A tight Cramér-Rao bound for joint parameter estimation with a pure two-mode squeezed probe

NASA Astrophysics Data System (ADS)

Bradshaw, Mark; Assad, Syed M.; Lam, Ping Koy

2017-08-01

We calculate the Holevo Cramér-Rao bound for estimation of the displacement experienced by one mode of an two-mode squeezed vacuum state with squeezing r and find that it is equal to 4 exp ⁡ (- 2 r). This equals the sum of the mean squared error obtained from a dual homodyne measurement, indicating that the bound is tight and that the dual homodyne measurement is optimal.

Simple Form of MMSE Estimator for Super-Gaussian Prior Densities

NASA Astrophysics Data System (ADS)

Kittisuwan, Pichid

2015-04-01

The denoising method that become popular in recent years for additive white Gaussian noise (AWGN) are Bayesian estimation techniques e.g., maximum a posteriori (MAP) and minimum mean square error (MMSE). In super-Gaussian prior densities, it is well known that the MMSE estimator in such a case has a complicated form. In this work, we derive the MMSE estimation with Taylor series. We show that the proposed estimator also leads to a simple formula. An extension of this estimator to Pearson type VII prior density is also offered. The experimental result shows that the proposed estimator to the original MMSE nonlinearity is reasonably good.

Shot noise-limited Cramér-Rao bound and algorithmic sensitivity for wavelength shifting interferometry

NASA Astrophysics Data System (ADS)

Chen, Shichao; Zhu, Yizheng

2017-02-01

Sensitivity is a critical index to measure the temporal fluctuation of the retrieved optical pathlength in quantitative phase imaging system. However, an accurate and comprehensive analysis for sensitivity evaluation is still lacking in current literature. In particular, previous theoretical studies for fundamental sensitivity based on Gaussian noise models are not applicable to modern cameras and detectors, which are dominated by shot noise. In this paper, we derive two shot noiselimited theoretical sensitivities, Cramér-Rao bound and algorithmic sensitivity for wavelength shifting interferometry, which is a major category of on-axis interferometry techniques in quantitative phase imaging. Based on the derivations, we show that the shot noise-limited model permits accurate estimation of theoretical sensitivities directly from measured data. These results can provide important insights into fundamental constraints in system performance and can be used to guide system design and optimization. The same concepts can be generalized to other quantitative phase imaging techniques as well.

Adaptive channel estimation for soft decision decoding over non-Gaussian optical channel

NASA Astrophysics Data System (ADS)

Xiang, Jing-song; Miao, Tao-tao; Huang, Sheng; Liu, Huan-lin

2016-10-01

An adaptive priori likelihood ratio (LLR) estimation method is proposed over non-Gaussian channel in the intensity modulation/direct detection (IM/DD) optical communication systems. Using the nonparametric histogram and the weighted least square linear fitting in the tail regions, the LLR is estimated and used for the soft decision decoding of the low-density parity-check (LDPC) codes. This method can adapt well to the three main kinds of intensity modulation/direct detection (IM/DD) optical channel, i.e., the chi-square channel, the Webb-Gaussian channel and the additive white Gaussian noise (AWGN) channel. The performance penalty of channel estimation is neglected.

Hartebeesthoek Radio Astronomy Observatory (HartRAO)

NASA Technical Reports Server (NTRS)

Nickola, Marisa; Gaylard, Mike; Quick, Jonathan; Combrinck, Ludwig

2013-01-01

HartRAO provides the only fiducial geodetic site in Africa, and it participates in global networks for VLBI, GNSS, SLR, and DORIS. This report provides an overview of geodetic VLBI activities at HartRAO during 2012, including the conversion of a 15-m alt-az radio telescope to an operational geodetic VLBI antenna.

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

PubMed

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

2016-01-01

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

Gaussian Process Interpolation for Uncertainty Estimation in Image Registration

PubMed Central

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

2014-01-01

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

Noise Estimation and Quality Assessment of Gaussian Noise Corrupted Images

NASA Astrophysics Data System (ADS)

Kamble, V. M.; Bhurchandi, K.

2018-03-01

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

Versatile Gaussian probes for squeezing estimation

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Measurements satisfying the quantum Cramer-Rao equality

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

Luczak, Andrzej

The situation where the quantum Cramer-Rao inequality for a general measurement becomes equality is analyzed in some detail in the case of a family of pure states. In particular, it turns out that under some natural assumptions, the measurement in question is simple, and the states must have a special form. This fact in turn allows us to obtain in the two-dimensional case a characterization of the pure states for which the quantum Cramer-Rao equality holds.

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

PubMed

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

2013-03-01

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

An unbiased risk estimator for image denoising in the presence of mixed poisson-gaussian noise.

PubMed

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.

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

PubMed

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

2017-08-01

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

Estimating Mixture of Gaussian Processes by Kernel Smoothing

PubMed Central

Huang, Mian; Li, Runze; Wang, Hansheng; Yao, Weixin

2014-01-01

When the functional data are not homogeneous, e.g., there exist multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimation procedure for the Mixture of Gaussian Processes, to incorporate both functional and inhomogeneous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. The model is shown to be identifiable, and can be estimated efficiently by a combination of the ideas from EM algorithm, kernel regression, and functional principal component analysis. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset. PMID:24976675

A double-gaussian, percentile-based method for estimating maximum blood flow velocity.

PubMed

Marzban, Caren; Illian, Paul R; Morison, David; Mourad, Pierre D

2013-11-01

Transcranial Doppler sonography allows for the estimation of blood flow velocity, whose maximum value, especially at systole, is often of clinical interest. Given that observed values of flow velocity are subject to noise, a useful notion of "maximum" requires a criterion for separating the signal from the noise. All commonly used criteria produce a point estimate (ie, a single value) of maximum flow velocity at any time and therefore convey no information on the distribution or uncertainty of flow velocity. This limitation has clinical consequences especially for patients in vasospasm, whose largest flow velocities can be difficult to measure. Therefore, a method for estimating flow velocity and its uncertainty is desirable. A gaussian mixture model is used to separate the noise from the signal distribution. The time series of a given percentile of the latter, then, provides a flow velocity envelope. This means of estimating the flow velocity envelope naturally allows for displaying several percentiles (e.g., 95th and 99th), thereby conveying uncertainty in the highest flow velocity. Such envelopes were computed for 59 patients and were shown to provide reasonable and useful estimates of the largest flow velocities compared to a standard algorithm. Moreover, we found that the commonly used envelope was generally consistent with the 90th percentile of the signal distribution derived via the gaussian mixture model. Separating the observed distribution of flow velocity into a noise component and a signal component, using a double-gaussian mixture model, allows for the percentiles of the latter to provide meaningful measures of the largest flow velocities and their uncertainty.

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

NASA Astrophysics Data System (ADS)

Berg, J.; Mann, J.; Natarajan, A.; Patton, E. G.

2014-12-01

In wind energy applications the turbulent velocity field of the Atmospheric Boundary Layer (ABL) is often characterised by Gaussian probability density functions. When estimating the dynamical loads on wind turbines this has been the rule more than anything else. From numerous studies in the laboratory, in Direct Numerical Simulations, and from in-situ measurements of the ABL we know, however, that turbulence is not purely Gaussian: the smallest and fastest scales often exhibit extreme behaviour characterised by strong non-Gaussian statistics. In this contribution we want to investigate whether these non-Gaussian effects are important when determining wind turbine loads, and hence of utmost importance to the design criteria and lifetime of a wind turbine. We devise a method based on Principal Orthogonal Decomposition where non-Gaussian velocity fields generated by high-resolution pseudo-spectral Large-Eddy Simulation (LES) of the ABL are transformed so that they maintain the exact same second-order statistics including variations of the statistics with height, but are otherwise Gaussian. In that way we can investigate in isolation the question whether it is important for wind turbine loads to include non-Gaussian properties of atmospheric turbulence. As an illustration the Figure show both a non-Gaussian velocity field (left) from our LES, and its transformed Gaussian Counterpart (right). Whereas the horizontal velocity components (top) look close to identical, the vertical components (bottom) are not: the non-Gaussian case is much more fluid-like (like in a sketch by Michelangelo). The question is then: Does the wind turbine see this? Using the load simulation software HAWC2 with both the non-Gaussian and newly constructed Gaussian fields, respectively, we show that the Fatigue loads and most of the Extreme loads are unaltered when using non-Gaussian velocity fields. The turbine thus acts like a low-pass filter which average out the non-Gaussian behaviour on time

Mean-square state and parameter estimation for stochastic linear systems with Gaussian and Poisson noises

NASA Astrophysics Data System (ADS)

Basin, M.; Maldonado, J. J.; Zendejo, O.

2016-07-01

This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.

Empirical Bayes Gaussian likelihood estimation of exposure distributions from pooled samples in human biomonitoring.

PubMed

Li, Xiang; Kuk, Anthony Y C; Xu, Jinfeng

2014-12-10

Human biomonitoring of exposure to environmental chemicals is important. Individual monitoring is not viable because of low individual exposure level or insufficient volume of materials and the prohibitive cost of taking measurements from many subjects. Pooling of samples is an efficient and cost-effective way to collect data. Estimation is, however, complicated as individual values within each pool are not observed but are only known up to their average or weighted average. The distribution of such averages is intractable when the individual measurements are lognormally distributed, which is a common assumption. We propose to replace the intractable distribution of the pool averages by a Gaussian likelihood to obtain parameter estimates. If the pool size is large, this method produces statistically efficient estimates, but regardless of pool size, the method yields consistent estimates as the number of pools increases. An empirical Bayes (EB) Gaussian likelihood approach, as well as its Bayesian analog, is developed to pool information from various demographic groups by using a mixed-effect formulation. We also discuss methods to estimate the underlying mean-variance relationship and to select a good model for the means, which can be incorporated into the proposed EB or Bayes framework. By borrowing strength across groups, the EB estimator is more efficient than the individual group-specific estimator. Simulation results show that the EB Gaussian likelihood estimates outperform a previous method proposed for the National Health and Nutrition Examination Surveys with much smaller bias and better coverage in interval estimation, especially after correction of bias. Copyright © 2014 John Wiley & Sons, Ltd.

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.

A fast elitism Gaussian estimation of distribution algorithm and application for PID optimization.

PubMed

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.

A Fast Elitism Gaussian Estimation of Distribution Algorithm and Application for PID Optimization

PubMed Central

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

Application of multivariate Gaussian detection theory to known non-Gaussian probability density functions

NASA Astrophysics Data System (ADS)

Schwartz, Craig R.; Thelen, Brian J.; Kenton, Arthur C.

1995-06-01

A statistical parametric multispectral sensor performance model was developed by ERIM to support mine field detection studies, multispectral sensor design/performance trade-off studies, and target detection algorithm development. The model assumes target detection algorithms and their performance models which are based on data assumed to obey multivariate Gaussian probability distribution functions (PDFs). The applicability of these algorithms and performance models can be generalized to data having non-Gaussian PDFs through the use of transforms which convert non-Gaussian data to Gaussian (or near-Gaussian) data. An example of one such transform is the Box-Cox power law transform. In practice, such a transform can be applied to non-Gaussian data prior to the introduction of a detection algorithm that is formally based on the assumption of multivariate Gaussian data. This paper presents an extension of these techniques to the case where the joint multivariate probability density function of the non-Gaussian input data is known, and where the joint estimate of the multivariate Gaussian statistics, under the Box-Cox transform, is desired. The jointly estimated multivariate Gaussian statistics can then be used to predict the performance of a target detection algorithm which has an associated Gaussian performance model.

Cramer-Rao Bound, MUSIC, and Maximum Likelihood. Effects of Temporal Phase Difference

DTIC Science & Technology

1990-11-01

Technical Report 1373 November 1990 Cramer-Rao Bound, MUSIC , And Maximum Likelihood Effects of Temporal Phase o Difference C. V. TranI OTIC Approved... MUSIC , and Maximum Likelihood (ML) asymptotic variances corresponding to the two-source direction-of-arrival estimation where sources were modeled as...1pI = 1.00, SNR = 20 dB ..................................... 27 2. MUSIC for two equipowered signals impinging on a 5-element ULA (a) IpI = 0.50, SNR

A neural-network based estimator to search for primordial non-Gaussianity in Planck CMB maps

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

Novaes, C.P.; Bernui, A.; Ferreira, I.S.

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-cleanedmore » 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.« less

Detection of image structures using the Fisher information and the Rao metric.

PubMed

Maybank, Stephen J

2004-12-01

In many detection problems, the structures to be detected are parameterized by the points of a parameter space. If the conditional probability density function for the measurements is known, then detection can be achieved by sampling the parameter space at a finite number of points and checking each point to see if the corresponding structure is supported by the data. The number of samples and the distances between neighboring samples are calculated using the Rao metric on the parameter space. The Rao metric is obtained from the Fisher information which is, in turn, obtained from the conditional probability density function. An upper bound is obtained for the probability of a false detection. The calculations are simplified in the low noise case by making an asymptotic approximation to the Fisher information. An application to line detection is described. Expressions are obtained for the asymptotic approximation to the Fisher information, the volume of the parameter space, and the number of samples. The time complexity for line detection is estimated. An experimental comparison is made with a Hough transform-based method for detecting lines.

Divergences and estimating tight bounds on Bayes error with applications to multivariate Gaussian copula and latent Gaussian copula

NASA Astrophysics Data System (ADS)

Thelen, Brian J.; Xique, Ismael J.; Burns, Joseph W.; Goley, G. Steven; Nolan, Adam R.; Benson, Jonathan W.

2017-04-01

In Bayesian decision theory, there has been a great amount of research into theoretical frameworks and information- theoretic quantities that can be used to provide lower and upper bounds for the Bayes error. These include well-known bounds such as Chernoff, Battacharrya, and J-divergence. Part of the challenge of utilizing these various metrics in practice is (i) whether they are "loose" or "tight" bounds, (ii) how they might be estimated via either parametric or non-parametric methods, and (iii) how accurate the estimates are for limited amounts of data. In general what is desired is a methodology for generating relatively tight lower and upper bounds, and then an approach to estimate these bounds efficiently from data. In this paper, we explore the so-called triangle divergence which has been around for a while, but was recently made more prominent in some recent research on non-parametric estimation of information metrics. Part of this work is motivated by applications for quantifying fundamental information content in SAR/LIDAR data, and to help in this, we have developed a flexible multivariate modeling framework based on multivariate Gaussian copula models which can be combined with the triangle divergence framework to quantify this information, and provide approximate bounds on Bayes error. In this paper we present an overview of the bounds, including those based on triangle divergence and verify that under a number of multivariate models, the upper and lower bounds derived from triangle divergence are significantly tighter than the other common bounds, and often times, dramatically so. We also propose some simple but effective means for computing the triangle divergence using Monte Carlo methods, and then discuss estimation of the triangle divergence from empirical data based on Gaussian Copula models.

Applied estimation for hybrid dynamical systems using perceptional information

NASA Astrophysics Data System (ADS)

Plotnik, Aaron M.

observation, complementing the information available from more traditional sensors. State tracking is achieved using a new form of Rao-Blackwellized particle filter called the mode-observed Gaussian Particle Filter. Performance is demonstrated using data from simulation and data collected on actual specimens in the ocean. The framework for estimation using both traditional and perceptional information is easily extensible to other stochastic hybrid systems with mode-related perceptional observations available.

Gaussian process inference for estimating pharmacokinetic parameters of dynamic contrast-enhanced MR images.

PubMed

Wang, Shijun; Liu, Peter; Turkbey, Baris; Choyke, Peter; Pinto, Peter; Summers, Ronald M

2012-01-01

In this paper, we propose a new pharmacokinetic model for parameter estimation of dynamic contrast-enhanced (DCE) MRI by using Gaussian process inference. Our model is based on the Tofts dual-compartment model for the description of tracer kinetics and the observed time series from DCE-MRI is treated as a Gaussian stochastic process. The parameter estimation is done through a maximum likelihood approach and we propose a variant of the coordinate descent method to solve this likelihood maximization problem. The new model was shown to outperform a baseline method on simulated data. Parametric maps generated on prostate DCE data with the new model also provided better enhancement of tumors, lower intensity on false positives, and better boundary delineation when compared with the baseline method. New statistical parameter maps from the process model were also found to be informative, particularly when paired with the PK parameter maps.

The Bayesian Cramér-Rao lower bound in Astrometry

NASA Astrophysics Data System (ADS)

Mendez, R. A.; Echeverria, A.; Silva, J.; Orchard, M.

2018-01-01

A determination of the highest precision that can be achieved in the measurement of the location of a stellar-like object has been a topic of permanent interest by the astrometric community. The so-called (parametric, or non-Bayesian) Cramér-Rao (CR hereafter) bound provides a lower bound for the variance with which one could estimate the position of a point source. This has been studied recently by Mendez et al. (2013, 2014, 2015). In this work we present a different approach to the same problem (Echeverria et al. 2016), using a Bayesian CR setting which has a number of advantages over the parametric scenario.

The Bayesian Cramér-Rao lower bound in Astrometry

NASA Astrophysics Data System (ADS)

Mendez, R. A.; Echeverria, A.; Silva, J.; Orchard, M.

2017-07-01

A determination of the highest precision that can be achieved in the measurement of the location of a stellar-like object has been a topic of permanent interest by the astrometric community. The so-called (parametric, or non-Bayesian) Cramér-Rao (CR hereafter) bound provides a lower bound for the variance with which one could estimate the position of a point source. This has been studied recently by Mendez and collaborators (2014, 2015). In this work we present a different approach to the same problem (Echeverria et al. 2016), using a Bayesian CR setting which has a number of advantages over the parametric scenario.

Cardiac conduction velocity estimation from sequential mapping assuming known Gaussian distribution for activation time estimation error.

PubMed

Shariat, Mohammad Hassan; Gazor, Saeed; Redfearn, Damian

2016-08-01

In this paper, we study the problem of the cardiac conduction velocity (CCV) estimation for the sequential intracardiac mapping. We assume that the intracardiac electrograms of several cardiac sites are sequentially recorded, their activation times (ATs) are extracted, and the corresponding wavefronts are specified. The locations of the mapping catheter's electrodes and the ATs of the wavefronts are used here for the CCV estimation. We assume that the extracted ATs include some estimation errors, which we model with zero-mean white Gaussian noise values with known variances. Assuming stable planar wavefront propagation, we derive the maximum likelihood CCV estimator, when the synchronization times between various recording sites are unknown. We analytically evaluate the performance of the CCV estimator and provide its mean square estimation error. Our simulation results confirm the accuracy of the proposed method and the error analysis of the proposed CCV estimator.

Poisson–Gaussian Noise Analysis and Estimation for Low-Dose X-ray Images in the NSCT Domain

PubMed Central

Lee, Sangyoon; Lee, Min Seok; Kang, Moon Gi

2018-01-01

The noise distribution of images obtained by X-ray sensors in low-dosage situations can be analyzed using the Poisson and Gaussian mixture model. Multiscale conversion is one of the most popular noise reduction methods used in recent years. Estimation of the noise distribution of each subband in the multiscale domain is the most important factor in performing noise reduction, with non-subsampled contourlet transform (NSCT) representing an effective method for scale and direction decomposition. In this study, we use artificially generated noise to analyze and estimate the Poisson–Gaussian noise of low-dose X-ray images in the NSCT domain. The noise distribution of the subband coefficients is analyzed using the noiseless low-band coefficients and the variance of the noisy subband coefficients. The noise-after-transform also follows a Poisson–Gaussian distribution, and the relationship between the noise parameters of the subband and the full-band image is identified. We then analyze noise of actual images to validate the theoretical analysis. Comparison of the proposed noise estimation method with an existing noise reduction method confirms that the proposed method outperforms traditional methods. PMID:29596335

Poisson-Gaussian Noise Analysis and Estimation for Low-Dose X-ray Images in the NSCT Domain.

PubMed

Lee, Sangyoon; Lee, Min Seok; Kang, Moon Gi

2018-03-29

The noise distribution of images obtained by X-ray sensors in low-dosage situations can be analyzed using the Poisson and Gaussian mixture model. Multiscale conversion is one of the most popular noise reduction methods used in recent years. Estimation of the noise distribution of each subband in the multiscale domain is the most important factor in performing noise reduction, with non-subsampled contourlet transform (NSCT) representing an effective method for scale and direction decomposition. In this study, we use artificially generated noise to analyze and estimate the Poisson-Gaussian noise of low-dose X-ray images in the NSCT domain. The noise distribution of the subband coefficients is analyzed using the noiseless low-band coefficients and the variance of the noisy subband coefficients. The noise-after-transform also follows a Poisson-Gaussian distribution, and the relationship between the noise parameters of the subband and the full-band image is identified. We then analyze noise of actual images to validate the theoretical analysis. Comparison of the proposed noise estimation method with an existing noise reduction method confirms that the proposed method outperforms traditional methods.

Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures

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

Procacci, Piero

2015-04-21

In this paper, we present an improved method for obtaining unbiased estimates of the free energy difference between two thermodynamic states using the work distribution measured in nonequilibrium driven experiments connecting these states. The method is based on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, whose normal components are identical in either direction of the nonequilibrium process, with weights regulated by the Crooks theorem. Using the prototypical example for the driven unfolding/folding of deca-alanine, we show that the predicted behavior of the forward and reverse work distributions, assuming a combination of onlymore » two Gaussian components with Crooks derived weights, explains surprisingly well the striking asymmetry in the observed distributions at fast pulling speeds. The proposed methodology opens the way for a perfectly parallel implementation of Jarzynski-based free energy calculations in complex systems.« less

H-SLAM: Rao-Blackwellized Particle Filter SLAM Using Hilbert Maps.

PubMed

Vallicrosa, Guillem; Ridao, Pere

2018-05-01

Occupancy Grid maps provide a probabilistic representation of space which is important for a variety of robotic applications like path planning and autonomous manipulation. In this paper, a SLAM (Simultaneous Localization and Mapping) framework capable of obtaining this representation online is presented. The H-SLAM (Hilbert Maps SLAM) is based on Hilbert Map representation and uses a Particle Filter to represent the robot state. Hilbert Maps offer a continuous probabilistic representation with a small memory footprint. We present a series of experimental results carried both in simulation and with real AUVs (Autonomous Underwater Vehicles). These results demonstrate that our approach is able to represent the environment more consistently while capable of running online.

Gaussian interferometric power and Black box estimation of Unruh temperature

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

Wang, Jieci, E-mail: jcwang@hunnu.edu.cn; Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190; Cao, Haixin

2016-10-15

We present a black box estimation paradigm of Unruh temperature in a relativistic bosonic continuous-variable setting. It is shown that the guaranteed precision for the estimation of Unruh temperature can be evaluated by the Gaussian interferometric power for a given probe state. We demonstrate that the amount of interferometric power is always beyond the entanglement type quantum correlations in a relativistic setting. It is found that due to the fact that Unruh radiation acts as a thermal bath on the probe system, it destroys available resources of the probe system and reduces the guaranteed precision of the estimation of Unruhmore » temperature. We also find that the thermal noise induced by Unruh effect will generate interferometric power between accelerated Bob and his auxiliary partner anti-Bob, while it does not generate any correlation between inertial Alice and anti-Bob.« less

Nonparametric autocovariance estimation from censored time series by Gaussian imputation.

PubMed

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.

Sequential state estimation of nonlinear/non-Gaussian systems with stochastic input for turbine degradation estimation

NASA Astrophysics Data System (ADS)

Hanachi, Houman; Liu, Jie; Banerjee, Avisekh; Chen, Ying

2016-05-01

Health state estimation of inaccessible components in complex systems necessitates effective state estimation techniques using the observable variables of the system. The task becomes much complicated when the system is nonlinear/non-Gaussian and it receives stochastic input. In this work, a novel sequential state estimation framework is developed based on particle filtering (PF) scheme for state estimation of general class of nonlinear dynamical systems with stochastic input. Performance of the developed framework is then validated with simulation on a Bivariate Non-stationary Growth Model (BNGM) as a benchmark. In the next step, three-year operating data of an industrial gas turbine engine (GTE) are utilized to verify the effectiveness of the developed framework. A comprehensive thermodynamic model for the GTE is therefore developed to formulate the relation of the observable parameters and the dominant degradation symptoms of the turbine, namely, loss of isentropic efficiency and increase of the mass flow. The results confirm the effectiveness of the developed framework for simultaneous estimation of multiple degradation symptoms in complex systems with noisy measured inputs.

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

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.

Medical and radiological aspects of emergency preparedness and response at SevRAO facilities.

PubMed

Savkin, M N; Sneve, M K; Grachev, M I; Frolov, G P; Shinkarev, S M; Jaworska, A

2008-12-01

Regulatory cooperation between the Norwegian Radiation Protection Authority and the Federal Medical Biological Agency (FMBA) of the Russian Federation has the overall goal of promoting improvements in radiation protection in Northwest Russia. One of the projects in this programme has the objectives to review and improve the existing medical emergency preparedness capabilities at the sites for temporary storage of spent nuclear fuel and radioactive waste. These are operated by SevRAO at Andreeva Bay and in Gremikha village on the Kola Peninsula. The work is also intended to provide a better basis for regulation of emergency response and medical emergency preparedness at similar facilities elsewhere in Russia. The purpose of this paper is to present the main results of that project, implemented by the Burnasyan Federal Medical Biophysical Centre. The first task was an analysis of the regulatory requirements and the current state of preparedness for medical emergency response at the SevRAO facilities. Although Russian regulatory documents are mostly consistent with international recommendations, some distinctions lead to numerical differences in operational intervention criteria under otherwise similar conditions. Radiological threats relating to possible accidents, and related gaps in the regulation of SevRAO facilities, were also identified. As part of the project, a special exercise on emergency medical response on-site at Andreeva Bay was prepared and carried out, and recommendations were proposed after the exercise. Following fruitful dialogue among regulators, designers and operators, special regulatory guidance has been issued by FMBA to account for the specific and unusual features of the SevRAO facilities. Detailed sections relate to the prevention of accidents, and emergency preparedness and response, supplementing the basic Russian regulatory requirements. Overall it is concluded that (a) the provision of medical and sanitary components of emergency

Comparison of Kasai Autocorrelation and Maximum Likelihood Estimators for Doppler Optical Coherence Tomography

PubMed Central

Chan, Aaron C.; Srinivasan, Vivek J.

2013-01-01

In optical coherence tomography (OCT) and ultrasound, unbiased Doppler frequency estimators with low variance are desirable for blood velocity estimation. Hardware improvements in OCT mean that ever higher acquisition rates are possible, which should also, in principle, improve estimation performance. Paradoxically, however, the widely used Kasai autocorrelation estimator’s performance worsens with increasing acquisition rate. We propose that parametric estimators based on accurate models of noise statistics can offer better performance. We derive a maximum likelihood estimator (MLE) based on a simple additive white Gaussian noise model, and show that it can outperform the Kasai autocorrelation estimator. In addition, we also derive the Cramer Rao lower bound (CRLB), and show that the variance of the MLE approaches the CRLB for moderate data lengths and noise levels. We note that the MLE performance improves with longer acquisition time, and remains constant or improves with higher acquisition rates. These qualities may make it a preferred technique as OCT imaging speed continues to improve. Finally, our work motivates the development of more general parametric estimators based on statistical models of decorrelation noise. PMID:23446044

Efficient, adaptive estimation of two-dimensional firing rate surfaces via Gaussian process methods.

PubMed

Rad, Kamiar Rahnama; Paninski, Liam

2010-01-01

Estimating two-dimensional firing rate maps is a common problem, arising in a number of contexts: the estimation of place fields in hippocampus, the analysis of temporally nonstationary tuning curves in sensory and motor areas, the estimation of firing rates following spike-triggered covariance analyses, etc. Here we introduce methods based on Gaussian process nonparametric Bayesian techniques for estimating these two-dimensional rate maps. These techniques offer a number of advantages: the estimates may be computed efficiently, come equipped with natural errorbars, adapt their smoothness automatically to the local density and informativeness of the observed data, and permit direct fitting of the model hyperparameters (e.g., the prior smoothness of the rate map) via maximum marginal likelihood. We illustrate the method's flexibility and performance on a variety of simulated and real data.

Orthogonal Gaussian process models

DOE PAGES

Plumlee, Matthew; Joseph, V. Roshan

2017-01-01

Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. As a result, this paper also discusses applications to multi-fidelity simulations using data examples.

Orthogonal Gaussian process models

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

Plumlee, Matthew; Joseph, V. Roshan

Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. As a result, this paper also discusses applications to multi-fidelity simulations using data examples.

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.

RSCABS: An R package for performing the Rao-Scott Adjusted Cochran-Armitage trend test By Slices

EPA Science Inventory

RSCABS[3] (Rao-Scott adjusted Cochran-Armitage trend test By Slices) is a modification to the Rao-Scott[5] adjusted Cochran-Armitage trend test[1, 2] that allows for testing at each individual severity score often seen in histopathological data. The test was originally developed ...

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

PubMed

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

2017-10-01

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

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.

EM-1 Countdown Simulation with Charlie Blackwell-Thompson

NASA Image and Video Library

2018-03-29

NASA Launch Director Charlie Blackwell-Thompson, center, stands next to her console in Firing Room 1 at the Kennedy Space Center's Launch Control Center. With her, from the left, are NASA intern Justin Connolly, NASA Engineering Project Manager Dan Tran, Blackwell-Thompson, Shawn Reverter, Project Manager for Red Canyon Software, Inc., and NASA Structures and Mechanisms Design Branch Chief Adam Dokos, during a countdown simulation for Exploration Mission 1. It was the agency's first simulation of a portion of the countdown for the first launch of a Space Launch System rocket and Orion spacecraft that will eventually take astronauts beyond low-Earth orbit to destinations such as the Moon and Mars.

Photometric redshifts for the next generation of deep radio continuum surveys - II. Gaussian processes and hybrid estimates

NASA Astrophysics Data System (ADS)

Duncan, Kenneth J.; Jarvis, Matt J.; Brown, Michael J. I.; Röttgering, Huub J. A.

2018-07-01

Building on the first paper in this series (Duncan et al. 2018), we present a study investigating the performance of Gaussian process photometric redshift (photo-z) estimates for galaxies and active galactic nuclei (AGNs) detected in deep radio continuum surveys. A Gaussian process redshift code is used to produce photo-z estimates targeting specific subsets of both the AGN population - infrared (IR), X-ray, and optically selected AGNs - and the general galaxy population. The new estimates for the AGN population are found to perform significantly better at z > 1 than the template-based photo-z estimates presented in our previous study. Our new photo-z estimates are then combined with template estimates through hierarchical Bayesian combination to produce a hybrid consensus estimate that outperforms both of the individual methods across all source types. Photo-z estimates for radio sources that are X-ray sources or optical/IR AGNs are significantly improved in comparison to previous template-only estimates - with outlier fractions and robust scatter reduced by up to a factor of ˜4. The ability of our method to combine the strengths of the two input photo-z techniques and the large improvements we observe illustrate its potential for enabling future exploitation of deep radio continuum surveys for both the study of galaxy and black hole coevolution and for cosmological studies.

Non-Gaussian probabilistic MEG source localisation based on kernel density estimation☆

PubMed Central

Mohseni, Hamid R.; Kringelbach, Morten L.; Woolrich, Mark W.; Baker, Adam; Aziz, Tipu Z.; Probert-Smith, Penny

2014-01-01

There is strong evidence to suggest that data recorded from magnetoencephalography (MEG) follows a non-Gaussian distribution. However, existing standard methods for source localisation model the data using only second order statistics, and therefore use the inherent assumption of a Gaussian distribution. In this paper, we present a new general method for non-Gaussian source estimation of stationary signals for localising brain activity from MEG data. By providing a Bayesian formulation for MEG source localisation, we show that the source probability density function (pdf), which is not necessarily Gaussian, can be estimated using multivariate kernel density estimators. In the case of Gaussian data, the solution of the method is equivalent to that of widely used linearly constrained minimum variance (LCMV) beamformer. The method is also extended to handle data with highly correlated sources using the marginal distribution of the estimated joint distribution, which, in the case of Gaussian measurements, corresponds to the null-beamformer. The proposed non-Gaussian source localisation approach is shown to give better spatial estimates than the LCMV beamformer, both in simulations incorporating non-Gaussian signals, and in real MEG measurements of auditory and visual evoked responses, where the highly correlated sources are known to be difficult to estimate. PMID:24055702

Information geometry of Gaussian channels

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

Monras, Alex; CNR-INFM Coherentia, Napoli; CNISM Unita di Salerno

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 desirablemore » 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).« less

Adaptive estimation of a time-varying phase with coherent states: Smoothing can give an unbounded improvement over filtering

NASA Astrophysics Data System (ADS)

Laverick, Kiarn T.; Wiseman, Howard M.; Dinani, Hossein T.; Berry, Dominic W.

2018-04-01

The problem of measuring a time-varying phase, even when the statistics of the variation is known, is considerably harder than that of measuring a constant phase. In particular, the usual bounds on accuracy, such as the 1 /(4 n ¯) standard quantum limit with coherent states, do not apply. Here, by restricting to coherent states, we are able to analytically obtain the achievable accuracy, the equivalent of the standard quantum limit, for a wide class of phase variation. In particular, we consider the case where the phase has Gaussian statistics and a power-law spectrum equal to κp -1/|ω| p for large ω , for some p >1 . For coherent states with mean photon flux N , we give the quantum Cramér-Rao bound on the mean-square phase error as [psin(π /p ) ] -1(4N /κ ) -(p -1 )/p . Next, we consider whether the bound can be achieved by an adaptive homodyne measurement in the limit N /κ ≫1 , which allows the photocurrent to be linearized. Applying the optimal filtering for the resultant linear Gaussian system, we find the same scaling with N , but with a prefactor larger by a factor of p . By contrast, if we employ optimal smoothing we can exactly obtain the quantum Cramér-Rao bound. That is, contrary to previously considered (p =2 ) cases of phase estimation, here the improvement offered by smoothing over filtering is not limited to a factor of 2 but rather can be unbounded by a factor of p . We also study numerically the performance of these estimators for an adaptive measurement in the limit where N /κ is not large and find a more complicated picture.

Continuous-variable phase estimation with unitary and random linear disturbance

NASA Astrophysics Data System (ADS)

Delgado de Souza, Douglas; Genoni, Marco G.; Kim, M. S.

2014-10-01

We address the problem of continuous-variable quantum phase estimation in the presence of linear disturbance at the Hamiltonian level by means of Gaussian probe states. In particular we discuss both unitary and random disturbance by considering the parameter which characterizes the unwanted linear term present in the Hamiltonian as fixed (unitary disturbance) or random with a given probability distribution (random disturbance). We derive the optimal input Gaussian states at fixed energy, maximizing the quantum Fisher information over the squeezing angle and the squeezing energy fraction, and we discuss the scaling of the quantum Fisher information in terms of the output number of photons, nout. We observe that, in the case of unitary disturbance, the optimal state is a squeezed vacuum state and the quadratic scaling is conserved. As regards the random disturbance, we observe that the optimal squeezing fraction may not be equal to one and, for any nonzero value of the noise parameter, the quantum Fisher information scales linearly with the average number of photons. Finally, we discuss the performance of homodyne measurement by comparing the achievable precision with the ultimate limit imposed by the quantum Cramér-Rao bound.

The effect of noise and lipid signals on determination of Gaussian and non-Gaussian diffusion parameters in skeletal muscle.

PubMed

Cameron, Donnie; Bouhrara, Mustapha; Reiter, David A; Fishbein, Kenneth W; Choi, Seongjin; Bergeron, Christopher M; Ferrucci, Luigi; Spencer, Richard G

2017-07-01

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 (�

Analysing Institutions Interdisciplinarity by Extensive Use of Rao-Stirling Diversity Index.

PubMed

Cassi, Lorenzo; Champeimont, Raphaël; Mescheba, Wilfriedo; de Turckheim, Élisabeth

2017-01-01

This paper shows how the Rao-Stirling diversity index may be extensively used for positioning and comparing institutions interdisciplinary practices. Two decompositions of this index make it possible to explore different components of the diversity of the cited references in a corpus of publications. The paper aims at demonstrating how these bibliometric tools can be used for comparing institutions in a research field by highlighting collaboration orientations and institutions strategies. To make the method available and easy to use for indicator users, this paper first recalls a previous result on the decomposition of the Rao-Stirling index into multidisciplinarity and interdisciplinarity components, then proposes a new decomposition to further explore the profile of research collaborations and finally presents an application to Neuroscience research in French universities.

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.

On Estimating the Phase of Periodic Waveform in Additive Gaussian Noise, Part 2

NASA Technical Reports Server (NTRS)

Rauch, L. L.

1984-01-01

Motivated by advances in signal processing technology that support more complex algorithms, a new look is taken at the problem of estimating the phase and other parameters of a periodic waveform in additive Gaussian noise. The general problem was introduced and the maximum a posteriori probability criterion with signal space interpretation was used to obtain the structures of optimum and some suboptimum phase estimators for known constant frequency and unknown constant phase with an a priori distribution. Optimal algorithms are obtained for some cases where the frequency is a parameterized function of time with the unknown parameters and phase having a joint a priori distribution. In the last section, the intrinsic and extrinsic geometry of hypersurfaces is introduced to provide insight to the estimation problem for the small noise and large noise cases.

Estimation of sum-to-one constrained parameters with non-Gaussian extensions of ensemble-based Kalman filters: application to a 1D ocean biogeochemical model

NASA Astrophysics Data System (ADS)

Simon, E.; Bertino, L.; Samuelsen, A.

2011-12-01

Combined state-parameter estimation in ocean biogeochemical models with ensemble-based Kalman filters is a challenging task due to the non-linearity of the models, the constraints of positiveness that apply to the variables and parameters, and the non-Gaussian distribution of the variables in which they result. Furthermore, these models are sensitive to numerous parameters that are poorly known. Previous works [1] demonstrated that the Gaussian anamorphosis extensions of ensemble-based Kalman filters were relevant tools to perform combined state-parameter estimation in such non-Gaussian framework. In this study, we focus on the estimation of the grazing preferences parameters of zooplankton species. These parameters are introduced to model the diet of zooplankton species among phytoplankton species and detritus. They are positive values and their sum is equal to one. Because the sum-to-one constraint cannot be handled by ensemble-based Kalman filters, a reformulation of the parameterization is proposed. We investigate two types of changes of variables for the estimation of sum-to-one constrained parameters. The first one is based on Gelman [2] and leads to the estimation of normal distributed parameters. The second one is based on the representation of the unit sphere in spherical coordinates and leads to the estimation of parameters with bounded distributions (triangular or uniform). These formulations are illustrated and discussed in the framework of twin experiments realized in the 1D coupled model GOTM-NORWECOM with Gaussian anamorphosis extensions of the deterministic ensemble Kalman filter (DEnKF). [1] Simon E., Bertino L. : Gaussian anamorphosis extension of the DEnKF for combined state and parameter estimation : application to a 1D ocean ecosystem model. Journal of Marine Systems, 2011. doi :10.1016/j.jmarsys.2011.07.007 [2] Gelman A. : Method of Moments Using Monte Carlo Simulation. Journal of Computational and Graphical Statistics, 4, 1, 36-54, 1995.

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

PubMed

Liu, Pan; Deng, Xiaoyan; Tang, Xin; Shen, Shijian

2017-05-01

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

Semisupervised Gaussian Process for Automated Enzyme Search.

PubMed

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

Analysing Institutions Interdisciplinarity by Extensive Use of Rao-Stirling Diversity Index

PubMed Central

Cassi, Lorenzo; Champeimont, Raphaël; Mescheba, Wilfriedo

2017-01-01

This paper shows how the Rao-Stirling diversity index may be extensively used for positioning and comparing institutions interdisciplinary practices. Two decompositions of this index make it possible to explore different components of the diversity of the cited references in a corpus of publications. The paper aims at demonstrating how these bibliometric tools can be used for comparing institutions in a research field by highlighting collaboration orientations and institutions strategies. To make the method available and easy to use for indicator users, this paper first recalls a previous result on the decomposition of the Rao-Stirling index into multidisciplinarity and interdisciplinarity components, then proposes a new decomposition to further explore the profile of research collaborations and finally presents an application to Neuroscience research in French universities. PMID:28114382

Outlier Detection in GNSS Pseudo-Range/Doppler Measurements for Robust Localization

PubMed Central

Zair, Salim; Le Hégarat-Mascle, Sylvie; Seignez, Emmanuel

2016-01-01

In urban areas or space-constrained environments with obstacles, vehicle localization using Global Navigation Satellite System (GNSS) data is hindered by Non-Line Of Sight (NLOS) and multipath receptions. These phenomena induce faulty data that disrupt the precise localization of the GNSS receiver. In this study, we detect the outliers among the observations, Pseudo-Range (PR) and/or Doppler measurements, and we evaluate how discarding them improves the localization. We specify a contrario modeling for GNSS raw data to derive an algorithm that partitions the dataset between inliers and outliers. Then, only the inlier data are considered in the localization process performed either through a classical Particle Filter (PF) or a Rao-Blackwellization (RB) approach. Both localization algorithms exclusively use GNSS data, but they differ by the way Doppler measurements are processed. An experiment has been performed with a GPS receiver aboard a vehicle. Results show that the proposed algorithms are able to detect the ‘outliers’ in the raw data while being robust to non-Gaussian noise and to intermittent satellite blockage. We compare the performance results achieved either estimating only PR outliers or estimating both PR and Doppler outliers. The best localization is achieved using the RB approach coupled with PR-Doppler outlier estimation. PMID:27110796

Outlier Detection in GNSS Pseudo-Range/Doppler Measurements for Robust Localization.

PubMed

Zair, Salim; Le Hégarat-Mascle, Sylvie; Seignez, Emmanuel

2016-04-22

In urban areas or space-constrained environments with obstacles, vehicle localization using Global Navigation Satellite System (GNSS) data is hindered by Non-Line Of Sight (NLOS) and multipath receptions. These phenomena induce faulty data that disrupt the precise localization of the GNSS receiver. In this study, we detect the outliers among the observations, Pseudo-Range (PR) and/or Doppler measurements, and we evaluate how discarding them improves the localization. We specify a contrario modeling for GNSS raw data to derive an algorithm that partitions the dataset between inliers and outliers. Then, only the inlier data are considered in the localization process performed either through a classical Particle Filter (PF) or a Rao-Blackwellization (RB) approach. Both localization algorithms exclusively use GNSS data, but they differ by the way Doppler measurements are processed. An experiment has been performed with a GPS receiver aboard a vehicle. Results show that the proposed algorithms are able to detect the 'outliers' in the raw data while being robust to non-Gaussian noise and to intermittent satellite blockage. We compare the performance results achieved either estimating only PR outliers or estimating both PR and Doppler outliers. The best localization is achieved using the RB approach coupled with PR-Doppler outlier estimation.

Haldane and Mayr: a response to Rao and Nanjundiah.

PubMed

Sarkar, Sahotra

2016-04-01

The discussion with Rao and Nanjundiah about the history of interactions between J. B. S. Haldane and Ernst Mayr is further extended in this note. The nature of the dispute about beanbag genetics is explicated as consisting of two separate issues, one about the role of mathematical analysis in evolutionary biology, and the other about the value of single-locus genic models.

A fast estimator for the bispectrum and beyond - a practical method for measuring non-Gaussianity in 21-cm maps

NASA Astrophysics Data System (ADS)

Watkinson, Catherine A.; Majumdar, Suman; Pritchard, Jonathan R.; Mondal, Rajesh

2017-12-01

In this paper, we establish the accuracy and robustness of a fast estimator for the bispectrum - the 'FFT-bispectrum estimator'. The implementation of the estimator presented here offers speed and simplicity benefits over a direct-measurement approach. We also generalize the derivation so it may be easily be applied to any order polyspectra, such as the trispectrum, with the cost of only a handful of Fast-Fourier Transforms (FFTs). All lower order statistics can also be calculated simultaneously for little extra cost. To test the estimator, we make use of a non-linear density field, and for a more strongly non-Gaussian test case, we use a toy-model of reionization in which ionized bubbles at a given redshift are all of equal size and are randomly distributed. Our tests find that the FFT-estimator remains accurate over a wide range of k, and so should be extremely useful for analysis of 21-cm observations. The speed of the FFT-bispectrum estimator makes it suitable for sampling applications, such as Bayesian inference. The algorithm we describe should prove valuable in the analysis of simulations and observations, and whilst, we apply it within the field of cosmology, this estimator is useful in any field that deals with non-Gaussian data.

Neutrophil and macrophage apoptosis in bronchoalveolar lavage fluid from healthy horses and horses with recurrent airway obstruction (RAO)

PubMed Central

2014-01-01

Background Dysregulation of apoptosis has been implicated in a range of diseases including tumors, neurodegenerative and autoimmine diseases, as well as allergic asthma and chronic obstructive pulmonary disease (COPD) in humans. Although it has a different pathophysiology, delayed apoptosis of various inflammatory cells may play a pivotal role in the development of recurrent airway obstruction (RAO) in horses. Reduction of inflammatory cell apoptosis or a dysregulation of this process could lead to chronic inflammation and tissue injury. Therefore, the aim of this study was to investigate the rate of apoptosis and necrosis of neutrophils and macrophages in bronchoalveolar lavage fluid obtained from seven horses suffering from RAO (study group) and seven control horses. Results We demonstrated that neutrophil/macrophage apoptosis is altered in RAO-affected horses compared with the control group in the BAL fluid. We found a significant difference between the median percentage of early and late apoptosis of neutrophils between the study and control group of horses. Moreover, we found a positive correlation between the rate of apoptosis and the median percentage of macrophages in RAO-affected horses. Conclusion The findings suggest that apoptosis dysregulation may play a significant role in the pathogenesis of RAO. However, further studies are needed to clarify the role of altered apoptosis in the course of equine recurrent airway obstruction. PMID:24460911

The impact of covariance misspecification in multivariate Gaussian mixtures on estimation and inference: an application to longitudinal modeling.

PubMed

Heggeseth, Brianna C; Jewell, Nicholas P

2013-07-20

Multivariate Gaussian mixtures are a class of models that provide a flexible parametric approach for the representation of heterogeneous multivariate outcomes. When the outcome is a vector of repeated measurements taken on the same subject, there is often inherent dependence between observations. However, a common covariance assumption is conditional independence-that is, given the mixture component label, the outcomes for subjects are independent. In this paper, we study, through asymptotic bias calculations and simulation, the impact of covariance misspecification in multivariate Gaussian mixtures. Although maximum likelihood estimators of regression and mixing probability parameters are not consistent under misspecification, they have little asymptotic bias when mixture components are well separated or if the assumed correlation is close to the truth even when the covariance is misspecified. We also present a robust standard error estimator and show that it outperforms conventional estimators in simulations and can indicate that the model is misspecified. Body mass index data from a national longitudinal study are used to demonstrate the effects of misspecification on potential inferences made in practice. Copyright © 2013 John Wiley & Sons, Ltd.

Non-Gaussian Methods for Causal Structure Learning.

PubMed

Shimizu, Shohei

2018-05-22

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

Comparing fixed and variable-width Gaussian networks.

PubMed

Kůrková, Věra; Kainen, Paul C

2014-09-01

The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is proven that if two Gaussian RBF networks have the same input-output functions, then they must have the same numbers of units with the same centers and widths. Further, it is shown that while sets of input-output functions of Gaussian kernel networks with two different widths are disjoint, each such set is large enough to be a universal approximator. Embedding of RKHSs induced by "flatter" Gaussians into RKHSs induced by "sharper" Gaussians is described and growth of the ratios of norms on these spaces with increasing input dimension is estimated. Finally, large sets of argminima of error functionals in sets of input-output functions of Gaussian RBFs are described. Copyright © 2014 Elsevier Ltd. All rights reserved.

Improving satellite-based PM2.5 estimates in China using Gaussian processes modeling in a Bayesian hierarchical setting.

PubMed

Yu, Wenxi; Liu, Yang; Ma, Zongwei; Bi, Jun

2017-08-01

Using satellite-based aerosol optical depth (AOD) measurements and statistical models to estimate ground-level PM 2.5 is a promising way to fill the areas that are not covered by ground PM 2.5 monitors. The statistical models used in previous studies are primarily Linear Mixed Effects (LME) and Geographically Weighted Regression (GWR) models. In this study, we developed a new regression model between PM 2.5 and AOD using Gaussian processes in a Bayesian hierarchical setting. Gaussian processes model the stochastic nature of the spatial random effects, where the mean surface and the covariance function is specified. The spatial stochastic process is incorporated under the Bayesian hierarchical framework to explain the variation of PM 2.5 concentrations together with other factors, such as AOD, spatial and non-spatial random effects. We evaluate the results of our model and compare them with those of other, conventional statistical models (GWR and LME) by within-sample model fitting and out-of-sample validation (cross validation, CV). The results show that our model possesses a CV result (R 2  = 0.81) that reflects higher accuracy than that of GWR and LME (0.74 and 0.48, respectively). Our results indicate that Gaussian process models have the potential to improve the accuracy of satellite-based PM 2.5 estimates.

Precision of proportion estimation with binary compressed Raman spectrum.

PubMed

Réfrégier, Philippe; Scotté, Camille; de Aguiar, Hilton B; Rigneault, Hervé; Galland, Frédéric

2018-01-01

The precision of proportion estimation with binary filtering of a Raman spectrum mixture is analyzed when the number of binary filters is equal to the number of present species and when the measurements are corrupted with Poisson photon noise. It is shown that the Cramer-Rao bound provides a useful methodology to analyze the performance of such an approach, in particular when the binary filters are orthogonal. It is demonstrated that a simple linear mean square error estimation method is efficient (i.e., has a variance equal to the Cramer-Rao bound). Evolutions of the Cramer-Rao bound are analyzed when the measuring times are optimized or when the considered proportion for binary filter synthesis is not optimized. Two strategies for the appropriate choice of this considered proportion are also analyzed for the binary filter synthesis.

Reaching the Quantum Cramér-Rao Bound for Transmission Measurements

NASA Astrophysics Data System (ADS)

Woodworth, Timothy; Chan, Kam Wai Clifford; Marino, Alberto

2017-04-01

The quantum Cramér-Rao bound (QCRB) is commonly used to quantify the lower bound for the uncertainty in the estimation of a given parameter. Here, we calculate the QCRB for transmission measurements of an optical system probed by a beam of light. Estimating the transmission of an optical element is important as it is required for the calibration of optimal states for interferometers, characterization of high efficiency photodetectors, or as part of other measurements, such as those in plasmonic sensors or in ellipsometry. We use a beam splitter model for the losses introduced by the optical system to calculate the QCRB for different input states. We compare the bound for a coherent state, a two-mode squeezed-state (TMSS), a single-mode squeezed-state (SMSS), and a Fock state and show that it is possible to obtain an ultimate lower bound, regardless of the state used to probe the system. We prove that the Fock state gives the lowest possible uncertainty in estimating the transmission for any state and demonstrate that the TMSS and SMSS approach this ultimate bound for large levels of squeezing. Finally, we show that a simple measurement strategy for the TMSS, namely an intensity difference measurement, is able to saturate the QCRB. Work supported by the W.M. Keck Foundation.

Renyi entropy measures of heart rate Gaussianity.

PubMed

Lake, Douglas E

2006-01-01

Sample entropy and approximate entropy are measures that have been successfully utilized to study the deterministic dynamics of heart rate (HR). A complementary stochastic point of view and a heuristic argument using the Central Limit Theorem suggests that the Gaussianity of HR is a complementary measure of the physiological complexity of the underlying signal transduction processes. Renyi entropy (or q-entropy) is a widely used measure of Gaussianity in many applications. Particularly important members of this family are differential (or Shannon) entropy (q = 1) and quadratic entropy (q = 2). We introduce the concepts of differential and conditional Renyi entropy rate and, in conjunction with Burg's theorem, develop a measure of the Gaussianity of a linear random process. Robust algorithms for estimating these quantities are presented along with estimates of their standard errors.

AGU and Wiley-Blackwell to partner on publication of journals and books

NASA Astrophysics Data System (ADS)

McEntee, Chris

2012-07-01

AGU has signed a memorandum of understanding (MOU) with Wiley-Blackwell to partner in journal and book publishing. The agreement, effective 1 January 2013, is a significant step forward in transforming AGU publishing consistent with our strategic plan goal of scientific leadership and collaboration. Wiley-Blackwell is the international scientific, technical, medical, and scholarly publishing business of John Wiley & Sons, Inc. Family-owned and publicly traded on the New York Stock Exchange, the company is strong in every major academic and professional field and partners with many of the world's leading societies. Wiley-Blackwell, a leader in developing models for open access and providing developing nations with access to science, publishes nearly 1500 peer-reviewed journals and more than 1500 new books annually. The company publishes approximately 700 society titles.

Gaussian statistics for palaeomagnetic vectors

USGS Publications Warehouse

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

2003-01-01

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

Gaussian statistics for palaeomagnetic vectors

NASA Astrophysics Data System (ADS)

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

2003-03-01

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

Quantum steering of Gaussian states via non-Gaussian measurements

NASA Astrophysics Data System (ADS)

Ji, Se-Wan; Lee, Jaehak; Park, Jiyong; Nha, Hyunchul

2016-07-01

Quantum steering—a strong correlation to be verified even when one party or its measuring device is fully untrusted—not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime.

Robust Gaussian Graphical Modeling via l1 Penalization

PubMed Central

Sun, Hokeun; Li, Hongzhe

2012-01-01

Summary Gaussian graphical models have been widely used as an effective method for studying the conditional independency structure among genes and for constructing genetic networks. However, gene expression data typically have heavier tails or more outlying observations than the standard Gaussian distribution. Such outliers in gene expression data can lead to wrong inference on the dependency structure among the genes. We propose a l1 penalized estimation procedure for the sparse Gaussian graphical models that is robustified against possible outliers. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its own likelihood. An efficient computational algorithm based on the coordinate gradient descent method is developed to obtain the minimizer of the negative penalized robustified-likelihood, where nonzero elements of the concentration matrix represents the graphical links among the genes. After the graphical structure is obtained, we re-estimate the positive definite concentration matrix using an iterative proportional fitting algorithm. Through simulations, we demonstrate that the proposed robust method performs much better than the graphical Lasso for the Gaussian graphical models in terms of both graph structure selection and estimation when outliers are present. We apply the robust estimation procedure to an analysis of yeast gene expression data and show that the resulting graph has better biological interpretation than that obtained from the graphical Lasso. PMID:23020775

The Theory and Practice of Estimating the Accuracy of Dynamic Flight-Determined Coefficients

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1981-01-01

Means of assessing the accuracy of maximum likelihood parameter estimates obtained from dynamic flight data are discussed. The most commonly used analytical predictors of accuracy are derived and compared from both statistical and simplified geometrics standpoints. The accuracy predictions are evaluated with real and simulated data, with an emphasis on practical considerations, such as modeling error. Improved computations of the Cramer-Rao bound to correct large discrepancies due to colored noise and modeling error are presented. The corrected Cramer-Rao bound is shown to be the best available analytical predictor of accuracy, and several practical examples of the use of the Cramer-Rao bound are given. Engineering judgement, aided by such analytical tools, is the final arbiter of accuracy estimation.

Recurrence plots of discrete-time Gaussian stochastic processes

NASA Astrophysics Data System (ADS)

Ramdani, Sofiane; Bouchara, Frédéric; Lagarde, Julien; Lesne, Annick

2016-09-01

We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1. These results allow us to obtain theoretical values of three measures: (i) the recurrence rate (REC) (ii) the percent determinism (DET) and (iii) RP-based estimation of the ε-entropy κ(ε) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.

Evaluating detection and estimation capabilities of magnetometer-based vehicle sensors

NASA Astrophysics Data System (ADS)

Slater, David M.; Jacyna, Garry M.

2013-05-01

In an effort to secure the northern and southern United States borders, MITRE has been tasked with developing Modeling and Simulation (M&S) tools that accurately capture the mapping between algorithm-level Measures of Performance (MOP) and system-level Measures of Effectiveness (MOE) for current/future surveillance systems deployed by the the Customs and Border Protection Office of Technology Innovations and Acquisitions (OTIA). This analysis is part of a larger M&S undertaking. The focus is on two MOPs for magnetometer-based Unattended Ground Sensors (UGS). UGS are placed near roads to detect passing vehicles and estimate properties of the vehicle's trajectory such as bearing and speed. The first MOP considered is the probability of detection. We derive probabilities of detection for a network of sensors over an arbitrary number of observation periods and explore how the probability of detection changes when multiple sensors are employed. The performance of UGS is also evaluated based on the level of variance in the estimation of trajectory parameters. We derive the Cramer-Rao bounds for the variances of the estimated parameters in two cases: when no a priori information is known and when the parameters are assumed to be Gaussian with known variances. Sample results show that UGS perform significantly better in the latter case.

Non-Gaussian diffusion in static disordered media

NASA Astrophysics Data System (ADS)

Luo, Liang; Yi, Ming

2018-04-01

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

A new fish in the pond: the C-BASS Migrates to HartRAO

NASA Astrophysics Data System (ADS)

Jonas, Justin

2007-04-01

On 14 February 2007 a new 7.2m dish was broughtto HartRAO to form the South African component of the C-BASS project, an international collaboration that will map the polarization of he radio emission from the Milky Way.

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.

Estimation of continuous multi-DOF finger joint kinematics from surface EMG using a multi-output Gaussian Process.

PubMed

Ngeo, Jimson; Tamei, Tomoya; Shibata, Tomohiro

2014-01-01

Surface electromyographic (EMG) signals have often been used in estimating upper and lower limb dynamics and kinematics for the purpose of controlling robotic devices such as robot prosthesis and finger exoskeletons. However, in estimating multiple and a high number of degrees-of-freedom (DOF) kinematics from EMG, output DOFs are usually estimated independently. In this study, we estimate finger joint kinematics from EMG signals using a multi-output convolved Gaussian Process (Multi-output Full GP) that considers dependencies between outputs. We show that estimation of finger joints from muscle activation inputs can be improved by using a regression model that considers inherent coupling or correlation within the hand and finger joints. We also provide a comparison of estimation performance between different regression methods, such as Artificial Neural Networks (ANN) which is used by many of the related studies. We show that using a multi-output GP gives improved estimation compared to multi-output ANN and even dedicated or independent regression models.

Speech Enhancement Using Gaussian Scale Mixture Models

PubMed Central

Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J.

2011-01-01

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. PMID:21359139

State-space models’ dirty little secrets: even simple linear Gaussian models can have estimation problems

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.

Image denoising in mixed Poisson-Gaussian noise.

PubMed

Luisier, Florian; Blu, Thierry; Unser, Michael

2011-03-01

We propose a general methodology (PURE-LET) to design and optimize a wide class of transform-domain thresholding algorithms for denoising images corrupted by mixed Poisson-Gaussian noise. We express the denoising process as a linear expansion of thresholds (LET) that we optimize by relying on a purely data-adaptive unbiased estimate of the mean-squared error (MSE), derived in a non-Bayesian framework (PURE: Poisson-Gaussian unbiased risk estimate). We provide a practical approximation of this theoretical MSE estimate for the tractable optimization of arbitrary transform-domain thresholding. We then propose a pointwise estimator for undecimated filterbank transforms, which consists of subband-adaptive thresholding functions with signal-dependent thresholds that are globally optimized in the image domain. We finally demonstrate the potential of the proposed approach through extensive comparisons with state-of-the-art techniques that are specifically tailored to the estimation of Poisson intensities. We also present denoising results obtained on real images of low-count fluorescence microscopy.

Recovering Sample Diversity in Rao-Blackwellized Particle Filters for Simultaneous Localization and Mapping

DTIC Science & Technology

2006-06-01

mnost wheel -lbased robo )ts. The lparamieter valut es a)re listed itt table 4.2, with the tatngential and angutlar velocities at each tithe 61 Commanded...in the age ut pose and map are redlced (B). a suite of other measurelnent devices designed to auggment inertial measurements: Doppler radar, wheel ...aunl relatixe spaci ng of landmluarks, giving thle age~nt more or fewer anchior features. or simply changing t le (-onlimnanded robo p lathi -oulld

Non-Gaussianity in a quasiclassical electronic circuit

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi J.; Hayakawa, Hisao

2017-05-01

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

Separation of components from a scale mixture of Gaussian white noises

NASA Astrophysics Data System (ADS)

Vamoş, Călin; Crăciun, Maria

2010-05-01

The time evolution of a physical quantity associated with a thermodynamic system whose equilibrium fluctuations are modulated in amplitude by a slowly varying phenomenon can be modeled as the product of a Gaussian white noise {Zt} and a stochastic process with strictly positive values {Vt} referred to as volatility. The probability density function (pdf) of the process Xt=VtZt is a scale mixture of Gaussian white noises expressed as a time average of Gaussian distributions weighted by the pdf of the volatility. The separation of the two components of {Xt} can be achieved by imposing the condition that the absolute values of the estimated white noise be uncorrelated. We apply this method to the time series of the returns of the daily S&P500 index, which has also been analyzed by means of the superstatistics method that imposes the condition that the estimated white noise be Gaussian. The advantage of our method is that this financial time series is processed without partitioning or removal of the extreme events and the estimated white noise becomes almost Gaussian only as result of the uncorrelation condition.

Analysis of randomly time varying systems by gaussian closure technique

NASA Astrophysics Data System (ADS)

Dash, P. K.; Iyengar, R. N.

1982-07-01

The Gaussian probability closure technique is applied to study the random response of multidegree of freedom stochastically time varying systems under non-Gaussian excitations. Under the assumption that the response, the coefficient and the excitation processes are jointly Gaussian, deterministic equations are derived for the first two response moments. It is further shown that this technique leads to the best Gaussian estimate in a minimum mean square error sense. An example problem is solved which demonstrates the capability of this technique for handling non-linearity, stochastic system parameters and amplitude limited responses in a unified manner. Numerical results obtained through the Gaussian closure technique compare well with the exact solutions.

EM-1 Countdown Simulation with Charlie Blackwell-Thompson

NASA Image and Video Library

2018-03-29

NASA Launch Director Charlie Blackwell-Thompson follows operations in Firing Room 1 at the Kennedy Space Center's Launch Control Center during a countdown simulation for Exploration Mission 1. It was the agency's first simulation of a portion of the countdown for the first launch of a Space Launch System rocket and Orion spacecraft that will eventually take astronauts beyond low-Earth orbit to destinations such as the Moon and Mars.

EM-1 Countdown Simulation with Charlie Blackwell-Thompson

NASA Image and Video Library

2018-03-29

NASA Launch Director Charlie Blackwell-Thompson at her console in Firing Room 1 at the Kennedy Space Center's Launch Control Center during a countdown simulation for Exploration Mission 1. It was the agency's first simulation of a portion of the countdown for the first launch of a Space Launch System rocket and Orion spacecraft that will eventually take astronauts beyond low-Earth orbit to destinations such as the Moon and Mars.

Optimisation of dispersion parameters of Gaussian plume model for CO₂ dispersion.

PubMed

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.

26. 'CITY HOSPITAL, BLACKWELL'S ISLAND.' (Source: New York City Department ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

26. 'CITY HOSPITAL, BLACKWELL'S ISLAND.' (Source: New York City Department of Public Finance, Real Estate Owned by the City of New York under Jurisdiction of the Department of Public Charities, 1909.) - Island Hospital, Roosevelt Island, New York County, NY

Rapid construction of pinhole SPECT system matrices by distance-weighted Gaussian interpolation method combined with geometric parameter estimations

NASA Astrophysics Data System (ADS)

Lee, Ming-Wei; Chen, Yi-Chun

2014-02-01

In pinhole SPECT applied to small-animal studies, it is essential to have an accurate imaging system matrix, called H matrix, for high-spatial-resolution image reconstructions. Generally, an H matrix can be obtained by various methods, such as measurements, simulations or some combinations of both methods. In this study, a distance-weighted Gaussian interpolation method combined with geometric parameter estimations (DW-GIMGPE) is proposed. It utilizes a simplified grid-scan experiment on selected voxels and parameterizes the measured point response functions (PRFs) into 2D Gaussians. The PRFs of missing voxels are interpolated by the relations between the Gaussian coefficients and the geometric parameters of the imaging system with distance-weighting factors. The weighting factors are related to the projected centroids of voxels on the detector plane. A full H matrix is constructed by combining the measured and interpolated PRFs of all voxels. The PRFs estimated by DW-GIMGPE showed similar profiles as the measured PRFs. OSEM reconstructed images of a hot-rod phantom and normal rat myocardium demonstrated the effectiveness of the proposed method. The detectability of a SKE/BKE task on a synthetic spherical test object verified that the constructed H matrix provided comparable detectability to that of the H matrix acquired by a full 3D grid-scan experiment. The reduction in the acquisition time of a full 1.0-mm grid H matrix was about 15.2 and 62.2 times with the simplified grid pattern on 2.0-mm and 4.0-mm grid, respectively. A finer-grid H matrix down to 0.5-mm spacing interpolated by the proposed method would shorten the acquisition time by 8 times, additionally.

Estimating replicate time shifts using Gaussian process regression

PubMed Central

Liu, Qiang; Andersen, Bogi; Smyth, Padhraic; Ihler, Alexander

2010-01-01

Motivation: Time-course gene expression datasets provide important insights into dynamic aspects of biological processes, such as circadian rhythms, cell cycle and organ development. In a typical microarray time-course experiment, measurements are obtained at each time point from multiple replicate samples. Accurately recovering the gene expression patterns from experimental observations is made challenging by both measurement noise and variation among replicates' rates of development. Prior work on this topic has focused on inference of expression patterns assuming that the replicate times are synchronized. We develop a statistical approach that simultaneously infers both (i) the underlying (hidden) expression profile for each gene, as well as (ii) the biological time for each individual replicate. Our approach is based on Gaussian process regression (GPR) combined with a probabilistic model that accounts for uncertainty about the biological development time of each replicate. Results: We apply GPR with uncertain measurement times to a microarray dataset of mRNA expression for the hair-growth cycle in mouse back skin, predicting both profile shapes and biological times for each replicate. The predicted time shifts show high consistency with independently obtained morphological estimates of relative development. We also show that the method systematically reduces prediction error on out-of-sample data, significantly reducing the mean squared error in a cross-validation study. Availability: Matlab code for GPR with uncertain time shifts is available at http://sli.ics.uci.edu/Code/GPRTimeshift/ Contact: ihler@ics.uci.edu PMID:20147305

A New Non-gaussian Turbulent Wind Field Generator to Estimate Design-Loads of Wind-Turbines

NASA Astrophysics Data System (ADS)

Schaffarczyk, A. P.; Gontier, H.; Kleinhans, D.; Friedrich, R.

Climate change and finite fossil fuel resources make it urgent to turn into electricity generation from mostly renewable energies. One major part will play wind-energy supplied by wind-turbines of rated power up to 10 MW. For their design and development wind field models have to be used. The standard models are based on the empirical spectra, for example by von Karman or Kaimal. From investigation of measured data it is clear that gusts are underrepresented in such models. Based on some fundamental discoveries of the nature of turbulence by Friedrich [1] derived from the Navier-Stokes equation directly, we used the concept of Continuous Time Random Walks to construct three dimensional wind fields obeying non-Gaussian statistics. These wind fields were used to estimate critical fatigue loads necessary within the certification process. Calculations are carried out with an implementation of a beam-model (FLEX5) for two types of state-of-the-art wind turbines The authors considered the edgewise and flapwise blade-root bending moments as well as tilt moment at tower top due to the standard wind field models and our new non-Gaussian wind field model. Clear differences in the loads were found.

Distilling Gaussian states with Gaussian operations is impossible.

PubMed

Eisert, J; Scheel, S; Plenio, M B

2002-09-23

We show that no distillation protocol for Gaussian quantum states exists that relies on (i) arbitrary local unitary operations that preserve the Gaussian character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local Gaussian unitary operations on two symmetric identically prepared copies. This is in contrast to the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time. The ramifications for the distribution of Gaussian states over large distances will be outlined. We also comment on the generality of the approach and sketch the most general form of a Gaussian local operation with classical communication in a bipartite setting.

EM-1 Countdown Simulation with Charlie Blackwell-Thompson

NASA Image and Video Library

2018-03-29

NASA Launch Director Charlie Blackwell-Thompson follows operations at her console in Firing Room 1 at the Kennedy Space Center's Launch Control Center during a countdown simulation for Exploration Mission 1. It was the agency's first simulation of a portion of the countdown for the first launch of a Space Launch System rocket and Orion spacecraft that will eventually take astronauts beyond low-Earth orbit to destinations such as the Moon and Mars.

EM-1 Countdown Simulation with Charlie Blackwell-Thompson

NASA Image and Video Library

2018-03-29

NASA Launch Director Charlie Blackwell-Thompson stands next to her console in Firing Room 1 at the Kennedy Space Center's Launch Control Center during a countdown simulation for Exploration Mission 1. It was the agency's first simulation of a portion of the countdown for the first launch of a Space Launch System rocket and Orion spacecraft that will eventually take astronauts beyond low-Earth orbit to destinations such as the Moon and Mars.

EM-1 Countdown Simulation with Charlie Blackwell-Thompson

NASA Image and Video Library

2018-03-29

NASA Launch Director Charlie Blackwell-Thompson follows operations at her console in Firing Room 1 at the Kennedy Space Center's Launch Control Center during a countdown simulation for Exploration Mission-1. It was the agency's first simulation of a portion of the countdown for the first launch of a Space Launch System rocket and Orion spacecraft that will eventually take astronauts beyond low-Earth orbit to destinations such as the Moon and Mars.

Fixing convergence of Gaussian belief propagation

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

Johnson, Jason K; Bickson, Danny; Dolev, Danny

Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm ismore » linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanari's linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.« less

Normal form decomposition for Gaussian-to-Gaussian superoperators

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

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

2015-05-15

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

Using Monte Carlo/Gaussian Based Small Area Estimates to Predict Where Medicaid Patients Reside.

PubMed

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 health 1,2 . With the national dialogue around Medicaid expansion 12 , 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 Carolina 11 . 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.

25. 'VIEW OF CITY HOSPITAL DISTRICT, BLACKWELL'S ISLAND, FROM MANHATTAN ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

25. 'VIEW OF CITY HOSPITAL DISTRICT, BLACKWELL'S ISLAND, FROM MANHATTAN SHORE.' (Source: New York City Department of Public Finance, Real Estate Owned by the City of New York Under Jurisdiction of the Department of Public Charities, 1909.) - Island Hospital, Roosevelt Island, New York County, NY

An algorithm for separation of mixed sparse and Gaussian sources

PubMed Central

Akkalkotkar, Ameya

2017-01-01

Independent component analysis (ICA) is a ubiquitous method for decomposing complex signal mixtures into a small set of statistically independent source signals. However, in cases in which the signal mixture consists of both nongaussian and Gaussian sources, the Gaussian sources will not be recoverable by ICA and will pollute estimates of the nongaussian sources. Therefore, it is desirable to have methods for mixed ICA/PCA which can separate mixtures of Gaussian and nongaussian sources. For mixtures of purely Gaussian sources, principal component analysis (PCA) can provide a basis for the Gaussian subspace. We introduce a new method for mixed ICA/PCA which we call Mixed ICA/PCA via Reproducibility Stability (MIPReSt). Our method uses a repeated estimations technique to rank sources by reproducibility, combined with decomposition of multiple subsamplings of the original data matrix. These multiple decompositions allow us to assess component stability as the size of the data matrix changes, which can be used to determinine the dimension of the nongaussian subspace in a mixture. We demonstrate the utility of MIPReSt for signal mixtures consisting of simulated sources and real-word (speech) sources, as well as mixture of unknown composition. PMID:28414814

An algorithm for separation of mixed sparse and Gaussian sources.

PubMed

Akkalkotkar, Ameya; Brown, Kevin Scott

2017-01-01

Independent component analysis (ICA) is a ubiquitous method for decomposing complex signal mixtures into a small set of statistically independent source signals. However, in cases in which the signal mixture consists of both nongaussian and Gaussian sources, the Gaussian sources will not be recoverable by ICA and will pollute estimates of the nongaussian sources. Therefore, it is desirable to have methods for mixed ICA/PCA which can separate mixtures of Gaussian and nongaussian sources. For mixtures of purely Gaussian sources, principal component analysis (PCA) can provide a basis for the Gaussian subspace. We introduce a new method for mixed ICA/PCA which we call Mixed ICA/PCA via Reproducibility Stability (MIPReSt). Our method uses a repeated estimations technique to rank sources by reproducibility, combined with decomposition of multiple subsamplings of the original data matrix. These multiple decompositions allow us to assess component stability as the size of the data matrix changes, which can be used to determinine the dimension of the nongaussian subspace in a mixture. We demonstrate the utility of MIPReSt for signal mixtures consisting of simulated sources and real-word (speech) sources, as well as mixture of unknown composition.

Sequential bearings-only-tracking initiation with particle filtering method.

PubMed

Liu, Bin; Hao, Chengpeng

2013-01-01

The tracking initiation problem is examined in the context of autonomous bearings-only-tracking (BOT) of a single appearing/disappearing target in the presence of clutter measurements. In general, this problem suffers from a combinatorial explosion in the number of potential tracks resulted from the uncertainty in the linkage between the target and the measurement (a.k.a the data association problem). In addition, the nonlinear measurements lead to a non-Gaussian posterior probability density function (pdf) in the optimal Bayesian sequential estimation framework. The consequence of this nonlinear/non-Gaussian context is the absence of a closed-form solution. This paper models the linkage uncertainty and the nonlinear/non-Gaussian estimation problem jointly with solid Bayesian formalism. A particle filtering (PF) algorithm is derived for estimating the model's parameters in a sequential manner. Numerical results show that the proposed solution provides a significant benefit over the most commonly used methods, IPDA and IMMPDA. The posterior Cramér-Rao bounds are also involved for performance evaluation.

Estimation of diffusion coefficients from voltammetric signals by support vector and gaussian process regression

PubMed Central

2014-01-01

Background Support vector regression (SVR) and Gaussian process regression (GPR) were used for the analysis of electroanalytical experimental data to estimate diffusion coefficients. Results For simulated cyclic voltammograms based on the EC, Eqr, and EqrC mechanisms these regression algorithms in combination with nonlinear kernel/covariance functions yielded diffusion coefficients with higher accuracy as compared to the standard approach of calculating diffusion coefficients relying on the Nicholson-Shain equation. The level of accuracy achieved by SVR and GPR is virtually independent of the rate constants governing the respective reaction steps. Further, the reduction of high-dimensional voltammetric signals by manual selection of typical voltammetric peak features decreased the performance of both regression algorithms compared to a reduction by downsampling or principal component analysis. After training on simulated data sets, diffusion coefficients were estimated by the regression algorithms for experimental data comprising voltammetric signals for three organometallic complexes. Conclusions Estimated diffusion coefficients closely matched the values determined by the parameter fitting method, but reduced the required computational time considerably for one of the reaction mechanisms. The automated processing of voltammograms according to the regression algorithms yields better results than the conventional analysis of peak-related data. PMID:24987463

Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data [Regularized maximum likelihood estimation of ground reflectivity from stripmap SAR data

DOE PAGES

West, R. Derek; Gunther, Jacob H.; Moon, Todd K.

2016-12-01

In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts tomore » a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.« less

Inverse problems-based maximum likelihood estimation of ground reflectivity for selected regions of interest from stripmap SAR data [Regularized maximum likelihood estimation of ground reflectivity from stripmap SAR data

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

West, R. Derek; Gunther, Jacob H.; Moon, Todd K.

In this study, we derive a comprehensive forward model for the data collected by stripmap synthetic aperture radar (SAR) that is linear in the ground reflectivity parameters. It is also shown that if the noise model is additive, then the forward model fits into the linear statistical model framework, and the ground reflectivity parameters can be estimated by statistical methods. We derive the maximum likelihood (ML) estimates for the ground reflectivity parameters in the case of additive white Gaussian noise. Furthermore, we show that obtaining the ML estimates of the ground reflectivity requires two steps. The first step amounts tomore » a cross-correlation of the data with a model of the data acquisition parameters, and it is shown that this step has essentially the same processing as the so-called convolution back-projection algorithm. The second step is a complete system inversion that is capable of mitigating the sidelobes of the spatially variant impulse responses remaining after the correlation processing. We also state the Cramer-Rao lower bound (CRLB) for the ML ground reflectivity estimates.We show that the CRLB is linked to the SAR system parameters, the flight path of the SAR sensor, and the image reconstruction grid.We demonstrate the ML image formation and the CRLB bound for synthetically generated data.« less

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

NASA Astrophysics Data System (ADS)

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

1998-03-01

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

EM-1 Countdown Simulation with Charlie Blackwell-Thompson

NASA Image and Video Library

2018-03-29

NASA Launch Director Charlie Blackwell-Thompson, above, confers with Senior NASA Test Director Jeff Spaulding, left, and Chief NASA Test Director Jeremy Graeber in Firing Room 1 at the Kennedy Space Center's Launch Control Center during a countdown simulation for Exploration Mission 1. It was the agency's first simulation of a portion of the countdown for the first launch of a Space Launch System rocket and Orion spacecraft that will eventually take astronauts beyond low-Earth orbit to destinations such as the Moon and Mars.

Fisher information theory for parameter estimation in single molecule microscopy: tutorial

PubMed Central

Chao, Jerry; Ward, E. Sally; Ober, Raimund J.

2016-01-01

Estimation of a parameter of interest from image data represents a task that is commonly carried out in single molecule microscopy data analysis. The determination of the positional coordinates of a molecule from its image, for example, forms the basis of standard applications such as single molecule tracking and localization-based superresolution image reconstruction. Assuming that the estimator used recovers, on average, the true value of the parameter, its accuracy, or standard deviation, is then at best equal to the square root of the Cramér-Rao lower bound. The Cramér-Rao lower bound can therefore be used as a benchmark in the evaluation of the accuracy of an estimator. Additionally, as its value can be computed and assessed for different experimental settings, it is useful as an experimental design tool. This tutorial demonstrates a mathematical framework that has been specifically developed to calculate the Cramér-Rao lower bound for estimation problems in single molecule microscopy and, more broadly, fluorescence microscopy. The material includes a presentation of the photon detection process that underlies all image data, various image data models that describe images acquired with different detector types, and Fisher information expressions that are necessary for the calculation of the lower bound. Throughout the tutorial, examples involving concrete estimation problems are used to illustrate the effects of various factors on the accuracy of parameter estimation, and more generally, to demonstrate the flexibility of the mathematical framework. PMID:27409706

The binned bispectrum estimator: template-based and non-parametric CMB non-Gaussianity searches

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

Bucher, Martin; Racine, Benjamin; Tent, Bartjan van, E-mail: bucher@apc.univ-paris7.fr, E-mail: benjar@uio.no, E-mail: vantent@th.u-psud.fr

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 f NL 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 ordermore » 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.« less

Grantee Spotlight: Veena Rao, Ph.D. - Unraveling the Mysteries of BRCA1 in African American Women

Cancer.gov

Dr. Veena N. Rao, a CRCHD PACHE U54 grantee, researches the BRCA1 gene and its role in breast and ovarian cancer in diverse populations and trains diverse scholars in cancer health disparities research.

Estimation of unemployment rates using small area estimation model by combining time series and cross-sectional data

NASA Astrophysics Data System (ADS)

Muchlisoh, Siti; Kurnia, Anang; Notodiputro, Khairil Anwar; Mangku, I. Wayan

2016-02-01

Labor force surveys conducted over time by the rotating panel design have been carried out in many countries, including Indonesia. Labor force survey in Indonesia is regularly conducted by Statistics Indonesia (Badan Pusat Statistik-BPS) and has been known as the National Labor Force Survey (Sakernas). The main purpose of Sakernas is to obtain information about unemployment rates and its changes over time. Sakernas is a quarterly survey. The quarterly survey is designed only for estimating the parameters at the provincial level. The quarterly unemployment rate published by BPS (official statistics) is calculated based on only cross-sectional methods, despite the fact that the data is collected under rotating panel design. The study purpose to estimate a quarterly unemployment rate at the district level used small area estimation (SAE) model by combining time series and cross-sectional data. The study focused on the application and comparison between the Rao-Yu model and dynamic model in context estimating the unemployment rate based on a rotating panel survey. The goodness of fit of both models was almost similar. Both models produced an almost similar estimation and better than direct estimation, but the dynamic model was more capable than the Rao-Yu model to capture a heterogeneity across area, although it was reduced over time.

Modeling Sea-Level Change using Errors-in-Variables Integrated Gaussian Processes

NASA Astrophysics Data System (ADS)

Cahill, Niamh; Parnell, Andrew; Kemp, Andrew; Horton, Benjamin

2014-05-01

We perform Bayesian inference on historical and late Holocene (last 2000 years) rates of sea-level change. The data that form the input to our model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. To accurately estimate rates of sea-level change and reliably compare tide-gauge compilations with proxy reconstructions it is necessary to account for the uncertainties that characterize each dataset. Many previous studies used simple linear regression models (most commonly polynomial regression) resulting in overly precise rate estimates. The model we propose uses an integrated Gaussian process approach, where a Gaussian process prior is placed on the rate of sea-level change and the data itself is modeled as the integral of this rate process. The non-parametric Gaussian process model is known to be well suited to modeling time series data. The advantage of using an integrated Gaussian process is that it allows for the direct estimation of the derivative of a one dimensional curve. The derivative at a particular time point will be representative of the rate of sea level change at that time point. The tide gauge and proxy data are complicated by multiple sources of uncertainty, some of which arise as part of the data collection exercise. Most notably, the proxy reconstructions include temporal uncertainty from dating of the sediment core using techniques such as radiocarbon. As a result of this, the integrated Gaussian process model is set in an errors-in-variables (EIV) framework so as to take account of this temporal uncertainty. The data must be corrected for land-level change known as glacio-isostatic adjustment (GIA) as it is important to isolate the climate-related sea-level signal. The correction for GIA introduces covariance between individual age and sea level observations into the model. The proposed integrated Gaussian process model allows for the estimation of instantaneous rates of sea-level change and accounts for all

Asymptotic Cramer-Rao bounds for Morlet wavelet filter bank transforms of FM signals

NASA Astrophysics Data System (ADS)

Scheper, Richard

2002-03-01

Wavelet filter banks are potentially useful tools for analyzing and extracting information from frequency modulated (FM) signals in noise. Chief among the advantages of such filter banks is the tendency of wavelet transforms to concentrate signal energy while simultaneously dispersing noise energy over the time-frequency plane, thus raising the effective signal to noise ratio of filtered signals. Over the past decade, much effort has gone into devising new algorithms to extract the relevant information from transformed signals while identifying and discarding the transformed noise. Therefore, estimates of the ultimate performance bounds on such algorithms would serve as valuable benchmarks in the process of choosing optimal algorithms for given signal classes. Discussed here is the specific case of FM signals analyzed by Morlet wavelet filter banks. By making use of the stationary phase approximation of the Morlet transform, and assuming that the measured signals are well resolved digitally, the asymptotic form of the Fisher Information Matrix is derived. From this, Cramer-Rao bounds are analytically derived for simple cases.

An internal reference model-based PRF temperature mapping method with Cramer-Rao lower bound noise performance analysis.

PubMed

Li, Cheng; Pan, Xinyi; Ying, Kui; Zhang, Qiang; An, Jing; Weng, Dehe; Qin, Wen; Li, Kuncheng

2009-11-01

The conventional phase difference method for MR thermometry suffers from disturbances caused by the presence of lipid protons, motion-induced error, and field drift. A signal model is presented with multi-echo gradient echo (GRE) sequence using a fat signal as an internal reference to overcome these problems. The internal reference signal model is fit to the water and fat signals by the extended Prony algorithm and the Levenberg-Marquardt algorithm to estimate the chemical shifts between water and fat which contain temperature information. A noise analysis of the signal model was conducted using the Cramer-Rao lower bound to evaluate the noise performance of various algorithms, the effects of imaging parameters, and the influence of the water:fat signal ratio in a sample on the temperature estimate. Comparison of the calculated temperature map and thermocouple temperature measurements shows that the maximum temperature estimation error is 0.614 degrees C, with a standard deviation of 0.06 degrees C, confirming the feasibility of this model-based temperature mapping method. The influence of sample water:fat signal ratio on the accuracy of the temperature estimate is evaluated in a water-fat mixed phantom experiment with an optimal ratio of approximately 0.66:1. (c) 2009 Wiley-Liss, Inc.

Gaussian entanglement revisited

NASA Astrophysics Data System (ADS)

Lami, Ludovico; Serafini, Alessio; Adesso, Gerardo

2018-02-01

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

Quantum key distillation from Gaussian states by Gaussian operations.

PubMed

Navascués, M; Bae, J; Cirac, J I; Lewestein, M; Sanpera, A; Acín, A

2005-01-14

We study the secrecy properties of Gaussian states under Gaussian operations. Although such operations are useless for quantum distillation, we prove that it is possible to distill a secret key secure against any attack from sufficiently entangled Gaussian states with nonpositive partial transposition. Moreover, all such states allow for key distillation, when Eve is assumed to perform finite-size coherent attacks before the reconciliation process.

Human retina-specific amine oxidase (RAO): cDNA cloning, tissue expression, and chromosomal mapping

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

Imamura, Yutaka; Kubota, Ryo; Wang, Yimin

In search of candidate genes for hereditary retinal disease, we have employed a subtractive and differential cDNA cloning strategy and isolated a novel retina-specific cDNA. Nucleotide sequence analysis revealed an open reading frame of 2187 bp, which encodes a 729-amino-acid protein with a calculated molecular mass of 80,644 Da. The putative protein contained a conserved domain of copper amine oxidase, which is found in various species from bacteria to mammals. It showed the highest homology to bovine serum amine oxidase, which is believed to control the level of serum biogenic amines. Northern blot analysis of human adult and fetal tissuesmore » revealed that the protein is expressed abundantly and specifically in retina as a 2.7-kb transcript. Thus, we considered this protein a human retina-specific amine oxidase (RAO). The RAO gene (AOC2) was mapped by fluorescence in situ hybridization to human chromosome 17q21. We propose that AOC2 may be a candidate gene for hereditary ocular diseases. 38 refs., 4 figs.« less

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

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

Monras, Alex; Illuminati, Fabrizio

2011-01-15

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

Automated nodule location and size estimation using a multi-scale Laplacian of Gaussian filtering approach.

PubMed

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.

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

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

Adesso, Gerardo; Illuminati, Fabrizio; INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi, SA

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 fixedmore » 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

A Gaussian beam method for ultrasonic non-destructive evaluation modeling

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Gaussian Curvature as an Identifier of Shell Rigidity

NASA Astrophysics Data System (ADS)

Harutyunyan, Davit

2017-11-01

In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shell for zero or periodic Dirichlet, Neumann, and Robin type boundary conditions. We prove that if the Gaussian curvature is positive, then the optimal constant in the first Korn inequality scales like h, and if the Gaussian curvature is negative, then the Korn constant scales like h 4/3, where h is the thickness of the shell. These results have a classical flavour in continuum mechanics, in particular shell theory. The Korn first inequalities are the linear version of the famous geometric rigidity estimate by Friesecke et al. for plates in Arch Ration Mech Anal 180(2):183-236, 2006 (where they show that the Korn constant in the nonlinear Korn's first inequality scales like h 2), extended to shells with nonzero curvature. We also recover the uniform Korn-Poincaré inequality proven for "boundary-less" shells by Lewicka and Müller in Annales de l'Institute Henri Poincare (C) Non Linear Anal 28(3):443-469, 2011 in the setting of our problem. The new estimates can also be applied to find the scaling law for the critical buckling load of the shell under in-plane loads as well as to derive energy scaling laws in the pre-buckled regime. The exponents 1 and 4/3 in the present work appear for the first time in any sharp geometric rigidity estimate.

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

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 novel Gaussian process regression model for state-of-health estimation of lithium-ion battery using charging curve

NASA Astrophysics Data System (ADS)

Yang, Duo; Zhang, Xu; Pan, Rui; Wang, Yujie; Chen, Zonghai

2018-04-01

The state-of-health (SOH) estimation is always a crucial issue for lithium-ion batteries. In order to provide an accurate and reliable SOH estimation, a novel Gaussian process regression (GPR) model based on charging curve is proposed in this paper. Different from other researches where SOH is commonly estimated by cycle life, in this work four specific parameters extracted from charging curves are used as inputs of the GPR model instead of cycle numbers. These parameters can reflect the battery aging phenomenon from different angles. The grey relational analysis method is applied to analyze the relational grade between selected features and SOH. On the other hand, some adjustments are made in the proposed GPR model. Covariance function design and the similarity measurement of input variables are modified so as to improve the SOH estimate accuracy and adapt to the case of multidimensional input. Several aging data from NASA data repository are used for demonstrating the estimation effect by the proposed method. Results show that the proposed method has high SOH estimation accuracy. Besides, a battery with dynamic discharging profile is used to verify the robustness and reliability of this method.

Pairwise alignment of chromatograms using an extended Fisher-Rao metric.

PubMed

Wallace, W E; Srivastava, A; Telu, K H; Simón-Manso, Y

2014-09-02

A conceptually new approach for aligning chromatograms is introduced and applied to examples of metabolite identification in human blood plasma by liquid chromatography-mass spectrometry (LC-MS). A square-root representation of the chromatogram's derivative coupled with an extended Fisher-Rao metric enables the computation of relative differences between chromatograms. Minimization of these differences using a common dynamic programming algorithm brings the chromatograms into alignment. Application to a complex sample, National Institute of Standards and Technology (NIST) Standard Reference Material 1950, Metabolites in Human Plasma, analyzed by two different LC-MS methods having significantly different ranges of elution time is described. Published by Elsevier B.V.

Gaussian Boson Sampling.

PubMed

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

2017-10-27

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

Generalized Ince Gaussian beams

NASA Astrophysics Data System (ADS)

Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

2006-08-01

In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.

Assessing Gaussian Assumption of PMU Measurement Error Using Field Data

DOE PAGES

Wang, Shaobu; Zhao, Junbo; Huang, Zhenyu; ...

2017-10-13

Gaussian PMU measurement error has been assumed for many power system applications, such as state estimation, oscillatory modes monitoring, voltage stability analysis, to cite a few. This letter proposes a simple yet effective approach to assess this assumption by using the stability property of a probability distribution and the concept of redundant measurement. Extensive results using field PMU data from WECC system reveal that the Gaussian assumption is questionable.

Stable Lévy motion with inverse Gaussian subordinator

NASA Astrophysics Data System (ADS)

Kumar, A.; Wyłomańska, A.; Gajda, J.

2017-09-01

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

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

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

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

Leading non-Gaussian corrections for diffusion orientation distribution function.

PubMed

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

2014-02-01

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

Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function

PubMed Central

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

2014-01-01

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

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

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

Stein, Michael

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

Quantifying non-Gaussianity for quantum information

NASA Astrophysics Data System (ADS)

Genoni, Marco G.; Paris, Matteo G. A.

2010-11-01

We address the quantification of non-Gaussianity (nG) of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in detail the properties and the relationships of two recently proposed measures of nG based on the Hilbert-Schmidt distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behavior in most of the examples taken into account. However, we also show that they introduce a different relation of order; that is, they are not strictly monotone to each other. We exploit the nG measures for states in order to introduce a measure of nG for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in detail the role played by nG in entanglement-distillation protocols. Besides, we exploit the QRE-based nG measure to provide different insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information, and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nG to the quantum Fisher information. Finally, since evaluation of the QRE nG measure requires the knowledge of the full density matrix, we derive some experimentally friendly lower bounds to nG for some classes of states and by considering the possibility of performing on the states only certain efficient or inefficient measurements.

Resource theory of non-Gaussian operations

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

The application of Gaussian mixture models for signal quantification in MALDI-TOF mass spectrometry of peptides.

PubMed

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

XDGMM: eXtreme Deconvolution Gaussian Mixture Modeling

NASA Astrophysics Data System (ADS)

Holoien, Thomas W.-S.; Marshall, Philip J.; Wechsler, Risa H.

2017-08-01

XDGMM uses Gaussian mixtures to do density estimation of noisy, heterogenous, and incomplete data using extreme deconvolution (XD) algorithms which is compatible with the scikit-learn machine learning methods. It implements both the astroML and Bovy et al. (2011) algorithms, and extends the BaseEstimator class from scikit-learn so that cross-validation methods work. It allows the user to produce a conditioned model if values of some parameters are known.

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.

2002-01-01

Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

Predicting minimum uncertainties in the inversion of ocean color geophysical parameters based on Cramer-Rao bounds.

PubMed

Jay, Sylvain; Guillaume, Mireille; Chami, Malik; Minghelli, Audrey; Deville, Yannick; Lafrance, Bruno; Serfaty, Véronique

2018-01-22

We present an analytical approach based on Cramer-Rao Bounds (CRBs) to investigate the uncertainties in estimated ocean color parameters resulting from the propagation of uncertainties in the bio-optical reflectance modeling through the inversion process. Based on given bio-optical and noise probabilistic models, CRBs can be computed efficiently for any set of ocean color parameters and any sensor configuration, directly providing the minimum estimation variance that can be possibly attained by any unbiased estimator of any targeted parameter. Here, CRBs are explicitly developed using (1) two water reflectance models corresponding to deep and shallow waters, resp., and (2) four probabilistic models describing the environmental noises observed within four Sentinel-2 MSI, HICO, Sentinel-3 OLCI and MODIS images, resp. For both deep and shallow waters, CRBs are shown to be consistent with the experimental estimation variances obtained using two published remote-sensing methods, while not requiring one to perform any inversion. CRBs are also used to investigate to what extent perfect a priori knowledge on one or several geophysical parameters can improve the estimation of remaining unknown parameters. For example, using pre-existing knowledge of bathymetry (e.g., derived from LiDAR) within the inversion is shown to greatly improve the retrieval of bottom cover for shallow waters. Finally, CRBs are shown to provide valuable information on the best estimation performances that may be achieved with the MSI, HICO, OLCI and MODIS configurations for a variety of oceanic, coastal and inland waters. CRBs are thus demonstrated to be an informative and efficient tool to characterize minimum uncertainties in inverted ocean color geophysical parameters.

The Gaussian atmospheric transport model and its sensitivity to the joint frequency distribution and parametric variability.

PubMed

Hamby, D M

2002-01-01

Reconstructed meteorological data are often used in some form of long-term wind trajectory models for estimating the historical impacts of atmospheric emissions. Meteorological data for the straight-line Gaussian plume model are put into a joint frequency distribution, a three-dimensional array describing atmospheric wind direction, speed, and stability. Methods using the Gaussian model and joint frequency distribution inputs provide reasonable estimates of downwind concentration and have been shown to be accurate to within a factor of four. We have used multiple joint frequency distributions and probabilistic techniques to assess the Gaussian plume model and determine concentration-estimate uncertainty and model sensitivity. We examine the straight-line Gaussian model while calculating both sector-averaged and annual-averaged relative concentrations at various downwind distances. The sector-average concentration model was found to be most sensitive to wind speed, followed by horizontal dispersion (sigmaZ), the importance of which increases as stability increases. The Gaussian model is not sensitive to stack height uncertainty. Precision of the frequency data appears to be most important to meteorological inputs when calculations are made for near-field receptors, increasing as stack height increases.

Determining the Gaussian Modulus and Edge Properties of 2D Materials: From Graphene to Lipid Bilayers

NASA Astrophysics Data System (ADS)

Zelisko, Matthew; Ahmadpoor, Fatemeh; Gao, Huajian; Sharma, Pradeep

2017-08-01

The dominant deformation behavior of two-dimensional materials (bending) is primarily governed by just two parameters: bending rigidity and the Gaussian modulus. These properties also set the energy scale for various important physical and biological processes such as pore formation, cell fission and generally, any event accompanied by a topological change. Unlike the bending rigidity, the Gaussian modulus is, however, notoriously difficult to evaluate via either experiments or atomistic simulations. In this Letter, recognizing that the Gaussian modulus and edge tension play a nontrivial role in the fluctuations of a 2D material edge, we derive closed-form expressions for edge fluctuations. Combined with atomistic simulations, we use the developed approach to extract the Gaussian modulus and edge tension at finite temperatures for both graphene and various types of lipid bilayers. Our results possibly provide the first reliable estimate of this elusive property at finite temperatures and appear to suggest that earlier estimates must be revised. In particular, we show that, if previously estimated properties are employed, the graphene-free edge will exhibit unstable behavior at room temperature. Remarkably, in the case of graphene, we show that the Gaussian modulus and edge tension even change sign at finite temperatures.

GPZ: non-stationary sparse Gaussian processes for heteroscedastic uncertainty estimation in photometric redshifts

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.

Multi-Target Tracking Using an Improved Gaussian Mixture CPHD Filter.

PubMed

Si, Weijian; Wang, Liwei; Qu, Zhiyu

2016-11-23

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.

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

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.

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: Semiclassical treatment

NASA Astrophysics Data System (ADS)

Tsang, Mankei

2018-02-01

I present a semiclassical analysis of a spatial-mode demultiplexing (SPADE) measurement scheme for far-field incoherent optical imaging under the effects of diffraction and photon shot noise. Building on previous results that assume two point sources or the Gaussian point-spread function, I generalize SPADE for a larger class of point-spread functions and evaluate its errors in estimating the moments of an arbitrary subdiffraction object. Compared with the limits to direct imaging set by the Cramér-Rao bounds, the results show that SPADE can offer far superior accuracy in estimating second- and higher-order moments.

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

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

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

2013-06-01

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

Towards a unifying approach to diversity measures: bridging the gap between the Shannon entropy and Rao's quadratic index.

PubMed

Ricotta, Carlo; Szeidl, Laszlo

2006-11-01

The diversity of a species assemblage has been studied extensively for many decades in relation to its possible connection with ecosystem functioning and organization. In this view most diversity measures, such as Shannon's entropy, rely upon information theory as a basis for the quantification of diversity. Also, traditional diversity measures are computed using species relative abundances and cannot account for the ecological differences between species. Rao first proposed a diversity index, termed quadratic diversity (Q) that incorporates both species relative abundances and pairwise distances between species. Quadratic diversity is traditionally defined as the expected distance between two randomly selected individuals. In this paper, we show that quadratic diversity can be interpreted as the expected conflict among the species of a given assemblage. From this unusual interpretation, it naturally follows that Rao's Q can be related to the Shannon entropy through a generalized version of the Tsallis parametric entropy.

Extended Decentralized Linear-Quadratic-Gaussian Control

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2000-01-01

A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.

Fast genomic predictions via Bayesian G-BLUP and multilocus models of threshold traits including censored Gaussian data.

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618

Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels

NASA Astrophysics Data System (ADS)

Sabapathy, Krishna Kumar; Winter, Andreas

2017-06-01

We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels, which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing such as entanglement distillation from Gaussian states and universal quantum computation. The single-mode photon-added channels we consider are obtained by using two-mode beam splitters and squeezing operators with photon addition applied to the ancilla ports giving rise to families of non-Gaussian channels. For each such channel, we derive its operator-sum representation, indispensable in the present context. We observe that these channels are Fock preserving (coherence nongenerating). We then report two examples of activation using our scheme of photon addition, that of quantum-optical nonclassicality at outputs of channels that would otherwise output only classical states and of both the quantum and private communication capacities, hinting at far-reaching applications for quantum-optical communication. Further, we see that noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We also present other physical and information-theoretic properties of these channels.

Moments and Root-Mean-Square Error of the Bayesian MMSE Estimator of Classification Error in the Gaussian Model.

PubMed

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.

Response measurement by laser Doppler vibrometry in vibration qualification tests with non-Gaussian random excitation

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.

Gaussian-input Gaussian mixture model for representing density maps and atomic models.

PubMed

Kawabata, Takeshi

2018-07-01

A new Gaussian mixture model (GMM) has been developed for better representations of both atomic models and electron microscopy 3D density maps. The standard GMM algorithm employs an EM algorithm to determine the parameters. It accepted a set of 3D points with weights, corresponding to voxel or atomic centers. Although the standard algorithm worked reasonably well; however, it had three problems. First, it ignored the size (voxel width or atomic radius) of the input, and thus it could lead to a GMM with a smaller spread than the input. Second, the algorithm had a singularity problem, as it sometimes stopped the iterative procedure due to a Gaussian function with almost zero variance. Third, a map with a large number of voxels required a long computation time for conversion to a GMM. To solve these problems, we have introduced a Gaussian-input GMM algorithm, which considers the input atoms or voxels as a set of Gaussian functions. The standard EM algorithm of GMM was extended to optimize the new GMM. The new GMM has identical radius of gyration to the input, and does not suddenly stop due to the singularity problem. For fast computation, we have introduced a down-sampled Gaussian functions (DSG) by merging neighboring voxels into an anisotropic Gaussian function. It provides a GMM with thousands of Gaussian functions in a short computation time. We also have introduced a DSG-input GMM: the Gaussian-input GMM with the DSG as the input. This new algorithm is much faster than the standard algorithm. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

Tables Of Gaussian-Type Orbital Basis Functions

NASA Technical Reports Server (NTRS)

Partridge, Harry

1992-01-01

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

A Joint Gaussian Process Model for Active Visual Recognition with Expertise Estimation in Crowdsourcing

PubMed Central

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

Hollow vortex Gaussian beams

NASA Astrophysics Data System (ADS)

Zhou, GuoQuan; Cai, YangJian; Dai, ChaoQing

2013-05-01

A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular momentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respectively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter γ, and transfer matrix elements A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in optical micromanipulation.

Estimation of visual maps with a robot network equipped with vision sensors.

PubMed

Gil, Arturo; Reinoso, Óscar; Ballesta, Mónica; Juliá, Miguel; Payá, Luis

2010-01-01

In this paper we present an approach to the Simultaneous Localization and Mapping (SLAM) problem using a team of autonomous vehicles equipped with vision sensors. The SLAM problem considers the case in which a mobile robot is equipped with a particular sensor, moves along the environment, obtains measurements with its sensors and uses them to construct a model of the space where it evolves. In this paper we focus on the case where several robots, each equipped with its own sensor, are distributed in a network and view the space from different vantage points. In particular, each robot is equipped with a stereo camera that allow the robots to extract visual landmarks and obtain relative measurements to them. We propose an algorithm that uses the measurements obtained by the robots to build a single accurate map of the environment. The map is represented by the three-dimensional position of the visual landmarks. In addition, we consider that each landmark is accompanied by a visual descriptor that encodes its visual appearance. The solution is based on a Rao-Blackwellized particle filter that estimates the paths of the robots and the position of the visual landmarks. The validity of our proposal is demonstrated by means of experiments with a team of real robots in a office-like indoor environment.

Estimation of Visual Maps with a Robot Network Equipped with Vision Sensors

PubMed Central

Gil, Arturo; Reinoso, Óscar; Ballesta, Mónica; Juliá, Miguel; Payá, Luis

2010-01-01

In this paper we present an approach to the Simultaneous Localization and Mapping (SLAM) problem using a team of autonomous vehicles equipped with vision sensors. The SLAM problem considers the case in which a mobile robot is equipped with a particular sensor, moves along the environment, obtains measurements with its sensors and uses them to construct a model of the space where it evolves. In this paper we focus on the case where several robots, each equipped with its own sensor, are distributed in a network and view the space from different vantage points. In particular, each robot is equipped with a stereo camera that allow the robots to extract visual landmarks and obtain relative measurements to them. We propose an algorithm that uses the measurements obtained by the robots to build a single accurate map of the environment. The map is represented by the three-dimensional position of the visual landmarks. In addition, we consider that each landmark is accompanied by a visual descriptor that encodes its visual appearance. The solution is based on a Rao-Blackwellized particle filter that estimates the paths of the robots and the position of the visual landmarks. The validity of our proposal is demonstrated by means of experiments with a team of real robots in a office-like indoor environment. PMID:22399930

Cluster Analysis and Gaussian Mixture Estimation of Correlated Time-Series by Means of Multi-dimensional Scaling

NASA Astrophysics Data System (ADS)

Ibuki, Takero; Suzuki, Sei; Inoue, Jun-ichi

We investigate cross-correlations between typical Japanese stocks collected through Yahoo!Japan website ( http://finance.yahoo.co.jp/ ). By making use of multi-dimensional scaling (MDS) for the cross-correlation matrices, we draw two-dimensional scattered plots in which each point corresponds to each stock. To make a clustering for these data plots, we utilize the mixture of Gaussians to fit the data set to several Gaussian densities. By minimizing the so-called Akaike Information Criterion (AIC) with respect to parameters in the mixture, we attempt to specify the best possible mixture of Gaussians. It might be naturally assumed that all the two-dimensional data points of stocks shrink into a single small region when some economic crisis takes place. The justification of this assumption is numerically checked for the empirical Japanese stock data, for instance, those around 11 March 2011.

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.

Electric dipole moments of actinide atoms and RaO molecule

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

Flambaum, V. V.

We have calculated the atomic electric dipole moments (EDMs) induced in {sup 229}Pa and {sup 225}Ac by their respective nuclear Schiff moments S. The results are d({sup 229}Pa)=-9.5x10{sup -17} [S/(e fm)]e cm=-1.1x10{sup -20}{eta} e cm and d({sup 225}Ac)=-8.6x10{sup -17} [S/(e fm)]e cm=-0.8x10{sup -21}{eta} e cm. EDM of {sup 229}Pa is 3x10{sup 4} times larger than {sup 199}Hg EDM and 40 times larger than {sup 225}Ra EDM. Possible use of actinides in solid state experiments is also discussed. The (T,P)-odd spin-axis interaction in RaO molecule is 500 times larger than in TlF.

Planck 2015 results: XVII. Constraints on primordial non-Gaussianity

DOE PAGES

Ade, P. A. R.; Aghanim, N.; Arnaud, M.; ...

2016-09-20

We report that 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 ƒ local NL = 2.5 ± 5.7, ƒ equil NL= -16 ± 70, , and ƒ ortho NL = -34 ± 32 (68% CL, statistical). Combining temperature and polarization data we obtain ƒ local NL = 0.8 ± 5.0,more » ƒ equil NL= -4 ± 43, and ƒ ortho NL = -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

Quantum entanglement beyond Gaussian criteria.

PubMed

Gomes, R M; Salles, A; Toscano, F; Souto Ribeiro, P H; Walborn, S P

2009-12-22

Most of the attention given to continuous variable systems for quantum information processing has traditionally been focused on Gaussian states. However, non-Gaussianity is an essential requirement for universal quantum computation and entanglement distillation, and can improve the efficiency of other quantum information tasks. Here we report the experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs. The quantum correlations are invisible to all second-order tests, which identify only Gaussian entanglement, and are revealed only under application of a higher-order entanglement criterion. Thus, the photons exhibit a variety of entanglement that cannot be reproduced by Gaussian states.

Optimal estimation of the optomechanical coupling strength

NASA Astrophysics Data System (ADS)

Bernád, József Zsolt; Sanavio, Claudio; Xuereb, André

2018-06-01

We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cramér-Rao-type inequality for the estimation of the coupling strength. Our estimation strategy reveals some cases where quantum statistical inference is inconclusive and merely results in the reinforcement of prior expectations. We show that these situations also involve the highest expected information losses. We demonstrate that interaction times on the order of one time period of mechanical oscillations are the most suitable for our estimation scenario, and compare situations involving different photon and phonon excitations.

Gaussian model for emission rate measurement of heated plumes using hyperspectral data

NASA Astrophysics Data System (ADS)

Grauer, Samuel J.; Conrad, Bradley M.; Miguel, Rodrigo B.; Daun, Kyle J.

2018-02-01

This paper presents a novel model for measuring the emission rate of a heated gas plume using hyperspectral data from an FTIR imaging spectrometer. The radiative transfer equation (RTE) is used to relate the spectral intensity of a pixel to presumed Gaussian distributions of volume fraction and temperature within the plume, along a line-of-sight that corresponds to the pixel, whereas previous techniques exclusively presume uniform distributions for these parameters. Estimates of volume fraction and temperature are converted to a column density by integrating the local molecular density along each path. Image correlation velocimetry is then employed on raw spectral intensity images to estimate the volume-weighted normal velocity at each pixel. Finally, integrating the product of velocity and column density along a control surface yields an estimate of the instantaneous emission rate. For validation, emission rate estimates were derived from synthetic hyperspectral images of a heated methane plume, generated using data from a large-eddy simulation. Calculating the RTE with Gaussian distributions of volume fraction and temperature, instead of uniform distributions, improved the accuracy of column density measurement by 14%. Moreover, the mean methane emission rate measured using our approach was within 4% of the ground truth. These results support the use of Gaussian distributions of thermodynamic properties in calculation of the RTE for optical gas diagnostics.

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

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

Dio, E. Di; Perrier, H.; Durrer, R.

2017-03-01

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

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

NASA Technical Reports Server (NTRS)

Murphy, Patrick Charles

1985-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

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.

Quantum entanglement beyond Gaussian criteria

PubMed Central

Gomes, R. M.; Salles, A.; Toscano, F.; Souto Ribeiro, P. H.; Walborn, S. P.

2009-01-01

Most of the attention given to continuous variable systems for quantum information processing has traditionally been focused on Gaussian states. However, non-Gaussianity is an essential requirement for universal quantum computation and entanglement distillation, and can improve the efficiency of other quantum information tasks. Here we report the experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs. The quantum correlations are invisible to all second-order tests, which identify only Gaussian entanglement, and are revealed only under application of a higher-order entanglement criterion. Thus, the photons exhibit a variety of entanglement that cannot be reproduced by Gaussian states. PMID:19995963

Characterization of Adrenal Adenoma by Gaussian Model-Based Algorithm.

PubMed

Hsu, Larson D; Wang, Carolyn L; Clark, Toshimasa J

2016-01-01

We confirmed that computed tomography (CT) attenuation values of pixels in an adrenal nodule approximate a Gaussian distribution. Building on this and the previously described histogram analysis method, we created an algorithm that uses mean and standard deviation to estimate the percentage of negative attenuation pixels in an adrenal nodule, thereby allowing differentiation of adenomas and nonadenomas. The institutional review board approved both components of this study in which we developed and then validated our criteria. In the first, we retrospectively assessed CT attenuation values of adrenal nodules for normality using a 2-sample Kolmogorov-Smirnov test. In the second, we evaluated a separate cohort of patients with adrenal nodules using both the conventional 10HU unit mean attenuation method and our Gaussian model-based algorithm. We compared the sensitivities of the 2 methods using McNemar's test. A total of 183 of 185 observations (98.9%) demonstrated a Gaussian distribution in adrenal nodule pixel attenuation values. The sensitivity and specificity of our Gaussian model-based algorithm for identifying adrenal adenoma were 86.1% and 83.3%, respectively. The sensitivity and specificity of the mean attenuation method were 53.2% and 94.4%, respectively. The sensitivities of the 2 methods were significantly different (P value < 0.001). In conclusion, the CT attenuation values within an adrenal nodule follow a Gaussian distribution. Our Gaussian model-based algorithm can characterize adrenal adenomas with higher sensitivity than the conventional mean attenuation method. The use of our algorithm, which does not require additional postprocessing, may increase workflow efficiency and reduce unnecessary workup of benign nodules. Copyright © 2016 Elsevier Inc. All rights reserved.

Simulation and analysis of scalable non-Gaussian statistically anisotropic random functions

NASA Astrophysics Data System (ADS)

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

2015-12-01

Many earth and environmental (as well as other) variables, Y, and their spatial or temporal increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture some key aspects of such scaling by treating Y or ΔY as standard sub-Gaussian random functions. We were however unable to reconcile two seemingly contradictory observations, namely that whereas sample frequency distributions of Y (or its logarithm) exhibit relatively mild non-Gaussian peaks and tails, those of ΔY display peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we overcame this difficulty by developing a new generalized sub-Gaussian model which captures both behaviors in a unified and consistent manner, exploring it on synthetically generated random functions in one dimension (Riva et al., 2015). Here we extend our generalized sub-Gaussian model to multiple dimensions, present an algorithm to generate corresponding random realizations of statistically isotropic or anisotropic sub-Gaussian functions and illustrate it in two dimensions. We demonstrate the accuracy of our algorithm by comparing ensemble statistics of Y and ΔY (such as, mean, variance, variogram and probability density function) with those of Monte Carlo generated realizations. We end by exploring the feasibility of estimating all relevant parameters of our model by analyzing jointly spatial moments of Y and ΔY obtained from a single realization of Y.

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.

Recovering Galaxy Properties Using Gaussian Process SED Fitting

NASA Astrophysics Data System (ADS)

Iyer, Kartheik; Awan, Humna

2018-01-01

Information about physical quantities like the stellar mass, star formation rates, and ages for distant galaxies is contained in their spectral energy distributions (SEDs), obtained through photometric surveys like SDSS, CANDELS, LSST etc. However, noise in the photometric observations often is a problem, and using naive machine learning methods to estimate physical quantities can result in overfitting the noise, or converging on solutions that lie outside the physical regime of parameter space.We use Gaussian Process regression trained on a sample of SEDs corresponding to galaxies from a Semi-Analytic model (Somerville+15a) to estimate their stellar masses, and compare its performance to a variety of different methods, including simple linear regression, Random Forests, and k-Nearest Neighbours. We find that the Gaussian Process method is robust to noise and predicts not only stellar masses but also their uncertainties. The method is also robust in the cases where the distribution of the training data is not identical to the target data, which can be extremely useful when generalized to more subtle galaxy properties.

Gaussian Hypothesis Testing and Quantum Illumination.

PubMed

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

2017-09-22

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

Three-photon Gaussian-Gaussian-Laguerre-Gaussian excitation of a localized atom to a highly excited Rydberg state

NASA Astrophysics Data System (ADS)

Mashhadi, L.

2017-12-01

Optical vortices are currently one of the most intensively studied topics in light-matter interaction. In this work, a three-step axial Doppler- and recoil-free Gaussian-Gaussian-Laguerre-Gaussian (GGLG) excitation of a localized atom to the highly excited Rydberg state is presented. By assuming a large detuning for intermediate states, an effective quadrupole excitation related to the Laguerre-Gaussian (LG) excitation to the highly excited Rydberg state is obtained. This special excitation system radially confines the single highly excited Rydberg atom independently of the trapping system into a sharp potential landscape into the so-called ‘far-off-resonance optical dipole-quadrupole trap’ (FORDQT). The key parameters of the Rydberg excitation to the highly excited state, namely the effective Rabi frequency and the effective detuning including a position-dependent AC Stark shift, are calculated in terms of the basic parameters of the LG beam and of the polarization of the excitation lasers. It is shown that the obtained parameters can be tuned to have a precise excitation of a single atom to the desired Rydberg state as well. The features of transferring the optical orbital and spin angular momentum of the polarized LG beam to the atom via quadrupole Rydberg excitation offer a long-lived and controllable qudit quantum memory. In addition, in contrast to the Gaussian laser beam, the doughnut-shaped LG beam makes it possible to use a high intensity laser beam to increase the signal-to-noise ratio in quadrupole excitation with minimized perturbations coming from stray light broadening in the last Rydberg excitation process.

Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution.

PubMed

García-Patrón, Raúl; Cerf, Nicolas J

2006-11-10

A fully general approach to the security analysis of continuous-variable quantum key distribution (CV-QKD) is presented. Provided that the quantum channel is estimated via the covariance matrix of the quadratures, Gaussian attacks are shown to be optimal against all collective eavesdropping strategies. The proof is made strikingly simple by combining a physical model of measurement, an entanglement-based description of CV-QKD, and a recent powerful result on the extremality of Gaussian states [M. M. Wolf, Phys. Rev. Lett. 96, 080502 (2006)10.1103/PhysRevLett.96.080502].

AUTONOMOUS GAUSSIAN DECOMPOSITION

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

Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.

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 velocitymore » 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.« less

Quantification of Gaussian quantum steering.

PubMed

Kogias, Ioannis; Lee, Antony R; Ragy, Sammy; Adesso, Gerardo

2015-02-13

Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible.

Comparing Approaches to Deal With Non-Gaussianity of Rainfall Data in Kriging-Based Radar-Gauge Rainfall Merging

NASA Astrophysics Data System (ADS)

Cecinati, F.; Wani, O.; Rico-Ramirez, M. A.

2017-11-01

Merging radar and rain gauge rainfall data is a technique used to improve the quality of spatial rainfall estimates and in particular the use of Kriging with External Drift (KED) is a very effective radar-rain gauge rainfall merging technique. However, kriging interpolations assume Gaussianity of the process. Rainfall has a strongly skewed, positive, probability distribution, characterized by a discontinuity due to intermittency. In KED rainfall residuals are used, implicitly calculated as the difference between rain gauge data and a linear function of the radar estimates. Rainfall residuals are non-Gaussian as well. The aim of this work is to evaluate the impact of applying KED to non-Gaussian rainfall residuals, and to assess the best techniques to improve Gaussianity. We compare Box-Cox transformations with λ parameters equal to 0.5, 0.25, and 0.1, Box-Cox with time-variant optimization of λ, normal score transformation, and a singularity analysis technique. The results suggest that Box-Cox with λ = 0.1 and the singularity analysis is not suitable for KED. Normal score transformation and Box-Cox with optimized λ, or λ = 0.25 produce satisfactory results in terms of Gaussianity of the residuals, probability distribution of the merged rainfall products, and rainfall estimate quality, when validated through cross-validation. However, it is observed that Box-Cox transformations are strongly dependent on the temporal and spatial variability of rainfall and on the units used for the rainfall intensity. Overall, applying transformations results in a quantitative improvement of the rainfall estimates only if the correct transformations for the specific data set are used.

A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula

PubMed Central

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

Bhaskar Rao: far from resigned.

PubMed

Khandekar, S

1992-03-01

In 1972, Dr. Bhaskar Rao 1st worked for Operations Research Group (ORG), a market research agency. He resigned as its President in December 1991 after it was sold to Business India. He was able to life ORG from just an audit organization to an organization that could conduct analyses and formulate strategies, and that was doing well financially. He was not willing to let this well-respected, independent, professional, and nonprofit group be viewed as part of a for-profit magazine company, however. After finishing his undergraduate education, he became involved in the social service organization directed by Nehru. In 1962, he worked full time for its mass awareness group and then worked to combat rumors during the India-China war. In 1963, he worked with farmers to educate them on how to use fertilizers to increase yield. This experience brought him a scholarship to study social science at Kansas State University in 1967. In the US, he took a course at Martin Luther King's School for Social Change to further his political interests. He received a Ph.D. in mass communications from the University of Iowa then returned to India. In 1970, he worked for the Ford Foundation as a consultant to the Ministry of Health and Family Planning which wanted to survey 25,000 people to learn their perceptions of family planning. He dealt with ORG. The owner convinced him to leave the Ford Foundation and work for ORG where he worked on the family planning survey and the national readership survey. In 1973, he challenged remarks made by the minister of information and broadcast during a public speech. Impressed, the minister offered him an evaluation advisor position. In 1977, however, he left and returned to ORG where he became widely known as a media analyst. In 1983, he became vice president of ORG and president in 1985.

Gaussian process-based Bayesian nonparametric inference of population size trajectories from gene genealogies.

PubMed

Palacios, Julia A; Minin, Vladimir N

2013-03-01

Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method. Copyright © 2013, The International Biometric Society.

Restructuring to Promote Collaboration and Exceed User Needs: The Blackwell Library Access Services Experience

ERIC Educational Resources Information Center

Chakraborty, Mou; English, Michael; Payne, Sharon

2013-01-01

Through vision, leadership, and creativity, Salisbury University's Blackwell Library transformed its access services department structurally and philosophically to better position itself to meet, and strive to exceed, today's user needs and expectations. Restructuring and the introduction of new leadership and new ideas provided the foundation for…

Differences in Gaussian diffusion tensor imaging and non-Gaussian diffusion kurtosis imaging model-based estimates of diffusion tensor invariants in the human brain.

PubMed

Lanzafame, S; Giannelli, M; Garaci, F; Floris, R; Duggento, A; Guerrisi, M; Toschi, N

2016-05-01

/RK/AK values, indicating substantial anatomical variability of these discrepancies. In the HCP dataset, the median voxelwise percentage differences across the whole white matter skeleton were (nonlinear least squares algorithm) 14.5% (8.2%-23.1%) for MD, 4.3% (1.4%-17.3%) for FA, -5.2% (-48.7% to -0.8%) for MO, 12.5% (6.4%-21.2%) for RD, and 16.1% (9.9%-25.6%) for AD (all ranges computed as 0.01 and 0.99 quantiles). All differences/trends were consistent between the discovery (HCP) and replication (local) datasets and between estimation algorithms. However, the relationships between such trends, estimated diffusion tensor invariants, and kurtosis estimates were impacted by the choice of fitting routine. Model-dependent differences in the estimation of conventional indexes of MD/FA/MO/RD/AD can be well beyond commonly seen disease-related alterations. While estimating diffusion tensor-derived indexes using the DKI model may be advantageous in terms of mitigating b-value dependence of diffusivity estimates, such estimates should not be referred to as conventional DTI-derived indexes in order to avoid confusion in interpretation as well as multicenter comparisons. In order to assess the potential and advantages of DKI with respect to DTI as well as to standardize diffusion-weighted imaging methods between centers, both conventional DTI-derived indexes and diffusion tensor invariants derived by fitting the non-Gaussian DKI model should be separately estimated and analyzed using the same combination of fitting routines.

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.

Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels

NASA Astrophysics Data System (ADS)

De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio

2017-04-01

We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p →q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.

Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels.

PubMed

De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio

2017-04-21

We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p→q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.

Non-Gaussian quantum states generation and robust quantum non-Gaussianity via squeezing field

NASA Astrophysics Data System (ADS)

Tang, Xu-Bing; Gao, Fang; Wang, Yao-Xiong; Kuang, Sen; Shuang, Feng

2015-03-01

Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaussian operations (namely subtracting and adding a single photon), we propose a scheme to generate non-Gaussian quantum states named single-photon-added and -subtracted coherent (SPASC) superposition states by implementing Bell measurements, and then investigate the corresponding nonclassical features. By squeezed the input field, we demonstrate that robustness of non-Gaussianity can be improved. Controllable phase space distribution offers the possibility to approximately generate a displaced coherent superposition states (DCSS). The fidelity can reach up to F ≥ 0.98 and F ≥ 0.90 for size of amplitude z = 1.53 and 2.36, respectively. Project supported by the National Natural Science Foundation of China (Grant Nos. 61203061 and 61074052), the Outstanding Young Talent Foundation of Anhui Province, China (Grant No. 2012SQRL040), and the Natural Science Foundation of Anhui Province, China (Grant No. KJ2012Z035).

Cramer-Rao Lower Bound Evaluation for Linear Frequency Modulation Based Active Radar Networks Operating in a Rice Fading Environment.

PubMed

Shi, Chenguang; Salous, Sana; Wang, Fei; Zhou, Jianjiang

2016-12-06

This paper investigates the joint target parameter (delay and Doppler) estimation performance of linear frequency modulation (LFM)-based radar networks in a Rice fading environment. The active radar networks are composed of multiple radar transmitters and multichannel receivers placed on moving platforms. First, the log-likelihood function of the received signal for a Rician target is derived, where the received signal scattered off the target comprises of dominant scatterer (DS) component and weak isotropic scatterers (WIS) components. Then, the analytically closed-form expressions of the Cramer-Rao lower bounds (CRLBs) on the Cartesian coordinates of target position and velocity are calculated, which can be adopted as a performance metric to access the target parameter estimation accuracy for LFM-based radar network systems in a Rice fading environment. It is found that the cumulative Fisher information matrix (FIM) is a linear combination of both DS component and WIS components, and it also demonstrates that the joint CRLB is a function of signal-to-noise ratio (SNR), target's radar cross section (RCS) and transmitted waveform parameters, as well as the relative geometry between the target and the radar network architectures. Finally, numerical results are provided to indicate that the joint target parameter estimation performance of active radar networks can be significantly improved with the exploitation of DS component.

Cramer-Rao Lower Bound Evaluation for Linear Frequency Modulation Based Active Radar Networks Operating in a Rice Fading Environment

PubMed Central

Shi, Chenguang; Salous, Sana; Wang, Fei; Zhou, Jianjiang

2016-01-01

This paper investigates the joint target parameter (delay and Doppler) estimation performance of linear frequency modulation (LFM)-based radar networks in a Rice fading environment. The active radar networks are composed of multiple radar transmitters and multichannel receivers placed on moving platforms. First, the log-likelihood function of the received signal for a Rician target is derived, where the received signal scattered off the target comprises of dominant scatterer (DS) component and weak isotropic scatterers (WIS) components. Then, the analytically closed-form expressions of the Cramer-Rao lower bounds (CRLBs) on the Cartesian coordinates of target position and velocity are calculated, which can be adopted as a performance metric to access the target parameter estimation accuracy for LFM-based radar network systems in a Rice fading environment. It is found that the cumulative Fisher information matrix (FIM) is a linear combination of both DS component and WIS components, and it also demonstrates that the joint CRLB is a function of signal-to-noise ratio (SNR), target’s radar cross section (RCS) and transmitted waveform parameters, as well as the relative geometry between the target and the radar network architectures. Finally, numerical results are provided to indicate that the joint target parameter estimation performance of active radar networks can be significantly improved with the exploitation of DS component. PMID:27929433

Estimation of the daily global solar radiation based on the Gaussian process regression methodology in the Saharan climate

NASA Astrophysics Data System (ADS)

Guermoui, Mawloud; Gairaa, Kacem; Rabehi, Abdelaziz; Djafer, Djelloul; Benkaciali, Said

2018-06-01

Accurate estimation of solar radiation is the major concern in renewable energy applications. Over the past few years, a lot of machine learning paradigms have been proposed in order to improve the estimation performances, mostly based on artificial neural networks, fuzzy logic, support vector machine and adaptive neuro-fuzzy inference system. The aim of this work is the prediction of the daily global solar radiation, received on a horizontal surface through the Gaussian process regression (GPR) methodology. A case study of Ghardaïa region (Algeria) has been used in order to validate the above methodology. In fact, several combinations have been tested; it was found that, GPR-model based on sunshine duration, minimum air temperature and relative humidity gives the best results in term of mean absolute bias error (MBE), root mean square error (RMSE), relative mean square error (rRMSE), and correlation coefficient ( r) . The obtained values of these indicators are 0.67 MJ/m2, 1.15 MJ/m2, 5.2%, and 98.42%, respectively.

Explicit formula for the Holevo bound for two-parameter qubit-state estimation problem

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

Suzuki, Jun, E-mail: junsuzuki@uec.ac.jp

The main contribution of this paper is to derive an explicit expression for the fundamental precision bound, the Holevo bound, for estimating any two-parameter family of qubit mixed-states in terms of quantum versions of Fisher information. The obtained formula depends solely on the symmetric logarithmic derivative (SLD), the right logarithmic derivative (RLD) Fisher information, and a given weight matrix. This result immediately provides necessary and sufficient conditions for the following two important classes of quantum statistical models; the Holevo bound coincides with the SLD Cramér-Rao bound and it does with the RLD Cramér-Rao bound. One of the important results ofmore » this paper is that a general model other than these two special cases exhibits an unexpected property: the structure of the Holevo bound changes smoothly when the weight matrix varies. In particular, it always coincides with the RLD Cramér-Rao bound for a certain choice of the weight matrix. Several examples illustrate these findings.« less

The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise

NASA Astrophysics Data System (ADS)

Guo, Qin; Sun, Zhongkui; Xu, Wei

2016-05-01

The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.

Laguerre-Gaussian, Hermite-Gaussian, Bessel-Gaussian, and Finite-Energy Airy Beams Carrying Orbital Angular Momentum in Strongly Nonlocal Nonlinear Media

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.

Cosmological information in Gaussianized weak lensing signals

NASA Astrophysics Data System (ADS)

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

2011-11-01

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

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

PubMed

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

2017-07-01

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

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.

Clustering of Multispectral Airborne Laser Scanning Data Using Gaussian Decomposition

NASA Astrophysics Data System (ADS)

Morsy, S.; Shaker, A.; El-Rabbany, A.

2017-09-01

With the evolution of the LiDAR technology, multispectral airborne laser scanning systems are currently available. The first operational multispectral airborne LiDAR sensor, the Optech Titan, acquires LiDAR point clouds at three different wavelengths (1.550, 1.064, 0.532 μm), allowing the acquisition of different spectral information of land surface. Consequently, the recent studies are devoted to use the radiometric information (i.e., intensity) of the LiDAR data along with the geometric information (e.g., height) for classification purposes. In this study, a data clustering method, based on Gaussian decomposition, is presented. First, a ground filtering mechanism is applied to separate non-ground from ground points. Then, three normalized difference vegetation indices (NDVIs) are computed for both non-ground and ground points, followed by histograms construction from each NDVI. The Gaussian function model is used to decompose the histograms into a number of Gaussian components. The maximum likelihood estimate of the Gaussian components is then optimized using Expectation - Maximization algorithm. The intersection points of the adjacent Gaussian components are subsequently used as threshold values, whereas different classes can be clustered. This method is used to classify the terrain of an urban area in Oshawa, Ontario, Canada, into four main classes, namely roofs, trees, asphalt and grass. It is shown that the proposed method has achieved an overall accuracy up to 95.1 % using different NDVIs.

Radiation pressure acceleration of corrugated thin foils by Gaussian and super-Gaussian beams

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

Adusumilli, K.; Goyal, D.; Tripathi, V. K.

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 ripplemore » 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.« less

Extremality of Gaussian quantum states.

PubMed

Wolf, Michael M; Giedke, Geza; Cirac, J Ignacio

2006-03-03

We investigate Gaussian quantum states in view of their exceptional role within the space of all continuous variables states. A general method for deriving extremality results is provided and applied to entanglement measures, secret key distillation and the classical capacity of bosonic quantum channels. We prove that for every given covariance matrix the distillable secret key rate and the entanglement, if measured appropriately, are minimized by Gaussian states. This result leads to a clearer picture of the validity of frequently made Gaussian approximations. Moreover, it implies that Gaussian encodings are optimal for the transmission of classical information through bosonic channels, if the capacity is additive.

A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula.

PubMed

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. 2016 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Breaking Gaussian incompatibility on continuous variable quantum systems

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

Heinosaari, Teiko, E-mail: teiko.heinosaari@utu.fi; Kiukas, Jukka, E-mail: jukka.kiukas@aber.ac.uk; Schultz, Jussi, E-mail: jussi.schultz@gmail.com

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.

Estimating modal abundances from the spectra of natural and laboratory pyroxene mixtures using the modified Gaussian model

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.

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.

A quick on-line state of health estimation method for Li-ion battery with incremental capacity curves processed by Gaussian filter

NASA Astrophysics Data System (ADS)

Li, Yi; Abdel-Monem, Mohamed; Gopalakrishnan, Rahul; Berecibar, Maitane; Nanini-Maury, Elise; Omar, Noshin; van den Bossche, Peter; Van Mierlo, Joeri

2018-01-01

This paper proposes an advanced state of health (SoH) estimation method for high energy NMC lithium-ion batteries based on the incremental capacity (IC) analysis. IC curves are used due to their ability of detect and quantify battery degradation mechanism. A simple and robust smoothing method is proposed based on Gaussian filter to reduce the noise on IC curves, the signatures associated with battery ageing can therefore be accurately identified. A linear regression relationship is found between the battery capacity with the positions of features of interest (FOIs) on IC curves. Results show that the developed SoH estimation function from one single battery cell is able to evaluate the SoH of other batteries cycled under different cycling depth with less than 2.5% maximum errors, which proves the robustness of the proposed method on SoH estimation. With this technique, partial charging voltage curves can be used for SoH estimation and the testing time can be therefore largely reduced. This method shows great potential to be applied in reality, as it only requires static charging curves and can be easily implemented in battery management system (BMS).

Non-Gaussian Multi-resolution Modeling of Magnetosphere-Ionosphere Coupling Processes

NASA Astrophysics Data System (ADS)

Fan, M.; Paul, D.; Lee, T. C. M.; Matsuo, T.

2016-12-01

The most dynamic coupling between the magnetosphere and ionosphere occurs in the Earth's polar atmosphere. Our objective is to model scale-dependent stochastic characteristics of high-latitude ionospheric electric fields that originate from solar wind magnetosphere-ionosphere interactions. The Earth's high-latitude ionospheric electric field exhibits considerable variability, with increasing non-Gaussian characteristics at decreasing spatio-temporal scales. Accurately representing the underlying stochastic physical process through random field modeling is crucial not only for scientific understanding of the energy, momentum and mass exchanges between the Earth's magnetosphere and ionosphere, but also for modern technological systems including telecommunication, navigation, positioning and satellite tracking. While a lot of efforts have been made to characterize the large-scale variability of the electric field in the context of Gaussian processes, no attempt has been made so far to model the small-scale non-Gaussian stochastic process observed in the high-latitude ionosphere. We construct a novel random field model using spherical needlets as building blocks. The double localization of spherical needlets in both spatial and frequency domains enables the model to capture the non-Gaussian and multi-resolutional characteristics of the small-scale variability. The estimation procedure is computationally feasible due to the utilization of an adaptive Gibbs sampler. We apply the proposed methodology to the computational simulation output from the Lyon-Fedder-Mobarry (LFM) global magnetohydrodynamics (MHD) magnetosphere model. Our non-Gaussian multi-resolution model results in characterizing significantly more energy associated with the small-scale ionospheric electric field variability in comparison to Gaussian models. By accurately representing unaccounted-for additional energy and momentum sources to the Earth's upper atmosphere, our novel random field modeling

Self-accelerating Airy-Ince-Gaussian and Airy-Helical-Ince-Gaussian light bullets in free space.

PubMed

Peng, Yulian; Chen, Bo; Peng, Xi; Zhou, Meiling; Zhang, Liping; Li, Dongdong; Deng, Dongmei

2016-08-22

The evolution of the three-dimensional (3D) self-accelerating Airy-Ince-Gaussian (AiIG) and Airy-Helical-Ince-Gaussian (AiHIG) light bullets is investigated by solving the (3+1)D linear spatiotemporal evolution equation of an optical field analytically. As far as we know, the numerical experimental demonstrations of the Ince-Gaussian (IG) and Helical-Ince-Gaussian (HIG) beams in various modes are first developed to study the evolution characteristics of the different 3D spatiotemporal light bullets. A conclusion can be drawn that the different photoelastics, pulse stacked, boundary, elliptical ring and physically separated in-line vortices can be achieved by adjusting the ellipticity, the evolution distance and the mode-number of light bullets.

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.

Hydraulic and biological analysis of the passability of select fish species at the U.S. Geological Survey streamgaging weir at Blackwells Mills, New Jersey

USGS Publications Warehouse

Haro, Alexander J.; Mulligan, Kevin; Suro, Thomas P.; Noreika, John; McHugh, Amy

2017-10-16

Recent efforts to advance river connectivity for the Millstone River watershed in New Jersey have led to the evaluation of a low-flow gauging weir that spans the full width of the river. The methods and results of a desktop modelling exercise were used to evaluate the potential ability of three anadromous fish species (Alosa sapidissima [American shad], Alosa pseudoharengus [alewife], and Alosa aestivalis [blueback herring]) to pass upstream over the U.S. Geological Survey Blackwells Mills streamgage (01402000) and weir on the Millstone River, New Jersey, at various streamflows, and to estimate the probability that the weir will be passable during the spring migratory season. Based on data from daily fishway counts downstream from the Blackwells Mills streamgage and weir between 1996 and 2014, the general migratory period was defined as April 14 to May 28. Recorded water levels and flow data were used to theoretically estimate water depths and velocities over the weir, as well as flow exceedances occurring during the migratory period.Results indicate that the weir is a potential depth barrier to fish passage when streamflows are below 200 cubic feet per second using a 1-body-depth criterion for American shad (the largest fish among the target species). Streamflows in that range occur on average 35 percent of the time during the migratory period. An increase of the depth criterion to 2 body depths causes the weir to become a possible barrier to passage when flows are below 400 cubic feet per second. Streamflows in that range occur on average 73 percent of the time during the migration season. Average cross-sectional velocities at several points along the weir do not seem to be limiting to the fish migration, but maximum theoretical velocities estimated without friction loss over the face of the weir could be potentially limiting.

Noncommuting observables in quantum detection and estimation theory

NASA Technical Reports Server (NTRS)

Helstrom, C. W.

1972-01-01

Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a larger Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.

Model-based estimation for dynamic cardiac studies using ECT.

PubMed

Chiao, P C; Rogers, W L; Clinthorne, N H; Fessler, J A; Hero, A O

1994-01-01

The authors develop a strategy for joint estimation of physiological parameters and myocardial boundaries using ECT (emission computed tomography). They construct an observation model to relate parameters of interest to the projection data and to account for limited ECT system resolution and measurement noise. The authors then use a maximum likelihood (ML) estimator to jointly estimate all the parameters directly from the projection data without reconstruction of intermediate images. They also simulate myocardial perfusion studies based on a simplified heart model to evaluate the performance of the model-based joint ML estimator and compare this performance to the Cramer-Rao lower bound. Finally, the authors discuss model assumptions and potential uses of the joint estimation strategy.

Full-wave generalizations of the fundamental Gaussian beam.

PubMed

Seshadri, S R

2009-12-01

The basic full wave corresponding to the fundamental Gaussian beam was discovered for the outwardly propagating wave in a half-space by the introduction of a source in the complex space. There is a class of extended full waves all of which reduce to the same fundamental Gaussian beam in the appropriate limit. For the extended full Gaussian waves that include the basic full Gaussian wave as a special case, the sources are in the complex space on different planes transverse to the propagation direction. The sources are cylindrically symmetric Gaussian distributions centered at the origin of the transverse planes, the axis of symmetry being the propagation direction. For the special case of the basic full Gaussian wave, the source is a point source. The radiation intensity of the extended full Gaussian waves is determined and their characteristics are discussed and compared with those of the fundamental Gaussian beam. The extended full Gaussian waves are also obtained for the oppositely propagating outwardly directed waves in the second half-space. The radiation intensity distributions in the two half-spaces have reflection symmetry about the midplane. The radiation intensity distributions of the various extended full Gaussian waves are not significantly different. The power carried by the extended full Gaussian waves is evaluated and compared with that of the fundamental Gaussian beam.

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.

Variability of non-Gaussian diffusion MRI and intravoxel incoherent motion (IVIM) measurements in the breast.

PubMed

Iima, Mami; Kataoka, Masako; Kanao, Shotaro; Kawai, Makiko; Onishi, Natsuko; Koyasu, Sho; Murata, Katsutoshi; Ohashi, Akane; Sakaguchi, Rena; Togashi, Kaori

2018-01-01

We prospectively examined the variability of non-Gaussian diffusion magnetic resonance imaging (MRI) and intravoxel incoherent motion (IVIM) measurements with different numbers of b-values and excitations in normal breast tissue and breast lesions. Thirteen volunteers and fourteen patients with breast lesions (seven malignant, eight benign; one patient had bilateral lesions) were recruited in this prospective study (approved by the Internal Review Board). Diffusion-weighted MRI was performed with 16 b-values (0-2500 s/mm2 with one number of excitations [NEX]) and five b-values (0-2500 s/mm2, 3 NEX), using a 3T breast MRI. Intravoxel incoherent motion (flowing blood volume fraction [fIVIM] and pseudodiffusion coefficient [D*]) and non-Gaussian diffusion (theoretical apparent diffusion coefficient [ADC] at b value of 0 sec/mm2 [ADC0] and kurtosis [K]) parameters were estimated from IVIM and Kurtosis models using 16 b-values, and synthetic apparent diffusion coefficient (sADC) values were obtained from two key b-values. The variabilities between and within subjects and between different diffusion acquisition methods were estimated. There were no statistical differences in ADC0, K, or sADC values between the different b-values or NEX. A good agreement of diffusion parameters was observed between 16 b-values (one NEX), five b-values (one NEX), and five b-values (three NEX) in normal breast tissue or breast lesions. Insufficient agreement was observed for IVIM parameters. There were no statistical differences in the non-Gaussian diffusion MRI estimated values obtained from a different number of b-values or excitations in normal breast tissue or breast lesions. These data suggest that a limited MRI protocol using a few b-values might be relevant in a clinical setting for the estimation of non-Gaussian diffusion MRI parameters in normal breast tissue and breast lesions.

Variability of non-Gaussian diffusion MRI and intravoxel incoherent motion (IVIM) measurements in the breast

PubMed Central

Kataoka, Masako; Kanao, Shotaro; Kawai, Makiko; Onishi, Natsuko; Koyasu, Sho; Murata, Katsutoshi; Ohashi, Akane; Sakaguchi, Rena; Togashi, Kaori

2018-01-01

We prospectively examined the variability of non-Gaussian diffusion magnetic resonance imaging (MRI) and intravoxel incoherent motion (IVIM) measurements with different numbers of b-values and excitations in normal breast tissue and breast lesions. Thirteen volunteers and fourteen patients with breast lesions (seven malignant, eight benign; one patient had bilateral lesions) were recruited in this prospective study (approved by the Internal Review Board). Diffusion-weighted MRI was performed with 16 b-values (0–2500 s/mm2 with one number of excitations [NEX]) and five b-values (0–2500 s/mm2, 3 NEX), using a 3T breast MRI. Intravoxel incoherent motion (flowing blood volume fraction [fIVIM] and pseudodiffusion coefficient [D*]) and non-Gaussian diffusion (theoretical apparent diffusion coefficient [ADC] at b value of 0 sec/mm2 [ADC0] and kurtosis [K]) parameters were estimated from IVIM and Kurtosis models using 16 b-values, and synthetic apparent diffusion coefficient (sADC) values were obtained from two key b-values. The variabilities between and within subjects and between different diffusion acquisition methods were estimated. There were no statistical differences in ADC0, K, or sADC values between the different b-values or NEX. A good agreement of diffusion parameters was observed between 16 b-values (one NEX), five b-values (one NEX), and five b-values (three NEX) in normal breast tissue or breast lesions. Insufficient agreement was observed for IVIM parameters. There were no statistical differences in the non-Gaussian diffusion MRI estimated values obtained from a different number of b-values or excitations in normal breast tissue or breast lesions. These data suggest that a limited MRI protocol using a few b-values might be relevant in a clinical setting for the estimation of non-Gaussian diffusion MRI parameters in normal breast tissue and breast lesions. PMID:29494639

Theoretical and simulated performance for a novel frequency estimation technique

NASA Technical Reports Server (NTRS)

Crozier, Stewart N.

1993-01-01

A low complexity, open-loop, discrete-time, delay-multiply-average (DMA) technique for estimating the frequency offset for digitally modulated MPSK signals is investigated. A nonlinearity is used to remove the MPSK modulation and generate the carrier component to be extracted. Theoretical and simulated performance results are presented and compared to the Cramer-Rao lower bound (CRLB) for the variance of the frequency estimation error. For all signal-to-noise ratios (SNR's) above threshold, it is shown that the CRLB can essentially be achieved with linear complexity.

Gaussian or non-Gaussian logconductivity distribution at the MADE site: What is its impact on the breakthrough curve?

PubMed

Fiori, Aldo; Volpi, Elena; Zarlenga, Antonio; Bohling, Geoffrey C

2015-08-01

The impact of the logconductivity (Y=ln K) distribution fY on transport at the MADE site is analyzed. Our principal interest is in non-Gaussian fY characterized by heavier tails than the Gaussian. Both the logconductivity moments and fY itself are inferred, taking advantage of the detailed measurements of Bohling et al. (2012). The resulting logconductivity distribution displays heavier tails than the Gaussian, although the departure from Gaussianity is not significant. The effect of the logconductivity distribution on the breakthrough curve (BTC) is studied through an analytical, physically based model. It is found that the non-Gaussianity of the MADE logconductivity distribution does not strongly affect the BTC. Counterintuitively, assuming heavier tailed distributions for Y, with same variance, leads to BTCs which are more symmetrical than those for the Gaussian fY, with less pronounced preferential flow. Results indicate that the impact of strongly non-Gaussian, heavy tailed distributions on solute transport in heterogeneous porous formations can be significant, especially in the presence of high heterogeneity, resulting in reduced preferential flow and retarded peak arrivals. Copyright © 2015 Elsevier B.V. All rights reserved.

Non-Gaussianity from isocurvature perturbations

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

Kawasaki, Masahiro; Nakayama, Kazunori; Sekiguchi, Toyokazu

2008-11-15

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

Non-Gaussianities in a two-field generalization of natural inflation

NASA Astrophysics Data System (ADS)

Riquelme M., Simon

2018-04-01

We describe a two-field model that generalizes natural inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spontaneously broken, and the radial mode is dynamical. We analyze how the dynamics fundamentally depends on the mass of the radial mode and calculate/estimate the non-Gaussianities arising from such a scenario.

Recent advances in scalable non-Gaussian geostatistics: The generalized sub-Gaussian model

NASA Astrophysics Data System (ADS)

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

2018-07-01

Geostatistical analysis has been introduced over half a century ago to allow quantifying seemingly random spatial variations in earth quantities such as rock mineral content or permeability. The traditional approach has been to view such quantities as multivariate Gaussian random functions characterized by one or a few well-defined spatial correlation scales. There is, however, mounting evidence that many spatially varying quantities exhibit non-Gaussian behavior over a multiplicity of scales. The purpose of this minireview is not to paint a broad picture of the subject and its treatment in the literature. Instead, we focus on very recent advances in the recognition and analysis of this ubiquitous phenomenon, which transcends hydrology and the Earth sciences, brought about largely by our own work. In particular, we use porosity data from a deep borehole to illustrate typical aspects of such scalable non-Gaussian behavior, describe a very recent theoretical model that (for the first time) captures all these behavioral aspects in a comprehensive manner, show how this allows generating random realizations of the quantity conditional on sampled values, point toward ways of incorporating scalable non-Gaussian behavior in hydrologic analysis, highlight the significance of doing so, and list open questions requiring further research.

Building unbiased estimators from non-gaussian likelihoods with application to shear estimation

DOE PAGES

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

Building unbiased estimators from non-Gaussian likelihoods with application to shear estimation

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

Madhavacheril, Mathew S.; Sehgal, Neelima; McDonald, Patrick

2015-01-01

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

Discretisation Schemes for Level Sets of Planar Gaussian Fields

NASA Astrophysics Data System (ADS)

Beliaev, D.; Muirhead, S.

2018-01-01

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

The Effect of a Non-Gaussian Random Loading on High-Cycle Fatigue of a Thermally Post-Buckled Structure

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.

Segmentation of 3D microPET images of the rat brain via the hybrid gaussian mixture method with kernel density estimation.

PubMed

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.

Gaussian mass optimization for kernel PCA parameters

NASA Astrophysics Data System (ADS)

Liu, Yong; Wang, Zulin

2011-10-01

This paper proposes a novel kernel parameter optimization method based on Gaussian mass, which aims to overcome the current brute force parameter optimization method in a heuristic way. Generally speaking, the choice of kernel parameter should be tightly related to the target objects while the variance between the samples, the most commonly used kernel parameter, doesn't possess much features of the target, which gives birth to Gaussian mass. Gaussian mass defined in this paper has the property of the invariance of rotation and translation and is capable of depicting the edge, topology and shape information. Simulation results show that Gaussian mass leads a promising heuristic optimization boost up for kernel method. In MNIST handwriting database, the recognition rate improves by 1.6% compared with common kernel method without Gaussian mass optimization. Several promising other directions which Gaussian mass might help are also proposed at the end of the paper.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Gaussian Quadrature is an efficient method for the back-transformation in estimating the usual intake distribution when assessing dietary exposure.

PubMed

Dekkers, A L M; Slob, W

2012-10-01

In dietary exposure assessment, statistical methods exist for estimating the usual intake distribution from daily intake data. These methods transform the dietary intake data to normal observations, eliminate the within-person variance, and then back-transform the data to the original scale. We propose Gaussian Quadrature (GQ), a numerical integration method, as an efficient way of back-transformation. We compare GQ with six published methods. One method uses a log-transformation, while the other methods, including GQ, use a Box-Cox transformation. This study shows that, for various parameter choices, the methods with a Box-Cox transformation estimate the theoretical usual intake distributions quite well, although one method, a Taylor approximation, is less accurate. Two applications--on folate intake and fruit consumption--confirmed these results. In one extreme case, some methods, including GQ, could not be applied for low percentiles. We solved this problem by modifying GQ. One method is based on the assumption that the daily intakes are log-normally distributed. Even if this condition is not fulfilled, the log-transformation performs well as long as the within-individual variance is small compared to the mean. We conclude that the modified GQ is an efficient, fast and accurate method for estimating the usual intake distribution. Copyright © 2012 Elsevier Ltd. All rights reserved.

Smoothing of Gaussian quantum dynamics for force detection

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

Huang, Zhishen; Sarovar, Mohan

Building on recent work by Gammelmark et al. we develop a formalism for prediction and retrodiction of Gaussian quantum systems undergoing continuous measurements. We apply the resulting formalism to study the advantage of incorporating a full measurement record and retrodiction for impulselike force detection and accelerometry. Here, we find that using retrodiction can only increase accuracy in a limited parameter regime, but that the reduction in estimation noise that it yields results in better detection of impulselike forces.

Smoothing of Gaussian quantum dynamics for force detection

DOE PAGES

Huang, Zhishen; Sarovar, Mohan

2018-04-10

Building on recent work by Gammelmark et al. we develop a formalism for prediction and retrodiction of Gaussian quantum systems undergoing continuous measurements. We apply the resulting formalism to study the advantage of incorporating a full measurement record and retrodiction for impulselike force detection and accelerometry. Here, we find that using retrodiction can only increase accuracy in a limited parameter regime, but that the reduction in estimation noise that it yields results in better detection of impulselike forces.

Model-based estimation for dynamic cardiac studies using ECT

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

Chiao, P.C.; Rogers, W.L.; Clinthorne, N.H.

1994-06-01

In this paper, the authors develop a strategy for joint estimation of physiological parameters and myocardial boundaries using ECT (Emission Computed Tomography). The authors construct an observation model to relate parameters of interest to the projection data and to account for limited ECT system resolution and measurement noise. The authors then use a maximum likelihood (ML) estimator to jointly estimate all the parameters directly from the projection data without reconstruction of intermediate images. The authors also simulate myocardial perfusion studies based on a simplified heart model to evaluate the performance of the model-based joint ML estimator and compare this performancemore » to the Cramer-Rao lower bound. Finally, model assumptions and potential uses of the joint estimation strategy are discussed.« less

Finite-error metrological bounds on multiparameter Hamiltonian estimation

NASA Astrophysics Data System (ADS)

Kura, Naoto; Ueda, Masahito

2018-01-01

Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed error tolerance δ . The lower bound is given on the basis of the Cramér-Rao inequality, where the quantum Fisher information is bounded by the squared evolution time. The upper bound is obtained by an explicit construction of estimation procedures. By comparing the cases with different numbers of Hamiltonian channels, we also find that the few-channel procedure with adaptive feedback and the many-channel procedure with entanglement are equivalent in the sense that they require the same amount of time resource up to a constant factor.

Gaussian operations and privacy

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

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.

Surrogacy assessment using principal stratification with multivariate normal and Gaussian copula models.

PubMed

Taylor, Jeremy M G; Conlon, Anna S C; Elliott, Michael R

2015-08-01

The validation of intermediate markers as surrogate markers (S) for the true outcome of interest (T) in clinical trials offers the possibility for trials to be run more quickly and cheaply by using the surrogate endpoint in place of the true endpoint. Working within a principal stratification framework, we propose causal quantities to evaluate surrogacy using a Gaussian copula model for an ordinal surrogate and time-to-event final outcome. The methods are applied to data from four colorectal cancer clinical trials, where S is tumor response and T is overall survival. For the Gaussian copula model, a Bayesian estimation strategy is used and, as some parameters are not identifiable from the data, we explore the use of informative priors that are consistent with reasonable assumptions in the surrogate marker setting to aid in estimation. While there is some bias in the estimation of the surrogacy quantities of interest, the estimation procedure does reasonably well at distinguishing between poor and good surrogate markers. Some of the parameters of the proposed model are not identifiable from the data, and therefore, assumptions must be made in order to aid in their estimation. The proposed quantities can be used in combination to provide evidence about the validity of S as a surrogate marker for T. © The Author(s) 2014.

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

Howell, L. W., Jr.

2003-01-01

A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Monogamy inequality for distributed gaussian entanglement.

PubMed

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.

Gaussian Process Model for Antarctic Surface Mass Balance and Ice Core Site Selection

NASA Astrophysics Data System (ADS)

White, P. A.; Reese, S.; Christensen, W. F.; Rupper, S.

2017-12-01

Surface mass balance (SMB) is an important factor in the estimation of sea level change, and data are collected to estimate models for prediction of SMB on the Antarctic ice sheet. Using Favier et al.'s (2013) quality-controlled aggregate data set of SMB field measurements, a fully Bayesian spatial model is posed to estimate Antarctic SMB and propose new field measurement locations. Utilizing Nearest-Neighbor Gaussian process (NNGP) models, SMB is estimated over the Antarctic ice sheet. An Antarctic SMB map is rendered using this model and is compared with previous estimates. A prediction uncertainty map is created to identify regions of high SMB uncertainty. The model estimates net SMB to be 2173 Gton yr-1 with 95% credible interval (2021,2331) Gton yr-1. On average, these results suggest lower Antarctic SMB and higher uncertainty than previously purported [Vaughan et al. (1999); Van de Berg et al. (2006); Arthern, Winebrenner and Vaughan (2006); Bromwich et al. (2004); Lenaerts et al. (2012)], even though this model utilizes significantly more observations than previous models. Using the Gaussian process' uncertainty and model parameters, we propose 15 new measurement locations for field study utilizing a maximin space-filling, error-minimizing design; these potential measurements are identied to minimize future estimation uncertainty. Using currently accepted Antarctic mass balance estimates and our SMB estimate, we estimate net mass loss [Shepherd et al. (2012); Jacob et al. (2012)]. Furthermore, we discuss modeling details for both space-time data and combining field measurement data with output from mathematical models using the NNGP framework.

Fatigue assessment of vibrating rail vehicle bogie components under non-Gaussian random excitations using power spectral densities

NASA Astrophysics Data System (ADS)

Wolfsteiner, Peter; Breuer, Werner

2013-10-01

The assessment of fatigue load under random vibrations is usually based on load spectra. Typically they are computed with counting methods (e.g. Rainflow) based on a time domain signal. Alternatively methods are available (e.g. Dirlik) enabling the estimation of load spectra directly from power spectral densities (PSDs) of the corresponding time signals; the knowledge of the time signal is then not necessary. These PSD based methods have the enormous advantage that if for example the signal to assess results from a finite element method based vibration analysis, the computation time of the simulation of PSDs in the frequency domain outmatches by far the simulation of time signals in the time domain. This is especially true for random vibrations with very long signals in the time domain. The disadvantage of the PSD based simulation of vibrations and also the PSD based load spectra estimation is their limitation to Gaussian distributed time signals. Deviations from this Gaussian distribution cause relevant deviations in the estimated load spectra. In these cases usually only computation time intensive time domain calculations produce accurate results. This paper presents a method dealing with non-Gaussian signals with real statistical properties that is still able to use the efficient PSD approach with its computation time advantages. Essentially it is based on a decomposition of the non-Gaussian signal in Gaussian distributed parts. The PSDs of these rearranged signals are then used to perform usual PSD analyses. In particular, detailed methods are described for the decomposition of time signals and the derivation of PSDs and cross power spectral densities (CPSDs) from multiple real measurements without using inaccurate standard procedures. Furthermore the basic intention is to design a general and integrated method that is not just able to analyse a certain single load case for a small time interval, but to generate representative PSD and CPSD spectra replacing

Optical Coherence Tomography Noise Reduction Using Anisotropic Local Bivariate Gaussian Mixture Prior in 3D Complex Wavelet Domain

PubMed Central

Sonka, Milan; Abramoff, Michael D.

2013-01-01

In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture the heavy-tailed property and inter- and intrascale dependencies of coefficients. In addition, based on the special structure of OCT images, we use an anisotropic windowing procedure for local parameters estimation that results in visual quality improvement. On this base, several OCT despeckling algorithms are obtained based on using Gaussian/two-sided Rayleigh noise distribution and homomorphic/nonhomomorphic model. In order to evaluate the performance of the proposed algorithm, we use 156 selected ROIs from 650 × 512 × 128 OCT dataset in the presence of wet AMD pathology. Our simulations show that the best MMSE estimator using local bivariate mixture prior is for the nonhomomorphic model in the presence of Gaussian noise which results in an improvement of 7.8 ± 1.7 in CNR. PMID:24222760

Optical Coherence Tomography Noise Reduction Using Anisotropic Local Bivariate Gaussian Mixture Prior in 3D Complex Wavelet Domain.

PubMed

Rabbani, Hossein; Sonka, Milan; Abramoff, Michael D

2013-01-01

In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture the heavy-tailed property and inter- and intrascale dependencies of coefficients. In addition, based on the special structure of OCT images, we use an anisotropic windowing procedure for local parameters estimation that results in visual quality improvement. On this base, several OCT despeckling algorithms are obtained based on using Gaussian/two-sided Rayleigh noise distribution and homomorphic/nonhomomorphic model. In order to evaluate the performance of the proposed algorithm, we use 156 selected ROIs from 650 × 512 × 128 OCT dataset in the presence of wet AMD pathology. Our simulations show that the best MMSE estimator using local bivariate mixture prior is for the nonhomomorphic model in the presence of Gaussian noise which results in an improvement of 7.8 ± 1.7 in CNR.

Non-gaussianity versus nonlinearity of cosmological perturbations.

PubMed

Verde, L

2001-06-01

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

Galaxy bias and primordial non-Gaussianity

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

Assassi, Valentin; Baumann, Daniel; Schmidt, Fabian, E-mail: assassi@ias.edu, E-mail: D.D.Baumann@uva.nl, E-mail: fabians@MPA-Garching.MPG.DE

2015-12-01

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

AMT-200S Motor Glider Parameter and Performance Estimation

NASA Technical Reports Server (NTRS)

Taylor, Brian R.

2011-01-01

Parameter and performance estimation of an instrumented motor glider was conducted at the National Aeronautics and Space Administration Dryden Flight Research Center in order to provide the necessary information to create a simulation of the aircraft. An output-error technique was employed to generate estimates from doublet maneuvers, and performance estimates were compared with results from a well-known flight-test evaluation of the aircraft in order to provide a complete set of data. Aircraft specifications are given along with information concerning instrumentation, flight-test maneuvers flown, and the output-error technique. Discussion of Cramer-Rao bounds based on both white noise and colored noise assumptions is given. Results include aerodynamic parameter and performance estimates for a range of angles of attack.

Tchebichef moment based restoration of Gaussian blurred images.

PubMed

Kumar, Ahlad; Paramesran, Raveendran; Lim, Chern-Loon; Dass, Sarat C

2016-11-10

With the knowledge of how edges vary in the presence of a Gaussian blur, a method that uses low-order Tchebichef moments is proposed to estimate the blur parameters: sigma (σ) and size (w). The difference between the Tchebichef moments of the original and the reblurred images is used as feature vectors to train an extreme learning machine for estimating the blur parameters (σ,w). The effectiveness of the proposed method to estimate the blur parameters is examined using cross-database validation. The estimated blur parameters from the proposed method are used in the split Bregman-based image restoration algorithm. A comparative analysis of the proposed method with three existing methods using all the images from the LIVE database is carried out. The results show that the proposed method in most of the cases performs better than the three existing methods in terms of the visual quality evaluated using the structural similarity index.

Second order Pseudo-gaussian shaper

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

Beche, Jean-Francois

2002-11-22

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

Real-Valued Covariance Vector Sparsity-Inducing DOA Estimation for Monostatic MIMO Radar

PubMed Central

Wang, Xianpeng; Wang, Wei; Li, Xin; Liu, Jing

2015-01-01

In this paper, a real-valued covariance vector sparsity-inducing method for direction of arrival (DOA) estimation is proposed in monostatic multiple-input multiple-output (MIMO) radar. Exploiting the special configuration of monostatic MIMO radar, low-dimensional real-valued received data can be obtained by using the reduced-dimensional transformation and unitary transformation technique. Then, based on the Khatri–Rao product, a real-valued sparse representation framework of the covariance vector is formulated to estimate DOA. Compared to the existing sparsity-inducing DOA estimation methods, the proposed method provides better angle estimation performance and lower computational complexity. Simulation results verify the effectiveness and advantage of the proposed method. PMID:26569241

Real-Valued Covariance Vector Sparsity-Inducing DOA Estimation for Monostatic MIMO Radar.

PubMed

Wang, Xianpeng; Wang, Wei; Li, Xin; Liu, Jing

2015-11-10

In this paper, a real-valued covariance vector sparsity-inducing method for direction of arrival (DOA) estimation is proposed in monostatic multiple-input multiple-output (MIMO) radar. Exploiting the special configuration of monostatic MIMO radar, low-dimensional real-valued received data can be obtained by using the reduced-dimensional transformation and unitary transformation technique. Then, based on the Khatri-Rao product, a real-valued sparse representation framework of the covariance vector is formulated to estimate DOA. Compared to the existing sparsity-inducing DOA estimation methods, the proposed method provides better angle estimation performance and lower computational complexity. Simulation results verify the effectiveness and advantage of the proposed method.

User's manual for the Gaussian windows program

NASA Technical Reports Server (NTRS)

Jaeckel, Louis A.

1992-01-01

'Gaussian Windows' is a method for exploring a set of multivariate data, in order to estimate the shape of the underlying density function. The method can be used to find and describe structural features in the data. The method is described in two earlier papers. I assume that the reader has access to both of these papers, so I will not repeat material from them. The program described herein is written in BASIC and it runs on an IBM PC or PS/2 with the DOS 3.3 operating system. Although the program is slow and has limited memory space, it is adequate for experimenting with the method. Since it is written in BASIC, it is relatively easy to modify. The program and some related files are available on a 3-inch diskette. A listing of the program is also available. This user's manual explains the use of the program. First, it gives a brief tutorial, illustrating some of the program's features with a set of artificial data. Then, it describes the results displayed after the program does a Gaussian window, and it explains each of the items on the various menus.

Parameter estimation of qubit states with unknown phase parameter

NASA Astrophysics Data System (ADS)

Suzuki, Jun

2015-02-01

We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean square errors (MSEs) when estimating relevant parameters with separable measurements based on known precision bounds; the symmetric logarithmic derivative (SLD) Cramér-Rao (CR) bound and Hayashi-Gill-Massar (HGM) bound. We investigate the optimal measurement which attains the HGM bound and discuss its properties. We show that the HGM bound for relevant parameters can be attained asymptotically by using some fraction of given n quantum states to estimate the phase parameter. We also discuss the Holevo bound which can be attained asymptotically by a collective measurement.

A biorthogonal decomposition for the identification and simulation of non-stationary and non-Gaussian random fields

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

Zentner, I.; Ferré, G., E-mail: gregoire.ferre@ponts.org; Poirion, F.

2016-06-01

In this paper, a new method for the identification and simulation of non-Gaussian and non-stationary stochastic fields given a database is proposed. It is based on two successive biorthogonal decompositions aiming at representing spatio–temporal stochastic fields. The proposed double expansion allows to build the model even in the case of large-size problems by separating the time, space and random parts of the field. A Gaussian kernel estimator is used to simulate the high dimensional set of random variables appearing in the decomposition. The capability of the method to reproduce the non-stationary and non-Gaussian features of random phenomena is illustrated bymore » applications to earthquakes (seismic ground motion) and sea states (wave heights).« less

Examining the effect of initialization strategies on the performance of Gaussian mixture modeling.

PubMed

Shireman, Emilie; Steinley, Douglas; Brusco, Michael J

2017-02-01

Mixture modeling is a popular technique for identifying unobserved subpopulations (e.g., components) within a data set, with Gaussian (normal) mixture modeling being the form most widely used. Generally, the parameters of these Gaussian mixtures cannot be estimated in closed form, so estimates are typically obtained via an iterative process. The most common estimation procedure is maximum likelihood via the expectation-maximization (EM) algorithm. Like many approaches for identifying subpopulations, finite mixture modeling can suffer from locally optimal solutions, and the final parameter estimates are dependent on the initial starting values of the EM algorithm. Initial values have been shown to significantly impact the quality of the solution, and researchers have proposed several approaches for selecting the set of starting values. Five techniques for obtaining starting values that are implemented in popular software packages are compared. Their performances are assessed in terms of the following four measures: (1) the ability to find the best observed solution, (2) settling on a solution that classifies observations correctly, (3) the number of local solutions found by each technique, and (4) the speed at which the start values are obtained. On the basis of these results, a set of recommendations is provided to the user.

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.

Multivariate Bayesian analysis of Gaussian, right censored Gaussian, ordered categorical and binary traits using Gibbs sampling

PubMed Central

Korsgaard, Inge Riis; Lund, Mogens Sandø; Sorensen, Daniel; Gianola, Daniel; Madsen, Per; Jensen, Just

2003-01-01

A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed. PMID:12633531

Elegant Gaussian beams for enhanced optical manipulation

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

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

2015-06-15

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

Cosmological perturbation theory and the spherical collapse model - II. Non-Gaussian initial conditions

NASA Astrophysics Data System (ADS)

Gaztanaga, Enrique; Fosalba, Pablo

1998-12-01

In Paper I of this series, we introduced the spherical collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants xi_J of density fluctuations in cosmological perturbation theory (PT). Within this approximation, the dynamics is decoupled from the statistics of the initial conditions, so we are able to present here the cumulants for generic non-Gaussian initial conditions, which can be estimated to arbitrary order including the smoothing effects. The SC model turns out to recover the exact leading-order non-linear contributions up to terms involving non-local integrals of the J-point functions. We argue that for the hierarchical ratios S_J, these non-local terms are subdominant and tend to compensate each other. The resulting predictions show a non-trivial time evolution that can be used to discriminate between models of structure formation. We compare these analytic results with non-Gaussian N-body simulations, which turn out to be in very good agreement up to scales where sigma<~1.

'The formula that killed Wall Street': the Gaussian copula and modelling practices in investment banking.

PubMed

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.

A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment.

PubMed

Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong

2016-05-13

In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student's t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods.

Distillation and purification of symmetric entangled Gaussian states

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

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 ofmore » single-photon addition and subtraction operations.« less

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.

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

NASA Astrophysics Data System (ADS)

Falsone, G.

2018-03-01

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

Propagation of elliptic-Gaussian beams in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Deng, Dongmei; Guo, Qi

2011-10-01

The propagation of the elliptic-Gaussian beams is studied in strongly nonlocal nonlinear media. The elliptic-Gaussian beams and elliptic-Gaussian vortex beams are obtained analytically and numerically. The patterns of the elegant Ince-Gaussian and the generalized Ince-Gaussian beams are varied periodically when the input power is equal to the critical power. The stability is verified by perturbing the initial beam by noise. By simulating the propagation of the elliptic-Gaussian beams in liquid crystal, we find that when the mode order is not big enough, there exists the quasi-elliptic-Gaussian soliton states.

Three dimensional indoor positioning based on visible light with Gaussian mixture sigma-point particle filter technique

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.

Analysis of the Bayesian Cramér-Rao lower bound in astrometry. Studying the impact of prior information in the location of an object

NASA Astrophysics Data System (ADS)

Echeverria, Alex; Silva, Jorge F.; Mendez, Rene A.; Orchard, Marcos

2016-10-01

Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims: We analyze bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (I.e., the position is a random variable) from observations that are statistically dependent on the position. Methods: We characterize the Bayesian Cramér-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background. Results: We quantify and analyze the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions: The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.

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).

Gaussian maximally multipartite-entangled states

NASA Astrophysics Data System (ADS)

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

2009-12-01

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

Smoothing of Gaussian quantum dynamics for force detection

NASA Astrophysics Data System (ADS)

Huang, Zhishen; Sarovar, Mohan

2018-04-01

Building on recent work by Gammelmark et al. [Phys. Rev. Lett. 111, 160401 (2013), 10.1103/PhysRevLett.111.160401] we develop a formalism for prediction and retrodiction of Gaussian quantum systems undergoing continuous measurements. We apply the resulting formalism to study the advantage of incorporating a full measurement record and retrodiction for impulselike force detection and accelerometry. We find that using retrodiction can only increase accuracy in a limited parameter regime, but that the reduction in estimation noise that it yields results in better detection of impulselike forces.

Loop corrections to primordial non-Gaussianity

NASA Astrophysics Data System (ADS)

Boran, Sibel; Kahya, E. O.

2018-02-01

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

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Large-scale velocities and primordial non-Gaussianity

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

Schmidt, Fabian

2010-09-15

We study the peculiar velocities of density peaks in the presence of primordial non-Gaussianity. Rare, high-density peaks in the initial density field can be identified with tracers such as galaxies and clusters in the evolved matter distribution. The distribution of relative velocities of peaks is derived in the large-scale limit using two different approaches based on a local biasing scheme. Both approaches agree, and show that halos still stream with the dark matter locally as well as statistically, i.e. they do not acquire a velocity bias. Nonetheless, even a moderate degree of (not necessarily local) non-Gaussianity induces a significant skewnessmore » ({approx}0.1-0.2) in the relative velocity distribution, making it a potentially interesting probe of non-Gaussianity on intermediate to large scales. We also study two-point correlations in redshift space. The well-known Kaiser formula is still a good approximation on large scales, if the Gaussian halo bias is replaced with its (scale-dependent) non-Gaussian generalization. However, there are additional terms not encompassed by this simple formula which become relevant on smaller scales (k > or approx. 0.01h/Mpc). Depending on the allowed level of non-Gaussianity, these could be of relevance for future large spectroscopic surveys.« less

Gaussian polarizable-ion tight binding.

PubMed

Boleininger, Max; Guilbert, Anne Ay; Horsfield, Andrew P

2016-10-14

To interpret ultrafast dynamics experiments on large molecules, computer simulation is required due to the complex response to the laser field. We present a method capable of efficiently computing the static electronic response of large systems to external electric fields. This is achieved by extending the density-functional tight binding method to include larger basis sets and by multipole expansion of the charge density into electrostatically interacting Gaussian distributions. Polarizabilities for a range of hydrocarbon molecules are computed for a multipole expansion up to quadrupole order, giving excellent agreement with experimental values, with average errors similar to those from density functional theory, but at a small fraction of the cost. We apply the model in conjunction with the polarizable-point-dipoles model to estimate the internal fields in amorphous poly(3-hexylthiophene-2,5-diyl).

Gaussian polarizable-ion tight binding

NASA Astrophysics Data System (ADS)

Boleininger, Max; Guilbert, Anne AY; Horsfield, Andrew P.

2016-10-01

To interpret ultrafast dynamics experiments on large molecules, computer simulation is required due to the complex response to the laser field. We present a method capable of efficiently computing the static electronic response of large systems to external electric fields. This is achieved by extending the density-functional tight binding method to include larger basis sets and by multipole expansion of the charge density into electrostatically interacting Gaussian distributions. Polarizabilities for a range of hydrocarbon molecules are computed for a multipole expansion up to quadrupole order, giving excellent agreement with experimental values, with average errors similar to those from density functional theory, but at a small fraction of the cost. We apply the model in conjunction with the polarizable-point-dipoles model to estimate the internal fields in amorphous poly(3-hexylthiophene-2,5-diyl).

Reference interval estimation: Methodological comparison using extensive simulations and empirical data.

PubMed

Daly, Caitlin H; Higgins, Victoria; Adeli, Khosrow; Grey, Vijay L; Hamid, Jemila S

2017-12-01

To statistically compare and evaluate commonly used methods of estimating reference intervals and to determine which method is best based on characteristics of the distribution of various data sets. Three approaches for estimating reference intervals, i.e. parametric, non-parametric, and robust, were compared with simulated Gaussian and non-Gaussian data. The hierarchy of the performances of each method was examined based on bias and measures of precision. The findings of the simulation study were illustrated through real data sets. In all Gaussian scenarios, the parametric approach provided the least biased and most precise estimates. In non-Gaussian scenarios, no single method provided the least biased and most precise estimates for both limits of a reference interval across all sample sizes, although the non-parametric approach performed the best for most scenarios. The hierarchy of the performances of the three methods was only impacted by sample size and skewness. Differences between reference interval estimates established by the three methods were inflated by variability. Whenever possible, laboratories should attempt to transform data to a Gaussian distribution and use the parametric approach to obtain the most optimal reference intervals. When this is not possible, laboratories should consider sample size and skewness as factors in their choice of reference interval estimation method. The consequences of false positives or false negatives may also serve as factors in this decision. Copyright © 2017 The Canadian Society of Clinical Chemists. Published by Elsevier Inc. All rights reserved.

Local Gaussian operations can enhance continuous-variable entanglement distillation

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

Zhang Shengli; Loock, Peter van; Institute of Theoretical Physics I, Universitaet Erlangen-Nuernberg, Staudtstrasse 7/B2, DE-91058 Erlangen

2011-12-15

Entanglement distillation is a fundamental building block in long-distance quantum communication. Though known to be useless on their own for distilling Gaussian entangled states, local Gaussian operations may still help to improve non-Gaussian entanglement distillation schemes. Here we show that by applying local squeezing operations both the performance and the efficiency of existing distillation protocols can be enhanced. We find that such an enhancement through local Gaussian unitaries can be obtained even when the initially shared Gaussian entangled states are mixed, as, for instance, after their distribution through a lossy-fiber communication channel.

Maximum-likelihood estimation of parameterized wavefronts from multifocal data

PubMed Central

Sakamoto, Julia A.; Barrett, Harrison H.

2012-01-01

A method for determining the pupil phase distribution of an optical system is demonstrated. Coefficients in a wavefront expansion were estimated using likelihood methods, where the data consisted of multiple irradiance patterns near focus. Proof-of-principle results were obtained in both simulation and experiment. Large-aberration wavefronts were handled in the numerical study. Experimentally, we discuss the handling of nuisance parameters. Fisher information matrices, Cramér-Rao bounds, and likelihood surfaces are examined. ML estimates were obtained by simulated annealing to deal with numerous local extrema in the likelihood function. Rapid processing techniques were employed to reduce the computational time. PMID:22772282

Simulation of the usage of Gaussian mixture models for the purpose of modelling virtual mass spectrometry data.

PubMed

Plechawska, Małgorzata; Polańska, Joanna

2009-01-01

This article presents the method of the processing of mass spectrometry data. Mass spectra are modelled with Gaussian Mixture Models. Every peak of the spectrum is represented by a single Gaussian. Its parameters describe the location, height and width of the corresponding peak of the spectrum. An authorial version of the Expectation Maximisation Algorithm was used to perform all calculations. Errors were estimated with a virtual mass spectrometer. The discussed tool was originally designed to generate a set of spectra within defined parameters.

Gaussian ancillary bombardment

NASA Astrophysics Data System (ADS)

Grimmer, Daniel; Brown, Eric; Kempf, Achim; Mann, Robert B.; Martín-Martínez, Eduardo

2018-05-01

We analyze in full detail the time evolution of an open Gaussian quantum system rapidly bombarded by Gaussian ancillae. As a particular case this analysis covers the thermalization (or not) of a harmonic oscillator coupled to a thermal reservoir made of harmonic oscillators. We derive general results for this scenario and apply them to the problem of thermalization. We show that only a particular family of system-environment couplings will cause the system to thermalize to the temperature of its environment. We discuss that if we want to understand thermalization as ensuing from the Markovian interaction of a system with the individual microconstituents of its (thermal) environment then the process of thermalization is not as robust as one might expect.

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

PubMed

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

2017-05-24

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

Linear quadratic Gaussian control of a deformable mirror adaptive optics system with time-delayed measurements

NASA Astrophysics Data System (ADS)

Paschall, Randall N.; Anderson, David J.

1993-11-01

A linear quadratic Gaussian method is proposed for a deformable mirror adaptive optics system control. Estimates of system states describing the distortion are generated by a Kalman filter based on Hartmann wave front measurements of the wave front gradient.

Apertured averaged scintillation of fully and partially coherent Gaussian, annular Gaussian, flat toped and dark hollow beams

NASA Astrophysics Data System (ADS)

Eyyuboğlu, Halil T.

2015-03-01

Apertured averaged scintillation requires the evaluation of rather complicated irradiance covariance function. Here we develop a much simpler numerical method based on our earlier introduced semi-analytic approach. Using this method, we calculate aperture averaged scintillation of fully and partially coherent Gaussian, annular Gaussian flat topped and dark hollow beams. For comparison, the principles of equal source beam power and normalizing the aperture averaged scintillation with respect to received power are applied. Our results indicate that for fully coherent beams, upon adjusting the aperture sizes to capture 10 and 20% of the equal source power, Gaussian beam needs the largest aperture opening, yielding the lowest aperture average scintillation, whilst the opposite occurs for annular Gaussian and dark hollow beams. When assessed on the basis of received power normalized aperture averaged scintillation, fixed propagation distance and aperture size, annular Gaussian and dark hollow beams seem to have the lowest scintillation. Just like the case of point-like scintillation, partially coherent beams will offer less aperture averaged scintillation in comparison to fully coherent beams. But this performance improvement relies on larger aperture openings. Upon normalizing the aperture averaged scintillation with respect to received power, fully coherent beams become more advantageous than partially coherent ones.

A derivation of the Cramer-Rao lower bound of euclidean parameters under equality constraints via score function

NASA Astrophysics Data System (ADS)

Susyanto, Nanang

2017-12-01

We propose a simple derivation of the Cramer-Rao Lower Bound (CRLB) of parameters under equality constraints from the CRLB without constraints in regular parametric models. When a regular parametric model and an equality constraint of the parameter are given, a parametric submodel can be defined by restricting the parameter under that constraint. The tangent space of this submodel is then computed with the help of the implicit function theorem. Finally, the score function of the restricted parameter is obtained by projecting the efficient influence function of the unrestricted parameter on the appropriate inner product spaces.

Limits on estimating the width of thin tubular structures in 3D images.

PubMed

Wörz, Stefan; Rohr, Karl

2006-01-01

This work studies limits on estimating the width of thin tubular structures in 3D images. Based on nonlinear estimation theory we analyze the minimal stochastic error of estimating the width. Given a 3D analytic model of the image intensities of tubular structures, we derive a closed-form expression for the Cramér-Rao bound of the width estimate under image noise. We use the derived lower bound as a benchmark and compare it with three previously proposed accuracy limits for vessel width estimation. Moreover, by experimental investigations we demonstrate that the derived lower bound can be achieved by fitting a 3D parametric intensity model directly to the image data.

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.

An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables

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

Liu, Yunlong; Wang, Aiping; Guo, Lei

This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic system. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization criterion is compared with the mean-square-error minimization in the simulation results.

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.

Taking Their Show on the Road: Becky Hebert & Siobhan Champ-Blackwell--National Network of Libraries of Medicine

ERIC Educational Resources Information Center

Library Journal, 2005

2005-01-01

They're two very different women with the same mission: outreach to medically underserved populations. Both work for the National Network of Libraries of Medicine. Becky Hebert (left) covers the Southeast/Atlantic region, and Siobhan Champ-Blackwell, the mid-continental region. They spend much of their lives on the road, exhibiting at minority…

Chemical Distances for Percolation of Planar Gaussian Free Fields and Critical Random Walk Loop Soups

NASA Astrophysics Data System (ADS)

Ding, Jian; Li, Li

2018-05-01

We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.

Chemical Distances for Percolation of Planar Gaussian Free Fields and Critical Random Walk Loop Soups

NASA Astrophysics Data System (ADS)

Ding, Jian; Li, Li

2018-06-01

We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.

Super-resolving random-Gaussian apodized photon sieve.

PubMed

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 intrinsic entanglement for states with partial minimum uncertainty

NASA Astrophysics Data System (ADS)

Mišta, Ladislav; Baksová, Klára

2018-01-01

We develop a recently proposed theory of a quantifier of bipartite Gaussian entanglement called Gaussian intrinsic entanglement (GIE) [L. Mišta, Jr. and R. Tatham, Phys. Rev. Lett. 117, 240505 (2016), 10.1103/PhysRevLett.117.240505]. Gaussian intrinsic entanglement provides a compromise between computable and physically meaningful entanglement quantifiers and so far it has been calculated for two-mode Gaussian states including all symmetric partial minimum-uncertainty states, weakly mixed asymmetric squeezed thermal states with partial minimum uncertainty, and weakly mixed symmetric squeezed thermal states. We improve the method of derivation of GIE and show that all previously derived formulas for GIE of weakly mixed states in fact hold for states with higher mixedness. In addition, we derive analytical formulas for GIE for several other classes of two-mode Gaussian states with partial minimum uncertainty. Finally, we show that, like for all previously known states, also for all currently considered states the GIE is equal to Gaussian Rényi-2 entanglement of formation. This finding strengthens a conjecture about the equivalence of GIE and Gaussian Rényi-2 entanglement of formation for all bipartite Gaussian states.

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.

Elegant Ince-Gaussian beams in a quadratic-index medium

NASA Astrophysics Data System (ADS)

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

2011-09-01

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

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.

Kinect Posture Reconstruction Based on a Local Mixture of Gaussian Process Models.

PubMed

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.

Comment on RamaRao et al. [1995] and LaVenue et al. [1995

USGS Publications Warehouse

Cooley, Richard L.; Hill, Mary C.

2000-01-01

A method for stochastic modeling of groundwater flow systems using a combination of pilot point parameterization and conditional simulation was presented by RamaRao et. al [1995] and LaVenue et. al [1995]. (We will collectively term these two papers RLMM and term the method developed in RLMM the CS method here.) RLMM (pp. 478-479) state that the CS method is intended to provide a frequency distribution of possible alternative spatial transmissivity T distributions that (1) are statistically similar to the observed T distribution, (2) are equally likely given the calibration data, and (3) closely reproduce the measured pressures. The frequency distribution of transmissivities is then used to form frequency distribution of derived functions, such as travel times, which are summarized in the form of uncertainty measures, such as (RLMM, p. 512) "confidence (or tolerance) intervals," on the actual values, which in the case of travels times, are values that could occur sometime in the future (RLMM, p.513). Cooley [2000] analyzes the RLMM method using linearization and bootstrap theory and concludes that that the method can yield accurate uncertainty estimates but only under some limited circumstances.  In this comment we use Cooley's analysis to critique the method. We also identify and discuss some statements made my by RLMM about model calibration and their methodology that appear to be misleading. It is unusual to comment on a paper so long after publication. Subsequent work has expanded the method of RLMM, and the method was used advantageously in the testing documented by Zimmerman et. al [1998], so it is clear the method has significant strengths. We go back to the 1995 papers for this comment, however, because they display most clearly the methodological difficulties with which we are concerned. 

Modified Gaussian influence function of deformable mirror actuators.

PubMed

Huang, Linhai; Rao, Changhui; Jiang, Wenhan

2008-01-07

A new deformable mirror influence function based on a Gaussian function is introduced to analyze the fitting capability of a deformable mirror. The modified expressions for both azimuthal and radial directions are presented based on the analysis of the residual error between a measured influence function and a Gaussian influence function. With a simplex search method, we further compare the fitting capability of our proposed influence function to fit the data produced by a Zygo interferometer with that of a Gaussian influence function. The result indicates that the modified Gaussian influence function provides much better performance in data fitting.

Gaussian Finite Element Method for Description of Underwater Sound Diffraction

NASA Astrophysics Data System (ADS)

Huang, Dehua

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

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 Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment

PubMed Central

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

Estimation of High-Dimensional Graphical Models Using Regularized Score Matching

PubMed Central

Lin, Lina; Drton, Mathias; Shojaie, Ali

2017-01-01

Graphical models are widely used to model stochastic dependences among large collections of variables. We introduce a new method of estimating undirected conditional independence graphs based on the score matching loss, introduced by Hyvärinen (2005), and subsequently extended in Hyvärinen (2007). The regularized score matching method we propose applies to settings with continuous observations and allows for computationally efficient treatment of possibly non-Gaussian exponential family models. In the well-explored Gaussian setting, regularized score matching avoids issues of asymmetry that arise when applying the technique of neighborhood selection, and compared to existing methods that directly yield symmetric estimates, the score matching approach has the advantage that the considered loss is quadratic and gives piecewise linear solution paths under ℓ1 regularization. Under suitable irrepresentability conditions, we show that ℓ1-regularized score matching is consistent for graph estimation in sparse high-dimensional settings. Through numerical experiments and an application to RNAseq data, we confirm that regularized score matching achieves state-of-the-art performance in the Gaussian case and provides a valuable tool for computationally efficient estimation in non-Gaussian graphical models. PMID:28638498

A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing

NASA Astrophysics Data System (ADS)

Zhou, Yuan; Rangarajan, Anand; Gader, Paul D.

2018-05-01

Hyperspectral unmixing while considering endmember variability is usually performed by the normal compositional model (NCM), where the endmembers for each pixel are assumed to be sampled from unimodal Gaussian distributions. However, in real applications, the distribution of a material is often not Gaussian. In this paper, we use Gaussian mixture models (GMM) to represent the endmember variability. We show, given the GMM starting premise, that the distribution of the mixed pixel (under the linear mixing model) is also a GMM (and this is shown from two perspectives). The first perspective originates from the random variable transformation and gives a conditional density function of the pixels given the abundances and GMM parameters. With proper smoothness and sparsity prior constraints on the abundances, the conditional density function leads to a standard maximum a posteriori (MAP) problem which can be solved using generalized expectation maximization. The second perspective originates from marginalizing over the endmembers in the GMM, which provides us with a foundation to solve for the endmembers at each pixel. Hence, our model can not only estimate the abundances and distribution parameters, but also the distinct endmember set for each pixel. We tested the proposed GMM on several synthetic and real datasets, and showed its potential by comparing it to current popular methods.

77 FR 14010 - Rocky Ridge Wind Project, LLC, Blackwell Wind, LLC, CPV Cimarron Renewable Energy Company, LLC...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-03-08

..., EG12-18-000, EG12-19-000, EG12- 20-000, EG12-21-000, EG12-22-000, EG12-23-000] Rocky Ridge Wind Project, LLC, Blackwell Wind, LLC, CPV Cimarron Renewable Energy Company, LLC, Minco Wind Interconnection Services, LLC, Shiloh III Lessee, LLC, California Ridge Wind Energy LLC, Perrin Ranch Wind, LLC, Erie Wind...

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

USGS Publications Warehouse

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.

CMB constraints on running non-Gaussianity

NASA Astrophysics Data System (ADS)

Oppizzi, F.; Liguori, M.; Renzi, A.; Arroja, F.; Bartolo, N.

2018-05-01

We develop a complete set of tools for CMB forecasting, simulation and estimation of primordial running bispectra, arising from a variety of curvaton and single-field (DBI) models of Inflation. We validate our pipeline using mock CMB running non-Gaussianity realizations and test it on real data by obtaining experimental constraints on the fNL running spectral index, nNG, using WMAP 9-year data. Our final bounds (68% C.L.) read ‑0.6< nNG<1.4}, ‑0.3< nNG<1.2, ‑1.1

Implementation of Information Management System for Radiation Safety of Personnel at the Russian Northwest Center for Radioactive Waste Management 'SevRAO' - 13131

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

Chizhov, K.; Simakov, A.; Seregin, V.

2013-07-01

The report is an overview of the information-analytical system designed to assure radiation safety of workers. The system was implemented in the Northwest Radioactive Waste Management Center 'SevRAO' (which is a branch of the Federal State Unitary Enterprise 'Radioactive Waste Management Enterprise RosRAO'). The center is located in the Northwest Russia. In respect to 'SevRAO', the Federal Medical-Biological Agency is the regulatory body, which deals with issues of radiation control. The main document to regulate radiation control is 'Reference levels of radiation factors in radioactive wastes management center'. This document contains about 250 parameters. We have developed a software toolmore » to simplify control of these parameters. The software includes: input interface, the database, dose calculating module and analytical block. Input interface is used to enter radiation environment data. Dose calculating module calculates the dose on the route. Analytical block optimizes and analyzes radiation situation maps. Much attention is paid to the GUI and graphical representation of results. The operator can enter the route at the industrial site or watch the fluctuations of the dose rate field on the map. Most of the results are presented in a visual form. Here we present some analytical tasks, such as comparison of the dose rate in some point with control levels at this point, to be solved for the purpose of radiation safety control. The program helps to identify points making the largest contribution to the collective dose of the personnel. The tool can automatically calculate the route with the lowest dose, compare and choose the best route. The program uses several options to visualize the radiation environment at the industrial site. This system will be useful for radiation monitoring services during the operation, planning of works and development of scenarios. The paper presents some applications of this system on real data over three years - from March

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.

Assessment of groundwater level estimation uncertainty using sequential Gaussian simulation and Bayesian bootstrapping

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

Revisiting non-Gaussianity from non-attractor inflation models

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Bivariate sub-Gaussian model for stock index returns

NASA Astrophysics Data System (ADS)

Jabłońska-Sabuka, Matylda; Teuerle, Marek; Wyłomańska, Agnieszka

2017-11-01

Financial time series are commonly modeled with methods assuming data normality. However, the real distribution can be nontrivial, also not having an explicitly formulated probability density function. In this work we introduce novel parameter estimation and high-powered distribution testing methods which do not rely on closed form densities, but use the characteristic functions for comparison. The approach applied to a pair of stock index returns demonstrates that such a bivariate vector can be a sample coming from a bivariate sub-Gaussian distribution. The methods presented here can be applied to any nontrivially distributed financial data, among others.

Gaussian Process Regression Model in Spatial Logistic Regression

NASA Astrophysics Data System (ADS)

Sofro, A.; Oktaviarina, A.

2018-01-01

Spatial analysis has developed very quickly in the last decade. One of the favorite approaches is based on the neighbourhood of the region. Unfortunately, there are some limitations such as difficulty in prediction. Therefore, we offer Gaussian process regression (GPR) to accommodate the issue. In this paper, we will focus on spatial modeling with GPR for binomial data with logit link function. The performance of the model will be investigated. We will discuss the inference of how to estimate the parameters and hyper-parameters and to predict as well. Furthermore, simulation studies will be explained in the last section.

Anomalous and non-Gaussian diffusion in Hertzian spheres

NASA Astrophysics Data System (ADS)

Ouyang, Wenze; Sun, Bin; Sun, Zhiwei; Xu, Shenghua

2018-09-01

By means of molecular dynamics simulations, we study the non-Gaussian diffusion in the fluid of Hertzian spheres. The time dependent non-Gaussian parameter, as an indicator of the dynamic heterogeneity, is increased with the increasing of temperature. When the temperature is high enough, the dynamic heterogeneity becomes very significant, and it seems counterintuitive that the maximum of non-Gaussian parameter and the position of its peak decrease monotonically with the increasing of density. By fitting the curves of self intermediate scattering function, we find that the character relaxation time τα is surprisingly not coupled with the time τmax where the non-Gaussian parameter reaches to a maximum. The intriguing features of non-Gaussian diffusion at high enough temperatures can be associated with the weakly correlated mean-field behavior of Hertzian spheres. Especially the time τmax is nearly inversely proportional to the density at extremely high temperatures.

Propagation properties of cylindrical sinc Gaussian beam

NASA Astrophysics Data System (ADS)

Eyyuboğlu, Halil T.; Bayraktar, Mert

2016-09-01

We investigate the propagation properties of cylindrical sinc Gaussian beam in turbulent atmosphere. Since an analytic solution is hardly derivable, the study is carried out with the aid of random phase screens. Evolutions of the beam intensity profile, beam size and kurtosis parameter are analysed. It is found that on the source plane, cylindrical sinc Gaussian beam has a dark hollow appearance, where the side lobes also start to emerge with increase in width parameter and Gaussian source size. During propagation, beams with small width and Gaussian source size exhibit off-axis behaviour, losing the dark hollow shape, accumulating the intensity asymmetrically on one side, whereas those with large width and Gaussian source size retain dark hollow appearance even at long propagation distances. It is seen that the beams with large widths expand more in beam size than the ones with small widths. The structure constant values chosen do not seem to alter this situation. The kurtosis parameters of the beams having small widths are seen to be larger than the ones with the small widths. Again the choice of the structure constant does not change this trend.

Quantifying entanglement in two-mode Gaussian states

NASA Astrophysics Data System (ADS)

Tserkis, Spyros; Ralph, Timothy C.

2017-12-01

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

Mode entanglement of Gaussian fermionic states

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Gaussian Mixture Model of Heart Rate Variability

PubMed Central

Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

2012-01-01

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

An Efficient Estimator for Moving Target Localization Using Multi-Station Dual-Frequency Radars.

PubMed

Huang, Jiyan; Zhang, Ying; Luo, Shan

2017-12-15

Localization of a moving target in a dual-frequency radars system has now gained considerable attention. The noncoherent localization approach based on a least squares (LS) estimator has been addressed in the literature. Compared with the LS method, a novel localization method based on a two-step weighted least squares estimator is proposed to increase positioning accuracy for a multi-station dual-frequency radars system in this paper. The effects of signal noise ratio and the number of samples on the performance of range estimation are also analyzed in the paper. Furthermore, both the theoretical variance and Cramer-Rao lower bound (CRLB) are derived. The simulation results verified the proposed method.

On Gaussian feedback capacity

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.

Isolated drops from capillary jets by means of Gaussian wave packets

NASA Astrophysics Data System (ADS)

Garcia, Francisco Javier; Gonzalez, Heliodoro; Castrejon-Pita, Alfonso Arturo; Castrejon-Pita, Jose Rafael; Gomez-Aguilar, Francisco Jose

2017-11-01

The possibility of obtaining isolated drops from a continuous liquid jet through localized velocity perturbations is explored analytically, numerically and experimentally. We show that Gaussian wave packets are appropriate for this goal. A temporal linear analysis predicts the early evolution of these wave packets and provides an estimate of the breakup length of the jet. Non-linear numerical simulations allow us both to corroborate these results and to obtain the shape of the surface of the jet prior to breakup. Finally, we show experimental evidence that stimulating with a Gaussian wave packet can lead to the formation of an isolated drop without disturbing the rest of the jet. The authors acknowledge support from the Spanish Government under Contract No. FIS2014-25161, the Junta de Andalucia under Contract No. P11-FQM-7919, the EPSRC-UK via the Grant EP/P024173/1, and the Royal Society.

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.

Gaussian discriminating strength

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

Back to Normal! Gaussianizing posterior distributions for cosmological probes

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

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

Capacity of PPM on Gaussian and Webb Channels

NASA Technical Reports Server (NTRS)

Divsalar, D.; Dolinar, S.; Pollara, F.; Hamkins, J.

2000-01-01

This paper computes and compares the capacities of M-ary PPM on various idealized channels that approximate the optical communication channel: (1) the standard additive white Gaussian noise (AWGN) channel;(2) a more general AWGN channel (AWGN2) allowing different variances in signal and noise slots;(3) a Webb-distributed channel (Webb2);(4) a Webb+Gaussian channel, modeling Gaussian thermal noise added to Webb-distributed channel outputs.

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.

Hunting high and low: disentangling primordial and late-time non-Gaussianity with cosmic densities in spheres

NASA Astrophysics Data System (ADS)

Uhlemann, C.; Pajer, E.; Pichon, C.; Nishimichi, T.; Codis, S.; Bernardeau, F.

2018-03-01

Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point probability distribution function and the two-point clustering of spherically averaged cosmic densities (sphere bias). Sphere bias extends the idea of halo bias to intermediate density environments and voids as underdense regions. In the presence of primordial non-Gaussianity, sphere bias displays a strong scale dependence relevant for both high- and low-density regions, which is predicted analytically. The statistics of densities in spheres are built to model primordial non-Gaussianity via an initial skewness with a scale dependence that depends on the bispectrum of the underlying model. The analytical formulas with the measured non-linear dark matter variance as input are successfully tested against numerical simulations. For local non-Gaussianity with a range from fNL = -100 to +100, they are found to agree within 2 per cent or better for densities ρ ∈ [0.5, 3] in spheres of radius 15 Mpc h-1 down to z = 0.35. The validity of the large deviation statistics formalism is thereby established for all observationally relevant local-type departures from perfectly Gaussian initial conditions. The corresponding estimators for the amplitude of the non-linear variance σ8 and primordial skewness fNL are validated using a fiducial joint maximum likelihood experiment. The influence of observational effects and the prospects for a future detection of primordial non-Gaussianity from joint one- and two-point densities-in-spheres statistics are discussed.

Analysis of Flow and Transport in non-Gaussian Heterogeneous Formations Using a Generalized Sub-Gaussian Model

NASA Astrophysics Data System (ADS)

Guadagnini, A.; Riva, M.; Neuman, S. P.

2016-12-01

Environmental quantities such as log hydraulic conductivity (or transmissivity), Y(x) = ln K(x), and their spatial (or temporal) increments, ΔY, are known to be generally non-Gaussian. Documented evidence of such behavior includes symmetry of increment distributions at all separation scales (or lags) between incremental values of Y with sharp peaks and heavy tails that decay asymptotically as lag increases. This statistical scaling occurs in porous as well as fractured media characterized by either one or a hierarchy of spatial correlation scales. In hierarchical media one observes a range of additional statistical ΔY scaling phenomena, all of which are captured comprehensibly by a novel generalized sub-Gaussian (GSG) model. In this model Y forms a mixture Y(x) = U(x) G(x) of single- or multi-scale Gaussian processes G having random variances, U being a non-negative subordinator independent of G. Elsewhere we developed ways to generate unconditional and conditional random realizations of isotropic or anisotropic GSG fields which can be embedded in numerical Monte Carlo flow and transport simulations. Here we present and discuss expressions for probability distribution functions of Y and ΔY as well as their lead statistical moments. We then focus on a simple flow setting of mean uniform steady state flow in an unbounded, two-dimensional domain, exploring ways in which non-Gaussian heterogeneity affects stochastic flow and transport descriptions. Our expressions represent (a) lead order autocovariance and cross-covariance functions of hydraulic head, velocity and advective particle displacement as well as (b) analogues of preasymptotic and asymptotic Fickian dispersion coefficients. We compare them with corresponding expressions developed in the literature for Gaussian Y.

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).

Heat source reconstruction from noisy temperature fields using an optimised derivative Gaussian filter

NASA Astrophysics Data System (ADS)

Delpueyo, D.; Balandraud, X.; Grédiac, M.

2013-09-01

The aim of this paper is to present a post-processing technique based on a derivative Gaussian filter to reconstruct heat source fields from temperature fields measured by infrared thermography. Heat sources can be deduced from temperature variations thanks to the heat diffusion equation. Filtering and differentiating are key-issues which are closely related here because the temperature fields which are processed are unavoidably noisy. We focus here only on the diffusion term because it is the most difficult term to estimate in the procedure, the reason being that it involves spatial second derivatives (a Laplacian for isotropic materials). This quantity can be reasonably estimated using a convolution of the temperature variation fields with second derivatives of a Gaussian function. The study is first based on synthetic temperature variation fields corrupted by added noise. The filter is optimised in order to reconstruct at best the heat source fields. The influence of both the dimension and the level of a localised heat source is discussed. Obtained results are also compared with another type of processing based on an averaging filter. The second part of this study presents an application to experimental temperature fields measured with an infrared camera on a thin plate in aluminium alloy. Heat sources are generated with an electric heating patch glued on the specimen surface. Heat source fields reconstructed from measured temperature fields are compared with the imposed heat sources. Obtained results illustrate the relevancy of the derivative Gaussian filter to reliably extract heat sources from noisy temperature fields for the experimental thermomechanics of materials.

Following a trend with an exponential moving average: Analytical results for a Gaussian model

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.; Serror, Jeremy

2014-01-01

We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both auto-correlation level and transaction costs. Theoretical results are illustrated on the Dow Jones index.

An adaptive Gaussian process-based method for efficient Bayesian experimental design in groundwater contaminant source identification problems: ADAPTIVE GAUSSIAN PROCESS-BASED INVERSION

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

Zhang, Jiangjiang; Li, Weixuan; Zeng, Lingzao

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 amore » 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.« less

Evaluation of non-Gaussian diffusion in cardiac MRI.

PubMed

McClymont, Darryl; Teh, Irvin; Carruth, Eric; Omens, Jeffrey; McCulloch, Andrew; Whittington, Hannah J; Kohl, Peter; Grau, Vicente; Schneider, Jürgen E

2017-09-01

The diffusion tensor model assumes Gaussian diffusion and is widely applied in cardiac diffusion MRI. However, diffusion in biological tissue deviates from a Gaussian profile as a result of hindrance and restriction from cell and tissue microstructure, and may be quantified better by non-Gaussian modeling. The aim of this study was to investigate non-Gaussian diffusion in healthy and hypertrophic hearts. Thirteen rat hearts (five healthy, four sham, four hypertrophic) were imaged ex vivo. Diffusion-weighted images were acquired at b-values up to 10,000 s/mm 2 . Models of diffusion were fit to the data and ranked based on the Akaike information criterion. The diffusion tensor was ranked best at b-values up to 2000 s/mm 2 but reflected the signal poorly in the high b-value regime, in which the best model was a non-Gaussian "beta distribution" model. Although there was considerable overlap in apparent diffusivities between the healthy, sham, and hypertrophic hearts, diffusion kurtosis and skewness in the hypertrophic hearts were more than 20% higher in the sheetlet and sheetlet-normal directions. Non-Gaussian diffusion models have a higher sensitivity for the detection of hypertrophy compared with the Gaussian model. In particular, diffusion kurtosis may serve as a useful biomarker for characterization of disease and remodeling in the heart. Magn Reson Med 78:1174-1186, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

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.

Non-Gaussianity from self-ordering scalar fields

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

Figueroa, Daniel G.; Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, 28049 Madrid; Caldwell, Robert R.

The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and providemore » a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges k{sub 1{approx_equal}}2k{sub 2{approx_equal}}2k{sub 3}) as opposed to the local-model bispectrum, which peaks for squeezed triangles (k{sub 1{approx_equal}}k{sub 2}>>k{sub 3}), and the equilateral bispectrum, which peaks at k{sub 1{approx_equal}}k{sub 2{approx_equal}}k{sub 3}. We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit.« less

Channel Estimation for Filter Bank Multicarrier Systems in Low SNR Environments

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

Driggs, Jonathan; Sibbett, Taylor; Moradiy, Hussein

Channel estimation techniques are crucial for reliable communications. This paper is concerned with channel estimation in a filter bank multicarrier spread spectrum (FBMCSS) system. We explore two channel estimator options: (i) a method that makes use of a periodic preamble and mimics the channel estimation techniques that are widely used in OFDM-based systems; and (ii) a method that stays within the traditional realm of filter bank signal processing. For the case where the channel noise is white, both methods are analyzed in detail and their performance is compared against their respective Cramer-Rao Lower Bounds (CRLB). Advantages and disadvantages of themore » two methods under different channel conditions are given to provide insight to the reader as to when one will outperform the other.« less

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.

Statistical study of generalized nonlinear phase step estimation methods in phase-shifting interferometry.

PubMed

Langoju, Rajesh; Patil, Abhijit; Rastogi, Pramod

2007-11-20

Signal processing methods based on maximum-likelihood theory, discrete chirp Fourier transform, and spectral estimation methods have enabled accurate measurement of phase in phase-shifting interferometry in the presence of nonlinear response of the piezoelectric transducer to the applied voltage. We present the statistical study of these generalized nonlinear phase step estimation methods to identify the best method by deriving the Cramér-Rao bound. We also address important aspects of these methods for implementation in practical applications and compare the performance of the best-identified method with other bench marking algorithms in the presence of harmonics and noise.

Blind identification of nonlinear models with non-Gaussian inputs

NASA Astrophysics Data System (ADS)

Prakriya, Shankar; Pasupathy, Subbarayan; Hatzinakos, Dimitrios

1995-12-01

Some methods are proposed for the blind identification of finite-order discrete-time nonlinear models with non-Gaussian circular inputs. The nonlinear models consist of two finite memory linear time invariant (LTI) filters separated by a zero-memory nonlinearity (ZMNL) of the polynomial type (the LTI-ZMNL-LTI models). The linear subsystems are allowed to be of non-minimum phase (NMP). The methods base their estimates of the impulse responses on slices of the N plus 1th order polyspectra of the output sequence. It is shown that the identification of LTI-ZMNL systems requires only a 1-D moment or polyspectral slice. The coefficients of the ZMNL are not estimated, and need not be known. The order of the nonlinearity can, in theory, be estimated from the received signal. These methods possess several noise and interference suppression characteristics, and have applications in modeling nonlinearly amplified QAM/QPSK signals in digital satellite and microwave communications.

Kurtosis, skewness, and non-Gaussian cosmological density perturbations

NASA Technical Reports Server (NTRS)

Luo, Xiaochun; Schramm, David N.

1993-01-01

Cosmological topological defects as well as some nonstandard inflation models can give rise to non-Gaussian density perturbations. Skewness and kurtosis are the third and fourth moments that measure the deviation of a distribution from a Gaussian. Measurement of these moments for the cosmological density field and for the microwave background temperature anisotropy can provide a test of the Gaussian nature of the primordial fluctuation spectrum. In the case of the density field, the importance of measuring the kurtosis is stressed since it will be preserved through the weakly nonlinear gravitational evolution epoch. Current constraints on skewness and kurtosis of primeval perturbations are obtained from the observed density contrast on small scales and from recent COBE observations of temperature anisotropies on large scales. It is also shown how, in principle, future microwave anisotropy experiments might be able to reveal the initial skewness and kurtosis. It is shown that present data argue that if the initial spectrum is adiabatic, then it is probably Gaussian, but non-Gaussian isocurvature fluctuations are still allowed, and these are what topological defects provide.

Analysis of multidimensional difference-of-Gaussians filters in terms of directly observable parameters.

PubMed

Cope, Davis; Blakeslee, Barbara; McCourt, Mark E

2013-05-01

The difference-of-Gaussians (DOG) filter is a widely used model for the receptive field of neurons in the retina and lateral geniculate nucleus (LGN) and is a potential model in general for responses modulated by an excitatory center with an inhibitory surrounding region. A DOG filter is defined by three standard parameters: the center and surround sigmas (which define the variance of the radially symmetric Gaussians) and the balance (which defines the linear combination of the two Gaussians). These parameters are not directly observable and are typically determined by nonlinear parameter estimation methods applied to the frequency response function. DOG filters show both low-pass (optimal response at zero frequency) and bandpass (optimal response at a nonzero frequency) behavior. This paper reformulates the DOG filter in terms of a directly observable parameter, the zero-crossing radius, and two new (but not directly observable) parameters. In the two-dimensional parameter space, the exact region corresponding to bandpass behavior is determined. A detailed description of the frequency response characteristics of the DOG filter is obtained. It is also found that the directly observable optimal frequency and optimal gain (the ratio of the response at optimal frequency to the response at zero frequency) provide an alternate coordinate system for the bandpass region. Altogether, the DOG filter and its three standard implicit parameters can be determined by three directly observable values. The two-dimensional bandpass region is a potential tool for the analysis of populations of DOG filters (for example, populations of neurons in the retina or LGN), because the clustering of points in this parameter space may indicate an underlying organizational principle. This paper concentrates on circular Gaussians, but the results generalize to multidimensional radially symmetric Gaussians and are given as an appendix.

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

NASA Technical Reports Server (NTRS)

Howell, L. W.

2002-01-01

A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from

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.

Quantum non-Gaussianity and quantification of nonclassicality

NASA Astrophysics Data System (ADS)

Kühn, B.; Vogel, W.

2018-05-01

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

Axial acoustic radiation force on a sphere in Gaussian field

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

Wu, Rongrong; Liu, Xiaozhou, E-mail: xzliu@nju.edu.cn; Gong, Xiufen

2015-10-28

Based on the finite series method, the acoustical radiation force resulting from a Gaussian beam incident on a spherical object is investigated analytically. When the position of the particles deviating from the center of the beam, the Gaussian beam is expanded as a spherical function at the center of the particles and the expanded coefficients of the Gaussian beam is calculated. The analytical expression of the acoustic radiation force on spherical particles deviating from the Gaussian beam center is deduced. The acoustic radiation force affected by the acoustic frequency and the offset distance from the Gaussian beam center is investigated.more » Results have been presented for Gaussian beams with different wavelengths and it has been shown that the interaction of a Gaussian beam with a sphere can result in attractive axial force under specific operational conditions. Results indicate the capability of manipulating and separating spherical spheres based on their mechanical and acoustical properties, the results provided here may provide a theoretical basis for development of single-beam acoustical tweezers.« less

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).

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

PubMed

Westgate, Philip M; Burchett, Woodrow W

2017-03-15

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

A comparison of likelihood ratio tests and Rao's score test for three separable covariance matrix structures.

PubMed

Filipiak, Katarzyna; Klein, Daniel; Roy, Anuradha

2017-01-01

The problem of testing the separability of a covariance matrix against an unstructured variance-covariance matrix is studied in the context of multivariate repeated measures data using Rao's score test (RST). The RST statistic is developed with the first component of the separable structure as a first-order autoregressive (AR(1)) correlation matrix or an unstructured (UN) covariance matrix under the assumption of multivariate normality. It is shown that the distribution of the RST statistic under the null hypothesis of any separability does not depend on the true values of the mean or the unstructured components of the separable structure. A significant advantage of the RST is that it can be performed for small samples, even smaller than the dimension of the data, where the likelihood ratio test (LRT) cannot be used, and it outperforms the standard LRT in a number of contexts. Monte Carlo simulations are then used to study the comparative behavior of the null distribution of the RST statistic, as well as that of the LRT statistic, in terms of sample size considerations, and for the estimation of the empirical percentiles. Our findings are compared with existing results where the first component of the separable structure is a compound symmetry (CS) correlation matrix. It is also shown by simulations that the empirical null distribution of the RST statistic converges faster than the empirical null distribution of the LRT statistic to the limiting χ 2 distribution. The tests are implemented on a real dataset from medical studies. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Comparisons of non-Gaussian statistical models in DNA methylation analysis.

PubMed

Ma, Zhanyu; Teschendorff, Andrew E; Yu, Hong; Taghia, Jalil; Guo, Jun

2014-06-16

As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance.

Comparisons of Non-Gaussian Statistical Models in DNA Methylation Analysis

PubMed Central

Ma, Zhanyu; Teschendorff, Andrew E.; Yu, Hong; Taghia, Jalil; Guo, Jun

2014-01-01

As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance. PMID:24937687

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

PubMed Central

Marias, Kostas; Lambregts, Doenja M. J.; Nikiforaki, Katerina; van Heeswijk, Miriam M.; Bakers, Frans C. H.; Beets-Tan, Regina G. H.

2017-01-01

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

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

PubMed

Manikis, Georgios C; Marias, Kostas; Lambregts, Doenja M J; Nikiforaki, Katerina; van Heeswijk, Miriam M; Bakers, Frans C H; Beets-Tan, Regina G H; Papanikolaou, Nikolaos

2017-01-01

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

How Gaussian can our Universe be?

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

Cabass, G.; Pajer, E.; Schmidt, F., E-mail: giovanni.cabass@roma1.infn.it, E-mail: e.pajer@uu.nl, E-mail: fabians@mpa-garching.mpg.de

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 happenmore » to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of k {sub ℓ}{sup 2}/ k {sub s} {sup 2}, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × ( n {sub s}−1).« less

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

PubMed Central

Teng, Ming; Nathoo, Farouk S.; Johnson, Timothy D.

2017-01-01

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data. PMID:29200537

An Efficient Estimator for Moving Target Localization Using Multi-Station Dual-Frequency Radars

PubMed Central

Zhang, Ying; Luo, Shan

2017-01-01

Localization of a moving target in a dual-frequency radars system has now gained considerable attention. The noncoherent localization approach based on a least squares (LS) estimator has been addressed in the literature. Compared with the LS method, a novel localization method based on a two-step weighted least squares estimator is proposed to increase positioning accuracy for a multi-station dual-frequency radars system in this paper. The effects of signal noise ratio and the number of samples on the performance of range estimation are also analyzed in the paper. Furthermore, both the theoretical variance and Cramer–Rao lower bound (CRLB) are derived. The simulation results verified the proposed method. PMID:29244727

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

PubMed

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

2007-04-01

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

Cosine-Gaussian Schell-model sources.

PubMed

Mei, Zhangrong; Korotkova, Olga

2013-07-15

We introduce a new class of partially coherent sources of Schell type with cosine-Gaussian spectral degree of coherence and confirm that such sources are physically genuine. Further, we derive the expression for the cross-spectral density function of a beam generated by the novel source propagating in free space and analyze the evolution of the spectral density and the spectral degree of coherence. It is shown that at sufficiently large distances from the source the degree of coherence of the propagating beam assumes Gaussian shape while the spectral density takes on the dark-hollow profile.

Ince-Gaussian series representation of the two-dimensional fractional Fourier transform.

PubMed

Bandres, Miguel A; Gutiérrez-Vega, Julio C

2005-03-01

We introduce the Ince-Gaussian series representation of the two-dimensional fractional Fourier transform in elliptical coordinates. A physical interpretation is provided in terms of field propagation in quadratic graded-index media whose eigenmodes in elliptical coordinates are derived for the first time to our knowledge. The kernel of the new series representation is expressed in terms of Ince-Gaussian functions. The equivalence among the Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian series representations is verified by establishing the relation among the three definitions.

Consistency relations for sharp inflationary non-Gaussian features

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

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

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

The impact of non-Gaussianity upon cosmological forecasts

NASA Astrophysics Data System (ADS)

Repp, A.; Szapudi, I.; Carron, J.; Wolk, M.

2015-12-01

The primary science driver for 3D galaxy surveys is their potential to constrain cosmological parameters. Forecasts of these surveys' effectiveness typically assume Gaussian statistics for the underlying matter density, despite the fact that the actual distribution is decidedly non-Gaussian. To quantify the effect of this assumption, we employ an analytic expression for the power spectrum covariance matrix to calculate the Fisher information for Baryon Acoustic Oscillation (BAO)-type model surveys. We find that for typical number densities, at kmax = 0.5h Mpc-1, Gaussian assumptions significantly overestimate the information on all parameters considered, in some cases by up to an order of magnitude. However, after marginalizing over a six-parameter set, the form of the covariance matrix (dictated by N-body simulations) causes the majority of the effect to shift to the `amplitude-like' parameters, leaving the others virtually unaffected. We find that Gaussian assumptions at such wavenumbers can underestimate the dark energy parameter errors by well over 50 per cent, producing dark energy figures of merit almost three times too large. Thus, for 3D galaxy surveys probing the non-linear regime, proper consideration of non-Gaussian effects is essential.

Speech Enhancement, Gain, and Noise Spectrum Adaptation Using Approximate Bayesian Estimation

PubMed Central

Hao, Jiucang; Attias, Hagai; Nagarajan, Srikantan; Lee, Te-Won; Sejnowski, Terrence J.

2010-01-01

This paper presents a new approximate Bayesian estimator for enhancing a noisy speech signal. The speech model is assumed to be a Gaussian mixture model (GMM) in the log-spectral domain. This is in contrast to most current models in frequency domain. Exact signal estimation is a computationally intractable problem. We derive three approximations to enhance the efficiency of signal estimation. The Gaussian approximation transforms the log-spectral domain GMM into the frequency domain using minimal Kullback–Leiber (KL)-divergency criterion. The frequency domain Laplace method computes the maximum a posteriori (MAP) estimator for the spectral amplitude. Correspondingly, the log-spectral domain Laplace method computes the MAP estimator for the log-spectral amplitude. Further, the gain and noise spectrum adaptation are implemented using the expectation–maximization (EM) algorithm within the GMM under Gaussian approximation. The proposed algorithms are evaluated by applying them to enhance the speeches corrupted by the speech-shaped noise (SSN). The experimental results demonstrate that the proposed algorithms offer improved signal-to-noise ratio, lower word recognition error rate, and less spectral distortion. PMID:20428253

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.

EXACT DISTRIBUTIONS OF INTRACLASS CORRELATION AND CRONBACH'S ALPHA WITH GAUSSIAN DATA AND GENERAL COVARIANCE.

PubMed

Kistner, Emily O; Muller, Keith E

2004-09-01

Intraclass correlation and Cronbach's alpha are widely used to describe reliability of tests and measurements. Even with Gaussian data, exact distributions are known only for compound symmetric covariance (equal variances and equal correlations). Recently, large sample Gaussian approximations were derived for the distribution functions. New exact results allow calculating the exact distribution function and other properties of intraclass correlation and Cronbach's alpha, for Gaussian data with any covariance pattern, not just compound symmetry. Probabilities are computed in terms of the distribution function of a weighted sum of independent chi-square random variables. New F approximations for the distribution functions of intraclass correlation and Cronbach's alpha are much simpler and faster to compute than the exact forms. Assuming the covariance matrix is known, the approximations typically provide sufficient accuracy, even with as few as ten observations. Either the exact or approximate distributions may be used to create confidence intervals around an estimate of reliability. Monte Carlo simulations led to a number of conclusions. Correctly assuming that the covariance matrix is compound symmetric leads to accurate confidence intervals, as was expected from previously known results. However, assuming and estimating a general covariance matrix produces somewhat optimistically narrow confidence intervals with 10 observations. Increasing sample size to 100 gives essentially unbiased coverage. Incorrectly assuming compound symmetry leads to pessimistically large confidence intervals, with pessimism increasing with sample size. In contrast, incorrectly assuming general covariance introduces only a modest optimistic bias in small samples. Hence the new methods seem preferable for creating confidence intervals, except when compound symmetry definitely holds.

Weakly anomalous diffusion with non-Gaussian propagators

NASA Astrophysics Data System (ADS)

Cressoni, J. C.; Viswanathan, G. M.; Ferreira, A. S.; da Silva, M. A. A.

2012-08-01

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H≈1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H=1/2 but with a non-Gaussian propagator.

Quantum estimation of parameters of classical spacetimes

NASA Astrophysics Data System (ADS)

Downes, T. G.; van Meter, J. R.; Knill, E.; Milburn, G. J.; Caves, C. M.

2017-11-01

We describe a quantum limit to the measurement of classical spacetimes. Specifically, we formulate a quantum Cramér-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly background-independent derivation. The result is an uncertainty relation that applies to all globally hyperbolic spacetimes. Among other examples, we apply our method to the detection of gravitational waves with the electromagnetic field as a probe, as in laser-interferometric gravitational-wave detectors. Other applications are discussed, from terrestrial gravimetry to cosmology.

Skewness in large-scale structure and non-Gaussian initial conditions

NASA Technical Reports Server (NTRS)

Fry, J. N.; Scherrer, Robert J.

1994-01-01

We compute the skewness of the galaxy distribution arising from the nonlinear evolution of arbitrary non-Gaussian intial conditions to second order in perturbation theory including the effects of nonlinear biasing. The result contains a term identical to that for a Gaussian initial distribution plus terms which depend on the skewness and kurtosis of the initial conditions. The results are model dependent; we present calculations for several toy models. At late times, the leading contribution from the initial skewness decays away relative to the other terms and becomes increasingly unimportant, but the contribution from initial kurtosis, previously overlooked, has the same time dependence as the Gaussian terms. Observations of a linear dependence of the normalized skewness on the rms density fluctuation therefore do not necessarily rule out initially non-Gaussian models. We also show that with non-Gaussian initial conditions the first correction to linear theory for the mean square density fluctuation is larger than for Gaussian models.

Period Estimation for Sparsely-sampled Quasi-periodic Light Curves Applied to Miras

NASA Astrophysics Data System (ADS)

He, Shiyuan; Yuan, Wenlong; Huang, Jianhua Z.; Long, James; Macri, Lucas M.

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequency parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period-luminosity relations.

A two-step super-Gaussian independent component analysis approach for fMRI data.

PubMed

Ge, Ruiyang; Yao, Li; Zhang, Hang; Long, Zhiying

2015-09-01

Independent component analysis (ICA) has been widely applied to functional magnetic resonance imaging (fMRI) data analysis. Although ICA assumes that the sources underlying data are statistically independent, it usually ignores sources' additional properties, such as sparsity. In this study, we propose a two-step super-GaussianICA (2SGICA) method that incorporates the sparse prior of the sources into the ICA model. 2SGICA uses the super-Gaussian ICA (SGICA) algorithm that is based on a simplified Lewicki-Sejnowski's model to obtain the initial source estimate in the first step. Using a kernel estimator technique, the source density is acquired and fitted to the Laplacian function based on the initial source estimates. The fitted Laplacian prior is used for each source at the second SGICA step. Moreover, the automatic target generation process for initial value generation is used in 2SGICA to guarantee the stability of the algorithm. An adaptive step size selection criterion is also implemented in the proposed algorithm. We performed experimental tests on both simulated data and real fMRI data to investigate the feasibility and robustness of 2SGICA and made a performance comparison between InfomaxICA, FastICA, mean field ICA (MFICA) with Laplacian prior, sparse online dictionary learning (ODL), SGICA and 2SGICA. Both simulated and real fMRI experiments showed that the 2SGICA was most robust to noises, and had the best spatial detection power and the time course estimation among the six methods. Copyright © 2015. Published by Elsevier Inc.

Comment on “Hydrolysis of neptunium(V) at variable temperatures (10 85 °C)” by L. Rao, T.G. Srinivasan, A.Yu. Garnov, P. Zanonato, P. Di Bernardo, and A. Bismondo

NASA Astrophysics Data System (ADS)

Neck, V.

2006-09-01

In a recent study [Rao, L., Srinivasan, T.G., Garnov, A.Yu., Zanonato, P., Di Bernardo, P., Bismondo, A., 2004. Hydrolysis of neptunium(V) at variable temperatures (10-85 °C). Geochim. Cosmochim. Acta68, 4821-4830.] the hydrolysis of Np(V) was investigated at 10-85 °C by absorption spectroscopy, potentiometry, and microcalorimetry along the titration of Np(V) solutions with tetramethylammonium hydroxide up to pH 10. However, there is strong evidence that the precautions to avoid competing reactions with carbonate were not sufficient and that the measured effects are not caused by the formation of Np(V) hydroxide complexes but primarily by the formation of Np(V) carbonate complexes. The reported equilibrium constants, enthalpies, entropies, and heat capacities for the complexes NpO 2OH(aq) and NpO(OH)2- are severely in error and must not be used for the geochemical modeling of neptunium. If the hydrolysis constants reported by Rao et al. [Rao, L., Srinivasan, T.G., Garnov, A.Yu., Zanonato, P., Di Bernardo, P., Bismondo, A., 2004. Hydrolysis of neptunium(V) at variable temperatures (10-85 °C). Geochim. Cosmochim. Acta68, 4821-4830] are used to calculate neptunium solubilities in alkaline solutions relevant for nuclear waste repositories, the Np(V) concentrations are overestimated by orders of magnitude.

Effects of scale-dependent non-Gaussianity on cosmological structures

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

LoVerde, Marilena; Miller, Amber; Shandera, Sarah

2008-04-15

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

Gaussian random bridges and a geometric model for information equilibrium

NASA Astrophysics Data System (ADS)

Mengütürk, Levent Ali

2018-03-01

The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.

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

NASA Astrophysics Data System (ADS)

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

2010-02-01

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

Gaussian mixture clustering and imputation of microarray data.

PubMed

Ouyang, Ming; Welsh, William J; Georgopoulos, Panos

2004-04-12

In microarray experiments, missing entries arise from blemishes on the chips. In large-scale studies, virtually every chip contains some missing entries and more than 90% of the genes are affected. Many analysis methods require a full set of data. Either those genes with missing entries are excluded, or the missing entries are filled with estimates prior to the analyses. This study compares methods of missing value estimation. Two evaluation metrics of imputation accuracy are employed. First, the root mean squared error measures the difference between the true values and the imputed values. Second, the number of mis-clustered genes measures the difference between clustering with true values and that with imputed values; it examines the bias introduced by imputation to clustering. The Gaussian mixture clustering with model averaging imputation is superior to all other imputation methods, according to both evaluation metrics, on both time-series (correlated) and non-time series (uncorrelated) data sets.

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

Treesearch

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

2016-01-01

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

Channel Simulation in Quantum Metrology

NASA Astrophysics Data System (ADS)

Laurenza, Riccardo; Lupo, Cosmo; Spedalieri, Gaetana; Braunstein, Samuel L.; Pirandola, Stefano

2018-04-01

In this review we discuss how channel simulation can be used to simplify the most general protocols of quantum parameter estimation, where unlimited entanglement and adaptive joint operations may be employed. Whenever the unknown parameter encoded in a quantum channel is completely transferred in an environmental program state simulating the channel, the optimal adaptive estimation cannot beat the standard quantum limit. In this setting, we elucidate the crucial role of quantum teleportation as a primitive operation which allows one to completely reduce adaptive protocols over suitable teleportation-covariant channels and derive matching upper and lower bounds for parameter estimation. For these channels,wemay express the quantum Cramér Rao bound directly in terms of their Choi matrices. Our review considers both discrete- and continuous-variable systems, also presenting some new results for bosonic Gaussian channels using an alternative sub-optimal simulation. It is an open problem to design simulations for quantum channels that achieve the Heisenberg limit.

Persistent homology and non-Gaussianity

NASA Astrophysics Data System (ADS)

Cole, Alex; Shiu, Gary

2018-03-01

In this paper, we introduce the topological persistence diagram as a statistic for Cosmic Microwave Background (CMB) temperature anisotropy maps. A central concept in 'Topological Data Analysis' (TDA), the idea of persistence is to represent a data set by a family of topological spaces. One then examines how long topological features 'persist' as the family of spaces is traversed. We compute persistence diagrams for simulated CMB temperature anisotropy maps featuring various levels of primordial non-Gaussianity of local type. Postponing the analysis of observational effects, we show that persistence diagrams are more sensitive to local non-Gaussianity than previous topological statistics including the genus and Betti number curves, and can constrain Δ fNLloc= 35.8 at the 68% confidence level on the simulation set, compared to Δ fNLloc= 60.6 for the Betti number curves. Given the resolution of our simulations, we expect applying persistence diagrams to observational data will give constraints competitive with those of the Minkowski Functionals. This is the first in a series of papers where we plan to apply TDA to different shapes of non-Gaussianity in the CMB and Large Scale Structure.

Optimization of spectroscopic surveys for testing non-Gaussianity

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

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

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

Statistical evaluation of a project to estimate fish trajectories through the intakes of Kaplan hydropower turbines

NASA Astrophysics Data System (ADS)

Sutton, Virginia Kay

This paper examines statistical issues associated with estimating paths of juvenile salmon through the intakes of Kaplan turbines. Passive sensors, hydrophones, detecting signals from ultrasonic transmitters implanted in individual fish released into the preturbine region were used to obtain the information to estimate fish paths through the intake. Aim and location of the sensors affects the spatial region in which the transmitters can be detected, and formulas relating this region to sensor aiming directions are derived. Cramer-Rao lower bounds for the variance of estimators of fish location are used to optimize placement of each sensor. Finally, a statistical methodology is developed for analyzing angular data collected from optimally placed sensors.

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

PubMed

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

2016-09-01

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

Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors

PubMed Central

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

2015-01-01

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

Propagation of Ince-Gaussian beams in a thermal lens medium

NASA Astrophysics Data System (ADS)

Xu, Ting; Wang, Shaomin

2006-09-01

The propagation of Ince-Gaussian beams in a thermal lens medium is studied in this paper. Based on the ABCD matrix for Gaussian beams passing through a thermal lens medium, distinct expressions for the beam transverse intensity distributions and the longitudinal phase shift are deduced and discussed. Similar to Laguerre and Hermite-Gaussian beams, Ince-Gaussian beams, which constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation, can also be used in other inhomogeneous media such as lenslike media and saturated absorption media.

A Modularized Efficient Framework for Non-Markov Time Series Estimation

NASA Astrophysics Data System (ADS)

Schamberg, Gabriel; Ba, Demba; Coleman, Todd P.

2018-06-01

We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal processing problems with non-Markov signal dynamics (e.g. group sparsity) and/or non-Gaussian measurement models (e.g. point process observation models used in neuroscience). Through the use of auxiliary variables in the MAP estimation problem, we show that a consensus formulation of the alternating direction method of multipliers (ADMM) enables iteratively computing separate estimates based on the likelihood and prior and subsequently "averaging" them in an appropriate sense using a Kalman smoother. As such, this can be applied to a broad class of problem settings and only requires modular adjustments when interchanging various aspects of the statistical model. Under broad log-concavity assumptions, we show that the separate estimation problems are convex optimization problems and that the iterative algorithm converges to the MAP estimate. As such, this framework can capture non-Markov latent time series models and non-Gaussian measurement models. We provide example applications involving (i) group-sparsity priors, within the context of electrophysiologic specrotemporal estimation, and (ii) non-Gaussian measurement models, within the context of dynamic analyses of learning with neural spiking and behavioral observations.

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

PubMed

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

2016-12-09

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

Effects of control inputs on the estimation of stability and control parameters of a light airplane

NASA Technical Reports Server (NTRS)

Cannaday, R. L.; Suit, W. T.

1977-01-01

The maximum likelihood parameter estimation technique was used to determine the values of stability and control derivatives from flight test data for a low-wing, single-engine, light airplane. Several input forms were used during the tests to investigate the consistency of parameter estimates as it relates to inputs. These consistencies were compared by using the ensemble variance and estimated Cramer-Rao lower bound. In addition, the relationship between inputs and parameter correlations was investigated. Results from the stabilator inputs are inconclusive but the sequence of rudder input followed by aileron input or aileron followed by rudder gave more consistent estimates than did rudder or ailerons individually. Also, square-wave inputs appeared to provide slightly improved consistency in the parameter estimates when compared to sine-wave inputs.

Revisiting the Cramér Rao Lower Bound for Elastography: Predicting the Performance of Axial, Lateral and Polar Strain Elastograms.

PubMed

Verma, Prashant; Doyley, Marvin M

2017-09-01

We derived the Cramér Rao lower bound for 2-D estimators employed in quasi-static elastography. To illustrate the theory, we modeled the 2-D point spread function as a sinc-modulated sine pulse in the axial direction and as a sinc function in the lateral direction. We compared theoretical predictions of the variance incurred in displacements and strains when quasi-static elastography was performed under varying conditions (different scanning methods, different configuration of conventional linear array imaging and different-size kernels) with those measured from simulated or experimentally acquired data. We performed studies to illustrate the application of the derived expressions when performing vascular elastography with plane wave and compounded plane wave imaging. Standard deviations in lateral displacements were an order higher than those in axial. Additionally, the derived expressions predicted that peak performance should occur when 2% strain is applied, the same order of magnitude as observed in simulations (1%) and experiments (1%-2%). We assessed how different configurations of conventional linear array imaging (number of active reception and transmission elements) influenced the quality of axial and lateral strain elastograms. The theoretical expressions predicted that 2-D echo tracking should be performed with wide kernels, but the length of the kernels should be selected using knowledge of the magnitude of the applied strain: specifically, longer kernels for small strains (<5%) and shorter kernels for larger strains. Although the general trends of theoretical predictions and experimental observations were similar, biases incurred during beamforming and subsample displacement estimation produced noticeable differences. Copyright © 2017 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Power spectrum and non-Gaussianities in anisotropic inflation

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

Dey, Anindya; Kovetz, Ely D.; Paban, Sonia, E-mail: anindya@physics.utexas.edu, E-mail: elykovetz@gmail.com, E-mail: paban@physics.utexas.edu

2014-06-01

We study the planar regime of curvature perturbations for single field inflationary models in an axially symmetric Bianchi I background. In a theory with standard scalar field action, the power spectrum for such modes has a pole as the planarity parameter goes to zero. We show that constraints from back reaction lead to a strong lower bound on the planarity parameter for high-momentum planar modes and use this bound to calculate the signal-to-noise ratio of the anisotropic power spectrum in the CMB, which in turn places an upper bound on the Hubble scale during inflation allowed in our model. Wemore » find that non-Gaussianities for these planar modes are enhanced for the flattened triangle and the squeezed triangle configurations, but show that the estimated values of the f{sub NL} parameters remain well below the experimental bounds from the CMB for generic planar modes (other, more promising signatures are also discussed). For a standard action, f{sub NL} from the squeezed configuration turns out to be larger compared to that from the flattened triangle configuration in the planar regime. However, in a theory with higher derivative operators, non-Gaussianities from the flattened triangle can become larger than the squeezed configuration in a certain limit of the planarity parameter.« less

An auxiliary adaptive Gaussian mixture filter applied to flowrate allocation using real data from a multiphase producer

NASA Astrophysics Data System (ADS)

Lorentzen, Rolf J.; Stordal, Andreas S.; Hewitt, Neal

2017-05-01

Flowrate allocation in production wells is a complicated task, especially for multiphase flow combined with several reservoir zones and/or branches. The result depends heavily on the available production data, and the accuracy of these. In the application we show here, downhole pressure and temperature data are available, in addition to the total flowrates at the wellhead. The developed methodology inverts these observations to the fluid flowrates (oil, water and gas) that enters two production branches in a real full-scale producer. A major challenge is accurate estimation of flowrates during rapid variations in the well, e.g. due to choke adjustments. The Auxiliary Sequential Importance Resampling (ASIR) filter was developed to handle such challenges, by introducing an auxiliary step, where the particle weights are recomputed (second weighting step) based on how well the particles reproduce the observations. However, the ASIR filter suffers from large computational time when the number of unknown parameters increase. The Gaussian Mixture (GM) filter combines a linear update, with the particle filters ability to capture non-Gaussian behavior. This makes it possible to achieve good performance with fewer model evaluations. In this work we present a new filter which combines the ASIR filter and the Gaussian Mixture filter (denoted ASGM), and demonstrate improved estimation (compared to ASIR and GM filters) in cases with rapid parameter variations, while maintaining reasonable computational cost.

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…

Measurements of refractive index and size of a spherical drop from Gaussian beam scattering in the primary rainbow region

NASA Astrophysics Data System (ADS)

Yu, Haitao; Sun, Hui; Shen, Jianqi; Tropea, Cameron

2018-03-01

The primary rainbow observed when light is scattered by a spherical drop has been exploited in the past to measure drop size and relative refractive index. However, if higher spatial resolution is required in denser drop ensembles/sprays, and to avoid then multiple drops simultaneously appearing in the measurement volume, a highly focused beam is desirable, inevitably with a Gaussian intensity profile. The present study examines the primary rainbow pattern resulting when a Gaussian beam is scattered by a spherical drop and estimates the attainable accuracy when extracting size and refractive index. The scattering is computed using generalized Lorenz-Mie theory (GLMT) and Debye series decomposition of the Gaussian beam scattering. The results of these simulations show that the measurement accuracy is dependent on both the beam waist radius and the position of the drop in the beam waist.

Ince Gaussian beams in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Deng, Dongmei; Guo, Qi

2008-07-01

Based on the Snyder-Mitchell model that describes the beam propagation in strongly nonlocal nonlinear media, the close forms of Ince-Gaussian (IG) beams have been found. The transverse structures of the IG beams are described by the product of the Ince polynomials and the Gaussian function. Depending on the input power of the beams, the IG beams can be either a soliton state or a breather state. The IG beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian beams. The IG vortex beams can be constructed by a linear combination of the even and odd IG beams. The transverse intensity pattern of IG vortex beams consists of elliptic rings, whose number and ellipticity can be controlled, and a phase displaying a number of in-line vortices, each with a unitary topological charge. The analytical solutions of the IG beams are confirmed by the numerical simulations of the nonlocal nonlinear Schr\\rm \\ddot{o} dinger equation.

The Gaussian copula model for the joint deficit index for droughts

NASA Astrophysics Data System (ADS)

Van de Vyver, H.; Van den Bergh, J.

2018-06-01

The characterization of droughts and their impacts is very dependent on the time scale that is involved. In order to obtain an overall drought assessment, the cumulative effects of water deficits over different times need to be examined together. For example, the recently developed joint deficit index (JDI) is based on multivariate probabilities of precipitation over various time scales from 1- to 12-months, and was constructed from empirical copulas. In this paper, we examine the Gaussian copula model for the JDI. We model the covariance across the temporal scales with a two-parameter function that is commonly used in the specific context of spatial statistics or geostatistics. The validity of the covariance models is demonstrated with long-term precipitation series. Bootstrap experiments indicate that the Gaussian copula model has advantages over the empirical copula method in the context of drought severity assessment: (i) it is able to quantify droughts outside the range of the empirical copula, (ii) provides adequate drought quantification, and (iii) provides a better understanding of the uncertainty in the estimation.

Screening and clustering of sparse regressions with finite non-Gaussian mixtures.

PubMed

Zhang, Jian

2017-06-01

This article proposes a method to address the problem that can arise when covariates in a regression setting are not Gaussian, which may give rise to approximately mixture-distributed errors, or when a true mixture of regressions produced the data. The method begins with non-Gaussian mixture-based marginal variable screening, followed by fitting a full but relatively smaller mixture regression model to the selected data with help of a new penalization scheme. Under certain regularity conditions, the new screening procedure is shown to possess a sure screening property even when the population is heterogeneous. We further prove that there exists an elbow point in the associated scree plot which results in a consistent estimator of the set of active covariates in the model. By simulations, we demonstrate that the new procedure can substantially improve the performance of the existing procedures in the content of variable screening and data clustering. By applying the proposed procedure to motif data analysis in molecular biology, we demonstrate that the new method holds promise in practice. © 2016, The International Biometric Society.

Statistics of Sxy estimates

NASA Technical Reports Server (NTRS)

Freilich, M. H.; Pawka, S. S.

1987-01-01

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman (1957), the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxy(tot). In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum-likelihood estimator for a posterior estimation is outlined.

Realistic continuous-variable quantum teleportation with non-Gaussian resources

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

Dell'Anno, F.; De Siena, S.; CNR-INFM Coherentia, Napoli, Italy, and CNISM and INFN Sezione di Napoli, Gruppo Collegato di Salerno, Baronissi, SA

2010-01-15

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

Compensation of Gaussian curvature in developable cones is local

NASA Astrophysics Data System (ADS)

Wang, Jin W.; Witten, Thomas A.

2009-10-01

We use the angular deficit scheme [V. Borrelli, F. Cazals, and J.-M. Morvan, Comput. Aided Geom. Des. 20, 319 (2003)] to determine the distribution of Gaussian curvature in developable cones (d-cones) [E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, Nature (London) 401, 46 (1999)] numerically. These d-cones are formed by pushing a thin elastic sheet into a circular container. Negative Gaussian curvatures are identified at the rim where the sheet touches the container. Around the rim there are two narrow bands with positive Gaussian curvatures. The integral of the (negative) Gaussian curvature near the rim is almost completely compensated by that of the two adjacent bands. This suggests that the Gauss-Bonnet theorem which constrains the integral of Gaussian curvature globally does not explain the spontaneous curvature cancellation phenomenon [T. Liang and T. A. Witten, Phys. Rev. E 73, 046604 (2006)]. The locality of the compensation seems to increase for decreasing d-cone thickness. The angular deficit scheme also provides a way to confirm the curvature cancellation phenomenon.

Anisotropic tensor power spectrum at interferometer scales induced by tensor squeezed non-Gaussianity

NASA Astrophysics Data System (ADS)

Ricciardone, Angelo; Tasinato, Gianmassimo

2018-02-01

We develop a scenario of inflation with spontaneously broken time and space diffeomorphisms, with distinctive features for the primordial tensor modes. Inflationary tensor fluctuations are not conserved outside the horizon, and can acquire a mass during the inflationary epoch. They can evade the Higuchi bound around de Sitter space, thanks to interactions with the fields driving expansion. Correspondingly, the primordial stochastic gravitational wave background (SGWB) is characterised by a tuneable scale dependence, and can be detectable at interferometer scales. In this set-up, tensor non-Gaussianity can be parametrically enhanced in the squeezed limit. This induces a coupling between long and short tensor modes, leading to a specific quadrupolar anisotropy in the primordial SGWB spectrum, which can be used to build estimators for tensor non-Gaussianity. We analyse how our inflationary system can be tested with interferometers, also discussing how an interferometer can be sensitive to a primordial anisotropic SGWB.

Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

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

Gaussian Curvature Directs Stress Fiber Orientation and Cell Migration.

PubMed

Bade, Nathan D; Xu, Tina; Kamien, Randall D; Assoian, Richard K; Stebe, Kathleen J

2018-03-27

We show that substrates with nonzero Gaussian curvature influence the organization of stress fibers and direct the migration of cells. To study the role of Gaussian curvature, we developed a sphere-with-skirt surface in which a positive Gaussian curvature spherical cap is seamlessly surrounded by a negative Gaussian curvature draping skirt, both with principal radii similar to cell-length scales. We find significant reconfiguration of two subpopulations of stress fibers when fibroblasts are exposed to these curvatures. Apical stress fibers in cells on skirts align in the radial direction and avoid bending by forming chords across the concave gap, whereas basal stress fibers bend along the convex direction. Cell migration is also strongly influenced by the Gaussian curvature. Real-time imaging shows that cells migrating on skirts repolarize to establish a leading edge in the azimuthal direction. Thereafter, they migrate in that direction. This behavior is notably different from migration on planar surfaces, in which cells typically migrate in the same direction as the apical stress fiber orientation. Thus, this platform reveals that nonzero Gaussian curvature not only affects the positioning of cells and alignment of stress fiber subpopulations but also directs migration in a manner fundamentally distinct from that of migration on planar surfaces. Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Orbit-product representation and correction of Gaussian belief propagation

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

Johnson, Jason K; Chertkov, Michael; Chernyak, Vladimir

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.

Robust transmission of non-Gaussian entanglement over optical fibers

NASA Astrophysics Data System (ADS)

Biswas, Asoka; Lidar, Daniel A.

2006-12-01

We show how the entanglement in a wide range of continuous variable non-Gaussian states can be preserved against decoherence for long-range quantum communication through an optical fiber. We apply protection via decoherence-free subspaces and quantum dynamical decoupling to this end. The latter is implemented by inserting phase shifters at regular intervals Δ inside the fiber, where Δ is roughly the ratio of the speed of light in the fiber to the bath high-frequency cutoff. Detailed estimates of relevant parameters are provided using the boson-boson model of system-bath interaction for silica fibers and Δ is found to be on the order of a millimeter.

Steady states of OQBM: Central Limit Theorem, Gaussian and non-Gaussian behavior

NASA Astrophysics Data System (ADS)

Petruccione, Francesco; Sinayskiy, Ilya

Open Quantum Brownian Motion (OQBM) describes a Brownian particle with an additional internal quantum degree of freedom. Originally, it was introduced as a scaling limit of Open Quantum Walks (OQWs). Recently, it was noted, that for the model of free OQBM with a two-level system as an internal degree of freedom and decoherent coupling to a dissipative environment, one could use weak external driving of the internal degree of freedom to manipulate the steady-state position of the walker. This observation establishes a useful connection between controllable parameters of the OQBM, e.g. driving strengths and magnitude of detuning, and its steady state properties. Although OQWs satisfy a central limit theorem (CLT), it is known, that OQBM, in general, does not. The aim of this work is to derive steady states for some particular OQBMs and observe possible transitions from Gaussian to non-Gaussian behavior depending on the choice of quantum coin and as a function of diffusion coefficient and dissipation strength.

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

PubMed

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

2018-06-01

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

Adaptive OFDM Radar Waveform Design for Improved Micro-Doppler Estimation

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

Sen, Satyabrata

Here we analyze the performance of a wideband orthogonal frequency division multiplexing (OFDM) signal in estimating the micro-Doppler frequency of a rotating target having multiple scattering centers. The use of a frequency-diverse OFDM signal enables us to independently analyze the micro-Doppler characteristics with respect to a set of orthogonal subcarrier frequencies. We characterize the accuracy of micro-Doppler frequency estimation by computing the Cramer-Rao bound (CRB) on the angular-velocity estimate of the target. Additionally, to improve the accuracy of the estimation procedure, we formulate and solve an optimization problem by minimizing the CRB on the angular-velocity estimate with respect to themore » OFDM spectral coefficients. We present several numerical examples to demonstrate the CRB variations with respect to the signal-to-noise ratios, number of temporal samples, and number of OFDM subcarriers. We also analysed numerically the improvement in estimation accuracy due to the adaptive waveform design. A grid-based maximum likelihood estimation technique is applied to evaluate the corresponding mean-squared error performance.« less

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

NASA Astrophysics Data System (ADS)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

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

Generation of hollow Gaussian beams by spatial filtering

NASA Astrophysics Data System (ADS)

Liu, Zhengjun; Zhao, Haifa; Liu, Jianlong; Lin, Jie; Ashfaq Ahmad, Muhammad; Liu, Shutian

2007-08-01

We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.

Generation of hollow Gaussian beams by spatial filtering.

PubMed

Liu, Zhengjun; Zhao, Haifa; Liu, Jianlong; Lin, Jie; Ahmad, Muhammad Ashfaq; Liu, Shutian

2007-08-01

We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.

Gaussian entanglement generation from coherence using beam-splitters

PubMed Central

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

2016-01-01

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

Synthetic Incoherence via Scanned Gaussian Beams

PubMed Central

Levine, Zachary H.

2006-01-01

Tomography, in most formulations, requires an incoherent signal. For a conventional transmission electron microscope, the coherence of the beam often results in diffraction effects that limit the ability to perform a 3D reconstruction from a tilt series with conventional tomographic reconstruction algorithms. In this paper, an analytic solution is given to a scanned Gaussian beam, which reduces the beam coherence to be effectively incoherent for medium-size (of order 100 voxels thick) tomographic applications. The scanned Gaussian beam leads to more incoherence than hollow-cone illumination. PMID:27274945

A classification of open Gaussian dynamics

NASA Astrophysics Data System (ADS)

Grimmer, Daniel; Brown, Eric; Kempf, Achim; Mann, Robert B.; Martín-Martínez, Eduardo

2018-06-01

We introduce a classification scheme for the generators of bosonic open Gaussian dynamics, providing instructive diagrams description for each type of dynamics. Using this classification, we discuss the consequences of imposing complete positivity on Gaussian dynamics. In particular, we show that non-symplectic operations must be active to allow for complete positivity. In addition, non-symplectic operations can, in fact, conserve the volume of phase space only if the restriction of complete positivity is lifted. We then discuss the implications for the relationship between information and energy flows in open quantum mechanics.

Simple proof that Gaussian attacks are optimal among collective attacks against continuous-variable quantum key distribution with a Gaussian modulation

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

Leverrier, Anthony; Grangier, Philippe; Laboratoire Charles Fabry, Institut d'Optique, CNRS, University Paris-Sud, Campus Polytechnique, RD 128, F-91127 Palaiseau Cedex

2010-06-15

In this article, we give a simple proof of the fact that the optimal collective attacks against continuous-variable quantum key distribution with a Gaussian modulation are Gaussian attacks. Our proof, which makes use of symmetry properties of the protocol in phase space, is particularly relevant for the finite-key analysis of the protocol and therefore for practical applications.

Distillation of squeezing from non-Gaussian quantum states.

PubMed

Heersink, J; Marquardt, Ch; Dong, R; Filip, R; Lorenz, S; Leuchs, G; Andersen, U L

2006-06-30

We show that single copy distillation of squeezing from continuous variable non-Gaussian states is possible using linear optics and conditional homodyne detection. A specific non-Gaussian noise source, corresponding to a random linear displacement, is investigated experimentally. Conditioning the signal on a tap measurement, we observe probabilistic recovery of squeezing.

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

PubMed

Lukin, Igor P

2016-04-20

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

Working covariance model selection for generalized estimating equations.

PubMed

Carey, Vincent J; Wang, You-Gan

2011-11-20

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

PERIOD ESTIMATION FOR SPARSELY SAMPLED QUASI-PERIODIC LIGHT CURVES APPLIED TO MIRAS

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

He, Shiyuan; Huang, Jianhua Z.; Long, James

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequencymore » parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period–luminosity relations.« less

Self-assembled structures of Gaussian nematic particles.

PubMed

Nikoubashman, Arash; Likos, Christos N

2010-03-17

We investigate the stable crystalline configurations of a nematic liquid crystal made of soft parallel ellipsoidal particles interacting via a repulsive, anisotropic Gaussian potential. For this purpose, we use genetic algorithms (GA) in order to predict all relevant and possible solid phase candidates into which this fluid can freeze. Subsequently we present and discuss the emerging novel structures and the resulting zero-temperature phase diagram of this system. The latter features a variety of crystalline arrangements, in which the elongated Gaussian particles in general do not align with any one of the high-symmetry crystallographic directions, a compromise arising from the interplay and competition between anisotropic repulsions and crystal ordering. Only at very strong degrees of elongation does a tendency of the Gaussian nematics to align with the longest axis of the elementary unit cell emerge.

Unitarily localizable entanglement of Gaussian states

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

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)more » 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.« less

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

Methods of Information Geometry to model complex shapes

NASA Astrophysics Data System (ADS)

De Sanctis, A.; Gattone, S. A.

2016-09-01

In this paper, a new statistical method to model patterns emerging in complex systems is proposed. A framework for shape analysis of 2- dimensional landmark data is introduced, in which each landmark is represented by a bivariate Gaussian distribution. From Information Geometry we know that Fisher-Rao metric endows the statistical manifold of parameters of a family of probability distributions with a Riemannian metric. Thus this approach allows to reconstruct the intermediate steps in the evolution between observed shapes by computing the geodesic, with respect to the Fisher-Rao metric, between the corresponding distributions. Furthermore, the geodesic path can be used for shape predictions. As application, we study the evolution of the rat skull shape. A future application in Ophthalmology is introduced.

Controllable gaussian-qubit interface for extremal quantum state engineering.

PubMed

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.

Quantum Teamwork for Unconditional Multiparty Communication with Gaussian States

NASA Astrophysics Data System (ADS)

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

2009-08-01

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

Curve fitting of the corporate recovery rates: the comparison of Beta distribution estimation and kernel density estimation.

PubMed

Chen, Rongda; Wang, Ze

2013-01-01

Recovery rate is essential to the estimation of the portfolio's loss and economic capital. Neglecting the randomness of the distribution of recovery rate may underestimate the risk. The study introduces two kinds of models of distribution, Beta distribution estimation and kernel density distribution estimation, to simulate the distribution of recovery rates of corporate loans and bonds. As is known, models based on Beta distribution are common in daily usage, such as CreditMetrics by J.P. Morgan, Portfolio Manager by KMV and Losscalc by Moody's. However, it has a fatal defect that it can't fit the bimodal or multimodal distributions such as recovery rates of corporate loans and bonds as Moody's new data show. In order to overcome this flaw, the kernel density estimation is introduced and we compare the simulation results by histogram, Beta distribution estimation and kernel density estimation to reach the conclusion that the Gaussian kernel density distribution really better imitates the distribution of the bimodal or multimodal data samples of corporate loans and bonds. Finally, a Chi-square test of the Gaussian kernel density estimation proves that it can fit the curve of recovery rates of loans and bonds. So using the kernel density distribution to precisely delineate the bimodal recovery rates of bonds is optimal in credit risk management.

Inflation in random Gaussian landscapes

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

Masoumi, Ali; Vilenkin, Alexander; Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu

2017-05-01

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

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

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

Rossi, Matteo A. C., E-mail: matteo.rossi@unimi.it; Paris, Matteo G. A., E-mail: matteo.paris@fisica.unimi.it; CNISM, Unità Milano Statale, I-20133 Milano

2016-01-14

We address the interaction of single- and two-qubit systems with an external transverse fluctuating field and analyze in detail the dynamical decoherence induced by Gaussian noise and random telegraph noise (RTN). Upon exploiting the exact RTN solution of the time-dependent von Neumann equation, we analyze in detail the behavior of quantum correlations and prove the non-Markovianity of the dynamical map in the full parameter range, i.e., for either fast or slow noise. The dynamics induced by Gaussian noise is studied numerically and compared to the RTN solution, showing the existence of (state dependent) regions of the parameter space where themore » two noises lead to very similar dynamics. We show that the effects of RTN noise and of Gaussian noise are different, i.e., the spectrum alone is not enough to summarize the noise effects, but the dynamics under the effect of one kind of noise may be simulated with high fidelity by the other one.« less

Gaussian decomposition of high-resolution melt curve derivatives for measuring genome-editing efficiency

PubMed Central

Zaboikin, Michail; Freter, Carl

2018-01-01

We describe a method for measuring genome editing efficiency from in silico analysis of high-resolution melt curve data. The melt curve data derived from amplicons of genome-edited or unmodified target sites were processed to remove the background fluorescent signal emanating from free fluorophore and then corrected for temperature-dependent quenching of fluorescence of double-stranded DNA-bound fluorophore. Corrected data were normalized and numerically differentiated to obtain the first derivatives of the melt curves. These were then mathematically modeled as a sum or superposition of minimal number of Gaussian components. Using Gaussian parameters determined by modeling of melt curve derivatives of unedited samples, we were able to model melt curve derivatives from genetically altered target sites where the mutant population could be accommodated using an additional Gaussian component. From this, the proportion contributed by the mutant component in the target region amplicon could be accurately determined. Mutant component computations compared well with the mutant frequency determination from next generation sequencing data. The results were also consistent with our earlier studies that used difference curve areas from high-resolution melt curves for determining the efficiency of genome-editing reagents. The advantage of the described method is that it does not require calibration curves to estimate proportion of mutants in amplicons of genome-edited target sites. PMID:29300734

Robust Tracking of Small Displacements with a Bayesian Estimator

PubMed Central

Dumont, Douglas M.; Byram, Brett C.

2016-01-01

Radiation-force-based elasticity imaging describes a group of techniques that use acoustic radiation force (ARF) to displace tissue in order to obtain qualitative or quantitative measurements of tissue properties. Because ARF-induced displacements are on the order of micrometers, tracking these displacements in vivo can be challenging. Previously, it has been shown that Bayesian-based estimation can overcome some of the limitations of a traditional displacement estimator like normalized cross-correlation (NCC). In this work, we describe a Bayesian framework that combines a generalized Gaussian-Markov random field (GGMRF) prior with an automated method for selecting the prior’s width. We then evaluate its performance in the context of tracking the micrometer-order displacements encountered in an ARF-based method like acoustic radiation force impulse (ARFI) imaging. The results show that bias, variance, and mean-square error performance vary with prior shape and width, and that an almost one order-of-magnitude reduction in mean-square error can be achieved by the estimator at the automatically-selected prior width. Lesion simulations show that the proposed estimator has a higher contrast-to-noise ratio but lower contrast than NCC, median-filtered NCC, and the previous Bayesian estimator, with a non-Gaussian prior shape having better lesion-edge resolution than a Gaussian prior. In vivo results from a cardiac, radiofrequency ablation ARFI imaging dataset show quantitative improvements in lesion contrast-to-noise ratio over NCC as well as the previous Bayesian estimator. PMID:26529761

Investigation of non-Gaussian effects in the Brazilian option market

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Probability density and exceedance rate functions of locally Gaussian turbulence

NASA Technical Reports Server (NTRS)

Mark, W. D.

1989-01-01

A locally Gaussian model of turbulence velocities is postulated which consists of the superposition of a slowly varying strictly Gaussian component representing slow temporal changes in the mean wind speed and a more rapidly varying locally Gaussian turbulence component possessing a temporally fluctuating local variance. Series expansions of the probability density and exceedance rate functions of the turbulence velocity model, based on Taylor's series, are derived. Comparisons of the resulting two-term approximations with measured probability density and exceedance rate functions of atmospheric turbulence velocity records show encouraging agreement, thereby confirming the consistency of the measured records with the locally Gaussian model. Explicit formulas are derived for computing all required expansion coefficients from measured turbulence records.

Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams

NASA Astrophysics Data System (ADS)

Dennis, M. R.; Alonso, M. A.

2017-02-01

The connection between Poincaré spheres for polarization and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic two-dimensional harmonic oscillator in Hamiltonian mechanics, its canonical quantization and semiclassical interpretation. This leads to the interpretation of structured Gaussian modes, the Hermite-Gaussian, Laguerre-Gaussian and generalized Hermite-Laguerre-Gaussian modes as eigenfunctions of operators corresponding to the classical constants of motion of the two-dimensional oscillator, which acquire an extra significance as families of classical ellipses upon semiclassical quantization. This article is part of the themed issue 'Optical orbital angular momentum'.

Characterization, parameter estimation, and aircraft response statistics of atmospheric turbulence

NASA Technical Reports Server (NTRS)

Mark, W. D.

1981-01-01

A nonGaussian three component model of atmospheric turbulence is postulated that accounts for readily observable features of turbulence velocity records, their autocorrelation functions, and their spectra. Methods for computing probability density functions and mean exceedance rates of a generic aircraft response variable are developed using nonGaussian turbulence characterizations readily extracted from velocity recordings. A maximum likelihood method is developed for optimal estimation of the integral scale and intensity of records possessing von Karman transverse of longitudinal spectra. Formulas for the variances of such parameter estimates are developed. The maximum likelihood and least-square approaches are combined to yield a method for estimating the autocorrelation function parameters of a two component model for turbulence.

Resampling methods in Microsoft Excel® for estimating reference intervals

PubMed Central

Theodorsson, Elvar

2015-01-01

Computer- intensive resampling/bootstrap methods are feasible when calculating reference intervals from non-Gaussian or small reference samples. Microsoft Excel® in version 2010 or later includes natural functions, which lend themselves well to this purpose including recommended interpolation procedures for estimating 2.5 and 97.5 percentiles.
The purpose of this paper is to introduce the reader to resampling estimation techniques in general and in using Microsoft Excel® 2010 for the purpose of estimating reference intervals in particular.
Parametric methods are preferable to resampling methods when the distributions of observations in the reference samples is Gaussian or can transformed to that distribution even when the number of reference samples is less than 120. Resampling methods are appropriate when the distribution of data from the reference samples is non-Gaussian and in case the number of reference individuals and corresponding samples are in the order of 40. At least 500-1000 random samples with replacement should be taken from the results of measurement of the reference samples. PMID:26527366

Resampling methods in Microsoft Excel® for estimating reference intervals.

PubMed

Theodorsson, Elvar

2015-01-01

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

Automatic image equalization and contrast enhancement using Gaussian mixture modeling.

PubMed

Celik, Turgay; Tjahjadi, Tardi