TETRAD freeware (Ramsey et al., 2013). We show that in most cases the limited accuracy of the several non-Gaussian methods in the Smith et al. (2011) simulations can be attributed to the high-pass Butterworth filter used in that study. Without that filter, or with the filter in the widely used FSL program (Jenkinson et al., 2012), the directional accuracies of several of the non-Gaussian methods are at or near ceiling in many conditions of the Smith et al. simulation. We show that the improvement of an apparently Gaussian method (Patel et al., 2006) when filtering is removed is due to non-Gaussian features of that method introduced by the Smith et al. implementation. We also investigate some conditions in which multi-subject data help with causal structure identification using higher moments, notably with non-stationary time series or with 2-cycles. We illustrate the accuracy of the methods with more complex graphs with and without 2-cycles, and with a 500 node graph; to illustrate applicability and provide a further test we apply the methods to an empirical case for which aspects of the causal structure are known. Finally, we note a number of cautions and issues that remain to be investigated, and some outstanding problems for determining the structure of effective connections from fMRI data.
2010-06-15
of-the-art inpainting [31]. Portilla et al. have shown image denoising impressive results June 15, 2010 DRAFT 2 by assuming Gaussian scale mixture...beta and Dirichlet processes, which leads to excellent results in denoising and inpainting [71]. The now popular sparse signal models, on the other...b) (c) (d) Fig. 2. (a) Some typical dictionary atoms learned from the image Lena (Figure 3-(a)) with K- SVD [2]. (b)-(d) A numerical procedure to
Bertsatos, Ioannis; Zanolin, Michele; Ratilal, Purnima; Chen, Tianrun; Makris, Nicholas C
2010-11-01
A method is provided for determining necessary conditions on sample size or signal to noise ratio (SNR) to obtain accurate parameter estimates from remote sensing measurements in fluctuating environments. These conditions are derived by expanding the bias and covariance of maximum likelihood estimates (MLEs) in inverse orders of sample size or SNR, where the first-order covariance term is the Cramer-Rao lower bound (CRLB). Necessary sample sizes or SNRs are determined by requiring that (i) the first-order bias and the second-order covariance are much smaller than the true parameter value and the CRLB, respectively, and (ii) the CRLB falls within desired error thresholds. An analytical expression is provided for the second-order covariance of MLEs obtained from general complex Gaussian data vectors, which can be used in many practical problems since (i) data distributions can often be assumed to be Gaussian by virtue of the central limit theorem, and (ii) it allows for both the mean and variance of the measurement to be functions of the estimation parameters. Here, conditions are derived to obtain accurate source localization estimates in a fluctuating ocean waveguide containing random internal waves, and the consequences of the loss of coherence on their accuracy are quantified.
NASA Astrophysics Data System (ADS)
Smith, Gregory; Qweak Collaboration
2016-09-01
As the Qweak collaboration gets closer to unblinding our final result, a method to account for the model uncertainty in the extraction of Qw(p) from a fit to existing parity-violating electron scattering data has been developed. Choices made in selecting the database used in the fit, the strange dipole mass, the functional form of GE, M s, axial constraints, charge-symmetry breaking effects, and in the electromagnetic form factors all contribute to this model uncertainty. An ideogram-inspired Gaussian estimator of this model uncertainty is derived from a fit to a sum of Gaussians, each characterized by the central value and uncertainty of the weak charge obtained from fits using each choice. The width of the resulting summed Gaussian is used to extract the model uncertainty in quadrature from the statistical and systematic errors assumed in the baseline analysis. Finally, this result is compared to the ``stand-alone'' weak charge determined from the single datum representing the asymmetry expected from the (as yet unblinded) Qweak experiment, using calculated electromagnetic, strange, and axial contributions. This work was supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Contract DE-AC05-06OR23177.
Zollanvari, Amin; Dougherty, Edward R
2014-06-01
The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been designed. Use of prior knowledge, in the form of a prior distribution on an uncertainty class of feature-label distributions to which the true, but unknown, feature-distribution belongs, can facilitate accurate error estimation (in the mean-square sense) in circumstances where accurate completely model-free error estimation is impossible. This paper provides analytic asymptotically exact finite-sample approximations for various performance metrics of the resulting Bayesian Minimum Mean-Square-Error (MMSE) error estimator in the case of linear discriminant analysis (LDA) in the multivariate Gaussian model. These performance metrics include the first, second, and cross moments of the Bayesian MMSE error estimator with the true error of LDA, and therefore, the Root-Mean-Square (RMS) error of the estimator. We lay down the theoretical groundwork for Kolmogorov double-asymptotics in a Bayesian setting, which enables us to derive asymptotic expressions of the desired performance metrics. From these we produce analytic finite-sample approximations and demonstrate their accuracy via numerical examples. Various examples illustrate the behavior of these approximations and their use in determining the necessary sample size to achieve a desired RMS. The Supplementary Material contains derivations for some equations and added figures.
Robustness of Estimators of Long-range Dependence and Self-Similarity for Non-Gaussian Datasets.
NASA Astrophysics Data System (ADS)
Watkins, N. W.; Franzke, C. L. E.; Graves, T.; Gramacy, R. B.; Hughes, C.
2012-04-01
Evidence for long-range dependence and non-Gaussianity is ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena frequently occur together in natural systems, and that self-similarity of a system can result from the superposition of both phenomena. These features, which are common in complex systems, impact the attribution of trends and the occurrence and clustering of extremes. The risk assessment of systems posessing these properties will lead to different outcomes (e.g. return periods) than the more common assumption of independence of extremes. We discuss two paradigmatic models which can simultaneously account for long-range dependence and non-Gaussianity: Autoregressive Fractional Integrated Moving Average (ARFIMA) and Linear Fractional Stable Motion (LFSM). The statistical properties of estimators for long-range dependence and self-similarity are critically assessed as applied to these models. It is seen that the most popular estimators are not robust. In particular, they can be biased in the presence of important features of many natural systems like annual cycles, trends and multiplicative noise. [Related paper in press, Phil. Trans. Roy. Soc. A; preprint at arXiv:1101.5018
On the Linear Term Correction for Needlet/Wavelet Non-Gaussianity Estimators
NASA Astrophysics Data System (ADS)
Donzelli, Simona; Hansen, Frode K.; Liguori, Michele; Marinucci, Domenico; Matarrese, Sabino
2012-08-01
We derive the linear correction term for needlet and wavelet estimators of the bispectrum and the nonlinearity parameter f NL on cosmic microwave background radiation data. We show that on masked WMAP-like data with anisotropic noise, the error bars improve by 10%-20% and almost reach the optimal error bars obtained with the bispectrum estimator also known as "KSW". In the limit of full-sky and isotropic noise, this term vanishes. We apply needlet and wavelet estimators to the WMAP 7-year data and obtain our best estimate f NL = 37.5 ± 21.8 (68% CL).
Lee, Wonyul; Liu, Yufeng
2012-10-01
Multivariate regression is a common statistical tool for practical problems. Many multivariate regression techniques are designed for univariate response cases. For problems with multiple response variables available, one common approach is to apply the univariate response regression technique separately on each response variable. Although it is simple and popular, the univariate response approach ignores the joint information among response variables. In this paper, we propose three new methods for utilizing joint information among response variables. All methods are in a penalized likelihood framework with weighted L(1) regularization. The proposed methods provide sparse estimators of conditional inverse co-variance matrix of response vector given explanatory variables as well as sparse estimators of regression parameters. Our first approach is to estimate the regression coefficients with plug-in estimated inverse covariance matrices, and our second approach is to estimate the inverse covariance matrix with plug-in estimated regression parameters. Our third approach is to estimate both simultaneously. Asymptotic properties of these methods are explored. Our numerical examples demonstrate that the proposed methods perform competitively in terms of prediction, variable selection, as well as inverse covariance matrix estimation.
Gaussian process models for reference ET estimation from alternative meteorological data sources
Technology Transfer Automated Retrieval System (TEKTRAN)
Accurate estimates of daily crop evapotranspiration (ET) are needed for efficient irrigation management, especially in arid and semi-arid regions where crop water demand exceeds rainfall. Daily grass or alfalfa reference ET values and crop coefficients are widely used to estimate crop water demand. ...
NASA Astrophysics Data System (ADS)
Sunshine, J. M.; Pieters, C. M.
1993-05-01
The modified Gaussian model (MGM) is used to explore spectra of samples containing multiple pyroxene components as a function of modal abundance. The MGM allows spectra to be analyzed directly, without the use of actual or assumed end-member spectra and therefore holds great promise for remote applications. A series of mass fraction mixtures created from several different particle size fractions are analyzed with the MGM to quantify the properties of pyroxene mixtures as a function of both modal abundance and grain size. Band centers, band widths, and relative band strengths of absorptions from individual pyroxenes in mixture spectra are found to be largely independent of particle size. Spectral properties of both zoned and exsolved pyroxene components are resolved in exsolved samples using the MGM, and modal abundances are accurately estimated to within 5-10 percent without predetermined knowledge of the end-member spectra.
NASA Technical Reports Server (NTRS)
Sunshine, Jessica M.; Pieters, Carle M.
1993-01-01
The modified Gaussian model (MGM) is used to explore spectra of samples containing multiple pyroxene components as a function of modal abundance. The MGM allows spectra to be analyzed directly, without the use of actual or assumed end-member spectra and therefore holds great promise for remote applications. A series of mass fraction mixtures created from several different particle size fractions are analyzed with the MGM to quantify the properties of pyroxene mixtures as a function of both modal abundance and grain size. Band centers, band widths, and relative band strengths of absorptions from individual pyroxenes in mixture spectra are found to be largely independent of particle size. Spectral properties of both zoned and exsolved pyroxene components are resolved in exsolved samples using the MGM, and modal abundances are accurately estimated to within 5-10 percent without predetermined knowledge of the end-member spectra.
NASA Astrophysics Data System (ADS)
Edwards, Darrin C.; Kupinski, Matthew A.; Nishikawa, Robert M.; Metz, Charles E.
2000-04-01
We extend a method for linear template estimation developed by Abbey et al. which demonstrated that a linear observer template can be estimated effectively through a two- alternative forced choice (2AFC) experiment, assuming the noise in the images is Gaussian, or multivariate normal (MVN). We relax this assumption, allowing the noise in the images to be drawn from a weighted sum of MVN distributions, which we call a multi-peaked MVN (MPMVN) distribution. Our motivation is that more complicated probability density functions might be approximated in general by such MPMVN distributions. Our extension of Abbey et al.'s method requires us to impose the additional constraint that the covariance matrices of the component peaks of the signal-present noise distribution all be equal, and that the covariance matrices of the component peaks of the signal-absent noise distribution all be equal (but different in general from the signal-present covariance matrices). Preliminary research shows that our generalized method is capable of producing unbiased estimates of linear observer templates in the presence of MPMVN noise under the stated assumptions. We believe this extension represents a next step toward the general treatment of arbitrary image noise distributions.
1990-11-01
findings contained in this report are thosE Df the author(s) and should not he construed as an official Department Df the Army position, policy , or...Marquardt methods" to perform linear and nonlinear estimations. One idea in this area by Box and Jenkins (1976) was the " backcasting " procedure to evaluate
From almost Gaussian to Gaussian
NASA Astrophysics Data System (ADS)
Costa, Max H. M.; Rioul, Olivier
2015-01-01
We consider lower and upper bounds on the difference of differential entropies of a Gaussian random vector and an approximately Gaussian random vector after they are "smoothed" by an arbitrarily distributed random vector of finite power. These bounds are important to establish the optimality of the corner points in the capacity region of Gaussian interference channels. A problematic issue in a previous attempt to establish these bounds was detected in 2004 and the mentioned corner points have since been dubbed "the missing corner points". The importance of the given bounds comes from the fact that they induce Fano-type inequalities for the Gaussian interference channel. Usual Fano inequalities are based on a communication requirement. In this case, the new inequalities are derived from a non-disturbance constraint. The upper bound on the difference of differential entropies is established by the data processing inequality (DPI). For the lower bound, we do not have a complete proof, but we present an argument based on continuity and the DPI.
NASA Astrophysics Data System (ADS)
Rugini, Luca; Banelli, Paolo
2016-12-01
The minimum mean-squared error (MMSE) is one of the most popular criteria for Bayesian estimation. Conversely, the signal-to-noise ratio (SNR) is a typical performance criterion in communications, radar, and generally detection theory. In this paper we first formalize an SNR criterion to design an estimator, and then we prove that there exists an equivalence between MMSE and maximum-SNR estimators, for any statistics. We also extend this equivalence to specific classes of suboptimal estimators, which are expressed by a basis expansion model (BEM). Then, by exploiting an orthogonal BEM for the estimator, we derive the MMSE estimator constrained to a given quantization resolution of the noisy observations, and we prove that this suboptimal MMSE estimator tends to the optimal MMSE estimator that uses an infinite resolution of the observation. Besides, we derive closed-form expressions for the mean-squared error (MSE) and for the SNR of the proposed suboptimal estimators, and we show that these expressions constitute tight, asymptotically exact, bounds for the optimal MMSE and maximum SNR.
NASA Astrophysics Data System (ADS)
Hollman, David S.; Schaefer, Henry F.; Valeev, Edward F.
2015-04-01
A new estimator for three-center two-particle Coulomb integrals is presented. Our estimator is exact for some classes of integrals and is much more efficient than the standard Schwartz counterpart due to the proper account of distance decay. Although it is not a rigorous upper bound, the maximum degree of underestimation can be controlled by two adjustable parameters. We also give numerical evidence of the excellent tightness of the estimator. The use of the estimator will lead to increased efficiency in reduced-scaling one- and many-body electronic structure theories.
Technology Transfer Automated Retrieval System (TEKTRAN)
Accurate estimates of daily crop evapotranspiration (ET) are needed for efficient irrigation management, especially in arid and semi-arid irrigated regions where crop water demand exceeds rainfall. The impact of inaccurate ET estimates can be tremendous in both irrigation cost and the increased dema...
Chen, Tai-Been; Chen, Jyh-Cheng; Lu, Henry Horng-Shing
2012-01-01
Segmentation of positron emission tomography (PET) is typically achieved using the K-Means method or other approaches. In preclinical and clinical applications, the K-Means method needs a prior estimation of parameters such as the number of clusters and appropriate initialized values. This work segments microPET images using a hybrid method combining the Gaussian mixture model (GMM) with kernel density estimation. Segmentation is crucial to registration of disordered 2-deoxy-2-fluoro-D-glucose (FDG) accumulation locations with functional diagnosis and to estimate standardized uptake values (SUVs) of region of interests (ROIs) in PET images. Therefore, simulation studies are conducted to apply spherical targets to evaluate segmentation accuracy based on Tanimoto's definition of similarity. The proposed method generates a higher degree of similarity than the K-Means method. The PET images of a rat brain are used to compare the segmented shape and area of the cerebral cortex by the K-Means method and the proposed method by volume rendering. The proposed method provides clearer and more detailed activity structures of an FDG accumulation location in the cerebral cortex than those by the K-Means method.
Some results on Gaussian mixtures
NASA Astrophysics Data System (ADS)
Felgueiras, Miguel; Santos, Rui; Martins, João Paulo
2014-10-01
We investigate Gaussian mixtures with independent components, whose parameters are numerically estimated. A decomposition of a Gaussian mixture is presented when the components have a common variance. We introduce a shifted and scaled t-Student distribution as an approximation for the distribution of Gaussian mixtures when their components have a common mean and develop a hypothesis test for testing the equality of the components means. Finally, we analyse the fitness of the approximate model to the logarithmic daily returns of the Portuguese stock index PSI-20.
Gaussian Decomposition of Laser Altimeter Waveforms
NASA Technical Reports Server (NTRS)
Hofton, Michelle A.; Minster, J. Bernard; Blair, J. Bryan
1999-01-01
We develop a method to decompose a laser altimeter return waveform into its Gaussian components assuming that the position of each Gaussian within the waveform can be used to calculate the mean elevation of a specific reflecting surface within the laser footprint. We estimate the number of Gaussian components from the number of inflection points of a smoothed copy of the laser waveform, and obtain initial estimates of the Gaussian half-widths and positions from the positions of its consecutive inflection points. Initial amplitude estimates are obtained using a non-negative least-squares method. To reduce the likelihood of fitting the background noise within the waveform and to minimize the number of Gaussians needed in the approximation, we rank the "importance" of each Gaussian in the decomposition using its initial half-width and amplitude estimates. The initial parameter estimates of all Gaussians ranked "important" are optimized using the Levenburg-Marquardt method. If the sum of the Gaussians does not approximate the return waveform to a prescribed accuracy, then additional Gaussians are included in the optimization procedure. The Gaussian decomposition method is demonstrated on data collected by the airborne Laser Vegetation Imaging Sensor (LVIS) in October 1997 over the Sequoia National Forest, California.
Braun, J; Buntkowsky, G; Bernarding, J; Tolxdorff, T; Sack, I
2001-06-01
New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.
Information geometry of Gaussian channels
Monras, Alex; Illuminati, Fabrizio
2010-06-15
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).
Lewis, C; Jiang, R; Chow, J
2015-06-15
Purpose: We developed a method to predict the change of DVH for PTV due to interfraction organ motion in prostate VMAT without repeating the CT scan and treatment planning. The method is based on a pre-calculated patient database with DVH curves of PTV modelled by the Gaussian error function (GEF). Methods: For a group of 30 patients with different prostate sizes, their VMAT plans were recalculated by shifting their PTVs 1 cm with 10 increments in the anterior-posterior, left-right and superior-inferior directions. The DVH curve of PTV in each replan was then fitted by the GEF to determine parameters describing the shape of curve. Information of parameters, varying with the DVH change due to prostate motion for different prostate sizes, was analyzed and stored in a database of a program written by MATLAB. Results: To predict a new DVH for PTV due to prostate interfraction motion, prostate size and shift distance with direction were input to the program. Parameters modelling the DVH for PTV were determined based on the pre-calculated patient dataset. From the new parameters, DVH curves of PTVs with and without considering the prostate motion were plotted for comparison. The program was verified with different prostate cases involving interfraction prostate shifts and replans. Conclusion: Variation of DVH for PTV in prostate VMAT can be predicted using a pre-calculated patient database with DVH curve fitting. The computing time is fast because CT rescan and replan are not required. This quick DVH estimation can help radiation staff to determine if the changed PTV coverage due to prostate shift is tolerable in the treatment. However, it should be noted that the program can only consider prostate interfraction motions along three axes, and is restricted to prostate VMAT plan using the same plan script in the treatment planning system.
Binomial Gaussian mixture filter
NASA Astrophysics Data System (ADS)
Raitoharju, Matti; Ali-Löytty, Simo; Piché, Robert
2015-12-01
In this work, we present a novel method for approximating a normal distribution with a weighted sum of normal distributions. The approximation is used for splitting normally distributed components in a Gaussian mixture filter, such that components have smaller covariances and cause smaller linearization errors when nonlinear measurements are used for the state update. Our splitting method uses weights from the binomial distribution as component weights. The method preserves the mean and covariance of the original normal distribution, and in addition, the resulting probability density and cumulative distribution functions converge to the original normal distribution when the number of components is increased. Furthermore, an algorithm is presented to do the splitting such as to keep the linearization error below a given threshold with a minimum number of components. The accuracy of the estimate provided by the proposed method is evaluated in four simulated single-update cases and one time series tracking case. In these tests, it is found that the proposed method is more accurate than other Gaussian mixture filters found in the literature when the same number of components is used and that the proposed method is faster and more accurate than particle filters.
Gaussian statistics for palaeomagnetic vectors
Love, J.J.; Constable, C.G.
2003-01-01
With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to
Gaussian entanglement of formation
Wolf, M.M.; Giedke, G.; Krueger, O.; Werner, R. F.; Cirac, J.I.
2004-05-01
We introduce a Gaussian version of the entanglement of formation adapted to bipartite Gaussian states by considering decompositions into pure Gaussian states only. We show that this quantity is an entanglement monotone under Gaussian operations and provide a simplified computation for states of arbitrary many modes. For the case of one mode per site the remaining variational problem can be solved analytically. If the considered state is in addition symmetric with respect to interchanging the two modes, we prove additivity of the considered entanglement measure. Moreover, in this case and considering only a single copy, our entanglement measure coincides with the true entanglement of formation.
Gaussian Intrinsic Entanglement
NASA Astrophysics Data System (ADS)
Mišta, Ladislav; Tatham, Richard
2016-12-01
We introduce a cryptographically motivated quantifier of entanglement in bipartite Gaussian systems called Gaussian intrinsic entanglement (GIE). The GIE is defined as the optimized mutual information of a Gaussian distribution of outcomes of measurements on parts of a system, conditioned on the outcomes of a measurement on a purifying subsystem. We show that GIE vanishes only on separable states and exhibits monotonicity under Gaussian local trace-preserving operations and classical communication. In the two-mode case, we compute GIE for all pure states as well as for several important classes of symmetric and asymmetric mixed states. Surprisingly, in all of these cases, GIE is equal to Gaussian Rényi-2 entanglement. As GIE is operationally associated with the secret-key agreement protocol and can be computed for several important classes of states, it offers a compromise between computable and physically meaningful entanglement quantifiers.
Information bounds for Gaussian copulas
Hoff, Peter D.; Niu, Xiaoyue; Wellner, Jon A.
2013-01-01
Often of primary interest in the analysis of multivariate data are the copula parameters describing the dependence among the variables, rather than the univariate marginal distributions. Since the ranks of a multivariate dataset are invariant to changes in the univariate marginal distributions, rank-based estimators are natural candidates for semiparametric copula estimation. Asymptotic information bounds for such estimators can be obtained from an asymptotic analysis of the rank likelihood, i.e. the probability of the multivariate ranks. In this article, we obtain limiting normal distributions of the rank likelihood for Gaussian copula models. Our results cover models with structured correlation matrices, such as exchangeable or circular correlation models, as well as unstructured correlation matrices. For all Gaussian copula models, the limiting distribution of the rank likelihood ratio is shown to be equal to that of a parametric likelihood ratio for an appropriately chosen multivariate normal model. This implies that the semiparametric information bounds for rank-based estimators are the same as the information bounds for estimators based on the full data, and that the multivariate normal distributions are least favorable. PMID:25313292
George: Gaussian Process regression
NASA Astrophysics Data System (ADS)
Foreman-Mackey, Daniel
2015-11-01
George is a fast and flexible library, implemented in C++ with Python bindings, for Gaussian Process regression useful for accounting for correlated noise in astronomical datasets, including those for transiting exoplanet discovery and characterization and stellar population modeling.
Hammouda, Boualem
2014-01-01
It is common practice to assume that Bragg scattering peaks have Gaussian shape. The Gaussian shape function is used to perform most instrumental smearing corrections. Using Monte Carlo ray tracing simulation, the resolution of a realistic small-angle neutron scattering (SANS) instrument is generated reliably. Including a single-crystal sample with large d-spacing, Bragg peaks are produced. Bragg peaks contain contributions from the resolution function and from spread in the sample structure. Results show that Bragg peaks are Gaussian in the resolution-limited condition (with negligible sample spread) while this is not the case when spread in the sample structure is non-negligible. When sample spread contributes, the exponentially modified Gaussian function is a better account of the Bragg peak shape. This function is characterized by a non-zero third moment (skewness) which makes Bragg peaks asymmetric for broad neutron wavelength spreads. PMID:26601025
Gaussian operations and privacy
Navascues, Miguel; Acin, Antonio
2005-07-15
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.
Semisupervised Gaussian Process for Automated Enzyme Search.
Mellor, Joseph; Grigoras, Ioana; Carbonell, Pablo; Faulon, Jean-Loup
2016-06-17
Synthetic biology is today harnessing the design of novel and greener biosynthesis routes for the production of added-value chemicals and natural products. The design of novel pathways often requires a detailed selection of enzyme sequences to import into the chassis at each of the reaction steps. To address such design requirements in an automated way, we present here a tool for exploring the space of enzymatic reactions. Given a reaction and an enzyme the tool provides a probability estimate that the enzyme catalyzes the reaction. Our tool first considers the similarity of a reaction to known biochemical reactions with respect to signatures around their reaction centers. Signatures are defined based on chemical transformation rules by using extended connectivity fingerprint descriptors. A semisupervised Gaussian process model associated with the similar known reactions then provides the probability estimate. The Gaussian process model uses information about both the reaction and the enzyme in providing the estimate. These estimates were validated experimentally by the application of the Gaussian process model to a newly identified metabolite in Escherichia coli in order to search for the enzymes catalyzing its associated reactions. Furthermore, we show with several pathway design examples how such ability to assign probability estimates to enzymatic reactions provides the potential to assist in bioengineering applications, providing experimental validation to our proposed approach. To the best of our knowledge, the proposed approach is the first application of Gaussian processes dealing with biological sequences and chemicals, the use of a semisupervised Gaussian process framework is also novel in the context of machine learning applied to bioinformatics. However, the ability of an enzyme to catalyze a reaction depends on the affinity between the substrates of the reaction and the enzyme. This affinity is generally quantified by the Michaelis constant KM
NASA Astrophysics Data System (ADS)
Wang, Yan; Huang, Hong; Huang, Lida; Ristic, Branko
2017-03-01
Source term estimation for atmospheric dispersion deals with estimation of the emission strength and location of an emitting source using all available information, including site description, meteorological data, concentration observations and prior information. In this paper, Bayesian methods for source term estimation are evaluated using Prairie Grass field observations. The methods include those that require the specification of the likelihood function and those which are likelihood free, also known as approximate Bayesian computation (ABC) methods. The performances of five different likelihood functions in the former and six different distance measures in the latter case are compared for each component of the source parameter vector based on Nemenyi test over all the 68 data sets available in the Prairie Grass field experiment. Several likelihood functions and distance measures are introduced to source term estimation for the first time. Also, ABC method is improved in many aspects. Results show that discrepancy measures which refer to likelihood functions and distance measures collectively have significant influence on source estimation. There is no single winning algorithm, but these methods can be used collectively to provide more robust estimates.
Gaussian particle flow implementation of PHD filter
NASA Astrophysics Data System (ADS)
Zhao, Lingling; Wang, Junjie; Li, Yunpeng; Coates, Mark J.
2016-05-01
Particle filter and Gaussian mixture implementations of random finite set filters have been proposed to tackle the issue of jointly estimating the number of targets and their states. The Gaussian mixture PHD (GM-PHD) filter has a closed-form expression for the PHD for linear and Gaussian target models, and extensions using the extended Kalman filter or unscented Kalman Filter have been developed to allow the GM-PHD filter to accommodate mildly nonlinear dynamics. Errors resulting from linearization or model mismatch are unavoidable. A particle filter implementation of the PHD filter (PF-PHD) is more suitable for nonlinear and non-Gaussian target models. The particle filter implementations are much more computationally expensive and performance can suffer when the proposal distribution is not a good match to the posterior. In this paper, we propose a novel implementation of the PHD filter named the Gaussian particle flow PHD filter (GPF-PHD). It employs a bank of particle flow filters to approximate the PHD; these play the same role as the Gaussian components in the GM-PHD filter but are better suited to non-linear dynamics and measurement equations. Using the particle flow filter allows the GPF-PHD filter to migrate particles to the dense regions of the posterior, which leads to higher eﬃciency than the PF-PHD. We explore the performance of the new algorithm through numerical simulations.
NASA Technical Reports Server (NTRS)
Dembo, Amir
1989-01-01
Pinsker and Ebert (1970) proved that in channels with additive Gaussian noise, feedback at most doubles the capacity. Cover and Pombra (1989) proved that feedback at most adds half a bit per transmission. Following their approach, the author proves that in the limit as signal power approaches either zero (very low SNR) or infinity (very high SNR), feedback does not increase the finite block-length capacity (which for nonstationary Gaussian channels replaces the standard notion of capacity that may not exist). Tighter upper bounds on the capacity are obtained in the process. Specializing these results to stationary channels, the author recovers some of the bounds recently obtained by Ozarow.
Optimal Gaussian entanglement swapping
Hoelscher-Obermaier, Jason; Loock, Peter van
2011-01-15
We consider entanglement swapping with general mixed two-mode Gaussian states and calculate the optimal gains for a broad class of such states including those states most relevant in communication scenarios. We show that, for this class of states, entanglement swapping adds no additional mixedness; that is, the ensemble-average output state has the same purity as the input states. This implies that, by using intermediate entanglement swapping steps, it is, in principle, possible to distribute entangled two-mode Gaussian states of higher purity as compared to direct transmission. We then apply the general results on optimal Gaussian swapping to the problem of quantum communication over a lossy fiber and demonstrate that, in contrast to the negative conclusions in the literature, swapping-based schemes in fact often perform better than direct transmission for high input squeezing. However, an effective transmission analysis reveals that the hope for improved performance based on optimal Gaussian entanglement swapping is spurious since the swapping does not lead to an enhancement of the effective transmission. This implies that the same or better results can always be obtained using direct transmission in combination with, in general, less squeezing.
AUTONOMOUS GAUSSIAN DECOMPOSITION
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Dickey, John
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.
Autonomous Gaussian Decomposition
NASA Astrophysics Data System (ADS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-04-01
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.
Speech Enhancement Using Gaussian Scale Mixture Models.
Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J
2010-08-11
This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress.
Temperature modes for nonlinear Gaussian beams.
Myers, Matthew R; Soneson, Joshua E
2009-07-01
In assessing the influence of nonlinear acoustic propagation on thermal bioeffects, approximate methods for quickly estimating the temperature rise as operational parameters are varied can be very useful. This paper provides a formula for the transient temperature rise associated with nonlinear propagation of Gaussian beams. The pressure amplitudes for the Gaussian modes can be obtained rapidly using a method previously published for simulating nonlinear propagation of Gaussian beams. The temperature-mode series shows that the nth temperature mode generated by nonlinear propagation, when normalized by the fundamental, is weaker than the nth heat-rate mode (also normalized by the fundamental in the heat-rate series) by a factor of log(n)/n, where n is the mode number. Predictions of temperature rise and thermal dose were found to be in close agreement with full, finite-difference calculations of the pressure fields, temperature rise, and thermal dose. Applications to non-Gaussian beams were made by fitting the main lobe of the significant modes to Gaussian functions.
Note on non-Gaussianities in two-field inflation
NASA Astrophysics Data System (ADS)
Wang, Tower
2010-12-01
Two-field slow-roll inflation is the most conservative modification of a single-field model. The main motivations to study it are its entropic mode and non-Gaussianity. Several years ago, for a two-field model with additive separable potentials, Vernizzi and Wands invented an analytic method to estimate its non-Gaussianities. Later on, Choi et al. applied this method to the model with multiplicative separable potentials. In this note, we design a larger class of models whose non-Gaussianity can be estimated by the same method. Under some simplistic assumptions, roughly these models are unlikely able to generate a large non-Gaussianity. We look over some specific models of this class by scanning the full parameter space, but still no large non-Gaussianity appears in the slow-roll region. These models and scanning techniques would be useful for a future model hunt if observational evidence shows up for two-field inflation.
On Gaussian random supergravity
NASA Astrophysics Data System (ADS)
Bachlechner, Thomas C.
2014-04-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kähler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with | F| ≪ M susy or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log( P ) ∝ - N. We argue that random supergravities lead to potentially interesting inflationary dynamics.
Adaptive Gaussian Pattern Classification
1988-08-01
redundant model of the data to be used in classification . There are two classes of learning, or adaptation schemes. The first, unsupervised learning...37, No. 3, pp. 242-247, 1983. [2] E. F. Codd, Cellular Automata , Academic Press, 1968. [31 H. Everett, G. Gilbreath, S. Alderson, D. J. Marchette...Na al Oca aytm aete !JTI FL E COPY AD-A 199 030 Technical Document 1335 August 1988 Adaptive Gaussian Pattern Classif ication C. E. Priebe D. J
Flauger, Raphael; Pajer, Enrico E-mail: ep295@cornell.edu
2011-01-01
We provide a derivation from first principles of the primordial bispectrum of scalar perturbations produced during inflation driven by a canonically normalized scalar field whose potential exhibits small sinusoidal modulations. A potential of this type has been derived in a class of string theory models of inflation based on axion monodromy. We use this model as a concrete example, but we present our derivations and results for a general slow-roll potential with superimposed modulations. We show analytically that a resonance between the oscillations of the background and the oscillations of the fluctuations is responsible for the production of an observably large non-Gaussian signal. We provide an explicit expression for the shape of this resonant non-Gaussianity. We show that there is essentially no overlap between this shape and the local, equilateral, and orthogonal shapes, and we stress that resonant non-Gaussianity is not captured by the simplest version of the effective field theory of inflation. We hope our analytic expression will be useful to further observationally constrain this class of models.
Non-Gaussianity effects in petrophysical quantities
NASA Astrophysics Data System (ADS)
Koohi Lai, Z.; Jafari, G. R.
2013-10-01
It has been proved that there are many indicators (petrophysical quantities) for the estimation of petroleum reservoirs. The value of information contained in each indicator is yet to be addressed. In this work, the most famous and applicable petrophysical quantities for a reservoir, which are the gamma emission (GR), sonic transient time (DT), neutron porosity (NPHI), bulk density (RHOB), and deep induced resistivity (ILD), have been analyzed in order to characterize a reservoir. The implemented technique is the well-logging method. Based on the log-normal model defined in random multiplicative processes, the probability distribution function (PDF) for the data sets is described. The shape of the PDF depends on the parameter λ2 which determines the efficiency of non-Gaussianity. When non-Gaussianity appears, it is a sign of uncertainty and phase transition in the critical regime. The large value and scale-invariant behavior of the non-Gaussian parameter λ2 is an indication of a new phase which proves adequate for the existence of petroleum reservoirs. Our results show that one of the indicators (GR) is more non-Gaussian than the other indicators, scale wise. This means that GR is a continuously critical indicator. But by moving windows with various scales, the estimated λ2 shows that the most appropriate indicator for distinguishing the critical regime is ILD, which shows an increase at the end of the measured region of the well.
Truncated Gaussians as tolerance sets
NASA Technical Reports Server (NTRS)
Cozman, Fabio; Krotkov, Eric
1994-01-01
This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.
NASA Astrophysics Data System (ADS)
Snoussi, Hichem; Mohammad-Djafari, Ali
2001-05-01
In this contribution, we present new algorithms to source separation for the case of noisy instantaneous linear mixture, within the Bayesian statistical framework. The source distribution prior is modeled by a mixture of Gaussians [1] and the mixing matrix elements distributions by a Gaussian [2]. We model the mixture of Gaussians hierarchically by mean of hidden variables representing the labels of the mixture. Then, we consider the joint a posteriori distribution of sources, mixing matrix elements, labels of the mixture and other parameters of the mixture with appropriate prior probability laws to eliminate degeneracy of the likelihood function of variance parameters and we propose two iterative algorithms to estimate jointly sources, mixing matrix and hyperparameters: Joint MAP (Maximum a posteriori) algorithm and penalized EM algorithm. The illustrative example is taken in [3] to compare with other algorithms proposed in literature. .
Non-Gaussian extrema counts for CMB maps
Pogosyan, Dmitri; Pichon, Christophe; Gay, Christophe
2011-10-15
In the context of the geometrical analysis of weakly non-Gaussian cosmic microwave background maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments expansion of the joint probability distribution of an isotropic random field, its gradient, and invariants of the Hessian. Analytic expressions for these counts are given to second order in the non-Gaussian correction, while a Monte Carlo method to compute them to arbitrary order is presented. Matching count statistics to these estimators is illustrated on fiducial non-Gaussian Planck data.
Noncommutative geometry modified non-Gaussianities of cosmological perturbation
Fang Kejie; Xue Wei; Chen Bin
2008-03-15
We investigate the noncommutative effect on the non-Gaussianities of primordial cosmological perturbation. In the lowest order of string length and slow-roll parameter, we find that in the models with small speed of sound the noncommutative modifications could be observable if assuming a relatively low string scale. In particular, the dominant modification of the non-Gaussianity estimator f{sub NL} could reach O(1) in Dirac-Born-Infeld (DBI) inflation and K-inflation. The corrections are sensitive to the speed of sound and the choice of string length scale. Moreover the shapes of the corrected non-Gaussianities are distinct from that of ordinary ones.
Minimal disturbance measurement for coherent states is non-Gaussian
Mista, Ladislav Jr.
2006-03-15
In standard coherent state teleportation with a shared two-mode squeezed vacuum (TMSV) state there is a trade-off between the teleportation fidelity and the fidelity of estimation of the teleported state from the results of the Bell measurement. Within the class of Gaussian operations this trade-off is optimal, i.e., there is not a Gaussian operation that would give a larger estimation fidelity for a given output fidelity. We show that this trade-off can be improved by up to 2.77% if we use a suitable non-Gaussian operation. This operation can be implemented by the standard teleportation protocol in which the shared TMSV state is replaced with a suitable non-Gaussian entangled state. We also demonstrate that this operation can be used to enhance the transmission fidelity of a certain noisy channel.
Normal form decomposition for Gaussian-to-Gaussian superoperators
De Palma, Giacomo; Mari, Andrea; Giovannetti, Vittorio; Holevo, Alexander S.
2015-05-15
In this paper, we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non-positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings, we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.
Normal form decomposition for Gaussian-to-Gaussian superoperators
NASA Astrophysics Data System (ADS)
De Palma, Giacomo; Mari, Andrea; Giovannetti, Vittorio; Holevo, Alexander S.
2015-05-01
In this paper, we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non-positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings, we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.
Detection of a non-Gaussian spot in WMAP
NASA Astrophysics Data System (ADS)
Cruz, M.; Martínez-González, E.; Vielva, P.; Cayón, L.
2005-01-01
An extremely cold and big spot in the Wilkinson Microwave Anisotropy Probe (WMAP) 1-yr data is analysed. Our work is a continuation of a previous paper by Vielva et al. that reported the detection of non-Gaussianity, with a method based on the spherical Mexican hat wavelet (SMHW) technique. We study the spots at different thresholds on the SMHW coefficient maps, considering six estimators, namely the number of maxima, the number of minima, the numbers of hot and cold spots, and the number of pixels of those spots. At SMHW scales around 4° (10° on the sky), the data deviate from Gaussianity. The analysis is performed on all of the sky, the Northern and Southern hemispheres, and on four regions covering all of the sky. A cold spot at (b=-57°,l= 209°) is found to be the source of this non-Gaussian signature. We compare the spots of our data with 10000 Gaussian simulations, and conclude that only around 0.2 per cent of them present such a cold spot. Excluding this spot, the remaining map is compatible with Gaussianity, and even the excess of kurtosis in the paper by Vielva et al. is found to be due exclusively to this spot. Finally, we study whether the spot causing the observed deviation from Gaussianity could be generated by systematics or foregrounds. None of them seem to be responsible for the non-Gaussian detection.
Gaussian and non-Gaussian fluctuations in pure classical fluids
NASA Astrophysics Data System (ADS)
Naleem, Nawavi; Ploetz, Elizabeth A.; Smith, Paul E.
2017-03-01
The particle number, energy, and volume probability distributions in the canonical, isothermal-isobaric, grand canonical, and isobaric-isenthalpic ensembles are investigated. In particular, we consider Gaussian and non-Gaussian behavior and formulate the results in terms of a single expression valid for all the ensembles employing common, experimentally accessible, thermodynamic derivatives. This is achieved using Fluctuation Solution Theory to help manipulate derivatives of the entropy. The properties of the distributions are then investigated using available equations of state for fluid water and argon. Purely Gaussian behavior is not observed for any of the state points considered here. A set of simple measures, involving thermodynamic derivatives, indicating non-Gaussian behavior is proposed. A general expression, valid in the high temperature limit, for small energy fluctuations in the canonical ensemble is provided.
Making tensor factorizations robust to non-gaussian noise.
Chi, Eric C.; 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).
Least-squares Gaussian beam migration
NASA Astrophysics Data System (ADS)
Yuan, Maolin; Huang, Jianping; Liao, Wenyuan; Jiang, Fuyou
2017-02-01
A theory of least-squares Gaussian beam migration (LSGBM) is presented to optimally estimate a subsurface reflectivity. In the iterative inversion scheme, a Gaussian beam (GB) propagator is used as the kernel of linearized forward modeling (demigration) and its adjoint (migration). Born approximation based GB demigration relies on the calculation of Green’s function by a Gaussian-beam summation for the downward and upward wavefields. The adjoint operator of GB demigration accounts for GB prestack depth migration under the cross-correlation imaging condition, where seismic traces are processed one by one for each shot. A numerical test on the point diffractors model suggests that GB demigration can successfully simulate primary scattered data, while migration (adjoint) can yield a corresponding image. The GB demigration/migration algorithms are used for the least-squares migration scheme to deblur conventional migrated images. The proposed LSGBM is illustrated with two synthetic data for a four-layer model and the Marmousi2 model. Numerical results show that LSGBM, compared to migration (adjoint) with GBs, produces images with more balanced amplitude, higher resolution and even fewer artifacts. Additionally, the LSGBM shows a robust convergence rate.
Arbitrage with fractional Gaussian processes
NASA Astrophysics Data System (ADS)
Zhang, Xili; Xiao, Weilin
2017-04-01
While the arbitrage opportunity in the Black-Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black-Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black-Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann-Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.
The Multilinear Compound Gaussian Distribution
2012-05-01
which we call the Multilinear Compound Gaussian (MCG) distribution, subsumes both GSM [1] and the previously developed MICA [3-4] distributions as...modeling various natural phenomena of interest. Index Terms— GSM, MICA , MCG, Bayesian, Nonlinear I. INTRODUCTION The compound Gaussian (CG) model—also...We will see how the MCG model developed subsumes both CG and the previously developed multilinear ICA ( MICA ) distribution [3-4] as complementary
Modulation depth of Michelson interferometer with Gaussian beam.
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.
Continuous ultrasound speckle tracking with Gaussian mixtures.
Schretter, Colas; Sun, Jianyong; Bundervoet, Shaun; Dooms, Ann; Schelkens, Peter; de Brito Carvalho, Catarina; Slagmolen, Pieter; D'hooge, Jan
2015-01-01
Speckle tracking echocardiography (STE) is now widely used for measuring strain, deformations, and motion in cardiology. STE involves three successive steps: acquisition of individual frames, speckle detection, and image registration using speckles as landmarks. This work proposes to avoid explicit detection and registration by representing dynamic ultrasound images as sparse collections of moving Gaussian elements in the continuous joint space-time space. Individual speckles or local clusters of speckles are approximated by a single multivariate Gaussian kernel with associated linear trajectory over a short time span. A hierarchical tree-structured model is fitted to sampled input data such that predicted image estimates can be retrieved by regression after reconstruction, allowing a (bias-variance) trade-off between model complexity and image resolution. The inverse image reconstruction problem is solved with an online Bayesian statistical estimation algorithm. Experiments on clinical data could estimate subtle sub-pixel accurate motion that is difficult to capture with frame-to-frame elastic image registration techniques.
Quantum correlations in Gaussian states via Gaussian channels: steering, entanglement, and discord
NASA Astrophysics Data System (ADS)
Wang, Zhong-Xiao; Wang, Shuhao; Li, Qiting; Wang, Tie-Jun; Wang, Chuan
2016-06-01
Here we study the quantum steering, quantum entanglement, and quantum discord for Gaussian Einstein-Podolsky-Rosen states via Gaussian channels. And the sudden death phenomena for Gaussian steering and Gaussian entanglement are theoretically observed. We find that some Gaussian states have only one-way steering, which confirms the asymmetry of quantum steering. Also we investigate that the entangled Gaussian states without Gaussian steering and correlated Gaussian states own no Gaussian entanglement. Meanwhile, our results support the assumption that quantum entanglement is intermediate between quantum discord and quantum steering. Furthermore, we give experimental recipes for preparing quantum states with desired types of quantum correlations.
Truncated Gaussian and derived methods
NASA Astrophysics Data System (ADS)
Beucher, Hélène; Renard, Didier
2016-09-01
The interest of a digital model to represent the geological characteristics of the field is well established. However, the way to obtain it is not straightforward because this translation is necessarily a simplification of the actual field. This paper describes a stochastic model called truncated Gaussian simulations (TGS), which distributes a collection of facies or lithotypes over an area of interest. This method is based on facies proportions, spatial distribution and relationships, which can be easily tuned to produce numerous different textures. Initially developed for ordered facies, this model has been extended to complex organizations, where facies are not sequentially ordered. This method called pluri-Gaussian simulation (PGS) considers several Gaussian random functions, which can be correlated. PGS can produce a large variety of lithotype setups, as illustrated by several examples such as oriented deposits or high frequency layering.
Gaussian entanglement distribution via satellite
NASA Astrophysics Data System (ADS)
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.
Cameron, Donnie; Bouhrara, Mustapha; Reiter, David A; Fishbein, Kenneth W; Choi, Seongjin; Bergeron, Christopher M; Ferrucci, Luigi; Spencer, Richard G
2017-04-06
This work characterizes the effect of lipid and noise signals on muscle diffusion parameter estimation in several conventional and non-Gaussian models, the ultimate objectives being to characterize popular fat suppression approaches for human muscle diffusion studies, to provide simulations to inform experimental work and to report normative non-Gaussian parameter values. The models investigated in this work were the Gaussian monoexponential and intravoxel incoherent motion (IVIM) models, and the non-Gaussian kurtosis and stretched exponential models. These were evaluated via simulations, and in vitro and in vivo experiments. Simulations were performed using literature input values, modeling fat contamination as an additive baseline to data, whereas phantom studies used a phantom containing aliphatic and olefinic fats and muscle-like gel. Human imaging was performed in the hamstring muscles of 10 volunteers. Diffusion-weighted imaging was applied with spectral attenuated inversion recovery (SPAIR), slice-select gradient reversal and water-specific excitation fat suppression, alone and in combination. Measurement bias (accuracy) and dispersion (precision) were evaluated, together with intra- and inter-scan repeatability. Simulations indicated that noise in magnitude images resulted in <6% bias in diffusion coefficients and non-Gaussian parameters (α, K), whereas baseline fitting minimized fat bias for all models, except IVIM. In vivo, popular SPAIR fat suppression proved inadequate for accurate parameter estimation, producing non-physiological parameter estimates without baseline fitting and large biases when it was used. Combining all three fat suppression techniques and fitting data with a baseline offset gave the best results of all the methods studied for both Gaussian diffusion and, overall, for non-Gaussian diffusion. It produced consistent parameter estimates for all models, except IVIM, and highlighted non-Gaussian behavior perpendicular to muscle fibers (
Multiqubit spectroscopy of Gaussian quantum noise
NASA Astrophysics Data System (ADS)
Paz-Silva, Gerardo A.; Norris, Leigh M.; Viola, Lorenza
2017-02-01
We introduce multipulse quantum noise spectroscopy protocols for spectral estimation of the noise affecting multiple qubits coupled to Gaussian dephasing environments including both classical and quantum sources. Our protocols are capable of reconstructing all the noise auto- and cross-correlation spectra entering the multiqubit dynamics, providing access, in particular, to the asymmetric spectra associated with nonclassical environments. Our result relies on (i) an exact analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control; (ii) the use of specific timing symmetries, which allow for a frequency comb to be engineered for all filter functions of interest, and for the spectra to be related to experimentally accessible observables. We show that quantum spectra have distinctive dynamical signatures, which we explore in two paradigmatic open-system models describing spin and charge qubits coupled to bosonic environments. Complete noise spectroscopy is demonstrated numerically in a realistic setting consisting of two-exciton qubits coupled to a phonon bath. The estimated spectra allow us to accurately predict the exciton dynamics as well as extract the temperature and spectral density of the quantum environment.
Gaussian-mixture umbrella sampling
van der Vaart, Arjan; Karplus, Martin
2009-01-01
We introduce the Gaussian-mixture umbrella sampling method (GAMUS), a biased molecular dynamics technique based on adaptive umbrella sampling that efficiently escapes free energy minima in multi-dimensional problems. The prior simulation data are reweighted with a maximum likelihood formulation, and the new approximate probability density is fit to a Gaussian-mixture model, augmented by information about the unsampled areas. The method can be used to identify free energy minima in multi-dimensional reaction coordinates. To illustrate GAMUS, we apply it to the alanine dipeptide (2D reaction coordinate) and tripeptide (4D reaction coordinate). PMID:19284746
2012 Problem 1: Gaussian Cannon
NASA Astrophysics Data System (ADS)
Xia, Qing; Gao, Wenli; Wang, Sihui; Zhou, Huijun
2015-10-01
Using the theory of elasticity, we establish an accurate collision model and quantitatively explain how Gaussian Cannon gains its most powerful shot under certain experimental parameters. The work done by magnetic force on the steel ball is obtained by measuring the magnetic force. Essential factors to acquire higher ejection speed have been found.
Non-Gaussian fluctuations near the QCD critical point.
Stephanov, M A
2009-01-23
We study the effect of the QCD critical point on non-Gaussian moments (cumulants) of fluctuations of experimental observables in heavy-ion collisions. We find that these moments are very sensitive to the proximity of the critical point, as measured by the magnitude of the correlation length xi. For example, the cubic central moment of multiplicity (deltaN)3 approximately xi4.5 and the quartic cumulant (deltaN)4c approximately xi7. We estimate the magnitude of critical point contributions to non-Gaussian fluctuations of pion and proton multiplicities.
GAUSSIAN BEAM LASER RESONATOR PROGRAM
NASA Technical Reports Server (NTRS)
Cross, P. L.
1994-01-01
In designing a laser cavity, the laser engineer is frequently concerned with more than the stability of the resonator. Other considerations include the size of the beam at various optical surfaces within the resonator or the performance of intracavity line-narrowing or other optical elements. Laser resonators obey the laws of Gaussian beam propagation, not geometric optics. The Gaussian Beam Laser Resonator Program models laser resonators using Gaussian ray trace techniques. It can be used to determine the propagation of radiation through laser resonators. The algorithm used in the Gaussian Beam Resonator program has three major components. First, the ray transfer matrix for the laser resonator must be calculated. Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed. Finally the propagation of the beam through the optical elements is computed. The optical elements can be modeled as parallel plates, lenses, mirrors, dummy surfaces, or Gradient Index (GRIN) lenses. A Gradient Index lens is a good approximation of a laser rod operating under a thermal load. The optical system may contain up to 50 elements. In addition to the internal beam elements the optical system may contain elements external to the resonator. The Gaussian Beam Resonator program was written in Microsoft FORTRAN (Version 4.01). It was developed for the IBM PS/2 80-071 microcomputer and has been implemented on an IBM PC compatible under MS DOS 3.21. The program was developed in 1988 and requires approximately 95K bytes to operate.
Gaussian Velocity Distributions in Avalanches
NASA Astrophysics Data System (ADS)
Shattuck, Mark
2004-03-01
Imagine a world where gravity is so strong that if an ice cube is tilted the shear forces melt the surface and water avalanches down. Further imagine that the ambient temperature is so low that the water re-freezes almost immediately. This is the world of granular flows. As a granular solid is tilted the surface undergoes a sublimation phase transition and a granular gas avalanches down the surface, but the inelastic collisions rapidly remove energy from the flow lowering the granular temperature (kinetic energy per particle) until the gas solidifies again. It is under these extreme conditions that we attempt to uncover continuum granular flow properties. Typical continuum theories like Navier-Stokes equation for fluids follow the space-time evolution of the first few moments of the velocity distribution. We study continuously avalanching flow in a rotating two-dimensional granular drum using high-speed video imaging and extract the position and velocities of the particles. We find a universal near Gaussian velocity distribution throughout the flowing regions, which are characterized by a liquid-like radial distribution function. In the remaining regions, in which the radial distribution function develops sharp crystalline peaks, the velocity distribution has a Gaussian peak but is much broader in the tails. In a companion experiment on a vibrated two-dimensional granular fluid under constant pressure, we find a clear gas-solid phase transition in which both the temperature and density change discontinuously. This suggests that a low temperature crystal and a high temperature gas can coexist in steady state. This coexistence could result in a narrower, cooler, Gaussian peak and a broader, warmer, Gaussian tail like the non-Gaussian behavior seen in the crystalline portions of the rotating drum.
Adaptive sampling for learning gaussian processes using mobile sensor networks.
Xu, Yunfei; Choi, Jongeun
2011-01-01
This paper presents a novel class of self-organizing sensing agents that adaptively learn an anisotropic, spatio-temporal gaussian process using noisy measurements and move in order to improve the quality of the estimated covariance function. This approach is based on a class of anisotropic covariance functions of gaussian processes introduced to model a broad range of spatio-temporal physical phenomena. The covariance function is assumed to be unknown a priori. Hence, it is estimated by the maximum a posteriori probability (MAP) estimator. The prediction of the field of interest is then obtained based on the MAP estimate of the covariance function. An optimal sampling strategy is proposed to minimize the information-theoretic cost function of the Fisher Information Matrix. Simulation results demonstrate the effectiveness and the adaptability of the proposed scheme.
A Gaussian Copula Model for Multivariate Survival Data
Othus, Megan; Li, Yi
2011-01-01
We consider a Gaussian copula model for multivariate survival times. Estimation of the copula association parameter is easily implemented with existing software using a two-stage estimation procedure. Using the Gaussian copula, we are able to test whether the association parameter is equal to zero. When the association term is positive, the model can be extended to incorporate cluster-level frailty terms. Asymptotic properties are derived under the two-stage estimation scheme. Simulation studies verify finite sample utility. We apply the method to a Children’s Oncology Group multi-center study of acute lymphoblastic leukemia. The analysis estimates marginal treatment effects and examines potential clustering within treatment institution. PMID:22162742
Adaptive Sampling for Learning Gaussian Processes Using Mobile Sensor Networks
Xu, Yunfei; Choi, Jongeun
2011-01-01
This paper presents a novel class of self-organizing sensing agents that adaptively learn an anisotropic, spatio-temporal Gaussian process using noisy measurements and move in order to improve the quality of the estimated covariance function. This approach is based on a class of anisotropic covariance functions of Gaussian processes introduced to model a broad range of spatio-temporal physical phenomena. The covariance function is assumed to be unknown a priori. Hence, it is estimated by the maximum a posteriori probability (MAP) estimator. The prediction of the field of interest is then obtained based on the MAP estimate of the covariance function. An optimal sampling strategy is proposed to minimize the information-theoretic cost function of the Fisher Information Matrix. Simulation results demonstrate the effectiveness and the adaptability of the proposed scheme. PMID:22163785
Inseparability of photon-added Gaussian states
Li Hongrong; Li Fuli; Zhu Shiyao
2007-06-15
The inseparability of photon-added Gaussian states which are generated from two-mode Gaussian states by adding photons is investigated. According to the established inseparability conditions [New J. Phys. 7, 211 (2005); Phys. Rev. Lett. 96, 050503 (2006)], we find that even if a two-mode Gaussian state is separable, the photon-added Gaussian state becomes entangled when the purity of the Gaussian state is larger than a certain value. The lower bound of entanglement of symmetric photon-added Gaussian states is derived. The result shows that entanglement of the photon-added Gaussian states is involved with high-order moment correlations. We find that fidelity of teleporting coherent states cannot be raised by employing the photon-added Gaussian states as a quantum channel of teleportation.
Improved kernel correlation filter tracking with Gaussian scale space
NASA Astrophysics Data System (ADS)
Tan, Shukun; Liu, Yunpeng; Li, Yicui
2016-10-01
Recently, Kernel Correlation Filter (KCF) has achieved great attention in visual tracking filed, which provide excellent tracking performance and high possessing speed. However, how to handle the scale variation is still an open problem. In this paper, focusing on this issue that a method based on Gaussian scale space is proposed. First, we will use KCF to estimate the location of the target, the context region which includes the target and its surrounding background will be the image to be matched. In order to get the matching image of a Gaussian scale space, image with Gaussian kernel convolution can be gotten. After getting the Gaussian scale space of the image to be matched, then, according to it to estimate target image under different scales. Combine with the scale parameter of scale space, for each corresponding scale image performing bilinear interpolation operation to change the size to simulate target imaging at different scales. Finally, matching the template with different size of images with different scales, use Mean Absolute Difference (MAD) as the match criterion. After getting the optimal matching in the image with the template, we will get the best zoom ratio s, consequently estimate the target size. In the experiments, compare with CSK, KCF etc. demonstrate that the proposed method achieves high improvement in accuracy, is an efficient algorithm.
Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation
NASA Technical Reports Server (NTRS)
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
Gravitational Wave Emulation Using Gaussian Process Regression
NASA Astrophysics Data System (ADS)
Doctor, Zoheyr; Farr, Ben; Holz, Daniel
2017-01-01
Parameter estimation (PE) for gravitational wave signals from compact binary coalescences (CBCs) requires reliable template waveforms which span the parameter space. Waveforms from numerical relativity are accurate but computationally expensive, so approximate templates are typically used for PE. These `approximants', while quick to compute, can introduce systematic errors and bias PE results. We describe a machine learning method for generating CBC waveforms and uncertainties using existing accurate waveforms as a training set. Coefficients of a reduced order waveform model are computed and each treated as arising from a Gaussian process. These coefficients and their uncertainties are then interpolated using Gaussian process regression (GPR). As a proof of concept, we construct a training set of approximant waveforms (rather than NR waveforms) in the two-dimensional space of chirp mass and mass ratio and interpolate new waveforms with GPR. We demonstrate that the mismatch between interpolated waveforms and approximants is below the 1% level for an appropriate choice of training set and GPR kernel hyperparameters.
Gaussianization for fast and accurate inference from cosmological data
NASA Astrophysics Data System (ADS)
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.
Non-Gaussian error bars in galaxy surveys - I
NASA Astrophysics Data System (ADS)
Harnois-Déraps, Joachim; Pen, Ue-Li
2012-07-01
We propose a method to estimate non-Gaussian error bars on the matter power spectrum from galaxy surveys in the presence of non-trivial survey selection functions. The estimators are often obtained from formalisms like Feldmann, Kaiser and Peacock (FKP) and pseudo-Karhunen-Loève (PKL), which rely on the assumption that the underlying field is Gaussian. The Monte Carlo method is more accurate but involves the tedious process of running and cross-correlating a large number of N-body simulations, in which the survey volume is embedded. From 200 N-body simulations, we extract a non-linear covariance matrix as a function of two scales and of the angle between two Fourier modes. All the non-Gaussian features of that matrix are then simply parametrized in terms of a few fitting functions and eigenvectors. We furthermore develop a fast and accurate strategy that combines our parametrization with a general galaxy survey selection function, and incorporate non-Gaussian Poisson uncertainty. We describe how to incorporate these two distinct non-Gaussian contributions into a typical analysis pipeline, and apply our method with the selection function from the 2dFGRS. We find that the observed Fourier modes correlate at much larger scales than that predicted by both FKP formalism or pure N-body simulations in a 'top hat' selection function. In particular, the observed Fourier modes are already 50 per cent correlated at k˜ 0.1 h Mpc-1, and the non-Gaussian fractional variance on the power spectrum [?] is about a factor of 3.0 larger than the FKP prescription. At k˜ 0.4 h Mpc-1, the deviations are an order of magnitude.
Non-Gaussianity and CMB aberration and Doppler
Catena, Riccardo; Liguori, Michele; Renzi, Alessandro; Notari, Alessio E-mail: michele.liguori@pd.infn.it E-mail: arenzi@pd.infn.it
2013-09-01
The peculiar motion of an observer with respect to the CMB rest frame induces a deflection in the arrival direction of the observed photons (also known as CMB aberration) and a Doppler shift in the measured photon frequencies. As a consequence, aberration and Doppler effects induce non trivial correlations between the harmonic coefficients of the observed CMB temperature maps. In this paper we investigate whether these correlations generate a bias on non-Gaussianity estimators f{sub NL}. We perform this analysis simulating a large number of temperature maps with Planck-like resolution (lmax = 2000) as different realizations of the same cosmological fiducial model (WMAP7yr). We then add to these maps aberration and Doppler effects employing a modified version of the HEALPix code. We finally evaluate a generalization of the Komatsu, Spergel and Wandelt non-Gaussianity estimator for all the simulated maps, both when peculiar velocity effects have been considered and when these phenomena have been neglected. Using the value v/c = 1.23 × 10{sup −3} for our peculiar velocity, we found that the aberration/Doppler induced non-Gaussian signal is at most of about half of the cosmic variance σ for f{sub NL} both in a full-sky and in a cut-sky experimental configuration, for local, equilateral and orthogonal estimators. We conclude therefore that when estimating f{sub NL} it is safe to ignore aberration and Doppler effects if the primordial map is already Gaussian. More work is necessary however to assess whether a map which contains non-Gaussianity can be significantly distorted by a peculiar velocity.
NASA Astrophysics Data System (ADS)
Troncossi, M.; Di Sante, R.; Rivola, A.
2014-05-01
High-cycle fatigue life tests conducted using controlled random vibrations are commonly used to evaluate failure in components and structures. In most cases, a Gaussian distribution of both the input vibration and the stress response is assumed, while real-life loads may be non-Gaussian causing the response to be non-Gaussian as well. Generating non-Gaussian drive signals with high kurtosis and a given power spectral density, however, does not always guarantee that the stress response will actually be non-Gaussian, because this depends on the adherence of the tested system to the Central Limit Theorem. On the other side, suitable measurement methods need to be developed in order to estimate the stress amplitude response at critical failure locations, and therefore to evaluate and select input loads. In this paper, a simple test rig with a notched cantilevered specimen was developed to measure the response and examine the kurtosis values in the case of stationary Gaussian, stationary non-Gaussian, and non-stationary non-Gaussian excitation signals. The Laser Doppler Vibrometry (LDV) technique was used for the first time in this type of test, to estimate the specimen stress amplitude response in terms of differential displacement at the notch section ends. A method based on the use of accelerometers to correct for the occasional signal drops occurring during the experiment is described and the results are discussed with respect to the ability of the test procedure to evaluate the output signal.
FPGA design and implementation of Gaussian filter
NASA Astrophysics Data System (ADS)
Yang, Zhihui; Zhou, Gang
2015-12-01
In this paper , we choose four different variances of 1,3,6 and 12 to conduct FPGA design with three kinds of Gaussian filtering algorithm ,they are implementing Gaussian filter with a Gaussian filter template, Gaussian filter approximation with mean filtering and Gaussian filter approximation with IIR filtering. By waveform simulation and synthesis, we get the processing results on the experimental image and the consumption of FPGA resources of the three methods. We set the result of Gaussian filter used in matlab as standard to get the result error. By comparing the FPGA resources and the error of FPGA implementation methods, we get the best FPGA design to achieve a Gaussian filter. Conclusions can be drawn based on the results we have already got. When the variance is small, the FPGA resources is enough for the algorithm to implement Gaussian filter with a Gaussian filter template which is the best choice. But when the variance is so large that there is no more FPGA resources, we can chose the mean to approximate Gaussian filter with IIR filtering.
Non-Gaussian Stochastic Processes.
1986-02-28
Underwriting Risk and Return Paradox Revisited," J. Risk and Insurance .24.L 621-627 (1982). P. Brockett and B. Arnold, "Identifiability for Dependent...Some Ruin Calculations," J. Risk and Insurance 5DIAL 727-731 (1983). P. Brockett, S. Cox, and R. Witt, "Self-Insurance and the Probability of...Financial Regret," J. Risk and Insurance 51(4) 720-729 (1984). P. Brockett, "The Likelihood Ratio Detector for Non-Gaussian Infinitely Divisible and Linear
Gaussian effective potential: Quantum mechanics
NASA Astrophysics Data System (ADS)
Stevenson, P. M.
1984-10-01
We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.
Bimodal and Gaussian Ising spin glasses in dimension two
NASA Astrophysics Data System (ADS)
Lundow, P. H.; Campbell, I. A.
2016-02-01
An analysis is given of numerical simulation data to size L =128 on the archetype square lattice Ising spin glasses (ISGs) with bimodal (±J ) and Gaussian interaction distributions. It is well established that the ordering temperature of both models is zero. The Gaussian model has a nondegenerate ground state and thus a critical exponent η ≡0 , and a continuous distribution of energy levels. For the bimodal model, above a size-dependent crossover temperature T*(L ) there is a regime of effectively continuous energy levels; below T*(L ) there is a distinct regime dominated by the highly degenerate ground state plus an energy gap to the excited states. T*(L ) tends to zero at very large L , leaving only the effectively continuous regime in the thermodynamic limit. The simulation data on both models are analyzed with the conventional scaling variable t =T and with a scaling variable τb=T2/(1 +T2) suitable for zero-temperature transition ISGs, together with appropriate scaling expressions. The data for the temperature dependence of the reduced susceptibility χ (τb,L ) and second moment correlation length ξ (τb,L ) in the thermodynamic limit regime are extrapolated to the τb=0 critical limit. The Gaussian critical exponent estimates from the simulations, η =0 and ν =3.55 (5 ) , are in full agreement with the well-established values in the literature. The bimodal critical exponents, estimated from the thermodynamic limit regime analyses using the same extrapolation protocols as for the Gaussian model, are η =0.20 (2 ) and ν =4.8 (3 ) , distinctly different from the Gaussian critical exponents.
NASA Astrophysics Data System (ADS)
Troncossi, M.; Di Sante, R.; Rivola, A.
2016-10-01
In the field of vibration qualification testing, random excitations are typically imposed on the tested system in terms of a power spectral density (PSD) profile. This is the one of the most popular ways to control the shaker or slip table for durability tests. However, these excitations (and the corresponding system responses) exhibit a Gaussian probability distribution, whereas not all real-life excitations are Gaussian, causing the response to be also non-Gaussian. In order to introduce non-Gaussian peaks, a further parameter, i.e., kurtosis, has to be controlled in addition to the PSD. However, depending on the specimen behaviour and input signal characteristics, the use of non-Gaussian excitations with high kurtosis and a given PSD does not automatically imply a non-Gaussian stress response. For an experimental investigation of these coupled features, suitable measurement methods need to be developed in order to estimate the stress amplitude response at critical failure locations and consequently evaluate the input signals most representative for real-life, non-Gaussian excitations. In this paper, a simple test rig with a notched cantilevered specimen was developed to measure the response and examine the kurtosis values in the case of stationary Gaussian, stationary non-Gaussian, and burst non-Gaussian excitation signals. The laser Doppler vibrometry technique was used in this type of test for the first time, in order to estimate the specimen stress amplitude response as proportional to the differential displacement measured at the notch section ends. A method based on the use of measurements using accelerometers to correct for the occasional signal dropouts occurring during the experiment is described. The results demonstrate the ability of the test procedure to evaluate the output signal features and therefore to select the most appropriate input signal for the fatigue test.
Troncossi, M; Di Sante, R; Rivola, A
2016-10-01
In the field of vibration qualification testing, random excitations are typically imposed on the tested system in terms of a power spectral density (PSD) profile. This is the one of the most popular ways to control the shaker or slip table for durability tests. However, these excitations (and the corresponding system responses) exhibit a Gaussian probability distribution, whereas not all real-life excitations are Gaussian, causing the response to be also non-Gaussian. In order to introduce non-Gaussian peaks, a further parameter, i.e., kurtosis, has to be controlled in addition to the PSD. However, depending on the specimen behaviour and input signal characteristics, the use of non-Gaussian excitations with high kurtosis and a given PSD does not automatically imply a non-Gaussian stress response. For an experimental investigation of these coupled features, suitable measurement methods need to be developed in order to estimate the stress amplitude response at critical failure locations and consequently evaluate the input signals most representative for real-life, non-Gaussian excitations. In this paper, a simple test rig with a notched cantilevered specimen was developed to measure the response and examine the kurtosis values in the case of stationary Gaussian, stationary non-Gaussian, and burst non-Gaussian excitation signals. The laser Doppler vibrometry technique was used in this type of test for the first time, in order to estimate the specimen stress amplitude response as proportional to the differential displacement measured at the notch section ends. A method based on the use of measurements using accelerometers to correct for the occasional signal dropouts occurring during the experiment is described. The results demonstrate the ability of the test procedure to evaluate the output signal features and therefore to select the most appropriate input signal for the fatigue test.
Random Walks and Branching Processes in Correlated Gaussian Environment
NASA Astrophysics Data System (ADS)
Aurzada, Frank; Devulder, Alexis; Guillotin-Plantard, Nadine; Pène, Françoise
2017-01-01
We study persistence probabilities for random walks in correlated Gaussian random environment investigated by Oshanin et al. (Phys Rev Lett, 110:100602, 2013). From the persistence results, we can deduce properties of critical branching processes with offspring sizes geometrically distributed with correlated random parameters. More precisely, we obtain estimates on the tail distribution of its total population size, of its maximum population, and of its extinction time.
Planck 2013 results. XXIV. Constraints on primordial non-Gaussianity
NASA Astrophysics Data System (ADS)
Planck Collaboration; Ade, P. A. R.; Aghanim, N.; 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.; Benoît, A.; Benoit-Lévy, 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, H. C.; Chiang, L.-Y.; 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.; Désert, F.-X.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, 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-Héraud, Y.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F. K.; Hanson, D.; Harrison, D.; Heavens, A.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T. S.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lacasa, F.; Lagache, G.; Lähteenmäki, 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-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maffei, B.; Maino, D.; Mandolesi, N.; Mangilli, A.; Marinucci, D.; Maris, M.; Marshall, D. J.; Martin, P. G.; Martínez-González, E.; Masi, S.; Massardi, M.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Meinhold, P. R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Natoli, P.; Netterfield, C. B.; Nørgaard-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.; Prézeau, 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.; Rubiño-Martín, 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.; Sutter, P.; 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.
2014-11-01
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 fNLlocal = 2.7 ± 5.8, fNLequil = -42 ± 75, and fNLorth = -25 ± 39 (68% CL statistical). Non-Gaussianity is detected in the data; using skew-Cℓ statistics we find a nonzero bispectrum from residual point sources, and the integrated-Sachs-Wolfe-lensing bispectrum at a level expected in the ΛCDM 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-Cℓ, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, three-dimensional reconstructions of the Planck CMB bispectrum and thus derive constraints on early-Universe scenarios that generate primordial NG, including general single-field models of inflation, excited initial states (non-Bunch-Davies vacua), and directionally-dependent vector models. We provide an initial survey of scale-dependent feature and resonance models. These results bound both general single-field and multi-field model parameter ranges, such as the speed of sound, cs ≥ 0.02 (95% CL), in an effective field theory parametrization, and the curvaton decay fraction rD ≥ 0.15 (95% CL). The Planck data significantly limit the viable parameter space of the ekpyrotic/cyclic scenarios. The amplitude of the four-point function in the local model τNL< 2800 (95% CL). Taken together, these constraints represent the highest precision tests to date of physical mechanisms for the origin of cosmic structure.
STATISTICS OF TURBULENT FIELD VARIATIONS, NON-GAUSSIANITY AND INTERMITTENCY
Ragot, B. R
2009-05-10
Statistics of magnetic field and velocity variations are important to the study of turbulence. Their departure from Gaussianity on the short separation scales has long been recognized and ascribed to intermittency. Non-Gaussian log-normal statistics of field-line separations are now predicted, however, from simple nonfluctuating turbulence Fourier spectra that do not model any intermittency, and one may wonder how this result may impact our interpretation of the statistics of field variations. It is shown in this paper how the intermittency of the turbulence can be taken into account to estimate the distributions of field-line separations and of field variations from the simple Fourier-spectra calculations. The first accurate theory/modeling predictions for the observed in situ distributions of turbulent field variations are thereby made, free of parameter adjustment. Magnetic field data from Helios 2 and Wind are used for the validation. Because the field variations are measured between points of constant separation and not between real field lines, intermittency remains the main cause for the observed non-Gaussianity of the statistics of field variations on the short scales, even if spatial limitations and/or short-scale phase correlations could also contribute to the deviations from Gaussianity.
Monogamy inequality for distributed gaussian entanglement.
Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio
2007-02-02
We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.
Extremes of Some Gaussian Random Interfaces
NASA Astrophysics Data System (ADS)
Chiarini, Alberto; Cipriani, Alessandra; Hazra, Rajat Subhra
2016-11-01
In this article we give a general criterion for some dependent Gaussian models to belong to maximal domain of attraction of Gumbel, following an application of the Stein-Chen method studied in Arratia et al. (Ann Probab 17(1):9-25, 1989). We also show the convergence of the associated point process. As an application, we show the conditions are satisfied by some of the well-known supercritical Gaussian interface models, namely, membrane model, massive and massless discrete Gaussian free field, fractional Gaussian free field.
Elegant Gaussian beams for enhanced optical manipulation
Alpmann, Christina Schöler, Christoph; Denz, Cornelia
2015-06-15
Generation of micro- and nanostructured complex light beams attains increasing impact in photonics and laser applications. In this contribution, we demonstrate the implementation and experimental realization of the relatively unknown, but highly versatile class of complex-valued Elegant Hermite- and Laguerre-Gaussian beams. These beams create higher trapping forces compared to standard Gaussian light fields due to their propagation changing properties. We demonstrate optical trapping and alignment of complex functional particles as nanocontainers with standard and Elegant Gaussian light beams. Elegant Gaussian beams will inspire manifold applications in optical manipulation, direct laser writing, or microscopy, where the design of the point-spread function is relevant.
An empirical analysis of the distribution of overshoots in a stationary Gaussian stochastic process
NASA Technical Reports Server (NTRS)
Carter, M. C.; Madison, M. W.
1973-01-01
The frequency distribution of overshoots in a stationary Gaussian stochastic process is analyzed. The primary processes involved in this analysis are computer simulation and statistical estimation. Computer simulation is used to simulate stationary Gaussian stochastic processes that have selected autocorrelation functions. An analysis of the simulation results reveals a frequency distribution for overshoots with a functional dependence on the mean and variance of the process. Statistical estimation is then used to estimate the mean and variance of a process. It is shown that for an autocorrelation function, the mean and the variance for the number of overshoots, a frequency distribution for overshoots can be estimated.
Breaking Gaussian incompatibility on continuous variable quantum systems
Heinosaari, Teiko; Kiukas, Jukka; Schultz, Jussi
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.
Optimisation of dispersion parameters of Gaussian plume model for CO₂ dispersion.
Liu, Xiong; Godbole, Ajit; Lu, Cheng; Michal, Guillaume; Venton, Philip
2015-11-01
The carbon capture and storage (CCS) and enhanced oil recovery (EOR) projects entail the possibility of accidental release of carbon dioxide (CO2) into the atmosphere. To quantify the spread of CO2 following such release, the 'Gaussian' dispersion model is often used to estimate the resulting CO2 concentration levels in the surroundings. The Gaussian model enables quick estimates of the concentration levels. However, the traditionally recommended values of the 'dispersion parameters' in the Gaussian model may not be directly applicable to CO2 dispersion. This paper presents an optimisation technique to obtain the dispersion parameters in order to achieve a quick estimation of CO2 concentration levels in the atmosphere following CO2 blowouts. The optimised dispersion parameters enable the Gaussian model to produce quick estimates of CO2 concentration levels, precluding the necessity to set up and run much more complicated models. Computational fluid dynamics (CFD) models were employed to produce reference CO2 dispersion profiles in various atmospheric stability classes (ASC), different 'source strengths' and degrees of ground roughness. The performance of the CFD models was validated against the 'Kit Fox' field measurements, involving dispersion over a flat horizontal terrain, both with low and high roughness regions. An optimisation model employing a genetic algorithm (GA) to determine the best dispersion parameters in the Gaussian plume model was set up. Optimum values of the dispersion parameters for different ASCs that can be used in the Gaussian plume model for predicting CO2 dispersion were obtained.
Correction Factor for Gaussian Deconvolution of Optically Thick Linewidths in Homogeneous Sources
NASA Technical Reports Server (NTRS)
Kastner, S. O.; Bhatia, A. K.
1999-01-01
Profiles of optically thick, non-Gaussian emission line profiles convoluted with Gaussian instrumental profiles are constructed, and are deconvoluted on the usual Gaussian basis to examine the departure from accuracy thereby caused in "measured" linewidths. It is found that "measured" linewidths underestimate the true linewidths of optically thick lines, by a factor which depends on the resolution factor r congruent to Doppler width/instrumental width and on the optical thickness tau(sub 0). An approximating expression is obtained for this factor, applicable in the range of at least 0 <= tau(sub 0) <= 10, which can provide estimates of the true linewidth and optical thickness.
A note on population analysis of dissolution-absorption models using the inverse Gaussian function.
Wang, Jian; Weiss, Michael; D'Argenio, David Z
2008-06-01
Because conventional absorption models often fail to describe plasma concentration-time profiles following oral administration, empirical input functions such as the inverse Gaussian function have been successfully used. The purpose of this note is to extend this model by adding a first-order absorption process and to demonstrate the application of population analysis using maximum likelihood estimation via the EM algorithm (implemented in ADAPT 5). In one example, the analysis of bioavailability data of an extended-release formulation, as well as the mean dissolution times estimated in vivo and in vitro with the use of the inverse Gaussian function, is well in accordance, suggesting that the inverse Gaussian function indeed accounts for the in vivo dissolution process. In the other example, the kinetics of trapidil in patients with liver disease, the absorption/dissolution parameters are characterized by a high interindividual variability. Adding a first-order absorption process to the inverse Gaussian function improved the fit in both cases.
Matching optics for Gaussian beams
NASA Technical Reports Server (NTRS)
Gunter, William D. (Inventor)
1991-01-01
A system of matching optics for Gaussian beams is described. The matching optics system is positioned between a light beam emitter (such as a laser) and the input optics of a second optics system whereby the output from the light beam emitter is converted into an optimum input for the succeeding parts of the second optical system. The matching optics arrangement includes the combination of a light beam emitter, such as a laser with a movable afocal lens pair (telescope) and a single movable lens placed in the laser's output beam. The single movable lens serves as an input to the telescope. If desired, a second lens, which may be fixed, is positioned in the beam before the adjustable lens to serve as an input processor to the movable lens. The system provides the ability to choose waist diameter and position independently and achieve the desired values with two simple adjustments not requiring iteration.
Cylindrical quasi-Gaussian beams.
Mitri, F G
2013-11-15
Making use of the complex-source-point method in cylindrical coordinates, an exact solution representing a cylindrical quasi-Gaussian beam of arbitrary waist w(0) satisfying both the Helmholtz and Maxwell's equations is introduced. The Cartesian components of the electromagnetic field are derived stemming from different polarizations of the magnetic and electric vector potentials based on Maxwell's vectorial equations and Lorenz's gauge condition, without any approximations. Computations illustrate the theory for tightly focused and quasi-collimated cylindrical beams. The results are particularly useful in beam-forming design using high-aperture or collimated cylindrical laser beams in imaging microscopy, particle manipulation, optical tweezers, and the study of scattering, radiation forces, and torque on cylindrical structures.
A Gaussian process based prognostics framework for composite structures
NASA Astrophysics Data System (ADS)
Liu, Yingtao; Mohanty, Subhasish; Chattopadhyay, Aditi
2009-03-01
Prognostic algorithms indicate the remaining useful life based on fault detection and diagnosis through condition monitoring framework. Due to the wide-spread applications of advanced composite materials in industry, the importance of prognosis on composite materials is being acknowledged by the research community. Prognosis has the potential to significantly enhance structural monitoring and maintenance planning. In this paper, a Gaussian process based prognostics framework is presented. Both off-line and on-line methods combined state estimation and life prediction of composite beam subject to fatigue loading. The framework consists of three main steps: 1) data acquisition, 2) feature extraction, 3) damage state prediction and remaining useful life estimation. Active piezoelectric and acoustic emission (AE) sensing techniques are applied to monitor the damage states. Wavelet transform is used to extract the piezoelectric sensing features. The number of counts from AE system was used as a feature. Piezoelectric or AE sensing features are used to build the input and output space of the Gaussian process. The future damage states and remaining useful life are predicted by Gaussian process based off-line and on-line algorithms. Accuracy of the Gaussian process based prognosis method is improved by including more training sets. Piezoelectric and AE features are also used for the state prediction. In the test cases presented, the piezoelectric features lead to better prognosis results. On-line prognosis is completed sequentially by combining experimental and predicted features. On-line damage state prediction and remaining useful life estimation shows good correlation with experimental data at later stages of fatigue life.
Statistical calibration via Gaussianization in hot-wire anemometry
NASA Astrophysics Data System (ADS)
Gluzman, Igal; Cohen, Jacob; Oshman, Yaakov
2017-03-01
A statistical method is introduced, that is based on Gaussianization to estimate the nonlinear calibration curve of a hot-wire probe, relating the input flow velocity to the output (measured) voltage. The method uses as input a measured sequence of voltage samples, corresponding to different unknown flow velocities in the desired operational range, and only two measured voltages along with their known (calibrated) flow velocities. The method relies on the conditions that (1) the velocity signal is Gaussian distributed (or has another known distribution), and (2) the measured signal covers the desired velocity range over which the sensor is to be calibrated. The novel calibration method is validated against standard calibration methods using data acquired by hot-wire probes in wind-tunnel experiments. In these experiments, a hot-wire probe is placed at a certain region downstream of a cube-shaped body in a freestream of air flow, properly selected, so that the central limit theorem, when applied to the random velocity increments composing the instantaneous velocity in the wake, roughly holds, and renders the measured signal nearly Gaussian distributed. The statistical distribution of the velocity field in the wake is validated by mapping the first four statistical moments of the measured signals in different regions of the wake and comparing them with corresponding moments of the Gaussian distribution. The experimental data are used to evaluate the sensitivity of the method to the distribution of the measured signal, and the method is demonstrated to possess some robustness with respect to deviations from the Gaussian distribution.
Measurement-induced Nonlocality for Gaussian States
NASA Astrophysics Data System (ADS)
Ma, Ruifen; Hou, Jinchuan; Qi, Xiaofei
2017-04-01
We establish an analytic formula of measurement-induced nonlocality (MIN) for two-mode squeezed thermal states and mixed thermal states. Different from the quantum discord case, we show that there is no Gaussian version of MIN by Gaussian positive operator valued measurements.
Conditional and unconditional Gaussian quantum dynamics
NASA Astrophysics Data System (ADS)
Genoni, Marco G.; Lami, Ludovico; Serafini, Alessio
2016-07-01
This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as 'general-dyne') quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.
Gaussian MRF rotation-invariant features for image classification.
Deng, Huawu; Clausi, David A
2004-07-01
Features based on Markov random field (MRF) models are sensitive to texture rotation. This paper develops an anisotropic circular Gaussian MRF (ACGMRF) model for retrieving rotation-invariant texture features. To overcome the singularity problem of the least squares estimate method, an approximate least squares estimate method is designed and implemented. Rotation-invariant features are obtained from the ACGMRF model parameters using the discrete Fourier transform. The ACGMRF model is demonstrated to be a statistical improvement over three published methods. The three methods include a Laplacian pyramid, an isotropic circular GMRF (ICGMRF), and gray level cooccurrence probability features.
Modeling the interferometric radius measurement using Gaussian beam propagation
Medicus, Katherine M.; Snyder, James J.; Davies, Angela
2006-12-01
We model the interferometric radius measurement using Gaussian beam propagation to identify biases in the measurement due to using a simple geometric ray-trace model instead of the more complex Gaussian model. The radius measurement is based on using an interferometer to identify the test part's position when it is at two null locations, and the distance between the positions is an estimate of the part's radius. The null condition is observed when there is no difference in curvature between the reflected reference and the test wavefronts, and a Gaussian model will provide a first-order estimate of curvature changes due to wave propagation and therefore changes to the radius measurement. We show that the geometric ray assumption leads to radius biases (errors) that are a strong function of the test part radius and increase as the radius of the part decreases. We tested for a bias for both microscaled(<1 mm) and macroscaled parts. The bias is of the order of parts in 105 for micro-optics with radii a small fraction of a millimeter and much smaller for macroscaled optics. The amount of bias depends on the interferometer configuration (numerical aperture, etc.), the nominal radius of the test part, and the distances in the interferometer.
Stochastic modeling of seafloor morphology: A parameterized Gaussian model
Goff, J.A.; Jordan, T.H. )
1989-01-01
Stochastic methods of analysis are useful for quantifying ensemble properties of small-scale bathymetric features such as abyssal hills. In this paper the authors model the seafloor as a stationary, zero-mean, Gaussian random field completely specified by its autocovariance function. They formulate an anisotropic autocovariance function that has five free parameters describing the amplitude, anisotropic orientation and aspect ratio, characteristic length, and Hausdorff (fractal) dimension of seafloor topography. Parameters estimated from various seafloor exhibits a wide range of stochastic characteristics within the constraints of the model. Synthetic topography can be generated at arbitrary scale and resolution from the Gaussian model using a Fourier method. Color images of these synthetics are useful for illustrating the stochastic behavior of the model.
Asymmetric Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-06-01
We introduce a family of asymmetric Laguerre-Gaussian (aLG) laser beams. The beams have been derived via a complex-valued shift of conventional LG beams in the Cartesian plane. While propagating in a uniform medium, the first bright ring of the aLG beam becomes less asymmetric and the energy is redistributed toward peripheral diffraction rings. The projection of the orbital angular momentum (OAM) onto the optical axis is calculated. The OAM is shown to grow quadratically with increasing asymmetry parameter of the aLG beam, which equals the ratio of the shift to the waist radius. Conditions for the OAM becoming equal to the topological charge have been derived. For aLG beams with zero radial index, we have deduced an expression to define the intensity maximum coordinates and shown the crescent-shaped intensity pattern to rotate during propagation. Results of the experimental generation and rotation of aLG beams agree well with theoretical predictions.
Quantum bit commitment under Gaussian constraints
NASA Astrophysics Data System (ADS)
Mandilara, Aikaterini; Cerf, Nicolas J.
2012-06-01
Quantum bit commitment has long been known to be impossible. Nevertheless, just as in the classical case, imposing certain constraints on the power of the parties may enable the construction of asymptotically secure protocols. Here, we introduce a quantum bit commitment protocol and prove that it is asymptotically secure if cheating is restricted to Gaussian operations. This protocol exploits continuous-variable quantum optical carriers, for which such a Gaussian constraint is experimentally relevant as the high optical nonlinearity needed to effect deterministic non-Gaussian cheating is inaccessible.
Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states
Adesso, Gerardo; Illuminati, Fabrizio
2005-09-15
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
Measuring primordial non-Gaussianity with weak lensing surveys
NASA Astrophysics Data System (ADS)
Hilbert, Stefan; Marian, Laura; Smith, Robert E.; Desjacques, Vincent
2012-11-01
not taken into account, a non-vanishing level of primordial non-Gaussianity will bias the estimated cosmological parameters and uncertainties for future surveys.
On the relationship between Gaussian stochastic blockmodels and label propagation algorithms
NASA Astrophysics Data System (ADS)
Zhang, Junhao; Chen, Tongfei; Hu, Junfeng
2015-03-01
The problem of community detection has received great attention in recent years. Many methods have been proposed to discover communities in networks. In this paper, we propose a Gaussian stochastic blockmodel that uses Gaussian distributions to fit weight of edges in networks for non-overlapping community detection. The maximum likelihood estimation of this model has the same objective function as general label propagation with node preference. The node preference of a specific vertex turns out to be a value proportional to the intra-community eigenvector centrality (the corresponding entry in principal eigenvector of the adjacency matrix of the subgraph inside that vertex's community) under maximum likelihood estimation. Additionally, the maximum likelihood estimation of a constrained version of our model is highly related to another extension of the label propagation algorithm, namely, the label propagation algorithm under constraint. Experiments show that the proposed Gaussian stochastic blockmodel performs well on various benchmark networks.
Log Gaussian Cox processes and spatially aggregated disease incidence data.
Li, Ye; Brown, Patrick; Gesink, Dionne C; Rue, Håvard
2012-10-01
This article presents a methodology for modeling aggregated disease incidence data with the spatially continuous log-Gaussian Cox process. Statistical models for spatially aggregated disease incidence data usually assign the same relative risk to all individuals in the same reporting region (census areas or postal regions). A further assumption that the relative risks in two regions are independent given their neighbor's risks (the Markov assumption) makes the commonly used Besag-York-Mollié model computationally simple. The continuous model proposed here uses a data augmentation step to sample from the posterior distribution of the exact locations at each step of an Markov chain Monte Carlo algorithm, and models the exact locations with an log-Gaussian Cox process. A simulation study shows the log-Gaussian Cox process model consistently outperforming the Besag-York-Mollié model. The method is illustrated by making inference on the spatial distribution of syphilis risk in North Carolina. The effect of several known social risk factors are estimated, and areas with risk well in excess of that expected given these risk factors are identified.
Second and third harmonic waves excited by focused Gaussian beams.
Levy, Uri; Silberberg, Yaron
2015-10-19
Harmonic generation by tightly-focused Gaussian beams is finding important applications, primarily in nonlinear microscopy. It is often naively assumed that the nonlinear signal is generated predominantly in the focal region. However, the intensity of Gaussian-excited electromagnetic harmonic waves is sensitive to the excitation geometry and to the phase matching condition, and may depend on quite an extended region of the material away from the focal plane. Here we solve analytically the amplitude integral for second harmonic and third harmonic waves and study the generated harmonic intensities vs. focal-plane position within the material. We find that maximum intensity for positive wave-vector mismatch values, for both second harmonic and third harmonic waves, is achieved when the fundamental Gaussian is focused few Rayleigh lengths beyond the front surface. Harmonic-generation theory predicts strong intensity oscillations with thickness if the material is very thin. We reproduced these intensity oscillations in glass slabs pumped at 1550nm. From the oscillations of the 517nm third-harmonic waves with slab thickness we estimate the wave-vector mismatch in a Soda-lime glass as Δk(H)= -0.249μm(-1).
Gaussian mapping of chemical fragments in ligand binding sites
NASA Astrophysics Data System (ADS)
Wang, Kun; Murcia, Marta; Constans, Pere; Pérez, Carlos; Ortiz, Angel R.
2004-02-01
We present a new approach to automatically define a quasi-optimal minimal set of pharmacophoric points mapping the interaction properties of a user-defined ligand binding site. The method is based on a fitting algorithm where a grid of sampled interaction energies of the target protein with small chemical fragments in the binding site is approximated by a linear expansion of Gaussian functions. A heuristic approximation selects from this expansion the smallest possible set of Gaussians required to describe the interaction properties of the binding site within a prespecified accuracy. We have evaluated the performance of the approach by comparing the computed Gaussians with the positions of aromatic sites found in experimental protein-ligand complexes. For a set of 53 complexes, good correspondence is found in general. At a 95% significance level, ˜65% of the predicted interaction points have an aromatic binding site within 1.5 Å. We then studied the utility of these points in docking using the program DOCK. Short docking times, with an average of ˜0.18 s per conformer, are obtained, while retaining, both for rigid and flexible docking, the ability to sample native-like binding modes for the ligand. An average 4-5-fold speed-up in docking times and a similar success rate is estimated with respect to the standard DOCK protocol. Abbreviations: RMSD - root mean square deviation; ASA - Atomic Shell Approximation; LSF - Least-Squares Fitting; 3D - three-dimensional; VDW - Van der Waals.
Multitracing anisotropic non-Gaussianity with galaxy shapes
NASA Astrophysics Data System (ADS)
Chisari, Nora Elisa; Dvorkin, Cora; Schmidt, Fabian; Spergel, David N.
2016-12-01
Correlations between intrinsic galaxy shapes on large scales arise due to the effect of the tidal field of the large-scale structure. Anisotropic primordial non-Gaussianity induces a distinct scale-dependent imprint in these tidal alignments on large scales. Motivated by the observational finding that the alignment strength of luminous red galaxies depends on how galaxy shapes are measured, we study the use of two different shape estimators as a multitracer probe of intrinsic alignments. We show, by means of a Fisher analysis, that this technique promises a significant improvement on anisotropic non-Gaussianity constraints over a single-tracer method. For future weak lensing surveys, the uncertainty in the anisotropic non-Gaussianity parameter, A2, is forecast to be σ (A2)≈50 , ˜40 % smaller than currently available constraints from the bispectrum of the cosmic microwave background. This corresponds to an improvement of a factor of 4-5 over the uncertainty from a single-tracer analysis.
Primordial non-Gaussianity from the DBI Galileons
NASA Astrophysics Data System (ADS)
Mizuno, Shuntaro; Koyama, Kazuya
2010-11-01
We study primordial fluctuations generated during inflation in a class of models motivated by the DBI Galileons, which are extensions of the DBI action that yield second-order field equations. This class of models generalizes the DBI Galileons in a similar way with K inflation. We calculate the primordial non-Gaussianity from the bispectrum of the curvature perturbations at leading order in the slow-varying approximations. We show that the estimator for the equilateral-type non-Gaussianity, fNLequil, can be applied to measure the amplitude of the primordial bispectrum even in the presence of the Galileon-like term although it gives a slightly different momentum dependence from K-inflation models. For the DBI Galileons, we find -0.32/cs2
Galaxy bias and primordial non-Gaussianity
Assassi, Valentin; Baumann, Daniel; Schmidt, Fabian E-mail: D.D.Baumann@uva.nl
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.
Non-Gaussianities in New Ekpyrotic Cosmology.
Buchbinder, Evgeny I; Khoury, Justin; Ovrut, Burt A
2008-05-02
The new ekpyrotic model is an alternative scenario of the early Universe which relies on a phase of slow contraction before the big bang. We calculate the 3-point and 4-point correlation functions of primordial density perturbations and find a generically large non-Gaussian signal, just below the current sensitivity level of cosmic microwave background experiments. This is in contrast with slow-roll inflation, which predicts negligible non-Gaussianity. The model is also distinguishable from alternative inflationary scenarios that can yield large non-Gaussianity, such as Dirac-Born-Infeld inflation and the simplest curvatonlike models, through the shape dependence of the correlation functions. Non-Gaussianity therefore provides a distinguishing and testable prediction of New Ekpyrotic Cosmology.
Improved Gaussian Beam-Scattering Algorithm
NASA Technical Reports Server (NTRS)
Lock, James A.
1995-01-01
The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.
Lecture Notes on Non-Gaussianity
NASA Astrophysics Data System (ADS)
Byrnes, Christian T.
We discuss how primordial non-Gaussianity of the curvature perturbation helps to constrain models of the early universe. Observations are consistent with Gaussian initial conditions, compatible with the predictions of the simplest models of inflation. Deviations are constrained to be at the sub percent level, constraining alternative models such as those with multiple fields, non-canonical kinetic terms or breaking the slow-roll conditions. We introduce some of the most important models of inflation which generate non-Gaussian perturbations and provide practical tools on how to calculate the three-point correlation function for a popular class of non-Gaussian models. The current state of the field is summarised and an outlook is given.
Optimal cloning of mixed Gaussian states
Guta, Madalin; Matsumoto, Keiji
2006-09-15
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.
Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
NASA Astrophysics Data System (ADS)
Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Arroja, F.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A. J.; Barreiro, R. B.; Bartolo, N.; Basak, S.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bock, J. J.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H. C.; Christensen, P. R.; Church, S.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Combet, C.; 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.; Désert, F.-X.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T. A.; Eriksen, H. K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A. A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Gauthier, C.; Ghosh, T.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J. E.; Hamann, J.; Hansen, F. K.; Hanson, D.; Harrison, D. L.; Heavens, A.; Helou, G.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huang, Z.; Huffenberger, K. M.; Hurier, G.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kim, J.; Kisner, T. S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lacasa, F.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C. R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Lewis, A.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Marinucci, D.; Maris, M.; Martin, P. G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McGehee, P.; Meinhold, P. R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Münchmeyer, M.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H. V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Racine, B.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rubiño-Martín, J. A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Shiraishi, M.; Smith, K.; Spencer, L. D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sutter, P.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Troja, A.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Wade, L. A.; Wandelt, B. D.; Wehus, I. K.; Yvon, D.; Zacchei, A.; Zonca, A.
2016-09-01
The Planck full mission cosmic microwave background (CMB) temperature and E-mode polarization maps are analysed to obtain constraints on primordial non-Gaussianity (NG). Using three classes of 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 from temperature alone ƒlocalNL = 2.5 ± 5.7, ƒequilNL= -16 ± 70, , and ƒorthoNL = -34 ± 32 (68% CL, statistical). Combining temperature and polarization data we obtain ƒlocalNL = 0.8 ± 5.0, ƒequilNL= -4 ± 43, and ƒorthoNL = -26 ± 21 (68% CL, statistical). 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 consistent with estimators based on measuring the Minkowski functionals of the CMB. The effect of time-domain de-glitching systematics on the bispectrum is negligible. In spite of these test outcomes we conservatively label the results including polarization data as preliminary, owing to a known mismatch of the noise model in simulations and the data. Beyond estimates of individual shape amplitudes, we present model-independent, three-dimensional reconstructions of the Planck CMB bispectrum and derive constraints on early universe scenarios that generate primordial NG, including general single-field models of inflation, axion inflation, initial state modifications, models producing parity-violating tensor bispectra, and directionally dependent vector models. We present a wide survey of scale-dependent feature and resonance models, accounting for the "look elsewhere" effect in estimating the statistical significance of features. We also look for isocurvature NG, and find no signal, but we obtain constraints that improve significantly with the inclusion of polarization. The primordial
Gaussian-Beam Laser-Resonator Program
NASA Technical Reports Server (NTRS)
Cross, Patricia L.; Bair, Clayton H.; Barnes, Norman
1989-01-01
Gaussian Beam Laser Resonator Program models laser resonators by use of Gaussian-beam-propagation techniques. Used to determine radii of beams as functions of position in laser resonators. Algorithm used in program has three major components. First, ray-transfer matrix for laser resonator must be calculated. Next, initial parameters of beam calculated. Finally, propagation of beam through optical elements computed. Written in Microsoft FORTRAN (Version 4.01).
Ultrasonic transducer with Gaussian radial pressure distribution
NASA Technical Reports Server (NTRS)
Claus, R. O.; Zerwekh, P. S. (Inventor)
1984-01-01
An ultrasonic transducer that produces an output that is a symmetrical function comprises a piezoelectric crystal with several concentric ring electrodes on one side of the crystal. A resistor network applies different amplitudes of an ac source to each of the several electrodes. A plot of the different amplitudes from the outermost electrode to the innermost electrode is the first half of a Gaussian function. Consequently, the output of the crystal from the side opposite the electrodes has a Gaussian profile.
Non-Gaussianity and intermittency in an ensemble of Gaussian fields
NASA Astrophysics Data System (ADS)
Wilczek, Michael
2016-12-01
Motivated by the need to capture statistical properties of turbulent systems in simple, analytically tractable models, an ensemble of Gaussian sub-ensembles with varying properties of the correlation function such as variance and length scale is investigated. The ensemble statistics naturally exhibit non-Gaussianity and intermittency. Due to the simplicity of Gaussian random fields, many explicit results can be obtained analytically, revealing the origin of non-Gaussianity in this framework. Potential applications of the proposed model ensemble for the description of non-equilibrium statistical mechanics of complex turbulent systems are briefly discussed.
Suborbital spaceplane optimization using non-stationary Gaussian processes
NASA Astrophysics Data System (ADS)
Dufour, Robin; de Muelenaere, Julien; Elham, Ali
2014-10-01
This paper presents multidisciplinary design optimization of a sub-orbital spaceplane. The optimization includes three disciplines: the aerodynamics, the structure and the trajectory. An Adjoint Euler code is used to calculate the aerodynamic lift and drag of the vehicle as well as their derivatives with respect to the design variables. A new surrogate model has been developed based on a non-stationary Gaussian process. That model was used to estimate the aerodynamic characteristics of the vehicle during the trajectory optimization. The trajectory of thevehicle has been optimized together with its geometry in order to maximize the amount of payload that can be carried by the spaceplane.
CMB lensing and primordial squeezed non-gaussianity
Pearson, Ruth; Lewis, Antony; Regan, Donough E-mail: antony@cosmologist.info
2012-03-01
Squeezed primordial non-Gaussianity can strongly constrain early-universe physics, but it can only be observed on the CMB after it has been gravitationally lensed. We give a new simple non-perturbative prescription for accurately calculating the effect of lensing on any squeezed primordial bispectrum shape, and test it with simulations. We give the generalization to polarization bispectra, and discuss the effect of lensing on the trispectrum. We explain why neglecting the lensing smoothing effect does not significantly bias estimators of local primordial non-Gaussianity, even though the change in shape can be ∼>10%. We also show how τ{sub NL} trispectrum estimators can be well approximated by much simpler CMB temperature modulation estimators, and hence that there is potentially a ∼ 10–30% bias due to very large-scale lensing modes, depending on the range of modulation scales included. Including dipole sky modulations can halve the τ{sub NL} error bar if kinematic effects can be subtracted using known properties of the CMB temperature dipole. Lensing effects on the g{sub NL} trispectrum are small compared to the error bar. In appendices we give the general result for lensing of any primordial bispectrum, and show how any full-sky squeezed bispectrum can be decomposed into orthogonal modes of distinct angular dependence.
NASA Technical Reports Server (NTRS)
Mashiku, Alinda; Garrison, James L.; Carpenter, J. Russell
2012-01-01
The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.
A Framework for Non-Gaussian Signal Modeling and Estimation
1999-06-01
1993. [38] B. P. Carlin , N. G. Polson, and D. S. Stoffer, "A Monte Carlo approach to nonnormal and nonlinear state-space modeling," Journal of the...NJ: Prentice-Hall, 1992. [198] J. R. Thompson, Empirical Model Building. New York: John Wiley & Sons, 1989. [199] J. R. Thompson and R. A. Tapia
Joint regression analysis of correlated data using Gaussian copulas.
Song, Peter X-K; Li, Mingyao; Yuan, Ying
2009-03-01
This article concerns a new joint modeling approach for correlated data analysis. Utilizing Gaussian copulas, we present a unified and flexible machinery to integrate separate one-dimensional generalized linear models (GLMs) into a joint regression analysis of continuous, discrete, and mixed correlated outcomes. This essentially leads to a multivariate analogue of the univariate GLM theory and hence an efficiency gain in the estimation of regression coefficients. The availability of joint probability models enables us to develop a full maximum likelihood inference. Numerical illustrations are focused on regression models for discrete correlated data, including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes. In the simulation studies, the proposed copula-based joint model is compared to the popular generalized estimating equations, which is a moment-based estimating equation method to join univariate GLMs. Two real-world data examples are used in the illustration.
NASA Astrophysics Data System (ADS)
Wu, L.; Seo, D.; Demargne, J.; Brown, J. D.
2008-12-01
In this presentation, we describe generation of ensemble precipitation forecasts from single-value quantitative precipitation forecasts (QPF) via the mixed-type bivariate meta-Gaussian model (Herr and Krzysztofowicz 2005). Because of the intermittent nature of precipitation, it is necessary to model precipitation amount as a mixed variable. The joint distribution of single-value QPF and observed precipitation amounts may then be modeled by the mixed-type bivariate meta-Gaussian distribution. From the single-value QPF, one may generate ensemble precipitation forecasts by sampling from the conditional distribution of the mixed-type bivariate meta-Gaussian distribution. The marginal distributions of the meta-Gaussian distribution are estimated using the Gaussian kernel smoothing technique with a plug-in bandwidth selection procedure. This methodology attempts to capture the skill and uncertainty in the QPF. We present both dependent and independent validation results for selected river basins in the AB-, CN-, and MA-RFC areas.
From particle counting to Gaussian tomography
NASA Astrophysics Data System (ADS)
Parthasarathy, K. R.; Sengupta, Ritabrata
2015-12-01
The momentum and position observables in an n-mode boson Fock space Γ(ℂn) have the whole real line ℝ as their spectrum. But the total number operator N has a discrete spectrum ℤ+ = {0, 1, 2,…}. An n-mode Gaussian state in Γ(ℂn) is completely determined by the mean values of momentum and position observables and their covariance matrix which together constitute a family of n(2n + 3) real parameters. Starting with N and its unitary conjugates by the Weyl displacement operators and operators from a representation of the symplectic group Sp(2n) in Γ(ℂn), we construct n(2n + 3) observables with spectrum ℤ+ but whose expectation values in a Gaussian state determine all its mean and covariance parameters. Thus measurements of discrete-valued observables enable the tomography of the underlying Gaussian state and it can be done by using five one-mode and four two-mode Gaussian symplectic gates in single and pair mode wires of Γ(ℂn) = Γ(ℂ)⊗n. Thus the tomography protocol admits a simple description in a language similar to circuits in quantum computation theory. Such a Gaussian tomography applied to outputs of a Gaussian channel with coherent input states permit a tomography of the channel parameters. However, in our procedure the number of counting measurements exceeds the number of channel parameters slightly. Presently, it is not clear whether a more efficient method exists for reducing this tomographic complexity. As a byproduct of our approach an elementary derivation of the probability generating function of N in a Gaussian state is given. In many cases the distribution turns out to be infinitely divisible and its underlying Lévy measure can be obtained. However, we are unable to derive the exact distribution in all cases. Whether this property of infinite divisibility holds in general is left as an open problem.
Hydraulic conductivity fields: Gaussian or not?
NASA Astrophysics Data System (ADS)
Meerschaert, Mark M.; Dogan, Mine; Dam, Remke L.; Hyndman, David W.; Benson, David A.
2013-08-01
Hydraulic conductivity (K) fields are used to parameterize groundwater flow and transport models. Numerical simulations require a detailed representation of the K field, synthesized to interpolate between available data. Several recent studies introduced high-resolution K data (HRK) at the Macro Dispersion Experiment (MADE) site, and used ground-penetrating radar (GPR) to delineate the main structural features of the aquifer. This paper describes a statistical analysis of these data, and the implications for K field modeling in alluvial aquifers. Two striking observations have emerged from this analysis. The first is that a simple fractional difference filter can have a profound effect on data histograms, organizing non-Gaussian ln K data into a coherent distribution. The second is that using GPR facies allows us to reproduce the significantly non-Gaussian shape seen in real HRK data profiles, using a simulated Gaussian ln K field in each facies. This illuminates a current controversy in the literature, between those who favor Gaussian ln K models, and those who observe non-Gaussian ln K fields. Both camps are correct, but at different scales.
Graphical calculus for Gaussian pure states
Menicucci, Nicolas C.; Flammia, Steven T.; Loock, Peter van
2011-04-15
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.
Hydraulic Conductivity Fields: Gaussian or Not?
Meerschaert, Mark M; Dogan, Mine; Van Dam, Remke L; Hyndman, David W; Benson, David A
2013-08-01
Hydraulic conductivity (K) fields are used to parameterize groundwater flow and transport models. Numerical simulations require a detailed representation of the K field, synthesized to interpolate between available data. Several recent studies introduced high resolution K data (HRK) at the Macro Dispersion Experiment (MADE) site, and used ground-penetrating radar (GPR) to delineate the main structural features of the aquifer. This paper describes a statistical analysis of these data, and the implications for K field modeling in alluvial aquifers. Two striking observations have emerged from this analysis. The first is that a simple fractional difference filter can have a profound effect on data histograms, organizing non-Gaussian ln K data into a coherent distribution. The second is that using GPR facies allows us to reproduce the significantly non-Gaussian shape seen in real HRK data profiles, using a simulated Gaussian ln K field in each facies. This illuminates a current controversy in the literature, between those who favor Gaussian ln K models, and those who observe non-Gaussian ln K fields. Both camps are correct, but at different scales.
Comparison of Gaussian and super Gaussian laser beams for addressing atomic qubits
NASA Astrophysics Data System (ADS)
Gillen-Christandl, Katharina; Gillen, Glen D.; Piotrowicz, M. J.; Saffman, M.
2016-05-01
We study the fidelity of single-qubit quantum gates performed with two-frequency laser fields that have a Gaussian or super Gaussian spatial mode. Numerical simulations are used to account for imperfections arising from atomic motion in an optical trap, spatially varying Stark shifts of the trapping and control beams, and transverse and axial misalignment of the control beams. Numerical results that account for the three-dimensional distribution of control light show that a super Gaussian mode with intensity I˜ e^{-2(r/w_0)^n} provides reduced sensitivity to atomic motion and beam misalignment. Choosing a super Gaussian with n=6 the decay time of finite temperature Rabi oscillations can be increased by a factor of 60 compared to an n=2 Gaussian beam, while reducing crosstalk to neighboring qubit sites.
Gaussian windows: A tool for exploring multivariate data
NASA Technical Reports Server (NTRS)
Jaeckel, Louis A.
1990-01-01
Presented here is a method for interactively exploring a large set of quantitative multivariate data, in order to estimate the shape of the underlying density function. It is assumed that the density function is more or less smooth, but no other specific assumptions are made concerning its structure. The local structure of the data in a given region may be examined by viewing the data through a Gaussian window, whose location and shape are chosen by the user. A Gaussian window is defined by giving each data point a weight based on a multivariate Gaussian function. The weighted sample mean and sample covariance matrix are then computed, using the weights attached to the data points. These quantities are used to compute an estimate of the shape of the density function in the window region. The local structure of the data is described by a method similar to the method of principal components. By taking many such local views of the data, we can form an idea of the structure of the data set. The method is applicable in any number of dimensions. The method can be used to find and describe simple structural features such as peaks, valleys, and saddle points in the density function, and also extended structures in higher dimensions. With some practice, we can apply our geometrical intuition to these structural features in any number of dimensions, so that we can think about and describe the structure of the data. Since the computations involved are relatively simple, the method can easily be implemented on a small computer.
Modelling non-Gaussianity of background and observational errors by the Maximum Entropy method
NASA Astrophysics Data System (ADS)
Pires, Carlos; Talagrand, Olivier; Bocquet, Marc
2010-05-01
The Best Linear Unbiased Estimator (BLUE) has widely been used in atmospheric-oceanic data assimilation. However, when data errors have non-Gaussian pdfs, the BLUE differs from the absolute Minimum Variance Unbiased Estimator (MVUE), minimizing the mean square analysis error. The non-Gaussianity of errors can be due to the statistical skewness and positiveness of some physical observables (e.g. moisture, chemical species) or due to the nonlinearity of the data assimilation models and observation operators acting on Gaussian errors. Non-Gaussianity of assimilated data errors can be justified from a priori hypotheses or inferred from statistical diagnostics of innovations (observation minus background). Following this rationale, we compute measures of innovation non-Gaussianity, namely its skewness and kurtosis, relating it to: a) the non-Gaussianity of the individual error themselves, b) the correlation between nonlinear functions of errors, and c) the heteroscedasticity of errors within diagnostic samples. Those relationships impose bounds for skewness and kurtosis of errors which are critically dependent on the error variances, thus leading to a necessary tuning of error variances in order to accomplish consistency with innovations. We evaluate the sub-optimality of the BLUE as compared to the MVUE, in terms of excess of error variance, under the presence of non-Gaussian errors. The error pdfs are obtained by the maximum entropy method constrained by error moments up to fourth order, from which the Bayesian probability density function and the MVUE are computed. The impact is higher for skewed extreme innovations and grows in average with the skewness of data errors, especially if those skewnesses have the same sign. Application has been performed to the quality-accepted ECMWF innovations of brightness temperatures of a set of High Resolution Infrared Sounder channels. In this context, the MVUE has led in some extreme cases to a potential reduction of 20-60% error
Cochlear toughening, protection, and potentiation of noise-induced trauma by non-Gaussian noise
NASA Astrophysics Data System (ADS)
Hamernik, Roger P.; Qiu, Wei; Davis, Bob
2003-02-01
An interrupted noise exposure of sufficient intensity, presented on a daily repeating cycle, produces a threshold shift (TS) following the first day of exposure. TSs measured on subsequent days of the exposure sequence have been shown to decrease relative to the initial TS. This reduction of TS, despite the continuing daily exposure regime, has been called a cochlear toughening effect and the exposures referred to as toughening exposures. Four groups of chinchillas were exposed to one of four different noises presented on an interrupted (6 h/day for 20 days) or noninterrupted (24 h/day for 5 days) schedule. The exposures had equivalent total energy, an overall level of 100 dB(A) SPL, and approximately the same flat, broadband long-term spectrum. The noises differed primarily in their temporal structures; two were Gaussian and two were non-Gausssian, nonstationary. Brainstem auditory evoked potentials were used to estimate hearing thresholds and surface preparation histology was used to determine sensory cell loss. The experimental results presented here show that: (1) Exposures to interrupted high-level, non-Gaussian signals produce a toughening effect comparable to that produced by an equivalent interrupted Gaussian noise. (2) Toughening, whether produced by Gaussian or non-Gaussian noise, results in reduced trauma compared to the equivalent uninterrupted noise, and (3) that both continuous and interrupted non-Gaussian exposures produce more trauma than do energy and spectrally equivalent Gaussian noises. Over the course of the 20-day exposure, the pattern of TS following each day's exposure could exhibit a variety of configurations. These results do not support the equal energy hypothesis as a unifying principal for estimating the potential of a noise exposure to produce hearing loss.
Majorization preservation of Gaussian bosonic channels
NASA Astrophysics Data System (ADS)
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2016-07-01
It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics.
CMB non-gaussianity from vector fields
Peloso, Marco
2014-01-01
The Planck satellite has recently measured the CMB temperature anisotropies with unprecedented accuracy, and it has provided strong bounds on primordial non-gaussianity. Such bounds constrain models of inflation, and mechanisms that produce the primordial perturbations. We discuss the non-gaussian signatures from the interactions of the inflation φ with spin-1 fields. We study the two different cases in which the inflaton is (i) a pseudo-scalar field with a (φ)/(fa) F·F interaction with a vector field, and (ii) a scalar field with a f (φ)F² interaction. In the first case we obtain the strong limit f{sub a} ≥ 10¹⁶GeV on the decay constant. In the second case, specific choices of the function f (φ) can lead to a non-gaussianity with a characteristic shape not encountered in standard models of scalar field inflation, and which has also been constrained by Planck.
Gaussian state for the bouncing quantum cosmology
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Piechocki, Włodzimierz
2012-10-01
We present results concerning propagation of the Gaussian state across the cosmological quantum bounce. The reduced phase space quantization of loop quantum cosmology is applied to the Friedman-Robertson-Walker universe with a free massless scalar field. Evolution of quantum moments of the canonical variables is investigated. The covariance turns out to be a monotonic function so it may be used as an evolution parameter having quantum origin. We show that for the Gaussian state the Universe is least quantum at the bounce. We propose explanation of this counter-intuitive feature using the entropy of squeezing. The obtained time dependence of entropy is in agreement with qualitative predictions based on von Neumann entropy for mixed states. We show that, for the considered Gaussian state, semiclassicality is preserved across the bounce, so there is no cosmic forgetfulness.
Index Distribution of Gaussian Random Matrices
Majumdar, Satya N.; Nadal, Celine; Scardicchio, Antonello; Vivo, Pierpaolo
2009-11-27
We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N{sub +}) of a random NxN matrix belonging to Gaussian orthogonal (beta=1), unitary (beta=2) or symplectic (beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N{sub +}/N scales, for large N, as P(c,N){approx_equal}exp[-betaN{sup 2}PHI(c)] where the rate function PHI(c), symmetric around c=1/2 and universal (independent of beta), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at c=1/2 it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function.
Gaussian entanglement in the turbulent atmosphere
NASA Astrophysics Data System (ADS)
Bohmann, M.; Semenov, A. A.; Sperling, J.; Vogel, W.
2016-07-01
We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a nontrivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.
Variational Bayesian localization of EEG sources with generalized Gaussian priors
NASA Astrophysics Data System (ADS)
Cortes, J. M.; Lopez, A.; Molina, R.; Katsaggelos, A. K.
2012-11-01
Although in the last decades the use of Magnetic Resonance Imaging has grown in popularity as a tool for the structural analysis of the brain, including MRI, fMRI and recently DTI, the ElectroEncephaloGraphy (EEG) is, still today, an interesting technique for the understanding of brain organization and function. The main reason for this is that the EEG is a direct measure of brain bioelectrical activity, and such activity can be monitorized in the millisecond time window. For some situations and cognitive scenarios, such fine temporal resolution might suffice for some aspects of brain function; however, the EEG spatial resolution is very poor since it is based on a small number of scalp recordings, thus turning the source localization problem into an ill-posed one in which infinite possibilities exist for the localization of the neuronal generators. This is an old problem in computational neuroimaging; indeed, many methods have been proposed to overcome this localization. Here, by performing a Variational Bayesian Inference procedure with a generalized Gaussian prior, we come out with an algorithm that performs simultaneously the estimation of both sources and model parameters. The novelty for the inclusion of the generalized Gaussian prior allows to control the smoothness degree of the estimated sources. Finally, the suggested algorithm is validated on simulated data.
Non-Gaussian Error Distributions of LMC Distance Moduli Measurements
NASA Astrophysics Data System (ADS)
Crandall, Sara; Ratra, Bharat
2015-12-01
We construct error distributions for a compilation of 232 Large Magellanic Cloud (LMC) distance moduli values from de Grijs et al. that give an LMC distance modulus of (m - M)0 = 18.49 ± 0.13 mag (median and 1σ symmetrized error). Central estimates found from weighted mean and median statistics are used to construct the error distributions. The weighted mean error distribution is non-Gaussian—flatter and broader than Gaussian—with more (less) probability in the tails (center) than is predicted by a Gaussian distribution; this could be the consequence of unaccounted-for systematic uncertainties. The median statistics error distribution, which does not make use of the individual measurement errors, is also non-Gaussian—more peaked than Gaussian—with less (more) probability in the tails (center) than is predicted by a Gaussian distribution; this could be the consequence of publication bias and/or the non-independence of the measurements. We also construct the error distributions of 247 SMC distance moduli values from de Grijs & Bono. We find a central estimate of {(m-M)}0=18.94+/- 0.14 mag (median and 1σ symmetrized error), and similar probabilities for the error distributions.
A non-Gaussian analysis scheme using rank histograms for ensemble data assimilation
NASA Astrophysics Data System (ADS)
Metref, S.; Cosme, E.; Snyder, C.; Brasseur, P.
2014-08-01
One challenge of geophysical data assimilation is to address the issue of non-Gaussianities in the distributions of the physical variables ensuing, in many cases, from nonlinear dynamical models. Non-Gaussian ensemble analysis methods fall into two categories, those remapping the ensemble particles by approximating the best linear unbiased estimate, for example, the ensemble Kalman filter (EnKF), and those resampling the particles by directly applying Bayes' rule, like particle filters. In this article, it is suggested that the most common remapping methods can only handle weakly non-Gaussian distributions, while the others suffer from sampling issues. In between those two categories, a new remapping method directly applying Bayes' rule, the multivariate rank histogram filter (MRHF), is introduced as an extension of the rank histogram filter (RHF) first introduced by Anderson (2010). Its performance is evaluated and compared with several data assimilation methods, on different levels of non-Gaussianity with the Lorenz 63 model. The method's behavior is then illustrated on a simple density estimation problem using ensemble simulations from a coupled physical-biogeochemical model of the North Atlantic ocean. The MRHF performs well with low-dimensional systems in strongly non-Gaussian regimes.
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
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.
Cosmological Applications of the Gaussian Kinematic Formula
NASA Astrophysics Data System (ADS)
Fantaye, Yabebal T.; Marinucci, Domenico
2014-05-01
The Gaussian Kinematic Formula (GKF, see Adler and Taylor (2007,2011)) is an extremely powerful tool allowing for explicit analytic predictions of expected values of Minkowski functionals under realistic experimental conditions for cosmological data collections. In this paper, we implement Minkowski functionals on multipoles and needlet components of CMB fields, thus allowing a better control of cosmic variance and extraction of information on both harmonic and real domains; we then exploit the GKF to provide their expected values on spherical maps, in the presence of arbitrary sky masks, and under nonGaussian circumstances.
Invariant measures on multimode quantum Gaussian states
NASA Astrophysics Data System (ADS)
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.
Gaussian Quadrature Formulae for Arbitrary Positive Measures
Fernandes, Andrew D.; Atchley, William R.
2007-01-01
We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student’s t, inverse-gamma, beta, and Fisher’s F) we present exact formulae for computing the respective quadrature scheme. PMID:19455218
NASA Astrophysics Data System (ADS)
Ji, Se-Wan; Kim, M. S.; Nha, Hyunchul
2015-04-01
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.
ERIC Educational Resources Information Center
Sichel, H. S.
1992-01-01
Discusses the use of the generalized inverse Gaussian-Poisson (GIGP) distribution in bibliometric studies. The main types of size-frequency distributions are described, bibliometric distributions in logarithms are examined; parameter estimation is discussed; and goodness-of-fit tests are considered. Examples of applications are included. (17…
An Accurate and Efficient Gaussian Fit Centroiding Algorithm for Star Trackers
NASA Astrophysics Data System (ADS)
Delabie, Tjorven; Schutter, Joris De; Vandenbussche, Bart
2015-06-01
This paper presents a novel centroiding algorithm for star trackers. The proposed algorithm, which is referred to as the Gaussian Grid algorithm, fits an elliptical Gaussian function to the measured pixel data and derives explicit expressions to determine the centroids of the stars. In tests, the algorithm proved to yield accuracy comparable to that of the most accurate existing algorithms, while being significantly less computationally intensive. Hence, the Gaussian Grid algorithm can deliver high centroiding accuracy to spacecraft with limited computational power. Furthermore, a hybrid algorithm is proposed in which the Gaussian Grid algorithm yields an accurate initial estimate for a least squares fitting method, resulting in a reduced number of iterations and hence reduced computational cost. The low computational cost allows to improve performance by acquiring the attitude estimates at a higher rate or use more stars in the estimation algorithms. It is also a valuable contribution to the expanding field of small satellites, where it could enable low-cost platforms to have highly accurate attitude estimation.
Large-scale structure non-Gaussianities with modal methods
NASA Astrophysics Data System (ADS)
Schmittfull, Marcel
2016-10-01
Relying on a separable modal expansion of the bispectrum, the implementation of a fast estimator for the full bispectrum of a 3d particle distribution is presented. The computational cost of accurate bispectrum estimation is negligible relative to simulation evolution, so the bispectrum can be used as a standard diagnostic whenever the power spectrum is evaluated. As an application, the time evolution of gravitational and primordial dark matter bispectra was measured in a large suite of N-body simulations. The bispectrum shape changes characteristically when the cosmic web becomes dominated by filaments and halos, therefore providing a quantitative probe of 3d structure formation. Our measured bispectra are determined by ~ 50 coefficients, which can be used as fitting formulae in the nonlinear regime and for non-Gaussian initial conditions. We also compare the measured bispectra with predictions from the Effective Field Theory of Large Scale Structures (EFTofLSS).
Inferring time derivatives including cell growth rates using Gaussian processes
Swain, Peter S.; Stevenson, Keiran; Leary, Allen; Montano-Gutierrez, Luis F.; Clark, Ivan B.N.; Vogel, Jackie; Pilizota, Teuta
2016-01-01
Often the time derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population's growth rate is typically more important than its size. Here we introduce a non-parametric method to infer first and second time derivatives as a function of time from time-series data. Our approach is based on Gaussian processes and applies to a wide range of data. In tests, the method is at least as accurate as others, but has several advantages: it estimates errors both in the inference and in any summary statistics, such as lag times, and allows interpolation with the corresponding error estimation. As illustrations, we infer growth rates of microbial cells, the rate of assembly of an amyloid fibril and both the speed and acceleration of two separating spindle pole bodies. Our algorithm should thus be broadly applicable. PMID:27941811
Inferring time derivatives including cell growth rates using Gaussian processes
NASA Astrophysics Data System (ADS)
Swain, Peter S.; Stevenson, Keiran; Leary, Allen; Montano-Gutierrez, Luis F.; Clark, Ivan B. N.; Vogel, Jackie; Pilizota, Teuta
2016-12-01
Often the time derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population's growth rate is typically more important than its size. Here we introduce a non-parametric method to infer first and second time derivatives as a function of time from time-series data. Our approach is based on Gaussian processes and applies to a wide range of data. In tests, the method is at least as accurate as others, but has several advantages: it estimates errors both in the inference and in any summary statistics, such as lag times, and allows interpolation with the corresponding error estimation. As illustrations, we infer growth rates of microbial cells, the rate of assembly of an amyloid fibril and both the speed and acceleration of two separating spindle pole bodies. Our algorithm should thus be broadly applicable.
Non-Gaussian states from continuous-wave Gaussian light sources
NASA Astrophysics Data System (ADS)
Mølmer, Klaus
2006-06-01
We present a general analysis of the state obtained by subjecting a continuous-wave (cw) Gaussian field to non-Gaussian measurements. The generic multimode state of a cw Gaussian field is fully characterized by the time dependent mean values and variances and the two-time covariances of the field quadrature variables. We present a general theory to extract from this information the results of detection and quantum state reduction within specific temporal output modes. The formalism is applied to schemes for heralded production of propagating light pulses with single photon and Schrödinger kitten states from a cw squeezed beam of light.
Primordial non-Gaussianity and reionization
NASA Astrophysics Data System (ADS)
Lidz, Adam; Baxter, Eric J.; Adshead, Peter; Dodelson, Scott
2013-07-01
The statistical properties of the primordial perturbations contain clues about their origins. Although the Planck collaboration has recently obtained tight constraints on primordial non-Gaussianity from cosmic microwave background measurements, it is still worthwhile to mine upcoming data sets in an effort to place independent or competitive limits. The ionized bubbles that formed at redshift z˜6-20 during the epoch of reionization were seeded by primordial overdensities, and so the statistics of the ionization field at high redshift are related to the statistics of the primordial field. Here we model the effect of primordial non-Gaussianity on the reionization field. The epoch and duration of reionization are affected, as are the sizes of the ionized bubbles, but these changes are degenerate with variations in the properties of the ionizing sources and the surrounding intergalactic medium. A more promising signature is the power spectrum of the spatial fluctuations in the ionization field, which may be probed by upcoming 21 cm surveys. This has the expected 1/k2 dependence on large scales, characteristic of a biased tracer of the matter field. We project how well upcoming 21 cm observations will be able to disentangle this signal from foreground contamination. Although foreground cleaning inevitably removes the large-scale modes most impacted by primordial non-Gaussianity, we find that primordial non-Gaussianity can be separated from foreground contamination for a narrow range of length scales. In principle, futuristic redshifted 21 cm surveys may allow constraints competitive with Planck.
Diffusion of Super-Gaussian Profiles
ERIC Educational Resources Information Center
Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.
2007-01-01
The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…
How Gaussian can our Universe be?
NASA Astrophysics Data System (ADS)
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).
Transitional behavior of quantum Gaussian memory channels
NASA Astrophysics Data System (ADS)
Lupo, C.; Mancini, S.
2010-05-01
We address the question of optimality of entangled input states in quantum Gaussian memory channels. For a class of such channels, which can be traced back to the memoryless setting, we state a criterion which relates the optimality of entangled inputs to the symmetry properties of the channels’ action. Several examples of channel models belonging to this class are discussed.
Gaussian benchmark for optical communication aiming towards ultimate capacity
NASA Astrophysics Data System (ADS)
Lee, Jaehak; Ji, Se-Wan; Park, Jiyong; Nha, Hyunchul
2016-05-01
We establish the fundamental limit of communication capacity within Gaussian schemes under phase-insensitive Gaussian channels, which employ multimode Gaussian states for encoding and collective Gaussian operations and measurements for decoding. We prove that this Gaussian capacity is additive, i.e., its upper bound occurs with separable encoding and separable receivers so that a single-mode communication suffices to achieve the largest capacity under Gaussian schemes. This rigorously characterizes the gap between the ultimate Holevo capacity and the capacity within Gaussian communication, showing that Gaussian regime is not sufficient to achieve the Holevo bound particularly in the low-photon regime. Furthermore, the Gaussian benchmark established here can be used to critically assess the performance of non-Gaussian protocols for optical communication. We move on to identify non-Gaussian schemes to beat the Gaussian capacity and show that a non-Gaussian receiver recently implemented by Becerra et al. [F. E. Becerra et al., Nat. Photon. 7, 147 (2013), 10.1038/nphoton.2012.316] can achieve this aim with an appropriately chosen encoding strategy.
Radiation pressure acceleration of corrugated thin foils by Gaussian and super-Gaussian beams
Adusumilli, K.; Goyal, D.; Tripathi, V. K.
2012-01-15
Rayleigh-Taylor instability of radiation pressure accelerated ultrathin foils by laser having Gaussian and super-Gaussian intensity distribution is investigated using a single fluid code. The foil is allowed to have ring shaped surface ripples. The radiation pressure force on such a foil is non-uniform with finite transverse component F{sub r}; F{sub r} varies periodically with r. Subsequently, the ripple grows as the foil moves ahead along z. With a Gaussian beam, the foil acquires an overall curvature due to non-uniformity in radiation pressure and gets thinner. In the process, the ripple perturbation is considerably washed off. With super-Gaussian beam, the ripple is found to be more strongly washed out. In order to avoid transmission of the laser through the thinning foil, a criterion on the foil thickness is obtained.
Shamis, Mira
2013-11-15
We use the supersymmetric formalism to derive an integral formula for the density of states of the Gaussian Orthogonal Ensemble, and then apply saddle-point analysis to give a new derivation of the 1/N-correction to Wigner's law. This extends the work of Disertori on the Gaussian Unitary Ensemble. We also apply our method to the interpolating ensembles of Mehta–Pandey.
Quantum Fisher information on two manifolds of two-mode Gaussian states
NASA Astrophysics Data System (ADS)
Marian, Paulina; Marian, Tudor A.
2016-05-01
We investigate two special classes of two-mode Gaussian states of light that are important from both the experimental and theoretical points of view: the mode-mixed thermal states and the squeezed thermal ones. Aiming to a parallel study, we write the Uhlmann fidelity between pairs of states belonging to each class in terms of their defining parameters. The quantum Fisher information matrices on the corresponding four-dimensional manifolds are diagonal and allow insightful parameter estimation. The scalar curvatures of the Bures metric on both Riemannian manifolds of special two-mode Gaussian states are evaluated and discussed. They are functions of two variables, namely, the mean numbers of photons in the incident thermal modes. Our comparative analysis opens the door to further investigation of the interplay between geometry and statistics for Gaussian states produced in simple optical devices.
Propagation of modified Bessel-Gaussian beams in turbulence
NASA Astrophysics Data System (ADS)
Eyyuboğlu, Halil Tanyer; Hardalaç, Fırat
2008-03-01
We investigate the propagation characteristics of modified Bessel-Gaussian beams traveling in a turbulent atmosphere. The source beam formulation comprises a Gaussian exponential and the summation of modified Bessel functions. Based on an extended Huygens-Fresnel principle, the receiver plane intensity is formulated and solved down to a double integral stage. Source beam illustrations show that modified Bessel-Gaussian beams, except the lowest order case, will have well-like shapes. Modified Bessel-Gaussian beams with summations will experience lobe slicing and will display more or less the same profile regardless of order content. After propagating in turbulent atmosphere, it is observed that a modified Bessel-Gaussian beam will transform into a Bessel-Gaussian beam. Furthermore it is seen that modified Bessel-Gaussian beams with different Bessel function combinations, but possessing nearly the same profile, will differentiate during propagation. Increasing turbulence strength is found to accelerate the beam transformation toward the eventual Gaussian shape.
Enhanced optical flow field of left ventricular motion using quasi-Gaussian DCT filter.
Riyadi, Slamet; Mustafa, Mohd Marzuki; Hussain, Aini; Maskon, Oteh; Nor, Ika Faizura Mohd
2011-01-01
Left ventricular motion estimation is very important for diagnosing cardiac abnormality. One of the popular techniques, optical flow technique, promises useful results for motion quantification. However, optical flow technique often failed to provide smooth vector field due to the complexity of cardiac motion and the presence of speckle noise. This chapter proposed a new filtering technique, called quasi-Gaussian discrete cosine transform (QGDCT)-based filter, to enhance the optical flow field for myocardial motion estimation. Even though Gaussian filter and DCT concept have been implemented in other previous researches, this filter introduces a different approach of Gaussian filter model based on high frequency properties of cosine function. The QGDCT is a customized quasi discrete Gaussian filter in which its coefficients are derived from a selected two-dimensional DCT. This filter was implemented before and after the computation of optical flow to reduce the speckle noise and to improve the flow field smoothness, respectively. The algorithm was first validated on synthetic echocardiography image that simulates a contracting myocardium motion. Subsequently, this method was also implemented on clinical echocardiography images. To evaluate the performance of the technique, several quantitative measurements such as magnitude error, angular error, and standard error of measurement are computed and analyzed. The final motion estimation results were in good agreement with the physician manual interpretation.
Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
Monras, Alex; Illuminati, Fabrizio
2011-01-15
We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than coherent, thermal, or single-mode squeezed states. This suggests that at high-energy regimes, two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result indicates a stronger form 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.
Segmentation of textured images using a multiresolution Gaussian autoregressive model.
Comer, M L; Delp, E J
1999-01-01
We present a new algorithm for segmentation of textured images using a multiresolution Bayesian approach. The new algorithm uses a multiresolution Gaussian autoregressive (MGAR) model for the pyramid representation of the observed image, and assumes a multiscale Markov random field model for the class label pyramid. The models used in this paper incorporate correlations between different levels of both the observed image pyramid and the class label pyramid. The criterion used for segmentation is the minimization of the expected value of the number of misclassified nodes in the multiresolution lattice. The estimate which satisfies this criterion is referred to as the "multiresolution maximization of the posterior marginals" (MMPM) estimate, and is a natural extension of the single-resolution "maximization of the posterior marginals" (MPM) estimate. Previous multiresolution segmentation techniques have been based on the maximum a posterior (MAP) estimation criterion, which has been shown to be less appropriate for segmentation than the MPM criterion. It is assumed that the number of distinct textures in the observed image is known. The parameters of the MGAR model-the means, prediction coefficients, and prediction error variances of the different textures-are unknown. A modified version of the expectation-maximization (EM) algorithm is used to estimate these parameters. The parameters of the Gibbs distribution for the label pyramid are assumed to be known. Experimental results demonstrating the performance of the algorithm are presented.
Non-Gaussianity from self-ordering scalar fields
Figueroa, Daniel G.; Kamionkowski, Marc
2010-06-15
The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and provide a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges k{sub 1{approx_equal}}2k{sub 2{approx_equal}}2k{sub 3}) as opposed to the local-model bispectrum, which peaks for squeezed triangles (k{sub 1{approx_equal}}k{sub 2}>>k{sub 3}), and the equilateral bispectrum, which peaks at k{sub 1{approx_equal}}k{sub 2{approx_equal}}k{sub 3}. We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit.
Fuzzy local Gaussian mixture model for brain MR image segmentation.
Ji, Zexuan; Xia, Yong; Sun, Quansen; Chen, Qiang; Xia, Deshen; Feng, David Dagan
2012-05-01
Accurate brain tissue segmentation from magnetic resonance (MR) images is an essential step in quantitative brain image analysis. However, due to the existence of noise and intensity inhomogeneity in brain MR images, many segmentation algorithms suffer from limited accuracy. In this paper, we assume that the local image data within each voxel's neighborhood satisfy the Gaussian mixture model (GMM), and thus propose the fuzzy local GMM (FLGMM) algorithm for automated brain MR image segmentation. This algorithm estimates the segmentation result that maximizes the posterior probability by minimizing an objective energy function, in which a truncated Gaussian kernel function is used to impose the spatial constraint and fuzzy memberships are employed to balance the contribution of each GMM. We compared our algorithm to state-of-the-art segmentation approaches in both synthetic and clinical data. Our results show that the proposed algorithm can largely overcome the difficulties raised by noise, low contrast, and bias field, and substantially improve the accuracy of brain MR image segmentation.
Theory and generation of conditional, scalable sub-Gaussian random fields
NASA Astrophysics Data System (ADS)
Panzeri, M.; Riva, M.; Guadagnini, A.; Neuman, S. P.
2016-03-01
Many earth and environmental (as well as a host of other) variables, Y, and their spatial (or temporal) increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture key aspects of such non-Gaussian scaling by treating Y and/or ΔY as sub-Gaussian random fields (or processes). This however left unaddressed the empirical finding that whereas sample frequency distributions of Y tend to display relatively mild non-Gaussian peaks and tails, those of ΔY often reveal peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we proposed a generalized sub-Gaussian model (GSG) which resolves this apparent inconsistency between the statistical scaling behaviors of observed variables and their increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. Most importantly, we demonstrated the feasibility of estimating all parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments, ΔY. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random fields, introduce two approximate versions of this algorithm to reduce CPU time, and explore them on one and two-dimensional synthetic test cases.
Xiao, Changyan; Staring, Marius; Wang, Yaonan; Shamonin, Denis P; Stoel, Berend C
2013-01-01
The intensity or gray-level derivatives have been widely used in image segmentation and enhancement. Conventional derivative filters often suffer from an undesired merging of adjacent objects because of their intrinsic usage of an inappropriately broad Gaussian kernel; as a result, neighboring structures cannot be properly resolved. To avoid this problem, we propose to replace the low-level Gaussian kernel with a bi-Gaussian function, which allows independent selection of scales in the foreground and background. By selecting a narrow neighborhood for the background with regard to the foreground, the proposed method will reduce interference from adjacent objects simultaneously preserving the ability of intraregion smoothing. Our idea is inspired by a comparative analysis of existing line filters, in which several traditional methods, including the vesselness, gradient flux, and medialness models, are integrated into a uniform framework. The comparison subsequently aids in understanding the principles of different filtering kernels, which is also a contribution of this paper. Based on some axiomatic scale-space assumptions, the full representation of our bi-Gaussian kernel is deduced. The popular γ-normalization scheme for multiscale integration is extended to the bi-Gaussian operators. Finally, combined with a parameter-free shape estimation scheme, a derivative filter is developed for the typical applications of curvilinear structure detection and vasculature image enhancement. It is verified in experiments using synthetic and real data that the proposed method outperforms several conventional filters in separating closely located objects and being robust to noise.
Improved Event Location Uncertainty Estimates
2008-06-30
model (such as Gaussian, spherical or exponential) typically used in geostatistics, we define the robust variogram model as the median regression curve...variogram model estimation We define the robust variogram model as the median regression curve of the residual difference squares for station pairs of...develop methodologies that improve location uncertainties in the presence of correlated, systematic model errors and non-Gaussian measurement errors. We
Palacios, Julia A; Minin, Vladimir N
2013-03-01
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method.
The Gaussian curvature elastic energy of intermediates in membrane fusion.
Siegel, David P
2008-12-01
The Gaussian curvature elastic energy contribution to the energy of membrane fusion intermediates has usually been neglected because the Gaussian curvature elastic modulus, kappa, was unknown. It is now possible to measure kappa for phospholipids that form bicontinuous inverted cubic (Q(II)) phases. Here, it is shown that one can estimate kappa for lipids that do not form Q(II) phases by studying the phase behavior of lipid mixtures. The method is used to estimate kappa for several lipid compositions in excess water. The values of kappa are used to compute the curvature elastic energies of stalks and catenoidal fusion pores according to recent models. The Gaussian curvature elastic contribution is positive and similar in magnitude to the bending energy contribution: it increases the total curvature energy of all the fusion intermediates by 100 units of k(B)T or more. It is important to note that this contribution makes the predicted intermediate energies compatible with observed lipid phase behavior in excess water. An order-of-magnitude fusion rate equation is used to estimate whether the predicted stalk energies are consistent with the observed rates of stalk-mediated processes in pure lipid systems. The current theory predicts a stalk energy that is slightly too large, by approximately 30 k(B)T, to rationalize the observed rates of stalk-mediated processes in phosphatidylethanolamine or N-monomethylated dioleoylphosphatidylethanolamine systems. Despite this discrepancy, the results show that models of fusion intermediate energy are accurate enough to make semiquantitative predictions about how proteins mediate biomembrane fusion. The same rate model shows that for proteins to drive biomembrane fusion at observed rates, they have to perform mediating functions corresponding to a reduction in the energy of a purely lipidic stalk by several tens of k(B)T. By binding particular peptide sequences to the monolayer surface, proteins could lower fusion intermediate
Analytic Matrix Elements and Gradients with Shifted Correlated Gaussians
NASA Astrophysics Data System (ADS)
Fedorov, D. V.
2017-01-01
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are shown to be analytic. Their gradients with respect to the non-linear parameters of the Gaussians are also analytic. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.
On the classical capacity of quantum Gaussian channels
NASA Astrophysics Data System (ADS)
Lupo, Cosmo; Pirandola, Stefano; Aniello, Paolo; Mancini, Stefano
2011-02-01
The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting the study to Gaussian encodings, for which we provide analytical expressions.
NASA Astrophysics Data System (ADS)
Meerburg, P. Daniel; Meyers, Joel; van Engelen, Alexander; Ali-Haïmoud, Yacine
2016-06-01
We study the degree to which the cosmic microwave background (CMB) can be used to constrain primordial non-Gaussianity involving one tensor and two scalar fluctuations, focusing on the correlation of one polarization B mode with two temperature modes. In the simplest models of inflation, the tensor-scalar-scalar primordial bispectrum is nonvanishing and is of the same order in slow-roll parameters as the scalar-scalar-scalar bispectrum. We calculate the ⟨B T T ⟩ correlation arising from a primordial tensor-scalar-scalar bispectrum, and show that constraints from an experiment like CMB-Stage IV using this observable are more than an order of magnitude better than those on the same primordial coupling obtained from temperature measurements alone. We argue that B -mode non-Gaussianity opens up an as-yet-unexplored window into the early Universe, demonstrating that significant information on primordial physics remains to be harvested from CMB anisotropies.
Quantum Fidelity for Arbitrary Gaussian States.
Banchi, Leonardo; Braunstein, Samuel L; Pirandola, Stefano
2015-12-31
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
A Fast Incremental Gaussian Mixture Model
Pinto, Rafael Coimbra; Engel, Paulo Martins
2015-01-01
This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of O(NKD3) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this work, we manage to reduce this complexity to O(NKD2) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets. PMID:26444880
Fock expansion of multimode pure Gaussian states
Cariolaro, Gianfranco; Pierobon, Gianfranco
2015-12-15
The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, as shown for two-mode and three-mode Gaussian states.
Large Non-Gaussianity in Axion Inflation
Barnaby, Neil; Peloso, Marco
2011-05-06
The inflationary paradigm has enjoyed phenomenological success; however, a compelling particle physics realization is still lacking. Axions are among the best-motivated inflaton candidates, since the flatness of their potential is naturally protected by a shift symmetry. We reconsider the cosmological perturbations in axion inflation, consistently accounting for the coupling to gauge fields c{phi}FF-tilde, which is generically present in these models. This coupling leads to production of gauge quanta, which provide a new source of inflaton fluctuations, {delta}{phi}. For c > or approx. 10{sup 2}M{sub p}{sup -1}, these dominate over the vacuum fluctuations, and non-Gaussianity exceeds the current observational bound. This regime is typical for concrete realizations that admit a UV completion; hence, large non-Gaussianity is easily obtained in minimal and natural realizations of inflation.
Gaussian quadrature for multiple orthogonal polynomials
NASA Astrophysics Data System (ADS)
Coussement, Jonathan; van Assche, Walter
2005-06-01
We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.
Remarkably Gaussian Tephra Fallout from Basaltic Eruptions
NASA Astrophysics Data System (ADS)
Courtland, L. M.; Kruse, S.; Connor, C.
2008-12-01
Tephra fallout models used to forecast volcanic hazards rely on the advection-diffusion equation to forecast hazards. If the advection-diffusion equation applies, then the thickness of tephra blanket deposits should show Gaussian crosswind profiles and exponential decay with distance from the vent. Complications may arise due to factors such as particle size distributions, particle density, and atmospheric effects not incorporated in the advection-diffusion model. Continuous profiles derived from GPR surveys collected on the tephra blanket of Cerro Negro Volcano, Nicaragua allow us to test the advection-diffusion model. Steady trade winds coupled with eruptions that tend to be brief and relatively low energy create relatively simple deposits. Data was collected for cross wind profiles at varying distances from the vent. Horizons identified in these profiles exhibit Gaussian distributions with a high degree of statistical confidence. Additionally, the shape of one continuous profile leading from the crater rim out onto the tephra blanket is examined.
Quantum Fidelity for Arbitrary Gaussian States
NASA Astrophysics Data System (ADS)
Banchi, Leonardo; Braunstein, Samuel L.; Pirandola, Stefano
2015-12-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
Entanglement Rate for Gaussian Continuous Variable Beams
2016-08-24
e.g. when cavities are involved. To exemplify itsmeaning and potential, we apply it to a four-mode optomechanical setup that enables the simultaneous up...natural characteristics of such a source is obviously the rate at which it generates entanglement. If the source sends out pairs of entangled particles...entanglement rate in such nontrivial situations. It will turn out that our general definition, when applied to stationaryGaussianCVbeams, gives rise to a
Non-Markovianity of Gaussian Channels.
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.
Entropic Fluctuations in Gaussian Dynamical Systems
NASA Astrophysics Data System (ADS)
Jakšić, V.; Pillet, C.-A.; Shirikyan, A.
2016-06-01
We study nonequilibrium statistical mechanics of a Gaussian dynamical system and compute in closed form the large deviation functionals describing the fluctuations of the entropy production observable with respect to the reference state and the nonequilibrium steady state. The entropy production observable of this model is an unbounded function on the phase space, and its large deviation functionals have a surprisingly rich structure. We explore this structure in some detail.
Unitarily localizable entanglement of Gaussian states
Serafini, Alessio; Adesso, Gerardo; Illuminati, Fabrizio
2005-03-01
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.
Wu, Xiao-Lin; Heringstad, Bjørg; Gianola, Daniel
2008-01-01
A Gaussian-threshold model is described under the general framework of structural equation models for inferring simultaneous and recursive relationships between binary and Gaussian characters, and estimating genetic parameters. Relationships between clinical mastitis (CM) and test-day milk yield (MY) in first-lactation Norwegian Red cows were examined using a recursive Gaussian-threshold model. For comparison, the data were also analyzed using a standard Gaussian-threshold, a multivariate linear model, and a recursive multivariate linear model. The first 180 days of lactation were arbitrarily divided into three periods of equal length, in order to investigate how these relationships evolve in the course of lactation. The recursive model showed negative within-period effects from (liability to) CM to test-day MY in all three lactation periods, and positive between-period effects from test-day MY to (liability to) CM in the following period. Estimates of recursive effects and of genetic parameters were time-dependent. The results suggested unfavorable effects of production on liability to mastitis, and dynamic relationships between mastitis and test-dayMYin the course of lactation. Fitting recursive effects had little influence on the estimation of genetic parameters. However, some differences were found in the estimates of heritability, genetic, and residual correlations, using different types of models (Gaussian-threshold vs. multivariate linear). PMID:18558070
Local Gaussian operations can enhance continuous-variable entanglement distillation
Zhang Shengli; Loock, Peter van
2011-12-15
Entanglement distillation is a fundamental building block in long-distance quantum communication. Though known to be useless on their own for distilling Gaussian entangled states, local Gaussian operations may still help to improve non-Gaussian entanglement distillation schemes. Here we show that by applying local squeezing operations both the performance and the efficiency of existing distillation protocols can be enhanced. We find that such an enhancement through local Gaussian unitaries can be obtained even when the initially shared Gaussian entangled states are mixed, as, for instance, after their distribution through a lossy-fiber communication channel.
Image recovery under nonlinear and non-Gaussian degradations.
Sadhar, S I; Rajagopalan, A N
2005-04-01
A new two-dimensional recursive filter for recovering degraded images is proposed that is based on particle-filter theory. The main contribution of this work lies in evolving a framework that has the potential to recover images suffering from a general class of degradations such as system nonlinearity and non-Gaussian observation noise. Samples of the prior probability distribution of the original image are obtained by propagating the samples through an appropriate state model. Given the measurement model and the degraded image, the weights of the samples are computed. The samples and their corresponding weights are used to calculate the conditional mean that yields an estimate of the original image. The proposed method is validated by demonstrating its effectiveness in recovering images degraded by film-grain noise. Synthetic as well as real examples are considered for this purpose. Performance is also compared with that of an existing scheme.
Orbit-product representation and correction of Gaussian belief propagation
Johnson, Jason K; Chertkov, Michael; Chernyak, Vladimir
2009-01-01
We present a new interpretation of Gaussian belief propagation (GaBP) based on the 'zeta function' representation of the determinant as a product over orbits of a graph. We show that GaBP captures back-tracking orbits of the graph and consider how to correct this estimate by accounting for non-backtracking orbits. We show that the product over non-backtracking orbits may be interpreted as the determinant of the non-backtracking adjacency matrix of the graph with edge weights based on the solution of GaBP. An efficient method is proposed to compute a truncated correction factor including all non-backtracking orbits up to a specified length.
Gaussian maximum likelihood and contextual classification algorithms for multicrop classification
NASA Technical Reports Server (NTRS)
Di Zenzo, Silvano; Bernstein, Ralph; Kolsky, Harwood G.; Degloria, Stephen D.
1987-01-01
The paper reviews some of the ways in which context has been handled in the remote-sensing literature, and additional possibilities are introduced. The problem of computing exhaustive and normalized class-membership probabilities from the likelihoods provided by the Gaussian maximum likelihood classifier (to be used as initial probability estimates to start relaxation) is discussed. An efficient implementation of probabilistic relaxation is proposed, suiting the needs of actual remote-sensing applications. A modified fuzzy-relaxation algorithm using generalized operations between fuzzy sets is presented. Combined use of the two relaxation algorithms is proposed to exploit context in multispectral classification of remotely sensed data. Results on both one artificially created image and one MSS data set are reported.
Adaptive fusion of multisensor precipitation using Gaussian-scale mixtures in the wavelet domain
NASA Astrophysics Data System (ADS)
Ebtehaj, Ardeshir Mohammad; Foufoula-Georgiou, Efi
2011-11-01
The past decades have witnessed a remarkable emergence of new sources of multiscale multisensor precipitation data, including global spaceborne active and passive sensors, regional ground-based weather surveillance radars, and local rain gauges. Optimal integration of these multisensor data promises a posteriori estimates of precipitation fluxes with increased accuracy and resolution to be used in hydrologic applications. In this context, a new framework is proposed for multiscale multisensor precipitation data fusion which capitalizes on two main observations: (1) non-Gaussian statistics of precipitation images, which are concisely parameterized in the wavelet domain via a class of Gaussian-scale mixtures, and (2) the conditionally Gaussian and weakly correlated local representation of remotely sensed precipitation data in the wavelet domain, which allows for exploiting the efficient linear estimation methodologies while capturing the non-Gaussian data structure of rainfall. The proposed methodology is demonstrated using a data set of coincidental observations of precipitation reflectivity images by the spaceborne precipitation radar aboard the Tropical Rainfall Measurement Mission satellite and by ground-based weather surveillance Doppler radars.
Intuitive understanding of non-Gaussianity in ekpyrotic and cyclic models
Lehners, Jean-Luc; Steinhardt, Paul J.
2008-07-15
It has been pointed out by several groups that ekpyrotic and cyclic models generate significant non-Gaussianity. In this paper, we present a physically intuitive, semianalytic estimate of the bispectrum. We show that, in all such models, there is an intrinsic contribution to the non-Gaussianity parameter f{sub NL} that is determined by the geometric mean of the equation of state w{sub ek} during the ekpyrotic phase and w{sub c} during the phase that curvature perturbations are generated, and whose value is O(100) or more times the intrinsic value predicted by simple slow-roll inflationary models, f{sub NL}{sup intrinsic}=O(0.1). Other contributions to f{sub NL}, which we also estimate, can increase |f{sub NL}| but are unlikely to decrease it significantly, making non-Gaussianity a useful test of these models. Furthermore, we discuss a predicted correlation between the non-Gaussianity and scalar spectral index that sharpens the test.
Spainhour, John Christian G.; Janech, Michael G.; Schwacke, John H.; Velez, Juan Carlos Q.; Ramakrishnan, Viswanathan
2014-01-01
Matrix assisted laser desorption/ionization time-of-flight (MALDI-TOF) coupled with stable isotope standards (SIS) has been used to quantify native peptides. This peptide quantification by MALDI-TOF approach has difficulties quantifying samples containing peptides with ion currents in overlapping spectra. In these overlapping spectra the currents sum together, which modify the peak heights and make normal SIS estimation problematic. An approach using Gaussian mixtures based on known physical constants to model the isotopic cluster of a known compound is proposed here. The characteristics of this approach are examined for single and overlapping compounds. The approach is compared to two commonly used SIS quantification methods for single compound, namely Peak Intensity method and Riemann sum area under the curve (AUC) method. For studying the characteristics of the Gaussian mixture method, Angiotensin II, Angiotensin-2-10, and Angiotenisn-1-9 and their associated SIS peptides were used. The findings suggest, Gaussian mixture method has similar characteristics as the two methods compared for estimating the quantity of isolated isotopic clusters for single compounds. All three methods were tested using MALDI-TOF mass spectra collected for peptides of the renin-angiotensin system. The Gaussian mixture method accurately estimated the native to labeled ratio of several isolated angiotensin peptides (5.2% error in ratio estimation) with similar estimation errors to those calculated using peak intensity and Riemann sum AUC methods (5.9% and 7.7%, respectively). For overlapping angiotensin peptides, (where the other two methods are not applicable) the estimation error of the Gaussian mixture was 6.8%, which is within the acceptable range. In summary, for single compounds the Gaussian mixture method is equivalent or marginally superior compared to the existing methods of peptide quantification and is capable of quantifying overlapping (convolved) peptides within the
Gaussian capacity of the quantum bosonic memory channel with additive correlated Gaussian noise
Schaefer, Joachim; Karpov, Evgueni; Cerf, Nicolas J.
2011-09-15
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.
Kinect Posture Reconstruction Based on a Local Mixture of Gaussian Process Models.
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.
Non-Gaussian noise in x-ray and γ-ray detectors
NASA Astrophysics Data System (ADS)
Chen, Liying; Barrett, Harrison H.
2005-04-01
Image statistics are usually modeled as Poisson in γ-ray imaging and as Gaussian in x-ray imaging. In nuclear medicine, event-driven detectors analyze the pulses from every absorbed gamma photon individually; the resulting images rigorously obey Poisson statistics but are approximately Gaussian when the mean number of counts per pixel is large. With integrating detectors, as in digital radiography, each x-ray photon makes a contribution to the image proportional to its pulse height. One pixel senses many photons in long exposures, so the image statistics approach Gaussian by the central limit theorem (CLT). If the exposure time is short enough, however, each pixel will usually respond to no more than one photon, and we can separate individual photons for position estimation. Integrating detectors are therefore event-driven when we use many short-exposure frames rather than one long exposure. In intermediate exposures, the number of photons in one pixel is too small to invoke CLT and apply Gaussian statistics, yet too large to identify individual photons and apply Poisson statistics. In this paper, we analyze the image quality in this intermediate case. Image quality is defined for detection tasks performed by the ideal observer. Because the frames in a data set are independent of each other, the probability density function (PDF) of the whole data set is a product of the frame PDFs. The log-likelihood ratio λ of the ideal observer is thus a sum across the frames and has Gaussian statistics even with non-Gaussian images. We compare the ideal observer's performance with the Hotelling observer's performance under this approximation. A data-thresholding technique to improve Hotelling observer's performance is also discussed.
NASA Astrophysics Data System (ADS)
de Lima Bernardo, Bertúlio; Azevedo, Sérgio; Rosas, Alexandre
2014-11-01
Weak measurements are recognized as a very powerful tool in measuring tiny effects that are perpendicular to the propagation direction of a light beam. In this paper, we develop a simple algebraic description of the weak measurement protocol for both Laguerre-Gaussian and Hermite-Gaussian pointer states in the Schrödinger representation. Since a novel class of position and momentum expectation values could be derived, the present scenario appeared to be very efficient and insightful when compared to analytical methods.
Learning rates of lq coefficient regularization learning with gaussian kernel.
Lin, Shaobo; Zeng, Jinshan; Fang, Jian; Xu, Zongben
2014-10-01
Regularization is a well-recognized powerful strategy to improve the performance of a learning machine and l(q) regularization schemes with 0 < q < ∞ are central in use. It is known that different q leads to different properties of the deduced estimators, say, l(2) regularization leads to a smooth estimator, while l(1) regularization leads to a sparse estimator. Then how the generalization capability of l(q) regularization learning varies with q is worthy of investigation. In this letter, we study this problem in the framework of statistical learning theory. Our main results show that implementing l(q) coefficient regularization schemes in the sample-dependent hypothesis space associated with a gaussian kernel can attain the same almost optimal learning rates for all 0 < q < ∞. That is, the upper and lower bounds of learning rates for l(q) regularization learning are asymptotically identical for all 0 < q < ∞. Our finding tentatively reveals that in some modeling contexts, the choice of q might not have a strong impact on the generalization capability. From this perspective, q can be arbitrarily specified, or specified merely by other nongeneralization criteria like smoothness, computational complexity or sparsity.
Monthly streamflow forecasting using Gaussian Process Regression
NASA Astrophysics Data System (ADS)
Sun, Alexander Y.; Wang, Dingbao; Xu, Xianli
2014-04-01
Streamflow forecasting plays a critical role in nearly all aspects of water resources planning and management. In this work, Gaussian Process Regression (GPR), an effective kernel-based machine learning algorithm, is applied to probabilistic streamflow forecasting. GPR is built on Gaussian process, which is a stochastic process that generalizes multivariate Gaussian distribution to infinite-dimensional space such that distributions over function values can be defined. The GPR algorithm provides a tractable and flexible hierarchical Bayesian framework for inferring the posterior distribution of streamflows. The prediction skill of the algorithm is tested for one-month-ahead prediction using the MOPEX database, which includes long-term hydrometeorological time series collected from 438 basins across the U.S. from 1948 to 2003. Comparisons with linear regression and artificial neural network models indicate that GPR outperforms both regression methods in most cases. The GPR prediction of MOPEX basins is further examined using the Budyko framework, which helps to reveal the close relationships among water-energy partitions, hydrologic similarity, and predictability. Flow regime modification and the resulting loss of predictability have been a major concern in recent years because of climate change and anthropogenic activities. The persistence of streamflow predictability is thus examined by extending the original MOPEX data records to 2012. Results indicate relatively strong persistence of streamflow predictability in the extended period, although the low-predictability basins tend to show more variations. Because many low-predictability basins are located in regions experiencing fast growth of human activities, the significance of sustainable development and water resources management can be even greater for those regions.
Twisted Gaussian Schell-model beams
Simon, R. ); Mukunda, N. Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore )
1993-01-01
The authors introduce a new class of partially coherent axially symmetric Gaussian Schell-model (GSM) beams incorporating a new twist phase quadratic in configuration variables. This phase twists the beam about its axis during propagation and is shown to be bounded in strength because of the positive semidefiniteness of the cross-spectral density. Propagation characteristics and invariants for such beams are derived and interpreted, and two different geometric representations are developed. Direct effects of the twist phase on free propagation as well as in parabolic index fibers are demonstrated. Production of such twisted GSM beams, starting with Li-Wolf anisotropic GSM beams, is described. 34 refs., 3 figs.
A Gaussian measure of quantum phase noise
NASA Technical Reports Server (NTRS)
Schleich, Wolfgang P.; Dowling, Jonathan P.
1992-01-01
We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.
Non-gaussianity from broken symmetries
Kolb, Edward W.; Riotto, Antonio; Vallinotto, Alberto; /Chicago U. /Fermilab
2005-11-01
Recently we studied inflation models in which the inflation 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{sub NL}, can be as large as 10{sup 2}.
Non-Gaussianities due to relativistic corrections to the observed galaxy bispectrum
NASA Astrophysics Data System (ADS)
Di Dio, E.; Perrier, H.; Durrer, R.; Marozzi, G.; Moradinezhad Dizgah, A.; Noreña, J.; Riotto, A.
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 fNL 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, fNL, 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 fNL 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 fNLloc ~ Script O(1).
Korsgaard, Inge Riis; Lund, Mogens Sandø; Sorensen, Daniel; Gianola, Daniel; Madsen, Per; Jensen, Just
2003-01-01
A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed.
Bag, Bidhan Chandra; Hu, Chin-Kun
2007-04-01
In a previous paper [Bag and Hu, Phys. Rev. E 73, 061107 (2006)], we studied the mean lifetime (MLT) for the escape of a Brownian particle through an unstable limit cycle driven by multiplicative colored Gaussian and additive Gaussian white noises and found resonant activation (RA) behavior. In the present paper we switch from Gaussian to non-Gaussian multiplicative colored noise. We find that in the RA phenomenon, the minimum appears at a smaller noise correlation time (tau) for non-Gaussian noises compared to Gaussian noises in the plot of MLT vs tau for a fixed noise variance; the same plot for a given noise strength increases linearly and the increasing rate is smaller for non-Gaussian noises than for the Gaussian noises; the plot of logarithm of inverse of MLT vs inverse of the strength of additive noise is Arrhenius-like for Gaussian colored noise and it becomes similar to the quantum-Kramers rate if the multiplicative noise is non-Gaussian.
Uncertainty in perception and the Hierarchical Gaussian Filter.
Mathys, Christoph D; Lomakina, Ekaterina I; Daunizeau, Jean; Iglesias, Sandra; Brodersen, Kay H; Friston, Karl J; Stephan, Klaas E
2014-01-01
In its full sense, perception rests on an agent's model of how its sensory input comes about and the inferences it draws based on this model. These inferences are necessarily uncertain. Here, we illustrate how the Hierarchical Gaussian Filter (HGF) offers a principled and generic way to deal with the several forms that uncertainty in perception takes. The HGF is a recent derivation of one-step update equations from Bayesian principles that rests on a hierarchical generative model of the environment and its (in)stability. It is computationally highly efficient, allows for online estimates of hidden states, and has found numerous applications to experimental data from human subjects. In this paper, we generalize previous descriptions of the HGF and its account of perceptual uncertainty. First, we explicitly formulate the extension of the HGF's hierarchy to any number of levels; second, we discuss how various forms of uncertainty are accommodated by the minimization of variational free energy as encoded in the update equations; third, we combine the HGF with decision models and demonstrate the inversion of this combination; finally, we report a simulation study that compared four optimization methods for inverting the HGF/decision model combination at different noise levels. These four methods (Nelder-Mead simplex algorithm, Gaussian process-based global optimization, variational Bayes and Markov chain Monte Carlo sampling) all performed well even under considerable noise, with variational Bayes offering the best combination of efficiency and informativeness of inference. Our results demonstrate that the HGF provides a principled, flexible, and efficient-but at the same time intuitive-framework for the resolution of perceptual uncertainty in behaving agents.
Gaussian beam decomposition of high frequency wave fields
Tanushev, Nicolay M. Engquist, Bjoern; Tsai, Richard
2009-12-10
In this paper, we present a method of decomposing a highly oscillatory wave field into a sparse superposition of Gaussian beams. The goal is to extract the necessary parameters for a Gaussian beam superposition from this wave field, so that further evolution of the high frequency waves can be computed by the method of Gaussian beams. The methodology is described for R{sup d} with numerical examples for d=2. In the first example, a field generated by an interface reflection of Gaussian beams is decomposed into a superposition of Gaussian beams. The beam parameters are reconstructed to a very high accuracy. The data in the second example is not a superposition of a finite number of Gaussian beams. The wave field to be approximated is generated by a finite difference method for a geometry with two slits. The accuracy in the decomposition increases monotonically with the number of beams.
Compressive tracking with incremental multivariate Gaussian distribution
NASA Astrophysics Data System (ADS)
Li, Dongdong; Wen, Gongjian; Zhu, Gao; Zeng, Qiaoling
2016-09-01
Various approaches have been proposed for robust visual tracking, among which compressive tracking (CT) yields promising performance. In CT, Haar-like features are efficiently extracted with a very sparse measurement matrix and modeled as an online updated naïve Bayes classifier to account for target appearance change. The naïve Bayes classifier ignores overlap between Haar-like features and assumes that Haar-like features are independently distributed, which leads to drift in complex scenario. To address this problem, we present an extended CT algorithm, which assumes that all Haar-like features are correlated with each other and have multivariate Gaussian distribution. The mean vector and covariance matrix of multivariate normal distribution are incrementally updated with constant computational complexity to adapt to target appearance change. Each frame is associated with a temporal weight to expend less modeling power on old observation. Based on temporal weight, an update scheme with changing but convergent learning rate is derived with strict mathematic proof. Compared with CT, our extended algorithm achieves a richer representation of target appearance. The incremental multivariate Gaussian distribution is integrated into the particle filter framework to achieve better tracking performance. Extensive experiments on the CVPR2013 tracking benchmark demonstrate that our proposed tracker achieves superior performance both qualitatively and quantitatively over several state-of-the-art trackers.
Radiation damping in pulsed Gaussian beams
NASA Astrophysics Data System (ADS)
Harvey, Chris; Marklund, Mattias
2012-01-01
We consider the effects of radiation damping on the electron dynamics in a Gaussian-beam model of a laser field. For high intensities, i.e., with dimensionless intensity a0≫1, it is found that the dynamics divides into three regimes. For low-energy electrons (low initial γ factor, γ0) the radiation damping effects are negligible. At higher energies, but still at 2γ0
On the optimization of Gaussian basis sets
NASA Astrophysics Data System (ADS)
Petersson, George A.; Zhong, Shijun; Montgomery, John A.; Frisch, Michael J.
2003-01-01
A new procedure for the optimization of the exponents, αj, of Gaussian basis functions, Ylm(ϑ,φ)rle-αjr2, is proposed and evaluated. The direct optimization of the exponents is hindered by the very strong coupling between these nonlinear variational parameters. However, expansion of the logarithms of the exponents in the orthonormal Legendre polynomials, Pk, of the index, j: ln αj=∑k=0kmaxAkPk((2j-2)/(Nprim-1)-1), yields a new set of well-conditioned parameters, Ak, and a complete sequence of well-conditioned exponent optimizations proceeding from the even-tempered basis set (kmax=1) to a fully optimized basis set (kmax=Nprim-1). The error relative to the exact numerical self-consistent field limit for a six-term expansion is consistently no more than 25% larger than the error for the completely optimized basis set. Thus, there is no need to optimize more than six well-conditioned variational parameters, even for the largest sets of Gaussian primitives.
Density Estimation with Mercer Kernels
NASA Technical Reports Server (NTRS)
Macready, William G.
2003-01-01
We present a new method for density estimation based on Mercer kernels. The density estimate can be understood as the density induced on a data manifold by a mixture of Gaussians fit in a feature space. As is usual, the feature space and data manifold are defined with any suitable positive-definite kernel function. We modify the standard EM algorithm for mixtures of Gaussians to infer the parameters of the density. One benefit of the approach is it's conceptual simplicity, and uniform applicability over many different types of data. Preliminary results are presented for a number of simple problems.
Super-Gaussian apodization in ground based telescopes for high contrast coronagraph imaging.
Cagigas, Miguel A; Valle, Pedro J; Cagigal, Manuel P
2013-05-20
We introduce the use of Super-Gaussian apodizing functions in the telescope pupil plane and/or the coronagraph Lyot plane to improve the imaging contrast in ground-based coronagraphs. We describe the properties of the Super-Gaussian function, we estimate its second-order moment in the pupil and Fourier planes and we check it as an apodizing function. We then use Super-Gaussian function to apodize the telescope pupil, the coronagraph Lyot plane or both of them. The result is that a proper apodizing masks combination can reduce the exoplanet detection distance up to a 45% with respect to the classic Lyot coronagraph, for moderately aberrated wavefronts. Compared to the prolate spheroidal function the Super-Gaussian apodizing function allows the planet light up to 3 times brighter. An extra help to increase the extinction rate is to perform a frame selection (Lucky Imaging technique). We show that a selection of the 10% best frames will reduce up to a 20% the detection angular distance when using the classic Lyot coronagraph but that the reduction is only around the 5% when using an apodized coronagraph.
Efficient calculation of integrals in mixed ramp-Gaussian basis sets.
McKemmish, Laura K
2015-04-07
Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RampItUp. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or very large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.
Simultaneous Gaussian and exponential inversion for improved analysis of shales by NMR relaxometry
Washburn, Kathryn E.; Anderssen, Endre; Vogt, Sarah J.; Seymour, Joseph D.; Birdwell, Justin E.; Kirkland, Catherine M.; Codd, Sarah L.
2014-01-01
Nuclear magnetic resonance (NMR) relaxometry is commonly used to provide lithology-independent porosity and pore-size estimates for petroleum resource evaluation based on fluid-phase signals. However in shales, substantial hydrogen content is associated with solid and fluid signals and both may be detected. Depending on the motional regime, the signal from the solids may be best described using either exponential or Gaussian decay functions. When the inverse Laplace transform, the standard method for analysis of NMR relaxometry results, is applied to data containing Gaussian decays, this can lead to physically unrealistic responses such as signal or porosity overcall and relaxation times that are too short to be determined using the applied instrument settings. We apply a new simultaneous Gaussian-Exponential (SGE) inversion method to simulated data and measured results obtained on a variety of oil shale samples. The SGE inversion produces more physically realistic results than the inverse Laplace transform and displays more consistent relaxation behavior at high magnetic field strengths. Residuals for the SGE inversion are consistently lower than for the inverse Laplace method and signal overcall at short T2 times is mitigated. Beyond geological samples, the method can also be applied in other fields where the sample relaxation consists of both Gaussian and exponential decays, for example in material, medical and food sciences.
Dependence of the Gaussian-Lévy transition on the disorder strength in random lasers
NASA Astrophysics Data System (ADS)
Uppu, Ravitej; Mujumdar, Sushil
2013-01-01
We examine the dependence of the Gaussian-Lévy transition in random lasers on the disorder strength, through experimental and theoretical studies. Experiments are performed on samples whose disorder strength varied over almost an order of magnitude. It is found that the Lévy regime is easily accessed under low excitation when the disorder is weak, compared to the energetically expensive transition in strong disorder. Besides, under conditions of weak disorder, the transition energy is mildly dependent on the disorder strength. The Gaussian-Lévy transition also progresses rapidly in weakly scattering samples. In the theoretical investigation, we employ an analytical-numerical method to estimate the parameters of intensity statistics in random lasers. A Monte Carlo simulation is implemented to accurately calculate the excitation region of the random laser, yielding the ℓg and the geometric features of this region. The aspect ratio of this pumped region allows us to further analytically calculate the scale parameter
Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong
2016-01-01
In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student’s t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods. PMID:27187405
MacKenzie, Donald; Spears, Taylor
2014-06-01
Drawing on documentary sources and 114 interviews with market participants, this and a companion article discuss the development and use in finance of the Gaussian copula family of models, which are employed to estimate the probability distribution of losses on a pool of loans or bonds, and which were centrally involved in the credit crisis. This article, which explores how and why the Gaussian copula family developed in the way it did, employs the concept of 'evaluation culture', a set of practices, preferences and beliefs concerning how to determine the economic value of financial instruments that is shared by members of multiple organizations. We identify an evaluation culture, dominant within the derivatives departments of investment banks, which we call the 'culture of no-arbitrage modelling', and explore its relation to the development of Gaussian copula models. The article suggests that two themes from the science and technology studies literature on models (modelling as 'impure' bricolage, and modelling as articulating with heterogeneous objectives and constraints) help elucidate the history of Gaussian copula models in finance.
Efficient calculation of integrals in mixed ramp-Gaussian basis sets
McKemmish, Laura K.
2015-04-07
Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RAMPITUP. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or very large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.
Simultaneous Gaussian and exponential inversion for improved analysis of shales by NMR relaxometry.
Washburn, Kathryn E; Anderssen, Endre; Vogt, Sarah J; Seymour, Joseph D; Birdwell, Justin E; Kirkland, Catherine M; Codd, Sarah L
2015-01-01
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.
Constraints on scale-dependent non-Gaussianity
Shandera, Sarah E.
2007-11-20
We review why detection of non-Gaussianity in the spectrum of primordial fluctuations would be an indication of interesting inflationary physics and discuss the observational constraints on a simple type of scale-dependent non-Gaussianity. In particular, if the amount non-Gaussianity increases during inflation then observations on scales smaller than those probed by the Cosmic Microwave Background may provide important constraints. Clusters number counts can be a useful tool in this context.
Relaxation oscillations in a laser with a Gaussian mirror.
Mossakowska-Wyszyńska, Agnieszka; Witoński, Piotr; Szczepański, Paweł
2002-03-20
We present an analysis of the relaxation oscillations in a laser with a Gaussian mirror by taking into account the three-dimensional spatial field distribution of the laser modes and the spatial hole burning effect. In particular, we discuss the influence of the Gaussian mirror peak reflectivity and a Gaussian parameter on the damping rate and frequency of the relaxation oscillation for two different laser structures, i.e., with a classically unstable resonator and a classically stable resonator.
Experimental Method of Generating Electromagnetic Gaussian Schell-model Beams
2015-03-26
EXPERIMENTAL METHOD OF GENERATING ELECTROMAGNETIC GAUSSIAN SCHELL-MODEL BEAMS THESIS Matthew J. Gridley, Captain, USAF AFIT-ENG-MS-15-M-058...not subject to copyright protection in the United States. AFIT-ENG-MS-15-M-058 EXPERIMENTAL METHOD OF GENERATING ELECTROMAGNETIC GAUSSIAN SCHELL-MODEL...UNLIMITED AFIT-ENG-MS-15-M-058 EXPERIMENTAL METHOD OF GENERATING ELECTROMAGNETIC GAUSSIAN SCHELL-MODEL BEAMS Matthew J. Gridley, B.S.E.E. Captain, USAF
Gaussian conditional random fields for regression in remote sensing
NASA Astrophysics Data System (ADS)
Radosavljevic, Vladan
In recent years many remote sensing instruments of various properties have been employed in an attempt to better characterize important geophysical phenomena. Satellite instruments provide an exceptional opportunity for global long-term observations of the land, the biosphere, the atmosphere, and the oceans. The collected data are used for estimation and better understanding of geophysical parameters such as land cover type, atmospheric properties, or ocean temperature. Achieving accurate estimations of such parameters is an important requirement for development of models able to predict global climate changes. One of the most challenging climate research problems is estimation of global composition, load, and variability of aerosols, small airborne particles that reflect and absorb incoming solar radiation. The existing algorithm for aerosol prediction from satellite observations is deterministic and manually tuned by domain scientist. In contrast to domain-driven method, we show that aerosol prediction is achievable by completely data-driven approaches. These statistical methods consist of learning of nonlinear regression models to predict aerosol load using the satellite observations as inputs. Measurements from unevenly distributed ground-based sites over the world are used as proxy to ground-truth outputs. Although statistical methods achieve better accuracy than deterministic method this setup is appropriate when data are independently and identically distributed (IID). The IID assumption is often violated in remote sensing where data exhibit temporal, spatial, or spatio-temporal dependencies. In such cases, the traditional supervised learning approaches could result in a model with degraded accuracy. Conditional random fields (CRF) are widely used for predicting output variables that have some internal structure. Most of the CRF research has been done on structured classification where the outputs are discrete. We propose a CRF model for continuous outputs
Post-Gaussian approximations in phase ordering kinetics
NASA Astrophysics Data System (ADS)
Mazenko, Gene F.
1994-05-01
Existing theories for the growth of order in unstable systems have successfully exploited the use of a Gaussian auxiliary field. The limitations imposed on such theories by assuming this field to be Gaussian have recently become clearer. In this paper it is shown how this Gaussian restriction can be removed in order to obtain improved approximations for the scaling properties of such systems. In particular it is shown how the improved theory can explain the recent numerical results of Blundell, Bray, and Sattler [Phys. Rev. E 48, 2476 (1993)] which are in qualitative disagreement with Gaussian theories.
NGMIX: Gaussian mixture models for 2D images
NASA Astrophysics Data System (ADS)
Sheldon, Erin
2015-08-01
NGMIX implements Gaussian mixture models for 2D images. Both the PSF profile and the galaxy are modeled using mixtures of Gaussians. Convolutions are thus performed analytically, resulting in fast model generation as compared to methods that perform the convolution in Fourier space. For the galaxy model, NGMIX supports exponential disks and de Vaucouleurs and Sérsic profiles; these are implemented approximately as a sum of Gaussians using the fits from Hogg & Lang (2013). Additionally, any number of Gaussians can be fit, either completely free or constrained to be cocentric and co-elliptical.
BEAM-BEAM SIMULATIONS FOR DOUBLE-GAUSSIAN BEAMS.
MONTAG, C.; MALITSKY, N.; BEN-ZVI, I.; LITVINENKO, V.
2005-05-16
Electron cooling together with intra-beam scattering results in a transverse distribution that can best be described by a sum of two gaussians, one for the high-density core and one for the tails of the distribution. Simulation studies are being performed to understand the beam-beam interaction of these double-gaussian beams. Here we report the effect of low-frequency random tune modulations on diffusion in double-gaussian beams and compare the effects to those in beam-beam interactions with regular gaussian beams and identical tune shift parameters.
Truncated multiGaussian fields and effective conductance of binary media.
Marzouk, Youssef M.; van Bloemen Waanders, Bart Gustaaf; Ray, Jaideep; McKenna, Sean Andrew
2011-01-01
Truncated Gaussian fields provide a flexible model for defining binary media with dispersed (as opposed to layered) inclusions. General properties of excursion sets on these truncated fields are coupled with a distance-based upscaling algorithm and approximations of point process theory to develop an estimation approach for effective conductivity in two-dimensions. Estimation of effective conductivity is derived directly from knowledge of the kernel size used to create the multiGaussian field, defined as the full-width at half maximum (FWHM), the truncation threshold and conductance values of the two modes. Therefore, instantiation of the multiGaussian field is not necessary for estimation of the effective conductance. The critical component of the effective medium approximation developed here is the mean distance between high conductivity inclusions. This mean distance is characterized as a function of the FWHM, the truncation threshold and the ratio of the two modal conductivities. Sensitivity of the resulting effective conductivity to this mean distance is examined for two levels of contrast in the two modal conductances and different FWHM sizes. Results demonstrate that the FWHM is a robust measure of mean travel distance in the background medium. The resulting effective conductivities are accurate when compared to numerical results and results obtained from effective media theory, distance-based upscaling and numerical simulation.
NASA Astrophysics Data System (ADS)
Xu, Qi; Ma, Xiaochuan; Yan, Shefeng; Hao, Chengpeng; Shi, Bo
2012-12-01
In this article, we consider the problem of adaptive detection for a multichannel signal in the presence of spatially and temporally colored compound-Gaussian disturbance. By modeling the disturbance as a multichannel autoregressive (AR) process, we first derive a parametric generalized likelihood ratio test against compound-Gaussian disturbance (CG-PGLRT) assuming that the true multichannel AR parameters are perfectly known. For the two-step GLRT design criterion, we combine the multichannel AR parameter estimation algorithm with three covariance matrix estimation strategies for compound-Gaussian environment, then obtain three adaptive CG-PGLRT detectors by replacing the ideal multichannel AR parameters with their estimates. Owing to treating the random texture components of disturbance as deterministic unknown parameters, all of the proposed detectors require no a priori knowledge about the disturbance statistics. The performance assessments are conducted by means of Monte Carlo trials. We focus on the issues of constant false alarm rate (CFAR) behavior, detection and false alarm probabilities. Numerical results show that the proposed adaptive CG-PGLRT detectors have dramatically ease the training and computational burden compared to the generalized likelihood ratio test-linear quadratic (GLRT-LQ) which is referred to as covariance matrix based detector and relies more heavily on training.
Adaptive subspace detection of extended target in white Gaussian noise using sinc basis
NASA Astrophysics Data System (ADS)
Zhang, Xiao-Wei; Li, Ming; Qu, Jian-She; Yang, Hui
2016-01-01
For the high resolution radar (HRR), the problem of detecting the extended target is considered in this paper. Based on a single observation, a new two-step detection based on sparse representation (TSDSR) method is proposed to detect the extended target in the presence of Gaussian noise with unknown covariance. In the new method, the Sinc dictionary is introduced to sparsely represent the high resolution range profile (HRRP). Meanwhile, adaptive subspace pursuit (ASP) is presented to recover the HRRP embedded in the Gaussian noise and estimate the noise covariance matrix. Based on the Sinc dictionary and the estimated noise covariance matrix, one step subspace detector (OSSD) for the first-order Gaussian (FOG) model without secondary data is adopted to realise the extended target detection. Finally, the proposed TSDSR method is applied to raw HRR data. Experimental results demonstrate that HRRPs of different targets can be sparsely represented very well with the Sinc dictionary. Moreover, the new method can estimate the noise power with tiny errors and have a good detection performance.
Scalable Indoor Localization via Mobile Crowdsourcing and Gaussian Process.
Chang, Qiang; Li, Qun; Shi, Zesen; Chen, Wei; Wang, Weiping
2016-03-16
Indoor localization using Received Signal Strength Indication (RSSI) fingerprinting has been extensively studied for decades. The positioning accuracy is highly dependent on the density of the signal database. In areas without calibration data, however, this algorithm breaks down. Building and updating a dense signal database is labor intensive, expensive, and even impossible in some areas. Researchers are continually searching for better algorithms to create and update dense databases more efficiently. In this paper, we propose a scalable indoor positioning algorithm that works both in surveyed and unsurveyed areas. We first propose Minimum Inverse Distance (MID) algorithm to build a virtual database with uniformly distributed virtual Reference Points (RP). The area covered by the virtual RPs can be larger than the surveyed area. A Local Gaussian Process (LGP) is then applied to estimate the virtual RPs' RSSI values based on the crowdsourced training data. Finally, we improve the Bayesian algorithm to estimate the user's location using the virtual database. All the parameters are optimized by simulations, and the new algorithm is tested on real-case scenarios. The results show that the new algorithm improves the accuracy by 25.5% in the surveyed area, with an average positioning error below 2.2 m for 80% of the cases. Moreover, the proposed algorithm can localize the users in the neighboring unsurveyed area.
Gaussian covariance matrices for anisotropic galaxy clustering measurements
NASA Astrophysics Data System (ADS)
Grieb, Jan Niklas; Sánchez, Ariel G.; Salazar-Albornoz, Salvador; Dalla Vecchia, Claudio
2016-04-01
Measurements of the redshift-space galaxy clustering have been a prolific source of cosmological information in recent years. Accurate covariance estimates are an essential step for the validation of galaxy clustering models of the redshift-space two-point statistics. Usually, only a limited set of accurate N-body simulations is available. Thus, assessing the data covariance is not possible or only leads to a noisy estimate. Further, relying on simulated realizations of the survey data means that tests of the cosmology dependence of the covariance are expensive. With these points in mind, this work presents a simple theoretical model for the linear covariance of anisotropic galaxy clustering observations with synthetic catalogues. Considering the Legendre moments (`multipoles') of the two-point statistics and projections into wide bins of the line-of-sight parameter (`clustering wedges'), we describe the modelling of the covariance for these anisotropic clustering measurements for galaxy samples with a trivial geometry in the case of a Gaussian approximation of the clustering likelihood. As main result of this paper, we give the explicit formulae for Fourier and configuration space covariance matrices. To validate our model, we create synthetic halo occupation distribution galaxy catalogues by populating the haloes of an ensemble of large-volume N-body simulations. Using linear and non-linear input power spectra, we find very good agreement between the model predictions and the measurements on the synthetic catalogues in the quasi-linear regime.
Scalable Indoor Localization via Mobile Crowdsourcing and Gaussian Process
Chang, Qiang; Li, Qun; Shi, Zesen; Chen, Wei; Wang, Weiping
2016-01-01
Indoor localization using Received Signal Strength Indication (RSSI) fingerprinting has been extensively studied for decades. The positioning accuracy is highly dependent on the density of the signal database. In areas without calibration data, however, this algorithm breaks down. Building and updating a dense signal database is labor intensive, expensive, and even impossible in some areas. Researchers are continually searching for better algorithms to create and update dense databases more efficiently. In this paper, we propose a scalable indoor positioning algorithm that works both in surveyed and unsurveyed areas. We first propose Minimum Inverse Distance (MID) algorithm to build a virtual database with uniformly distributed virtual Reference Points (RP). The area covered by the virtual RPs can be larger than the surveyed area. A Local Gaussian Process (LGP) is then applied to estimate the virtual RPs’ RSSI values based on the crowdsourced training data. Finally, we improve the Bayesian algorithm to estimate the user’s location using the virtual database. All the parameters are optimized by simulations, and the new algorithm is tested on real-case scenarios. The results show that the new algorithm improves the accuracy by 25.5% in the surveyed area, with an average positioning error below 2.2 m for 80% of the cases. Moreover, the proposed algorithm can localize the users in the neighboring unsurveyed area. PMID:26999139
NASA Astrophysics Data System (ADS)
Wu, Zhenkun; Gu, Yuzong
2016-12-01
The propagation of two-dimensional beams is analytically and numerically investigated in strongly nonlocal nonlinear media (SNNM) based on the ABCD matrix. The two-dimensional beams reported in this paper are described by the product of the superposition of generalized Laguerre-Gaussian (LG), Hermite-Gaussian (HG), Bessel-Gaussian (BG), and circular Airy (CA) beams, carrying an orbital angular momentum (OAM). Owing to OAM and the modulation of SNNM, we find that the propagation of these two-dimensional beams exhibits complete rotation and periodic inversion: the spatial intensity profile first extends and then diminishes, and during the propagation the process repeats to form a breath-like phenomenon.
Non-Gaussianity in the foreground-reduced CMB maps
Bernui, A.; Reboucas, M. J.
2010-03-15
A detection or nondetection of primordial non-Gaussianity by using the cosmic microwave background radiation (CMB) data is crucial not only to discriminate inflationary models but also to test alternative scenarios. Non-Gaussianity offers, therefore, a powerful probe of the physics of the primordial Universe. The extraction of primordial non-Gaussianity is a difficult enterprise since several effects of a nonprimordial nature can produce non-Gaussianity. 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 a range of different statistical tools to quantify and/or constrain its amount in order to have information that may be helpful for identifying its causes. Moreover, different indicators can in principle provide information about distinct forms of non-Gaussianity that can be present in CMB data. Most of the Gaussianity analyses of CMB data have been performed by using part-sky frequency, where the mask is used to deal with the galactic diffuse foreground emission. However, full-sky map seems to be potentially more appropriate to test for Gaussianity of the CMB data. On the other hand, masks can induce bias in some non-Gaussianity analyses. Here we use two recent large-angle non-Gaussianity indicators, based on skewness and kurtosis of large-angle patches of CMB maps, to examine the question of non-Gaussianity in the available full-sky five-year and seven-year Wilkinson Microwave Anisotropy Probe (WMAP) maps. We show that these full-sky foreground-reduced maps present a significant deviation from Gaussianity of different levels, which vary with the foreground-reducing procedures. We also make a Gaussianity analysis of the foreground-reduced five-year and seven-year WMAP maps with a KQ75 mask, and compare with the similar analysis performed with the corresponding full-sky foreground-reduced maps. This comparison shows a significant reduction in the levels of non-Gaussianity
IBS for non-gaussian distributions
Fedotov, A.; Sidorin, A.O.; Smirnov, A.V.
2010-09-27
In many situations distribution can significantly deviate from Gaussian which requires accurate treatment of IBS. Our original interest in this problem was motivated by the need to have an accurate description of beam evolution due to IBS while distribution is strongly affected by the external electron cooling force. A variety of models with various degrees of approximation were developed and implemented in BETACOOL in the past to address this topic. A more complete treatment based on the friction coefficient and full 3-D diffusion tensor was introduced in BETACOOL at the end of 2007 under the name 'local IBS model'. Such a model allowed us calculation of IBS for an arbitrary beam distribution. The numerical benchmarking of this local IBS algorithm and its comparison with other models was reported before. In this paper, after briefly describing the model and its limitations, they present its comparison with available experimental data.
Length of Inflation and Non-Gaussianity
NASA Astrophysics Data System (ADS)
Hirai, Shiro; Takami, Tomoyuki
Certain inflation models are shown to have large non-Gaussianity in special cases. Namely, slow-roll inflation models with an effective higher derivative interaction, in which the length of inflation is finite and a scalar-matter-dominated period or power inflation is adopted as pre-inflation, are considered. Using Holman and Tolley's formula of the nonlinearity parameter in the flattened triangle configurations f flattened NL, we calculate the value of f flattened NL. The value of f flattened NL is found to be largest (f flattened NL>10) when the inflation length is approximately 60 e-folds, and f flattened NL is found to depend strongly on the length of inflation and the cut-off scale.
Semiconductor band gap localization via Gaussian function
NASA Astrophysics Data System (ADS)
Ullrich, B.; Brown, G. J.; Xi, H.
2012-10-01
To determine the band gap of bulk semiconductors with transmission spectroscopy alone is considered as an extremely difficult task because in the higher energy range, approaching and exceeding the band gap energy, the material is opaque yielding no useful data to be recorded. In this paper, by investigating the transmission of industrial GaSb wafers with a thickness of 500 µm, we demonstrate how these obstacles of transmission spectroscopy can be overcome. The key is the transmission spectrums’ derivative, which coincides with the Gaussian function. This understanding can be used to transfer Beers’ law in an integral form opening the pathway of band gap determinations based on mathematical parameters only. The work also emphasizes the correlation between the thermal band gap variation and Debye temperature.
Exploring scalar field dynamics with Gaussian processes
Nair, Remya; Jhingan, Sanjay; Jain, Deepak E-mail: sanjay.jhingan@gmail.com
2014-01-01
The origin of the accelerated expansion of the Universe remains an unsolved mystery in Cosmology. In this work we consider a spatially flat Friedmann-Robertson-Walker (FRW) Universe with non-relativistic matter and a single scalar field contributing to the energy density of the Universe. Properties of this scalar field, like potential, kinetic energy, equation of state etc. are reconstructed from Supernovae and BAO data using Gaussian processes. We also reconstruct energy conditions and kinematic variables of expansion, such as the jerk and the slow roll parameter. We find that the reconstructed scalar field variables and the kinematic quantities are consistent with a flat ΛCDM Universe. Further, we find that the null energy condition is satisfied for the redshift range of the Supernovae data considered in the paper, but the strong energy condition is violated.
Primordial non-Gaussianity from G inflation
Kobayashi, Tsutomu; Yamaguchi, Masahide; Yokoyama, Jun'ichi
2011-05-15
We present a comprehensive study of primordial fluctuations generated from G inflation, in which the inflaton Lagrangian is of the form K({phi},X)-G({phi},X){open_square}{phi} with X=-({partial_derivative}{phi}){sup 2}/2. The Lagrangian still gives rise to second-order gravitational and scalar field equations, and thus offers a more generic class of single-field inflation than ever studied, with a richer phenomenology. We compute the power spectrum and the bispectrum, and clarify how the non-Gaussian amplitude depends upon parameters such as the sound speed. In so doing we try to keep as great generality as possible, allowing for non slow-roll and deviation from the exact scale invariance.
Absolute instability of the Gaussian wake profile
NASA Technical Reports Server (NTRS)
Hultgren, Lennart S.; Aggarwal, Arun K.
1987-01-01
Linear parallel-flow stability theory has been used to investigate the effect of viscosity on the local absolute instability of a family of wake profiles with a Gaussian velocity distribution. The type of local instability, i.e., convective or absolute, is determined by the location of a branch-point singularity with zero group velocity of the complex dispersion relation for the instability waves. The effects of viscosity were found to be weak for values of the wake Reynolds number, based on the center-line velocity defect and the wake half-width, larger than about 400. Absolute instability occurs only for sufficiently large values of the center-line wake defect. The critical value of this parameter increases with decreasing wake Reynolds number, thereby indicating a shrinking region of absolute instability with decreasing wake Reynolds number. If backflow is not allowed, absolute instability does not occur for wake Reynolds numbers smaller than about 38.
Development and modification of a Gaussian and non-Gaussian noise exposure system
NASA Astrophysics Data System (ADS)
Schlag, Adam W.
Millions of people across the world currently have noise induced hearing loss, and many are working in conditions with both continuous Gaussian and non-Gaussian noises that could affect their hearing. It was hypothesized that the energy of the noise was the cause of the hearing loss and did not depend on temporal pattern of a noise. This was referred to as the equal energy hypothesis. This hypothesis has been shown to have limitations though. This means that there is a difference in the types of noise a person receives to induce hearing loss and it is necessary to build a system that can easily mimic various conditions to conduct research. This study builds a system that can produce both non-Gaussian impulse/impact noises and continuous Gaussian noise. It was found that the peak sound pressure level of the system could reach well above the needed 120 dB level to represent acoustic trauma and could replicate well above the 85 dB A-weighted sound pressure level to produce conditions of gradual developing hearing loss. The system reached a maximum of 150 dB sound peak pressure level and a maximum of 133 dB A-weighted sound pressure level. Various parameters could easily be adjusted to control the sound, such as the high and low cutoff frequency to center the sound at 4 kHz. The system build can easily be adjusted to create numerous sound conditions and will hopefully be modified and improved in hopes of eventually being used for animal studies to lead to the creation of a method to treat or prevent noise induced hearing loss.
Degeneracy of energy levels of pseudo-Gaussian oscillators
Iacob, Theodor-Felix; Iacob, Felix; Lute, Marina
2015-12-07
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.
When Does the Uncertainty Become Non-Gaussian
NASA Astrophysics Data System (ADS)
Alfriend, K.; Park, I.
2016-09-01
The orbit state covariance is used in the conjunction assessment/probability of collision calculation. It can also be a valuable tool in track association, maneuver detection and sensor tasking. These uses all assume that the uncertainty is Gaussian. Studies have shown that the uncertainty at epoch (time of last observation) is reasonably Gaussian, but the neglected nonlinearities in the covariance propagation eventually result in the uncertainty becoming non-Gaussian. Numerical studies have shown that for space objects in low Earth orbit the covariance remains Gaussian the longest in orbital element space. It has been shown that the covariance remains Gaussian for up to 10 days in orbital element space, but becomes non-Gaussian after 2-3 days in Cartesian coordinates for a typical LEO orbit. The fundamental question is when does it become non-Gaussian and how can one given the orbit state and covariance at epoch determine when it occurs. A tool that an operator could use to compute the approximate time when the when the uncertainty becomes non-Gaussian would be useful This paper addresses the development of such a tool.
A Paper-and-Pencil gcd Algorithm for Gaussian Integers
ERIC Educational Resources Information Center
Szabo, Sandor
2005-01-01
As with natural numbers, a greatest common divisor of two Gaussian (complex) integers "a" and "b" is a Gaussian integer "d" that is a common divisor of both "a" and "b". This article explores an algorithm for such gcds that is easy to do by hand.
Gaussian and mean curvatures for discrete asymptotic nets
NASA Astrophysics Data System (ADS)
Schief, W. K.
2017-04-01
We propose discretisations of Gaussian and mean curvatures of surfaces parametrised in terms of asymptotic coordinates and examine their relevance in the context of integrable discretisations of classical classes of surfaces and their underlying integrable systems. We also record discrete analogues of the classical relation between the Gaussian curvature of hyperbolic surfaces and the torsion of their asymptotic lines.
Connections between Graphical Gaussian Models and Factor Analysis
ERIC Educational Resources Information Center
Salgueiro, M. Fatima; Smith, Peter W. F.; McDonald, John W.
2010-01-01
Connections between graphical Gaussian models and classical single-factor models are obtained by parameterizing the single-factor model as a graphical Gaussian model. Models are represented by independence graphs, and associations between each manifest variable and the latent factor are measured by factor partial correlations. Power calculations…
NASA Technical Reports Server (NTRS)
Frehlich, Rod
1993-01-01
Calculations of the exact Cramer-Rao Bound (CRB) for unbiased estimates of the mean frequency, signal power, and spectral width of Doppler radar/lidar signals (a Gaussian random process) are presented. Approximate CRB's are derived using the Discrete Fourier Transform (DFT). These approximate results are equal to the exact CRB when the DFT coefficients are mutually uncorrelated. Previous high SNR limits for CRB's are shown to be inaccurate because the discrete summations cannot be approximated with integration. The performance of an approximate maximum likelihood estimator for mean frequency approaches the exact CRB for moderate signal to noise ratio and moderate spectral width.
Multipartite Gaussian steering: Monogamy constraints and quantum cryptography applications
NASA Astrophysics Data System (ADS)
Xiang, Yu; Kogias, Ioannis; Adesso, Gerardo; He, Qiongyi
2017-01-01
We derive laws for the distribution of quantum steering among different parties in multipartite Gaussian states under Gaussian measurements. We prove that a monogamy relation akin to the generalized Coffman-Kundu-Wootters inequality holds quantitatively for a recently introduced measure of Gaussian steering. We then define the residual Gaussian steering, stemming from the monogamy inequality, as an indicator of collective steering-type correlations. For pure three-mode Gaussian states, the residual acts as a quantifier of genuine multipartite steering, and is interpreted operationally in terms of the guaranteed key rate in the task of secure quantum secret sharing. Optimal resource states for the latter protocol are identified, and their possible experimental implementation discussed. Our results pin down the role of multipartite steering for quantum communication.
Non-ideal boson system in the Gaussian approximation
Tommasini, P.R.; de Toledo Piza, A.F.
1997-01-01
We investigate ground-state and thermal properties of a system of non-relativistic bosons interacting through repulsive, two-body interactions in a self-consistent Gaussian mean-field approximation which consists in writing the variationally determined density operator as the most general Gaussian functional of the quantized field operators. Finite temperature results are obtained in a grand canonical framework. Contact is made with the results of Lee, Yang, and Huang in terms of particular truncations of the Gaussian approximation. The full Gaussian approximation supports a free phase or a thermodynamically unstable phase when contact forces and a standard renormalization scheme are used. When applied to a Hamiltonian with zero range forces interpreted as an effective theory with a high momentum cutoff, the full Gaussian approximation generates a quasi-particle spectrum having an energy gap, in conflict with perturbation theory results. {copyright} 1997 Academic Press, Inc.
Distillation and purification of symmetric entangled Gaussian states
Fiurasek, Jaromir
2010-10-15
We propose an entanglement distillation and purification scheme for symmetric two-mode entangled Gaussian states that allows to asymptotically extract a pure entangled Gaussian state from any input entangled symmetric Gaussian state. The proposed scheme is a modified and extended version of the entanglement distillation protocol originally developed by Browne et al. [Phys. Rev. A 67, 062320 (2003)]. A key feature of the present protocol is that it utilizes a two-copy degaussification procedure that involves a Mach-Zehnder interferometer with single-mode non-Gaussian filters inserted in its two arms. The required non-Gaussian filtering operations can be implemented by coherently combining two sequences of single-photon addition and subtraction operations.
Gaussian cloning of coherent states with known phases
Alexanian, Moorad
2006-04-15
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.
Multi-Target Tracking Using an Improved Gaussian Mixture CPHD Filter
Si, Weijian; Wang, Liwei; Qu, Zhiyu
2016-01-01
The cardinalized probability hypothesis density (CPHD) filter is an alternative approximation to the full multi-target Bayesian filter for tracking multiple targets. However, although the joint propagation of the posterior intensity and cardinality distribution in its recursion allows more reliable estimates of the target number than the PHD filter, the CPHD filter suffers from the spooky effect where there exists arbitrary PHD mass shifting in the presence of missed detections. To address this issue in the Gaussian mixture (GM) implementation of the CPHD filter, this paper presents an improved GM-CPHD filter, which incorporates a weight redistribution scheme into the filtering process to modify the updated weights of the Gaussian components when missed detections occur. In addition, an efficient gating strategy that can adaptively adjust the gate sizes according to the number of missed detections of each Gaussian component is also presented to further improve the computational efficiency of the proposed filter. Simulation results demonstrate that the proposed method offers favorable performance in terms of both estimation accuracy and robustness to clutter and detection uncertainty over the existing methods. PMID:27886106
Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion.
Wyłomańska, A; Kumar, A; Połoczański, R; Vellaisamy, P
2016-10-01
In this paper we study the fractional Brownian motion (FBM) time changed by the inverse Gaussian (IG) process and its inverse, called the inverse to the inverse Gaussian (IIG) process. Some properties of the time-changed processes are similar to those of the classical FBM, such as long-range dependence. However, one can also observe different characteristics that are not satisfied by the FBM. We study the distributional properties of both subordinators, namely, IG and IIG processes, and also that of the FBM time changed by these subordinators. We establish also the connections between the subordinated processes considered and the continuous-time random-walk model. For the application part, we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters. The effectiveness of these methods is checked for simulated trajectories.
Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion
NASA Astrophysics Data System (ADS)
Wyłomańska, A.; Kumar, A.; Połoczański, R.; Vellaisamy, P.
2016-10-01
In this paper we study the fractional Brownian motion (FBM) time changed by the inverse Gaussian (IG) process and its inverse, called the inverse to the inverse Gaussian (IIG) process. Some properties of the time-changed processes are similar to those of the classical FBM, such as long-range dependence. However, one can also observe different characteristics that are not satisfied by the FBM. We study the distributional properties of both subordinators, namely, IG and IIG processes, and also that of the FBM time changed by these subordinators. We establish also the connections between the subordinated processes considered and the continuous-time random-walk model. For the application part, we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters. The effectiveness of these methods is checked for simulated trajectories.
A sharp interpolation between the Hölder and Gaussian Young inequalities
NASA Astrophysics Data System (ADS)
da Pelo, Paolo; Lanconelli, Alberto; Stan, Aurel I.
2016-03-01
We prove a very general sharp inequality of the Hölder-Young-type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative products for functions which interpolates between the pointwise and Wick products; this family arises naturally in the context of stochastic differential equations, through Wong-Zakai-type approximation theorems, and plays a key role in some generalizations of the Beckner-type Poincaré inequality. We then obtain a crucial integral representation for that family of products which is employed, together with a generalization of the classic Young inequality due to Lieb, to prove our main theorem. We stress that our main inequality contains as particular cases the Hölder inequality and Nelson’s hyper-contractive estimate, thus providing a unified framework for two fundamental results of the Gaussian analysis.
Zentner, I.; Ferré, G.; Poirion, F.; Benoit, M.
2016-06-01
In this paper, a new method for the identification and simulation of non-Gaussian and non-stationary stochastic fields given a database is proposed. It is based on two successive biorthogonal decompositions aiming at representing spatio–temporal stochastic fields. The proposed double expansion allows to build the model even in the case of large-size problems by separating the time, space and random parts of the field. A Gaussian kernel estimator is used to simulate the high dimensional set of random variables appearing in the decomposition. The capability of the method to reproduce the non-stationary and non-Gaussian features of random phenomena is illustrated by applications to earthquakes (seismic ground motion) and sea states (wave heights).
NASA Astrophysics Data System (ADS)
Bianchi, Davide; Chiesa, Matteo; Guzzo, Luigi
2016-10-01
As a step towards a more accurate modelling of redshift-space distortions (RSD) in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation , such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean μ and variance σ2. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.
Dynamical phase diagram of Gaussian wave packets in optical lattices
NASA Astrophysics Data System (ADS)
Hennig, H.; Neff, T.; Fleischmann, R.
2016-03-01
We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the discrete nonlinear Schrödinger equation (DNLSE). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping, and moving breathers. However, we find that the actual DNLSE dynamics shows a completely different diagram than the variational prediction. We calculate numerically a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure that can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian.
Surrogacy Assessment Using Principal Stratification and a Gaussian Copula Model
Taylor, J.M.G.; Elliott, M.R.
2014-01-01
In clinical trials, a surrogate outcome (S) can be measured before the outcome of interest (T) and may provide early information regarding the treatment (Z) effect on T. Many methods of surrogacy validation rely on models for the conditional distribution of T given Z and S. However, S is a post-randomization variable, and unobserved, simultaneous predictors of S and T may exist, resulting in a non-causal interpretation. Frangakis and Rubin1 developed the concept of principal surrogacy, stratifying on the joint distribution of the surrogate marker under treatment and control to assess the association between the causal effects of treatment on the marker and the causal effects of treatment on the clinical outcome. Working within the principal surrogacy framework, we address the scenario of an ordinal categorical variable as a surrogate for a censored failure time true endpoint. A Gaussian copula model is used to model the joint distribution of the potential outcomes of T, given the potential outcomes of S. Because the proposed model cannot be fully identified from the data, we use a Bayesian estimation approach with prior distributions consistent with reasonable assumptions in the surrogacy assessment setting. The method is applied to data from a colorectal cancer clinical trial, previously analyzed by Burzykowski et al..2 PMID:24947559
Bayesian Gaussian Mixture Models for High-Density Genotyping Arrays
Sabatti, Chiara; Lange, Kenneth
2011-01-01
Affymetrix's SNP (single-nucleotide polymorphism) genotyping chips have increased the scope and decreased the cost of gene-mapping studies. Because each SNP is queried by multiple DNA probes, the chips present interesting challenges in genotype calling. Traditional clustering methods distinguish the three genotypes of an SNP fairly well given a large enough sample of unrelated individuals or a training sample of known genotypes. This article describes our attempt to improve genotype calling by constructing Gaussian mixture models with empirically derived priors. The priors stabilize parameter estimation and borrow information collectively gathered on tens of thousands of SNPs. When data from related family members are available, our models capture the correlations in signals between relatives. With these advantages in mind, we apply the models to Affymetrix probe intensity data on 10,000 SNPs gathered on 63 genotyped individuals spread over eight pedigrees. We integrate the genotype-calling model with pedigree analysis and examine a sequence of symmetry hypotheses involving the correlated probe signals. The symmetry hypotheses raise novel mathematical issues of parameterization. Using the Bayesian information criterion, we select the best combination of symmetry assumptions. Compared to Affymetrix's software, our model leads to a reduction in no-calls with little sacrifice in overall calling accuracy. PMID:21572926
Dynamical phase diagram of Gaussian wave packets in optical lattices.
Hennig, H; Neff, T; Fleischmann, R
2016-03-01
We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the discrete nonlinear Schrödinger equation (DNLSE). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping, and moving breathers. However, we find that the actual DNLSE dynamics shows a completely different diagram than the variational prediction. We calculate numerically a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure that can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian.
Model-Based Visual Self-localization Using Gaussian Spheres
NASA Astrophysics Data System (ADS)
Gonzalez-Aguirre, David; Asfour, Tamim; Bayro-Corrochano, Eduardo; Dillmann, Ruediger
A novel model-based approach for global self-localization using active stereo vision and density Gaussian spheres is presented. The proposed object recognition components deliver noisy percept subgraphs, which are filtered and fused into an ego-centered reference frame. In subsequent stages, the required vision-to-model associations are extracted by selecting ego-percept subsets in order to prune and match the corresponding world-model subgraph. Ideally, these coupled subgraphs hold necessary information to obtain the model-to-world transformation, i.e., the pose of the robot. However, the estimation of the pose is not robust due to the uncertainties introduced when recovering Euclidean metric from images and during the mapping from the camera to the ego-center. The approach models the uncertainty of the percepts with a radial normal distribution. This formulation allows a closed-form solution which not only derives the maximal density position depicting the optimal ego-center but also ensures the solution even in situations where pure geometric spheres might not intersect.
Confronting Passive and Active Sensors with Non-Gaussian Statistics
Rodríguez-Gonzálvez, Pablo.; Garcia-Gago, Jesús.; Gomez-Lahoz, Javier.; González-Aguilera, Diego.
2014-01-01
This paper has two motivations: firstly, to compare the Digital Surface Models (DSM) derived by passive (digital camera) and by active (terrestrial laser scanner) remote sensing systems when applied to specific architectural objects, and secondly, to test how well the Gaussian classic statistics, with its Least Squares principle, adapts to data sets where asymmetrical gross errors may appear and whether this approach should be changed for a non-parametric one. The field of geomatic technology automation is immersed in a high demanding competition in which any innovation by one of the contenders immediately challenges the opponents to propose a better improvement. Nowadays, we seem to be witnessing an improvement of terrestrial photogrammetry and its integration with computer vision to overcome the performance limitations of laser scanning methods. Through this contribution some of the issues of this “technological race” are examined from the point of view of photogrammetry. A new software is introduced and an experimental test is designed, performed and assessed to try to cast some light on this thrilling match. For the case considered in this study, the results show good agreement between both sensors, despite considerable asymmetry. This asymmetry suggests that the standard Normal parameters are not adequate to assess this type of data, especially when accuracy is of importance. In this case, standard deviation fails to provide a good estimation of the results, whereas the results obtained for the Median Absolute Deviation and for the Biweight Midvariance are more appropriate measures. PMID:25196104
Sample variance of non-Gaussian sky distributions
NASA Astrophysics Data System (ADS)
Luo, Xiaochun
1995-02-01
Non-Gaussian distributions of cosmic microwave background (CMB) anistropics have been proposed to reconcile the discrepancies between different experiments at half-degree scales (Coulson et al. 1994). Each experiment probes a different part of the sky, furthermore, sky coverage is very small, hence the sample variance of each experiment can be large, especially when the sky signal is non-Gaussian. We model the degree-scale CMB sky as a chin exp 2 field with n-degress of freedom and show that the sample variance is enhanced over that a Gaussian distribution by a factor of (n + 6)/n. The sample variance for different experiments are calculated, both for Gaussian and non-Gaussian distributions. We also show that if the distribution is highly non-Gaussian (n less than or approximately = 4) at half-degree scales, than the non-Gaussian signature of the CMB could be detected in the FIRS map, though probably not in the Cosmic Background Explorer (COBE) map.
Recovering dark-matter clustering from galaxies with Gaussianization
NASA Astrophysics Data System (ADS)
McCullagh, Nuala; Neyrinck, Mark; Norberg, Peder; Cole, Shaun
2016-04-01
The Gaussianization transform has been proposed as a method to remove the issues of scale-dependent galaxy bias and non-linearity from galaxy clustering statistics, but these benefits have yet to be thoroughly tested for realistic galaxy samples. In this paper, we test the effectiveness of the Gaussianization transform for different galaxy types by applying it to realistic simulated blue and red galaxy samples. We show that in real space, the shapes of the Gaussianized power spectra of both red and blue galaxies agree with that of the underlying dark matter, with the initial power spectrum, and with each other to smaller scales than do the statistics of the usual (untransformed) density field. However, we find that the agreement in the Gaussianized statistics breaks down in redshift space. We attribute this to the fact that red and blue galaxies exhibit very different fingers of god in redshift space. After applying a finger-of-god compression, the agreement on small scales between the Gaussianized power spectra is restored. We also compare the Gaussianization transform to the clipped galaxy density field and find that while both methods are effective in real space, they have more complicated behaviour in redshift space. Overall, we find that Gaussianization can be useful in recovering the shape of the underlying dark-matter power spectrum to k ˜ 0.5 h Mpc-1 and of the initial power spectrum to k ˜ 0.4 h Mpc-1 in certain cases at z = 0.
Axial acoustic radiation force on a sphere in Gaussian field
Wu, Rongrong; Liu, Xiaozhou Gong, Xiufen
2015-10-28
Based on the finite series method, the acoustical radiation force resulting from a Gaussian beam incident on a spherical object is investigated analytically. When the position of the particles deviating from the center of the beam, the Gaussian beam is expanded as a spherical function at the center of the particles and the expanded coefficients of the Gaussian beam is calculated. The analytical expression of the acoustic radiation force on spherical particles deviating from the Gaussian beam center is deduced. The acoustic radiation force affected by the acoustic frequency and the offset distance from the Gaussian beam center is investigated. Results have been presented for Gaussian beams with different wavelengths and it has been shown that the interaction of a Gaussian beam with a sphere can result in attractive axial force under specific operational conditions. Results indicate the capability of manipulating and separating spherical spheres based on their mechanical and acoustical properties, the results provided here may provide a theoretical basis for development of single-beam acoustical tweezers.
New window on primordial non-gaussianity.
Pajer, Enrico; Zaldarriaga, Matias
2012-07-13
We know very little about primordial curvature perturbations on scales smaller than about a Mpc. Measurements of the μ distortion of the cosmic microwave background spectrum provide the unique opportunity to probe these scales over the unexplored range from 50 to 10(4) Mpc(-1). This is a very clean probe, in that it relies only on well understood linear evolution. Also, just the information about the low multipoles (l∼100) of μ is necessary. We point out that correlations between μ distortion and temperature anisotropies can be used to test gaussianity at these very small scales. In particular the μT two-point correlation is proportional to the very squeezed limit of the primordial bispectrum and hence measures f(NL)(loc), while μμ is proportional to the primordial trispectrum and measures τ(NL). We present a Fisher matrix forecast of the observational constraints on f(NL)(loc) and stress that a cosmic variance limited experiment could in principle reach Δf(NL)(loc)∼O(10(-3)).
A tremor detector based on Gaussianity differences
NASA Astrophysics Data System (ADS)
Dorman, L. M.; Schwartz, S. Y.; Tryon, M. D.
2011-12-01
Slip occurring at plate boundaries creates seismic tremor as well as "normal" earthquakes. This nonvolcanic tremor appears to consist of swarms of low-frequency earthquakes which lack impulsive P and S arrivals. Tremor is accompanied by slip observed by GPS and can show anomalies in fluid flow. The seismic radiation resembles continuous microseismic noise more than discrete events. We report dual-frequency coherence (DFC) calculations on tremor and normal microseismic background noise observed on Ocean-Bottom Seismographs and land seismic stations around the Nicoya Peninsula, Costa Rica. Both the OBS and land tremor signals show a banded pattern in DFC that is absent in normal noise. The similarity in the DFC patterns between OBS and land tremor signals suggests a common source, eliminating the possibility that DFC is a property of the OBS or seafloor environment. Banded DFC patterns can be generated by repeated events with a repeat time equal to the reciprocal of the offset frequency between bands. If, as is becoming widely accepted, nonvolcanic tremor consists of swarms of low frequency earthquakes (LFE), DFC analysis may help to reveal LFE periodicities or intervals. Timeseries statistics measuring departures from Gaussianity differ between time periods containing tremor and those with only background noise, and the statistic "S" can be used as a detection statistic. We show the Receiver Operating Characteristic for such a detector.
Stochastic resonance in Gaussian quantum channels
NASA Astrophysics Data System (ADS)
Lupo, Cosmo; Mancini, Stefano; Wilde, Mark M.
2013-02-01
We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a ‘forbidden interval’. We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case, the symmetry between sender and receiver is broken and the ‘forbidden interval’ may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold.
Anomalous dimensions and non-gaussianity
Green, Daniel; Lewandowski, Matthew; Senatore, Leonardo; Silverstein, Eva; Zaldarriaga, Matias
2013-10-01
We analyze the signatures of inflationary models that are coupled to interacting field theories, a basic class of multifield models also motivated by their role in providing dynamically small scales. Near the squeezed limit of the bispectrum, we find a simple scaling behavior determined by operator dimensions, which are constrained by the appropriate unitarity bounds. Specifically, we analyze two simple and calculable classes of examples: conformal field theories (CFTs), and large-N CFTs deformed by relevant time-dependent double-trace operators. Together these two classes of examples exhibit a wide range of scalings and shapes of the bispectrum, including nearly equilateral, orthogonal and local non-Gaussianity in different regimes. Along the way, we compare and contrast the shape and amplitude with previous results on weakly coupled fields coupled to inflation. This signature provides a precision test for strongly coupled sectors coupled to inflation via irrelevant operators suppressed by a high mass scale up to ~ 103 times the inflationary Hubble scale.
A comparison of tail probability estimators for flood frequency analysis
NASA Astrophysics Data System (ADS)
Moon, Young-Il; Lall, Upmanu; Bosworth, Ken
1993-11-01
Selected techniques for estimating exceedance frequencies of annual maximum flood events at a gaged site are compared in this paper. Four tail probability estimators proposed by Hill (PT1), Hosking and Wallis (PT2) and by Breiman and Stone (ET and QT), and a variable kernel distribution function estimator (VK-C-AC) were compared for three situations — Gaussian data, skewed data (three-parameter gamma) and Gaussian mixture data. The performance of these estimators was compared with method of moment estimates of tail probabilities, using the Gaussian, Pearson Type III, and extreme value distributions. Since the results of the tail probability estimators (PT1, PT2, ET, QT) varied according to the situation, it is not easy to say which tail probability estimator is the best. However, the performance of the variable kernel estimator was relatively consistent across the estimation situations considered in terms of bias and r.m.s.e.
Pseudospectral Gaussian quantum dynamics: Efficient sampling of potential energy surfaces.
Heaps, Charles W; Mazziotti, David A
2016-04-28
Trajectory-based Gaussian basis sets have been tremendously successful in describing high-dimensional quantum molecular dynamics. In this paper, we introduce a pseudospectral Gaussian-based method that achieves accurate quantum dynamics using efficient, real-space sampling of the time-dependent basis set. As in other Gaussian basis methods, we begin with a basis set expansion using time-dependent Gaussian basis functions guided by classical mechanics. Unlike other Gaussian methods but characteristic of the pseudospectral and collocation methods, the basis set is tested with N Dirac delta functions, where N is the number of basis functions, rather than using the basis function as test functions. As a result, the integration for matrix elements is reduced to function evaluation. Pseudospectral Gaussian dynamics only requires O(N) potential energy calculations, in contrast to O(N(2)) evaluations in a variational calculation. The classical trajectories allow small basis sets to sample high-dimensional potentials. Applications are made to diatomic oscillations in a Morse potential and a generalized version of the Henon-Heiles potential in two, four, and six dimensions. Comparisons are drawn to full analytical evaluation of potential energy integrals (variational) and the bra-ket averaged Taylor (BAT) expansion, an O(N) approximation used in Gaussian-based dynamics. In all cases, the pseudospectral Gaussian method is competitive with full variational calculations that require a global, analytical, and integrable potential energy surface. Additionally, the BAT breaks down when quantum mechanical coherence is particularly strong (i.e., barrier reflection in the Morse oscillator). The ability to obtain variational accuracy using only the potential energy at discrete points makes the pseudospectral Gaussian method a promising avenue for on-the-fly dynamics, where electronic structure calculations become computationally significant.
Applicability of Gaussian plume dispersion parameters to acute radionuclide releases
Miller, C.W.; Fields, D.E.
1980-01-01
The Gaussian plume atmospheric dispersion model is one of the most widely used models for assessing the impact of radionuclides released to the atmosphere. This model is a statistical solution to the basic atmospheric diffusion equation. As a result, the Gaussian model should give more accurate results when used to calculate average air concentrations from long-term releases rather than for short-term concentrations from acute releases. However, the Gaussian model is routinely applied to such short-term radionuclide releases. The purpose of this paper is to examine the applicability of standard plume dispersion parameters for calculations of air concentrations resulting from such acute releases.
Exchangeable, stationary, and entangled chains of Gaussian states
NASA Astrophysics Data System (ADS)
Parthasarathy, K. R.; Sengupta, Ritabrata
2015-10-01
We explore conditions on the covariance matrices of a consistent chain of mean zero finite mode Gaussian states in order that the chain may be exchangeable or stationary. For an exchangeable chain, our conditions are necessary and sufficient. Every stationary Gaussian chain admits an asymptotic entropy rate. Whereas an exchangeable chain admits a simple expression for its entropy rate, in our examples of stationary chains, the same admits an integral formula based on the asymptotic eigenvalue distribution for Toeplitz matrices. An example of a stationary entangled Gaussian chain is given.
Generalised Hermite-Gaussian beams and mode transformations
NASA Astrophysics Data System (ADS)
Wang, Yi; Chen, Yujie; Zhang, Yanfeng; Chen, Hui; Yu, Siyuan
2016-05-01
Generalised Hermite-Gaussian modes (gHG modes), an extended notion of Hermite-Gaussian modes (HG modes), are formed by the summation of normal HG modes with a characteristic function α, which can be used to unite conventional HG modes and Laguerre-Gaussian modes (LG modes). An infinite number of normalised orthogonal modes can thus be obtained by modulation of the function α. The gHG mode notion provides a useful tool in analysis of the deformation and transformation phenomena occurring in propagation of HG and LG modes with astigmatic perturbation.
Controllable gaussian-qubit interface for extremal quantum state engineering.
Adesso, Gerardo; Campbell, Steve; Illuminati, Fabrizio; Paternostro, Mauro
2010-06-18
We study state engineering through bilinear interactions between two remote qubits and two-mode gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.
Gaussian quantum computation with oracle-decision problems
NASA Astrophysics Data System (ADS)
Adcock, Mark R. A.; Høyer, Peter; Sanders, Barry C.
2013-04-01
We study a simple-harmonic-oscillator quantum computer solving oracle decision problems. We show that such computers can perform better by using nonorthogonal Gaussian wave functions rather than orthogonal top-hat wave functions as input to the information encoding process. Using the Deutsch-Jozsa problem as an example, we demonstrate that Gaussian modulation with optimized width parameter results in a lower error rate than for the top-hat encoding. We conclude that Gaussian modulation can allow for an improved trade-off between encoding, processing and measurement of the information.
Gaussian entanglement generation from coherence using beam-splitters
NASA Astrophysics Data System (ADS)
Wang, Zhong-Xiao; Wang, Shuhao; Ma, Teng; Wang, Tie-Jun; Wang, Chuan
2016-11-01
The generation and quantification of quantum entanglement is crucial for quantum information processing. Here we study the transition of Gaussian correlation under the effect of linear optical beam-splitters. We find the single-mode Gaussian coherence acts as the resource in generating Gaussian entanglement for two squeezed states as the input states. With the help of consecutive beam-splitters, single-mode coherence and quantum entanglement can be converted to each other. Our results reveal that by using finite number of beam-splitters, it is possible to extract all the entanglement from the single-mode coherence even if the entanglement is wiped out before each beam-splitter.
Methods to characterize non-Gaussian noise in TAMA
NASA Astrophysics Data System (ADS)
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.; TAMA Collaboration
2003-09-01
We present a data characterization method for the main output signal of the interferometric gravitational-wave detector, in particular targetting 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 103 times with this non-Gaussian noise evaluation and rejection method.
NASA Astrophysics Data System (ADS)
Tsuchida, Takahiro; Kimura, Koji
2016-09-01
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.
Non-Gaussian forecasts of weak lensing with and without priors
NASA Astrophysics Data System (ADS)
Sellentin, Elena; Schäfer, Björn Malte
2016-02-01
Including priors into a data analysis can mask the information content of a given data set alone. However, since the information content of a data set is usually estimated with the Fisher matrix, priors are added to enforce an approximately Gaussian likelihood. Here, we estimate the information content of a Euclid-like weak lensing data set with and without priors. Without priors, the Fisher matrix for 2d-weak lensing includes unphysical values of Ωm and h. The Cramer-Rao inequality then does not need to apply. We find that the new DALI expansion and Monte Carlo Markov Chains agree well and predict the presence of a dark energy with high significance, whereas a Fisher forecast also allows decelerated expansion. We find that a 2d-weak lensing analysis provides a sharp lower limit on the Hubble constant of h > 0.4, even if the equation of state of dark energy is jointly estimated. This is not predicted by the Fisher matrix and usually masked in other works by a sharp prior on h. Additionally, we find that DALI estimates Figures of Merit in the presence of non-Gaussianities better than the Fisher matrix and demonstrate how DALI allows switching to a speedy Hamiltonian Monte Carlo sampling of a highly curved likelihood with acceptance rates of ≈0.5. This shows how quick forecasts can be upgraded to accurate forecasts whenever needed. Results were gained with the public code from DALI.
NASA Astrophysics Data System (ADS)
Hazarika, Deepika; Nath, Vijay Kumar; Bhuyan, Manbendra
2016-12-01
A new Lapped transform domain SAR image despeckling algorithm using a two-state Gaussian mixture probability density function that uses local parameters for the mixture model, is proposed. The use of lapped orthogonal transform (LOT) is motivated by its low computational complexity and robustness to oversmoothing. It is shown that the dyadic rearranged LOT coefficients of logarithmically transformed SAR images can be well approximated using two-state Gaussian mixture distribution compared to Laplacian, Gamma, generalized Gaussian and Cauchy distributions, based on the Kolmogorov-Smirnov (KS) goodness of fit test. The LOT coefficients of speckle noise are modeled using zero mean Gaussian distributions. A maximum a posteriori (MAP) estimator within Bayesian framework is developed using this proposed prior distribution and is used to restore the noisy LOT coefficients. The parameters of mixture distribution are estimated using the expectation-maximization algorithm. This paper presents a new technique to identify LOT modulus maxima which allows us to classify LOT coefficients into the edge and non edge coefficients. The classified edge coefficients are kept unmodified by the proposed algorithm whereas the noise-free estimates of non-edge coefficients are obtained using Bayesian MAP estimator developed using two state Gaussian mixture distribution with local parameters. Finally the proposed technique is combined with the cycle spinning scheme to further improve the despeckling performance. Experimental results show that the proposed method very efficiently reduces speckle in homogeneous regions while preserving more edge structures compared to some recent well known methods.
JIMWLK evolution in the Gaussian approximation
NASA Astrophysics Data System (ADS)
Iancu, E.; Triantafyllopoulos, D. N.
2012-04-01
We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors N c . This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it re-produces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite N c . Any higher n-point function with n ≥ 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.
Analysis of regularized inversion of data corrupted by white Gaussian noise
NASA Astrophysics Data System (ADS)
Kekkonen, Hanne; Lassas, Matti; Siltanen, Samuli
2014-04-01
Tikhonov regularization is studied in the case of linear pseudodifferential operator as the forward map and additive white Gaussian noise as the measurement error. The measurement model for an unknown function u(x) is \\begin{eqnarray*} m(x) = Au(x) + \\delta \\varepsilon (x), \\end{eqnarray*} where δ > 0 is the noise magnitude. If ɛ was an L2-function, Tikhonov regularization gives an estimate \\begin{eqnarray*} T_\\alpha (m) = \\mathop {{arg\\, min}}_{u\\in H^r} \\big \\lbrace \\Vert A u-m\\Vert _{L^2}^2+ \\alpha \\Vert u\\Vert _{H^r}^2 \\big \\rbrace \\end{eqnarray*} for u where α = α(δ) is the regularization parameter. Here penalization of the Sobolev norm \\Vert u\\Vert _{H^r} covers the cases of standard Tikhonov regularization (r = 0) and first derivative penalty (r = 1). Realizations of white Gaussian noise are almost never in L2, but do belong to Hs with probability one if s < 0 is small enough. A modification of Tikhonov regularization theory is presented, covering the case of white Gaussian measurement noise. Furthermore, the convergence of regularized reconstructions to the correct solution as δ → 0 is proven in appropriate function spaces using microlocal analysis. The convergence of the related finite-dimensional problems to the infinite-dimensional problem is also analysed.
Gaussian process based intelligent sampling for measuring nano-structure surfaces
NASA Astrophysics Data System (ADS)
Sun, L. J.; Ren, M. J.; Yin, Y. H.
2016-09-01
Nanotechnology is the science and engineering that manipulate matters at nano scale, which can be used to create many new materials and devices with a vast range of applications. As the nanotech product increasingly enters the commercial marketplace, nanometrology becomes a stringent and enabling technology for the manipulation and the quality control of the nanotechnology. However, many measuring instruments, for instance scanning probe microscopy, are limited to relatively small area of hundreds of micrometers with very low efficiency. Therefore some intelligent sampling strategies should be required to improve the scanning efficiency for measuring large area. This paper presents a Gaussian process based intelligent sampling method to address this problem. The method makes use of Gaussian process based Bayesian regression as a mathematical foundation to represent the surface geometry, and the posterior estimation of Gaussian process is computed by combining the prior probability distribution with the maximum likelihood function. Then each sampling point is adaptively selected by determining the position which is the most likely outside of the required tolerance zone among the candidates and then inserted to update the model iteratively. Both simulationson the nominal surface and manufactured surface have been conducted on nano-structure surfaces to verify the validity of the proposed method. The results imply that the proposed method significantly improves the measurement efficiency in measuring large area structured surfaces.
A Rough Set Bounded Spatially Constrained Asymmetric Gaussian Mixture Model for Image Segmentation
Ji, Zexuan; Huang, Yubo; Sun, Quansen; Cao, Guo; Zheng, Yuhui
2017-01-01
Accurate image segmentation is an important issue in image processing, where Gaussian mixture models play an important part and have been proven effective. However, most Gaussian mixture model (GMM) based methods suffer from one or more limitations, such as limited noise robustness, over-smoothness for segmentations, and lack of flexibility to fit data. In order to address these issues, in this paper, we propose a rough set bounded asymmetric Gaussian mixture model with spatial constraint for image segmentation. First, based on our previous work where each cluster is characterized by three automatically determined rough-fuzzy regions, we partition the target image into three rough regions with two adaptively computed thresholds. Second, a new bounded indicator function is proposed to determine the bounded support regions of the observed data. The bounded indicator and posterior probability of a pixel that belongs to each sub-region is estimated with respect to the rough region where the pixel lies. Third, to further reduce over-smoothness for segmentations, two novel prior factors are proposed that incorporate the spatial information among neighborhood pixels, which are constructed based on the prior and posterior probabilities of the within- and between-clusters, and considers the spatial direction. We compare our algorithm to state-of-the-art segmentation approaches in both synthetic and real images to demonstrate the superior performance of the proposed algorithm. PMID:28045950
Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian
NASA Astrophysics Data System (ADS)
Teneng, Dean
2013-09-01
We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.
More on loops in reheating: non-gaussianities and tensor power spectrum
Katırcı, Nihan; Kaya, Ali; Tarman, Merve
2014-06-11
We consider the single field chaotic m{sup 2}ϕ{sup 2} inflationary model with a period of preheating, where the inflaton decays to another scalar field χ in the parametric resonance regime. In a recent work, one of us has shown that the χ modes circulating in the loops during preheating notably modify the <ζζ> correlation function. We first rederive this result using a different gauge condition hence reconfirm that superhorizon ζ modes are affected by the loops in preheating. Further, we examine how χ loops give rise to non-gaussianity and affect the tensor perturbations. For that, all cubic and some higher order interactions involving two χ fields are determined and their contribution to the non-gaussianity parameter f{sub NL} and the tensor power spectrum are calculated at one loop. Our estimates for these corrections show that while a large amount of non-gaussianity can be produced during reheating, the tensor power spectrum receive moderate corrections. We observe that the loop quantum effects increase with more χ fields circulating in the loops indicating that the perturbation theory might be broken down. These findings demonstrate that the loop corrections during reheating are significant and they must be taken into account for precision inflationary cosmology.
An Improved Detection Method for Hyperspectral Imagery Based on White Gaussian Noise.
Wang, Yiting; Huang, Shiqi; Wang, Hongxia; Liu, Daizhi
2015-07-01
To solve the low detection efficiency of the present hyperspectral detection method based on adaptive coherence estimator (ACE), an improved detection method based on white Gaussian noise (WGN) is proposed in this paper. Primarily the method uses the spectral angle mapping (SAM) method to adaptively set an optimal signal-to-noise (SNR) parameter based on the hyperspectral image. Then, a corresponding white Gaussian noise is generated according to this SNR parameter and is added to the original image to get a new image data. Finally, based on the new image data, a better target detection result can be obtained by using the ACE detection algorithm. The image data, added to the white Gaussian noise, are more consistent with the theoretical hypotheses of the ACE algorithm. Therefore the detection performance of the algorithm can be efficiently improved. Meanwhile, the adaptivity of setting the optimum SNR parameter in various images can make the method more universal. Experimental results of real world hyperspectral data show that the proposed ACE-WGN method can effectively improve detection performance.
Optimization of spectroscopic surveys for testing non-Gaussianity
Raccanelli, Alvise; Doré, Olivier; Dalal, Neal E-mail: Olivier.P.Dore@jpl.nasa.gov
2015-08-01
We investigate optimization strategies to measure primordial non-Gaussianity with future spectroscopic surveys. We forecast measurements coming from the 3D galaxy power spectrum and compute constraints on primordial non-Gaussianity parameters f{sub NL} and n{sub NG}. After studying the dependence on those parameters upon survey specifications such as redshift range, area, number density, we assume a reference mock survey and investigate the trade-off between number density and area surveyed. We then define the observational requirements to reach the detection of f{sub NL} of order 1. Our results show that power spectrum constraints on non-Gaussianity from future spectroscopic surveys can improve on current CMB limits, but the multi-tracer technique and higher order correlations will be needed in order to reach an even better precision in the measurements of the non-Gaussianity parameter f{sub NL}.
On the robustness of the q-Gaussian family
NASA Astrophysics Data System (ADS)
Sicuro, Gabriele; Tempesta, Piergiulio; Rodríguez, Antonio; Tsallis, Constantino
2015-12-01
We introduce three deformations, called α-, β- and γ-deformation respectively, of a N-body probabilistic model, first proposed by Rodríguez et al. (2008), having q-Gaussians as N → ∞ limiting probability distributions. The proposed α- and β-deformations are asymptotically scale-invariant, whereas the γ-deformation is not. We prove that, for both α- and β-deformations, the resulting deformed triangles still have q-Gaussians as limiting distributions, with a value of q independent (dependent) on the deformation parameter in the α-case (β-case). In contrast, the γ-case, where we have used the celebrated Q-numbers and the Gauss binomial coefficients, yields other limiting probability distribution functions, outside the q-Gaussian family. These results suggest that scale-invariance might play an important role regarding the robustness of the q-Gaussian family.
Electron acceleration by a tightly focused cylindrical vector Gaussian beam
NASA Astrophysics Data System (ADS)
Xu, Jian; Yang, Zhen-Jun; Li, Jian-Xing; Zang, Wei-Ping
2017-02-01
We have studied the electron acceleration by a tightly focused cylindrical vector Gaussian beam. Different from the Lax series field, cylindrical vector Gaussian beams are vector-beam solutions of Maxwell’s equations and its focusing property can be numerically analyzed by the Richards-Wolf vectorial diffraction theory. Field differences exist between the cylindrical vector Gaussian beam and the Lax series field. The cylindrical vector Gaussian beam increases the asymmetry of the electromagnetic fields, which is more beneficial to the electron acceleration. When the beam waist falls down to the order of the wavelength, the high laser intensity zone is more proper to define the reflection, capture and transmission conditions of the electrons. The injection energy and the injected angle of the electron and the initial phase of the laser beam play important roles for the electron to enter and be trapped by the high laser intensity zone.
Super-resolving random-Gaussian apodized photon sieve.
Sabatyan, Arash; Roshaninejad, Parisa
2012-09-10
A novel apodized photon sieve is presented in which random dense Gaussian distribution is implemented to modulate the pinhole density in each zone. The random distribution in dense Gaussian distribution causes intrazone discontinuities. Also, the dense Gaussian distribution generates a substantial number of pinholes in order to form a large degree of overlap between the holes in a few innermost zones of the photon sieve; thereby, clear zones are formed. The role of the discontinuities on the focusing properties of the photon sieve is examined as well. Analysis shows that secondary maxima have evidently been suppressed, transmission has increased enormously, and the central maxima width is approximately unchanged in comparison to the dense Gaussian distribution. Theoretical results have been completely verified by experiment.
Gaussian mixture models as flux prediction method for central receivers
NASA Astrophysics Data System (ADS)
Grobler, Annemarie; Gauché, Paul; Smit, Willie
2016-05-01
Flux prediction methods are crucial to the design and operation of central receiver systems. Current methods such as the circular and elliptical (bivariate) Gaussian prediction methods are often used in field layout design and aiming strategies. For experimental or small central receiver systems, the flux profile of a single heliostat often deviates significantly from the circular and elliptical Gaussian models. Therefore a novel method of flux prediction was developed by incorporating the fitting of Gaussian mixture models onto flux profiles produced by flux measurement or ray tracing. A method was also developed to predict the Gaussian mixture model parameters of a single heliostat for a given time using image processing. Recording the predicted parameters in a database ensures that more accurate predictions are made in a shorter time frame.
Radiation patterns of the HE11 mode and Gaussian approximations
NASA Astrophysics Data System (ADS)
Rebuffi, L.; Crenn, J. P.
1989-03-01
The problem of the approximation of the HE11 radiation pattern by a Gaussian distribution is discussed. A numerical comparison between the HE11 far-field theoretical pattern, and the Gaussian approximations derived by Abrams and by Crenn, permits and evaluation of the precision of these approximations. A new optimized HE11 Gaussian approximation is calculated: the value of ro=0.421a (or wo=0.596a) for the beam radius at the waist is demonstrated to give the best HE11 Gaussian approximation in the far-field and is very close to the result given by Crenn, while the Abrams value is less precise. The calculations are extended to the near-field. Universal curves for intensity, amplitude and power distribution are given for the HE11 radiated mode. These results are of interest for laser waveguide applications and for plasma ECRH transmission systems.
Optimal multicopy asymmetric Gaussian cloning of coherent states
Fiurasek, Jaromir; Cerf, Nicolas J.
2007-05-15
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.
Peyvandi, Shahram; Amirshahi, Seyed Hossein; Hernández-Andrés, Javier; Nieves, Juan Luis; Romero, Javier
2012-10-01
The Bayesian inference approach to the inverse problem of spectral signal recovery has been extended to mixtures of Gaussian probability distributions of a training dataset in order to increase the efficiency of estimating the spectral signal from the response of a transformation system. Bayesian (BIC) and Akaike (AIC) information criteria were assessed in order to provide the Gaussian mixture model (GMM) with the optimum number of clusters within the spectral space. The spectra of 2600 solar illuminations measured in Granada (Spain) were recovered over the range of 360-830 nm from their corresponding tristimulus values using a linear model of basis functions, the Wiener inverse (WI) method, and the Bayesian inverse approach extended to the GMM (BGMM). A model of Gaussian mixtures for solar irradiance was deemed to be more appropriate than a single Gaussian distribution for representing the probability distribution of the solar spectral data. The results showed that the estimation performance of the BGMM method was better than either the linear model or the WI method for the spectral approximation of daylight from the three-dimensional tristimulus values.
A linear-time algorithm for Gaussian and non-Gaussian trait evolution models.
Ho, Lam si Tung; Ané, Cécile
2014-05-01
We developed a linear-time algorithm applicable to a large class of trait evolution models, for efficient likelihood calculations and parameter inference on very large trees. Our algorithm solves the traditional computational burden associated with two key terms, namely the determinant of the phylogenetic covariance matrix V and quadratic products involving the inverse of V. Applications include Gaussian models such as Brownian motion-derived models like Pagel's lambda, kappa, delta, and the early-burst model; Ornstein-Uhlenbeck models to account for natural selection with possibly varying selection parameters along the tree; as well as non-Gaussian models such as phylogenetic logistic regression, phylogenetic Poisson regression, and phylogenetic generalized linear mixed models. Outside of phylogenetic regression, our algorithm also applies to phylogenetic principal component analysis, phylogenetic discriminant analysis or phylogenetic prediction. The computational gain opens up new avenues for complex models or extensive resampling procedures on very large trees. We identify the class of models that our algorithm can handle as all models whose covariance matrix has a 3-point structure. We further show that this structure uniquely identifies a rooted tree whose branch lengths parametrize the trait covariance matrix, which acts as a similarity matrix. The new algorithm is implemented in the R package phylolm, including functions for phylogenetic linear regression and phylogenetic logistic regression.
NASA Astrophysics Data System (ADS)
Kenfack, Lionel Tenemeza; Tchoffo, Martin; Fai, Lukong Cornelius; Fouokeng, Georges Collince
2017-04-01
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.
Jiang, Tao; Shan, Guogen
2016-01-01
Residue fluctuations in protein structures have been shown to be highly associated with various protein functions. Gaussian network model (GNM), a simple representative coarse-grained model, was widely adopted to reveal function-related protein dynamics. We directly utilized the high frequency modes generated by GNM and further performed Gaussian Naive Bayes (GNB) to identify hot spot residues. Two coding schemes about the feature vectors were implemented with varying distance cutoffs for GNM and sliding window sizes for GNB based on tenfold cross validations: one by using only a single high mode and the other by combining multiple modes with the highest frequency. Our proposed methods outperformed the previous work that did not directly utilize the high frequency modes generated by GNM, with regard to overall performance evaluated using F1 measure. Moreover, we found that inclusion of more high frequency modes for a GNB classifier can significantly improve the sensitivity. The present study provided additional valuable insights into the relation between the hot spots and the residue fluctuations. PMID:27882325
Non-Gaussianity and Excursion Set Theory: Halo Bias
Adshead, Peter; Baxter, Eric J.; Dodelson, Scott; Lidz, Adam
2012-09-01
We study the impact of primordial non-Gaussianity generated during inflation on the bias of halos using excursion set theory. We recapture the familiar result that the bias scales as $k^{-2}$ on large scales for local type non-Gaussianity but explicitly identify the approximations that go into this conclusion and the corrections to it. We solve the more complicated problem of non-spherical halos, for which the collapse threshold is scale dependent.
A note on the wideband Gaussian broadcast channel
NASA Technical Reports Server (NTRS)
Mceliece, R. J.; Posner, E. C.; Swanson, L.
1986-01-01
It is well known that for the Gaussian broadcast channel, timeshared coding is not as efficient as more sophisticated broadcast coding strategies. However, the relative advantage of broadcast coding over timeshared coding is shown to be small if the signal-to-noise ratios of both receivers are small. One surprising consequence of this is that for the wideband Gaussian broadcast channel, which is defined, broadcast coding offers no advantage over timeshared coding at all, and so timeshared coding is optimal.
Sub-Fidelity and Super-Fidelity Between Gaussian States
NASA Astrophysics Data System (ADS)
Qi, Xiao-Fei; Wang, Li
2015-09-01
In this paper, we analyze the sub-fidelity and super-fidelity of an arbitrary pair of n-mode Gaussian states. Particularly, an explicit formula for the sub-fidelity and super-fidelity between any two-mode Gaussian states is obtained. Supported by Natural Science Foundation of China under Grant Nos. 11171249, 11201329, and Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi
Simulations of Gaussian electron guns for RHIC electron lens
Pikin, A.
2014-02-28
Simulations of two versions of the electron gun for RHIC electron lens are presented. The electron guns have to generate an electron beam with Gaussian radial profile of the electron beam density. To achieve the Gaussian electron emission profile on the cathode we used a combination of the gun electrodes and shaping of the cathode surface. Dependence of electron gun performance parameters on the geometry of electrodes and the margins for electrodes positioning are presented.
Unstable laser resonators with super-Gaussian mirrors
De Silvestri, S.; Laporta, P.; Magni, V.; Svelto, O.; Majocchi, B.
1988-03-01
A new class of tapered reflectivity mirrors with a super-Gaussian profile R atmI exp(-kr/sup n/) is introduced, and a geometrical-optics approach for analysis and design of unstable resonators made with these mirrors is presented. A super-Gaussian mirror, built by a special evaporation technique, has been tested in an unstable resonator of a pulsed Nd:YAG laser, demonstrating its effectiveness in generating diffraction-limited beams.
Optical rogue waves generated on Gaussian background beam.
Liu, Chong; Yang, Zhan-Ying; Zhao, Li-Chen; Xin, Guo-Guo; Yang, Wen-Li
2014-02-15
We study optical rogue waves (RWs) in a nonlinear graded-index waveguide with variable coefficients. An exact RW solution on Gaussian background beam is presented, in contrast to the previous studies about RWs, on plane wave background. It is shown that the characteristics of RWs are maintained on Gaussian background beam and that the beam's width is even a bit smaller than the RWs scale. These results may raise the possibility of related experiments and potential applications in nonlinear optics.
GAUSSIAN 76: An ab initio Molecular Orbital Program
DOE R&D Accomplishments Database
Binkley, J. S.; Whiteside, R.; Hariharan, P. C.; Seeger, R.; Hehre, W. J.; Lathan, W. A.; Newton, M. D.; Ditchfield, R.; Pople, J. A.
1978-01-01
Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type Gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally for easy use. Closed shell (RHF) or unrestricted open shell (UHF) wave functions can be obtained. Facilities are provided for geometry optimization to potential minima and for limited potential surface scans.
Non-gaussianity versus nonlinearity of cosmological perturbations.
Verde, L
2001-06-01
Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.
Do wavelets really detect non-Gaussianity in the 4-year COBE data?
NASA Astrophysics Data System (ADS)
Mukherjee, P.; Hobson, M. P.; Lasenby, A. N.
2000-11-01
We investigate the detection of non-Gaussianity in the 4-year COBE data reported by Pando, Valls-Gabaud & Fang, using a technique based on the discrete wavelet transform. Their analysis was performed on the two DMR faces centred on the North and South Galactic poles, respectively, using the Daubechies 4 wavelet basis. We show that these results depend critically on the orientation of the data, and so should be treated with caution. For two distinct orientations of the data, we calculate estimates of the skewness, kurtosis and scale-scale correlation of the corresponding wavelet coefficients in all of the available scale domains of the transform. We obtain several detections of non-Gaussianity in the DMR-DSMB map at greater than the 99per cent confidence level, but most of these occur on pixel-pixel scales and are therefore not cosmological in origin. Indeed, after removing all multipoles beyond l=40 from the COBE maps, only one robust detection remains. Moreover, using Monte Carlo simulations, we find that the probability of obtaining such a detection by chance is 0.59. We repeat the analysis for the 53+90GHz coadded COBE map. In this case, after removing l>40 multipoles, two non-Gaussian detections at the 99per cent level remain. Nevertheless, again using Monte Carlo simulations, we find that the probability of obtaining two such detections by chance is 0.28. Thus, we conclude the wavelet technique does not yield strong evidence for non-Gaussianity of cosmological origin in the 4-year COBE data.
Free energy calculations, enhanced by a Gaussian ansatz, for the "chemical work" distribution.
Boulougouris, Georgios C
2014-05-15
The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the "chemical work" of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the "irreversible" work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible "chemical work" minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the "chemical work," accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the "chemical work." For a more general free energy perturbation scheme that the Gaussian ansatz may not be
Some error bounds for K-iterated Gaussian recursive filters
NASA Astrophysics Data System (ADS)
Cuomo, Salvatore; Galletti, Ardelio; Giunta, Giulio; Marcellino, Livia
2016-10-01
Recursive filters (RFs) have achieved a central role in several research fields over the last few years. For example, they are used in image processing, in data assimilation and in electrocardiogram denoising. More in particular, among RFs, the Gaussian RFs are an efficient computational tool for approximating Gaussian-based convolutions and are suitable for digital image processing and applications of the scale-space theory. As is a common knowledge, the Gaussian RFs, applied to signals with support in a finite domain, generate distortions and artifacts, mostly localized at the boundaries. Heuristic and theoretical improvements have been proposed in literature to deal with this issue (namely boundary conditions). They include the case in which a Gaussian RF is applied more than once, i.e. the so called K-iterated Gaussian RFs. In this paper, starting from a summary of the comprehensive mathematical background, we consider the case of the K-iterated first-order Gaussian RF and provide the study of its numerical stability and some component-wise theoretical error bounds.
Testing Nonclassicality and Non-Gaussianity in Phase Space
NASA Astrophysics Data System (ADS)
Park, Jiyong; Zhang, Junhua; Lee, Jaehak; Ji, Se-Wan; Um, Mark; Lv, Dingshun; Kim, Kihwan; Nha, Hyunchul
2015-05-01
We theoretically propose and experimentally demonstrate a nonclassicality test of a single-mode field in phase space, which has an analogy with the nonlocality test proposed by Banaszek and Wódkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Our approach to deriving the classical bound draws on the fact that the Wigner function of a coherent state is a product of two independent distributions as if the orthogonal quadratures (position and momentum) in phase space behave as local realistic variables. Our method detects every pure nonclassical Gaussian state, which can also be extended to mixed states. Furthermore, it sets a bound for all Gaussian states and their mixtures, thereby providing a criterion to detect a genuine quantum non-Gaussian state. Remarkably, our phase-space approach with invariance under Gaussian unitary operations leads to an optimized test for a given non-Gaussian state. We experimentally show how this enhanced method can manifest quantum non-Gaussianity of a state by simply choosing phase-space points appropriately, which is essentially equivalent to implementing a squeezing operation on a given state.
Gaussian Analytic Centroiding method of star image of star tracker
NASA Astrophysics Data System (ADS)
Wang, Haiyong; Xu, Ershuai; Li, Zhifeng; Li, Jingjin; Qin, Tianmu
2015-11-01
The energy distribution of an actual star image coincides with the Gaussian law statistically in most cases, so the optimized processing algorithm about star image centroiding should be constructed also by following Gaussian law. For a star image spot covering a certain number of pixels, the marginal distribution of the gray accumulation on rows and columns are shown and analyzed, based on which the formulas of Gaussian Analytic Centroiding method (GAC) are deduced, and the robustness is also promoted due to the inherited filtering effect of gray accumulation. Ideal reference star images are simulated by the PSF (point spread function) with integral form. Precision and speed tests for the Gaussian Analytic formulas are conducted under three scenarios of Gaussian radius (0.5, 0.671, 0.8 pixel), The simulation results show that the precision of GAC method is better than that of the other given algorithms when the Gaussian radius is not bigger than 5 × 5 pixel window, a widely used parameter. Above all, the algorithm which consumes the least time is still the novel GAC method. GAC method helps to promote the comprehensive performance in the attitude determination of a star tracker.
Noise robust estimates of correlation dimension and K2 entropy
NASA Astrophysics Data System (ADS)
Nolte, Guido; Ziehe, Andreas; Müller, Klaus-Robert
2001-07-01
Using Gaussian kernels to define the correlation sum we derive simple formulas that correct the noise bias in estimates of the correlation dimension and K2 entropy of chaotic time series. The corrections are only based on the difference of correlation dimensions for adjacent embedding dimensions and hence preserve the full functional dependencies on both the scale parameter and embedding dimension. It is shown theoretically that the estimates, which are derived for additive white Gaussian noise, are also robust for moderately colored noise. Simulations underline the usefulness of the proposed correction schemes. It is demonstrated that the method gives satisfactory results also for non-Gaussian and dynamical noise.
Regression models for the analysis of longitudinal Gaussian data from multiple sources.
O'Brien, Liam M; Fitzmaurice, Garrett M
2005-06-15
We present a regression model for the joint analysis of longitudinal multiple source Gaussian data. Longitudinal multiple source data arise when repeated measurements are taken from two or more sources, and each source provides a measure of the same underlying variable and on the same scale. This type of data generally produces a relatively large number of observations per subject; thus estimation of an unstructured covariance matrix often may not be possible. We consider two methods by which parsimonious models for the covariance can be obtained for longitudinal multiple source data. The methods are illustrated with an example of multiple informant data arising from a longitudinal interventional trial in psychiatry.
Sensor Fusion of Gaussian Mixtures for Ballistic Target Tracking in the Re-Entry Phase
Lu, Kelin; Zhou, Rui
2016-01-01
A sensor fusion methodology for the Gaussian mixtures model is proposed for ballistic target tracking with unknown ballistic coefficients. To improve the estimation accuracy, a track-to-track fusion architecture is proposed to fuse tracks provided by the local interacting multiple model filters. During the fusion process, the duplicate information is removed by considering the first order redundant information between the local tracks. With extensive simulations, we show that the proposed algorithm improves the tracking accuracy in ballistic target tracking in the re-entry phase applications. PMID:27537883
Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes
Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D.
2016-01-01
This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. PMID:26993062
Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon
2017-04-10
Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes.
Adaptive Gaussian quadrature detection for continuous-variable quantum key distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, L.; Imre, S.
2016-03-01
We propose the adaptive quadrature detection for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD scheme uses Gaussian subcarrier continuous variables for the information conveying and Gaussian sub-channels for the transmission. The proposed multicarrier detection scheme dynamically adapts to the subchannel conditions using a corresponding statistics which is provided by our sophisticated sub-channel estimation procedure. The sub-channel estimation phase determines the transmittance coefficients of the sub-channels, which information are used further in the adaptive quadrature decoding process. We define a technique to estimate the transmittance conditions of the sub-channels. We introduce the terms of single and collective adaptive quadrature detection. We prove the achievable error probabilities, the signal-to-noise ratios, and quantify the attributes of the framework. The adaptive detection scheme allows to utilize the extra resources of multicarrier CVQKD and to maximize the amount of transmittable valuable information in diverse measurement and transmission conditions. The framework is particularly convenient for experimental CVQKD scenarios.
Multi-photon resonance phenomena using Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Hamideh Kazemi, Seyedeh; Mahmoudi, Mohammad
2016-12-01
We study the influence of laser profile on the linewidth of the optical spectrum of multi-photon resonance phenomena. First, we investigate the dependence of the absorption spectrum on the laser profile in a two-level system. Thanks to the Laguerre-Gaussian field, the linewidth of the one-photon optical pumping and two-photon absorption peaks are explicitly narrower than that obtained with a Gaussian field. In the next section, it is shown that, compared to the Gaussian fields, the Laguerre-Gaussian ones reduce the linewidth of the optical spectrum in the coherent population trapping. Interestingly, it turns out that the use of a Laguerre-Gaussian beam makes the linewidth of the spectrum narrower as compared with a Gaussian one in Doppler-broadened electromagnetically induced transparency. Moreover, we study the effect of the laser profile on the Autler-Townes doublet structure in the absorption spectrum for a laser-driven four-level atomic system. We also consider the different values of the Laguerre-Gaussian mode beam waist, and, perhaps more remarkably, we find that for the small waist values, the Autler-Townes doublet can be removed and a prominent narrow central peak appears in the absorption spectrum. Finally, we investigate the effect of the laser profile on the linewidth of the sub-natural three-photon absorption peak of double dark resonance. The differences in the linewidth are quite large, offering potential applications in metrology and isotope separation methods. Our results can be used for super ultra-high resolution laser spectroscopy and to improve the resolution of the technology of isotope/isomer separation and photo-biology even at essential overlap of the spectra of the different particles.
Zhang, Jiangjiang; Li, Weixuan; Zeng, Lingzao; Wu, Laosheng
2016-08-01
Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU-demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimations of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two-stage manner. Since the two-stage MCMC requires extra original model evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate approximation of the original model can be adaptively constructed with low computational cost. Based on this idea, we propose a Gaussian process (GP) surrogate-based Bayesian experimental design and parameter estimation approach for groundwater contaminant source identification problems. A major advantage of the GP surrogate is that it provides a convenient estimation of the approximation error, which can be incorporated in the Bayesian formula to avoid over-confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed-up compared to our previous work using two-stage MCMC.
Capacity and optimal collusion attack channels for Gaussian fingerprinting games
NASA Astrophysics Data System (ADS)
Wang, Ying; Moulin, Pierre
2007-02-01
In content fingerprinting, the same media covertext - image, video, audio, or text - is distributed to many users. A fingerprint, a mark unique to each user, is embedded into each copy of the distributed covertext. In a collusion attack, two or more users may combine their copies in an attempt to "remove" their fingerprints and forge a pirated copy. To trace the forgery back to members of the coalition, we need fingerprinting codes that can reliably identify the fingerprints of those members. Researchers have been focusing on designing or testing fingerprints for Gaussian host signals and the mean square error (MSE) distortion under some classes of collusion attacks, in terms of the detector's error probability in detecting collusion members. For example, under the assumptions of Gaussian fingerprints and Gaussian attacks (the fingerprinted signals are averaged and then the result is passed through a Gaussian test channel), Moulin and Briassouli1 derived optimal strategies in a game-theoretic framework that uses the detector's error probability as the performance measure for a binary decision problem (whether a user participates in the collusion attack or not); Stone2 and Zhao et al. 3 studied average and other non-linear collusion attacks for Gaussian-like fingerprints; Wang et al. 4 stated that the average collusion attack is the most efficient one for orthogonal fingerprints; Kiyavash and Moulin 5 derived a mathematical proof of the optimality of the average collusion attack under some assumptions. In this paper, we also consider Gaussian cover signals, the MSE distortion, and memoryless collusion attacks. We do not make any assumption about the fingerprinting codes used other than an embedding distortion constraint. Also, our only assumptions about the attack channel are an expected distortion constraint, a memoryless constraint, and a fairness constraint. That is, the colluders are allowed to use any arbitrary nonlinear strategy subject to the above
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Behnke, marlana N.; Przekop, Adam
2010-01-01
High-cycle fatigue of an elastic-plastic beam structure under the combined action of thermal and high-intensity non-Gaussian acoustic loadings is considered. Such loadings can be highly damaging when snap-through motion occurs between thermally post-buckled equilibria. The simulated non-Gaussian loadings investigated have a range of skewness and kurtosis typical of turbulent boundary layer pressure fluctuations in the vicinity of forward facing steps. Further, the duration and steadiness of high excursion peaks is comparable to that found in such turbulent boundary layer data. Response and fatigue life estimates are found to be insensitive to the loading distribution, with the minor exception of cases involving plastic deformation. In contrast, the fatigue life estimate was found to be highly affected by a different type of non-Gaussian loading having bursts of high excursion peaks.
Reactive power in the full Gaussian light wave.
Seshadri, S R
2009-11-01
The electric current sources that are required for the excitation of the fundamental Gaussian beam and the corresponding full Gaussian light wave are determined. The current sources are situated on the secondary source plane that forms the boundary between the two half-spaces in which the waves are launched. The electromagnetic fields and the complex power generated by the current sources are evaluated. For the fundamental Gaussian beam, the reactive power vanishes, and the normalization is chosen such that the real power is 2 W. The various full Gaussian waves are identified by the length parameter b(t) that lies in the range 0 < or = b(t) < or = b, where b is the Rayleigh distance. The other parameters are the wavenumber k, the free-space wavelength lambda, and the beam waist w0 at the input plane. The dependence of the real power of the full Gaussian light wave on b(t)/b and w0/lambda is examined. For a specified w0/lambda, the reactive power, which can be positive or negative, increases as b(t)/b is increased from 0 to 1 and becomes infinite for b(t)/b=1. For a specified b(t)/b, the reactive power approaches zero as kw0 is increased and reaches the limiting value of zero of the paraxial beam.
Passive interferometric symmetries of multimode Gaussian pure states
NASA Astrophysics Data System (ADS)
Gabay, Natasha; Menicucci, Nicolas C.
2016-05-01
As large-scale multimode Gaussian states begin to become accessible in the laboratory, their representation and analysis become a useful topic of research in their own right. The graphical calculus for Gaussian pure states provides powerful tools for their representation, while this work presents a useful tool for their analysis: passive interferometric (i.e., number-conserving) symmetries. Here we show that these symmetries of multimode Gaussian states simplify calculations in measurement-based quantum computing and provide constructive tools for engineering large-scale harmonic systems with specific physical properties, and we provide a general mathematical framework for deriving them. Such symmetries are generated by linear combinations of operators expressed in the Schwinger representation of U (2 ) , called nullifiers because the Gaussian state in question is a zero eigenstate of them. This general framework is shown to have applications in the noise analysis of continuous-various cluster states and is expected to have additional applications in future work with large-scale multimode Gaussian states.
Robust Gaussian teleportation with attenuation and nonunity gain
NASA Astrophysics Data System (ADS)
de Faria, Alencar J.
2016-12-01
The average fidelity of the teleportation of coherent states is calculated for general Gaussian bipartite systems shared by the partners of the protocol, Alice and Bob. It is considered that the shared Gaussian bipartite modes suffer independent attenuations before the processing of Alice and Bob. In addition, the classical communication between the partners can be controlled by a gain not necessarily unitary. Comparing with the classical fidelity threshold of measure-and-prepare methods, we establish several genuinely quantum teleportation conditions which depend on the gain and the local attenuations. If the gain can be tuned to maximize the bipartite state set capable of performing genuinely quantum teleportation, then a condition for teleportation robust against local attenuations is found. This condition is demonstrated to be essentially equivalent to the condition of robust Gaussian bipartite entanglement, obtained in previous articles, showing that the robustness against attenuations is an entanglement property relevant for characterization and application of bipartite systems. For the derivation of the robust teleportation conditions, the Gaussian operations onto the bipartite system are thoroughly studied, so that the transformations that maintain the fidelity invariant are found. Some scenarios for different Gaussian bipartite states are presented and discussed.
Non-gaussian mode coupling and the statistical cosmological principle
LoVerde, Marilena; Nelson, Elliot; Shandera, Sarah E-mail: eln121@psu.edu
2013-06-01
Local-type primordial non-Gaussianity couples statistics of the curvature perturbation ζ on vastly different physical scales. Because of this coupling, statistics (i.e. the polyspectra) of ζ in our Hubble volume may not be representative of those in the larger universe — that is, they may be biased. The bias depends on the local background value of ζ, which includes contributions from all modes with wavelength k∼
Non-Gaussian error distribution of 7Li abundance measurements
NASA Astrophysics Data System (ADS)
Crandall, Sara; Houston, Stephen; Ratra, Bharat
2015-07-01
We construct the error distribution of 7Li abundance measurements for 66 observations (with error bars) used by Spite et al. (2012) that give A(Li) = 2.21 ± 0.065 (median and 1σ symmetrized error). This error distribution is somewhat non-Gaussian, with larger probability in the tails than is predicted by a Gaussian distribution. The 95.4% confidence limits are 3.0σ in terms of the quoted errors. We fit the data to four commonly used distributions: Gaussian, Cauchy, Student’s t and double exponential with the center of the distribution found with both weighted mean and median statistics. It is reasonably well described by a widened n = 8 Student’s t distribution. Assuming Gaussianity, the observed A(Li) is 6.5σ away from that expected from standard Big Bang Nucleosynthesis (BBN) given the Planck observations. Accounting for the non-Gaussianity of the observed A(Li) error distribution reduces the discrepancy to 4.9σ, which is still significant.
Non-Gaussian bias: insights from discrete density peaks
Desjacques, Vincent; Riotto, Antonio; Gong, Jinn-Ouk E-mail: jinn-ouk.gong@apctp.org
2013-09-01
Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering 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 that statistics of thresholded regions can be computed using the same formalism. Our results suggest that halo clustering statistics can be modelled consistently (in the sense that the Gaussian and non-Gaussian bias factors agree with peak-background split expectations) from a Lagrangian bias relation only if the latter is specified as a set of constraints imposed on the linear density field. This is clearly not the case of standard Lagrangian local bias. Therefore, one is led to consider additional variables beyond the local mass overdensity.
The Gaussian CLs method for searches of new physics
Qian, X.; Tan, A.; Ling, J. J.; ...
2016-04-23
Here we describe a method based on the CLs approach to present results in searches of new physics, under the condition that the relevant parameter space is continuous. Our method relies on a class of test statistics developed for non-nested hypotheses testing problems, denoted by ΔT, which has a Gaussian approximation to its parent distribution when the sample size is large. This leads to a simple procedure of forming exclusion sets for the parameters of interest, which we call the Gaussian CLs method. Our work provides a self-contained mathematical proof for the Gaussian CLs method, that explicitly outlines the requiredmore » conditions. These conditions are milder than that required by the Wilks' theorem to set confidence intervals (CIs). We illustrate the Gaussian CLs method in an example of searching for a sterile neutrino, where the CLs approach was rarely used before. We also compare data analysis results produced by the Gaussian CLs method and various CI methods to showcase their differences.« less
Canales-Rodríguez, Erick J; Daducci, Alessandro; Sotiropoulos, Stamatios N; Caruyer, Emmanuel; Aja-Fernández, Santiago; Radua, Joaquim; Yurramendi Mendizabal, Jesús M; Iturria-Medina, Yasser; Melie-García, Lester; Alemán-Gómez, Yasser; Thiran, Jean-Philippe; Sarró, Salvador; Pomarol-Clotet, Edith; Salvador, Raymond
2015-01-01
Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data.
Canales-Rodríguez, Erick J.; Caruyer, Emmanuel; Aja-Fernández, Santiago; Radua, Joaquim; Yurramendi Mendizabal, Jesús M.; Iturria-Medina, Yasser; Melie-García, Lester; Alemán-Gómez, Yasser; Thiran, Jean-Philippe; Sarró, Salvador; Pomarol-Clotet, Edith; Salvador, Raymond
2015-01-01
Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data. PMID:26470024
ENSO's non-stationary and non-Gaussian character: the role of climate shifts
NASA Astrophysics Data System (ADS)
Boucharel, J.; Dewitte, B.; Garel, B.; Du Penhoat, Y.
2009-07-01
El Niño Southern Oscillation (ENSO) is the dominant mode of climate variability in the Pacific, having socio-economic impacts on surrounding regions. ENSO exhibits significant modulation on decadal to inter-decadal time scales which is related to changes in its characteristics (onset, amplitude, frequency, propagation, and predictability). Some of these characteristics tend to be overlooked in ENSO studies, such as its asymmetry (the number and amplitude of warm and cold events are not equal) and the deviation of its statistics from those of the Gaussian distribution. These properties could be related to the ability of the current generation of coupled models to predict ENSO and its modulation. Here, ENSO's non-Gaussian nature and asymmetry are diagnosed from in situ data and a variety of models (from intermediate complexity models to full-physics coupled general circulation models (CGCMs)) using robust statistical tools initially designed for financial mathematics studies. In particular α-stable laws are used as theoretical background material to measure (and quantify) the non-Gaussian character of ENSO time series and to estimate the skill of ``naïve'' statistical models in producing deviation from Gaussian laws and asymmetry. The former are based on non-stationary processes dominated by abrupt changes in mean state and empirical variance. It is shown that the α-stable character of ENSO may result from the presence of climate shifts in the time series. Also, cool (warm) periods are associated with ENSO statistics having a stronger (weaker) tendency towards Gaussianity and lower (greater) asymmetry. This supports the hypothesis of ENSO being rectified by changes in mean state through nonlinear processes. The relationship between changes in mean state and nonlinearity (skewness) is further investigated both in the Zebiak and Cane (1987)'s model and the models of the Intergovernmental Panel for Climate Change (IPCC). Whereas there is a clear relationship in all
NASA Astrophysics Data System (ADS)
Malli, G. L.; Da Silva, A. B. F.; Ishikawa, Yasuyuki
1994-10-01
A universal Gaussian basis set is developed that leads to relativistic Dirac-Fock SCF energies of comparable accuracy as that obtained by the accurate numerical finite-difference method (GRASP2 package) [J. Phys. B 25, 1 (1992)]. The Gaussian-type functions of our universal basis set satisfy the relativistic boundary conditions associated with the finite nuclear model for a finite speed of light and conform to the so-called kinetic balance at the nonrelativistic limit. We attribute the exceptionally high accuracy obtained in our calculations to the fact that the representation of the relativistic dynamics of an electron in a spherical ball finite nucleus near the origin in terms of our universal Gaussian basis set is as accurate as that provided by the numerical finite-difference method. Results of the Dirac-Fock-Coulomb energies for a number of atoms up to No (Z=102) and some negative ions are presented and compared with the recent results obtained with the numerical finite-difference method and geometrical Gaussian basis sets by Parpia, Mohanty, and Clementi [J. Phys. B 25, 1 (1992)]. The accuracy of our calculations is estimated to be within a few parts in 109 for all the atomic systems studied.
Park, Jun-Koo; Jernigan, Robert; Wu, Zhijun
2013-01-01
We investigate several approaches to coarse grained normal mode analysis on protein residual-level structural fluctuations by choosing different ways of representing the residues and the forces among them. Single-atom representations using the backbone atoms C(α), C, N, and C(β) are considered. Combinations of some of these atoms are also tested. The force constants between the representative atoms are extracted from the Hessian matrix of the energy function and served as the force constants between the corresponding residues. The residue mean-square-fluctuations and their correlations with the experimental B-factors are calculated for a large set of proteins. The results are compared with all-atom normal mode analysis and the residue-level Gaussian Network Model. The coarse-grained methods perform more efficiently than all-atom normal mode analysis, while their B-factor correlations are also higher. Their B-factor correlations are comparable with those estimated by the Gaussian Network Model and in many cases better. The extracted force constants are surveyed for different pairs of residues with different numbers of separation residues in sequence. The statistical averages are used to build a refined Gaussian Network Model, which is able to predict residue-level structural fluctuations significantly better than the conventional Gaussian Network Model in many test cases.
NASA Astrophysics Data System (ADS)
Gu, Wenjun; Zhang, Weizhi; Wang, Jin; Amini Kashani, M. R.; Kavehrad, Mohsen
2015-01-01
Over the past decade, location based services (LBS) have found their wide applications in indoor environments, such as large shopping malls, hospitals, warehouses, airports, etc. Current technologies provide wide choices of available solutions, which include Radio-frequency identification (RFID), Ultra wideband (UWB), wireless local area network (WLAN) and Bluetooth. With the rapid development of light-emitting-diodes (LED) technology, visible light communications (VLC) also bring a practical approach to LBS. As visible light has a better immunity against multipath effect than radio waves, higher positioning accuracy is achieved. LEDs are utilized both for illumination and positioning purpose to realize relatively lower infrastructure cost. In this paper, an indoor positioning system using VLC is proposed, with LEDs as transmitters and photo diodes as receivers. The algorithm for estimation is based on received-signalstrength (RSS) information collected from photo diodes and trilateration technique. By appropriately making use of the characteristics of receiver movements and the property of trilateration, estimation on three-dimensional (3-D) coordinates is attained. Filtering technique is applied to enable tracking capability of the algorithm, and a higher accuracy is reached compare to raw estimates. Gaussian mixture Sigma-point particle filter (GM-SPPF) is proposed for this 3-D system, which introduces the notion of Gaussian Mixture Model (GMM). The number of particles in the filter is reduced by approximating the probability distribution with Gaussian components.
Wave propagation in non-Gaussian random media
NASA Astrophysics Data System (ADS)
Franco, Mariano; Calzetta, Esteban
2015-01-01
We develop a compact perturbative series for acoustic wave propagation in a medium with a non-Gaussian stochastic speed of sound. We use Martin-Siggia and Rose auxiliary field techniques to render the classical wave propagation problem into a ‘quantum’ field theory one, and then frame this problem within the so-called Schwinger-Keldysh of closed time-path (CTP) formalism. Variation of the so-called two-particle irreducible (2PI) effective action (EA), whose arguments are both the mean fields and the irreducible two point correlations, yields the Schwinger-Dyson and the Bethe-Salpeter equations. We work out the loop expansion of the 2PI CTP EA and show that, in the paradigmatic problem of overlapping spherical intrusions in an otherwise homogeneous medium, non-Gaussian corrections might be much larger than Gaussian ones at the same order of loops.
Qubit Noise Spectroscopy for Non-Gaussian Dephasing Environments
NASA Astrophysics Data System (ADS)
Norris, Leigh M.; Paz-Silva, Gerardo A.; Viola, Lorenza
2016-04-01
We introduce open-loop quantum control protocols for characterizing the spectral properties of non-Gaussian noise, applicable to both classical and quantum dephasing environments. By engineering a multidimensional frequency comb via repetition of suitably designed pulse sequences, the desired high-order spectra may be related to observable properties of the qubit probe. We prove that access to a high time resolution is key to achieving spectral reconstruction over an extended bandwidth, overcoming the limitations of existing schemes. Non-Gaussian spectroscopy is demonstrated for a classical noise model describing quadratic dephasing at an optimal point, as well as a quantum spin-boson model out of equilibrium. In both cases, we obtain spectral reconstructions that accurately predict the qubit dynamics in the non-Gaussian regime.
Higher order annular Gaussian laser beam propagation in free space
NASA Astrophysics Data System (ADS)
Eyyuboglu, Halil T.; Yenice, Yusuf E.; Baykal, Yahya K.
2006-03-01
Propagation of higher order annular Gaussian (HOAG) laser beams in free space is examined. HOAG beams are defined as the difference of two Hermite-Gaussian (HG) beams; thus, they can be produced by subtracting a smaller beam from a larger beam, that are cocentered and both possess HG mode field distributions. Such beams can be considered as a generalization of the well-known annular Gaussian beams. We formulate the source and receiver plane characteristics and kurtosis parameter of HOAG beams propagating in free space and evaluate them numerically. In comparison to HG beams, HOAG beams have a broader beam size with outer lobes of kidney shape. The amount of received power within the same receiver aperture size, that is, power in bucket, is generally lower for higher order beams. The convergence of the kurtosis parameter to an asymptotic value for higher order beams takes much longer propagation distances compared to zero-order beams.
Analysis of fractional Gaussian noises using level crossing method
NASA Astrophysics Data System (ADS)
Vahabi, M.; Jafari, G. R.; Sadegh Movahed, M.
2011-11-01
The so-called level crossing analysis has been used to investigate the empirical data set, but there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic series could be a suitable benchmark to make more sense of the level crossing findings. In this paper, we calculated the average frequency of upcrossing for a wide range of fractional Gaussian noises from logarithmic (zero Hurst exponent, H = 0), to Gaussian, H = 1 (0 < H < 1). By introducing the relative change of the total number of upcrossings for original data with respect to the so-called shuffled data, {R} , an empirical function for the Hurst exponent versus {R} has been established. Finally to make the concept more obvious, we applied this approach to some financial series.
Bloch-Messiah reduction of Gaussian unitaries by Takagi factorization
NASA Astrophysics Data System (ADS)
Cariolaro, Gianfranco; Pierobon, Gianfranco
2016-12-01
The Bloch-Messiah (BM) reduction allows the decomposition of an arbitrarily complicated Gaussian unitary into a very simple scheme in which linear optical components are separated from nonlinear ones. The nonlinear part is due to the squeezing possibly present in the Gaussian unitary. The reduction is usually obtained by exploiting the singular value decomposition (SVD) of the matrices appearing in the Bogoliubov transformation of the given Gaussian unitary. This paper discusses a different approach, where the BM reduction is obtained in a straightforward way. It is based on the Takagi factorization of the (complex and symmetric) squeeze matrix and has the advantage of avoiding several matrix operations of the previous approach (polar decomposition, eigendecomposition, SVD, and Takagi factorization). The theory is illustrated with an application example in which the previous and present approaches are compared.
Continuous-variable quantum teleportation with non-Gaussian resources
Dell'Anno, F.; De Siena, S.; Albano, L.; Illuminati, F.
2007-08-15
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.
Gaussian geometric discord in terms of Hellinger distance
Suciu, Serban Isar, Aurelian
2015-12-07
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we address the quantification of general non-classical correlations in Gaussian states of continuous variable systems from a geometric perspective. We give a description of the Gaussian geometric discord by using the Hellinger distance as a measure for quantum correlations between two non-interacting non-resonant bosonic modes embedded in a thermal environment. We evaluate the Gaussian geometric discord by taking two-mode squeezed thermal states as initial states of the system and show that it has finite values between 0 and 1 and that it decays asymptotically to zero in time under the effect of the thermal bath.
Quantum Entanglement and Quantum Discord in Gaussian Open Systems
Isar, Aurelian
2011-10-03
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum entanglement and quantum discord for a system consisting of two noninteracting modes embedded in a thermal environment. Entanglement and discord are used to quantify the quantum correlations of the system. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. In the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place for non-zero temperatures of the environment. Only for a zero temperature of the thermal bath the initial entangled state remains entangled for finite times. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal bath.
Large non-gaussianity in slow-roll inflation
NASA Astrophysics Data System (ADS)
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo
2016-04-01
Canonical models of single-field, slow-roll inflation do not lead to appreciable non-Gaussianity, unless derivative interactions of the inflaton become uncontrollably large. We propose a novel slow-roll scenario where scalar perturbations propagate at a subluminal speed, leading to sizeable equilateral non-Gaussianity, f NL equil ∝ 1/ c s 4 , largely insensitive to the ultraviolet physics. The model is based on a low-energy effective theory characterized by weakly broken invariance under internal galileon transformations, ϕ → ϕ + b μ x μ , which protects the properties of perturbations from large quantum corrections. This provides the unique alternative to models such as DBI inflation in generating strongly subluminal/non-Gaussian scalar perturbations.
Primordial non-Gaussianity in noncanonical warm inflation
NASA Astrophysics Data System (ADS)
Zhang, Xiao-Min; Zhu, Jian-Yang
2015-03-01
We study the bispectrum of the primordial curvature perturbation on uniform density hypersurfaces generated by a kind of the noncanonical warm inflation, wherein the inflation is provided by a noncanonical scalar inflaton field that is coupled to radiation through a thermal dissipation effect. We obtain an analytic form for the nonlinear parameter fNL that describes the non-Gaussianity in first-order cosmological perturbation theory and analyze the magnitude of this nonlinear parameter. We make a comparison between our result and those of the standard inflation and the canonical warm inflation. We also discuss when the contribution to the non-Gaussianity due to the second-order perturbation theory becomes more important and what the observations predict. We take the Dirac-Born-Infeld inflation as a concrete example to find how the sound speed and the thermal dissipation strength to decide the non-Gaussianity and get a lower bound of the sound speed constrained by Planck.
Gaussian entanglement generation from coherence using beam-splitters
Wang, Zhong-Xiao; Wang, Shuhao; Ma, Teng; Wang, Tie-Jun; Wang, Chuan
2016-01-01
The generation and quantification of quantum entanglement is crucial for quantum information processing. Here we study the transition of Gaussian correlation under the effect of linear optical beam-splitters. We find the single-mode Gaussian coherence acts as the resource in generating Gaussian entanglement for two squeezed states as the input states. With the help of consecutive beam-splitters, single-mode coherence and quantum entanglement can be converted to each other. Our results reveal that by using finite number of beam-splitters, it is possible to extract all the entanglement from the single-mode coherence even if the entanglement is wiped out before each beam-splitter. PMID:27892537
Universal non-Gaussian velocity distribution in violent gravitational processes.
Iguchi, Osamu; Sota, Yasuhide; Tatekawa, Takayuki; Nakamichi, Akika; Morikawa, Masahiro
2005-01-01
We study the velocity distribution in spherical collapses and cluster-pair collisions by use of N -body simulations. Reflecting the violent gravitational processes, the velocity distribution of the resultant quasistationary state generally becomes non-Gaussian. Through the strong mixing of the violent process, there appears a universal non-Gaussian velocity distribution, which is a democratic (equal-weighted) superposition of many Gaussian distributions (DT distribution). This is deeply related with the local virial equilibrium and the linear mass-temperature relation which characterize the system. We show the robustness of this distribution function against various initial conditions which leads to the violent gravitational process. The DT distribution has a positive correlation with the energy fluctuation of the system. On the other hand, the coherent motion such as the radial motion in the spherical collapse and the rotation with the angular momentum suppress the appearance of the DT distribution.
Gaussian white noise as a resource for work extraction
NASA Astrophysics Data System (ADS)
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.
Vargas Cardona, Hernán Darío; Orozco, Álvaro Ángel; Álvarez, Mauricio A
2013-01-01
Automatic identification of biosignals is one of the more studied fields in biomedical engineering. In this paper, we present an approach for the unsupervised recognition of biomedical signals: Microelectrode Recordings (MER) and Electrocardiography signals (ECG). The unsupervised learning is based in classic and bayesian estimation theory. We employ gaussian mixtures models with two estimation methods. The first is derived from the frequentist estimation theory, known as Expectation-Maximization (EM) algorithm. The second is obtained from bayesian probabilistic estimation and it is called variational inference. In this framework, both methods are used for parameters estimation of Gaussian mixtures. The mixtures models are used for unsupervised pattern classification, through the responsibility matrix. The algorithms are applied in two real databases acquired in Parkinson's disease surgeries and electrocardiograms. The results show an accuracy over 85% in MER and 90% in ECG for identification of two classes. These results are statistically equal or even better than parametric (Naive Bayes) and nonparametric classifiers (K-nearest neighbor).
Assessing clustering strategies for Gaussian mixture filtering a subsurface contaminant model
NASA Astrophysics Data System (ADS)
Liu, B.; Gharamti, M. E.; Hoteit, I.
2016-04-01
An ensemble-based Gaussian mixture (GM) filtering framework is studied in this paper in term of its dependence on the choice of the clustering method to construct the GM. In this approach, a number of particles sampled from the posterior distribution are first integrated forward with the dynamical model for forecasting. A GM representation of the forecast distribution is then constructed from the forecast particles. Once an observation becomes available, the forecast GM is updated according to Bayes' rule. This leads to (i) a Kalman filter-like update of the particles, and (ii) a Particle filter-like update of their weights, generalizing the ensemble Kalman filter update to non-Gaussian distributions. We focus on investigating the impact of the clustering strategy on the behavior of the filter. Three different clustering methods for constructing the prior GM are considered: (i) a standard kernel density estimation, (ii) clustering with a specified mixture component size, and (iii) adaptive clustering (with a variable GM size). Numerical experiments are performed using a two-dimensional reactive contaminant transport model in which the contaminant concentration and the heterogenous hydraulic conductivity fields are estimated within a confined aquifer using solute concentration data. The experimental results suggest that the performance of the GM filter is sensitive to the choice of the GM model. In particular, increasing the size of the GM does not necessarily result in improved performances. In this respect, the best results are obtained with the proposed adaptive clustering scheme.
SIMULATIONS OF WIDE-FIELD WEAK LENSING SURVEYS. I. BASIC STATISTICS AND NON-GAUSSIAN EFFECTS
Sato, Masanori; Takahashi, Ryuichi; Matsubara, Takahiko; Sugiyama, Naoshi; Hamana, Takashi; Takada, Masahiro; Yoshida, Naoki
2009-08-20
We study the lensing convergence power spectrum and its covariance for a standard {lambda}CDM cosmology. We run 400 cosmological N-body simulations and use the outputs to perform a total of 1000 independent ray-tracing simulations. We compare the simulation results with analytic model predictions. The semianalytic model based on Smith et al. fitting formula underestimates the convergence power by {approx} 30% at arcmin angular scales. For the convergence power spectrum covariance, the halo model reproduces the simulation results remarkably well over a wide range of angular scales and source redshifts. The dominant contribution at small angular scales comes from the sample variance due to the number fluctuations of halos in a finite survey volume. The signal-to-noise ratio for the convergence power spectrum is degraded by the non-Gaussian covariances by up to a factor of 5 for a weak lensing survey to z{sub s} {approx} 1. The probability distribution of the convergence power spectrum estimators, among the realizations, is well approximated by a {chi}{sup 2} distribution with broadened variance given by the non-Gaussian covariance, but has a larger positive tail. The skewness and kurtosis have non-negligible values especially for a shallow survey. We argue that a prior knowledge on the full distribution may be needed to obtain an unbiased estimate on the ensemble-averaged band power at each angular scale from a finite volume survey.
CMB constraint on non-Gaussianity in isocurvature perturbations
Hikage, Chiaki; Kawasaki, Masahiro; Sekiguchi, Toyokazu; Takahashi, Tomo E-mail: kawasaki@icrr.u-tokyo.ac.jp E-mail: tomot@cc.saga-u.ac.jp
2013-07-01
We study the CMB constraints on non-Gaussianity in CDM isocurvature perturbations. Non-Gaussian isocurvature perturbations can be produced in various models at the very early stage of the Universe. Since the isocurvature perturbations little affect the structure formation at late times, CMB is the best probe of isocurvature non-Gaussianity at least in the near future. In this paper, we focus on non-Gaussian curvature and isocurvature perturbations of the local-type, which are uncorrelated and in the form ζ = ζ{sub G}+(3/5)f{sub NL}(ζ{sub G}{sup 2}−(ζ{sub G}{sup 2})) and S = S{sub G}+f{sub NL}{sup (ISO)}(S{sub G}−(S{sub G}{sup 2})), and constrain the non-linearity parameter of isocurvature perturbations, f{sub NL}{sup (ISO)}, as well as the curvature one f{sub NL}. For this purpose, we employ several state-of-art techniques for the analysis of CMB data and simulation. Assuming that isocurvature perturbations are subdominant, we apply our method to the WMAP 7-year data of temperature anisotropy and obtain constraints on a combination α{sup 2}f{sub NL}{sup (ISO)}, where α is the ratio of the power spectrum of isocurvature perturbations to that of the adiabatic ones. When the adiabatic perturbations are assumed to be Gaussian, we obtained a constraint α{sup 2}f{sub NL}{sup (ISO)} = 40±66 assuming the power spectrum of isocurvature perturbations is scale-invariant. When we assume that the adiabatic perturbations can also be non-Gaussian, we obtain f{sub NL} = 38±24 and α{sup 2}f{sub NL}{sup (ISO)} = −8±72. We also discuss implications of our results for the axion CDM isocurvature model.
A study of Gaussian approximations of fluorescence microscopy PSF models
NASA Astrophysics Data System (ADS)
Zhang, Bo; Zerubia, Josiane; Olivo-Marin, Jean-Christophe
2006-02-01
Despite the availability of rigorous physical models of microscopy point spread functions (PSFs), approximative PSFs, particularly separable Gaussian approximations are widely used in practical microscopic data processing. In fact, compared with a physical PSF model, which usually involves non-trivial terms such as integrals and infinite series, a Gaussian function has the advantage that it is much simpler and can be computed much faster. Moreover, due to its special analytical form, a Gaussian PSF is often preferred to facilitate the analysis of theoretical models such as Fluorescence Recovery After Photobleaching (FRAP) process and of processing algorithms such as EM deconvolution. However, in these works, the selection of Gaussian parameters and the approximation accuracy were rarely investigated. In this paper, we present a comprehensive study of Gaussian approximations for diffraction-limited 2D/3D paraxial/non-paraxial PSFs of Wide Field Fluorescence Microscopy (WFFM), Laser Scanning Confocal Microscopy (LSCM) and Disk Scanning Confocal Microscopy (DSCM) described using the Debye integral. Besides providing an optimal Gaussian parameter for the 2D paraxial WFFM PSF case, we further derive nearly optimal parameters in explicit forms for each of the other cases, based on Maclaurin series matching. Numerical results show that the accuracy of the 2D approximations is very high (Relative Squared Error (RSE) < 2% in WFFM, < 0.3% in LSCM and < 4% in DSCM). For the 3D PSFs, the approximations are average in WFFM (RSE ~= 16-20%), accurate in DSCM (RSE~= 3-6%) and nearly perfect in LSCM (RSE ~= 0.3-0.5%).
Fresnel-Gaussian shape invariant for optical ray tracing.
Cywiak, Moisés; Morales, A; Flores, J Mauricio; Servín, Manuel
2009-06-22
We propose a technique for ray tracing, based in the propagation of a Gaussian shape invariant under the Fresnel diffraction integral. The technique uses two driving independent terms to direct the ray and is based on the fact that at any arbitrary distance, the center of the propagated Gaussian beam corresponds to the geometrical projection of the center of the incident beam. We present computer simulations as examples of the use of the technique consisting in the calculation of rays through lenses and optical media where the index of refraction varies as a function of position.
Nonclassicality Invariant of General Two-Mode Gaussian States
Arkhipov, Ievgen I.; Peřina Jr., Jan; Svozilík, Jiří; Miranowicz, Adam
2016-01-01
We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given. PMID:27210547
Multi-Gaussian Schell-model vortex beam
NASA Astrophysics Data System (ADS)
Zhang, Yongtao; Liu, Lin; Zhao, Chengliang; Cai, Yangjian
2014-02-01
Multi-Gaussian Schell-model (MGSM) beam was introduced recently (Sahin and Korotkova, 2012 [34], and Korotkova et al., 2012 [35]). In this paper, multi-Gaussian Schell-model vortex (MGSMV) beam is introduced as a natural extension of MGSM beam. The explicit expression for the cross-spectral density of a MGSMV beam propagating through a stigmatic ABCD optical system is derived and the focusing properties of a MGSMV beam are studied in detail. It is found that we can shape the focused beam profile by varying the initial beam parameters, which will be useful in material thermal processing and particle trapping.
Non-gaussian statistics of pencil beam surveys
NASA Technical Reports Server (NTRS)
Amendola, Luca
1994-01-01
We study the effect of the non-Gaussian clustering of galaxies on the statistics of pencil beam surveys. We derive the probability from the power spectrum peaks by means of Edgeworth expansion and find that the higher order moments of the galaxy distribution play a dominant role. The probability of obtaining the 128 Mpc/h periodicity found in pencil beam surveys is raised by more than one order of magnitude, up to 1%. Further data are needed to decide if non-Gaussian distribution alone is sufficient to explain the 128 Mpc/h periodicity, or if extra large-scale power is necessary.
Genuine multipartite nonlocality of permutationally invariant Gaussian states
NASA Astrophysics Data System (ADS)
Xu, Buqing; Tufarelli, Tommaso; Adesso, Gerardo
2017-01-01
We investigate genuine multipartite nonlocality of pure permutationally invariant multimode Gaussian states of continuous variable systems, as detected by the violation of Svetlichny inequality. We identify the phase space settings leading to the largest violation of the inequality when using displaced parity measurements, distinguishing our results between the cases of even and odd total number of modes. We further consider pseudospin measurements and show that, for three-mode states with asymptotically large squeezing degree, particular settings of these measurements allow one to approach the maximum violation of Svetlichny inequality allowed by quantum mechanics. This indicates that the strongest manifestation of genuine multipartite quantum nonlocality is in principle verifiable on Gaussian states.
A new method for generating a hollow Gaussian beam
NASA Astrophysics Data System (ADS)
Wei, Cun; Lu, Xingyuan; Wu, Gaofeng; Wang, Fei; Cai, Yangjian
2014-04-01
Hollow Gaussian beam (HGB) was introduced 10 years ago (Cai et al. in Opt Lett 28:1084, 2003). In this paper, we introduce a new method for generating a HGB through transforming a Laguerre-Gaussian beam with radial index 0 and azimuthal index l into a HGB with mode n = l/2. Furthermore, we report experimental generation of a HGB based on the proposed method, and we carry out experimental study of the focusing properties of the generated HGB. Our experimental results agree well with the theoretical predictions.
Truncated Gaussian simulation of discrete-valued, ordinal coregionalized variables
NASA Astrophysics Data System (ADS)
Emery, Xavier; Cornejo, Javier
2010-10-01
This paper deals with the modeling and cosimulation of ordinal coregionalized variables, such as indicators, counts or continuous-valued variables discretized into a limited number of classes. The proposed model relies on truncations of a set of cross-correlated stationary Gaussian random fields. We provide guidelines and algorithms for inferring and validating the structural model (direct and cross variograms of the underlying Gaussian random fields) and constructing realizations conditioned to data. The algorithms are implemented in a set of computer programs and are illustrated with applications to datasets in pest management and mineral resources evaluation.
Trans-Planckian enhancements of the primordial non-Gaussianities
Collins, Hael; Holman, R.
2009-08-15
This article examines how breaking a Lorentz-invariant description of nature at tiny space-time intervals would affect the non-Gaussian character of the pattern of primordial perturbations left by inflation. We specifically study a set of irrelevant operators that preserve the spatial symmetries of the usual inflationary background. The non-Gaussian component in the primordial fluctuations can be much larger than the usual, small, inflationary prediction and can thus lead to much stronger constraints on the role of 'trans-Planckian' physics in inflation than those from the measurements of the primordial power spectrum.
Economical Gaussian cloning of coherent states with known phase
Dong Yuli; Zou Xubo; Guo Guangcan; Li Shangbin
2007-07-15
We investigate the economical Gaussian cloning of coherent states with the known phase, which produces M copies from N input replica and can be implemented with degenerate parametric amplifiers and beam splitters.The achievable fidelity of single copy is given by 2M{radical}(N)/[{radical}(N)(M-1)+{radical}((1+N)(M{sup 2}+N))], which is bigger than the optimal fidelity of the universal Gaussian cloning. The cloning machine presented here works without ancillary optical modes and can be regarded as the continuous variable generalization of the economical cloning machine for qudits.
Rajdl, Kamil; Lansky, Petr
2014-02-01
Fano factor is one of the most widely used measures of variability of spike trains. Its standard estimator is the ratio of sample variance to sample mean of spike counts observed in a time window and the quality of the estimator strongly depends on the length of the window. We investigate this dependence under the assumption that the spike train behaves as an equilibrium renewal process. It is shown what characteristics of the spike train have large effect on the estimator bias. Namely, the effect of refractory period is analytically evaluated. Next, we create an approximate asymptotic formula for the mean square error of the estimator, which can also be used to find minimum of the error in estimation from single spike trains. The accuracy of the Fano factor estimator is compared with the accuracy of the estimator based on the squared coefficient of variation. All the results are illustrated for spike trains with gamma and inverse Gaussian probability distributions of interspike intervals. Finally, we discuss possibilities of how to select a suitable observation window for the Fano factor estimation.
Nguyen, Nha; Huang, Heng; Oraintara, Soontorn; Vo, An
2010-01-01
Motivation: Peaks are the key information in mass spectrometry (MS) which has been increasingly used to discover diseases-related proteomic patterns. Peak detection is an essential step for MS-based proteomic data analysis. Recently, several peak detection algorithms have been proposed. However, in these algorithms, there are three major deficiencies: (i) because the noise is often removed, the true signal could also be removed; (ii) baseline removal step may get rid of true peaks and create new false peaks; (iii) in peak quantification step, a threshold of signal-to-noise ratio (SNR) is usually used to remove false peaks; however, noise estimations in SNR calculation are often inaccurate in either time or wavelet domain. In this article, we propose new algorithms to solve these problems. First, we use bivariate shrinkage estimator in stationary wavelet domain to avoid removing true peaks in denoising step. Second, without baseline removal, zero-crossing lines in multi-scale of derivative Gaussian wavelets are investigated with mixture of Gaussian to estimate discriminative parameters of peaks. Third, in quantification step, the frequency, SD, height and rank of peaks are used to detect both high and small energy peaks with robustness to noise. Results: We propose a novel Gaussian Derivative Wavelet (GDWavelet) method to more accurately detect true peaks with a lower false discovery rate than existing methods. The proposed GDWavelet method has been performed on the real Surface-Enhanced Laser Desorption/Ionization Time-Of-Flight (SELDI-TOF) spectrum with known polypeptide positions and on two synthetic data with Gaussian and real noise. All experimental results demonstrate that our method outperforms other commonly used methods. The standard receiver operating characteristic (ROC) curves are used to evaluate the experimental results. Availability: http://ranger.uta.edu/∼heng/MS/GDWavelet.html or http://www.naaan.org/nhanguyen/archive.htm Contact: heng
Cramér-Rao bound for time-continuous measurements in linear Gaussian quantum systems
NASA Astrophysics Data System (ADS)
Genoni, Marco G.
2017-01-01
We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve the numerical integration of a stochastic master equation for the corresponding density operator in a Hilbert space of infinite dimension, the formulas here derived depend only on the evolution of first and second moments of the quantum states and thus can be easily evaluated without the need of any approximation. We also present some basic but physically meaningful examples where this result is exploited, calculating analytical and numerical bounds on the estimation of the squeezing parameter for a quantum parametric amplifier and of a constant force acting on a mechanical oscillator in a standard optomechanical scenario.
Exploration, Sampling, And Reconstruction of Free Energy Surfaces with Gaussian Process Regression.
Mones, Letif; Bernstein, Noam; Csányi, Gábor
2016-10-11
Practical free energy reconstruction algorithms involve three separate tasks: biasing, measuring some observable, and finally reconstructing the free energy surface from those measurements. In more than one dimension, adaptive schemes make it possible to explore only relatively low lying regions of the landscape by progressively building up the bias toward the negative of the free energy surface so that free energy barriers are eliminated. Most schemes use the final bias as their best estimate of the free energy surface. We show that large gains in computational efficiency, as measured by the reduction of time to solution, can be obtained by separating the bias used for dynamics from the final free energy reconstruction itself. We find that biasing with metadynamics, measuring a free energy gradient estimator, and reconstructing using Gaussian process regression can give an order of magnitude reduction in computational cost.
Dynamic design of ecological monitoring networks for non-Gaussian spatio-temporal data
Wikle, C.K.; Royle, J. Andrew
2005-01-01
Many ecological processes exhibit spatial structure that changes over time in a coherent, dynamical fashion. This dynamical component is often ignored in the design of spatial monitoring networks. Furthermore, ecological variables related to processes such as habitat are often non-Gaussian (e.g. Poisson or log-normal). We demonstrate that a simulation-based design approach can be used in settings where the data distribution is from a spatio-temporal exponential family. The key random component in the conditional mean function from this distribution is then a spatio-temporal dynamic process. Given the computational burden of estimating the expected utility of various designs in this setting, we utilize an extended Kalman filter approximation to facilitate implementation. The approach is motivated by, and demonstrated on, the problem of selecting sampling locations to estimate July brood counts in the prairie pothole region of the U.S.
NASA Astrophysics Data System (ADS)
Bianchi, Davide; Chiesa, Matteo; Guzzo, Luigi
2015-01-01
As a step towards a more accurate modelling of redshift-space distortions (RSD) in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation r, such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean μ and dispersion σ. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distortions on all scales, fully capturing the overall linear and non-linear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of RSD is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. We also show how this description naturally allows for the Taylor expansion of 1 + ξS(s) around 1 + ξR(r), which leads to the Kaiser linear formula when truncated to second order, explicating its connection with the moments of the velocity distribution functions. More work is needed, but these results indicate a very promising path to make definitive progress in our programme to improve RSD estimators.
Generating Nice Linear Systems for Matrix Gaussian Elimination
ERIC Educational Resources Information Center
Homewood, L. James
2004-01-01
In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…
X-ray optics simulation using Gaussian superposition technique.
Idir, Mourad; Cywiak, Moisés; Morales, Arquímedes; Modi, Mohammed H
2011-09-26
We present an efficient method to perform x-ray optics simulation with high or partially coherent x-ray sources using Gaussian superposition technique. In a previous paper, we have demonstrated that full characterization of optical systems, diffractive and geometric, is possible by using the Fresnel Gaussian Shape Invariant (FGSI) previously reported in the literature. The complex amplitude distribution in the object plane is represented by a linear superposition of complex Gaussians wavelets and then propagated through the optical system by means of the referred Gaussian invariant. This allows ray tracing through the optical system and at the same time allows calculating with high precision the complex wave-amplitude distribution at any plane of observation. This technique can be applied in a wide spectral range where the Fresnel diffraction integral applies including visible, x-rays, acoustic waves, etc. We describe the technique and include some computer simulations as illustrative examples for x-ray optical component. We show also that this method can be used to study partial or total coherence illumination problem.
Oblivious Transfer from the Additive White Gaussian Noise Channel
NASA Astrophysics Data System (ADS)
Isaka, Motohiko
We consider the use of the additive white Gaussian noise channel to achieve information theoretically secure oblivious transfer. A protocol for this primitive that ensures the correctness and privacy for players is presented together with the signal design. We also study the information theoretic efficiency of the protocol, and some more practical issues where the parameter of the channel is unknown to the players.
Navigating the protein fitness landscape with Gaussian processes.
Romero, Philip A; Krause, Andreas; Arnold, Frances H
2013-01-15
Knowing how protein sequence maps to function (the "fitness landscape") is critical for understanding protein evolution as well as for engineering proteins with new and useful properties. We demonstrate that the protein fitness landscape can be inferred from experimental data, using Gaussian processes, a Bayesian learning technique. Gaussian process landscapes can model various protein sequence properties, including functional status, thermostability, enzyme activity, and ligand binding affinity. Trained on experimental data, these models achieve unrivaled quantitative accuracy. Furthermore, the explicit representation of model uncertainty allows for efficient searches through the vast space of possible sequences. We develop and test two protein sequence design algorithms motivated by Bayesian decision theory. The first one identifies small sets of sequences that are informative about the landscape; the second one identifies optimized sequences by iteratively improving the Gaussian process model in regions of the landscape that are predicted to be optimized. We demonstrate the ability of Gaussian processes to guide the search through protein sequence space by designing, constructing, and testing chimeric cytochrome P450s. These algorithms allowed us to engineer active P450 enzymes that are more thermostable than any previously made by chimeragenesis, rational design, or directed evolution.
Velocity fields in non-Gaussian cold dark matter models
NASA Astrophysics Data System (ADS)
Lucchin, F.; Matarrese, S.; Messina, A.; Moscardini, L.; Tormen, G.
1995-02-01
We analyse the large-scale velocity field obtained by N-body simulations of cold dark matter (CDM) models with non-Gaussian primordial density fluctuations, considering models with both positive and negative primordial skewness in the density fluctuation distribution. We study the velocity probability distribution and calculate the dependence of the bulk flow, one-point velocity dispersion and cosmic Mach number on the filtering size. We find that the sign of the primordial skewness of the density field provides poor discriminatory power on the evolved velocity field. All non-Gaussian models considered here tend to have lower velocity dispersion and bulk flow than the standard Gaussian CDM model, while the cosmic Mach number turns out to be a poor statistic in characterizing the models. We also compare the large-scale velocity field of a composite sample of optically selected galaxies as described by the Local Group properties, bulk flow, velocity correlation function and cosmic Mach number with the velocity field of mock catalogues extracted from the N-body simulations. The comparison does not clearly single out the best model: the standard Gaussian model is, however, marginally preferred by the maximum likelihood analysis.
An optimal nonorthogonal separation of the anisotropic Gaussian convolution filter.
Lampert, Christoph H; Wirjadi, Oliver
2006-11-01
We give an analytical and geometrical treatment of what it means to separate a Gaussian kernel along arbitrary axes in R(n), and we present a separation scheme that allows us to efficiently implement anisotropic Gaussian convolution filters for data of arbitrary dimensionality. Based on our previous analysis we show that this scheme is optimal with regard to the number of memory accesses and interpolation operations needed. The proposed method relies on nonorthogonal convolution axes and works completely in image space. Thus, it avoids the need for a fast Fourier transform (FFT)-subroutine. Depending on the accuracy and speed requirements, different interpolation schemes and methods to implement the one-dimensional Gaussian (finite impulse response and infinite impulse response) can be integrated. Special emphasis is put on analyzing the performance and accuracy of the new method. In particular, we show that without any special optimization of the source code, it can perform anisotropic Gaussian filtering faster than methods relying on the FFT.
Non Gaussian Minkowski functionals and extrema counts for CMB maps
NASA Astrophysics Data System (ADS)
Pogosyan, Dmitri; Codis, Sandrine; Pichon, Christophe
2016-10-01
In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky was suggested, but never rigorously developed. In this paper we present such development treating the effects of the curvature and finiteness of the spherical space $S_2$ exactly, without relying on flat-sky approximation. We present Minkowski functionals, including Euler characteristic and extrema counts to the first non-Gaussian correction, suitable for weakly non-Gaussian fields on a sphere, of which CMB is the prime example.
Pseudo-Hermitian ensemble of random Gaussian matrices
NASA Astrophysics Data System (ADS)
Marinello, G.; Pato, M. P.
2016-07-01
It is shown how pseudo-Hermiticity, a necessary condition satisfied by operators of PT symmetric systems can be introduced in the three Gaussian classes of random matrix theory. The model describes transitions from real eigenvalues to a situation in which, apart from a residual number, the eigenvalues are complex conjugate.
Stochastic Schroedinger equations with general complex Gaussian noises
Bassi, Angelo
2003-06-01
Within the framework of non-Markovian stochastic Schroedinger equations, we generalize the results of [W. T. Strunz, Phys. Lett. A 224, 25 (1996)] to the case of general complex Gaussian noises; we analyze the two important cases of purely real and purely imaginary stochastic processes.
The conditional entropy power inequality for Gaussian quantum states
Koenig, Robert
2015-02-15
We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications for entanglement-assisted classical communication over additive bosonic noise channels.
Frozen Gaussian approximation for 3-D seismic wave propagation
NASA Astrophysics Data System (ADS)
Chai, Lihui; Tong, Ping; Yang, Xu
2017-01-01
We present a systematic introduction on applying frozen Gaussian approximation (FGA) to compute synthetic seismograms in 3-D earth models. In this method, seismic wavefield is decomposed into frozen (fixed-width) Gaussian functions, which propagate along ray paths. Rather than the coherent state solution to the wave equation, this method is rigorously derived by asymptotic expansion on phase plane, with analysis of its accuracy determined by the ratio of short wavelength over large domain size. Similar to other ray-based beam methods (e.g. Gaussian beam methods), one can use relatively small number of Gaussians to get accurate approximations of high-frequency wavefield. The algorithm is embarrassingly parallel, which can drastically speed up the computation with a multicore-processor computer station. We illustrate the accuracy and efficiency of the method by comparing it to the spectral element method for a 3-D seismic wave propagation in homogeneous media, where one has the analytical solution as a benchmark. As another proof of methodology, simulations of high-frequency seismic wave propagation in heterogeneous media are performed for 3-D waveguide model and smoothed Marmousi model, respectively. The second contribution of this paper is that, we incorporate the Snell's law into the FGA formulation, and asymptotically derive reflection, transmission and free surface conditions for FGA to compute high-frequency seismic wave propagation in high contrast media. We numerically test these conditions by computing traveltime kernels of different phases in the 3-D crust-over-mantle model.
Frozen Gaussian approximation for three-dimensional seismic wave propagation
NASA Astrophysics Data System (ADS)
Chai, Lihui; Tong, Ping; Yang, Xu
2016-09-01
We present a systematic introduction on applying frozen Gaussian approximation (FGA) to compute synthetic seismograms in three-dimensional earth models. In this method, seismic wavefield is decomposed into frozen (fixed-width) Gaussian functions, which propagate along ray paths. Rather than the coherent state solution to the wave equation, this method is rigorously derived by asymptotic expansion on phase plane, with analysis of its accuracy determined by the ratio of short wavelength over large domain size. Similar to other ray-based beam methods (e.g. Gaussian beam methods), one can use relatively small number of Gaussians to get accurate approximations of high-frequency wavefield. The algorithm is embarrassingly parallel, which can drastically speed up the computation with a multicore-processor computer station. We illustrate the accuracy and efficiency of the method by comparing it to the spectral element method for a three-dimensional (3D) seismic wave propagation in homogeneous media, where one has the analytical solution as a benchmark. As another proof of methodology, simulations of high-frequency seismic wave propagation in heterogeneous media are performed for 3D waveguide model and smoothed Marmousi model respectively. The second contribution of this paper is that, we incorporate the Snell's law into the FGA formulation, and asymptotically derive reflection, transmission and free surface conditions for FGA to compute high-frequency seismic wave propagation in high contrast media. We numerically test these conditions by computing traveltime kernels of different phases in the 3D crust-over-mantle model.
Understanding non-Gaussianity signatures in general relativity
NASA Astrophysics Data System (ADS)
Dai, Liang
2016-03-01
Possible departure from Gaussian statistics in cosmological perturbations can shed much light on the physics of their generation in the primordial Universe. Many of the forthcoming surveys of the large-scale structure with unprecedented survey volume aim at detecting these signatures. However, ignoring the ``gauge artifacts'' in general relativity that arise from the freedom to choose arbitrary space-time coordinates to describe the perturbed Universe can lead to incorrect interpretation on the observational consequences of these non-Gaussian signatures. I present two important examples of non-Gaussianity signatures. I show that in the ``separate universes'' formalism it can be clarified that they are strictly forbidden in canonical inflation scenarios involving only one scalar degree of freedom. One is a quadrupolar direction-dependence in the power spectrum of matter density, which is naively expected from a non-Gaussian correlation between a primordial gravitational wave of super-horizon wavelength and two density perturbations of shorter wavelengths. The other is a galaxy biasing that grows toward large scales, which is naively expected from nonlinearity in general relativity that couples a long-wavelength gravitational potential with two short-wavelength density fluctuations. Conversely, general models of single-field inflation can be falsified if it turns out that either of those signatures is actually observed.
X-ray optics simulation using Gaussian superposition technique
Idir, M.; Cywiak, M.; Morales, A. and Modi, M.H.
2011-09-15
We present an efficient method to perform x-ray optics simulation with high or partially coherent x-ray sources using Gaussian superposition technique. In a previous paper, we have demonstrated that full characterization of optical systems, diffractive and geometric, is possible by using the Fresnel Gaussian Shape Invariant (FGSI) previously reported in the literature. The complex amplitude distribution in the object plane is represented by a linear superposition of complex Gaussians wavelets and then propagated through the optical system by means of the referred Gaussian invariant. This allows ray tracing through the optical system and at the same time allows calculating with high precision the complex wave-amplitude distribution at any plane of observation. This technique can be applied in a wide spectral range where the Fresnel diffraction integral applies including visible, x-rays, acoustic waves, etc. We describe the technique and include some computer simulations as illustrative examples for x-ray optical component. We show also that this method can be used to study partial or total coherence illumination problem.
Optical trapping of spermatozoa using Laguerre-Gaussian laser modes
NASA Astrophysics Data System (ADS)
Dasgupta, Raktim; Ahlawat, Sunita; Verma, Ravi Shanker; Shukla, Sunita; Gupta, Pradeep Kumar
2010-11-01
We report results of a study on the use of Laguerre-Gaussian (LG) modes for optical trapping of spermatozoa. The results show that for a given trap beam power the first-order LG mode (LG01) leads to lower photodamage to the cells without compromising the trapping efficiency.
Triangular Numbers, Gaussian Integers, and KenKen
ERIC Educational Resources Information Center
Watkins, John J.
2012-01-01
Latin squares form the basis for the recreational puzzles sudoku and KenKen. In this article we show how useful several ideas from number theory are in solving a KenKen puzzle. For example, the simple notion of triangular number is surprisingly effective. We also introduce a variation of KenKen that uses the Gaussian integers in order to…
Gaussian quantum steering and its asymmetry in curved spacetime
NASA Astrophysics Data System (ADS)
Wang, Jieci; Cao, Haixin; Jing, Jiliang; Fan, Heng
2016-06-01
We study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of Hawking radiation. We find that thermal noise introduced by the Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside the event horizon, while it generates steerability between Bob and a hypothetical observer anti-Bob inside the event horizon. Unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a "sudden death" and the steering from anti-Bob to Bob experiences a "sudden birth" with increasing Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry cannot exceed ln 2 , which means the state never evolves to an extremal asymmetry state. Furthermore, we obtain the parameter settings that maximize steering asymmetry and find that (i) s =arccosh cosh/2r 1 -sinh2r is the critical point of steering asymmetry and (ii) the attainment of maximal steering asymmetry indicates the transition between one-way steerability and both-way steerability for the two-mode Gaussian state under the influence of Hawking radiation.
On the evaluation of derivatives of Gaussian integrals
NASA Technical Reports Server (NTRS)
Helgaker, Trygve; Taylor, Peter R.
1992-01-01
We show that by a suitable change of variables, the derivatives of molecular integrals over Gaussian-type functions required for analytic energy derivatives can be evaluated with significantly less computational effort than current formulations. The reduction in effort increases with the order of differentiation.
Non-Gaussian microwave background fluctuations from nonlinear gravitational effects
NASA Technical Reports Server (NTRS)
Salopek, D. S.; Kunstatter, G. (Editor)
1991-01-01
Whether the statistics of primordial fluctuations for structure formation are Gaussian or otherwise may be determined if the Cosmic Background Explorer (COBE) Satellite makes a detection of the cosmic microwave-background temperature anisotropy delta T(sub CMB)/T(sub CMB). Non-Gaussian fluctuations may be generated in the chaotic inflationary model if two scalar fields interact nonlinearly with gravity. Theoretical contour maps are calculated for the resulting Sachs-Wolfe temperature fluctuations at large angular scales (greater than 3 degrees). In the long-wavelength approximation, one can confidently determine the nonlinear evolution of quantum noise with gravity during the inflationary epoch because: (1) different spatial points are no longer in causal contact; and (2) quantum gravity corrections are typically small-- it is sufficient to model the system using classical random fields. If the potential for two scalar fields V(phi sub 1, phi sub 2) possesses a sharp feature, then non-Gaussian fluctuations may arise. An explicit model is given where cold spots in delta T(sub CMB)/T(sub CMB) maps are suppressed as compared to the Gaussian case. The fluctuations are essentially scale-invariant.
SINR estimation for SATCOM in the environment with jamming signals
NASA Astrophysics Data System (ADS)
Li, Lun; Wang, Gang; Tian, Xin; Shen, Dan; Pham, Khanh; Blasch, Erik; Chen, Genshe
2016-05-01
In this paper we consider a problem of estimating the signal-to-interference-plus-noise ratio (SINR) for satellite transmission system in the presence of jamming signals. Additive white Gaussian noise (AWGN) channels are considered for baseband quadrature phase shift keying (QPSK) data transmission system. Two interference models are proposed with Gaussian or non-Gaussian interference signals in order to investigate the SINR for different satellite transmission jamming scenarios. Both non-data-aided moment-based and data-aided maxi-mum likelihood SINR estimators are derived for the systems. The normalized mean square errors of the SINR estimation algorithms are examined by means of computer simulations. The numerical results show the robust-ness of derived SINR estimators. The development of the SINR estimators are applicable to a large number of applications utilizing satellite communication systems.
On dimension reduction in Gaussian filters
NASA Astrophysics Data System (ADS)
Solonen, Antti; Cui, Tiangang; Hakkarainen, Janne; Marzouk, Youssef
2016-04-01
A priori dimension reduction is a widely adopted technique for reducing the computational complexity of stationary inverse problems. In this setting, the solution of an inverse problem is parameterized by a low-dimensional basis that is often obtained from the truncated Karhunen-Loève expansion of the prior distribution. For high-dimensional inverse problems equipped with smoothing priors, this technique can lead to drastic reductions in parameter dimension and significant computational savings. In this paper, we extend the concept of a priori dimension reduction to non-stationary inverse problems, in which the goal is to sequentially infer the state of a dynamical system. Our approach proceeds in an offline-online fashion. We first identify a low-dimensional subspace in the state space before solving the inverse problem (the offline phase), using either the method of ‘snapshots’ or regularized covariance estimation. Then this subspace is used to reduce the computational complexity of various filtering algorithms—including the Kalman filter, extended Kalman filter, and ensemble Kalman filter—within a novel subspace-constrained Bayesian prediction-and-update procedure (the online phase). We demonstrate the performance of our new dimension reduction approach on various numerical examples. In some test cases, our approach reduces the dimensionality of the original problem by orders of magnitude and yields up to two orders of magnitude in computational savings.
Receiver deghosting in the t-x domain based on super-Gaussianity
NASA Astrophysics Data System (ADS)
Lu, Wenkai; Xu, Ziqiang; Fang, Zhongyu; Wang, Ruiliang; Yan, Chengzhi
2017-01-01
Deghosting methods in the time-space (t-x) domain have attracted a lot of attention because of their flexibility for various source/receiver configurations. Based on the well-known knowledge that the seismic signal has a super-Gaussian distribution, we present a Super-Gaussianity based Receiver Deghosting (SRD) method in the t-x domain. In our method, we denote the upgoing wave and its ghost (downgoing wave) as a single seismic signal, and express the relationship between the upgoing wave and its ghost using two ghost parameters: the sea surface reflection coefficient and the time-shift between the upgoing wave and its ghost. For a single seismic signal, we estimate these two parameters by maximizing the super-Gaussianity of the deghosted output, which is achieved by a 2D grid search method using an adaptively predefined discrete solution space. Since usually a large number of seismic signals are mixed together in a seismic trace, in the proposed method we divide the seismic trace into overlapping frames using a sliding time window with a step of one time sample, and consider each frame as a replacement for a single seismic signal. For a 2D seismic gather, we obtain two 2D maps of the ghost parameters. By assuming that these two parameters vary slowly in the t-x domain, we apply a 2D average filter to these maps, to improve their reliability further. Finally, these deghosted outputs are merged to form the final deghosted result. To demonstrate the flexibility of the proposed method for arbitrary variable depths of the receivers, we apply it to several synthetic and field seismic datasets acquired by variable depth streamer.
NASA Technical Reports Server (NTRS)
Jacobson, R. A.
1978-01-01
The formulation of the classical Linear-Quadratic-Gaussian stochastic control problem as employed in low thrust navigation analysis is reviewed. A reformulation is then presented which eliminates a potentially unreliable matrix subtraction in the control calculations, improves the computational efficiency, and provides for a cleaner computational interface between the estimation and control processes. Lastly, the application of the U-D factorization method to the reformulated equations is examined with the objective of achieving a complete set of factored equations for the joint estimation and control problem.
NASA Technical Reports Server (NTRS)
Parrish, R. S.; Carter, M. C.
1974-01-01
This analysis utilizes computer simulation and statistical estimation. Realizations of stationary gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrelation parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters was estimated. Thus, given the autocorrelation parameter, crossing level, mean, and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time was calculated.
Asymmetric Gaussian harmonic steering in second-harmonic generation
NASA Astrophysics Data System (ADS)
Olsen, M. K.
2013-11-01
Intracavity second-harmonic generation is one of the simplest of the quantum optical processes and is well within the expertise of most optical laboratories. It is well understood and characterized, both theoretically and experimentally. We show that it can be a source of continuous-variable asymmetric Gaussian harmonic steering with fields which have a coherent excitation, hence combining the important effects of harmonic entanglement and asymmetric steering in one easily controllable device, adjustable by the simple means of tuning the cavity loss rates at the fundamental and harmonic frequencies. We find that whether quantum steering is available via the standard measurements of the Einstein-Podolsky-Rosen correlations can depend on which quadrature measurements are inferred from output spectral measurements of the fundamental and the harmonic. Altering the ratios of the cavity loss rates can be used to tune the regions where symmetric steering is available, with the results becoming asymmetric over all frequencies as the cavity damping at the fundamental frequency becomes significantly greater than at the harmonic. This asymmetry and its functional dependence on frequency is a potential new tool for experimental quantum information science, with possible utility for quantum key distribution. Although we show the effect here for Gaussian measurements of the quadratures, and cannot rule out a return of the steering symmetry for some class of non-Gaussian measurements, we note here that the system obeys Gaussian statistics in the operating regime investigated and Gaussian inference is at least as accurate as any other method for calculating the necessary correlations. Perhaps most importantly, this system is simpler than any other methods we are aware of which have been used or proposed to create asymmetric steering.
Near grazing scattering from non-Gaussian ocean surfaces
NASA Technical Reports Server (NTRS)
Kim, Yunjin; Rodriguez, Ernesto
1993-01-01
We investigate the behavior of the scattered electromagnetic waves from non-Gaussian ocean surfaces at near grazing incidence. Even though the scattering mechanisms at moderate incidence angles are relatively well understood, the same is not true for near grazing rough surface scattering. However, from the experimental ocean scattering data, it has been observed that the backscattering cross section of a horizontally polarized wave can be as large as the vertical counterpart at near grazing incidence. In addition, these returns are highly intermittent in time. There have been some suggestions that these unexpected effects may come from shadowing or feature scattering. Using numerical scattering simulations, it can be shown that the horizontal backscattering cannot be larger than the vertical one for the Gaussian surfaces. Our main objective of this study is to gain a clear understanding of scattering mechanisms underlying the near grazing ocean scattering. In order to evaluate the backscattering cross section from ocean surfaces at near grazing incidence, both the hydrodynamic modeling of ocean surfaces and an accurate near grazing scattering theory are required. For the surface modeling, we generate Gaussian surfaces from the ocean surface power spectrum which is derived using several experimental data. Then, weakly nonlinear large scale ocean surfaces are generated following Longuet-Higgins. In addition, the modulation of small waves by large waves is included using the conservation of wave action. For surface scattering, we use MOM (Method of Moments) to calculate the backscattering from scattering patches with the two scale shadowing approximation. The differences between Gaussian and non-Gaussian surface scattering at near grazing incidence are presented.
Estimating the uncertainty in underresolved nonlinear dynamics
Chorin, Alelxandre; Hald, Ole
2013-06-12
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise term that describes the uncertainty turns out to be neither Markovian nor Gaussian. It is argued that this is the general situation.
Jiang, Mingxin; Pan, Zhigeng; Tang, Zhenzhou
2017-01-01
Visual object tracking technology is one of the key issues in computer vision. In this paper, we propose a visual object tracking algorithm based on cross-modality featuredeep learning using Gaussian-Bernoulli deep Boltzmann machines (DBM) with RGB-D sensors. First, a cross-modality featurelearning network based on aGaussian-Bernoulli DBM is constructed, which can extract cross-modality features of the samples in RGB-D video data. Second, the cross-modality features of the samples are input into the logistic regression classifier, andthe observation likelihood model is established according to the confidence score of the classifier. Finally, the object tracking results over RGB-D data are obtained using aBayesian maximum a posteriori (MAP) probability estimation algorithm. The experimental results show that the proposed method has strong robustness to abnormal changes (e.g., occlusion, rotation, illumination change, etc.). The algorithm can steadily track multiple targets and has higher accuracy. PMID:28075373
Gang, Luo; Chutatape, Opas; Krishnan, Shankar M
2002-02-01
In this paper, the fitness of estimating vessel profiles with Gaussian function is evaluated and an amplitude-modified second-order Gaussian filter is proposed for the detection and measurement of vessels. Mathematical analysis is given and supported by a simulation and experiments to demonstrate that the vessel width can be measured in linear relationship with the "spreading factor" of the matched filter when the magnitude coefficient of the filter is suitably assigned. The absolute value of vessel diameter can be determined simply by using a precalibrated line, which is typically required since images are always system dependent. The experiment shows that the inclusion of the width measurement in the detection process can improve the performance of matched filter and result in a significant increase in success rate of detection.
Serdyuk, Vladimir; Rudnitsky, Anton
2015-05-01
We present an approximate 2D asymptotic analytic theory of light field excitation in a plane thin dielectric layer under conditions of frustrated total internal reflection, when an inclined Gaussian beam, falling from a triangular prism, excites a decaying field in air spacing between a prism and a plane dielectric. Ignoring the radiation scattering on the sharp edges of a prism, we have obtained the formulas that allow us to compute spatial structures of an electromagnetic field in every point of space and to estimate the integral efficiency of waveguide mode excitation in a plane dielectric layer and the total energy of a reflected beam. It is shown that the width of an initial Gaussian beam has an effect on waveguide mode intensity.
Jiang, Mingxin; Pan, Zhigeng; Tang, Zhenzhou
2017-01-10
Visual object tracking technology is one of the key issues in computer vision. In this paper, we propose a visual object tracking algorithm based on cross-modality featuredeep learning using Gaussian-Bernoulli deep Boltzmann machines (DBM) with RGB-D sensors. First, a cross-modality featurelearning network based on aGaussian-Bernoulli DBM is constructed, which can extract cross-modality features of the samples in RGB-D video data. Second, the cross-modality features of the samples are input into the logistic regression classifier, andthe observation likelihood model is established according to the confidence score of the classifier. Finally, the object tracking results over RGB-D data are obtained using aBayesian maximum a posteriori (MAP) probability estimation algorithm. The experimental results show that the proposed method has strong robustness to abnormal changes (e.g., occlusion, rotation, illumination change, etc.). The algorithm can steadily track multiple targets and has higher accuracy.
Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic
YOKOYAMA, Jun’ichi
2014-01-01
After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student’s t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case. PMID:25504231
NASA Astrophysics Data System (ADS)
Piringer, Martin; Knauder, Werner; Petz, Erwin; Schauberger, Günther
2016-09-01
Direction-dependent separation distances to avoid odour annoyance, calculated with the Gaussian Austrian Odour Dispersion Model AODM and the Lagrangian particle diffusion model LASAT at two sites, are analysed and compared. The relevant short-term peak odour concentrations are calculated with a stability-dependent peak-to-mean algorithm. The same emission and meteorological data, but model-specific atmospheric stability classes are used. The estimate of atmospheric stability is obtained from three-axis ultrasonic anemometers using the standard deviations of the three wind components and the Obukhov stability parameter. The results are demonstrated for the Austrian villages Reidling and Weissbach with very different topographical surroundings and meteorological conditions. Both the differences in the wind and stability regimes as well as the decrease of the peak-to-mean factors with distance lead to deviations in the separation distances between the two sites. The Lagrangian model, due to its model physics, generally calculates larger separation distances. For worst-case calculations necessary with environmental impact assessment studies, the use of a Lagrangian model is therefore to be preferred over that of a Gaussian model. The study and findings relate to the Austrian odour impact criteria.
NASA Astrophysics Data System (ADS)
Shin, Min-Su; Sekora, Michael; Byun, Yong-Ik
2009-12-01
We present a new framework to detect various types of variable objects within massive astronomical time series data. Assuming that the dominant population of objects is non-variable, we find outliers from this population by using a non-parametric Bayesian clustering algorithm based on an infinite Gaussian mixture model (GMM) and the Dirichlet process. The algorithm extracts information from a given data set, which is described by six variability indices. The GMM uses those variability indices to recover clusters that are described by six-dimensional multivariate Gaussian distributions, allowing our approach to consider the sampling pattern of time series data, systematic biases, the number of data points for each light curve and photometric quality. Using the Northern Sky Variability Survey data, we test our approach and prove that the infinite GMM is useful at detecting variable objects, while providing statistical inference estimation that suppresses false detection. The proposed approach will be effective in the exploration of future surveys such as Gaia, Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) and Large Synoptic Survey Telescope (LSST), which will produce massive time series data.
Nonlinear derating of high-intensity focused ultrasound beams using Gaussian modal sums.
Dibaji, Seyed Ahmad Reza; Banerjee, Rupak K; Soneson, Joshua E; Myers, Matthew R
2013-11-01
A method is introduced for using measurements made in water of the nonlinear acoustic pressure field produced by a high-intensity focused ultrasound transducer to compute the acoustic pressure and temperature rise in a tissue medium. The acoustic pressure harmonics generated by nonlinear propagation are represented as a sum of modes having a Gaussian functional dependence in the radial direction. While the method is derived in the context of Gaussian beams, final results are applicable to general transducer profiles. The focal acoustic pressure is obtained by solving an evolution equation in the axial variable. The nonlinear term in the evolution equation for tissue is modeled using modal amplitudes measured in water and suitably reduced using a combination of "source derating" (experiments in water performed at a lower source acoustic pressure than in tissue) and "endpoint derating" (amplitudes reduced at the target location). Numerical experiments showed that, with proper combinations of source derating and endpoint derating, direct simulations of acoustic pressure and temperature in tissue could be reproduced by derating within 5% error. Advantages of the derating approach presented include applicability over a wide range of gains, ease of computation (a single numerical quadrature is required), and readily obtained temperature estimates from the water measurements.
Content-adaptive pentary steganography using the multivariate generalized Gaussian cover model
NASA Astrophysics Data System (ADS)
Sedighi, Vahid; Fridrich, Jessica; Cogranne, Rémi
2015-03-01
The vast majority of steganographic schemes for digital images stored in the raster format limit the amplitude of embedding changes to the smallest possible value. In this paper, we investigate the possibility to further improve the empirical security by allowing the embedding changes in highly textured areas to have a larger amplitude and thus embedding there a larger payload. Our approach is entirely model driven in the sense that the probabilities with which the cover pixels should be changed by a certain amount are derived from the cover model to minimize the power of an optimal statistical test. The embedding consists of two steps. First, the sender estimates the cover model parameters, the pixel variances, when modeling the pixels as a sequence of independent but not identically distributed generalized Gaussian random variables. Then, the embedding change probabilities for changing each pixel by 1 or 2, which can be transformed to costs for practical embedding using syndrome-trellis codes, are computed by solving a pair of non-linear algebraic equations. Using rich models and selection-channel-aware features, we compare the security of our scheme based on the generalized Gaussian model with pentary versions of two popular embedding algorithms: HILL and S-UNIWARD.
NASA Astrophysics Data System (ADS)
Gluzman, Igal; Cohen, Jacob; Oshman, Yaakov
2016-11-01
We introduce a statistical method based on Gaussianization to estimate the nonlinear calibration curve of a hot-wire probe, that relates the input flow velocity to the output (measured) voltage. The method uses as input a measured sequence of voltage samples, corresponding to different unknown flow velocities in the desired operational range, and only two measured voltages along with their known (calibrated) flow velocities. The novel method is validated against standard calibration methods using data acquired by hot-wire probes using wind-tunnel experiments. We demonstrate our new calibration technique by placing the hot-wire probe at certain region downstream of a cube-shaped body in a free stream of air flow. For testing our calibration method we rely on flow statistics that exist, among others, in a certain region of a turbulent wake formed downstream of the cube-shaped body. The specific properties are: first, the velocity signal in the wake should be as close to Gaussian as possible. Second, the signal should cover the desired velocity range that should be calibrated. The appropriate region to place our probe is determined via computation of the first four statistical moments of the measured signals in different regions of the wake.
Gaussian wavelet based dynamic filtering (GWDF) method for medical ultrasound systems.
Wang, Peidong; Shen, Yi; Wang, Qiang
2007-05-01
In this paper, a novel dynamic filtering method using Gaussian wavelet filters is proposed to remove noise from ultrasound echo signal. In the proposed method, a mother wavelet is first selected with its central frequency (CF) and frequency bandwidth (FB) equal to those of the transmitted signal. The actual frequency of the received signal at a given depth is estimated through the autocorrelation technique. Then the mother wavelet is dilated using the ratio between the transmitted central frequency and the actual frequency as the scale factor. The generated daughter wavelet is finally used as the dynamic filter at this depth. Frequency-demodulated Gaussian wavelet is chosen in this paper because its power spectrum is well-matched with that of the transmitted ultrasound signal. The proposed method is evaluated by simulations using Field II program. Experiments are also conducted out on a standard ultrasound phantom using a 192-element transducer with the center frequency of 5 MHz. The phantom contains five point targets, five circular high scattering regions with diameters of 2, 3, 4, 5, 6 mm respectively, and five cysts with diameters of 6, 5, 4, 3, 2 mm respectively. Both simulation and experimental results show that optimal signal-to-noise ratio (SNR) can be obtained and useful information can be extracted along the depth direction irrespective of the diagnostic objects.
The Rician inverse Gaussian distribution: a new model for non-Rayleigh signal amplitude statistics.
Eltoft, Torbjørn
2005-11-01
In this paper, we introduce a new statistical distribution for modeling non-Rayleigh amplitude statistics, which we have called the Rician inverse Gaussian (RiIG) distribution. It is a mixture of the Rice distribution and the inverse Gaussian distribution. The probability density function (pdf) is given in closed form as a function of three parameters. This makes the pdf very flexible in the sense that it may be fitted to a variety of shapes, ranging from the Rayleigh-shaped pdf to a noncentral chi2-shaped pdf. The theoretical basis of the new model is quite thoroughly discussed, and we also give two iterative algorithms for estimating its parameters from data. Finally, we include some modeling examples, where we have tested the ability of the distribution to represent locale amplitude histograms of linear medical ultrasound data and single-look synthetic aperture radar data. We compare the goodness of fit of the RiIG model with that of the K model, and, in most cases, the new model turns out as a better statistical model for the data. We also include a series of log-likelihood tests to evaluate the predictive performance of the proposed model.
Upscaling for unsaturated flow for non-Gaussian heterogeneous porous media
NASA Astrophysics Data System (ADS)
Neuweiler, Insa; Vogel, Hans-JöRg
2007-03-01
Large-scale models of transient flow processes in the unsaturated zone require, in general, upscaling of the flow problem in order to capture the impact of heterogeneities on a small scale, which cannot be resolved by the model. Effective parameters for the upscaled models are often derived from second-order stochastic properties of the parameter fields. Such properties are good quantifications for parameter fields, which are multi-Gaussian. However, the structure of soil does rarely resemble these kinds of fields. The non-multi-Gaussian field properties can lead to strong discrepancies between predictions of upscaled models and the averaged real flow process. In particular, the connected paths of parameter ranges of the medium are important features, which are usually not taken into account in stochastic approaches. They are determined here by the Euler number of one-cut indicator fields. Methods to predict effective parameters are needed that incorporate this type of information. We discuss different simple and fast approaches for estimating the effective parameter for upscaled models of slow transient flow processes in the unsaturated zone, where connected paths of the material may be taken into account. Upscaled models are derived with the assumption of capillary equilibrium. The effective parameters are calculated using effective media approaches. We also discuss the limits of the applicability of these methods.
Huang, Yi-Fei; Golding, G Brian
2014-01-01
A critical question in biology is the identification of functionally important amino acid sites in proteins. Because functionally important sites are under stronger purifying selection, site-specific substitution rates tend to be lower than usual at these sites. A large number of phylogenetic models have been developed to estimate site-specific substitution rates in proteins and the extraordinarily low substitution rates have been used as evidence of function. Most of the existing tools, e.g. Rate4Site, assume that site-specific substitution rates are independent across sites. However, site-specific substitution rates may be strongly correlated in the protein tertiary structure, since functionally important sites tend to be clustered together to form functional patches. We have developed a new model, GP4Rate, which incorporates the Gaussian process model with the standard phylogenetic model to identify slowly evolved regions in protein tertiary structures. GP4Rate uses the Gaussian process to define a nonparametric prior distribution of site-specific substitution rates, which naturally captures the spatial correlation of substitution rates. Simulations suggest that GP4Rate can potentially estimate site-specific substitution rates with a much higher accuracy than Rate4Site and tends to report slowly evolved regions rather than individual sites. In addition, GP4Rate can estimate the strength of the spatial correlation of substitution rates from the data. By applying GP4Rate to a set of mammalian B7-1 genes, we found a highly conserved region which coincides with experimental evidence. GP4Rate may be a useful tool for the in silico prediction of functionally important regions in the proteins with known structures.
Constraining primordial non-Gaussianity with cosmological weak lensing: shear and flexion
Fedeli, C.; Bartelmann, M.; Moscardini, L. E-mail: bartelmann@uni-heidelberg.de
2012-10-01
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{sub 8}, are at the level of Δf{sub 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{sub NL} ∼ 340 (equilateral shape) up to Δf{sub NL} ∼ 500 (orthogonal shape). Also, constraints on the level of non-Gaussianity and on the amplitude of the matter power spectrum σ{sub 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{sub max} = 20,000 cosmic flexion, while
Bayesian and maximum likelihood estimation of hierarchical response time models
Farrell, Simon; Ludwig, Casimir
2008-01-01
Hierarchical (or multilevel) statistical models have become increasingly popular in psychology in the last few years. We consider the application of multilevel modeling to the ex-Gaussian, a popular model of response times. Single-level estimation is compared with hierarchical estimation of parameters of the ex-Gaussian distribution. Additionally, for each approach maximum likelihood (ML) estimation is compared with Bayesian estimation. A set of simulations and analyses of parameter recovery show that although all methods perform adequately well, hierarchical methods are better able to recover the parameters of the ex-Gaussian by reducing the variability in recovered parameters. At each level, little overall difference was observed between the ML and Bayesian methods. PMID:19001592
Research on Bayes matting algorithm based on Gaussian mixture model
NASA Astrophysics Data System (ADS)
Quan, Wei; Jiang, Shan; Han, Cheng; Zhang, Chao; Jiang, Zhengang
2015-12-01
The digital matting problem is a classical problem of imaging. It aims at separating non-rectangular foreground objects from a background image, and compositing with a new background image. Accurate matting determines the quality of the compositing image. A Bayesian matting Algorithm Based on Gaussian Mixture Model is proposed to solve this matting problem. Firstly, the traditional Bayesian framework is improved by introducing Gaussian mixture model. Then, a weighting factor is added in order to suppress the noises of the compositing images. Finally, the effect is further improved by regulating the user's input. This algorithm is applied to matting jobs of classical images. The results are compared to the traditional Bayesian method. It is shown that our algorithm has better performance in detail such as hair. Our algorithm eliminates the noise well. And it is very effectively in dealing with the kind of work, such as interested objects with intricate boundaries.
Laser plasma accelerator driven by a super-Gaussian pulse
NASA Astrophysics Data System (ADS)
Ostermayr, Tobias; Petrovics, Stefan; Iqbal, Khalid; Klier, Constantin; Ruhl, Hartmut; Nakajima, Kazuhisa; Deng, Aihua; Zhang, Xiaomei; Shen, Baifei; Liu, Jiansheng; Li, Ruxin; Xu, Zhizhan; Tajima, Toshiki; Tajima
2012-08-01
A laser wakefield accelerator (LWFA) with a weak focusing force is considered to seek improved beam quality in LWFA. We employ super-Gaussian laser pulses to generate the wakefield and study the behavior of the electron beam dynamics and synchrotron radiation arising from the transverse betatron oscillations through analysis and computation. We note that the super-Gaussian wakefields radically reduce the betatron oscillations and make the electron orbits mainly ballistic over a single stage. This feature permits to obtain small emittance and thus high luminosity, while still benefitting from the low-density operation of LWFA (Nakajima et al. 2011 Phys. Rev. ST Accel. Beams 14, 091301), such as the reduced radiation loss, less number of stages, less beam instabilities, and less required wall plug power than in higher density regimes.
Statistics of Gaussian packets on metric and decorated graphs.
Chernyshev, V L; Shafarevich, A I
2014-01-28
We study a semiclassical asymptotics of the Cauchy problem for a time-dependent Schrödinger equation on metric and decorated graphs with a localized initial function. A decorated graph is a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds. The main term of an asymptotic solution at an arbitrary finite time is a sum of Gaussian packets and generalized Gaussian packets (localized near a certain set of codimension one). We study the number of packets as time tends to infinity. We prove that under certain assumptions this number grows in time as a polynomial and packets fill the graph uniformly. We discuss a simple example of the opposite situation: in this case, a numerical experiment shows a subexponential growth.
Mean-field fluid behavior of the gaussian core model
Louis; Bolhuis; Hansen
2000-12-01
We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger [J. Chem. Phys. 65, 3968 (1976)], behaves as a weakly correlated "mean-field fluid" over a surprisingly wide density and temperature range. In the bulk, the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated hypernetted chain integral equation. The resulting pressure deviates very little from a simple mean-field-like quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against demixing at high densities. Possible implications for semidilute polymer solutions are discussed.
Stability criterion for Gaussian pulse propagation through negative index materials
Joseph, Ancemma; Porsezian, K.
2010-02-15
We analyze the dynamics of propagation of a Gaussian light pulse through a medium having a negative index of refraction employing the recently reported projection operator technique. The governing modified nonlinear Schroedinger equation, obtained by taking into account the Drude dispersive model, is expressed in terms of the parameters of Gaussian pulse, called collective variables, such as width, amplitude, chirp, and phase. This approach yields a system of ordinary differential equations for the evolution of all the pulse parameters. We demonstrate the dependence of stability of the fixed-point solutions of these ordinary differential equations on the linear and nonlinear dispersion parameters. In addition, we validate the analytical approach numerically utilizing the method of split-step Fourier transform.
Tissue deformation induced by radiation force from Gaussian transducers.
Myers, Matthew R
2006-05-01
Imaging techniques based upon the tissue mechanical response to an acoustic radiation force are being actively researched. In this paper a model for predicting steady-state tissue displacement induced by a radiation force arising from the absorption of Gaussian ultrasound beams is presented. A simple analytic expression is derived that agrees closely with the numerical quadrature of the displacement convolution integrals. The analytic result reveals the dependence of the steady-state axial displacement upon the operational parameters, e.g., an inverse proportional relationship to the tissue shear modulus. The derivation requires that the transducer radius be small compared to the focal length, but accurate results were obtained for transducer radii comparable to the focal length. Favorable comparisons with displacement predictions for non-Gaussian transducers indicate that the theory is also useful for a broader range of transducer intensity profiles.
Diffraction of Gaussian beams on intracavity Bragg gratings
NASA Astrophysics Data System (ADS)
Bitauld, David; Menez, Ludivine; Zaquine, Isabelle; Maruani, Alain; Frey, Robert
2005-06-01
The diffraction of Gaussian beams on intracavity Bragg gratings is analyzed theoretically. For reasonable waists the associated beam divergence does not significantly influence the diffraction efficiency of such devices. Nevertheless, the tilt angle of the incident beam, imposed by the Bragg resonance condition, strongly reduces the diffraction efficiency at short grating periods. However, the angular selectivity can be maintained if the Fabry-Perot cavity is tuned to the incident beam direction, which allows the use of small-volume holograms together with a dense angular multiplex. This theoretical analysis can be applied to the optimization of the diffraction properties of Gaussian beams on any intracavity Bragg grating, which could then be used for free-space parallel signal processing.
Elliptic Hermite-Gaussian soliton in anisotropic strong nonlocal media
NASA Astrophysics Data System (ADS)
Wang, Qing; Li, JingZhen
2016-01-01
The propagation of elliptic Hermite-Gaussian (HG) beam in strong nonlocal media with elliptic Gaussian-shaped response function was studied by variational approach as well as numerical simulate. The evolution equations of the beam widths in x- and y-directions are obtained and the elliptic HG soliton is found. For forming such a soliton, the ratio of the square of the beam width must be proportional to the ratio of the characteristic length of the material, and the initial power should be equal to the two critical powers in x- and y-directions. For the anisotropic nonlinearity of the media, the instability of the high-order elliptic HG beam is increase as the increase of the order.
Minkowski structure for purity and entanglement of Gaussian bipartite states
NASA Astrophysics Data System (ADS)
de Oliveira, Marcos C.; Nicacio, Fernando; Mizrahi, Salomon S.
2013-11-01
The relation between the symplectic and Lorentz groups is explored to investigate entanglement features in a two-mode bipartite Gaussian state. We verify that the correlation matrix of arbitrary Gaussian states can be associated with a hyperbolic space with a Minkowski metric, which is divided in two regions: separabilitylike and entanglementlike, in equivalence to timelike and spacelike in special relativity. This correspondence naturally allows the definition of two insightful invariant squared distance measures: one related to the purity and another related to amount of entanglement. The second distance allows us to define a measure for entanglement in terms of the invariant interval between the given state and its closest separable state, given in a natural manner without the requirement of a minimization procedure.
Optimal focusing conditions of lenses using Gaussian beams
Franco, Juan Manuel; Cywiak, Moisés; Cywiak, David; ...
2016-04-02
By using the analytical equations of the propagation of Gaussian beams in which truncation exhibits negligible consequences, we describe a method that uses the value of the focal length of a focusing lens to classify its focusing performance. In this study, we show that for different distances between a laser and a focusing lens there are different planes where best focusing conditions can be obtained and we demonstrate how the value of the focal length impacts the lens focusing properties. To perform the classification we introduce the term delimiting focal length. As the value of the focal length used inmore » wave propagation theory is nominal and difficult to measure accurately, we describe an experimental approach to calculate its value matching our analytical description. Finally, we describe possible applications of the results for characterizing Gaussian sources, for measuring focal lengths and/or alternatively for characterizing piston-like movements.« less
Optimal focusing conditions of lenses using Gaussian beams
Franco, Juan Manuel; Cywiak, Moisés; Cywiak, David; Mourad, Idir
2016-04-02
By using the analytical equations of the propagation of Gaussian beams in which truncation exhibits negligible consequences, we describe a method that uses the value of the focal length of a focusing lens to classify its focusing performance. In this study, we show that for different distances between a laser and a focusing lens there are different planes where best focusing conditions can be obtained and we demonstrate how the value of the focal length impacts the lens focusing properties. To perform the classification we introduce the term delimiting focal length. As the value of the focal length used in wave propagation theory is nominal and difficult to measure accurately, we describe an experimental approach to calculate its value matching our analytical description. Finally, we describe possible applications of the results for characterizing Gaussian sources, for measuring focal lengths and/or alternatively for characterizing piston-like movements.
Interpretation of Extinction in Gaussian-Beam Scattering
NASA Technical Reports Server (NTRS)
Lock, James A.
1995-01-01
The extinction efficiency for the interaction of a plane wave with a large nonabsorbing spherical particle is approximately 2.0. When a Gaussian beam of half-width w(sub 0) is incident upon a spherical particle of radius a with w(sub 0)/a less than 1, the extinction efficiency attains unexpectedly high or low values, contrary to intuitive expectations. The reason for this is associated with the so-called compensating term in the scattered field, which cancels the field of the Gaussian beam behind the particle, thereby producing the particle's shadow. I introduce a decomposition of the total exterior field into incoming and outgoing portions that are free of compensating terms. It is then shown that a suitably defined interaction efficiency has the intuitively expected asymptotic values of 2.0 for w(sub 0)/a much greater than 1 and 1.0 for w(sub 0)/a much less than 1.
Weighted Feature Gaussian Kernel SVM for Emotion Recognition
Jia, Qingxuan
2016-01-01
Emotion recognition with weighted feature based on facial expression is a challenging research topic and has attracted great attention in the past few years. This paper presents a novel method, utilizing subregion recognition rate to weight kernel function. First, we divide the facial expression image into some uniform subregions and calculate corresponding recognition rate and weight. Then, we get a weighted feature Gaussian kernel function and construct a classifier based on Support Vector Machine (SVM). At last, the experimental results suggest that the approach based on weighted feature Gaussian kernel function has good performance on the correct rate in emotion recognition. The experiments on the extended Cohn-Kanade (CK+) dataset show that our method has achieved encouraging recognition results compared to the state-of-the-art methods. PMID:27807443
Statistics of Gaussian packets on metric and decorated graphs
Chernyshev, V. L.; Shafarevich, A. I.
2014-01-01
We study a semiclassical asymptotics of the Cauchy problem for a time-dependent Schrödinger equation on metric and decorated graphs with a localized initial function. A decorated graph is a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds. The main term of an asymptotic solution at an arbitrary finite time is a sum of Gaussian packets and generalized Gaussian packets (localized near a certain set of codimension one). We study the number of packets as time tends to infinity. We prove that under certain assumptions this number grows in time as a polynomial and packets fill the graph uniformly. We discuss a simple example of the opposite situation: in this case, a numerical experiment shows a subexponential growth. PMID:24344346