Error estimates for Gaussian quadratures of analytic functions
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2009-12-01
For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points ±1 and the sum of semi-axes [varrho]>1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures.
Trispectrum estimator in equilateral type non-Gaussian models
Mizuno, Shuntaro; Koyama, Kazuya E-mail: Kazuya.Koyama@port.ac.uk
2010-10-01
We investigate an estimator to measure the primordial trispectrum in equilateral type non-Gaussian models such as k-inflation, single field DBI inflation and multi-field DBI inflation models from Cosmic Microwave Background (CMB) anisotropies. The shape of the trispectrum whose amplitude is not constrained by the bispectrum in the context of effective theory of inflation and k-inflation is known to admit a separable form of the estimator for CMB anisotropies. We show that this shape is 87% correlated with the full quantum trispectrum in single field DBI inflation, while it is 33% correlated with the one in multi-field DBI inflation when curvature perturbation is originated from purely entropic contribution. This suggests that g{sub NL}{sup equil}, the amplitude of this particular shape, provides a reasonable measure of the non-Gaussianity from the trispectrum in equilateral non-Gaussian models. We relate model parameters such as the sound speed, c{sub s} and the transfer coefficient from entropy perturbations to the curvature perturbation, T{sub RS} with g{sub NL}{sup equil}, which enables us to constrain model parameters in these models once g{sub NL}{sup equil} is measured in WMAP and Planck.
Estimating Mixture of Gaussian Processes by Kernel Smoothing.
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
Articulated and Generalized Gaussian Kernel Correlation for Human Pose Estimation.
Ding, Meng; Fan, Guoliang
2016-02-01
In this paper, we propose an articulated and generalized Gaussian kernel correlation (GKC)-based framework for human pose estimation. We first derive a unified GKC representation that generalizes the previous sum of Gaussians (SoG)-based methods for the similarity measure between a template and an observation both of which are represented by various SoG variants. Then, we develop an articulated GKC (AGKC) by integrating a kinematic skeleton in a multivariate SoG template that supports subject-specific shape modeling and articulated pose estimation for both the full body and the hands. We further propose a sequential (body/hand) pose tracking algorithm by incorporating three regularization terms in the AGKC function, including visibility, intersection penalty, and pose continuity. Our tracking algorithm is simple yet effective and computationally efficient. We evaluate our algorithm on two benchmark depth data sets. The experimental results are promising and competitive when compared with the state-of-the-art algorithms. PMID:26672042
Next generation strong lensing time delay estimation with Gaussian processes
NASA Astrophysics Data System (ADS)
Hojjati, Alireza; Linder, Eric V.
2014-12-01
Strong gravitational lensing forms multiple, time delayed images of cosmological sources, with the "focal length" of the lens serving as a cosmological distance probe. Robust estimation of the time delay distance can tightly constrain the Hubble constant as well as the matter density and dark energy. Current and next generation surveys will find hundreds to thousands of lensed systems but accurate time delay estimation from noisy, gappy light curves is potentially a limiting systematic. Using a large sample of blinded light curves from the Strong Lens Time Delay Challenge we develop and demonstrate a Gaussian process cross correlation technique that delivers an average bias within 0.1% depending on the sampling, necessary for subpercent Hubble constant determination. The fits are accurate (80% of them within one day) for delays from 5-100 days and robust against cadence variations shorter than six days. We study the effects of survey characteristics such as cadence, season, and campaign length, and derive requirements for time delay cosmology: in order not to bias the cosmology determination by 0.5 σ , the mean time delay fit accuracy must be better than 0.2%.
A sparse Gaussian process framework for photometric redshift estimation
NASA Astrophysics Data System (ADS)
Almosallam, Ibrahim A.; Lindsay, Sam N.; Jarvis, Matt J.; Roberts, Stephen J.
2016-01-01
Accurate photometric redshifts are a lynchpin for many future experiments to pin down the cosmological model and for studies of galaxy evolution. In this study, a novel sparse regression framework for photometric redshift estimation is presented. Synthetic data set simulating the Euclid survey and real data from SDSS DR12 are used to train and test the proposed models. We show that approaches which include careful data preparation and model design offer a significant improvement in comparison with several competing machine learning algorithms. Standard implementations of most regression algorithms use the minimization of the sum of squared errors as the objective function. For redshift inference, this induces a bias in the posterior mean of the output distribution, which can be problematic. In this paper, we directly minimize the target metric Δz = (zs - zp)/(1 + zs) and address the bias problem via a distribution-based weighting scheme, incorporated as part of the optimization objective. The results are compared with other machine learning algorithms in the field such as artificial neural networks (ANN), Gaussian processes (GPs) and sparse GPs. The proposed framework reaches a mean absolute Δz = 0.0026(1 + zs), over the redshift range of 0 ≤ zs ≤ 2 on the simulated data, and Δz = 0.0178(1 + zs) over the entire redshift range on the SDSS DR12 survey, outperforming the standard ANNz used in the literature. We also investigate how the relative size of the training sample affects the photometric redshift accuracy. We find that a training sample of >30 per cent of total sample size, provides little additional constraint on the photometric redshifts, and note that our GP formalism strongly outperforms ANNz in the sparse data regime for the simulated data set.
Searching for primordial non-Gaussianity in Planck CMB maps using a combined estimator
NASA Astrophysics Data System (ADS)
Novaes, C. P.; Bernui, A.; Ferreira, I. S.; Wuensche, C. A.
2014-01-01
The extensive search for deviations from Gaussianity in cosmic microwave background radiation (CMB) data is very important due to the information about the very early moments of the universe encoded there. Recent analyses from Planck CMB data do not exclude the presence of non-Gaussianity of small amplitude, although they are consistent with the Gaussian hypothesis. The use of different techniques is essential to provide information about types and amplitudes of non-Gaussianities in the CMB data. In particular, we find interesting to construct an estimator based upon the combination of two powerful statistical tools that appears to be sensitive enough to detect tiny deviations from Gaussianity in CMB maps. This estimator combines the Minkowski functionals with a Neural Network, maximizing a tool widely used to study non-Gaussian signals with a reinforcement of another tool designed to identify patterns in a data set. We test our estimator by analyzing simulated CMB maps contaminated with different amounts of local primordial non-Gaussianity quantified by the dimensionless parameter f NL. We apply it to these sets of CMB maps and find gtrsim 98% of chance of positive detection, even for small intensity local non-Gaussianity like f NL = 38±18, the current limit from Planck data for large angular scales. Additionally, we test the suitability to distinguish between primary and secondary non-Gaussianities: first we train the Neural Network with two sets, one of nearly Gaussian CMB maps (|f NL| <= 10) but contaminated with realistic inhomogeneous Planck noise (i.e., secondary non-Gaussianity) and the other of non-Gaussian CMB maps, that is, maps endowed with weak primordial non-Gaussianity (28 <= f NL <= 48); after that we test an ensemble composed of CMB maps either with one of these non-Gaussian contaminations, and find out that our method successfully classifies ~ 95% of the tested maps as being CMB maps containing primordial or secondary non-Gaussianity. Furthermore
Searching for primordial non-Gaussianity in Planck CMB maps using a combined estimator
Novaes, C.P.; Wuensche, C.A.; Bernui, A.; Ferreira, I.S. E-mail: bernui@on.br E-mail: ca.wuensche@inpe.br
2014-01-01
The extensive search for deviations from Gaussianity in cosmic microwave background radiation (CMB) data is very important due to the information about the very early moments of the universe encoded there. Recent analyses from Planck CMB data do not exclude the presence of non-Gaussianity of small amplitude, although they are consistent with the Gaussian hypothesis. The use of different techniques is essential to provide information about types and amplitudes of non-Gaussianities in the CMB data. In particular, we find interesting to construct an estimator based upon the combination of two powerful statistical tools that appears to be sensitive enough to detect tiny deviations from Gaussianity in CMB maps. This estimator combines the Minkowski functionals with a Neural Network, maximizing a tool widely used to study non-Gaussian signals with a reinforcement of another tool designed to identify patterns in a data set. We test our estimator by analyzing simulated CMB maps contaminated with different amounts of local primordial non-Gaussianity quantified by the dimensionless parameter f{sub NL}. We apply it to these sets of CMB maps and find ∼> 98% of chance of positive detection, even for small intensity local non-Gaussianity like f{sub NL} = 38±18, the current limit from Planck data for large angular scales. Additionally, we test the suitability to distinguish between primary and secondary non-Gaussianities: first we train the Neural Network with two sets, one of nearly Gaussian CMB maps (|f{sub NL}| ≤ 10) but contaminated with realistic inhomogeneous Planck noise (i.e., secondary non-Gaussianity) and the other of non-Gaussian CMB maps, that is, maps endowed with weak primordial non-Gaussianity (28 ≤ f{sub NL} ≤ 48); after that we test an ensemble composed of CMB maps either with one of these non-Gaussian contaminations, and find out that our method successfully classifies ∼ 95% of the tested maps as being CMB maps containing primordial or
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 estimation for discretely observed Cox-Ingersoll-Ross model
NASA Astrophysics Data System (ADS)
Wei, Chao; Shu, Huisheng; Liu, Yurong
2016-07-01
This paper is concerned with the parameter estimation problem for Cox-Ingersoll-Ross model based on discrete observation. First, a new discretized process is built based on the Euler-Maruyama scheme. Then, the parameter estimators are obtained by employing the maximum likelihood method and the explicit expressions of the error of estimation are given. Subsequently, the consistency property of all parameter estimators are proved by applying the law of large numbers for martingales, Holder's inequality, B-D-G inequality and Cauchy-Schwarz inequality. Finally, a numerical simulation example for estimators and the absolute error between estimators and true values is presented to demonstrate the effectiveness of the estimation approach used in this paper.
Sivakumar, Vidyashankar; Banerjee, Arindam; Ravikumar, Pradeep
2016-01-01
We consider the problem of high-dimensional structured estimation with norm-regularized estimators, such as Lasso, when the design matrix and noise are drawn from sub-exponential distributions. Existing results only consider sub-Gaussian designs and noise, and both the sample complexity and non-asymptotic estimation error have been shown to depend on the Gaussian width of suitable sets. In contrast, for the sub-exponential setting, we show that the sample complexity and the estimation error will depend on the exponential width of the corresponding sets, and the analysis holds for any norm. Further, using generic chaining, we show that the exponential width for any set will be at most logp times the Gaussian width of the set, yielding Gaussian width based results even for the sub-exponential case. Further, for certain popular estimators, viz Lasso and Group Lasso, using a VC-dimension based analysis, we show that the sample complexity will in fact be the same order as Gaussian designs. Our general analysis and results are the first in the sub-exponential setting, and are readily applicable to special sub-exponential families such as log-concave and extreme-value distributions. PMID:27563230
Stellar atmospheric parameter estimation using Gaussian process regression
NASA Astrophysics Data System (ADS)
Bu, Yude; Pan, Jingchang
2015-02-01
As is well known, it is necessary to derive stellar parameters from massive amounts of spectral data automatically and efficiently. However, in traditional automatic methods such as artificial neural networks (ANNs) and kernel regression (KR), it is often difficult to optimize the algorithm structure and determine the optimal algorithm parameters. Gaussian process regression (GPR) is a recently developed method that has been proven to be capable of overcoming these difficulties. Here we apply GPR to derive stellar atmospheric parameters from spectra. Through evaluating the performance of GPR on Sloan Digital Sky Survey (SDSS) spectra, Medium resolution Isaac Newton Telescope Library of Empirical Spectra (MILES) spectra, ELODIE spectra and the spectra of member stars of galactic globular clusters, we conclude that GPR can derive stellar parameters accurately and precisely, especially when we use data preprocessed with principal component analysis (PCA). We then compare the performance of GPR with that of several widely used regression methods (ANNs, support-vector regression and KR) and find that with GPR it is easier to optimize structures and parameters and more efficient and accurate to extract atmospheric parameters.
A Gaussian Model-Based Probabilistic Approach for Pulse Transit Time Estimation.
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. PMID:25420274
EXACT MINIMAX ESTIMATION OF THE PREDICTIVE DENSITY IN SPARSE GAUSSIAN MODELS1
Mukherjee, Gourab; Johnstone, Iain M.
2015-01-01
We consider estimating the predictive density under Kullback–Leibler loss in an ℓ0 sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable priors and optimal predictive density estimates are derived. Compared to the sparse recovery results involving point estimation of the normal mean, new decision theoretic phenomena are seen. Suboptimal performance of the class of plug-in density estimates reflects the predictive nature of the problem and optimal strategies need diversification of the future risk. We find that minimax optimal strategies lie outside the Gaussian family but can be constructed with threshold predictive density estimates. Novel minimax techniques involving simultaneous calibration of the sparsity adjustment and the risk diversification mechanisms are used to design optimal predictive density estimates. PMID:26448678
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.
NASA Astrophysics Data System (ADS)
Zhou, Xiang; Baird, John P.; Arnold, John F.
1999-02-01
We analyze the effect of image noise on the estimation of fringe orientation in principle and interpret the application of a texture-analysis technique to the problem of estimating fringe orientation in interferograms. The gradient of a Gaussian filter and neighboring-direction averaging are shown to meet the requirements of fringe-orientation estimation by reduction of the effects of low-frequency background and contrast variances as well as high-frequency random image noise. The technique also improves inaccurate orientation estimation at low-modulation points, such as fringe centers and broken fringes. Experiments demonstrate that the scales of the Gaussian gradient filter and the direction averaging should be chosen according to the fringe spacings of the interferograms.
Weng, Yang; Xiao, Wendong; Xie, Lihua
2011-01-01
Distributed estimation of Gaussian mixtures has many applications in wireless sensor network (WSN), and its energy-efficient solution is still challenging. This paper presents a novel diffusion-based EM algorithm for this problem. A diffusion strategy is introduced for acquiring the global statistics in EM algorithm in which each sensor node only needs to communicate its local statistics to its neighboring nodes at each iteration. This improves the existing consensus-based distributed EM algorithm which may need much more communication overhead for consensus, especially in large scale networks. The robustness and scalability of the proposed approach can be achieved by distributed processing in the networks. In addition, we show that the proposed approach can be considered as a stochastic approximation method to find the maximum likelihood estimation for Gaussian mixtures. Simulation results show the efficiency of this approach. PMID:22163956
Nonlinear Bayesian estimation of BOLD signal under non-Gaussian noise.
Khan, Ali Fahim; Younis, Muhammad Shahzad; Bajwa, Khalid Bashir
2015-01-01
Modeling the blood oxygenation level dependent (BOLD) signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF. PMID:25691911
Residual foreground contamination in the WMAP data and bias in non-Gaussianity estimation
Chingangbam, Pravabati; Park, Changbom E-mail: cbp@kias.re.kr
2013-02-01
We analyze whether there is any residual foreground contamination in the cleaned WMAP 7 years data for the differential assemblies, Q, V and W. We calculate the correlation between the foreground map, from which long wavelength correlations have been subtracted, and the foreground reduced map for each differential assembly after applying the Galaxy and point sources masks. We find positive correlations for all the differential assemblies, with high statistical significance. For Q and V, we find that a large fraction of the contamination comes from pixels where the foreground maps have positive values larger than three times the rms values. These findings imply the presence of residual contamination from Galactic emissions and unresolved point sources. We redo the analysis after masking the extended point sources cataloque of Scodeller et al. [7] and find a drop in the correlation and corresponding significance values. To quantify the effect of the residual contamination on the search for primordial non-Gaussianity in the CMB we add estimated contaminant fraction to simulated Gaussian CMB maps and calculate the characteristic non-Gaussian deviation shapes of Minkowski Functionals that arise due to the contamination. We find remarkable agreement of these deviation shapes with those measured from WMAP data, which imply that a major fraction of the observed non-Gaussian deviation comes from residual foreground contamination. We also compute non-Gaussian deviations of Minkowski Functionals after applying the point sources mask of Scodeller et al. and find a decrease in the overall amplitudes of the deviations which is consistent with a decrease in the level of contamination.
Robustness of Estimators of Long-Range Dependence and Self-Similarity under non-Gaussianity
NASA Astrophysics Data System (ADS)
Franzke, C.; Watkins, N. W.; Graves, T.; Gramacy, R.; Hughes, C.
2011-12-01
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that self-similarity in a system can be a superposition of both phenomena. These features, which are common in complex systems, impact the attribution of trends and the occurrence and clustering of extremes. The risk assessment of systems with these properties will lead to different outcomes (e.g. return periods) than the more common assumption of independence of extremes. Two paradigmatic models are discussed which can simultaneously account for long-range dependence and non-Gaussianity: Autoregressive Fractional Integrated Moving Average (ARFIMA) and Linear Fractional Stable Motion (LFSM). Statistical properties of estimators for long-range dependence and self-similarity are critically assessed. It is found that the most popular estimators can be biased in the presence of important features of many natural systems like trends and multiplicative noise. Also the long-range dependence and non-Gaussianity of two typical natural time series are discussed.
Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures
Procacci, Piero
2015-04-21
In this paper, we present an improved method for obtaining unbiased estimates of the free energy difference between two thermodynamic states using the work distribution measured in nonequilibrium driven experiments connecting these states. The method is based on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, whose normal components are identical in either direction of the nonequilibrium process, with weights regulated by the Crooks theorem. Using the prototypical example for the driven unfolding/folding of deca-alanine, we show that the predicted behavior of the forward and reverse work distributions, assuming a combination of only two Gaussian components with Crooks derived weights, explains surprisingly well the striking asymmetry in the observed distributions at fast pulling speeds. The proposed methodology opens the way for a perfectly parallel implementation of Jarzynski-based free energy calculations in complex systems.
Impact of secondary non-Gaussianities in the CMB on cosmological parameter estimation
Smidt, Joseph; Joudaki, Shahab; Amblard, Alexandre; Serra, Paolo; Cooray, Asantha
2010-06-15
We consider corrections to the underlying cosmology due to secondary contributions from weak gravitational lensing, the integrated Sachs-Wolfe effect, and the Sunyaev-Zel'dovich effect contained in the trispectrum. We incorporate these additional contributions to the covariance of a binned angular power spectrum of temperature anisotropies in the analysis of current and prospective data sets. Although recent experiments such as the Arcminute Cosmology Bolometer Array Receiver and the Cosmic Background Imager are not particularly sensitive to these additional non-Gaussian effects, the interpretation of Planck and CMBPol anisotropy spectra will require an accounting of non-Gaussian covariance leading to a degradation in cosmological parameter estimates by up to 20% and 30%, respectively.
Gaussian process models for reference ET estimation from alternative meteorological data sources
NASA Astrophysics Data System (ADS)
Holman, Daniel; Sridharan, Mohan; Gowda, Prasanna; Porter, Dana; Marek, Thomas; Howell, Terry; Moorhead, Jerry
2014-09-01
Accurate estimates of daily crop evapotranspiration (ET) are needed for efficient irrigation management, especially in arid and semi-arid regions where crop water demand exceeds rainfall. Daily grass or alfalfa reference ET values and crop coefficients are widely used to estimate crop water demand. Inaccurate reference ET estimates can hence have a tremendous impact on irrigation costs and the demands on U.S. freshwater resources, particularly within the Ogallala aquifer region. ET networks calculate reference ET using local meteorological data. With gaps in spatial coverage of existing networks and the agriculture-based Texas High Plains ET (TXHPET) network in jeopardy due to lack of funding, there is an immediate need for alternative sources capable of filling data gaps without high maintenance and field-based support costs. Non-agricultural weather stations located throughout the Texas High Plains are providing publicly accessible meteorological data. However, there are concerns that the data may not be suitable for estimating reference ET due to factors such as weather station siting, fetch requirements, data formats, parameters recorded, and quality control issues. The goal of the research reported in this paper is to assess the use of alternative data sources for reference ET computation. Towards this objective, we trained Gaussian process models, an instance of kernel-based machine learning algorithms, on data collected from weather stations to estimate reference ET values and augment the TXHPET database. Results show that Gaussian process models provide much greater accuracy than baseline least square regression models.
On estimating the phase of periodic waveform in additive Gaussian noise, part 2
NASA Astrophysics Data System (ADS)
Rauch, L. L.
1984-11-01
Motivated by advances in signal processing technology that support more complex algorithms, a new look is taken at the problem of estimating the phase and other parameters of a periodic waveform in additive Gaussian noise. The general problem was introduced and the maximum a posteriori probability criterion with signal space interpretation was used to obtain the structures of optimum and some suboptimum phase estimators for known constant frequency and unknown constant phase with an a priori distribution. Optimal algorithms are obtained for some cases where the frequency is a parameterized function of time with the unknown parameters and phase having a joint a priori distribution. In the last section, the intrinsic and extrinsic geometry of hypersurfaces is introduced to provide insight to the estimation problem for the small noise and large noise cases.
Bayesian estimation of airborne fugitive emissions using a Gaussian plume model
NASA Astrophysics Data System (ADS)
Hosseini, Bamdad; Stockie, John M.
2016-09-01
A new method is proposed for estimating the rate of fugitive emissions of particulate matter from multiple time-dependent sources via measurements of deposition and concentration. We cast this source inversion problem within the Bayesian framework, and use a forward model based on a Gaussian plume solution. We present three alternate models for constructing the prior distribution on the emission rates as functions of time. Next, we present an industrial case study in which our framework is applied to estimate the rate of fugitive emissions of lead particulates from a smelter in Trail, British Columbia, Canada. The Bayesian framework not only provides an approximate solution to the inverse problem, but also quantifies the uncertainty in the solution. Using this information we perform an uncertainty propagation study in order to assess the impact of the estimated sources on the area surrounding the industrial site.
The cluster graphical lasso for improved estimation of Gaussian graphical models
Tan, Kean Ming; Witten, Daniela; Shojaie, Ali
2015-01-01
The task of estimating a Gaussian graphical model in the high-dimensional setting is considered. The graphical lasso, which involves maximizing the Gaussian log likelihood subject to a lasso penalty, is a well-studied approach for this task. A surprising connection between the graphical lasso and hierarchical clustering is introduced: the graphical lasso in effect performs a two-step procedure, in which (1) single linkage hierarchical clustering is performed on the variables in order to identify connected components, and then (2) a penalized log likelihood is maximized on the subset of variables within each connected component. Thus, the graphical lasso determines the connected components of the estimated network via single linkage clustering. The single linkage clustering is known to perform poorly in certain finite-sample settings. Therefore, the cluster graphical lasso, which involves clustering the features using an alternative to single linkage clustering, and then performing the graphical lasso on the subset of variables within each cluster, is proposed. Model selection consistency for this technique is established, and its improved performance relative to the graphical lasso is demonstrated in a simulation study, as well as in applications to a university webpage and a gene expression data sets. PMID:25642008
EM-based Gaussian mixture model estimation for GMTI-based tracking using speedboat data
NASA Astrophysics Data System (ADS)
Akselrod, David; McDonald, Michael; Kirubarajan, T.
2009-08-01
In this paper, the problem of detection, classification and tracking of highly manoeuvring boats in sea clutter is considered. The considered problem is challenging due to numerous inherent issues: abrupt direction changes, high level of false alarms, lowered detectability, group movement and re-grouping, among many others. The results of applying a proposed measurement extraction and estimation technique to a set of real data from DRDC-Ottawa trials using Ground Moving Target Indicator (GMTI) radar are described. Real radar data containing a small manoeuvring boat in sea clutter is processed using Expectation Maximization (EM) Gaussian Mixture Model (GMM) based estimation. A trial was undertaken to collect data against highly maneuvering speedboats in the sea. All the data were collected in the GMTI single-channel high-resolution spotlight mode. True data were collected using GPS recording equipment. Real data processing results are presented.
Building unbiased estimators from non-gaussian likelihoods with application to shear estimation
Madhavacheril, Mathew S.; McDonald, Patrick; Sehgal, Neelima; Slosar, Anze
2015-01-15
We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next we apply the approach to estimation of shear lensing, closely following the work of Bernstein and Armstrong (2014). Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods. Both our first-order estimator and Bernstein and Armstrong’s estimator exhibit a bias which is quadratic in true shear. Our third-order estimator is, at least in the realm of the toy problem of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors Δg/g for shears up to |g| = 0.2.
Building unbiased estimators from non-gaussian likelihoods with application to shear estimation
Madhavacheril, Mathew S.; McDonald, Patrick; Sehgal, Neelima; Slosar, Anze
2015-01-15
We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next we apply the approach to estimation of shear lensing, closely following the 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
Madhavacheril, Mathew S.; Sehgal, Neelima; McDonald, Patrick; Slosar, Anže E-mail: pvmcdonald@lbl.gov E-mail: anze@bnl.gov
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 work of Bernstein and Armstrong (2014). Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods. Both our first-order estimator and Bernstein and Armstrong's estimator exhibit a bias which is quadratic in true shear. Our third-order estimator is, at least in the realm of the toy problem of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors Δg/g for shears up to |g|=0.2.
Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M; Derocher, Andrew E; Lewis, Mark A; Jonsen, Ian D; Mills Flemming, Joanna
2016-01-01
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results. PMID:27220686
Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M.; Derocher, Andrew E.; Lewis, Mark A.; Jonsen, Ian D.; Mills Flemming, Joanna
2016-01-01
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results. PMID:27220686
Ma, Denglong; Zhang, Zaoxiao
2016-07-01
Gas dispersion model is important for predicting the gas concentrations when contaminant gas leakage occurs. Intelligent network models such as radial basis function (RBF), back propagation (BP) neural network and support vector machine (SVM) model can be used for gas dispersion prediction. However, the prediction results from these network models with too many inputs based on original monitoring parameters are not in good agreement with the experimental data. Then, a new series of machine learning algorithms (MLA) models combined classic Gaussian model with MLA algorithm has been presented. The prediction results from new models are improved greatly. Among these models, Gaussian-SVM model performs best and its computation time is close to that of classic Gaussian dispersion model. Finally, Gaussian-MLA models were applied to identifying the emission source parameters with the particle swarm optimization (PSO) method. The estimation performance of PSO with Gaussian-MLA is better than that with Gaussian, Lagrangian stochastic (LS) dispersion model and network models based on original monitoring parameters. Hence, the new prediction model based on Gaussian-MLA is potentially a good method to predict contaminant gas dispersion as well as a good forward model in emission source parameters identification problem. PMID:27035273
Non-stationary noise estimation using dictionary learning and Gaussian mixture models
NASA Astrophysics Data System (ADS)
Hughes, James M.; Rockmore, Daniel N.; Wang, Yang
2014-02-01
Stationarity of the noise distribution is a common assumption in image processing. This assumption greatly simplifies denoising estimators and other model parameters and consequently assuming stationarity is often a matter of convenience rather than an accurate model of noise characteristics. The problematic nature of this assumption is exacerbated in real-world contexts, where noise is often highly non-stationary and can possess time- and space-varying characteristics. Regardless of model complexity, estimating the parameters of noise dis- tributions in digital images is a difficult task, and estimates are often based on heuristic assumptions. Recently, sparse Bayesian dictionary learning methods were shown to produce accurate estimates of the level of additive white Gaussian noise in images with minimal assumptions. We show that a similar model is capable of accu- rately modeling certain kinds of non-stationary noise processes, allowing for space-varying noise in images to be estimated, detected, and removed. We apply this modeling concept to several types of non-stationary noise and demonstrate the model's effectiveness on real-world problems, including denoising and segmentation of images according to noise characteristics, which has applications in image forensics.
Wavelet and Gaussian Approaches for Estimation of Groundwater Variations Using GRACE Data.
Fatolazadeh, Farzam; Voosoghi, Behzad; Naeeni, Mehdi Raoofian
2016-01-01
In this study, a scheme is presented to estimate groundwater storage variations in Iran. The variations are estimated using 11 years of Gravity Recovery and Climate Experiments (GRACE) observations from period of 2003 to April 2014 in combination with the outputs of Global Land Data Assimilation Systems (GLDAS) model including soil moisture, snow water equivalent, and total canopy water storage. To do so, the sums of GLDAS outputs are subtracted from terrestrial water storage variations determined by GRACE observations. Because of stripping errors in the GRACE data, two methodologies based on wavelet analysis and Gaussian filtering are applied to refine the GRACE data. It is shown that the wavelet approach could better localize the desired signal and increase the signal-to-noise ratio and thus results in more accurate estimation of groundwater storage variations. To validate the results of our procedure in estimation of ground water storage variations, they are compared with the measurements of pisometric wells data near the Urmia Lake which shows favorable agreements with our results. PMID:25962402
SAR amplitude probability density function estimation based on a generalized Gaussian model.
Moser, Gabriele; Zerubia, Josiane; Serpico, Sebastiano B
2006-06-01
In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed "method-of-log-cumulants" (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena. PMID:16764268
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
The binned bispectrum estimator: template-based and non-parametric CMB non-Gaussianity searches
NASA Astrophysics Data System (ADS)
Bucher, Martin; Racine, Benjamin; van Tent, Bartjan
2016-05-01
We describe the details of the binned bispectrum estimator as used for the official 2013 and 2015 analyses of the temperature and polarization CMB maps from the ESA Planck satellite. The defining aspect of this estimator is the determination of a map bispectrum (3-point correlation function) that has been binned in harmonic space. For a parametric determination of the non-Gaussianity in the map (the so-called fNL parameters), one takes the inner product of this binned bispectrum with theoretically motivated templates. However, as a complementary approach one can also smooth the binned bispectrum using a variable smoothing scale in order to suppress noise and make coherent features stand out above the noise. This allows one to look in a model-independent way for any statistically significant bispectral signal. This approach is useful for characterizing the bispectral shape of the galactic foreground emission, for which a theoretical prediction of the bispectral anisotropy is lacking, and for detecting a serendipitous primordial signal, for which a theoretical template has not yet been put forth. Both the template-based and the non-parametric approaches are described in this paper.
Scalable Hyper-parameter Estimation for Gaussian Process Based Time Series Analysis
Chandola, Varun; Vatsavai, Raju
2010-01-01
Gaussian process (GP) is increasingly becoming popular as a kernel machine learning tool for non-parametric data analysis. Recently, GP has been applied to model non-linear dependencies in time series data. GP based analysis can be used to solve problems of time series prediction, forecasting, missing data imputation, change point detection, anomaly detection, etc. But the use of GP to handle massive scientific time series data sets has been limited, owing to its expensive computational complexity. The primary bottleneck is the handling of the covariance matrix whose size is quadratic in the length of the time series. In this paper we propose a scalable method that exploit the special structure of the covariance matrix for hyper-parameter estimation in GP based learning. The proposed method allows estimation of hyper parameters associated with GP in quadratic time, which is an order of magnitude improvement over standard methods with cubic complexity. Moreover, the proposed method does not require explicit computation of the covariance matrix and hence has memory requirement linear to the length of the time series as opposed to the quadratic memory requirement of standard methods. To further improve the computational complexity of the proposed method, we provide a parallel version to concurrently estimate the log likelihood for a set of time series which is the key step in the hyper-parameter estimation. Performance results on a multi-core system show that our proposed method provides significant speedups as high as 1000, even when running in serial mode, while maintaining a small memory footprint. The parallel version exploits the natural parallelization potential of the serial algorithm and is shown to perform significantly better than the serial faster algorithm, with speedups as high as 10.
NASA Astrophysics Data System (ADS)
Mangilli, A.; Wandelt, B.; Elsner, F.; Liguori, M.
2013-07-01
We present the tools to optimally extract the lensing-integrated Sachs Wolfe (L-ISW) bispectrum signal from future cosmic microwave background (CMB) data. We implemented two different methods to simulate the non-Gaussian CMB maps with the L-ISW signal: a non-perturbative method based on the FLINTS lensing code and the separable mode-expansion method. We implemented the Komatsu, Spergel, and Wandelt (KSW) optimal estimator analysis for the L-ISW bispectrum and tested it on the non-Gaussian simulations for realistic CMB experimental settings with an inhomogeneous sky coverage. We show that the estimator approaches the Cramer-Rao bound and that Wiener filtering the L-ISW simulations slightly improves the estimate of fNLL-ISW by ≤ 10%. For a realistic CMB experimental setting that accounts for anisotropic noise and masked sky, we show that the linear term of the estimator is highly correlated to the cubic term and it is necessary to recover the signal and the optimal error bars. We also show that the L-ISW bispectrum, if not correctly accounted for, yields an underestimation of the fNLlocal error bars of ≃ 4%. A joint analysis of the non-Gaussian shapes and/or L-ISW template subtraction is needed to recover unbiased results of the primordial non-Gaussian signal from ongoing and future CMB experiments.
NASA Astrophysics Data System (ADS)
Verrelst, Jochem; Rivera, Juan Pablo; Moreno, José; Camps-Valls, Gustavo
2013-12-01
ESA's upcoming Sentinel-2 (S2) Multispectral Instrument (MSI) foresees to provide continuity to land monitoring services by relying on optical payload with visible, near infrared and shortwave infrared sensors with high spectral, spatial and temporal resolution. This unprecedented data availability leads to an urgent need for developing robust and accurate retrieval methods, which ideally should provide uncertainty intervals for the predictions. Statistical learning regression algorithms are powerful candidats for the estimation of biophysical parameters from satellite reflectance measurements because of their ability to perform adaptive, nonlinear data fitting. In this paper, we focus on a new emerging technique in the field of Bayesian nonparametric modeling. We exploit Gaussian process regression (GPR) for retrieval, which is an accurate method that also provides uncertainty intervals along with the mean estimates. This distinct feature is not shared by other machine learning approaches. In view of implementing the regressor into operational monitoring applications, here the portability of locally trained GPR models was evaluated. Experimental data came from the ESA-led field campaign SPARC (Barrax, Spain). For various simulated S2 configurations (S2-10m, S2-20m and S2-60m) two important biophysical parameters were estimated: leaf chlorophyll content (LCC) and leaf area index (LAI). Local evaluation of an extended training dataset with more variation over bare soil sites led to improved LCC and LAI mapping with reduced uncertainties. GPR reached the 10% precision required by end users, with for LCC a NRMSE of 3.5-9.2% (r2: 0.95-0.99) and for LAI a NRMSE of 6.5-7.3% (r2: 0.95-0.96). The developed GPR models were subsequently applied to simulated Sentinel images over various sites. The associated uncertainty maps proved to be a good indicator for evaluating the robustness of the retrieval performance. The generally low uncertainty intervals over vegetated surfaces
NASA Astrophysics Data System (ADS)
Ryu, Ji-Woo; Lee, Seon-Oh; Sim, Dong-Gyu; Han, Jong-Ki
2012-02-01
We present a no-reference peak signal to noise ratio (PSNR) estimation algorithm based on discrete cosine transform (DCT) coefficient distributions from H.264/MPEG-4 part 10 advanced video codec (H.264/AVC) bitstreams. To estimate the PSNR of a compressed picture without the original picture on the decoder side, it is important to model the distribution of transform coefficients obtained from quantized coefficients accurately. Whereas several conventional algorithms use the Laplacian or Cauchy distribution to model the DCT coefficient distribution, the proposed algorithm uses a generalized Gaussian distribution. Pearson's χ2 (chi-square) test was applied to show that the generalized Gaussian distribution is more appropriate than the other models for modeling the transform coefficients. The χ2 test was also used to find optimum parameters for the generalized Gaussian model. It was found that the generalized Gaussian model improves the accuracy of the DCT coefficient distribution, thus reducing the mean squared error between the real and the estimated PSNR.
NASA Astrophysics Data System (ADS)
Foster-Wittig, Tierney A.; Thoma, Eben D.; Albertson, John D.
2015-08-01
Emerging mobile fugitive emissions detection and measurement approaches require robust inverse source algorithms to be effective. Two Gaussian plume inverse approaches are described for estimating emission rates from ground-level point sources observed from remote vantage points. The techniques were tested using data from 41 controlled methane release experiments (14 studies) and further investigated using 7 field studies executed downwind of oil and gas well pads in Wyoming. Analyzed measurements were acquired from stationary observation locations 18-106 m downwind of the emission sources. From the fluctuating wind direction, the lateral plume geometry is reconstructed using a derived relationship between the wind direction and crosswind plume position. The crosswind plume spread is determined with both modeled and reconstructed Gaussian plume approaches and estimates of source emission rates are found through inversion. The source emission rates were compared to a simple point source Gaussian emission estimation approach that is part of Draft EPA Method OTM 33A. Compared to the known release rates, the modeled, reconstructed, and point source Gaussian controlled release results yield average percent errors of -5%, -2%, and 6% with standard deviations of 29%, 25%, and 37%, respectively. Compared to each other, the three methods agree within 30% for 78% of all 48 observations (41 CR and 7 Wyoming).
Determining the Mass of Kepler-78b with Nonparametric Gaussian Process Estimation
NASA Astrophysics Data System (ADS)
Grunblatt, Samuel K.; Howard, Andrew W.; Haywood, Raphaëlle D.
2015-08-01
Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hr. The mass of Kepler-78b has been independently reported by two teams based on radial velocity (RV) measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in RV data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the RV data sets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV data sets, giving a Doppler amplitude of 1.86 ± 0.25 m s-1 and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of {1.87}-0.26+0.27 {M}\\oplus is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of {6.0}-1.4+1.9 g cm-3. We estimate that Kepler-78b is 32% ± 26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.
Determining the Mass of Kepler-78b With Nonparametric Gaussian Process Estimation
NASA Astrophysics Data System (ADS)
Grunblatt, Samuel K.; Howard, Andrew; Haywood, Raphaëlle
2015-12-01
Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hours. The mass of Kepler-78b has been independently reported by two teams based on radial velocity measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in radial velocity data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the radial velocity datasets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV datasets, giving a Doppler amplitude of 1.86 ± 0.25 m s-1 and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87 +0.27-0.26 M⊕ is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0+1.9-1.4 g cm-3. We estimate that Kepler-78b is 32±26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.
Determining the Mass of Kepler-78b with Nonparametric Gaussian Process Estimation
NASA Astrophysics Data System (ADS)
Grunblatt, Samuel Kai; Howard, Andrew; Haywood, Raphaëlle
2016-01-01
Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hr. The mass of Kepler-78b has been independently reported by two teams based on radial velocity (RV) measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in RV data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the RV data sets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV data sets, giving a Doppler amplitude of 1.86 ± 0.25 m s-1 and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87-0.26+0.27 ME is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0-1.4+1.9 g cm-3. We estimate that Kepler-78b is 32% ± 26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.
A neural-network based estimator to search for primordial non-Gaussianity in Planck CMB maps
NASA Astrophysics Data System (ADS)
Novaes, C. P.; Bernui, A.; Ferreira, I. S.; Wuensche, C. A.
2015-09-01
We present an upgraded combined estimator, based on Minkowski Functionals and Neural Networks, with excellent performance in detecting primordial non-Gaussianity in simulated maps that also contain a weighted mixture of Galactic contaminations, besides real pixel's noise from Planck cosmic microwave background radiation data. We rigorously test the efficiency of our estimator considering several plausible scenarios for residual non-Gaussianities in the foreground-cleaned Planck maps, with the intuition to optimize the training procedure of the Neural Network to discriminate between contaminations with primordial and secondary non-Gaussian signatures. We look for constraints of primordial local non-Gaussianity at large angular scales in the foreground-cleaned Planck maps. For the SMICA map we found fNL = 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 fNL in [33, 41], concomitant with the fact that these maps manifest distinct features in reported analyses, like having different pixel's noise intensities.
Removing the ISW-lensing bias from the local-form primordial non-Gaussianity estimation
Kim, Jaiseung; Komatsu, Eiichiro; Rotti, Aditya E-mail: aditya@iucaa.ernet.in
2013-04-01
The Integrated Sachs-Wolfe (ISW) effect produces a secondary temperature aniso\\-tropy of the cosmic microwave background (CMB), as CMB photons travel through time-varying potentials along the line-of-sight. The main contribution comes from redshifts z∼<2, where dark energy leads to a decay of potentials. As the same photons are gravitationally lensed by these decaying potentials, there exists a high degree of correlation between the ISW effect and CMB lensing, leading to a non-zero three-point correlation (bispectrum) of the observed temperature anisotropy. This ISW-lensing bispectrum, whose shape resembles that of the so-called ''local-form'' primordial bispectrum parametrized by f{sub NL}, is known to be the largest contamination of f{sub NL}. In order to avoid a spurious detection of primordial non-Gaussianity, we need to remove the ISW-lensing bias. In this work, we investigate three debiasing methods: (I) subtraction of an expected, ensemble average of the ISW-lensing bispectrum; (II) subtraction of a measured ISW-lensing bispectrum; and (III) direct subtraction of an estimated ISW signal from an observed temperature map. One may use an estimation of the ISW map from external non-CMB data or that from the CMB data themselves. As the methods II and III are based on fewer assumptions about the nature of dark energy, they are preferred over the method I. While the methods I and II yield unbiased estimates of f{sub NL} with comparable error bars, the method III yields a biased result when the underlying primordial f{sub NL} is non-zero and the ISW map is estimated from a lensing potential reconstructed from the observed temperature map. One of the sources of the bias is a lensing reconstruction noise bias which is independent of f{sub NL} and can be calculated precisely, but other f{sub NL}-dependent terms are difficult to compute reliably. We thus conclude that the method II is the best, model-independent way to remove the ISW-lensing bias of f{sub NL
A new method based on the subpixel Gaussian model for accurate estimation of asteroid coordinates
NASA Astrophysics Data System (ADS)
Savanevych, V. E.; Briukhovetskyi, O. B.; Sokovikova, N. S.; Bezkrovny, M. M.; Vavilova, I. B.; Ivashchenko, Yu. M.; Elenin, L. V.; Khlamov, S. V.; Movsesian, Ia. S.; Dashkova, A. M.; Pogorelov, A. V.
2015-08-01
We describe a new iteration method to estimate asteroid coordinates, based on a subpixel Gaussian model of the discrete object image. The method operates by continuous parameters (asteroid coordinates) in a discrete observational space (the set of pixel potentials) of the CCD frame. In this model, the kind of coordinate distribution of the photons hitting a pixel of the CCD frame is known a priori, while the associated parameters are determined from a real digital object image. The method that is developed, which is flexible in adapting to any form of object image, has a high measurement accuracy along with a low calculating complexity, due to the maximum-likelihood procedure that is implemented to obtain the best fit instead of a least-squares method and Levenberg-Marquardt algorithm for minimization of the quadratic form. Since 2010, the method has been tested as the basis of our Collection Light Technology (COLITEC) software, which has been installed at several observatories across the world with the aim of the automatic discovery of asteroids and comets in sets of CCD frames. As a result, four comets (C/2010 X1 (Elenin), P/2011 NO1(Elenin), C/2012 S1 (ISON) and P/2013 V3 (Nevski)) as well as more than 1500 small Solar system bodies (including five near-Earth objects (NEOs), 21 Trojan asteroids of Jupiter and one Centaur object) have been discovered. We discuss these results, which allowed us to compare the accuracy parameters of the new method and confirm its efficiency. In 2014, the COLITEC software was recommended to all members of the Gaia-FUN-SSO network for analysing observations as a tool to detect faint moving objects in frames.
Parameter estimation with an iterative version of the adaptive Gaussian mixture filter
NASA Astrophysics Data System (ADS)
Stordal, A.; Lorentzen, R.
2012-04-01
The adaptive Gaussian mixture filter (AGM) was introduced in Stordal et. al. (ECMOR 2010) as a robust filter technique for large scale applications and an alternative to the well known ensemble Kalman filter (EnKF). It consists of two analysis steps, one linear update and one weighting/resampling step. The bias of AGM is determined by two parameters, one adaptive weight parameter (forcing the weights to be more uniform to avoid filter collapse) and one pre-determined bandwidth parameter which decides the size of the linear update. It has been shown that if the adaptive parameter approaches one and the bandwidth parameter decrease with increasing sample size, the filter can achieve asymptotic optimality. For large scale applications with a limited sample size the filter solution may be far from optimal as the adaptive parameter gets close to zero depending on how well the samples from the prior distribution match the data. The bandwidth parameter must often be selected significantly different from zero in order to make large enough linear updates to match the data, at the expense of bias in the estimates. In the iterative AGM we take advantage of the fact that the history matching problem is usually estimation of parameters and initial conditions. If the prior distribution of initial conditions and parameters is close to the posterior distribution, it is possible to match the historical data with a small bandwidth parameter and an adaptive weight parameter that gets close to one. Hence the bias of the filter solution is small. In order to obtain this scenario we iteratively run the AGM throughout the data history with a very small bandwidth to create a new prior distribution from the updated samples after each iteration. After a few iterations, nearly all samples from the previous iteration match the data and the above scenario is achieved. A simple toy problem shows that it is possible to reconstruct the true posterior distribution using the iterative version of
NASA Astrophysics Data System (ADS)
Varouchakis, Emmanouil; Hristopulos, Dionissios
2015-04-01
Space-time geostatistical approaches can improve the reliability of dynamic groundwater level models in areas with limited spatial and temporal data. Space-time residual Kriging (STRK) is a reliable method for spatiotemporal interpolation that can incorporate auxiliary information. The method usually leads to an underestimation of the prediction uncertainty. The uncertainty of spatiotemporal models is usually estimated by determining the space-time Kriging variance or by means of cross validation analysis. For de-trended data the former is not usually applied when complex spatiotemporal trend functions are assigned. A Bayesian approach based on the bootstrap idea and sequential Gaussian simulation are employed to determine the uncertainty of the spatiotemporal model (trend and covariance) parameters. These stochastic modelling approaches produce multiple realizations, rank the prediction results on the basis of specified criteria and capture the range of the uncertainty. The correlation of the spatiotemporal residuals is modeled using a non-separable space-time variogram based on the Spartan covariance family (Hristopulos and Elogne 2007, Varouchakis and Hristopulos 2013). We apply these simulation methods to investigate the uncertainty of groundwater level variations. The available dataset consists of bi-annual (dry and wet hydrological period) groundwater level measurements in 15 monitoring locations for the time period 1981 to 2010. The space-time trend function is approximated using a physical law that governs the groundwater flow in the aquifer in the presence of pumping. The main objective of this research is to compare the performance of two simulation methods for prediction uncertainty estimation. In addition, we investigate the performance of the Spartan spatiotemporal covariance function for spatiotemporal geostatistical analysis. Hristopulos, D.T. and Elogne, S.N. 2007. Analytic properties and covariance functions for a new class of generalized Gibbs
Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation
NASA Technical Reports Server (NTRS)
Mcreynolds, S. R.
1975-01-01
A simplified technique is proposed for calculating multidimensional Hermite-Gaussian quadratures that involves taking the square root of a matrix by the Cholesky algorithm rather than computation of the eigenvectors of the matrix. Ways of reducing the dimension, number, and order of the quadratures are set forth. If the function f(x) under the integral sign is not well approximated by a low-order algebraic expression, the order of the quadrature may be reduced by factoring f(x) into an expression that is nearly algebraic and one that is Gaussian.
Mehranian, Abolfazl; Zaidi, Habib
2015-09-01
It has recently been shown that the attenuation map can be estimated from time-of-flight (TOF) PET emission data using joint maximum likelihood reconstruction of attenuation and activity (MLAA). In this work, we propose a novel MRI-guided MLAA algorithm for emission-based attenuation correction in whole-body PET/MR imaging. The algorithm imposes MR spatial and CT statistical constraints on the MLAA estimation of attenuation maps using a constrained Gaussian mixture model (GMM) and a Markov random field smoothness prior. Dixon water and fat MR images were segmented into outside air, lung, fat and soft-tissue classes and an MR low-intensity (unknown) class corresponding to air cavities, cortical bone and susceptibility artifacts. The attenuation coefficients over the unknown class were estimated using a mixture of four Gaussians, and those over the known tissue classes using unimodal Gaussians, parameterized over a patient population. To eliminate misclassification of spongy bones with surrounding tissues, and thus include them in the unknown class, we heuristically suppressed fat in water images and also used a co-registered bone probability map. The proposed MLAA-GMM algorithm was compared with the MLAA algorithms proposed by Rezaei and Salomon using simulation and clinical studies with two different tracer distributions. The results showed that our proposed algorithm outperforms its counterparts in suppressing the cross-talk and scaling problems of activity and attenuation and thus produces PET images of improved quantitative accuracy. It can be concluded that the proposed algorithm effectively exploits the MR information and can pave the way toward accurate emission-based attenuation correction in TOF PET/MRI. PMID:25769148
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.
NASA Astrophysics Data System (ADS)
Baghi, Quentin; Métris, Gilles; Bergé, Joël; Christophe, Bruno; Touboul, Pierre; Rodrigues, Manuel
2016-06-01
We present a Gaussian regression method for time series with missing data and stationary residuals of unknown power spectral density (PSD). The missing data are efficiently estimated by their conditional expectation as in universal Kriging based on the circulant approximation of the complete data covariance. After initialization with an autoregressive fit of the noise, a few iterations of estimation/reconstruction steps are performed until convergence of the regression and PSD estimates, in a way similar to the expectation-conditional-maximization algorithm. The estimation can be performed for an arbitrary PSD provided that it is sufficiently smooth. The algorithm is developed in the framework of the MICROSCOPE space mission whose goal is to test the weak equivalence principle (WEP) with a precision of 10-15. We show by numerical simulations that the developed method allows us to meet three major requirements: to maintain the targeted precision of the WEP test in spite of the loss of data, to calculate a reliable estimate of this precision and of the noise level, and finally to provide consistent and faithful reconstructed data to the scientific community.
NASA Astrophysics Data System (ADS)
Qian, Cheng
2016-07-01
Quantifying the urbanization effect on trends in climate extremes is important both for detection and attribution studies and for human adaptation; however, a fundamental problem is how to accurately estimate a trend and its statistical significance, especially for non-Gaussian and serially dependent data. In this paper, the choice of trend estimation and significance testing method is suggested as important for these kinds of studies, as illustrated by quantifying the urbanization effect on trends in seven hot-extreme indices for the megacity of Shanghai during 1961-2013. Both linear and nonlinear trend estimation methods were used. The trends and corresponding statistical significances were estimated by taking into account potential non-Gaussian and serial dependence in the extreme indices. A new method based on adaptive surrogate data is proposed to test the statistical significance of the ensemble empirical mode decomposition (EEMD) nonlinear trend. The urbanization contribution was found to be approximately 34 % (43 %) for the trend in the non-Gaussian distributed heat wave index based on nonparametric linear trend (EEMD nonlinear trend) estimation. For some of the other six hot-extreme indices analyzed, the urbanization contributions estimated based on linear and nonlinear trends varied greatly, with as much as a twofold difference between them. For the linear trend estimation itself, the ordinary least squares fit can give a substantially biased estimation of the urbanization contribution for some of the non-Gaussian extreme indices.
ON THE LINEAR TERM CORRECTION FOR NEEDLET/WAVELET NON-GAUSSIANITY ESTIMATORS
Donzelli, Simona; Hansen, Frode K.; Liguori, Michele; Matarrese, Sabino; Marinucci, Domenico
2012-08-10
We derive the linear correction term for needlet and wavelet estimators of the bispectrum and the nonlinearity parameter f{sub NL} on cosmic microwave background radiation data. We show that on masked WMAP-like data with anisotropic noise, the error bars improve by 10%-20% and almost reach the optimal error bars obtained with the bispectrum estimator also known as 'KSW'. In the limit of full-sky and isotropic noise, this term vanishes. We apply needlet and wavelet estimators to the WMAP 7-year data and obtain our best estimate f{sub NL} = 37.5 {+-} 21.8 (68% CL).
Gaussian process models for reference ET estimation from alternative meteorological data sources
Technology Transfer Automated Retrieval System (TEKTRAN)
Accurate estimates of daily crop evapotranspiration (ET) are needed for efficient irrigation management, especially in arid and semi-arid regions where crop water demand exceeds rainfall. Daily grass or alfalfa reference ET values and crop coefficients are widely used to estimate crop water demand. ...
NASA Astrophysics Data System (ADS)
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.
Dubois, Rémi; Maison-Blanche, Pierre; Quenet, Brigitte; Dreyfus, Gérard
2007-12-01
This paper describes the automatic extraction of the P, Q, R, S and T waves of electrocardiographic recordings (ECGs), through the combined use of a new machine-learning algorithm termed generalized orthogonal forward regression (GOFR) and of a specific parameterized function termed Gaussian mesa function (GMF). GOFR breaks up the heartbeat signal into Gaussian mesa functions, in such a way that each wave is modeled by a single GMF; the model thus generated is easily interpretable by the physician. GOFR is an essential ingredient in a global procedure that locates the R wave after some simple pre-processing, extracts the characteristic shape of each heart beat, assigns P, Q, R, S and T labels through automatic classification, discriminates normal beats (NB) from abnormal beats (AB), and extracts features for diagnosis. The efficiency of the detection of the QRS complex, and of the discrimination of NB from AB, is assessed on the MIT and AHA databases; the labeling of the P and T wave is validated on the QTDB database. PMID:17997186
NASA Astrophysics Data System (ADS)
Béal, D.; Brasseur, P.; Brankart, J.-M.; Ourmières, Y.; Verron, J.
2010-02-01
of this anamorphosis method into sequential assimilation schemes can substantially improve the accuracy of the estimation with respect to classical computations based on the Gaussian assumption.
A note on generalized averaged Gaussian formulas
NASA Astrophysics Data System (ADS)
Spalevic, Miodrag
2007-11-01
We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss?Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss?Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.
Hollman, David S.; Schaefer, Henry F.; Valeev, Edward F.
2015-04-21
A new estimator for three-center two-particle Coulomb integrals is presented. Our estimator is exact for some classes of integrals and is much more efficient than the standard Schwartz counterpart due to the proper account of distance decay. Although it is not a rigorous upper bound, the maximum degree of underestimation can be controlled by two adjustable parameters. We also give numerical evidence of the excellent tightness of the estimator. The use of the estimator will lead to increased efficiency in reduced-scaling one- and many-body electronic structure theories.
Technology Transfer Automated Retrieval System (TEKTRAN)
Accurate estimates of daily crop evapotranspiration (ET) are needed for efficient irrigation management, especially in arid and semi-arid irrigated regions where crop water demand exceeds rainfall. The impact of inaccurate ET estimates can be tremendous in both irrigation cost and the increased dema...
Chen, Tai-Been; Chen, Jyh-Cheng; Lu, Henry Horng-Shing
2012-01-01
Segmentation of positron emission tomography (PET) is typically achieved using the K-Means method or other approaches. In preclinical and clinical applications, the K-Means method needs a prior estimation of parameters such as the number of clusters and appropriate initialized values. This work segments microPET images using a hybrid method combining the Gaussian mixture model (GMM) with kernel density estimation. Segmentation is crucial to registration of disordered 2-deoxy-2-fluoro-D-glucose (FDG) accumulation locations with functional diagnosis and to estimate standardized uptake values (SUVs) of region of interests (ROIs) in PET images. Therefore, simulation studies are conducted to apply spherical targets to evaluate segmentation accuracy based on Tanimoto's definition of similarity. The proposed method generates a higher degree of similarity than the K-Means method. The PET images of a rat brain are used to compare the segmented shape and area of the cerebral cortex by the K-Means method and the proposed method by volume rendering. The proposed method provides clearer and more detailed activity structures of an FDG accumulation location in the cerebral cortex than those by the K-Means method. PMID:22948355
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.
NASA Astrophysics Data System (ADS)
Lambers, James V.
2016-06-01
The stiffness of systems of ODEs that arise from spatial discretization of PDEs causes difficulties for both explicit and implicit time-stepping methods. Krylov Subspace Spectral (KSS) methods present a balance between the efficiency of explicit methods and the stability of implicit methods by computing each Fourier coefficient from an individualized approximation of the solution operator of the PDE. While KSS methods are explicit methods that exhibit a high order of accuracy and stability similar to that of implicit methods, their efficiency needs to be improved. Here, a detailed asymptotic study is performed in order to rapidly estimate all nodes, thus drastically reducing computational expense without sacrificing accuracy. Extension to PDEs on a disk, through expansions built on Legendre polynomials, is also discussed. Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff nonlinear systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this talk, it is proposed to modify EPI methods by using KSS methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. Numerical experiments demonstrate that this modification causes the number of Krylov projection steps to become bounded independently of the grid size, thus dramatically improving efficiency and scalability. It is also demonstrated that the convergence of Krylov projection can be significantly accelerated, without noticeable loss of accuracy, through filtering techniques, thus improving performance and scalability even further.
Information geometry of Gaussian channels
Monras, Alex; Illuminati, Fabrizio
2010-06-15
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).
Lewis, C; Jiang, R; Chow, J
2015-06-15
Purpose: We developed a method to predict the change of DVH for PTV due to interfraction organ motion in prostate VMAT without repeating the CT scan and treatment planning. The method is based on a pre-calculated patient database with DVH curves of PTV modelled by the Gaussian error function (GEF). Methods: For a group of 30 patients with different prostate sizes, their VMAT plans were recalculated by shifting their PTVs 1 cm with 10 increments in the anterior-posterior, left-right and superior-inferior directions. The DVH curve of PTV in each replan was then fitted by the GEF to determine parameters describing the shape of curve. Information of parameters, varying with the DVH change due to prostate motion for different prostate sizes, was analyzed and stored in a database of a program written by MATLAB. Results: To predict a new DVH for PTV due to prostate interfraction motion, prostate size and shift distance with direction were input to the program. Parameters modelling the DVH for PTV were determined based on the pre-calculated patient dataset. From the new parameters, DVH curves of PTVs with and without considering the prostate motion were plotted for comparison. The program was verified with different prostate cases involving interfraction prostate shifts and replans. Conclusion: Variation of DVH for PTV in prostate VMAT can be predicted using a pre-calculated patient database with DVH curve fitting. The computing time is fast because CT rescan and replan are not required. This quick DVH estimation can help radiation staff to determine if the changed PTV coverage due to prostate shift is tolerable in the treatment. However, it should be noted that the program can only consider prostate interfraction motions along three axes, and is restricted to prostate VMAT plan using the same plan script in the treatment planning system.
NASA Astrophysics Data System (ADS)
Monien, H.
2010-04-01
Gaussian quadrature is a well-known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums has found some new interest. In this paper we apply these ideas to infinite sums in general and give an explicit construction for the weights and abscissae of Gaussian formulas. The abscissae of the Gaussian summation have a very interesting asymptotic distribution function with a kink singularity. We apply the Gaussian summation technique to two problems which have been discussed in the literature. We find that the Gaussian summation has a very rapid convergence rate for the Hardy-Littlewood sum for a large range of parameters.
Gaussian statistics for palaeomagnetic vectors
Love, J.J.; Constable, C.G.
2003-01-01
With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to
Gaussian processes for machine learning.
Seeger, Matthias
2004-04-01
Gaussian processes (GPs) are natural generalisations of multivariate Gaussian random variables to infinite (countably or continuous) index sets. GPs have been applied in a large number of fields to a diverse range of ends, and very many deep theoretical analyses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level with special emphasis on characteristics relevant in machine learning. It draws explicit connections to branches such as spline smoothing models and support vector machines in which similar ideas have been investigated. Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible non-parametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of uncertainties in our predictions and generic model selection procedures cast as nonlinear optimization problems. Their main drawback of heavy computational scaling has recently been alleviated by the introduction of generic sparse approximations.13,78,31 The mathematical literature on GPs is large and often uses deep concepts which are not required to fully understand most machine learning applications. In this tutorial paper, we aim to present characteristics of GPs relevant to machine learning and to show up precise connections to other "kernel machines" popular in the community. Our focus is on a simple presentation, but references to more detailed sources are provided. PMID:15112367
Gaussian entanglement of formation
Wolf, M.M.; Giedke, G.; Krueger, O.; Werner, R. F.; Cirac, J.I.
2004-05-01
We introduce a Gaussian version of the entanglement of formation adapted to bipartite Gaussian states by considering decompositions into pure Gaussian states only. We show that this quantity is an entanglement monotone under Gaussian operations and provide a simplified computation for states of arbitrary many modes. For the case of one mode per site the remaining variational problem can be solved analytically. If the considered state is in addition symmetric with respect to interchanging the two modes, we prove additivity of the considered entanglement measure. Moreover, in this case and considering only a single copy, our entanglement measure coincides with the true entanglement of formation.
Kawasaki, Masahiro; Nakayama, Kazunori; Takahashi, Fuminobu E-mail: nakayama@icrr.u-tokyo.ac.jp
2009-01-15
We study non-Gaussianity induced by a pseudo Nambu-Goldstone boson with a cosine-type scalar potential. We focus on how the non-Gaussianity is affected when the pseudo Nambu-Goldstone boson rolls down from near the top of the scalar potential where the deviation from a quadratic potential is large. We find that the resultant non-Gaussianity is similar to that obtained in the quadratic potential, if the pseudo Nambu-Goldstone boson accounts for the curvature perturbation; the non-Gaussianity is enhanced, otherwise.
NASA Astrophysics Data System (ADS)
Hirao, Akiko; Nishizawa, Hideyuki; Tsukamoto, Takayuki; Matsumoto, Kazuki
1999-10-01
The proportionality of the logarithm of the mobility to the square root of the electric field is most likely caused by the broadening of the density of states according to both the Gaussian disorder model and the 3D correlated disorder model (CDM). Using these models, the relation between the slope of the mobility against the electric field and the dipolar component of the width of the density of states ((sigma) d) is analyzed. The (sigma) d for the donor and the host polymer are calculated using the dipolar disorder model in which a random distribution of permanent dipoles generates fluctuation in electric potential. A successful interpretation of the relation between (beta) and (sigma) d has been achieved using the formula based on the CDM. Assuming that all components of the density of states are described using Gaussian statistics, the van der Waals component is evaluated to be negligibly small from analyses of temperature dependence of the relation between (beta) and (sigma) d. The experimental results also shows that the value of the DOS width that is derived from the analysis of the temperature dependence of the zero-field mobility is different for the value of the DOS width that is derived from the analysis of the electric field dependence.
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
Principal components of CMB non-Gaussianity
NASA Astrophysics Data System (ADS)
Regan, Donough; Munshi, Dipak
2015-04-01
The skew-spectrum statistic introduced by Munshi & Heavens has recently been used in studies of non-Gaussianity from diverse cosmological data sets including the detection of primary and secondary non-Gaussianity of cosmic microwave background (CMB) radiation. Extending previous work, focused on independent estimation, here we deal with the question of joint estimation of multiple skew-spectra from the same or correlated data sets. We consider the optimum skew-spectra for various models of primordial non-Gaussianity as well as secondary bispectra that originate from the cross-correlation of secondaries and lensing of CMB: coupling of lensing with the Integrated Sachs-Wolfe effect, coupling of lensing with thermal Sunyaev-Zeldovich, as well as from unresolved point sources. For joint estimation of various types of non-Gaussianity, we use the principal component analysis (PCA) to construct the linear combinations of amplitudes of various models of non-Gaussianity, e.g. f^loc_NL,f^eq_NL,f^ortho_NL that can be estimated from CMB maps. We describe how the bias induced in the estimation of primordial non-Gaussianity due to secondary non-Gaussianity may be evaluated for arbitrary primordial models using a PCA analysis. The PCA approach allows one to infer approximate (but generally accurate) constraints using CMB data sets on any reasonably smooth model by use of a look-up table and performing a simple computation. This principle is validated by computing constraints on the Dirac-Born-Infeld bispectrum using a PCA analysis of the standard templates.
George: Gaussian Process regression
NASA Astrophysics Data System (ADS)
Foreman-Mackey, Daniel
2015-11-01
George is a fast and flexible library, implemented in C++ with Python bindings, for Gaussian Process regression useful for accounting for correlated noise in astronomical datasets, including those for transiting exoplanet discovery and characterization and stellar population modeling.
Gaussian Multipole Model (GMM)
Elking, Dennis M.; Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.; Pedersen, Lee G.
2009-01-01
An electrostatic model based on charge density is proposed as a model for future force fields. The model is composed of a nucleus and a single Slater-type contracted Gaussian multipole charge density on each atom. The Gaussian multipoles are fit to the electrostatic potential (ESP) calculated at the B3LYP/6-31G* and HF/aug-cc-pVTZ levels of theory and tested by comparing electrostatic dimer energies, inter-molecular density overlap integrals, and permanent molecular multipole moments with their respective ab initio values. For the case of water, the atomic Gaussian multipole moments Qlm are shown to be a smooth function of internal geometry (bond length and bond angle), which can be approximated by a truncated linear Taylor series. In addition, results are given when the Gaussian multipole charge density is applied to a model for exchange-repulsion energy based on the inter-molecular density overlap. PMID:20209077
Gaussian operations and privacy
Navascues, Miguel; Acin, Antonio
2005-07-15
We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in [Navascues et al. Phys. Rev. Lett. 94, 010502 (2005)]. Then, we prove that a generalized version of this protocol does not allow one to distill a secret key out of bound entangled Gaussian states.
Rényi entropy and complexity measure for skew-gaussian distributions and related families
NASA Astrophysics Data System (ADS)
Contreras-Reyes, Javier E.
2015-09-01
In this paper, we provide the Rényi entropy and complexity measure for a novel, flexible class of skew-gaussian distributions and their related families, as a characteristic form of the skew-gaussian Shannon entropy. We give closed expressions considering a more general class of closed skew-gaussian distributions and the weighted moments estimation method. In addition, closed expressions of Rényi entropy are presented for extended skew-gaussian and truncated skew-gaussian distributions. Finally, additional inequalities for skew-gaussian and extended skew-gaussian Rényi and Shannon entropies are reported.
Semisupervised Gaussian Process for Automated Enzyme Search.
Mellor, Joseph; Grigoras, Ioana; Carbonell, Pablo; Faulon, Jean-Loup
2016-06-17
Synthetic biology is today harnessing the design of novel and greener biosynthesis routes for the production of added-value chemicals and natural products. The design of novel pathways often requires a detailed selection of enzyme sequences to import into the chassis at each of the reaction steps. To address such design requirements in an automated way, we present here a tool for exploring the space of enzymatic reactions. Given a reaction and an enzyme the tool provides a probability estimate that the enzyme catalyzes the reaction. Our tool first considers the similarity of a reaction to known biochemical reactions with respect to signatures around their reaction centers. Signatures are defined based on chemical transformation rules by using extended connectivity fingerprint descriptors. A semisupervised Gaussian process model associated with the similar known reactions then provides the probability estimate. The Gaussian process model uses information about both the reaction and the enzyme in providing the estimate. These estimates were validated experimentally by the application of the Gaussian process model to a newly identified metabolite in Escherichia coli in order to search for the enzymes catalyzing its associated reactions. Furthermore, we show with several pathway design examples how such ability to assign probability estimates to enzymatic reactions provides the potential to assist in bioengineering applications, providing experimental validation to our proposed approach. To the best of our knowledge, the proposed approach is the first application of Gaussian processes dealing with biological sequences and chemicals, the use of a semisupervised Gaussian process framework is also novel in the context of machine learning applied to bioinformatics. However, the ability of an enzyme to catalyze a reaction depends on the affinity between the substrates of the reaction and the enzyme. This affinity is generally quantified by the Michaelis constant KM
Impact of secondary non-Gaussianities on the search for primordial non-Gaussianity with CMB maps
Serra, Paolo; Cooray, Asantha
2008-05-15
When constraining the primordial non-Gaussianity parameter f{sub NL} with cosmic microwave background anisotropy maps, the bias resulting from the covariance between primordial non-Gaussianity and secondary non-Gaussianities to the estimator of f{sub NL} is generally assumed to be negligible. We show that this assumption may not hold when attempting to measure the primordial non-Gaussianity out to angular scales below a few tens arcminutes with an experiment like Planck, especially if the primordial non-Gaussianity parameter is around the minimum detectability level with f{sub NL} between 5 and 10. In the future, it will be necessary to jointly estimate the combined primordial and secondary contributions to the cosmic microwave background bispectrum and establish f{sub NL} by properly accounting for the confusion from secondary non-Gaussianiti0008.
Renyi entropy measures of heart rate Gaussianity.
Lake, Douglas E
2006-01-01
Sample entropy and approximate entropy are measures that have been successfully utilized to study the deterministic dynamics of heart rate (HR). A complementary stochastic point of view and a heuristic argument using the Central Limit Theorem suggests that the Gaussianity of HR is a complementary measure of the physiological complexity of the underlying signal transduction processes. Renyi entropy (or q-entropy) is a widely used measure of Gaussianity in many applications. Particularly important members of this family are differential (or Shannon) entropy (q = 1) and quadratic entropy (q = 2). We introduce the concepts of differential and conditional Renyi entropy rate and, in conjunction with Burg's theorem, develop a measure of the Gaussianity of a linear random process. Robust algorithms for estimating these quantities are presented along with estimates of their standard errors. PMID:16402599
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.
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.
Quantum steering of Gaussian states via non-Gaussian measurements
Ji, Se-Wan; Lee, Jaehak; Park, Jiyong; Nha, Hyunchul
2016-01-01
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. PMID:27411853
Autonomous Gaussian Decomposition
NASA Astrophysics Data System (ADS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-04-01
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
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.
Adaptive Gaussian pattern classification. Final report
Priebe, C.E.; Marchette, D.J.
1988-08-01
A massively parallel architecture for pattern classification is described. The architecture is based on the field of density estimation. It makes use of a variant of the adaptive-kernel estimator to approximate the distributions of the classes as a sum of Gaussian distributions. These Gaussians are learned using a moved-mean, moving-covariance learning scheme. A temporal ordering scheme is implemented using decay at the input level, allowing the network to learn to recognize sequences. The learning scheme requires a single pass through the data, giving the architecture the capability of real-time learning. The first part of the paper develops the adaptive-kernel estimator. The parallel architecture is then described, and issues relevant to implementation are discussed. Finally, applications to robotic sensor fusion, intended word recognition, and vision are described.
Flauger, Raphael; Pajer, Enrico E-mail: ep295@cornell.edu
2011-01-01
We provide a derivation from first principles of the primordial bispectrum of scalar perturbations produced during inflation driven by a canonically normalized scalar field whose potential exhibits small sinusoidal modulations. A potential of this type has been derived in a class of string theory models of inflation based on axion monodromy. We use this model as a concrete example, but we present our derivations and results for a general slow-roll potential with superimposed modulations. We show analytically that a resonance between the oscillations of the background and the oscillations of the fluctuations is responsible for the production of an observably large non-Gaussian signal. We provide an explicit expression for the shape of this resonant non-Gaussianity. We show that there is essentially no overlap between this shape and the local, equilateral, and orthogonal shapes, and we stress that resonant non-Gaussianity is not captured by the simplest version of the effective field theory of inflation. We hope our analytic expression will be useful to further observationally constrain this class of models.
Gaussian-optimized preparation of non-Gaussian pure states
NASA Astrophysics Data System (ADS)
Menzies, David; Filip, Radim
2009-01-01
Non-Gaussian states are highly sought-after resources in continuous-variable quantum optical information processing protocols. We outline a method for the optimized preparation of any pure non-Gaussian state to a given desired accuracy. Our proposal arises from two connected concepts. First, we define the operational cost of a desired state as the largest Fock state required for its approximate preparation. Second, we suggest that this non-Gaussian operational cost can be reduced by judicial application of optimized Gaussian operations. In particular, we identify a minimal core non-Gaussian state for any target pure state, which is related to the core state by Gaussian operations alone. We demonstrate this method for Schrödinger cat states.
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.
Non-Gaussian extrema counts for CMB maps
Pogosyan, Dmitri; Pichon, Christophe; Gay, Christophe
2011-10-15
In the context of the geometrical analysis of weakly non-Gaussian cosmic microwave background maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments expansion of the joint probability distribution of an isotropic random field, its gradient, and invariants of the Hessian. Analytic expressions for these counts are given to second order in the non-Gaussian correction, while a Monte Carlo method to compute them to arbitrary order is presented. Matching count statistics to these estimators is illustrated on fiducial non-Gaussian Planck data.
Noncommutative geometry modified non-Gaussianities of cosmological perturbation
Fang Kejie; Xue Wei; Chen Bin
2008-03-15
We investigate the noncommutative effect on the non-Gaussianities of primordial cosmological perturbation. In the lowest order of string length and slow-roll parameter, we find that in the models with small speed of sound the noncommutative modifications could be observable if assuming a relatively low string scale. In particular, the dominant modification of the non-Gaussianity estimator f{sub NL} could reach O(1) in Dirac-Born-Infeld (DBI) inflation and K-inflation. The corrections are sensitive to the speed of sound and the choice of string length scale. Moreover the shapes of the corrected non-Gaussianities are distinct from that of ordinary ones.
Minimal disturbance measurement for coherent states is non-Gaussian
Mista, Ladislav Jr.
2006-03-15
In standard coherent state teleportation with a shared two-mode squeezed vacuum (TMSV) state there is a trade-off between the teleportation fidelity and the fidelity of estimation of the teleported state from the results of the Bell measurement. Within the class of Gaussian operations this trade-off is optimal, i.e., there is not a Gaussian operation that would give a larger estimation fidelity for a given output fidelity. We show that this trade-off can be improved by up to 2.77% if we use a suitable non-Gaussian operation. This operation can be implemented by the standard teleportation protocol in which the shared TMSV state is replaced with a suitable non-Gaussian entangled state. We also demonstrate that this operation can be used to enhance the transmission fidelity of a certain noisy channel.
Geometry of Gaussian quantum states
NASA Astrophysics Data System (ADS)
Link, Valentin; Strunz, Walter T.
2015-07-01
We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi-mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert-Schmidt measure.
Fixing convergence of Gaussian belief propagation
Johnson, Jason K; Bickson, Danny; Dolev, Danny
2009-01-01
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 is 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.
Normal form decomposition for Gaussian-to-Gaussian superoperators
De Palma, Giacomo; Mari, Andrea; Giovannetti, Vittorio; Holevo, Alexander S.
2015-05-15
In this paper, we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non-positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings, we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.
CMB lensing and primordial non-Gaussianity
Hanson, Duncan; Smith, Kendrick M.; Challinor, Anthony; Liguori, Michele
2009-10-15
We study the effects of gravitational lensing on the estimation of non-Gaussianity from the bispectrum of the CMB temperature anisotropies. We find that the effect of lensing on the bispectrum may qualitatively be described as a smoothing of the acoustic features analogous to the temperature power spectrum. In contrast to previous results, for a Planck-like experiment which is cosmic-variance limited to l{sub max}=2000, we find that lensing causes no significant degradation of our ability to constrain the non-Gaussianity amplitude f{sub NL} for both local and equilateral configurations, provided that the biases due to the cross correlation between the lensing potential and the integrated-Sachs-Wolfe contribution to the CMB temperature are adequately understood. With numerical simulations, we also verify that low-order Taylor approximations to the lensed bispectrum and integrated-Sachs-Wolfe-lensing biases are accurate.
Growth of Gaussian instabilities in Gaussian laser beams
Abbi, S.C.; Kothari, N.C.
1980-03-01
We present a theory for the growth of a Gaussian perturbation superimposed on a Gaussian profile laser beam. This theory gives an exponential growth of the perturbation for small distances z traveled inside the nonlinear medium. For larger values of z, the growth is not exponential. The growth parameter ..cap alpha.. is defined and an analytical expression for this parameter is obtained. Our theory gives a smooth matching between the exponential growth of perturbations in a linearized instability theory and the sharp self-focusing thresholds expected for smooth Gaussian profile laser beams propagating in nonlinear media.
Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements.
Nha, Hyunchul; Lee, Su-Yong; Ji, Se-Wan; Kim, M S
2012-01-20
We present a formalism to derive entanglement criteria beyond the Gaussian regime that can be readily tested by only homodyne detection. The measured observable is the Einstein-Podolsky-Rosen (EPR) correlation. Its arbitrary functional form enables us to detect non-Gaussian entanglement even when an entanglement test based on second-order moments fails. We illustrate the power of our experimentally friendly criteria for a broad class of non-Gaussian states under realistic conditions. We also show rigorously that quantum teleportation for continuous variables employs a specific functional form of EPR correlation. PMID:22400723
Mapping possible non-Gaussianity in the Planck maps
NASA Astrophysics Data System (ADS)
Bernui, A.; Rebouças, M. J.
2015-01-01
Context. The study of the non-Gaussianity of the temperature fluctuations of cosmic background radiation (CMB) can be used to break the degeneracy between the inflationary models and to test alternative scenarios of the early universe. However, there are several sources of non-Gaussian contaminants in the CMB data, which make a convincing extraction of primordial non-Gaussianity into an ambitious observational and statistical enterprise. It is conceivable that no single statistical estimator can be sensitive to all forms and levels of non-Gaussianity that may be present in observed CMB data. In recent works a statistical procedure based upon the calculation of the skewness and kurtosis of the patches of CMB sky sphere has been proposed and used to find out significant large-angle deviation from Gaussianity in the foreground-reduced WMAP maps. Aims: Here we address the question of how previous recent analyses of Gaussianity of WMAP maps are modified if the nearly full-sky foreground-cleaned Planck maps are used, therefore extending and complementing such an examination in several regards. Methods: Once the foregrounds are cleaned through different component separation procedures, each of the resulting Planck maps is then tested for Gaussianity. We determine quantitatively the effects for Gaussianity when masking the foreground-cleaned Planck maps with the inpmask, valmask, and U73 Planck masks. Results: We show that although the foreground-cleaned Planck maps present significant deviation from Gaussianity of different degrees when the less severe inpmask and valmask are used, they become consistent with Gaussianity as detected by our indicator S when masked with the union U73 mask. A slightly smaller consistency with Gaussianity is found when the K indicator is employed, which seems to be associated with the large-angle anomalies reported by the Planck team. Finally, we examine the robustness of the Gaussianity analyses with respect to the real pixel's noise as
Making tensor factorizations robust to non-gaussian noise.
Chi, Eric C.; Kolda, Tamara Gibson
2011-03-01
Tensors are multi-way arrays, and the CANDECOMP/PARAFAC (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of independent and identically distributed (i.i.d.) Gaussian noise. We demonstrate that this loss function can be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization (MM) algorithm for fitting a CP model using our proposed loss function (CPAL1) and compare its performance to the workhorse algorithm for fitting CP models, CP alternating least squares (CPALS).
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.
Control charts for non-Gaussian distributions
NASA Astrophysics Data System (ADS)
Babus, Florina; Kobi, Abdessamad; Tiplica, Th.; Bacivarov, Ioan; Bacivarov, Angelica
2007-05-01
Traditional statistical process control (SPC) techniques applied in the industrial processes field consider often that the distribution ofdata is Gaussian. The estimation ofparameters, the detection ofthe out oforder situations and the control of the followed characteristics are easy to achieve for the normal populations. In reality, whatever the origin of a characteristic (large series productions for components, mechanical parts of OE communication systems, etc. ) the curve of distributions of the measured values is generally far from being normal. The simple approximation to the Gauss distribution and the use of the classical control methods sometimes induces serious errors. In this paper, a study on the statistical control of non Gaussian populations is presented. Particularly we discuss the Rayleigh and the Weibull distribution as being representatives in (SPC for some category of data. The X control charts with variable limits are tested. Experimental simulations are presented for different parameters of the two distributions. The results confirm the methodology and encourage the research in the field of non Gaussian processes.
Non-Gaussian probabilistic MEG source localisation based on kernel density estimation☆
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
2DPUF: A sequential gaussian puff model
Addis, R.P.; O`Steen, B.L.
1990-12-31
This report documents the Environmental Transport Section`s (ETS) two-dimensional, sequential gaussian puff transport and dispersion model for emergency response. The sequential puff scheme is described, and the dispersion equations are presented. The advantages of this model over the ETS`s PUFF/PLUME model are discussed. Options are calculating a two-dimensional wind field, interpolation procedures, and the wind field grid are described. The various grid systems for puff transport calculations and dose estimates are also described. A flow diagram for the modules comprising the 2DPUF code and a description of each module is presented.
2DPUF: A sequential gaussian puff model
Addis, R.P.; O'Steen, B.L.
1990-01-01
This report documents the Environmental Transport Section's (ETS) two-dimensional, sequential gaussian puff transport and dispersion model for emergency response. The sequential puff scheme is described, and the dispersion equations are presented. The advantages of this model over the ETS's PUFF/PLUME model are discussed. Options are calculating a two-dimensional wind field, interpolation procedures, and the wind field grid are described. The various grid systems for puff transport calculations and dose estimates are also described. A flow diagram for the modules comprising the 2DPUF code and a description of each module is presented.
Quantum correlations in Gaussian states via Gaussian channels: steering, entanglement, and discord
NASA Astrophysics Data System (ADS)
Wang, Zhong-Xiao; Wang, Shuhao; Li, Qiting; Wang, Tie-Jun; Wang, Chuan
2016-06-01
Here we study the quantum steering, quantum entanglement, and quantum discord for Gaussian Einstein-Podolsky-Rosen states via Gaussian channels. And the sudden death phenomena for Gaussian steering and Gaussian entanglement are theoretically observed. We find that some Gaussian states have only one-way steering, which confirms the asymmetry of quantum steering. Also we investigate that the entangled Gaussian states without Gaussian steering and correlated Gaussian states own no Gaussian entanglement. Meanwhile, our results support the assumption that quantum entanglement is intermediate between quantum discord and quantum steering. Furthermore, we give experimental recipes for preparing quantum states with desired types of quantum correlations.
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.
Hierarchical similarity transformations between Gaussian mixtures.
Rigas, George; Nikou, Christophoros; Goletsis, Yorgos; Fotiadis, Dimitrios I
2013-11-01
In this paper, we propose a method to estimate the density of a data space represented by a geometric transformation of an initial Gaussian mixture model. The geometric transformation is hierarchical, and it is decomposed into two steps. At first, the initial model is assumed to undergo a global similarity transformation modeled by translation, rotation, and scaling of the model components. Then, to increase the degrees of freedom of the model and allow it to capture fine data structures, each individual mixture component may be transformed by another, local similarity transformation, whose parameters are distinct for each component of the mixture. In addition, to constrain the order of magnitude of the local transformation (LT) with respect to the global transformation (GT), zero-mean Gaussian priors are imposed onto the local parameters. The estimation of both GT and LT parameters is obtained through the expectation maximization framework. Experiments on artificial data are conducted to evaluate the proposed model, with varying data dimensionality, number of model components, and transformation parameters. In addition, the method is evaluated using real data from a speech recognition task. The obtained results show a high model accuracy and demonstrate the potential application of the proposed method to similar classification problems. PMID:24808615
On generalized averaged Gaussian formulas
NASA Astrophysics Data System (ADS)
Spalevic, Miodrag M.
2007-09-01
We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions w(x)equiv w^{(alpha,beta)}(x)D(1-x)^alpha(1+x)^beta ( alpha,beta>-1 ) we give a necessary and sufficient condition on the parameters alpha and beta such that the optimal averaged Gaussian quadrature formulas are internal.
Tachyon mediated non-Gaussianity
Dutta, Bhaskar; Leblond, Louis; Kumar, Jason
2008-10-15
We describe a general scenario where primordial non-Gaussian curvature perturbations are generated in models with extra scalar fields. The extra scalars communicate to the inflaton sector mainly through the tachyonic (waterfall) field condensing at the end of hybrid inflation. These models can yield significant non-Gaussianity of the local shape, and both signs of the bispectrum can be obtained. These models have cosmic strings and a nearly flat power spectrum, which together have been recently shown to be a good fit to WMAP data. We illustrate with a model of inflation inspired from intersecting brane models.
Diagnosing non-Gaussianity of forecast and analysis errors in a convective-scale model
NASA Astrophysics Data System (ADS)
Legrand, R.; Michel, Y.; Montmerle, T.
2016-01-01
In numerical weather prediction, the problem of estimating initial conditions with a variational approach is usually based on a Bayesian framework associated with a Gaussianity assumption of the probability density functions of both observations and background errors. In practice, Gaussianity of errors is tied to linearity, in the sense that a nonlinear model will yield non-Gaussian probability density functions. In this context, standard methods relying on Gaussian assumption may perform poorly. This study aims to describe some aspects of non-Gaussianity of forecast and analysis errors in a convective-scale model using a Monte Carlo approach based on an ensemble of data assimilations. For this purpose, an ensemble of 90 members of cycled perturbed assimilations has been run over a highly precipitating case of interest. Non-Gaussianity is measured using the K2 statistics from the D'Agostino test, which is related to the sum of the squares of univariate skewness and kurtosis. Results confirm that specific humidity is the least Gaussian variable according to that measure and also that non-Gaussianity is generally more pronounced in the boundary layer and in cloudy areas. The dynamical control variables used in our data assimilation, namely vorticity and divergence, also show distinct non-Gaussian behaviour. It is shown that while non-Gaussianity increases with forecast lead time, it is efficiently reduced by the data assimilation step especially in areas well covered by observations. Our findings may have implication for the choice of the control variables.
Robust Gaussian Graphical Modeling via l1 Penalization
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
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.
Non-gaussian shape recognition
Byun, Joyce; Bean, Rachel E-mail: rbean@astro.cornell.edu
2013-09-01
A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming cosmic microwave background (CMB) and large-scale structure (LSS) surveys raises a natural question: if a detection given a particular template is made, what does this truly tell us about the underlying theory? Even in the case of non-detections and upper bounds on deviations from Gaussianity, what can we then infer about the viable theories that remain? In this paper we present a systematic way to constrain a wide range of non-Gaussian shapes, including general single and multi-field models and models with excited initial states. We present a separable, divergent basis able to recreate many shapes in the literature to high accuracy with between three and seven basis functions. The basis allows shapes to be grouped into broad ''template classes'', satisfying theoretically-relevant priors on their divergence properties in the squeezed limit. We forecast how well a Planck-like CMB survey could not only detect a general non-Gaussian signal but discern more about its shape, using existing templates and new ones we propose. This approach offers an opportunity to tie together minimal theoretical priors with observational constraints on the shape in general, and in the squeezed limit, to gain a deeper insight into what drove inflation.
Adaptive Sampling for Learning Gaussian Processes Using Mobile Sensor Networks
Xu, Yunfei; Choi, Jongeun
2011-01-01
This paper presents a novel class of self-organizing sensing agents that adaptively learn an anisotropic, spatio-temporal Gaussian process using noisy measurements and move in order to improve the quality of the estimated covariance function. This approach is based on a class of anisotropic covariance functions of Gaussian processes introduced to model a broad range of spatio-temporal physical phenomena. The covariance function is assumed to be unknown a priori. Hence, it is estimated by the maximum a posteriori probability (MAP) estimator. The prediction of the field of interest is then obtained based on the MAP estimate of the covariance function. An optimal sampling strategy is proposed to minimize the information-theoretic cost function of the Fisher Information Matrix. Simulation results demonstrate the effectiveness and the adaptability of the proposed scheme. PMID:22163785
GAUSSIAN BEAM LASER RESONATOR PROGRAM
NASA Technical Reports Server (NTRS)
Cross, P. L.
1994-01-01
In designing a laser cavity, the laser engineer is frequently concerned with more than the stability of the resonator. Other considerations include the size of the beam at various optical surfaces within the resonator or the performance of intracavity line-narrowing or other optical elements. Laser resonators obey the laws of Gaussian beam propagation, not geometric optics. The Gaussian Beam Laser Resonator Program models laser resonators using Gaussian ray trace techniques. It can be used to determine the propagation of radiation through laser resonators. The algorithm used in the Gaussian Beam Resonator program has three major components. First, the ray transfer matrix for the laser resonator must be calculated. Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed. Finally the propagation of the beam through the optical elements is computed. The optical elements can be modeled as parallel plates, lenses, mirrors, dummy surfaces, or Gradient Index (GRIN) lenses. A Gradient Index lens is a good approximation of a laser rod operating under a thermal load. The optical system may contain up to 50 elements. In addition to the internal beam elements the optical system may contain elements external to the resonator. The Gaussian Beam Resonator program was written in Microsoft FORTRAN (Version 4.01). It was developed for the IBM PS/2 80-071 microcomputer and has been implemented on an IBM PC compatible under MS DOS 3.21. The program was developed in 1988 and requires approximately 95K bytes to operate.
Gaussian Velocity Distributions in Avalanches
NASA Astrophysics Data System (ADS)
Shattuck, Mark
2004-03-01
Imagine a world where gravity is so strong that if an ice cube is tilted the shear forces melt the surface and water avalanches down. Further imagine that the ambient temperature is so low that the water re-freezes almost immediately. This is the world of granular flows. As a granular solid is tilted the surface undergoes a sublimation phase transition and a granular gas avalanches down the surface, but the inelastic collisions rapidly remove energy from the flow lowering the granular temperature (kinetic energy per particle) until the gas solidifies again. It is under these extreme conditions that we attempt to uncover continuum granular flow properties. Typical continuum theories like Navier-Stokes equation for fluids follow the space-time evolution of the first few moments of the velocity distribution. We study continuously avalanching flow in a rotating two-dimensional granular drum using high-speed video imaging and extract the position and velocities of the particles. We find a universal near Gaussian velocity distribution throughout the flowing regions, which are characterized by a liquid-like radial distribution function. In the remaining regions, in which the radial distribution function develops sharp crystalline peaks, the velocity distribution has a Gaussian peak but is much broader in the tails. In a companion experiment on a vibrated two-dimensional granular fluid under constant pressure, we find a clear gas-solid phase transition in which both the temperature and density change discontinuously. This suggests that a low temperature crystal and a high temperature gas can coexist in steady state. This coexistence could result in a narrower, cooler, Gaussian peak and a broader, warmer, Gaussian tail like the non-Gaussian behavior seen in the crystalline portions of the rotating drum.
Inseparability of photon-added Gaussian states
Li Hongrong; Li Fuli; Zhu Shiyao
2007-06-15
The inseparability of photon-added Gaussian states which are generated from two-mode Gaussian states by adding photons is investigated. According to the established inseparability conditions [New J. Phys. 7, 211 (2005); Phys. Rev. Lett. 96, 050503 (2006)], we find that even if a two-mode Gaussian state is separable, the photon-added Gaussian state becomes entangled when the purity of the Gaussian state is larger than a certain value. The lower bound of entanglement of symmetric photon-added Gaussian states is derived. The result shows that entanglement of the photon-added Gaussian states is involved with high-order moment correlations. We find that fidelity of teleporting coherent states cannot be raised by employing the photon-added Gaussian states as a quantum channel of teleportation.
Gaussian weighted projection for visualization of cardiac calcification
NASA Astrophysics Data System (ADS)
Chen, Xiang; Li, Ke; Gilkeson, Robert; Fei, Baowei
2008-03-01
At our institution, we are using dual-energy digital radiography (DEDR) as a cost-effective screening tool for the detection of cardiac calcification. We are evaluating DEDR using CT as the gold standard. We are developing image projection methods for the generation of digitally reconstructed radiography (DRR) from CT image volumes. Traditional visualization methods include maximum intensity projection (MIP) and average-based projection (AVG) that have difficulty to show cardiac calcification. Furthermore, MIP can over estimate the calcified lesion as it displays the maximum intensity along the projection rays regardless of tissue types. For AVG projection, the calcified tissue is usually overlapped with bone, lung and mediastinum. In order to improve the visualization of calcification on DRR images, we developed a Gaussian-weighted projection method for this particular application. We assume that the CT intensity values of calcified tissues have a Gaussian distribution. We then use multiple Gaussian functions to fit the intensity histogram. Based on the mean and standard deviation parameters, we incorporate a Gaussian weighted function into the perspective projection and display the calcification exclusively. Our digital and physical phantom studies show that the new projection method can display tissues selectively. In addition, clinical images show that the Gaussian-weighted projection method better visualizes cardiac calcification than either the AVG or MIP method and can be used to evaluate DEDR as a screening tool for the detection of coronary artery diseases.
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.
Harmonic Pinnacles in the Discrete Gaussian Model
NASA Astrophysics Data System (ADS)
Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan
2016-06-01
The 2 D Discrete Gaussian model gives each height function {η : Z^2to{Z}} a probability proportional to {exp(-β {H}(η))}, where {β} is the inverse-temperature and {{H}(η) = sum_{x˜ y}(η_x-η_y)^2} sums over nearest-neighbor bonds. We consider the model at large fixed {β}, where it is flat unlike its continuous analog (the Discrete Gaussian Free Field). We first establish that the maximum height in an {L× L} box with 0 boundary conditions concentrates on two integers M, M + 1 with {M˜ √{(1/2πβ)log Llog log L}}. The key is a large deviation estimate for the height at the origin in {{Z}2}, dominated by "harmonic pinnacles", integer approximations of a harmonic variational problem. Second, in this model conditioned on {η≥ 0} (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels H, H + 1 where {H˜ M/√{2}}. This in particular pins down the asymptotics, and corrects the order, in results of Bricmont et al. (J. Stat. Phys. 42(5-6):743-798, 1986), where it was argued that the maximum and the height of the surface above a floor are both of order {√{log L}}. Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to p-harmonic analysis and alternating sign matrices.
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.
Non-Gaussianity and CMB aberration and Doppler
Catena, Riccardo; Liguori, Michele; Renzi, Alessandro; Notari, Alessio E-mail: michele.liguori@pd.infn.it E-mail: arenzi@pd.infn.it
2013-09-01
The peculiar motion of an observer with respect to the CMB rest frame induces a deflection in the arrival direction of the observed photons (also known as CMB aberration) and a Doppler shift in the measured photon frequencies. As a consequence, aberration and Doppler effects induce non trivial correlations between the harmonic coefficients of the observed CMB temperature maps. In this paper we investigate whether these correlations generate a bias on non-Gaussianity estimators f{sub NL}. We perform this analysis simulating a large number of temperature maps with Planck-like resolution (lmax = 2000) as different realizations of the same cosmological fiducial model (WMAP7yr). We then add to these maps aberration and Doppler effects employing a modified version of the HEALPix code. We finally evaluate a generalization of the Komatsu, Spergel and Wandelt non-Gaussianity estimator for all the simulated maps, both when peculiar velocity effects have been considered and when these phenomena have been neglected. Using the value v/c = 1.23 × 10{sup −3} for our peculiar velocity, we found that the aberration/Doppler induced non-Gaussian signal is at most of about half of the cosmic variance σ for f{sub NL} both in a full-sky and in a cut-sky experimental configuration, for local, equilateral and orthogonal estimators. We conclude therefore that when estimating f{sub NL} it is safe to ignore aberration and Doppler effects if the primordial map is already Gaussian. More work is necessary however to assess whether a map which contains non-Gaussianity can be significantly distorted by a peculiar velocity.
POTENTIAL FLOW MODEL FOR GAUSSIAN PLUME INTERACTION WITH SIMPLE TERRAIN FEATURES
The theory of turbulent plumes embedded within potential flow fields is discussed for flows modified by special complex terrain situations. Both two-dimensional and three-dimensional isolated terrain obstacles are considered. Concentration estimates are evaluated using a Gaussian...
Focusing of truncated Gaussian beams
NASA Astrophysics Data System (ADS)
Horváth, Zoltán L.; Bor, Zsolt
2003-07-01
It is shown that the focusing of truncated Gaussian beams can be treated by the same manner as uniform spherical waves, i.e., the diffraction integral can be expressed by the Lommel functions, which offers a very efficient way for the calculation of the three-dimensional light distribution near focus. All the expressions for the uniform spherical waves hold good for Gaussian beams if the first variable in the Lommel functions is extended to the complex domain. The intensity distribution depending on the Fresnel number and the truncation coefficient is calculated. The location of the first few minima and maxima of the intensity in focal plane is given for different values of the truncation coefficient. The phase behavior depending on the truncation coefficient is studied.
Nurmi, Sami; Byrnes, Christian T.; Tasinato, Gianmassimo E-mail: ctb22@sussex.ac.uk
2013-06-01
Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our observable patch from their global averages over the inflating space. This leads to a landscape picture where the properties of our observable patch depend on its location and may significantly differ from the expectation values predicted by the underlying fundamental inflationary model. We show that if multiple fields are present during inflation, this may happen even if our horizon exit would be preceded by only a few e-foldings of inflation. Non-Gaussian statistics are especially affected: for example models of local non-Gaussianity predicting |f{sub NL}{sup 0}| >> 10 over the entire inflating volume can have a probability up to a few tens of percent to generate a non-detectable bispectrum in our observable patch |f{sub NL}{sup obs.}|∼<10. In this work we establish systematic connections between the observable local properties of primordial perturbations and the global properties of the inflating space which reflect the underlying high energy physics. We study in detail the implications of both a detection and non-detection of primordial non-Gaussianity by Planck, and discover novel ways of characterising the naturalness of different observational configurations.
Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation
NASA Technical Reports Server (NTRS)
Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet
2015-01-01
When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating
Area scintillations of Bessel Gaussian and modified Bessel Gaussian beams of zeroth order
NASA Astrophysics Data System (ADS)
Eyyuboğlu, H. T.
2010-01-01
As an extension of our previous study, the area scintillation aspects of Bessel Gaussian and modified Bessel Gaussian beams of zeroth order are investigated. The analysis is carried out on the basis of equal source sizes and equal source powers. It is found that, when compared on equal source size basis, modified Bessel Gaussian beams always have less area scintillations than a Gaussian beam, while Bessel Gaussian beams exhibit more area scintillations. Comparison on equal source power basis, however, removes the advantage of modified Bessel Gaussian beams, that is, their area scintillations become nearly the same as those of the Gaussian beam. On the other hand, for the case of equal source powers, Bessel Gaussian beams with larger width parameters continue to have higher area scintillations than the Gaussian beam. We provide graphical illustrations for profiles of equal source size beams, equal source power beams and the curves to aid the selection of equal source power beams.
FPGA design and implementation of Gaussian filter
NASA Astrophysics Data System (ADS)
Yang, Zhihui; Zhou, Gang
2015-12-01
In this paper , we choose four different variances of 1,3,6 and 12 to conduct FPGA design with three kinds of Gaussian filtering algorithm ,they are implementing Gaussian filter with a Gaussian filter template, Gaussian filter approximation with mean filtering and Gaussian filter approximation with IIR filtering. By waveform simulation and synthesis, we get the processing results on the experimental image and the consumption of FPGA resources of the three methods. We set the result of Gaussian filter used in matlab as standard to get the result error. By comparing the FPGA resources and the error of FPGA implementation methods, we get the best FPGA design to achieve a Gaussian filter. Conclusions can be drawn based on the results we have already got. When the variance is small, the FPGA resources is enough for the algorithm to implement Gaussian filter with a Gaussian filter template which is the best choice. But when the variance is so large that there is no more FPGA resources, we can chose the mean to approximate Gaussian filter with IIR filtering.
Bimodal and Gaussian Ising spin glasses in dimension two
NASA Astrophysics Data System (ADS)
Lundow, P. H.; Campbell, I. A.
2016-02-01
An analysis is given of numerical simulation data to size L =128 on the archetype square lattice Ising spin glasses (ISGs) with bimodal (±J ) and Gaussian interaction distributions. It is well established that the ordering temperature of both models is zero. The Gaussian model has a nondegenerate ground state and thus a critical exponent η ≡0 , and a continuous distribution of energy levels. For the bimodal model, above a size-dependent crossover temperature T*(L ) there is a regime of effectively continuous energy levels; below T*(L ) there is a distinct regime dominated by the highly degenerate ground state plus an energy gap to the excited states. T*(L ) tends to zero at very large L , leaving only the effectively continuous regime in the thermodynamic limit. The simulation data on both models are analyzed with the conventional scaling variable t =T and with a scaling variable τb=T2/(1 +T2) suitable for zero-temperature transition ISGs, together with appropriate scaling expressions. The data for the temperature dependence of the reduced susceptibility χ (τb,L ) and second moment correlation length ξ (τb,L ) in the thermodynamic limit regime are extrapolated to the τb=0 critical limit. The Gaussian critical exponent estimates from the simulations, η =0 and ν =3.55 (5 ) , are in full agreement with the well-established values in the literature. The bimodal critical exponents, estimated from the thermodynamic limit regime analyses using the same extrapolation protocols as for the Gaussian model, are η =0.20 (2 ) and ν =4.8 (3 ) , distinctly different from the Gaussian critical exponents.
Bimodal and Gaussian Ising spin glasses in dimension two.
Lundow, P H; Campbell, I A
2016-02-01
An analysis is given of numerical simulation data to size L=128 on the archetype square lattice Ising spin glasses (ISGs) with bimodal (±J) and Gaussian interaction distributions. It is well established that the ordering temperature of both models is zero. The Gaussian model has a nondegenerate ground state and thus a critical exponent η≡0, and a continuous distribution of energy levels. For the bimodal model, above a size-dependent crossover temperature T(*)(L) there is a regime of effectively continuous energy levels; below T(*)(L) there is a distinct regime dominated by the highly degenerate ground state plus an energy gap to the excited states. T(*)(L) tends to zero at very large L, leaving only the effectively continuous regime in the thermodynamic limit. The simulation data on both models are analyzed with the conventional scaling variable t=T and with a scaling variable τ(b)=T(2)/(1+T(2)) suitable for zero-temperature transition ISGs, together with appropriate scaling expressions. The data for the temperature dependence of the reduced susceptibility χ(τ(b),L) and second moment correlation length ξ(τ(b),L) in the thermodynamic limit regime are extrapolated to the τ(b)=0 critical limit. The Gaussian critical exponent estimates from the simulations, η=0 and ν=3.55(5), are in full agreement with the well-established values in the literature. The bimodal critical exponents, estimated from the thermodynamic limit regime analyses using the same extrapolation protocols as for the Gaussian model, are η=0.20(2) and ν=4.8(3), distinctly different from the Gaussian critical exponents. PMID:26986300
Gaussian model-based statistical matching for image enhancement and segmentation
NASA Astrophysics Data System (ADS)
Zheng, Yufeng
2008-04-01
A Gaussian model-based statistical matching procedure is proposed for image enhancement and segmentation. Generally speaking, enhanced images are desired for visual analysis whereas segmented images are required for target recognition. A histogram matching procedure is used to enhance a given image. To perform histogram matching, two histograms are needed, an original histogram computed from the given image and a specified histogram to be matched to. For image enhancement, the specified histogram is a Gaussian model (mean & standard deviation) that can be estimated from a number of well-exposed images or properly processed images. Certainly the Gaussian model varies with the category of imagery. For image segmentation, N Gaussian models (means & standard deviations) are estimated from the original histogram of a given image. The number of Gaussian models (N) is decided by analyzing the original histogram. A statistical matching procedure is used to map the original histogram onto one of the Gaussian models defined by their means and standard deviations. Specifically, the mapped image can be computed by subtracting the mean of original image from the original image, scaling with the ratio of the standard deviation of Gaussian model to the standard deviation of original image and plus the mean of Gaussian model. The statistically mapped image is thresheld by using the mean of Gaussian model, which results one set of expected segments. The statistical matching plus thresholding procedure is repeated N times for N Gaussian models. Finally, all N sets of segments are fully obtained. The proposed image enhancement and segmentation procedure are validated with multi-sensor imagery.
Planck 2013 results. XXIV. Constraints on primordial non-Gaussianity
NASA Astrophysics Data System (ADS)
Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartlett, J. G.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J. J.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R. C.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H. C.; Chiang, L.-Y.; Christensen, P. R.; Church, S.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Couchot, F.; Coulais, A.; Crill, B. P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.-M.; Désert, F.-X.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T. A.; Eriksen, H. K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Galeotta, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F. K.; Hanson, D.; Harrison, D.; Heavens, A.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T. S.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lacasa, F.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Laureijs, R. J.; Lawrence, C. R.; Leahy, J. P.; Leonardi, R.; Lesgourgues, J.; Lewis, A.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maffei, B.; Maino, D.; Mandolesi, N.; Mangilli, A.; Marinucci, D.; Maris, M.; Marshall, D. J.; Martin, P. G.; Martínez-González, E.; Masi, S.; Massardi, M.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Meinhold, P. R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Noviello, F.; Novikov, D.; Novikov, I.; Osborne, S.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H. V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Racine, B.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rubiño-Martín, J. A.; Rusholme, B.; Sandri, M.; Santos, D.; Savini, G.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Smith, K.; Spencer, L. D.; Starck, J.-L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sureau, F.; Sutter, P.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L. A.; Wandelt, B. D.; White, M.; White, S. D. M.; Yvon, D.; Zacchei, A.; Zonca, A.
2014-11-01
The Planck nominal mission cosmic microwave background (CMB) maps yield unprecedented constraints on primordial non-Gaussianity (NG). Using three optimal bispectrum estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result fNLlocal = 2.7 ± 5.8, fNLequil = -42 ± 75, and fNLorth = -25 ± 39 (68% CL statistical). Non-Gaussianity is detected in the data; using skew-Cℓ statistics we find a nonzero bispectrum from residual point sources, and the integrated-Sachs-Wolfe-lensing bispectrum at a level expected in the ΛCDM scenario. The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are confirmed by skew-Cℓ, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, three-dimensional reconstructions of the Planck CMB bispectrum and thus derive constraints on early-Universe scenarios that generate primordial NG, including general single-field models of inflation, excited initial states (non-Bunch-Davies vacua), and directionally-dependent vector models. We provide an initial survey of scale-dependent feature and resonance models. These results bound both general single-field and multi-field model parameter ranges, such as the speed of sound, cs ≥ 0.02 (95% CL), in an effective field theory parametrization, and the curvaton decay fraction rD ≥ 0.15 (95% CL). The Planck data significantly limit the viable parameter space of the ekpyrotic/cyclic scenarios. The amplitude of the four-point function in the local model τNL< 2800 (95% CL). Taken together, these constraints represent the highest precision tests to date of physical mechanisms for the origin of cosmic structure.
Extreme value statistics of smooth Gaussian random fields
NASA Astrophysics Data System (ADS)
Colombi, Stéphane; Davis, Olaf; Devriendt, Julien; Prunet, Simon; Silk, Joe
2011-07-01
We consider the Gumbel or extreme value statistics describing the distribution function pG(νmax) of the maximum values of a random field ν within patches of fixed size. We present, for smooth Gaussian random fields in two and three dimensions, an analytical estimate of pG which is expected to hold in a regime where local maxima of the field are moderately high and weakly clustered. When the patch size becomes sufficiently large, the negative of the logarithm of the cumulative extreme value distribution is simply equal to the average of the Euler characteristic of the field in the excursion ν≥νmax inside the patches. The Gumbel statistics therefore represents an interesting alternative probe of the genus as a test of non-Gaussianity, e.g. in cosmic microwave background temperature maps or in 3D galaxy catalogues. It can be approximated, except in the remote positive tail, by a negative Weibull-type form, converging slowly to the expected Gumbel-type form for infinitely large patch size. Convergence is facilitated when large-scale correlations are weaker. We compare the analytic predictions to numerical experiments for the case of a scale-free Gaussian field in two dimensions, achieving impressive agreement between approximate theory and measurements. We also discuss the generalization of our formalism to non-Gaussian fields.
Monogamy inequality for distributed gaussian entanglement.
Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio
2007-02-01
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. PMID:17358836
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.
Elegant Gaussian beams for enhanced optical manipulation
Alpmann, Christina Schöler, Christoph; Denz, Cornelia
2015-06-15
Generation of micro- and nanostructured complex light beams attains increasing impact in photonics and laser applications. In this contribution, we demonstrate the implementation and experimental realization of the relatively unknown, but highly versatile class of complex-valued Elegant Hermite- and Laguerre-Gaussian beams. These beams create higher trapping forces compared to standard Gaussian light fields due to their propagation changing properties. We demonstrate optical trapping and alignment of complex functional particles as nanocontainers with standard and Elegant Gaussian light beams. Elegant Gaussian beams will inspire manifold applications in optical manipulation, direct laser writing, or microscopy, where the design of the point-spread function is relevant.
Breaking Gaussian incompatibility on continuous variable quantum systems
Heinosaari, Teiko; Kiukas, Jukka; Schultz, Jussi
2015-08-15
We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.
Optimisation of dispersion parameters of Gaussian plume model for CO₂ dispersion.
Liu, Xiong; Godbole, Ajit; Lu, Cheng; Michal, Guillaume; Venton, Philip
2015-11-01
The carbon capture and storage (CCS) and enhanced oil recovery (EOR) projects entail the possibility of accidental release of carbon dioxide (CO2) into the atmosphere. To quantify the spread of CO2 following such release, the 'Gaussian' dispersion model is often used to estimate the resulting CO2 concentration levels in the surroundings. The Gaussian model enables quick estimates of the concentration levels. However, the traditionally recommended values of the 'dispersion parameters' in the Gaussian model may not be directly applicable to CO2 dispersion. This paper presents an optimisation technique to obtain the dispersion parameters in order to achieve a quick estimation of CO2 concentration levels in the atmosphere following CO2 blowouts. The optimised dispersion parameters enable the Gaussian model to produce quick estimates of CO2 concentration levels, precluding the necessity to set up and run much more complicated models. Computational fluid dynamics (CFD) models were employed to produce reference CO2 dispersion profiles in various atmospheric stability classes (ASC), different 'source strengths' and degrees of ground roughness. The performance of the CFD models was validated against the 'Kit Fox' field measurements, involving dispersion over a flat horizontal terrain, both with low and high roughness regions. An optimisation model employing a genetic algorithm (GA) to determine the best dispersion parameters in the Gaussian plume model was set up. Optimum values of the dispersion parameters for different ASCs that can be used in the Gaussian plume model for predicting CO2 dispersion were obtained. PMID:26374541
Gaussian beam decomposition of high frequency wave fields using expectation-maximization
Ariel, Gil; Engquist, Bjoern; Tanushev, Nicolay M.; Tsai, Richard
2011-03-20
A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation-maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.
Scale-dependent non-Gaussianity as a generalization of the local model
Becker, Adam; Huterer, Dragan; Kadota, Kenji E-mail: huterer@umich.edu
2011-01-01
We generalize the local model of primordial non-Gaussianity by promoting the parameter f{sub NL} to a general scale-dependent function f{sub NL}(k). We calculate the resulting bispectrum and the effect on the bias of dark matter halos, and thus the extent to which f{sub NL}(k) can be measured from the large-scale structure observations. By calculating the principal components of f{sub NL}(k), we identify scales where this form of non-Gaussianity is best constrained and estimate the overlap with previously studied local and equilateral non-Gaussian models.
Gaussianity and localization of N -qubit states
NASA Astrophysics Data System (ADS)
Gaeta, M.; Muñoz, C.; Klimov, A. B.
2016-06-01
We analyze collective properties of N -qubit states. In particular, we exhaustively discuss the localization aspect of distributions in the measurement space and introduce the concept of Gaussian states in the macroscopic limit. The effect of local shifts on the localization and Gaussianity is analyzed.
A Renormalisation Group Method. I. Gaussian Integration and Normed Algebras
NASA Astrophysics Data System (ADS)
Brydges, David C.; Slade, Gordon
2015-05-01
This paper is the first in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. Our immediate motivation is a specific model, involving both boson and fermion fields, which arises as a representation of the continuous-time weakly self-avoiding walk. In this paper, we define normed algebras suitable for a renormalisation group analysis, and develop methods for performing analysis on these algebras. We also develop the theory of Gaussian integration on these normed algebras, and prove estimates for Gaussian integrals. The concepts and results developed here provide a foundation for the continuation of the method presented in subsequent papers in the series.
Image denoising in mixed Poisson-Gaussian noise.
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. PMID:20840902
Log-amplitude statistics of intermittent and non-Gaussian time series.
Kiyono, Ken
2009-03-01
In studies of hydrodynamic turbulence and nonequilibrium systems, it has been demonstrated that the observed non-Gaussian probability density functions are often described effectively by a superposition of Gaussian distributions with fluctuating variances. Based on this framework, we propose a general method to characterize intermittent and non-Gaussian time series. In our approach, an observed time series is assumed to be described by the multiplication of Gaussian and amplitude random variables, where the amplitude variable describes the variance fluctuation. It is shown analytically that statistical properties of the log-amplitude fluctuations can be estimated using the logarithmic-absolute moments of the observed time series. This method is applicable to a wide variety of symmetric unimodal distributions with heavy tails in order to quantify the deviation from a Gaussian distribution. By analyzing random cascade-type processes and superstatistical non-Gaussian models with power-law tails, we demonstrate that our method can provide detailed characterization in a wide range of non-Gaussian fluctuations. PMID:19391924
Gaussian interferometric power as a measure of continuous-variable non-Markovianity
NASA Astrophysics Data System (ADS)
Souza, Leonardo A. M.; Dhar, Himadri Shekhar; Bera, Manabendra Nath; Liuzzo-Scorpo, Pietro; Adesso, Gerardo
2015-11-01
We investigate the non-Markovianity of continuous-variable Gaussian quantum channels through the evolution of an operational metrological quantifier, namely, the Gaussian interferometric power, which captures the minimal precision that can be achieved using bipartite Gaussian probes in a black-box phase estimation setup, where the phase shift generator is a priori unknown. We observe that the monotonicity of the Gaussian interferometric power under the action of local Gaussian quantum channels on the ancillary arm of the bipartite probes is a natural indicator of Markovian dynamics; consequently, its breakdown for specific maps can be used to construct a witness and an effective quantifier of non-Markovianity. In our work, we consider two paradigmatic Gaussian models, the damping master equation and the quantum Brownian motion, and identify analytically and numerically the parameter regimes that give rise to non-Markovian dynamics. We then quantify the degree of non-Markovianity of the channels in terms of Gaussian interferometric power, showing, in particular, that even nonentangled probes can be useful to witness non-Markovianity. This establishes an interesting link between the dynamics of bipartite continuous-variable open systems and their potential for optical interferometry. The results are an important supplement to the recent research on characterization of non-Markovianity in continuous-variable systems.
Scintillation reduction in pseudo Multi-Gaussian Schell Model beams in the maritime environment
NASA Astrophysics Data System (ADS)
Nelson, C.; Avramov-Zamurovic, S.; Korotkova, O.; Guth, S.; Malek-Madani, R.
2016-04-01
Irradiance fluctuations of a pseudo Multi-Gaussian Schell Model beam propagating in the maritime environment is explored as a function of spatial light modulator cycling rate and estimated atmospheric turnover rate. Analysis of the data demonstrates a strong negative correlation between the scintillation index of received optical intensity and cycling speed for the estimated atmospheric turnover rate.
Gaussian translation operator in a multilevel scheme
NASA Astrophysics Data System (ADS)
Hansen, Thorkild B.; Borries, Oscar
2015-08-01
A multilevel computation scheme for time-harmonic fields in three dimensions will be formulated with a new Gaussian translation operator that decays exponentially outside a circular cone centered on the line connecting the source and observation groups. This Gaussian translation operator is directional and diagonal with its sharpness determined by a beam parameter. When the beam parameter is set to zero, the Gaussian translation operator reduces to the standard fast multipole method translation operator. The directionality of the Gaussian translation operator makes it possible to reduce the number of plane waves required to achieve a given accuracy. The sampling rate can be determined straightforwardly to achieve any desired accuracy. The use of the computation scheme will be illustrated through a near-field scanning problem where the far-field pattern of a source is determined from near-field measurements with a known probe. Here the Gaussian translation operator improves the condition number of the matrix equation that determines the far-field pattern. The Gaussian translation operator can also be used when the probe pattern is known only in one hemisphere, as is common in practice. Also, the Gaussian translation operator will be used to solve the scattering problem of the perfectly conducting sphere.
Asymmetric Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-06-01
We introduce a family of asymmetric Laguerre-Gaussian (aLG) laser beams. The beams have been derived via a complex-valued shift of conventional LG beams in the Cartesian plane. While propagating in a uniform medium, the first bright ring of the aLG beam becomes less asymmetric and the energy is redistributed toward peripheral diffraction rings. The projection of the orbital angular momentum (OAM) onto the optical axis is calculated. The OAM is shown to grow quadratically with increasing asymmetry parameter of the aLG beam, which equals the ratio of the shift to the waist radius. Conditions for the OAM becoming equal to the topological charge have been derived. For aLG beams with zero radial index, we have deduced an expression to define the intensity maximum coordinates and shown the crescent-shaped intensity pattern to rotate during propagation. Results of the experimental generation and rotation of aLG beams agree well with theoretical predictions.
Random Copolymer: Gaussian Variational Approach
NASA Astrophysics Data System (ADS)
Moskalenko, A.; Kuznetsov, Yu. A.; Dawson, K. A.
1997-03-01
We study the phase transitions of a random copolymer chain with quenched disorder. We calculate the average over the quenched disorder in replica space and apply a Gaussian variational approach based on a generic quadratic trial Hamiltonian in terms of the correlation functions of monomer Fourier coordinates. This has the advantage that it allows us to incorporate fluctuations of the density, determined self-consistently, and to study collapse, phase separation transitions and the onset of the freezing transition within the same mean field theory. The effective free energy of the system is derived analytically and analyzed numerically in the one-step Parisi scheme. Such quantities as the radius of gyration, end-to-end distance or the average value of the overlap between different replicas are treated as observables and evaluated by introducing appropriate external fields to the Hamiltonian. As a result we obtain the phase diagram in terms of model parameters, scaling for the freezing transition and the dependence of correlation functions on the chain index.
Cloning of Gaussian states by linear optics
Olivares, Stefano; Paris, Matteo G. A.; Andersen, Ulrik L.
2006-06-15
We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)]. The input-output fidelity is evaluated for a generic (pure or mixed) Gaussian state taking into account the effect of nonunit quantum efficiency and unbalanced mode mixing. In addition, since in most quantum information protocols the covariance matrix of the set of input states is not perfectly known, we evaluate the average cloning fidelity for classes of Gaussian states with the degree of squeezing and the number of thermal photons being only partially known.
Equilateral non-Gaussianity from heavy fields
Gong, Jinn-Ouk; Pi, Shi; Sasaki, Misao E-mail: spi@apctp.org
2013-11-01
The effect of self-interactions of heavy scalar fields during inflation on the primordial non-Gaussianity is studied. We take a specific constant-turn quasi-single field inflation as an example. We derive an effective theory with emphasis on non-linear self-interactions of heavy fields and calculate the corresponding non-Gaussianity, which is of equilateral type and can be as relevant as those computed previously in the literature. We also derive the non-Gaussianity by directly using the in-in formalism, and verify the equivalence of these two approaches.
Gaussian Mixture Model of Heart Rate Variability
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
Quark and Lepton Masses from Gaussian Landscapes
Hall, Lawrence J.; Salem, Michael P.; Watari, Taizan
2008-04-11
The flavor structure of the standard model (SM) might arise from random selection on a landscape. We propose a class of simple models, 'Gaussian landscapes', where Yukawa couplings derive from overlap integrals of Gaussian wave functions on extra-dimensions. Statistics of vacua are generated by scanning the peak positions of these zero-modes, giving probability distributions for all flavor observables. Gaussian landscapes can account for all observed flavor patterns with few free parameters. Although they give broad probability distributions, the predictions are correlated and accounting for measured parameters sharpens the distributions of future neutrino measurements.
Quantum bit commitment under Gaussian constraints
NASA Astrophysics Data System (ADS)
Mandilara, Aikaterini; Cerf, Nicolas J.
2012-06-01
Quantum bit commitment has long been known to be impossible. Nevertheless, just as in the classical case, imposing certain constraints on the power of the parties may enable the construction of asymptotically secure protocols. Here, we introduce a quantum bit commitment protocol and prove that it is asymptotically secure if cheating is restricted to Gaussian operations. This protocol exploits continuous-variable quantum optical carriers, for which such a Gaussian constraint is experimentally relevant as the high optical nonlinearity needed to effect deterministic non-Gaussian cheating is inaccessible.
Non-Gaussianity from isocurvature perturbations
Kawasaki, Masahiro; Nakayama, Kazunori; Sekiguchi, Toyokazu; Suyama, Teruaki; Takahashi, Fuminobu E-mail: nakayama@icrr.u-tokyo.ac.jp E-mail: suyama@icrr.u-tokyo.ac.jp
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.
Reionization and CMB non-Gaussianity
NASA Astrophysics Data System (ADS)
Munshi, D.; Corasaniti, P. S.; Coles, P.; Heavens, A.; Pandolfi, S.
2014-08-01
We show how cross-correlating a high-redshift external tracer field, such as the 21-cm neutral hydrogen distribution and product maps involving cosmic microwave background (CMB) temperature and polarization fields, that probe mixed bispectrum involving these fields, can help to determine the reionization history of the Universe, beyond what can be achieved from cross-spectrum analysis. Taking clues from recent studies for the detection of primordial non-Gaussianity, we develop a set of estimators that can study reionization using a power spectrum associated with the bispectrum (or skew-spectrum). We use the matched filtering inherent in this method to investigate different reionization histories. We check to what extent they can be used to rule out various models of reionization and study cross-contamination from different sources such as the lensing of the CMB. The estimators can be fine-tuned to optimize study of a specific reionization history. We consider three different types of tracers in our study, namely: proto-galaxies; 21-cm maps of neutral hydrogen; and quasars. We also consider four alternative models of reionization. We find that the cumulative signal-to-noise ratio (S/N) for detection at ℓmax = 2000 can reach O(70) for cosmic variance limited all-sky experiments. Combining 100 GHz, 143 GHz and 217 GHz channels of the Planck experiment, we find that the S/N lies in the range O(5)-O(35). The S/N depends on the specific choice of a tracer field, and multiple tracers can be effectively used to map out the entire reionization history with reasonable S/N. Contamination from weak lensing is investigated and found to be negligible, and the effects of Thomson scattering from patchy reionization are also considered.
Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states
Adesso, Gerardo; Illuminati, Fabrizio
2005-09-15
We study the entanglement of general (pure or mixed) two-mode Gaussian states of continuous-variable systems by comparing the two available classes of computable measures of entanglement: entropy-inspired Gaussian convex-roof measures and positive partial transposition-inspired measures (negativity and logarithmic negativity). We first review the formalism of Gaussian measures of entanglement, adopting the framework introduced in M. M. Wolf et al., Phys. Rev. A 69, 052320 (2004), where the Gaussian entanglement of formation was defined. We compute explicitly Gaussian measures of entanglement for two important families of nonsymmetric two-mode Gaussian state: namely, the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in G. Adesso et al., Phys. Rev. Lett. 92, 087901 (2004). This analysis allows us to compare the different orderings induced on the set of entangled two-mode Gaussian states by the negativities and by the Gaussian measures of entanglement. We find that in a certain range of values of the global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement of formation than states of maximum negativity. Consequently, Gaussian measures and negativities are definitely inequivalent measures of entanglement on nonsymmetric two-mode Gaussian states, even when restricted to a class of extremal states. On the other hand, the two families of entanglement measures are completely equivalent on symmetric states, for which the Gaussian entanglement of formation coincides with the true entanglement of formation. Finally, we show that the inequivalence between the two families of continuous-variable entanglement measures is somehow limited. Namely, we rigorously prove that, at fixed negativities, the Gaussian measures of entanglement are bounded from below. Moreover, we provide some strong evidence suggesting that they
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.
Gaussian quadrature inference for continuous-variable quantum key distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, L.; Imre, S.
2016-05-01
We propose the Gaussian quadrature inference (GQI) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The GQI framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. GQI utilizes the fundamentals of regularization theory and statistical information processing. We characterize GQI for multicarrier CVQKD, and define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We demonstrate the results through the adaptive multicarrier quadrature division (AMQD) scheme. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of GQI. We prove the secret key rate formulas for a multiple access multicarrier CVQKD via the AMQD-MQA (multiuser quadrature allocation) scheme. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario.
Second and third harmonic waves excited by focused Gaussian beams.
Levy, Uri; Silberberg, Yaron
2015-10-19
Harmonic generation by tightly-focused Gaussian beams is finding important applications, primarily in nonlinear microscopy. It is often naively assumed that the nonlinear signal is generated predominantly in the focal region. However, the intensity of Gaussian-excited electromagnetic harmonic waves is sensitive to the excitation geometry and to the phase matching condition, and may depend on quite an extended region of the material away from the focal plane. Here we solve analytically the amplitude integral for second harmonic and third harmonic waves and study the generated harmonic intensities vs. focal-plane position within the material. We find that maximum intensity for positive wave-vector mismatch values, for both second harmonic and third harmonic waves, is achieved when the fundamental Gaussian is focused few Rayleigh lengths beyond the front surface. Harmonic-generation theory predicts strong intensity oscillations with thickness if the material is very thin. We reproduced these intensity oscillations in glass slabs pumped at 1550nm. From the oscillations of the 517nm third-harmonic waves with slab thickness we estimate the wave-vector mismatch in a Soda-lime glass as Δk(H)= -0.249μm(-1). PMID:26480441
Primordial non-Gaussianity from the DBI Galileons
NASA Astrophysics Data System (ADS)
Mizuno, Shuntaro; Koyama, Kazuya
2010-11-01
We study primordial fluctuations generated during inflation in a class of models motivated by the DBI Galileons, which are extensions of the DBI action that yield second-order field equations. This class of models generalizes the DBI Galileons in a similar way with K inflation. We calculate the primordial non-Gaussianity from the bispectrum of the curvature perturbations at leading order in the slow-varying approximations. We show that the estimator for the equilateral-type non-Gaussianity, fNLequil, can be applied to measure the amplitude of the primordial bispectrum even in the presence of the Galileon-like term although it gives a slightly different momentum dependence from K-inflation models. For the DBI Galileons, we find -0.32/cs2
Improved Gaussian beam-scattering algorithm.
Lock, J A
1995-01-20
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. PMID:20963151
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.
Optimal cloning of mixed Gaussian states
Guta, Madalin; Matsumoto, Keiji
2006-09-15
We construct the optimal one to two cloning transformation for the family of displaced thermal equilibrium states of a harmonic oscillator, with a fixed and known temperature. The transformation is Gaussian and it is optimal with respect to the figure of merit based on the joint output state and norm distance. The proof of the result is based on the equivalence between the optimal cloning problem and that of optimal amplification of Gaussian states which is then reduced to an optimization problem for diagonal states of a quantum oscillator. A key concept in finding the optimum is that of stochastic ordering which plays a similar role in the purely classical problem of Gaussian cloning. The result is then extended to the case of n to m cloning of mixed Gaussian states.
Galaxy bias and primordial non-Gaussianity
NASA Astrophysics Data System (ADS)
Assassi, Valentin; Baumann, Daniel; Schmidt, Fabian
2015-12-01
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation.
Why Should We Pivot in Gaussian Elimination?
ERIC Educational Resources Information Center
Rozema, Edward
1988-01-01
The article discusses the use of computers to teacher college level mathematics. In particular, the Gaussian elimination procedure for solving a system of n linear equations in n unknowns, using a computer, is examined. (PK)
Gaussian Multiplicative Chaos for Symmetric Isotropic Matrices
NASA Astrophysics Data System (ADS)
Chevillard, Laurent; Rhodes, Rémi; Vargas, Vincent
2013-02-01
Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.
Ultrasonic transducer with Gaussian radial pressure distribution
NASA Technical Reports Server (NTRS)
Claus, R. O.; Zerwekh, P. S. (Inventor)
1984-01-01
An ultrasonic transducer that produces an output that is a symmetrical function comprises a piezoelectric crystal with several concentric ring electrodes on one side of the crystal. A resistor network applies different amplitudes of an ac source to each of the several electrodes. A plot of the different amplitudes from the outermost electrode to the innermost electrode is the first half of a Gaussian function. Consequently, the output of the crystal from the side opposite the electrodes has a Gaussian profile.
Gaussian maximally multipartite-entangled states
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Lupo, Cosmo; Mancini, Stefano
2009-12-15
We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n<=7.
Gaussian-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).
PREDICTION INTERVALS FOR INTEGRALS OF GAUSSIAN RANDOM FIELDS.
De Oliveira, Victor; Kone, Bazoumana
2015-03-01
Methodology is proposed for the construction of prediction intervals for integrals of Gaussian random fields over bounded regions (called block averages in the geostatistical literature) based on observations at a finite set of sampling locations. Two bootstrap calibration algorithms are proposed, termed indirect and direct, aimed at improving upon plug-in prediction intervals in terms of coverage probability. A simulation study is carried out that illustrates the effectiveness of both procedures, and these procedures are applied to estimate block averages of chromium traces in a potentially contaminated region in Switzerland. PMID:25431507
PREDICTION INTERVALS FOR INTEGRALS OF GAUSSIAN RANDOM FIELDS
De Oliveira, Victor; Kone, Bazoumana
2014-01-01
Methodology is proposed for the construction of prediction intervals for integrals of Gaussian random fields over bounded regions (called block averages in the geostatistical literature) based on observations at a finite set of sampling locations. Two bootstrap calibration algorithms are proposed, termed indirect and direct, aimed at improving upon plug-in prediction intervals in terms of coverage probability. A simulation study is carried out that illustrates the effectiveness of both procedures, and these procedures are applied to estimate block averages of chromium traces in a potentially contaminated region in Switzerland. PMID:25431507
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.
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.
Retinal image registration via feature-guided Gaussian mixture model.
Liu, Chengyin; Ma, Jiayi; Ma, Yong; Huang, Jun
2016-07-01
Registration of retinal images taken at different times, from different perspectives, or with different modalities is a critical prerequisite for the diagnoses and treatments of various eye diseases. This problem can be formulated as registration of two sets of sparse feature points extracted from the given images, and it is typically solved by first creating a set of putative correspondences and then removing the false matches as well as estimating the spatial transformation between the image pairs or solved by estimating the correspondence and transformation jointly involving an iteration process. However, the former strategy suffers from missing true correspondences, and the latter strategy does not make full use of local appearance information, which may be problematic for low-quality retinal images due to a lack of reliable features. In this paper, we propose a feature-guided Gaussian mixture model (GMM) to address these issues. We formulate point registration as the estimation of a feature-guided mixture of densities: A GMM is fitted to one point set, such that both the centers and local features of the Gaussian densities are constrained to coincide with the other point set. The problem is solved under a unified maximum-likelihood framework together with an iterative expectation-maximization algorithm initialized by the confident feature correspondences, where the image transformation is modeled by an affine function. Extensive experiments on various retinal images show the robustness of our approach, which consistently outperforms other state-of-the-art methods, especially when the data is badly degraded. PMID:27409682
CMB lensing and primordial squeezed non-gaussianity
Pearson, Ruth; Lewis, Antony; Regan, Donough E-mail: antony@cosmologist.info
2012-03-01
Squeezed primordial non-Gaussianity can strongly constrain early-universe physics, but it can only be observed on the CMB after it has been gravitationally lensed. We give a new simple non-perturbative prescription for accurately calculating the effect of lensing on any squeezed primordial bispectrum shape, and test it with simulations. We give the generalization to polarization bispectra, and discuss the effect of lensing on the trispectrum. We explain why neglecting the lensing smoothing effect does not significantly bias estimators of local primordial non-Gaussianity, even though the change in shape can be ∼>10%. We also show how τ{sub NL} trispectrum estimators can be well approximated by much simpler CMB temperature modulation estimators, and hence that there is potentially a ∼ 10–30% bias due to very large-scale lensing modes, depending on the range of modulation scales included. Including dipole sky modulations can halve the τ{sub NL} error bar if kinematic effects can be subtracted using known properties of the CMB temperature dipole. Lensing effects on the g{sub NL} trispectrum are small compared to the error bar. In appendices we give the general result for lensing of any primordial bispectrum, and show how any full-sky squeezed bispectrum can be decomposed into orthogonal modes of distinct angular dependence.
NASA Astrophysics Data System (ADS)
Adam, W.; Frühwirth, R.; Strandlie, A.; Todorov, T.
2005-09-01
The bremsstrahlung energy loss distribution of electrons propagating in matter is highly non-Gaussian. Because the Kalman filter relies solely on Gaussian probability density functions, it is not necessarily the optimal reconstruction algorithm for electron tracks. A Gaussian-sum filter (GSF) algorithm for electron reconstruction in the CMS tracker has therefore been developed and implemented. The basic idea is to model the bremsstrahlung energy loss distribution by a Gaussian mixture rather than by a single Gaussian. It is shown that the GSF is able to improve the momentum resolution of electrons compared to the standard Kalman filter. The momentum resolution and the quality of the error estimate are studied both with a fast simulation, modelling the radiative energy loss in a simplified detector, and the full CMS tracker simulation.
NASA Astrophysics Data System (ADS)
Wu, L.; Seo, D.; Demargne, J.; Brown, J. D.
2008-12-01
In this presentation, we describe generation of ensemble precipitation forecasts from single-value quantitative precipitation forecasts (QPF) via the mixed-type bivariate meta-Gaussian model (Herr and Krzysztofowicz 2005). Because of the intermittent nature of precipitation, it is necessary to model precipitation amount as a mixed variable. The joint distribution of single-value QPF and observed precipitation amounts may then be modeled by the mixed-type bivariate meta-Gaussian distribution. From the single-value QPF, one may generate ensemble precipitation forecasts by sampling from the conditional distribution of the mixed-type bivariate meta-Gaussian distribution. The marginal distributions of the meta-Gaussian distribution are estimated using the Gaussian kernel smoothing technique with a plug-in bandwidth selection procedure. This methodology attempts to capture the skill and uncertainty in the QPF. We present both dependent and independent validation results for selected river basins in the AB-, CN-, and MA-RFC areas.
Gaussian Process Modeling of Protein Turnover.
Rahman, Mahbubur; Previs, Stephen F; Kasumov, Takhar; Sadygov, Rovshan G
2016-07-01
We describe a stochastic model to compute in vivo protein turnover rate constants from stable-isotope labeling and high-throughput liquid chromatography-mass spectrometry experiments. We show that the often-used one- and two-compartment nonstochastic models allow explicit solutions from the corresponding stochastic differential equations. The resulting stochastic process is a Gaussian processes with Ornstein-Uhlenbeck covariance matrix. We applied the stochastic model to a large-scale data set from (15)N labeling and compared its performance metrics with those of the nonstochastic curve fitting. The comparison showed that for more than 99% of proteins, the stochastic model produced better fits to the experimental data (based on residual sum of squares). The model was used for extracting protein-decay rate constants from mouse brain (slow turnover) and liver (fast turnover) samples. We found that the most affected (compared to two-exponent curve fitting) results were those for liver proteins. The ratio of the median of degradation rate constants of liver proteins to those of brain proteins increased 4-fold in stochastic modeling compared to the two-exponent fitting. Stochastic modeling predicted stronger differences of protein turnover processes between mouse liver and brain than previously estimated. The model is independent of the labeling isotope. To show this, we also applied the model to protein turnover studied in induced heart failure in rats, in which metabolic labeling was achieved by administering heavy water. No changes in the model were necessary for adapting to heavy-water labeling. The approach has been implemented in a freely available R code. PMID:27229456
From particle counting to Gaussian tomography
NASA Astrophysics Data System (ADS)
Parthasarathy, K. R.; Sengupta, Ritabrata
2015-12-01
The momentum and position observables in an n-mode boson Fock space Γ(ℂn) have the whole real line ℝ as their spectrum. But the total number operator N has a discrete spectrum ℤ+ = {0, 1, 2,…}. An n-mode Gaussian state in Γ(ℂn) is completely determined by the mean values of momentum and position observables and their covariance matrix which together constitute a family of n(2n + 3) real parameters. Starting with N and its unitary conjugates by the Weyl displacement operators and operators from a representation of the symplectic group Sp(2n) in Γ(ℂn), we construct n(2n + 3) observables with spectrum ℤ+ but whose expectation values in a Gaussian state determine all its mean and covariance parameters. Thus measurements of discrete-valued observables enable the tomography of the underlying Gaussian state and it can be done by using five one-mode and four two-mode Gaussian symplectic gates in single and pair mode wires of Γ(ℂn) = Γ(ℂ)⊗n. Thus the tomography protocol admits a simple description in a language similar to circuits in quantum computation theory. Such a Gaussian tomography applied to outputs of a Gaussian channel with coherent input states permit a tomography of the channel parameters. However, in our procedure the number of counting measurements exceeds the number of channel parameters slightly. Presently, it is not clear whether a more efficient method exists for reducing this tomographic complexity. As a byproduct of our approach an elementary derivation of the probability generating function of N in a Gaussian state is given. In many cases the distribution turns out to be infinitely divisible and its underlying Lévy measure can be obtained. However, we are unable to derive the exact distribution in all cases. Whether this property of infinite divisibility holds in general is left as an open problem.
Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
Verde, Licia; Jimenez, Raul; Alvarez-Gaume, Luis; Heavens, Alan F.; Matarrese, Sabino E-mail: raul.jimenez@icc.ub.edu E-mail: a.heavens@imperial.ac.uk
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 ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.
Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
NASA Astrophysics Data System (ADS)
Verde, Licia; Jimenez, Raul; Alvarez-Gaume, Luis; Heavens, Alan F.; Matarrese, Sabino
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 fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.
Primordial non-Gaussianity in the bispectrum of the halo density field
Baldauf, Tobias; Seljak, Uroš; Senatore, Leonardo E-mail: seljak@physik.uzh.ch
2011-04-01
The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and their dependence on scale, shape and the non-Gaussianity parameter f{sub NL}. We compute the terms based on a multivariate bias expansion and the peak-background split method and show that non-Gaussian modifications to the bias parameters lead to amplifications of the tree level bispectrum that were ignored in previous studies. Our results are in a good agreement with published simulation measurements of the halo bispectrum. Finally, we estimate the expected signal to noise on f{sub NL} and show that the constraint obtainable from the bispectrum analysis significantly exceeds the one obtainable from the power spectrum analysis.
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.
Graphical calculus for Gaussian pure states
Menicucci, Nicolas C.; Flammia, Steven T.; Loock, Peter van
2011-04-15
We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.
Hydraulic Conductivity Fields: Gaussian or Not?
Meerschaert, Mark M.; Dogan, Mine; Van Dam, Remke L.; Hyndman, David W.; Benson, David A.
2013-01-01
Hydraulic conductivity (K) fields are used to parameterize groundwater flow and transport models. Numerical simulations require a detailed representation of the K field, synthesized to interpolate between available data. Several recent studies introduced high resolution K data (HRK) at the Macro Dispersion Experiment (MADE) site, and used ground-penetrating radar (GPR) to delineate the main structural features of the aquifer. This paper describes a statistical analysis of these data, and the implications for K field modeling in alluvial aquifers. Two striking observations have emerged from this analysis. The first is that a simple fractional difference filter can have a profound effect on data histograms, organizing non-Gaussian ln K data into a coherent distribution. The second is that using GPR facies allows us to reproduce the significantly non-Gaussian shape seen in real HRK data profiles, using a simulated Gaussian ln K field in each facies. This illuminates a current controversy in the literature, between those who favor Gaussian ln K models, and those who observe non-Gaussian ln K fields. Both camps are correct, but at different scales. PMID:24415806
Comparison of Gaussian and super Gaussian laser beams for addressing atomic qubits
NASA Astrophysics Data System (ADS)
Gillen-Christandl, Katharina; Gillen, Glen D.; Piotrowicz, M. J.; Saffman, M.
2016-05-01
We study the fidelity of single-qubit quantum gates performed with two-frequency laser fields that have a Gaussian or super Gaussian spatial mode. Numerical simulations are used to account for imperfections arising from atomic motion in an optical trap, spatially varying Stark shifts of the trapping and control beams, and transverse and axial misalignment of the control beams. Numerical results that account for the three-dimensional distribution of control light show that a super Gaussian mode with intensity I˜ e^{-2(r/w_0)^n} provides reduced sensitivity to atomic motion and beam misalignment. Choosing a super Gaussian with n=6 the decay time of finite temperature Rabi oscillations can be increased by a factor of 60 compared to an n=2 Gaussian beam, while reducing crosstalk to neighboring qubit sites.
A Gaussian field for aggregation and disaggregation of radar rainfall data
NASA Astrophysics Data System (ADS)
Krebsbach, Katharina; Friederichs, Petra
2014-05-01
The generation of reliable precipitation products that explicitly account for spatial and temporal structures of precipitation events is challenging, since it requires a combination of data with a variety of error structures and temporal resolutions. In-situ measurements are relatively accurate quantities, but available only at sparse and irregularly distributed locations. Remote measurements cover complete areas but suffer from spatially and temporally inhomogeneous systematic errors and non-linear relations between the measured value reflectivity and the precipitation rate. Our aim is to provide a statistical model based on a latent Gaussian random field that suitably models radar precipitation rates and enables us to aggregate and disaggregate them in space and time. We first transform radar rainfall rates such that they follow a truncated Gaussian distribution using a power transformation proposed by D. Allcroft and C. Glasbey (2003). The advantage of using a truncated Gaussian random field is that occurrence and intensity of rainfall are modeled using a single process. To parameterize the latent Gaussian random field we estimate the empirical correlation as function of lag distance in space using the maximum likelihood method and fit a parametric correlation function to the estimates. This yields a spatial Gaussian random field. The transformation only allocates censored values to dry locations, i.e. the locations below some threshold. In order to obtain a Gaussian random field that covers the whole domain, we need to simulate the unobserved values below the threshold conditional on the observed values. The parametrically defined Gaussian random field now allows us to aggregate and disaggregate the radar measurements to different scales and compare them to measurements from ground based instruments.
Cochlear toughening, protection, and potentiation of noise-induced trauma by non-Gaussian noise
NASA Astrophysics Data System (ADS)
Hamernik, Roger P.; Qiu, Wei; Davis, Bob
2003-02-01
An interrupted noise exposure of sufficient intensity, presented on a daily repeating cycle, produces a threshold shift (TS) following the first day of exposure. TSs measured on subsequent days of the exposure sequence have been shown to decrease relative to the initial TS. This reduction of TS, despite the continuing daily exposure regime, has been called a cochlear toughening effect and the exposures referred to as toughening exposures. Four groups of chinchillas were exposed to one of four different noises presented on an interrupted (6 h/day for 20 days) or noninterrupted (24 h/day for 5 days) schedule. The exposures had equivalent total energy, an overall level of 100 dB(A) SPL, and approximately the same flat, broadband long-term spectrum. The noises differed primarily in their temporal structures; two were Gaussian and two were non-Gausssian, nonstationary. Brainstem auditory evoked potentials were used to estimate hearing thresholds and surface preparation histology was used to determine sensory cell loss. The experimental results presented here show that: (1) Exposures to interrupted high-level, non-Gaussian signals produce a toughening effect comparable to that produced by an equivalent interrupted Gaussian noise. (2) Toughening, whether produced by Gaussian or non-Gaussian noise, results in reduced trauma compared to the equivalent uninterrupted noise, and (3) that both continuous and interrupted non-Gaussian exposures produce more trauma than do energy and spectrally equivalent Gaussian noises. Over the course of the 20-day exposure, the pattern of TS following each day's exposure could exhibit a variety of configurations. These results do not support the equal energy hypothesis as a unifying principal for estimating the potential of a noise exposure to produce hearing loss.
Gaussian entanglement in the turbulent atmosphere
NASA Astrophysics Data System (ADS)
Bohmann, M.; Semenov, A. A.; Sperling, J.; Vogel, W.
2016-07-01
We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a nontrivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.
Gaussian state for the bouncing quantum cosmology
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Piechocki, Włodzimierz
2012-10-01
We present results concerning propagation of the Gaussian state across the cosmological quantum bounce. The reduced phase space quantization of loop quantum cosmology is applied to the Friedman-Robertson-Walker universe with a free massless scalar field. Evolution of quantum moments of the canonical variables is investigated. The covariance turns out to be a monotonic function so it may be used as an evolution parameter having quantum origin. We show that for the Gaussian state the Universe is least quantum at the bounce. We propose explanation of this counter-intuitive feature using the entropy of squeezing. The obtained time dependence of entropy is in agreement with qualitative predictions based on von Neumann entropy for mixed states. We show that, for the considered Gaussian state, semiclassicality is preserved across the bounce, so there is no cosmic forgetfulness.
Gaussian beam photothermal single particle microscopy.
Selmke, Markus; Braun, Marco; Cichos, Frank
2012-10-01
We explore the intuitive lensing picture of laser-heated nanoparticles occurring in single particle photothermal (PT) microscopy. The effective focal length of the thermal lens (TL) is derived from a ray-optics treatment and used to transform the probing focused Gaussian beam with ABCD Gaussian matrix optics. The relative PT signal is obtained from the relative beam-waist change far from the TL. The analytical expression is semiquantitative, capable of describing the entire phenomenology of single particle PT microscopy, and shows that the signal is the product of the point-spread functions of the involved lasers times a linear function of the axial coordinate. The presented particularly simple and intuitive Gaussian beam lensing picture compares favorably to the experimental results for 60 nm gold nanoparticles and provides the prescription for optimum setup calibration. PMID:23201674
Tilted Gaussian beam propagation in inhomogeneous media.
Hadad, Yakir; Melamed, Timor
2010-08-01
The present work is concerned with applying a ray-centered non-orthogonal coordinate system which is a priori matched to linearly-phased localized aperture field distributions. The resulting beam-waveobjects serve as the building blocks for beam-type spectral expansions of aperture fields in 2D inhomogeneous media that are characterized by a generic wave-velocity profile. By applying a rigorous paraxial-asymptotic analysis, a novel parabolic wave equation is obtained and termed "Non-orthogonal domain parabolic equation"--NoDope. Tilted Gaussian beams, which are exact solutions to this equation, match Gaussian aperture distributions over a plane that is tilted with respect to the beam-axes initial directions. A numerical example, which demonstrates the enhanced accuracy of the tilted Gaussian beams over the conventional ones, is presented as well. PMID:20686589
Ab initio molar volumes and Gaussian radii.
Parsons, Drew F; Ninham, Barry W
2009-02-12
Ab initio molar volumes are calculated and used to derive radii for ions and neutral molecules using a spatially diffuse model of the electron distribution with Gaussian spread. The Gaussian radii obtained can be used for computation of nonelectrostatic ion-ion dispersion forces that underlie Hofmeister specific ion effects. Equivalent hard-sphere radii are also derived, and these are in reasonable agreement with crystalline ionic radii. The Born electrostatic self-energy is derived for a Gaussian model of the electronic charge distribution. It is shown that the ionic volumes used in electrostatic calculations of strongly hydrated cosmotropic ions ought best to include the first hydration shell. Ionic volumes for weakly hydrated chaotropic metal cations should exclude electron overlap (in electrostatic calculations). Spherical radii are calculated as well as nonisotropic ellipsoidal radii for nonspherical ions, via their nonisotropic static polarizability tensors. PMID:19140766
Partially polarized Gaussian Schell-model beams
NASA Astrophysics Data System (ADS)
Gori, F.; Santarsiero, M.; Piquero, G.; Borghi, R.; Mondello, A.; Simon, R.
2001-01-01
We consider a class of beams that are both partially polarized and partially coherent from the spatial standpoint. They are characterized by a correlation matrix whose elements have the same form as the mutual intensity of a Gaussian Schell-model beam. We focus our attention on those beams that would appear identical to ordinary Gaussian Schell-model beams in a scalar treatment. After establishing some inequalities that limit the choice of the matrix parameters, we study the main effects of propagation. Starting from the source plane, in which the beam is assumed to be uniformly polarized, we find that in the course of propagation the degree of polarization generally becomes non-uniform across a typical section of the beam. Furthermore, we find that the intensity distribution at the output of an arbitrarily oriented linear polarizer is Gaussian shaped at the source plane whereas it can be quite different at other planes.
Index distribution of gaussian random matrices.
Majumdar, Satya N; Nadal, Céline; Scardicchio, Antonello; Vivo, Pierpaolo
2009-11-27
We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N+) of a random N x N matrix belonging to Gaussian orthogonal (beta=1), unitary (beta=2) or symplectic (beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N+/N scales, for large N, as P(c,N) approximately = exp[-betaN(2)Phi(c)] where the rate function Phi(c), symmetric around c=1/2 and universal (independent of beta), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at c=1/2 it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function. PMID:20366083
Majorization preservation of Gaussian bosonic channels
NASA Astrophysics Data System (ADS)
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2016-07-01
It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics.
Index Distribution of Gaussian Random Matrices
Majumdar, Satya N.; Nadal, Celine; Scardicchio, Antonello; Vivo, Pierpaolo
2009-11-27
We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N{sub +}) of a random NxN matrix belonging to Gaussian orthogonal (beta=1), unitary (beta=2) or symplectic (beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N{sub +}/N scales, for large N, as P(c,N){approx_equal}exp[-betaN{sup 2}PHI(c)] where the rate function PHI(c), symmetric around c=1/2 and universal (independent of beta), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at c=1/2 it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function.
CMB non-gaussianity from vector fields
Peloso, Marco
2014-01-01
The Planck satellite has recently measured the CMB temperature anisotropies with unprecedented accuracy, and it has provided strong bounds on primordial non-gaussianity. Such bounds constrain models of inflation, and mechanisms that produce the primordial perturbations. We discuss the non-gaussian signatures from the interactions of the inflation φ with spin-1 fields. We study the two different cases in which the inflaton is (i) a pseudo-scalar field with a (φ)/(fa) F·F interaction with a vector field, and (ii) a scalar field with a f (φ)F² interaction. In the first case we obtain the strong limit f{sub a} ≥ 10¹⁶GeV on the decay constant. In the second case, specific choices of the function f (φ) can lead to a non-gaussianity with a characteristic shape not encountered in standard models of scalar field inflation, and which has also been constrained by Planck.
Informationally complete sets of Gaussian measurements
NASA Astrophysics Data System (ADS)
Kiukas, Jukka; Schultz, Jussi
2013-12-01
We prove the necessary and sufficient conditions for the informational completeness of an arbitrary set of Gaussian observables on continuous variable systems with a finite number of degrees of freedom. In particular, we show that an informationally complete set either contains a single informationally complete observable, or includes infinitely many observables. We show that for a single informationally complete observable, the minimal outcome space is the phase space, and the corresponding probability distribution can always be obtained from the quantum optical Q-function by linear postprocessing and Gaussian convolution, in a suitable symplectic coordinatization of the phase space. In the case of projection valued Gaussian observables, e.g., generalized field quadratures, we show that an informationally complete set of observables is necessarily infinite. Finally, we generalize the treatment to the case where the measurement coupling is given by a general linear bosonic channel, and characterize informational completeness for an arbitrary set of the associated observables.
NASA Astrophysics Data System (ADS)
Mancini, L.
2009-03-01
Aims: We discuss whether the Gaussian is a reasonable approximation of the velocity distribution of stellar systems that are not spherically distributed. Methods: By using a non-Gaussian velocity distribution to describe the sources in the Large Magellanic Cloud (LMC), we reinvestigate the expected microlensing parameters of a lens population isotropically distributed either in the Milky Way halo or in the LMC (self lensing). We compare our estimates with the experimental results of the MACHO collaboration. Results: An interesting result that emerges from our analysis is that, moving from the Gaussian to the non-Gaussian case, we do not observe any change in the form of the distribution curves describing the rate of microlensing events for lenses in the Galactic halo. The corresponding expected timescales and number of expected events also do not vary. Conversely, with respect to the self-lensing case, we observe a moderate increase in the rate and number of expected events. We conclude that the error in the estimate of the most likely value for the MACHO mass and the Galactic halo fraction in form of MACHOs, calculated with a Gaussian velocity distribution for the LMC sources, is not higher than 2%.
METHODS FOR ESTIMATING ON-SITE AMBIENT AIR CONCENTRATIONS AT DISPOSAL SITES
Currently, Gaussian type dispersion modeling and point source approximation are combined to estimate the ambient air concentrations of pollutants dispersed downwind of an areawide emission source, using the approach of virtual point source approximation. The Gaussian dispersion m...
From weak lensing to non-Gaussianity via Minkowski functionals
NASA Astrophysics Data System (ADS)
Munshi, Dipak; van Waerbeke, Ludovic; Smidt, Joseph; Coles, Peter
2012-01-01
We present a new harmonic-domain-based approach for extracting morphological information, in the form of Minkowski functionals (MFs), from weak-lensing convergence maps. Using a perturbative expansion of the MFs, which is expected to be valid for the range of angular scales probed by most current weak-lensing surveys, we show that the study of three generalized skewness parameters is equivalent to the study of the three MFs defined in 2D. We then extend these skewness parameters to three associated skew spectra which carry more information about the convergence bispectrum than their one-point counterparts. We discuss various issues such as noise and incomplete sky coverage in the context of estimation of these skew spectra from realistic data. Our technique provides an alternative to the pixel-space approaches typically used in the estimation of MFs, and it can be particularly useful in the presence of masks with non-trivial topology. Analytical modelling of weak-lensing statistics relies on an accurate modelling of the statistics of the underlying density distribution. We apply three different formalisms to model the underlying dark matter bispectrum: the hierarchical ansatz, halo model and a fitting function based on numerical simulations; MFs resulting from each of these formalisms are computed and compared. We investigate the extent to which late-time gravity-induced non-Gaussianity (to which weak lensing is primarily sensitive) can be separated from primordial non-Gaussianity and how this separation depends on source redshift and angular scale.
Learning Gaussian mixture models with entropy-based criteria.
Penalver Benavent, Antonio; Escolano Ruiz, Francisco; Saez, Juan Manuel
2009-11-01
In this paper, we address the problem of estimating the parameters of Gaussian mixture models. Although the expectation-maximization (EM) algorithm yields the maximum-likelihood (ML) solution, its sensitivity to the selection of the starting parameters is well-known and it may converge to the boundary of the parameter space. Furthermore, the resulting mixture depends on the number of selected components, but the optimal number of kernels may be unknown beforehand. We introduce the use of the entropy of the probability density function (pdf) associated to each kernel to measure the quality of a given mixture model with a fixed number of kernels. We propose two methods to approximate the entropy of each kernel and a modification of the classical EM algorithm in order to find the optimum number of components of the mixture. Moreover, we use two stopping criteria: a novel global mixture entropy-based criterion called Gaussianity deficiency (GD) and a minimum description length (MDL) principle-based one. Our algorithm, called entropy-based EM (EBEM), starts with a unique kernel and performs only splitting by selecting the worst kernel attending to GD. We have successfully tested it in probability density estimation, pattern classification, and color image segmentation. Experimental results improve the ones of other state-of-the-art model order selection methods. PMID:19770090
Non-Gaussian Error Distributions of LMC Distance Moduli Measurements
NASA Astrophysics Data System (ADS)
Crandall, Sara; Ratra, Bharat
2015-12-01
We construct error distributions for a compilation of 232 Large Magellanic Cloud (LMC) distance moduli values from de Grijs et al. that give an LMC distance modulus of (m - M)0 = 18.49 ± 0.13 mag (median and 1σ symmetrized error). Central estimates found from weighted mean and median statistics are used to construct the error distributions. The weighted mean error distribution is non-Gaussian—flatter and broader than Gaussian—with more (less) probability in the tails (center) than is predicted by a Gaussian distribution; this could be the consequence of unaccounted-for systematic uncertainties. The median statistics error distribution, which does not make use of the individual measurement errors, is also non-Gaussian—more peaked than Gaussian—with less (more) probability in the tails (center) than is predicted by a Gaussian distribution; this could be the consequence of publication bias and/or the non-independence of the measurements. We also construct the error distributions of 247 SMC distance moduli values from de Grijs & Bono. We find a central estimate of {(m-M)}0=18.94+/- 0.14 mag (median and 1σ symmetrized error), and similar probabilities for the error distributions.
Gaussian Molecular Dynamics in Imaginary and Real Time
NASA Astrophysics Data System (ADS)
Georgescu, Ionut; Mandelshtam, Vladimir
2010-03-01
The variational Gaussian wavepacket (VGW) method can be used to estimate the equilibrium density matrix by propagating Gaussian wavepackets in imaginary time [1,2]. It has proven to be practically accurate and computationally less expensive than the path integral methods. We compare the VGW method to the Feynman-Kleinert approximation (FKA), which has comparable computational cost. Although both methods are variational, they utilize different variational principles: In FKA the partition function is optimized, while in VGW it is the imaginary-time-dependent wave packet. We show that the VGW method is more accurate for a wide variety of systems. The differences are particularly important when thermodynamic properties, such as heat capacity, are of main interest. Moreover, unlike the case of FKA, in the VGW method the imaginary frequencies do not arise. In the spirit of the Centroid Molecular Dynamics the VGW method has also been extended to simulate the real-time dynamics, e.g., it can be used to estimate the Kubo-transformed quantum time correlation functions. The latter are exact in the high-temperature and harmonic limits. [1] P. Frantsuzov and V.A. Mandelshtam, J. Chem. Phys 121, 9247 (2004)[2] C. Predescu, P. Frantsuzov and V.A. Mandelshtam J. Chem. Phys 122, 154305 (2005)
Entropic characterization of separability in Gaussian states
Sudha; Devi, A. R. Usha; Rajagopal, A. K.
2010-02-15
We explore separability of bipartite divisions of mixed Gaussian states based on the positivity of the Abe-Rajagopal (AR) q-conditional entropy. The AR q-conditional entropic characterization provide more stringent restrictions on separability (in the limit q{yields}{infinity}) than that obtained from the corresponding von Neumann conditional entropy (q=1 case)--similar to the situation in finite dimensional states. Effectiveness of this approach, in relation to the results obtained by partial transpose criterion, is explicitly analyzed in three illustrative examples of two-mode Gaussian states of physical significance.
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-12-15
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Gaussian quadrature formulae for arbitrary positive measures.
Fernandes, Andrew D; Atchley, William R
2006-01-01
We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student's t, inverse-gamma, beta, and Fisher's F) we present exact formulae for computing the respective quadrature scheme. PMID:19455218
Fresnel filtering of Gaussian beams in microcavities.
Shinohara, Susumu; Harayama, Takahisa; Fukushima, Takehiro
2011-03-15
We study the output from the modes described by the superposition of Gaussian beams confined in the quasi-stadium microcavities. We experimentally observe the deviation from Snell's law in the output when the incident angle of the Gaussian beam at the cavity interface is near the critical angle for total internal reflection, providing direct experimental evidence on the Fresnel filtering. The theory of the Fresnel filtering for a planar interface qualitatively reproduces experimental data, and a discussion is given on small deviation between the measured data and the theory. PMID:21403763
TUPOS: A MULTIPLE SOURCE GAUSSIAN DISPERSION ALGORITHM USING ON-SITE TURBULENCE DATA
TUPOS and its postprocessor, TUPOS-P, form a Gaussian model which resembles MPTER but offers several technical improvements. TUPOS estimates dispersion directly from fluctuation statistics at plume level and calculates plume rise and partial penetration of the plume into stable l...
NASA Astrophysics Data System (ADS)
Ji, Se-Wan; Kim, M. S.; Nha, Hyunchul
2015-04-01
It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous manner is relevant to study it under certain circumstances and here we address quantum steerability of Gaussian states to this aim. In particular, we attempt to reformulate the criterion for Gaussian steering in terms of local and global purities and show that it is sufficient and necessary for the case of steering a 1-mode system by an N-mode system. It subsequently enables us to reinforce a strong monogamy relation under which only one party can steer a local system of 1-mode. Moreover, we show that only a negative partial-transpose state can manifest quantum steerability by Gaussian measurements in relation to the Peres conjecture. We also discuss our formulation for the case of distributing a two-mode squeezed state via one-way quantum channels making dissipation and amplification effects, respectively. Finally, we extend our approach to include non-Gaussian measurements, more precisely, all orders of higher-order squeezing measurements, and find that this broad set of non-Gaussian measurements is not useful to demonstrate steering for Gaussian states beyond Gaussian measurements.
Encoding information using Laguerre Gaussian modes
NASA Astrophysics Data System (ADS)
Trichili, Abderrahmen; Dudley, Angela; Ben Salem, Amine; Ndagano, Bienvenu; Zghal, Mourad; Forbes, Andrew
2015-08-01
We experimentally demonstrate an information encoding protocol using the two degrees of freedom of Laguerre Gaussian modes having different radial and azimuthal components. A novel method, based on digital holography, for information encoding and decoding using different data transmission scenarios is presented. The effects of the atmospheric turbulence introduced in free space communication is discussed as well.
The Gaussian entropy of fermionic systems
Prokopec, Tomislav; Schmidt, Michael G.; Weenink, Jan
2012-12-15
We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of these correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence and classicalization. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields. - Highlights: Black-Right-Pointing-Pointer We construct the Gaussian density operator for relativistic fermionic systems. Black-Right-Pointing-Pointer The Gaussian entropy of relativistic fermionic systems is described in terms of 2-point correlators. Black-Right-Pointing-Pointer We explicitly show the growth of entropy for fermionic fields mixing with a thermal fermionic environment.
Diffusion of Super-Gaussian Profiles
ERIC Educational Resources Information Center
Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.
2007-01-01
The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…
Multi-output local Gaussian process regression: Applications to uncertainty quantification
NASA Astrophysics Data System (ADS)
Bilionis, Ilias; Zabaras, Nicholas
2012-07-01
We develop an efficient, Bayesian Uncertainty Quantification framework using a novel treed Gaussian process model. The tree is adaptively constructed using information conveyed by the observed data about the length scales of the underlying process. On each leaf of the tree, we utilize Bayesian Experimental Design techniques in order to learn a multi-output Gaussian process. The constructed surrogate can provide analytical point estimates, as well as error bars, for the statistics of interest. We numerically demonstrate the effectiveness of the suggested framework in identifying discontinuities, local features and unimportant dimensions in the solution of stochastic differential equations.
Procedures for the measurement of the extinction cross section of one particle using a Gaussian beam
NASA Astrophysics Data System (ADS)
Bosch, Salvador; Sancho-Parramon, Jordi
2016-09-01
Two procedures for the measurement of the extinction cross section (ECS) of one particle using a slightly focused Gaussian beam have been introduced and numerically tested. While the first one relies on previously introduced ideas and has close connection with the optical theorem, the second procedure is new and is mostly related with light measurements where the detector collects much of the energy of the incident beam. Both procedures prove to be valid and somehow complementary up to particle sizes of the order of the beam waist, thus enlarging the capability of simple measurement set-ups based on Gaussian beams for the estimation of the ECS of one particle.
Gaussian benchmark for optical communication aiming towards ultimate capacity
NASA Astrophysics Data System (ADS)
Lee, Jaehak; Ji, Se-Wan; Park, Jiyong; Nha, Hyunchul
2016-05-01
We establish the fundamental limit of communication capacity within Gaussian schemes under phase-insensitive Gaussian channels, which employ multimode Gaussian states for encoding and collective Gaussian operations and measurements for decoding. We prove that this Gaussian capacity is additive, i.e., its upper bound occurs with separable encoding and separable receivers so that a single-mode communication suffices to achieve the largest capacity under Gaussian schemes. This rigorously characterizes the gap between the ultimate Holevo capacity and the capacity within Gaussian communication, showing that Gaussian regime is not sufficient to achieve the Holevo bound particularly in the low-photon regime. Furthermore, the Gaussian benchmark established here can be used to critically assess the performance of non-Gaussian protocols for optical communication. We move on to identify non-Gaussian schemes to beat the Gaussian capacity and show that a non-Gaussian receiver recently implemented by Becerra et al. [F. E. Becerra et al., Nat. Photon. 7, 147 (2013), 10.1038/nphoton.2012.316] can achieve this aim with an appropriately chosen encoding strategy.
Multi-resolution low-power Gaussian filtering by reconfigurable focal-plane binning
NASA Astrophysics Data System (ADS)
Fernández-Berni, J.; Carmona-Galán, R.; Pozas-Flores, F.; Zarándy, Á.; Rodríguez-Vázquez, Á.
2011-05-01
Gaussian filtering is a basic tool for image processing. Noise reduction, scale-space generation or edge detection are examples of tasks where different Gaussian filters can be successfully utilized. However, their implementation in a conventional digital processor by applying a convolution kernel throughout the image is quite inefficient. Not only the value of every single pixel is taken into consideration sucessively, but also contributions from their neighbors need to be taken into account. Processing of the frame is serialized and memory access is intensive and recurrent. The result is a low operation speed or, alternatively, a high power consumption. This inefficiency is specially remarkable for filters with large variance, as the kernel size increases significantly. In this paper, a different approach to achieve Gaussian filtering is proposed. It is oriented to applications with very low power budgets. The key point is a reconfigurable focal-plane binning. Pixels are grouped according to the targeted resolution by means of a division grid. Then, two consecutive shifts of this grid in opposite directions carry out the spread of information to the neighborhood of each pixel in parallel. The outcome is equivalent to the application of a 3×3 binomial filter kernel, which in turns is a good approximation of a Gaussian filter, on the original image. The variance of the closest Gaussian filter is around 0.5. By repeating the operation, Gaussian filters with larger variances can be achieved. A rough estimation of the necessary energy for each repetition until reaching the desired filter is below 20nJ for a QCIF-size array. Finally, experimental results of a QCIF proofof- concept focal-plane array manufactured in 0.35μm CMOS technology are presented. A maximum RMSE of only 1.2% is obtained by the on-chip Gaussian filtering with respect to the corresponding equivalent ideal filter implemented off-chip.
Shamis, Mira
2013-11-15
We use the supersymmetric formalism to derive an integral formula for the density of states of the Gaussian Orthogonal Ensemble, and then apply saddle-point analysis to give a new derivation of the 1/N-correction to Wigner's law. This extends the work of Disertori on the Gaussian Unitary Ensemble. We also apply our method to the interpolating ensembles of Mehta–Pandey.
A Network of Kalman Filters for MAI and ISI Compensation in a Non-Gaussian Environment
NASA Astrophysics Data System (ADS)
Sayadi, Bessem; Marcos, Sylvie
2005-12-01
This paper develops a new multiuser detector based on a network of kalman filters (NKF) dealing with multiple access-interference (MAI), intersymbol Interference (ISI), and an impulsive observation noise. The two proposed schemes are based on the modeling of the DS-CDMA system by a discrete-time linear system that has non-Gaussian state and measurement noises. By approximating the non-Gaussian densities of the noises by a weighted sum of Gaussian terms and under the common MMSE estimation criterion, we first derive an NKF detector. This version is further optimized by introducing a feedback exploiting the ISI interference structure. The resulting scheme is an NKF detector based on a likelihood ratio test (LRT). Monte-Carlo simulations have shown that the NKF and the NKF based on LRT detectors significantly improve the efficiency and the performance of the classical Kalman algorithm.
Quantum Fisher information on two manifolds of two-mode Gaussian states
NASA Astrophysics Data System (ADS)
Marian, Paulina; Marian, Tudor A.
2016-05-01
We investigate two special classes of two-mode Gaussian states of light that are important from both the experimental and theoretical points of view: the mode-mixed thermal states and the squeezed thermal ones. Aiming to a parallel study, we write the Uhlmann fidelity between pairs of states belonging to each class in terms of their defining parameters. The quantum Fisher information matrices on the corresponding four-dimensional manifolds are diagonal and allow insightful parameter estimation. The scalar curvatures of the Bures metric on both Riemannian manifolds of special two-mode Gaussian states are evaluated and discussed. They are functions of two variables, namely, the mean numbers of photons in the incident thermal modes. Our comparative analysis opens the door to further investigation of the interplay between geometry and statistics for Gaussian states produced in simple optical devices.
Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
Monras, Alex; Illuminati, Fabrizio
2011-01-15
We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than coherent, thermal, or single-mode squeezed states. This suggests that at high-energy regimes, two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result indicates a stronger form of compatibility for the estimation of the two parameters. Indeed, not only the minimum variance can be achieved at fixed probe states, but also the optimal state is common to both parameters. Additionally, we explore numerically the performance of non-Gaussian states for particular parameter values to find that maximally entangled states within d-dimensional cutoff subspaces (d{<=}6) perform better than any randomly sampled states with similar energy. However, we also find that states with very similar performance and energy exist with much less entanglement than the maximally entangled ones.
Measurement of primordial non-Gaussianity using the WMAP 5-year temperature skewness power spectrum
Smidt, Joseph; Amblard, Alexandre; Serra, Paolo; Cooray, Asantha
2009-12-15
We constrain the primordial non-Gaussianity parameter of the local model f{sub NL} using the skewness power spectrum associated with the two-to-one cumulant correlator of cosmic microwave background temperature anisotropies. This bispectrum-related power spectrum was constructed after weighting the temperature map with the appropriate window functions to form an estimator that probes the multipolar dependence of the underlying bispectrum associated with the primordial non-Gaussianity. We also estimate a separate skewness power spectrum sensitive more strongly to unresolved point sources. When compared to previous attempts at measuring the primordial non-Gaussianity with WMAP data, our estimators have the main advantage that we do not collapse information to a single number. When model fitting the two-to-one skewness power spectrum, we make use of bispectra generated by the primordial non-Gaussianity, radio point sources, and lensing-secondary correlation. We analyze Q, V, and W-band WMAP 5-year data using the KQ75 mask out to l{sub max}=600. Using V and W-band data and marginalizing over model parameters related to point sources and lensing-secondary bispectrum, our overall and preferred constraint on f{sub NL} is 11.0{+-}23.7 at the 68% confidence level (-36.4
BER of Gaussian beam propagation in non-Kolmogorov turbulent atmosphere on slant path
NASA Astrophysics Data System (ADS)
Yang, Rui-ke; Chen, Yuan; Hou, Jie; Chen, Hui
2013-08-01
The propagation characteristic of a Gaussian beam through turbulent atmosphere have been studied in the past several years. The main advantage of Gaussian beam wave model is that the infinite plant wave and a spherical wave are being included. Non-Kolmogorov spectrum can describe generalized turbulent atmosphere environment. The propagation properties of Gaussian beam propagating through the turbulent atmosphere described by non-Kolmogorov spectrum are studied on slant path. The scintillation index is analyzed with the Gaussian beam of different turbulent strength, zenith angle, φ , and the spectral exponent, α, of non-Kolmogorov, respectively. The effect of the turbulent structure constant on the ground on sicntillation is notable. The scintillation index reduces remarkably with zenith angle and structure parameter decrease. At weak turbulenc, scintillation index increases as spectral exponent decreases. The bit error rate (BER) of a Gaussian beam propagating in non-Kolmogorov atmospheric turbulence channel is estimated on Earth-space slant path. By comparing the effect of the spectral power with the structure constant on BER at moderate and strong turbulence, the effect of the spectral power change on BER is small. With turbulence weakening , at the order of 10-15m-2/3 , the relative effect of the spectral power on BER is gradually increase. Hence, at the small structure constant on the ground, or weak turbulence, the effect of the turbulent spectral power on BER is required to take into account.
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.
Constraining primordial non-Gaussianity with high-redshift probes
Xia, Jun-Qing; Baccigalupi, Carlo; Bonaldi, Anna; Zotti, Gianfranco De; Matarrese, Sabino; Verde, Licia; Viel, Matteo E-mail: anna.bonaldi@oapd.inaf.it E-mail: gianfranco.dezotti@oapd.inaf.it E-mail: liciaverde@icc.ub.edu
2010-08-01
We present an analysis of the constraints on the amplitude of primordial non-Gaussianity of local type described by the dimensionless parameter f{sub NL}. These constraints are set by the auto-correlation functions (ACFs) of two large scale structure probes, the radio sources from NRAO VLA Sky Survey (NVSS) and the QSO catalogue of Sloan Digital Sky Survey Release Six (SDSS DR6 QSOs), as well as by their cross-correlation functions (CCFs) with the cosmic microwave background (CMB) temperature map (Integrated Sachs-Wolfe effect). Several systematic effects that may affect the observational estimates of the ACFs and of the CCFs are investigated and conservatively accounted for. Our approach exploits the large-scale scale-dependence of the non-Gaussian halo bias. The derived constraints on (f{sub NL}) coming from the NVSS CCF and from the QSO ACF and CCF are weaker than those previously obtained from the NVSS ACF, but still consistent with them. Finally, we obtain the constraints on f{sub NL} = 53±25 (1 σ) and f{sub NL} = 58±24 (1 σ) from NVSS data and SDSS DR6 QSO data, respectively.
Non-Gaussianity from self-ordering scalar fields
Figueroa, Daniel G.; Kamionkowski, Marc
2010-06-15
The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and provide a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges k{sub 1{approx_equal}}2k{sub 2{approx_equal}}2k{sub 3}) as opposed to the local-model bispectrum, which peaks for squeezed triangles (k{sub 1{approx_equal}}k{sub 2}>>k{sub 3}), and the equilateral bispectrum, which peaks at k{sub 1{approx_equal}}k{sub 2{approx_equal}}k{sub 3}. We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit.
Power spectrum and non-Gaussianities in anisotropic inflation
Dey, Anindya; Kovetz, Ely D.; Paban, Sonia E-mail: elykovetz@gmail.com
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. We 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.
USER'S GUIDE FOR PAL 2.0: A GAUSSIAN-PLUME ALGORITHM FOR POINT, AREA, AND LINE SOURCES
PAL is an acronym for the Point, Area, and Line source algorithm. PAL is a method of estimating short-term dispersion using Gaussian-plume steady state assumptions. The algorithm can be used for estimating concentrations of non-reactive pollutants at 99 receptors for averaging ti...
NASA Astrophysics Data System (ADS)
Meerburg, P. Daniel; Meyers, Joel; van Engelen, Alexander; Ali-Haïmoud, Yacine
2016-06-01
We study the degree to which the cosmic microwave background (CMB) can be used to constrain primordial non-Gaussianity involving one tensor and two scalar fluctuations, focusing on the correlation of one polarization B mode with two temperature modes. In the simplest models of inflation, the tensor-scalar-scalar primordial bispectrum is nonvanishing and is of the same order in slow-roll parameters as the scalar-scalar-scalar bispectrum. We calculate the ⟨B T T ⟩ correlation arising from a primordial tensor-scalar-scalar bispectrum, and show that constraints from an experiment like CMB-Stage IV using this observable are more than an order of magnitude better than those on the same primordial coupling obtained from temperature measurements alone. We argue that B -mode non-Gaussianity opens up an as-yet-unexplored window into the early Universe, demonstrating that significant information on primordial physics remains to be harvested from CMB anisotropies.
Quantum Fidelity for Arbitrary Gaussian States
NASA Astrophysics Data System (ADS)
Banchi, Leonardo; Braunstein, Samuel L.; Pirandola, Stefano
2015-12-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
A Fast Incremental Gaussian Mixture Model
Pinto, Rafael Coimbra; Engel, Paulo Martins
2015-01-01
This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of O(NKD3) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this work, we manage to reduce this complexity to O(NKD2) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets. PMID:26444880
Fock expansion of multimode pure Gaussian states
Cariolaro, Gianfranco; Pierobon, Gianfranco
2015-12-15
The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, as shown for two-mode and three-mode Gaussian states.
Quantum Fidelity for Arbitrary Gaussian States.
Banchi, Leonardo; Braunstein, Samuel L; Pirandola, Stefano
2015-12-31
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources. PMID:26764978
Gaussian fidelity distorted by external fields
NASA Astrophysics Data System (ADS)
Santos, Jonas F. G.; Bernardini, Alex E.
2016-03-01
Gaussian state decoherence aspects due to interacting magnetic-like and gravitational fields are quantified through the quantum fidelity and Shannon entropy in the scope of the phase-space representation of elementary quantum systems. For Gaussian Wigner functions describing harmonic oscillator states, an interacting external field destroys the quantum fidelity and introduces a quantum beating behavior. Likewise, it introduces harmonic profiles for free particle systems. Some aspects of quantum decoherence for the quantum harmonic oscillator and for the free particle limit are also quantified through the Shannon entropy. For the gravitational quantum well, the effect of a magnetic-like field on the quantum fidelity is suppressed by the linear term of the gravitational potential. To conclude, one identifies a fine formal connection of the quantum decoherence aspects discussed here with the noncommutative quantum mechanics.
2010-01-01
Background Liquid chromatography-mass spectrometry (LC-MS) is one of the major techniques for the quantification of metabolites in complex biological samples. Peak modeling is one of the key components in LC-MS data pre-processing. Results To quantify asymmetric peaks with high noise level, we developed an estimation procedure using the bi-Gaussian function. In addition, to accurately quantify partially overlapping peaks, we developed a deconvolution method using the bi-Gaussian mixture model combined with statistical model selection. Conclusions Using extensive simulations and real data, we demonstrated the advantage of the bi-Gaussian mixture model over the Gaussian mixture model and the method of kernel smoothing combined with signal summation in peak quantification and deconvolution. The method is implemented in the R package apLCMS: http://www.sph.emory.edu/apLCMS/. PMID:21073736
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
Microwave Realization of the Gaussian Symplectic Ensemble.
Rehemanjiang, A; Allgaier, M; Joyner, C H; Müller, S; Sieber, M; Kuhl, U; Stöckmann, H-J
2016-08-01
Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)], a microwave graph with an antiunitary symmetry T obeying T^{2}=-1 is realized. The Kramers doublets expected for such systems are clearly identified and can be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble expected for chaotic systems with such a symmetry. PMID:27541466
Talbot effect in Gaussian optical systems
Kandidov, V P; Kondrat'ev, Andrei V
2001-11-30
It is shown that the diffraction reproduction of a periodically modulated wave field takes place when light propagates through Gaussian optical systems. Generally, such a reproduction is accompanied by image scaling. Equations are derived that relate the reproducton distance and scaling factor to the ABCD matrix elements of the optical system. The Talbot effect in a convergent (divergent) wave is considered. (laser applications and other topics in quantum electronics)
Computational aspects of Gaussian beam migration
Hale, D.
1992-08-01
The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.
Computational aspects of Gaussian beam migration
Hale, D.
1992-01-01
The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.
Non-Markovianity of Gaussian Channels.
Torre, G; Roga, W; Illuminati, F
2015-08-14
We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states. PMID:26317700
Entropic Fluctuations in Gaussian Dynamical Systems
NASA Astrophysics Data System (ADS)
Jakšić, V.; Pillet, C.-A.; Shirikyan, A.
2016-06-01
We study nonequilibrium statistical mechanics of a Gaussian dynamical system and compute in closed form the large deviation functionals describing the fluctuations of the entropy production observable with respect to the reference state and the nonequilibrium steady state. The entropy production observable of this model is an unbounded function on the phase space, and its large deviation functionals have a surprisingly rich structure. We explore this structure in some detail.
Consistency relations for non-Gaussianity
NASA Astrophysics Data System (ADS)
Li, Miao; Wang, Yi
2008-09-01
We investigate consistency relations for non-Gaussianity. We provide a model-independent dynamical proof for the consistency relation for three-point correlation functions from the Hamiltonian and field redefinition. This relation can be applied to single-field inflation, multi-field inflation and the curvaton scenario. This relation can also be generalized to n-point correlation functions up to arbitrary order in perturbation theory and with arbitrary number of loops.