Precision Measurements of the Cluster Red Sequence using an Error Corrected Gaussian Mixture Model
Energy Technology Data Exchange (ETDEWEB)
Hao, Jiangang; /Fermilab /Michigan U.; Koester, Benjamin P.; /Chicago U.; Mckay, Timothy A.; /Michigan U.; Rykoff, Eli S.; /UC, Santa Barbara; Rozo, Eduardo; /Ohio State U.; Evrard, August; /Michigan U.; Annis, James; /Fermilab; Becker, Matthew; /Chicago U.; Busha, Michael; /KIPAC, Menlo Park /SLAC; Gerdes, David; /Michigan U.; Johnston, David E.; /Northwestern U. /Brookhaven
2009-07-01
The red sequence is an important feature of galaxy clusters and plays a crucial role in optical cluster detection. Measurement of the slope and scatter of the red sequence are affected both by selection of red sequence galaxies and measurement errors. In this paper, we describe a new error corrected Gaussian Mixture Model for red sequence galaxy identification. Using this technique, we can remove the effects of measurement error and extract unbiased information about the intrinsic properties of the red sequence. We use this method to select red sequence galaxies in each of the 13,823 clusters in the maxBCG catalog, and measure the red sequence ridgeline location and scatter of each. These measurements provide precise constraints on the variation of the average red galaxy populations in the observed frame with redshift. We find that the scatter of the red sequence ridgeline increases mildly with redshift, and that the slope decreases with redshift. We also observe that the slope does not strongly depend on cluster richness. Using similar methods, we show that this behavior is mirrored in a spectroscopic sample of field galaxies, further emphasizing that ridgeline properties are independent of environment. These precise measurements serve as an important observational check on simulations and mock galaxy catalogs. The observed trends in the slope and scatter of the red sequence ridgeline with redshift are clues to possible intrinsic evolution of the cluster red-sequence itself. Most importantly, the methods presented in this work lay the groundwork for further improvements in optically-based cluster cosmology.
PRECISION MEASUREMENTS OF THE CLUSTER RED SEQUENCE USING AN ERROR-CORRECTED GAUSSIAN MIXTURE MODEL
International Nuclear Information System (INIS)
Hao Jiangang; Annis, James; Koester, Benjamin P.; Mckay, Timothy A.; Evrard, August; Gerdes, David; Rykoff, Eli S.; Rozo, Eduardo; Becker, Matthew; Busha, Michael; Wechsler, Risa H.; Johnston, David E.; Sheldon, Erin
2009-01-01
The red sequence is an important feature of galaxy clusters and plays a crucial role in optical cluster detection. Measurement of the slope and scatter of the red sequence are affected both by selection of red sequence galaxies and measurement errors. In this paper, we describe a new error-corrected Gaussian Mixture Model for red sequence galaxy identification. Using this technique, we can remove the effects of measurement error and extract unbiased information about the intrinsic properties of the red sequence. We use this method to select red sequence galaxies in each of the 13,823 clusters in the maxBCG catalog, and measure the red sequence ridgeline location and scatter of each. These measurements provide precise constraints on the variation of the average red galaxy populations in the observed frame with redshift. We find that the scatter of the red sequence ridgeline increases mildly with redshift, and that the slope decreases with redshift. We also observe that the slope does not strongly depend on cluster richness. Using similar methods, we show that this behavior is mirrored in a spectroscopic sample of field galaxies, further emphasizing that ridgeline properties are independent of environment. These precise measurements serve as an important observational check on simulations and mock galaxy catalogs. The observed trends in the slope and scatter of the red sequence ridgeline with redshift are clues to possible intrinsic evolution of the cluster red sequence itself. Most importantly, the methods presented in this work lay the groundwork for further improvements in optically based cluster cosmology.
Markov random field and Gaussian mixture for segmented MRI-based partial volume correction in PET
International Nuclear Information System (INIS)
Bousse, Alexandre; Thomas, Benjamin A; Erlandsson, Kjell; Hutton, Brian F; Pedemonte, Stefano; Ourselin, Sébastien; Arridge, Simon
2012-01-01
In this paper we propose a segmented magnetic resonance imaging (MRI) prior-based maximum penalized likelihood deconvolution technique for positron emission tomography (PET) images. The model assumes the existence of activity classes that behave like a hidden Markov random field (MRF) driven by the segmented MRI. We utilize a mean field approximation to compute the likelihood of the MRF. We tested our method on both simulated and clinical data (brain PET) and compared our results with PET images corrected with the re-blurred Van Cittert (VC) algorithm, the simplified Guven (SG) algorithm and the region-based voxel-wise (RBV) technique. We demonstrated our algorithm outperforms the VC algorithm and outperforms SG and RBV corrections when the segmented MRI is inconsistent (e.g. mis-segmentation, lesions, etc) with the PET image. (paper)
Iterative Mixture Component Pruning Algorithm for Gaussian Mixture PHD Filter
Directory of Open Access Journals (Sweden)
Xiaoxi Yan
2014-01-01
Full Text Available As far as the increasing number of mixture components in the Gaussian mixture PHD filter is concerned, an iterative mixture component pruning algorithm is proposed. The pruning algorithm is based on maximizing the posterior probability density of the mixture weights. The entropy distribution of the mixture weights is adopted as the prior distribution of mixture component parameters. The iterative update formulations of the mixture weights are derived by Lagrange multiplier and Lambert W function. Mixture components, whose weights become negative during iterative procedure, are pruned by setting corresponding mixture weights to zeros. In addition, multiple mixture components with similar parameters describing the same PHD peak can be merged into one mixture component in the algorithm. Simulation results show that the proposed iterative mixture component pruning algorithm is superior to the typical pruning algorithm based on thresholds.
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
Modeling text with generalizable Gaussian mixtures
DEFF Research Database (Denmark)
Hansen, Lars Kai; Sigurdsson, Sigurdur; Kolenda, Thomas
2000-01-01
We apply and discuss generalizable Gaussian mixture (GGM) models for text mining. The model automatically adapts model complexity for a given text representation. We show that the generalizability of these models depends on the dimensionality of the representation and the sample size. We discuss...
Loop corrections to primordial non-Gaussianity
Boran, Sibel; Kahya, E. O.
2018-02-01
We discuss quantum gravitational loop effects to observable quantities such as curvature power spectrum and primordial non-Gaussianity of cosmic microwave background (CMB) radiation. We first review the previously shown case where one gets a time dependence for zeta-zeta correlator due to loop corrections. Then we investigate the effect of loop corrections to primordial non-Gaussianity of CMB. We conclude that, even with a single scalar inflaton, one might get a huge value for non-Gaussianity which would exceed the observed value by at least 30 orders of magnitude. Finally we discuss the consequences of this result for scalar driven inflationary models.
Direct Importance Estimation with Gaussian Mixture Models
Yamada, Makoto; Sugiyama, Masashi
The ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extention of the Kullback-Leibler importance estimation procedure (KLIEP), an importance estimation method using linear or kernel models. An advantage of GMMs is that covariance matrices can also be learned through an expectation-maximization procedure, so the proposed method — which we call the Gaussian mixture KLIEP (GM-KLIEP) — is expected to work well when the true importance function has high correlation. Through experiments, we show the validity of the proposed approach.
Gaussian Process-Mixture Conditional Heteroscedasticity.
Platanios, Emmanouil A; Chatzis, Sotirios P
2014-05-01
Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an alternative approach based on methodologies widely used in the field of statistical machine learning. Specifically, we propose a novel nonparametric Bayesian mixture of Gaussian process regression models, each component of which models the noise variance process that contaminates the observed data as a separate latent Gaussian process driven by the observed data. This way, we essentially obtain a Gaussian process-mixture conditional heteroscedasticity (GPMCH) model for volatility modeling in financial return series. We impose a nonparametric prior with power-law nature over the distribution of the model mixture components, namely the Pitman-Yor process prior, to allow for better capturing modeled data distributions with heavy tails and skewness. Finally, we provide a copula-based approach for obtaining a predictive posterior for the covariances over the asset returns modeled by means of a postulated GPMCH model. We evaluate the efficacy of our approach in a number of benchmark scenarios, and compare its performance to state-of-the-art methodologies.
Finite Gaussian Mixture Approximations to Analytically Intractable Density Kernels
DEFF Research Database (Denmark)
Khorunzhina, Natalia; Richard, Jean-Francois
The objective of the paper is that of constructing finite Gaussian mixture approximations to analytically intractable density kernels. The proposed method is adaptive in that terms are added one at the time and the mixture is fully re-optimized at each step using a distance measure that approxima...
Detection Performance of Signals in Dependent Noise From a Gaussian Mixture Uncertainty Class
National Research Council Canada - National Science Library
Gerlach, K
1998-01-01
... (correlated) multivariate noise from a Gaussian mixture uncertainty class. This uncertainty class is defined using upper and lower bounding functions on the univariate Gaussian mixing distribution function...
Evaluation of Distance Measures Between Gaussian Mixture Models of MFCCs
DEFF Research Database (Denmark)
Jensen, Jesper Højvang; Ellis, Dan P. W.; Christensen, Mads Græsbøll
2007-01-01
In music similarity and in the related task of genre classification, a distance measure between Gaussian mixture models is frequently needed. We present a comparison of the Kullback-Leibler distance, the earth movers distance and the normalized L2 distance for this application. Although...
Supervised Gaussian mixture model based remote sensing image ...
African Journals Online (AJOL)
Using the supervised classification technique, both simulated and empirical satellite remote sensing data are used to train and test the Gaussian mixture model algorithm. For the purpose of validating the experiment, the resulting classified satellite image is compared with the ground truth data. For the simulated modelling, ...
Color Texture Segmentation by Decomposition of Gaussian Mixture Model
Czech Academy of Sciences Publication Activity Database
Grim, Jiří; Somol, Petr; Haindl, Michal; Pudil, Pavel
2006-01-01
Roč. 19, č. 4225 (2006), s. 287-296 ISSN 0302-9743. [Iberoamerican Congress on Pattern Recognition. CIARP 2006 /11./. Cancun, 14.11.2006-17.11.2006] R&D Projects: GA AV ČR 1ET400750407; GA MŠk 1M0572; GA MŠk 2C06019 EU Projects: European Commission(XE) 507752 - MUSCLE Institutional research plan: CEZ:AV0Z10750506 Keywords : texture segmentation * gaussian mixture model * EM algorithm Subject RIV: IN - Informatics, Computer Science Impact factor: 0.402, year: 2005 http://library.utia.cas.cz/separaty/historie/grim-color texture segmentation by decomposition of gaussian mixture model.pdf
XDGMM: eXtreme Deconvolution Gaussian Mixture Modeling
Holoien, Thomas W.-S.; Marshall, Philip J.; Wechsler, Risa H.
2017-08-01
XDGMM uses Gaussian mixtures to do density estimation of noisy, heterogenous, and incomplete data using extreme deconvolution (XD) algorithms which is compatible with the scikit-learn machine learning methods. It implements both the astroML and Bovy et al. (2011) algorithms, and extends the BaseEstimator class from scikit-learn so that cross-validation methods work. It allows the user to produce a conditioned model if values of some parameters are known.
Perturbative corrections for approximate inference in gaussian latent variable models
DEFF Research Database (Denmark)
Opper, Manfred; Paquet, Ulrich; Winther, Ole
2013-01-01
Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact b...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....
Gaussian mixture clustering and imputation of microarray data.
Ouyang, Ming; Welsh, William J; Georgopoulos, Panos
2004-04-12
In microarray experiments, missing entries arise from blemishes on the chips. In large-scale studies, virtually every chip contains some missing entries and more than 90% of the genes are affected. Many analysis methods require a full set of data. Either those genes with missing entries are excluded, or the missing entries are filled with estimates prior to the analyses. This study compares methods of missing value estimation. Two evaluation metrics of imputation accuracy are employed. First, the root mean squared error measures the difference between the true values and the imputed values. Second, the number of mis-clustered genes measures the difference between clustering with true values and that with imputed values; it examines the bias introduced by imputation to clustering. The Gaussian mixture clustering with model averaging imputation is superior to all other imputation methods, according to both evaluation metrics, on both time-series (correlated) and non-time series (uncorrelated) data sets.
Efficient Kernel-Based Ensemble Gaussian Mixture Filtering
Liu, Bo
2015-11-11
We consider the Bayesian filtering problem for data assimilation following the kernel-based ensemble Gaussian-mixture filtering (EnGMF) approach introduced by Anderson and Anderson (1999). In this approach, the posterior distribution of the system state is propagated with the model using the ensemble Monte Carlo method, providing a forecast ensemble that is then used to construct a prior Gaussian-mixture (GM) based on the kernel density estimator. This results in two update steps: a Kalman filter (KF)-like update of the ensemble members and a particle filter (PF)-like update of the weights, followed by a resampling step to start a new forecast cycle. After formulating EnGMF for any observational operator, we analyze the influence of the bandwidth parameter of the kernel function on the covariance of the posterior distribution. We then focus on two aspects: i) the efficient implementation of EnGMF with (relatively) small ensembles, where we propose a new deterministic resampling strategy preserving the first two moments of the posterior GM to limit the sampling error; and ii) the analysis of the effect of the bandwidth parameter on contributions of KF and PF updates and on the weights variance. Numerical results using the Lorenz-96 model are presented to assess the behavior of EnGMF with deterministic resampling, study its sensitivity to different parameters and settings, and evaluate its performance against ensemble KFs. The proposed EnGMF approach with deterministic resampling suggests improved estimates in all tested scenarios, and is shown to require less localization and to be less sensitive to the choice of filtering parameters.
Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures
Directory of Open Access Journals (Sweden)
Nishchal K. Verma
2012-01-01
Full Text Available This paper presents a novel computational approach for estimating fuzzy measures directly from Gaussian mixtures model (GMM. The mixture components of GMM provide the membership functions for the input-output fuzzy sets. By treating consequent part as a function of fuzzy measures, we derived its coefficients from the covariance matrices found directly from GMM and the defuzzified output constructed from both the premise and consequent parts of the nonadditive fuzzy rules that takes the form of Choquet integral. The computational burden involved with the solution of λ-measure is minimized using Q-measure. The fuzzy model whose fuzzy measures were computed using covariance matrices found in GMM has been successfully applied on two benchmark problems and one real-time electric load data of Indian utility. The performance of the resulting model for many experimental studies including the above-mentioned application is found to be better and comparable to recent available fuzzy models. The main contribution of this paper is the estimation of fuzzy measures efficiently and directly from covariance matrices found in GMM, avoiding the computational burden greatly while learning them iteratively and solving polynomial equations of order of the number of input-output variables.
Performance of BICM-T transceivers over Gaussian mixture noise channels
Malik, Muhammad Talha; Hossain, Md Jahangir; Alouini, Mohamed-Slim
2014-01-01
in the Gaussian mixture. The results presented for 16-QAM show that the BICM-T can result in gains up to 1.5 dB for a target BER of 10-6 if the impulsive noise in the Gaussian mixture is below a certain threshold level. The simulation results verify the tightness
International Nuclear Information System (INIS)
Yu, Jie; Chen, Kuilin; Mori, Junichi; Rashid, Mudassir M.
2013-01-01
Optimizing wind power generation and controlling the operation of wind turbines to efficiently harness the renewable wind energy is a challenging task due to the intermittency and unpredictable nature of wind speed, which has significant influence on wind power production. A new approach for long-term wind speed forecasting is developed in this study by integrating GMCM (Gaussian mixture copula model) and localized GPR (Gaussian process regression). The time series of wind speed is first classified into multiple non-Gaussian components through the Gaussian mixture copula model and then Bayesian inference strategy is employed to incorporate the various non-Gaussian components using the posterior probabilities. Further, the localized Gaussian process regression models corresponding to different non-Gaussian components are built to characterize the stochastic uncertainty and non-stationary seasonality of the wind speed data. The various localized GPR models are integrated through the posterior probabilities as the weightings so that a global predictive model is developed for the prediction of wind speed. The proposed GMCM–GPR approach is demonstrated using wind speed data from various wind farm locations and compared against the GMCM-based ARIMA (auto-regressive integrated moving average) and SVR (support vector regression) methods. In contrast to GMCM–ARIMA and GMCM–SVR methods, the proposed GMCM–GPR model is able to well characterize the multi-seasonality and uncertainty of wind speed series for accurate long-term prediction. - Highlights: • A novel predictive modeling method is proposed for long-term wind speed forecasting. • Gaussian mixture copula model is estimated to characterize the multi-seasonality. • Localized Gaussian process regression models can deal with the random uncertainty. • Multiple GPR models are integrated through Bayesian inference strategy. • The proposed approach shows higher prediction accuracy and reliability
Multiple Response Regression for Gaussian Mixture Models with Known Labels.
Lee, Wonyul; Du, Ying; Sun, Wei; Hayes, D Neil; Liu, Yufeng
2012-12-01
Multiple response regression is a useful regression technique to model multiple response variables using the same set of predictor variables. Most existing methods for multiple response regression are designed for modeling homogeneous data. In many applications, however, one may have heterogeneous data where the samples are divided into multiple groups. Our motivating example is a cancer dataset where the samples belong to multiple cancer subtypes. In this paper, we consider modeling the data coming from a mixture of several Gaussian distributions with known group labels. A naive approach is to split the data into several groups according to the labels and model each group separately. Although it is simple, this approach ignores potential common structures across different groups. We propose new penalized methods to model all groups jointly in which the common and unique structures can be identified. The proposed methods estimate the regression coefficient matrix, as well as the conditional inverse covariance matrix of response variables. Asymptotic properties of the proposed methods are explored. Through numerical examples, we demonstrate that both estimation and prediction can be improved by modeling all groups jointly using the proposed methods. An application to a glioblastoma cancer dataset reveals some interesting common and unique gene relationships across different cancer subtypes.
Gaussian mixture models and semantic gating improve reconstructions from human brain activity
Directory of Open Access Journals (Sweden)
Sanne eSchoenmakers
2015-01-01
Full Text Available Better acquisition protocols and analysis techniques are making it possible to use fMRI to obtain highly detailed visualizations of brain processes. In particular we focus on the reconstruction of natural images from BOLD responses in visual cortex. We expand our linear Gaussian framework for percept decoding with Gaussian mixture models to better represent the prior distribution of natural images. Reconstruction of such images then boils down to probabilistic inference in a hybrid Bayesian network. In our set-up, different mixture components correspond to different character categories. Our framework can automatically infer higher-order semantic categories from lower-level brain areas. Furthermore the framework can gate semantic information from higher-order brain areas to enforce the correct category during reconstruction. When categorical information is not available, we show that automatically learned clusters in the data give a similar improvement in reconstruction. The hybrid Bayesian network leads to highly accurate reconstructions in both supervised and unsupervised settings.
Statistical imitation system using relational interest points and Gaussian mixture models
CSIR Research Space (South Africa)
Claassens, J
2009-11-01
Full Text Available The author proposes an imitation system that uses relational interest points (RIPs) and Gaussian mixture models (GMMs) to characterize a behaviour. The system's structure is inspired by the Robot Programming by Demonstration (RDP) paradigm...
Background based Gaussian mixture model lesion segmentation in PET
Energy Technology Data Exchange (ETDEWEB)
Soffientini, Chiara Dolores, E-mail: chiaradolores.soffientini@polimi.it; Baselli, Giuseppe [DEIB, Department of Electronics, Information, and Bioengineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milan 20133 (Italy); De Bernardi, Elisabetta [Department of Medicine and Surgery, Tecnomed Foundation, University of Milano—Bicocca, Monza 20900 (Italy); Zito, Felicia; Castellani, Massimo [Nuclear Medicine Department, Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico, via Francesco Sforza 35, Milan 20122 (Italy)
2016-05-15
Purpose: Quantitative {sup 18}F-fluorodeoxyglucose positron emission tomography is limited by the uncertainty in lesion delineation due to poor SNR, low resolution, and partial volume effects, subsequently impacting oncological assessment, treatment planning, and follow-up. The present work develops and validates a segmentation algorithm based on statistical clustering. The introduction of constraints based on background features and contiguity priors is expected to improve robustness vs clinical image characteristics such as lesion dimension, noise, and contrast level. Methods: An eight-class Gaussian mixture model (GMM) clustering algorithm was modified by constraining the mean and variance parameters of four background classes according to the previous analysis of a lesion-free background volume of interest (background modeling). Hence, expectation maximization operated only on the four classes dedicated to lesion detection. To favor the segmentation of connected objects, a further variant was introduced by inserting priors relevant to the classification of neighbors. The algorithm was applied to simulated datasets and acquired phantom data. Feasibility and robustness toward initialization were assessed on a clinical dataset manually contoured by two expert clinicians. Comparisons were performed with respect to a standard eight-class GMM algorithm and to four different state-of-the-art methods in terms of volume error (VE), Dice index, classification error (CE), and Hausdorff distance (HD). Results: The proposed GMM segmentation with background modeling outperformed standard GMM and all the other tested methods. Medians of accuracy indexes were VE <3%, Dice >0.88, CE <0.25, and HD <1.2 in simulations; VE <23%, Dice >0.74, CE <0.43, and HD <1.77 in phantom data. Robustness toward image statistic changes (±15%) was shown by the low index changes: <26% for VE, <17% for Dice, and <15% for CE. Finally, robustness toward the user-dependent volume initialization was
Quantum error correction of continuous-variable states against Gaussian noise
Energy Technology Data Exchange (ETDEWEB)
Ralph, T. C. [Centre for Quantum Computation and Communication Technology, School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072 (Australia)
2011-08-15
We describe a continuous-variable error correction protocol that can correct the Gaussian noise induced by linear loss on Gaussian states. The protocol can be implemented using linear optics and photon counting. We explore the theoretical bounds of the protocol as well as the expected performance given current knowledge and technology.
Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures
Huser, Raphaël
2017-06-23
Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.
Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures
Huser, Raphaë l; Opitz, Thomas; Thibaud, Emeric
2017-01-01
Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.
Assessing clustering strategies for Gaussian mixture filtering a subsurface contaminant model
Liu, Bo; El Gharamti, Mohamad; Hoteit, Ibrahim
2016-01-01
An ensemble-based Gaussian mixture (GM) filtering framework is studied in this paper in term of its dependence on the choice of the clustering method to construct the GM. In this approach, a number of particles sampled from the posterior
Directory of Open Access Journals (Sweden)
Masaru Yokoe
2009-03-01
Full Text Available This paper proposes a method to quantitatively measure and evaluate finger tapping movements for the assessment of motor function using log-linearized Gaussian mixture networks (LLGMNs. First, finger tapping movements are measured using magnetic sensors, and eleven indices are computed for evaluation. After standardizing these indices based on those of normal subjects, they are input to LLGMNs to assess motor function. Then, motor ability is probabilistically discriminated to determine whether it is normal or not using a classifier combined with the output of multiple LLGMNs based on bagging and entropy. This paper reports on evaluation and discrimination experiments performed on finger tapping movements in 33 Parkinson’s disease (PD patients and 32 normal elderly subjects. The results showed that the patients could be classified correctly in terms of their impairment status with a high degree of accuracy (average rate: 93:1 § 3:69% using 12 LLGMNs, which was about 5% higher than the results obtained using a single LLGMN.
Directory of Open Access Journals (Sweden)
Abdenaceur Boudlal
2010-01-01
Full Text Available This article investigates a new method of motion estimation based on block matching criterion through the modeling of image blocks by a mixture of two and three Gaussian distributions. Mixture parameters (weights, means vectors, and covariance matrices are estimated by the Expectation Maximization algorithm (EM which maximizes the log-likelihood criterion. The similarity between a block in the current image and the more resembling one in a search window on the reference image is measured by the minimization of Extended Mahalanobis distance between the clusters of mixture. Performed experiments on sequences of real images have given good results, and PSNR reached 3 dB.
Performance of BICM-T transceivers over Gaussian mixture noise channels
Malik, Muhammad Talha
2014-04-01
Experimental measurements have shown that the noise in many communication channels is non-Gaussian. Bit interleaved coded modulation (BICM) is very popular for spectrally efficient transmission. Recent results have shown that the performance of BICM using convolutional codes in non-fading channels can be significantly improved if the coded bits are not interleaved at all. This particular BICM design is called BICM trivial (BICM-T). In this paper, we analyze the performance of a generalized BICM-T design for communication over Gaussian mixture noise (GMN) channels. The results disclose that for an optimal bit error rate (BER) performance, the use of an interleaver in BICM for GMN channels depends upon the strength of the impulsive noise components in the Gaussian mixture. The results presented for 16-QAM show that the BICM-T can result in gains up to 1.5 dB for a target BER of 10-6 if the impulsive noise in the Gaussian mixture is below a certain threshold level. The simulation results verify the tightness of developed union bound (UB) on BER performance.
Lee, Soojeong; Rajan, Sreeraman; Jeon, Gwanggil; Chang, Joon-Hyuk; Dajani, Hilmi R; Groza, Voicu Z
2017-06-01
Blood pressure (BP) is one of the most important vital indicators and plays a key role in determining the cardiovascular activity of patients. This paper proposes a hybrid approach consisting of nonparametric bootstrap (NPB) and machine learning techniques to obtain the characteristic ratios (CR) used in the blood pressure estimation algorithm to improve the accuracy of systolic blood pressure (SBP) and diastolic blood pressure (DBP) estimates and obtain confidence intervals (CI). The NPB technique is used to circumvent the requirement for large sample set for obtaining the CI. A mixture of Gaussian densities is assumed for the CRs and Gaussian mixture model (GMM) is chosen to estimate the SBP and DBP ratios. The K-means clustering technique is used to obtain the mixture order of the Gaussian densities. The proposed approach achieves grade "A" under British Society of Hypertension testing protocol and is superior to the conventional approach based on maximum amplitude algorithm (MAA) that uses fixed CR ratios. The proposed approach also yields a lower mean error (ME) and the standard deviation of the error (SDE) in the estimates when compared to the conventional MAA method. In addition, CIs obtained through the proposed hybrid approach are also narrower with a lower SDE. The proposed approach combining the NPB technique with the GMM provides a methodology to derive individualized characteristic ratio. The results exhibit that the proposed approach enhances the accuracy of SBP and DBP estimation and provides narrower confidence intervals for the estimates. Copyright © 2015 Elsevier Ltd. All rights reserved.
Kinect Posture Reconstruction Based on a Local Mixture of Gaussian Process Models.
Liu, Zhiguang; Zhou, Liuyang; Leung, Howard; Shum, Hubert P H
2016-11-01
Depth sensor based 3D human motion estimation hardware such as Kinect has made interactive applications more popular recently. However, it is still challenging to accurately recognize postures from a single depth camera due to the inherently noisy data derived from depth images and self-occluding action performed by the user. In this paper, we propose a new real-time probabilistic framework to enhance the accuracy of live captured postures that belong to one of the action classes in the database. We adopt the Gaussian Process model as a prior to leverage the position data obtained from Kinect and marker-based motion capture system. We also incorporate a temporal consistency term into the optimization framework to constrain the velocity variations between successive frames. To ensure that the reconstructed posture resembles the accurate parts of the observed posture, we embed a set of joint reliability measurements into the optimization framework. A major drawback of Gaussian Process is its cubic learning complexity when dealing with a large database due to the inverse of a covariance matrix. To solve the problem, we propose a new method based on a local mixture of Gaussian Processes, in which Gaussian Processes are defined in local regions of the state space. Due to the significantly decreased sample size in each local Gaussian Process, the learning time is greatly reduced. At the same time, the prediction speed is enhanced as the weighted mean prediction for a given sample is determined by the nearby local models only. Our system also allows incrementally updating a specific local Gaussian Process in real time, which enhances the likelihood of adapting to run-time postures that are different from those in the database. Experimental results demonstrate that our system can generate high quality postures even under severe self-occlusion situations, which is beneficial for real-time applications such as motion-based gaming and sport training.
Chabdarov, Shamil M.; Nadeev, Adel F.; Chickrin, Dmitry E.; Faizullin, Rashid R.
2011-04-01
In this paper we discuss unconventional detection technique also known as «full resolution receiver». This receiver uses Gaussian probability mixtures for interference structure adaptation. Full resolution receiver is alternative to conventional matched filter receivers in the case of non-Gaussian interferences. For the DS-CDMA forward channel with presence of complex interferences sufficient performance increasing was shown.
Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures
International Nuclear Information System (INIS)
Procacci, Piero
2015-01-01
In this paper, we present an improved method for obtaining unbiased estimates of the free energy difference between two thermodynamic states using the work distribution measured in nonequilibrium driven experiments connecting these states. The method is based on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, whose normal components are identical in either direction of the nonequilibrium process, with weights regulated by the Crooks theorem. Using the prototypical example for the driven unfolding/folding of deca-alanine, we show that the predicted behavior of the forward and reverse work distributions, assuming a combination of only two Gaussian components with Crooks derived weights, explains surprisingly well the striking asymmetry in the observed distributions at fast pulling speeds. The proposed methodology opens the way for a perfectly parallel implementation of Jarzynski-based free energy calculations in complex systems
International Nuclear Information System (INIS)
Fouque, A.L.; Ciuciu, Ph.; Risser, L.; Fouque, A.L.; Ciuciu, Ph.; Risser, L.
2009-01-01
In this paper, a novel statistical parcellation of intra-subject functional MRI (fMRI) data is proposed. The key idea is to identify functionally homogenous regions of interest from their hemodynamic parameters. To this end, a non-parametric voxel-based estimation of hemodynamic response function is performed as a prerequisite. Then, the extracted hemodynamic features are entered as the input data of a Multivariate Spatial Gaussian Mixture Model (MSGMM) to be fitted. The goal of the spatial aspect is to favor the recovery of connected components in the mixture. Our statistical clustering approach is original in the sense that it extends existing works done on univariate spatially regularized Gaussian mixtures. A specific Gibbs sampler is derived to account for different covariance structures in the feature space. On realistic artificial fMRI datasets, it is shown that our algorithm is helpful for identifying a parsimonious functional parcellation required in the context of joint detection estimation of brain activity. This allows us to overcome the classical assumption of spatial stationarity of the BOLD signal model. (authors)
DEFF Research Database (Denmark)
Franchin, P.; Ditlevsen, Ove Dalager; Kiureghian, Armen Der
2002-01-01
The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals ...
Zhang, Hong; Hou, Rui; Yi, Lei; Meng, Juan; Pan, Zhisong; Zhou, Yuhuan
2016-07-01
The accurate identification of encrypted data stream helps to regulate illegal data, detect network attacks and protect users' information. In this paper, a novel encrypted data stream identification algorithm is introduced. The proposed method is based on randomness characteristics of encrypted data stream. We use a l1-norm regularized logistic regression to improve sparse representation of randomness features and Fuzzy Gaussian Mixture Model (FGMM) to improve identification accuracy. Experimental results demonstrate that the method can be adopted as an effective technique for encrypted data stream identification.
Assessing clustering strategies for Gaussian mixture filtering a subsurface contaminant model
Liu, Bo
2016-02-03
An ensemble-based Gaussian mixture (GM) filtering framework is studied in this paper in term of its dependence on the choice of the clustering method to construct the GM. In this approach, a number of particles sampled from the posterior distribution are first integrated forward with the dynamical model for forecasting. A GM representation of the forecast distribution is then constructed from the forecast particles. Once an observation becomes available, the forecast GM is updated according to Bayes’ rule. This leads to (i) a Kalman filter-like update of the particles, and (ii) a Particle filter-like update of their weights, generalizing the ensemble Kalman filter update to non-Gaussian distributions. We focus on investigating the impact of the clustering strategy on the behavior of the filter. Three different clustering methods for constructing the prior GM are considered: (i) a standard kernel density estimation, (ii) clustering with a specified mixture component size, and (iii) adaptive clustering (with a variable GM size). Numerical experiments are performed using a two-dimensional reactive contaminant transport model in which the contaminant concentration and the heterogenous hydraulic conductivity fields are estimated within a confined aquifer using solute concentration data. The experimental results suggest that the performance of the GM filter is sensitive to the choice of the GM model. In particular, increasing the size of the GM does not necessarily result in improved performances. In this respect, the best results are obtained with the proposed adaptive clustering scheme.
A brain MRI bias field correction method created in the Gaussian multi-scale space
Chen, Mingsheng; Qin, Mingxin
2017-07-01
A pre-processing step is needed to correct for the bias field signal before submitting corrupted MR images to such image-processing algorithms. This study presents a new bias field correction method. The method creates a Gaussian multi-scale space by the convolution of the inhomogeneous MR image with a two-dimensional Gaussian function. In the multi-Gaussian space, the method retrieves the image details from the differentiation of the original image and convolution image. Then, it obtains an image whose inhomogeneity is eliminated by the weighted sum of image details in each layer in the space. Next, the bias field-corrected MR image is retrieved after the Υ correction, which enhances the contrast and brightness of the inhomogeneity-eliminated MR image. We have tested the approach on T1 MRI and T2 MRI with varying bias field levels and have achieved satisfactory results. Comparison experiments with popular software have demonstrated superior performance of the proposed method in terms of quantitative indices, especially an improvement in subsequent image segmentation.
ADAPTIVE BACKGROUND DENGAN METODE GAUSSIAN MIXTURE MODELS UNTUK REAL-TIME TRACKING
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Silvia Rostianingsih
2008-01-01
Full Text Available Nowadays, motion tracking application is widely used for many purposes, such as detecting traffic jam and counting how many people enter a supermarket or a mall. A method to separate background and the tracked object is required for motion tracking. It will not be hard to develop the application if the tracking is performed on a static background, but it will be difficult if the tracked object is at a place with a non-static background, because the changing part of the background can be recognized as a tracking area. In order to handle the problem an application can be made to separate background where that separation can adapt to change that occur. This application is made to produce adaptive background using Gaussian Mixture Models (GMM as its method. GMM method clustered the input pixel data with pixel color value as it’s basic. After the cluster formed, dominant distributions are choosen as background distributions. This application is made by using Microsoft Visual C 6.0. The result of this research shows that GMM algorithm could made adaptive background satisfactory. This proofed by the result of the tests that succeed at all condition given. This application can be developed so the tracking process integrated in adaptive background maker process. Abstract in Bahasa Indonesia : Saat ini, aplikasi motion tracking digunakan secara luas untuk banyak tujuan, seperti mendeteksi kemacetan dan menghitung berapa banyak orang yang masuk ke sebuah supermarket atau sebuah mall. Sebuah metode untuk memisahkan antara background dan obyek yang di-track dibutuhkan untuk melakukan motion tracking. Membuat aplikasi tracking pada background yang statis bukanlah hal yang sulit, namun apabila tracking dilakukan pada background yang tidak statis akan lebih sulit, dikarenakan perubahan background dapat dikenali sebagai area tracking. Untuk mengatasi masalah tersebut, dapat dibuat suatu aplikasi untuk memisahkan background dimana aplikasi tersebut dapat
Schellenberg, Graham; Stortz, Greg; Goertzen, Andrew L
2016-02-07
A typical positron emission tomography detector is comprised of a scintillator crystal array coupled to a photodetector array or other position sensitive detector. Such detectors using light sharing to read out crystal elements require the creation of a crystal lookup table (CLUT) that maps the detector response to the crystal of interaction based on the x-y position of the event calculated through Anger-type logic. It is vital for system performance that these CLUTs be accurate so that the location of events can be accurately identified and so that crystal-specific corrections, such as energy windowing or time alignment, can be applied. While using manual segmentation of the flood image to create the CLUT is a simple and reliable approach, it is both tedious and time consuming for systems with large numbers of crystal elements. In this work we describe the development of an automated algorithm for CLUT generation that uses a Gaussian mixture model paired with thin plate splines (TPS) to iteratively fit a crystal layout template that includes the crystal numbering pattern. Starting from a region of stability, Gaussians are individually fit to data corresponding to crystal locations while simultaneously updating a TPS for predicting future Gaussian locations at the edge of a region of interest that grows as individual Gaussians converge to crystal locations. The algorithm was tested with flood image data collected from 16 detector modules, each consisting of a 409 crystal dual-layer offset LYSO crystal array readout by a 32 pixel SiPM array. For these detector flood images, depending on user defined input parameters, the algorithm runtime ranged between 17.5-82.5 s per detector on a single core of an Intel i7 processor. The method maintained an accuracy above 99.8% across all tests, with the majority of errors being localized to error prone corner regions. This method can be easily extended for use with other detector types through adjustment of the initial
International Nuclear Information System (INIS)
Schellenberg, Graham; Goertzen, Andrew L; Stortz, Greg
2016-01-01
A typical positron emission tomography detector is comprised of a scintillator crystal array coupled to a photodetector array or other position sensitive detector. Such detectors using light sharing to read out crystal elements require the creation of a crystal lookup table (CLUT) that maps the detector response to the crystal of interaction based on the x–y position of the event calculated through Anger-type logic. It is vital for system performance that these CLUTs be accurate so that the location of events can be accurately identified and so that crystal-specific corrections, such as energy windowing or time alignment, can be applied. While using manual segmentation of the flood image to create the CLUT is a simple and reliable approach, it is both tedious and time consuming for systems with large numbers of crystal elements. In this work we describe the development of an automated algorithm for CLUT generation that uses a Gaussian mixture model paired with thin plate splines (TPS) to iteratively fit a crystal layout template that includes the crystal numbering pattern. Starting from a region of stability, Gaussians are individually fit to data corresponding to crystal locations while simultaneously updating a TPS for predicting future Gaussian locations at the edge of a region of interest that grows as individual Gaussians converge to crystal locations. The algorithm was tested with flood image data collected from 16 detector modules, each consisting of a 409 crystal dual-layer offset LYSO crystal array readout by a 32 pixel SiPM array. For these detector flood images, depending on user defined input parameters, the algorithm runtime ranged between 17.5–82.5 s per detector on a single core of an Intel i7 processor. The method maintained an accuracy above 99.8% across all tests, with the majority of errors being localized to error prone corner regions. This method can be easily extended for use with other detector types through adjustment of the initial
Schellenberg, Graham; Stortz, Greg; Goertzen, Andrew L.
2016-02-01
A typical positron emission tomography detector is comprised of a scintillator crystal array coupled to a photodetector array or other position sensitive detector. Such detectors using light sharing to read out crystal elements require the creation of a crystal lookup table (CLUT) that maps the detector response to the crystal of interaction based on the x-y position of the event calculated through Anger-type logic. It is vital for system performance that these CLUTs be accurate so that the location of events can be accurately identified and so that crystal-specific corrections, such as energy windowing or time alignment, can be applied. While using manual segmentation of the flood image to create the CLUT is a simple and reliable approach, it is both tedious and time consuming for systems with large numbers of crystal elements. In this work we describe the development of an automated algorithm for CLUT generation that uses a Gaussian mixture model paired with thin plate splines (TPS) to iteratively fit a crystal layout template that includes the crystal numbering pattern. Starting from a region of stability, Gaussians are individually fit to data corresponding to crystal locations while simultaneously updating a TPS for predicting future Gaussian locations at the edge of a region of interest that grows as individual Gaussians converge to crystal locations. The algorithm was tested with flood image data collected from 16 detector modules, each consisting of a 409 crystal dual-layer offset LYSO crystal array readout by a 32 pixel SiPM array. For these detector flood images, depending on user defined input parameters, the algorithm runtime ranged between 17.5-82.5 s per detector on a single core of an Intel i7 processor. The method maintained an accuracy above 99.8% across all tests, with the majority of errors being localized to error prone corner regions. This method can be easily extended for use with other detector types through adjustment of the initial
Yu, Wangyang; Chen, Xiangguang; Wu, Lei
2015-04-01
Passive millimeter wave (PMMW) imaging has become one of the most effective means to detect the objects concealed under clothing. Due to the limitations of the available hardware and the inherent physical properties of PMMW imaging systems, images often exhibit poor contrast and low signal-to-noise ratios. Thus, it is difficult to achieve ideal results by using a general segmentation algorithm. In this paper, an advanced Gaussian Mixture Model (GMM) algorithm for the segmentation of concealed objects in PMMW images is presented. Our work is concerned with the fact that the GMM is a parametric statistical model, which is often used to characterize the statistical behavior of images. Our approach is three-fold: First, we remove the noise from the image using both a notch reject filter and a total variation filter. Next, we use an adaptive parameter initialization GMM algorithm (APIGMM) for simulating the histogram of images. The APIGMM provides an initial number of Gaussian components and start with more appropriate parameter. Bayesian decision is employed to separate the pixels of concealed objects from other areas. At last, the confidence interval (CI) method, alongside local gradient information, is used to extract the concealed objects. The proposed hybrid segmentation approach detects the concealed objects more accurately, even compared to two other state-of-the-art segmentation methods.
Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.
de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos
2011-01-01
In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.
Clustering gene expression time series data using an infinite Gaussian process mixture model.
McDowell, Ian C; Manandhar, Dinesh; Vockley, Christopher M; Schmid, Amy K; Reddy, Timothy E; Engelhardt, Barbara E
2018-01-01
Transcriptome-wide time series expression profiling is used to characterize the cellular response to environmental perturbations. The first step to analyzing transcriptional response data is often to cluster genes with similar responses. Here, we present a nonparametric model-based method, Dirichlet process Gaussian process mixture model (DPGP), which jointly models data clusters with a Dirichlet process and temporal dependencies with Gaussian processes. We demonstrate the accuracy of DPGP in comparison to state-of-the-art approaches using hundreds of simulated data sets. To further test our method, we apply DPGP to published microarray data from a microbial model organism exposed to stress and to novel RNA-seq data from a human cell line exposed to the glucocorticoid dexamethasone. We validate our clusters by examining local transcription factor binding and histone modifications. Our results demonstrate that jointly modeling cluster number and temporal dependencies can reveal shared regulatory mechanisms. DPGP software is freely available online at https://github.com/PrincetonUniversity/DP_GP_cluster.
Clustering gene expression time series data using an infinite Gaussian process mixture model.
Directory of Open Access Journals (Sweden)
Ian C McDowell
2018-01-01
Full Text Available Transcriptome-wide time series expression profiling is used to characterize the cellular response to environmental perturbations. The first step to analyzing transcriptional response data is often to cluster genes with similar responses. Here, we present a nonparametric model-based method, Dirichlet process Gaussian process mixture model (DPGP, which jointly models data clusters with a Dirichlet process and temporal dependencies with Gaussian processes. We demonstrate the accuracy of DPGP in comparison to state-of-the-art approaches using hundreds of simulated data sets. To further test our method, we apply DPGP to published microarray data from a microbial model organism exposed to stress and to novel RNA-seq data from a human cell line exposed to the glucocorticoid dexamethasone. We validate our clusters by examining local transcription factor binding and histone modifications. Our results demonstrate that jointly modeling cluster number and temporal dependencies can reveal shared regulatory mechanisms. DPGP software is freely available online at https://github.com/PrincetonUniversity/DP_GP_cluster.
Remaining Useful Life Prediction for Lithium-Ion Batteries Based on Gaussian Processes Mixture
Li, Lingling; Wang, Pengchong; Chao, Kuei-Hsiang; Zhou, Yatong; Xie, Yang
2016-01-01
The remaining useful life (RUL) prediction of Lithium-ion batteries is closely related to the capacity degeneration trajectories. Due to the self-charging and the capacity regeneration, the trajectories have the property of multimodality. Traditional prediction models such as the support vector machines (SVM) or the Gaussian Process regression (GPR) cannot accurately characterize this multimodality. This paper proposes a novel RUL prediction method based on the Gaussian Process Mixture (GPM). It can process multimodality by fitting different segments of trajectories with different GPR models separately, such that the tiny differences among these segments can be revealed. The method is demonstrated to be effective for prediction by the excellent predictive result of the experiments on the two commercial and chargeable Type 1850 Lithium-ion batteries, provided by NASA. The performance comparison among the models illustrates that the GPM is more accurate than the SVM and the GPR. In addition, GPM can yield the predictive confidence interval, which makes the prediction more reliable than that of traditional models. PMID:27632176
Almeida, Javier; Velasco, Nelson; Alvarez, Charlens; Romero, Eduardo
2017-11-01
Autism Spectrum Disorder (ASD) is a complex neurological condition characterized by a triad of signs: stereotyped behaviors, verbal and non-verbal communication problems. The scientific community has been interested on quantifying anatomical brain alterations of this disorder. Several studies have focused on measuring brain cortical and sub-cortical volumes. This article presents a fully automatic method which finds out differences among patients diagnosed with autism and control patients. After the usual pre-processing, a template (MNI152) is registered to an evaluated brain which becomes then a set of regions. Each of these regions is the represented by the normalized histogram of intensities which is approximated by mixture of Gaussian (GMM). The gray and white matter are separated to calculate the mean and standard deviation of each Gaussian. These features are then used to train, region per region, a binary SVM classifier. The method was evaluated in an adult population aged from 18 to 35 years, from the public database Autism Brain Imaging Data Exchange (ABIDE). Highest discrimination values were found for the Right Middle Temporal Gyrus, with an Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC) the curve of 0.72.
Mixed Platoon Flow Dispersion Model Based on Speed-Truncated Gaussian Mixture Distribution
Directory of Open Access Journals (Sweden)
Weitiao Wu
2013-01-01
Full Text Available A mixed traffic flow feature is presented on urban arterials in China due to a large amount of buses. Based on field data, a macroscopic mixed platoon flow dispersion model (MPFDM was proposed to simulate the platoon dispersion process along the road section between two adjacent intersections from the flow view. More close to field observation, truncated Gaussian mixture distribution was adopted as the speed density distribution for mixed platoon. Expectation maximum (EM algorithm was used for parameters estimation. The relationship between the arriving flow distribution at downstream intersection and the departing flow distribution at upstream intersection was investigated using the proposed model. Comparison analysis using virtual flow data was performed between the Robertson model and the MPFDM. The results confirmed the validity of the proposed model.
Gaussian mixture models-based ship target recognition algorithm in remote sensing infrared images
Yao, Shoukui; Qin, Xiaojuan
2018-02-01
Since the resolution of remote sensing infrared images is low, the features of ship targets become unstable. The issue of how to recognize ships with fuzzy features is an open problem. In this paper, we propose a novel ship target recognition algorithm based on Gaussian mixture models (GMMs). In the proposed algorithm, there are mainly two steps. At the first step, the Hu moments of these ship target images are calculated, and the GMMs are trained on the moment features of ships. At the second step, the moment feature of each ship image is assigned to the trained GMMs for recognition. Because of the scale, rotation, translation invariance property of Hu moments and the power feature-space description ability of GMMs, the GMMs-based ship target recognition algorithm can recognize ship reliably. Experimental results of a large simulating image set show that our approach is effective in distinguishing different ship types, and obtains a satisfactory ship recognition performance.
Liu, Sijia; Sa, Ruhan; Maguire, Orla; Minderman, Hans; Chaudhary, Vipin
2015-03-01
Cytogenetic abnormalities are important diagnostic and prognostic criteria for acute myeloid leukemia (AML). A flow cytometry-based imaging approach for FISH in suspension (FISH-IS) was established that enables the automated analysis of several log-magnitude higher number of cells compared to the microscopy-based approaches. The rotational positioning can occur leading to discordance between spot count. As a solution of counting error from overlapping spots, in this study, a Gaussian Mixture Model based classification method is proposed. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) of GMM are used as global image features of this classification method. Via Random Forest classifier, the result shows that the proposed method is able to detect closely overlapping spots which cannot be separated by existing image segmentation based spot detection methods. The experiment results show that by the proposed method we can obtain a significant improvement in spot counting accuracy.
Estimation of Seismic Wavelets Based on the Multivariate Scale Mixture of Gaussians Model
Directory of Open Access Journals (Sweden)
Jing-Huai Gao
2009-12-01
Full Text Available This paper proposes a new method for estimating seismic wavelets. Suppose a seismic wavelet can be modeled by a formula with three free parameters (scale, frequency and phase. We can transform the estimation of the wavelet into determining these three parameters. The phase of the wavelet is estimated by constant-phase rotation to the seismic signal, while the other two parameters are obtained by the Higher-order Statistics (HOS (fourth-order cumulant matching method. In order to derive the estimator of the Higher-order Statistics (HOS, the multivariate scale mixture of Gaussians (MSMG model is applied to formulating the multivariate joint probability density function (PDF of the seismic signal. By this way, we can represent HOS as a polynomial function of second-order statistics to improve the anti-noise performance and accuracy. In addition, the proposed method can work well for short time series.
LEARNING VECTOR QUANTIZATION FOR ADAPTED GAUSSIAN MIXTURE MODELS IN AUTOMATIC SPEAKER IDENTIFICATION
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IMEN TRABELSI
2017-05-01
Full Text Available Speaker Identification (SI aims at automatically identifying an individual by extracting and processing information from his/her voice. Speaker voice is a robust a biometric modality that has a strong impact in several application areas. In this study, a new combination learning scheme has been proposed based on Gaussian mixture model-universal background model (GMM-UBM and Learning vector quantization (LVQ for automatic text-independent speaker identification. Features vectors, constituted by the Mel Frequency Cepstral Coefficients (MFCC extracted from the speech signal are used to train the New England subset of the TIMIT database. The best results obtained (90% for gender- independent speaker identification, 97 % for male speakers and 93% for female speakers for test data using 36 MFCC features.
Qin, Yong; Ma, Hong; Chen, Jinfeng; Cheng, Li
2015-12-01
Conventional multitarget tracking systems presume that each target can produce at most one measurement per scan. Due to the multiple ionospheric propagation paths in over-the-horizon radar (OTHR), this assumption is not valid. To solve this problem, this paper proposes a novel tracking algorithm based on the theory of finite set statistics (FISST) called the multipath probability hypothesis density (MP-PHD) filter in cluttered environments. First, the FISST is used to derive the update equation, and then Gaussian mixture (GM) is introduced to derive the closed-form solution of the MP-PHD filter. Moreover, the extended Kalman filter (EKF) is presented to deal with the nonlinear problem of the measurement model in OTHR. Eventually, the simulation results are provided to demonstrate the effectiveness of the proposed filter.
A Grasp-Pose Generation Method Based on Gaussian Mixture Models
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Wenjia Wu
2015-11-01
Full Text Available A Gaussian Mixture Model (GMM-based grasp-pose generation method is proposed in this paper. Through offline training, the GMM is set up and used to depict the distribution of the robot's reachable orientations. By dividing the robot's workspace into small 3D voxels and training the GMM for each voxel, a look-up table covering all the workspace is built with the x, y and z positions as the index and the GMM as the entry. Through the definition of Task Space Regions (TSR, an object's feasible grasp poses are expressed as a continuous region. With the GMM, grasp poses can be preferentially sampled from regions with high reachability probabilities in the online grasp-planning stage. The GMM can also be used as a preliminary judgement of a grasp pose's reachability. Experiments on both a simulated and a real robot show the superiority of our method over the existing method.
Non-Gaussianities due to relativistic corrections to the observed galaxy bispectrum
International Nuclear Information System (INIS)
Dio, E. Di; Perrier, H.; Durrer, R.; Dizgah, A. Moradinezhad; Riotto, A.; Marozzi, G.; Noreña, J.
2017-01-01
High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for relativistic corrections to the clustering statistics is particularly important for the upcoming galaxy surveys covering progressively larger fraction of the sky. We focus on relativistic projection effects due to the fact that we observe the galaxies through the light that reaches the telescope on perturbed geodesics. These projection effects can give rise to an effective f NL that can be misinterpreted as the primordial non-Gaussianity signal and hence is a systematic to be carefully computed and accounted for in modelling of the bispectrum. We develop the technique to properly account for relativistic effects in terms of purely observable quantities, namely angles and redshifts. We give some examples by applying this approach to a subset of the contributions to the tree-level bispectrum of the observed galaxy number counts calculated within perturbation theory and estimate the corresponding non-Gaussianity parameter, f NL , for the local, equilateral and orthogonal shapes. For the local shape, we also compute the local non-Gaussianity resulting from terms obtained using the consistency relation for observed number counts. Our goal here is not to give a precise estimate of f NL for each shape but rather we aim to provide a scheme to compute the non-Gaussian contamination due to relativistic projection effects. For the terms considered in this work, we obtain contamination of f NL loc ∼ O(1).
Non-Gaussianities due to relativistic corrections to the observed galaxy bispectrum
Energy Technology Data Exchange (ETDEWEB)
Dio, E. Di [INAF—Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, Trieste, I-34143 Italy (Italy); Perrier, H.; Durrer, R.; Dizgah, A. Moradinezhad; Riotto, A. [University of Geneva, Department of Theoretical Physics and Center for Astroparticle Physics (CAP), 24 quai E. Ansermet, Geneva 4, CH-1211 Switzerland (Switzerland); Marozzi, G. [Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Urca, Rio de Janeiro, CEP 22290-180 Brazil (Brazil); Noreña, J., E-mail: Enea.DiDio@oats.inaf.it, E-mail: Hideki.Perrier@unige.ch, E-mail: Ruth.Durrer@unige.ch, E-mail: Marozzi@cbpf.br, E-mail: amoradinejad@physics.harvard.edu, E-mail: jorge.norena@pucv.cl, E-mail: Antonio.Riotto@unige.ch [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla, Valparaíso, 4059 Chile (Chile)
2017-03-01
High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for relativistic corrections to the clustering statistics is particularly important for the upcoming galaxy surveys covering progressively larger fraction of the sky. We focus on relativistic projection effects due to the fact that we observe the galaxies through the light that reaches the telescope on perturbed geodesics. These projection effects can give rise to an effective f {sub NL} that can be misinterpreted as the primordial non-Gaussianity signal and hence is a systematic to be carefully computed and accounted for in modelling of the bispectrum. We develop the technique to properly account for relativistic effects in terms of purely observable quantities, namely angles and redshifts. We give some examples by applying this approach to a subset of the contributions to the tree-level bispectrum of the observed galaxy number counts calculated within perturbation theory and estimate the corresponding non-Gaussianity parameter, f {sub NL}, for the local, equilateral and orthogonal shapes. For the local shape, we also compute the local non-Gaussianity resulting from terms obtained using the consistency relation for observed number counts. Our goal here is not to give a precise estimate of f {sub NL} for each shape but rather we aim to provide a scheme to compute the non-Gaussian contamination due to relativistic projection effects. For the terms considered in this work, we obtain contamination of f {sub NL}{sup loc} ∼ O(1).
International Nuclear Information System (INIS)
Kamiya, Ryo; Ogawa, Koichi
2013-01-01
The aim of the study is to improve the spatial resolution of single photon emission computed tomography (SPECT) images acquired with a fan-beam collimator. The aperture angle of a hole in the fan-beam collimator depends on the position of the collimator. To correct the aperture effect in an iterative image reconstruction, an asymmetrically trimmed Gaussian weight was used for a model. To confirm the validity of our method, point source phantoms and brain phantom were used in the simulation, and we applied the method to the clinical data. The results of the simulation showed that the spatial resolution of point sources improved from about 6 to 2 pixels full width at half maximum, and the corrected point sources were isotropic. The results of the simulation with the brain phantom showed that our proposed method could improve the spatial resolution of the phantom, and our method was effective for different fan-beam collimators with different focal lengths. The results of clinical data showed that the quality of the reconstructed image was improved with our proposed method. Our proposed aperture correction method with the asymmetrically trimmed Gaussian weighting function was effective in improving the spatial resolution of SPECT images acquired with the fan-beam collimator. (author)
A Gaussian mixture model for definition of lung tumor volumes in positron emission tomography
International Nuclear Information System (INIS)
Aristophanous, Michalis; Penney, Bill C.; Martel, Mary K.; Pelizzari, Charles A.
2007-01-01
The increased interest in 18 F-fluorodeoxyglucose (FDG) positron emission tomography (PET) in radiation treatment planning in the past five years necessitated the independent and accurate segmentation of gross tumor volume (GTV) from FDG-PET scans. In some studies the radiation oncologist contours the GTV based on a computed tomography scan, while incorporating pertinent data from the PET images. Alternatively, a simple threshold, typically 40% of the maximum intensity, has been employed to differentiate tumor from normal tissue, while other researchers have developed algorithms to aid the PET based GTV definition. None of these methods, however, results in reliable PET tumor segmentation that can be used for more sophisticated treatment plans. For this reason, we developed a Gaussian mixture model (GMM) based segmentation technique on selected PET tumor regions from non-small cell lung cancer patients. The purpose of this study was to investigate the feasibility of using a GMM-based tumor volume definition in a robust, reliable and reproducible way. A GMM relies on the idea that any distribution, in our case a distribution of image intensities, can be expressed as a mixture of Gaussian densities representing different classes. According to our implementation, each class belongs to one of three regions in the image; the background (B), the uncertain (U) and the target (T), and from these regions we can obtain the tumor volume. User interaction in the implementation is required, but is limited to the initialization of the model parameters and the selection of an ''analysis region'' to which the modeling is restricted. The segmentation was developed on three and tested on another four clinical cases to ensure robustness against differences observed in the clinic. It also compared favorably with thresholding at 40% of the maximum intensity and a threshold determination function based on tumor to background image intensities proposed in a recent paper. The parts of the
Sworn testimony of the model evidence: Gaussian Mixture Importance (GAME) sampling
Volpi, Elena; Schoups, Gerrit; Firmani, Giovanni; Vrugt, Jasper A.
2017-07-01
What is the "best" model? The answer to this question lies in part in the eyes of the beholder, nevertheless a good model must blend rigorous theory with redeeming qualities such as parsimony and quality of fit. Model selection is used to make inferences, via weighted averaging, from a set of K candidate models, Mk; k=>(1,…,K>), and help identify which model is most supported by the observed data, Y>˜=>(y˜1,…,y˜n>). Here, we introduce a new and robust estimator of the model evidence, p>(Y>˜|Mk>), which acts as normalizing constant in the denominator of Bayes' theorem and provides a single quantitative measure of relative support for each hypothesis that integrates model accuracy, uncertainty, and complexity. However, p>(Y>˜|Mk>) is analytically intractable for most practical modeling problems. Our method, coined GAussian Mixture importancE (GAME) sampling, uses bridge sampling of a mixture distribution fitted to samples of the posterior model parameter distribution derived from MCMC simulation. We benchmark the accuracy and reliability of GAME sampling by application to a diverse set of multivariate target distributions (up to 100 dimensions) with known values of p>(Y>˜|Mk>) and to hypothesis testing using numerical modeling of the rainfall-runoff transformation of the Leaf River watershed in Mississippi, USA. These case studies demonstrate that GAME sampling provides robust and unbiased estimates of the evidence at a relatively small computational cost outperforming commonly used estimators. The GAME sampler is implemented in the MATLAB package of DREAM and simplifies considerably scientific inquiry through hypothesis testing and model selection.
A Gaussian mixture model based cost function for parameter estimation of chaotic biological systems
Shekofteh, Yasser; Jafari, Sajad; Sprott, Julien Clinton; Hashemi Golpayegani, S. Mohammad Reza; Almasganj, Farshad
2015-02-01
As we know, many biological systems such as neurons or the heart can exhibit chaotic behavior. Conventional methods for parameter estimation in models of these systems have some limitations caused by sensitivity to initial conditions. In this paper, a novel cost function is proposed to overcome those limitations by building a statistical model on the distribution of the real system attractor in state space. This cost function is defined by the use of a likelihood score in a Gaussian mixture model (GMM) which is fitted to the observed attractor generated by the real system. Using that learned GMM, a similarity score can be defined by the computed likelihood score of the model time series. We have applied the proposed method to the parameter estimation of two important biological systems, a neuron and a cardiac pacemaker, which show chaotic behavior. Some simulated experiments are given to verify the usefulness of the proposed approach in clean and noisy conditions. The results show the adequacy of the proposed cost function.
Damage Detection of Refractory Based on Principle Component Analysis and Gaussian Mixture Model
Directory of Open Access Journals (Sweden)
Changming Liu
2018-01-01
Full Text Available Acoustic emission (AE technique is a common approach to identify the damage of the refractories; however, there is a complex problem since there are as many as fifteen involved parameters, which calls for effective data processing and classification algorithms to reduce the level of complexity. In this paper, experiments involving three-point bending tests of refractories were conducted and AE signals were collected. A new data processing method of merging the similar parameters in the description of the damage and reducing the dimension was developed. By means of the principle component analysis (PCA for dimension reduction, the fifteen related parameters can be reduced to two parameters. The parameters were the linear combinations of the fifteen original parameters and taken as the indexes for damage classification. Based on the proposed approach, the Gaussian mixture model was integrated with the Bayesian information criterion to group the AE signals into two damage categories, which accounted for 99% of all damage. Electronic microscope scanning of the refractories verified the two types of damage.
Hierarchical heuristic search using a Gaussian mixture model for UAV coverage planning.
Lin, Lanny; Goodrich, Michael A
2014-12-01
During unmanned aerial vehicle (UAV) search missions, efficient use of UAV flight time requires flight paths that maximize the probability of finding the desired subject. The probability of detecting the desired subject based on UAV sensor information can vary in different search areas due to environment elements like varying vegetation density or lighting conditions, making it likely that the UAV can only partially detect the subject. This adds another dimension of complexity to the already difficult (NP-Hard) problem of finding an optimal search path. We present a new class of algorithms that account for partial detection in the form of a task difficulty map and produce paths that approximate the payoff of optimal solutions. The algorithms use the mode goodness ratio heuristic that uses a Gaussian mixture model to prioritize search subregions. The algorithms search for effective paths through the parameter space at different levels of resolution. We compare the performance of the new algorithms against two published algorithms (Bourgault's algorithm and LHC-GW-CONV algorithm) in simulated searches with three real search and rescue scenarios, and show that the new algorithms outperform existing algorithms significantly and can yield efficient paths that yield payoffs near the optimal.
Identification of damage in composite structures using Gaussian mixture model-processed Lamb waves
Wang, Qiang; Ma, Shuxian; Yue, Dong
2018-04-01
Composite materials have comprehensively better properties than traditional materials, and therefore have been more and more widely used, especially because of its higher strength-weight ratio. However, the damage of composite structures is usually varied and complicated. In order to ensure the security of these structures, it is necessary to monitor and distinguish the structural damage in a timely manner. Lamb wave-based structural health monitoring (SHM) has been proved to be effective in online structural damage detection and evaluation; furthermore, the characteristic parameters of the multi-mode Lamb wave varies in response to different types of damage in the composite material. This paper studies the damage identification approach for composite structures using the Lamb wave and the Gaussian mixture model (GMM). The algorithm and principle of the GMM, and the parameter estimation, is introduced. Multi-statistical characteristic parameters of the excited Lamb waves are extracted, and the parameter space with reduced dimensions is adopted by principal component analysis (PCA). The damage identification system using the GMM is then established through training. Experiments on a glass fiber-reinforced epoxy composite laminate plate are conducted to verify the feasibility of the proposed approach in terms of damage classification. The experimental results show that different types of damage can be identified according to the value of the likelihood function of the GMM.
Personalized Risk Scoring for Critical Care Prognosis Using Mixtures of Gaussian Processes.
Alaa, Ahmed M; Yoon, Jinsung; Hu, Scott; van der Schaar, Mihaela
2018-01-01
In this paper, we develop a personalized real-time risk scoring algorithm that provides timely and granular assessments for the clinical acuity of ward patients based on their (temporal) lab tests and vital signs; the proposed risk scoring system ensures timely intensive care unit admissions for clinically deteriorating patients. The risk scoring system is based on the idea of sequential hypothesis testing under an uncertain time horizon. The system learns a set of latent patient subtypes from the offline electronic health record data, and trains a mixture of Gaussian Process experts, where each expert models the physiological data streams associated with a specific patient subtype. Transfer learning techniques are used to learn the relationship between a patient's latent subtype and her static admission information (e.g., age, gender, transfer status, ICD-9 codes, etc). Experiments conducted on data from a heterogeneous cohort of 6321 patients admitted to Ronald Reagan UCLA medical center show that our score significantly outperforms the currently deployed risk scores, such as the Rothman index, MEWS, APACHE, and SOFA scores, in terms of timeliness, true positive rate, and positive predictive value. Our results reflect the importance of adopting the concepts of personalized medicine in critical care settings; significant accuracy and timeliness gains can be achieved by accounting for the patients' heterogeneity. The proposed risk scoring methodology can confer huge clinical and social benefits on a massive number of critically ill inpatients who exhibit adverse outcomes including, but not limited to, cardiac arrests, respiratory arrests, and septic shocks.
Vehicle speed detection based on gaussian mixture model using sequential of images
Setiyono, Budi; Ratna Sulistyaningrum, Dwi; Soetrisno; Fajriyah, Farah; Wahyu Wicaksono, Danang
2017-09-01
Intelligent Transportation System is one of the important components in the development of smart cities. Detection of vehicle speed on the highway is supporting the management of traffic engineering. The purpose of this study is to detect the speed of the moving vehicles using digital image processing. Our approach is as follows: The inputs are a sequence of frames, frame rate (fps) and ROI. The steps are following: First we separate foreground and background using Gaussian Mixture Model (GMM) in each frames. Then in each frame, we calculate the location of object and its centroid. Next we determine the speed by computing the movement of centroid in sequence of frames. In the calculation of speed, we only consider frames when the centroid is inside the predefined region of interest (ROI). Finally we transform the pixel displacement into a time unit of km/hour. Validation of the system is done by comparing the speed calculated manually and obtained by the system. The results of software testing can detect the speed of vehicles with the highest accuracy is 97.52% and the lowest accuracy is 77.41%. And the detection results of testing by using real video footage on the road is included with real speed of the vehicle.
Multi-atlas segmentation for abdominal organs with Gaussian mixture models
Burke, Ryan P.; Xu, Zhoubing; Lee, Christopher P.; Baucom, Rebeccah B.; Poulose, Benjamin K.; Abramson, Richard G.; Landman, Bennett A.
2015-03-01
Abdominal organ segmentation with clinically acquired computed tomography (CT) is drawing increasing interest in the medical imaging community. Gaussian mixture models (GMM) have been extensively used through medical segmentation, most notably in the brain for cerebrospinal fluid / gray matter / white matter differentiation. Because abdominal CT exhibit strong localized intensity characteristics, GMM have recently been incorporated in multi-stage abdominal segmentation algorithms. In the context of variable abdominal anatomy and rich algorithms, it is difficult to assess the marginal contribution of GMM. Herein, we characterize the efficacy of an a posteriori framework that integrates GMM of organ-wise intensity likelihood with spatial priors from multiple target-specific registered labels. In our study, we first manually labeled 100 CT images. Then, we assigned 40 images to use as training data for constructing target-specific spatial priors and intensity likelihoods. The remaining 60 images were evaluated as test targets for segmenting 12 abdominal organs. The overlap between the true and the automatic segmentations was measured by Dice similarity coefficient (DSC). A median improvement of 145% was achieved by integrating the GMM intensity likelihood against the specific spatial prior. The proposed framework opens the opportunities for abdominal organ segmentation by efficiently using both the spatial and appearance information from the atlases, and creates a benchmark for large-scale automatic abdominal segmentation.
Speech Enhancement Using Gaussian Mixture Models, Explicit Bayesian Estimation and Wiener Filtering
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M. H. Savoji
2014-09-01
Full Text Available Gaussian Mixture Models (GMMs of power spectral densities of speech and noise are used with explicit Bayesian estimations in Wiener filtering of noisy speech. No assumption is made on the nature or stationarity of the noise. No voice activity detection (VAD or any other means is employed to estimate the input SNR. The GMM mean vectors are used to form sets of over-determined system of equations whose solutions lead to the first estimates of speech and noise power spectra. The noise source is also identified and the input SNR estimated in this first step. These first estimates are then refined using approximate but explicit MMSE and MAP estimation formulations. The refined estimates are then used in a Wiener filter to reduce noise and enhance the noisy speech. The proposed schemes show good results. Nevertheless, it is shown that the MAP explicit solution, introduced here for the first time, reduces the computation time to less than one third with a slight higher improvement in SNR and PESQ score and also less distortion in comparison to the MMSE solution.
Directory of Open Access Journals (Sweden)
Chin-Teng Lin
2018-01-01
Full Text Available Electroencephalogram (EEG signals are usually contaminated with various artifacts, such as signal associated with muscle activity, eye movement, and body motion, which have a noncerebral origin. The amplitude of such artifacts is larger than that of the electrical activity of the brain, so they mask the cortical signals of interest, resulting in biased analysis and interpretation. Several blind source separation methods have been developed to remove artifacts from the EEG recordings. However, the iterative process for measuring separation within multichannel recordings is computationally intractable. Moreover, manually excluding the artifact components requires a time-consuming offline process. This work proposes a real-time artifact removal algorithm that is based on canonical correlation analysis (CCA, feature extraction, and the Gaussian mixture model (GMM to improve the quality of EEG signals. The CCA was used to decompose EEG signals into components followed by feature extraction to extract representative features and GMM to cluster these features into groups to recognize and remove artifacts. The feasibility of the proposed algorithm was demonstrated by effectively removing artifacts caused by blinks, head/body movement, and chewing from EEG recordings while preserving the temporal and spectral characteristics of the signals that are important to cognitive research.
GGRaSP: A R-package for selecting representative genomes using Gaussian mixture models.
Clarke, Thomas H; Brinkac, Lauren M; Sutton, Granger; Fouts, Derrick E
2018-04-14
The vast number of available sequenced bacterial genomes occasionally exceeds the facilities of comparative genomic methods or is dominated by a single outbreak strain, and thus a diverse and representative subset is required. Generation of the reduced subset currently requires a priori supervised clustering and sequence-only selection of medoid genomic sequences, independent of any additional genome metrics or strain attributes. The GGRaSP R-package described below generates a reduced subset of genomes that prioritizes maintaining genomes of interest to the user as well as minimizing the loss of genetic variation. The package also allows for unsupervised clustering by modeling the genomic relationships using a Gaussian Mixture Model to select an appropriate cluster threshold. We demonstrate the capabilities of GGRaSP by generating a reduced list of 315 genomes from a genomic dataset of 4600 Escherichia coli genomes, prioritizing selection by type strain and by genome completeness. GGRaSP is available at https://github.com/JCVenterInstitute/ggrasp/. tclarke@jcvi.org. Supplementary data are available at the GitHub site.
Raymond, Neil; Iouchtchenko, Dmitri; Roy, Pierre-Nicholas; Nooijen, Marcel
2018-05-01
We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition function in a product basis of continuous nuclear and discrete electronic degrees of freedom without the use of any mapping schemes. We separate our Hamiltonian into a harmonic portion and a coupling portion; the partition function can then be calculated as the product of a Monte Carlo estimator (of the coupling contribution to the partition function) and a normalization factor (that is evaluated analytically). A Gaussian mixture model is used to evaluate the Monte Carlo estimator in a computationally efficient manner. Using two model systems, we demonstrate our approach to reduce the stochastic error associated with the Monte Carlo estimator. We show that the selection of the harmonic oscillators comprising the sampling distribution directly affects the efficiency of the method. Our results demonstrate that our path integral Monte Carlo method's deviation from exact Trotter calculations is dominated by the choice of the sampling distribution. By improving the sampling distribution, we can drastically reduce the stochastic error leading to lower computational cost.
Monthly streamflow forecasting based on hidden Markov model and Gaussian Mixture Regression
Liu, Yongqi; Ye, Lei; Qin, Hui; Hong, Xiaofeng; Ye, Jiajun; Yin, Xingli
2018-06-01
Reliable streamflow forecasts can be highly valuable for water resources planning and management. In this study, we combined a hidden Markov model (HMM) and Gaussian Mixture Regression (GMR) for probabilistic monthly streamflow forecasting. The HMM is initialized using a kernelized K-medoids clustering method, and the Baum-Welch algorithm is then executed to learn the model parameters. GMR derives a conditional probability distribution for the predictand given covariate information, including the antecedent flow at a local station and two surrounding stations. The performance of HMM-GMR was verified based on the mean square error and continuous ranked probability score skill scores. The reliability of the forecasts was assessed by examining the uniformity of the probability integral transform values. The results show that HMM-GMR obtained reasonably high skill scores and the uncertainty spread was appropriate. Different HMM states were assumed to be different climate conditions, which would lead to different types of observed values. We demonstrated that the HMM-GMR approach can handle multimodal and heteroscedastic data.
Missing Value Imputation Based on Gaussian Mixture Model for the Internet of Things
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Xiaobo Yan
2015-01-01
Full Text Available This paper addresses missing value imputation for the Internet of Things (IoT. Nowadays, the IoT has been used widely and commonly by a variety of domains, such as transportation and logistics domain and healthcare domain. However, missing values are very common in the IoT for a variety of reasons, which results in the fact that the experimental data are incomplete. As a result of this, some work, which is related to the data of the IoT, can’t be carried out normally. And it leads to the reduction in the accuracy and reliability of the data analysis results. This paper, for the characteristics of the data itself and the features of missing data in IoT, divides the missing data into three types and defines three corresponding missing value imputation problems. Then, we propose three new models to solve the corresponding problems, and they are model of missing value imputation based on context and linear mean (MCL, model of missing value imputation based on binary search (MBS, and model of missing value imputation based on Gaussian mixture model (MGI. Experimental results showed that the three models can improve the accuracy, reliability, and stability of missing value imputation greatly and effectively.
International Nuclear Information System (INIS)
Wang Ying; Yuan Chengxun; Gao Ruilin; Zhou Zhongxiang
2012-01-01
Theoretical investigations of a Gaussian laser beam propagating in relativistic plasmas have been performed with the WKB method and complex eikonal function. We consider the relativistic nonlinearity induced by intense laser beam, and present the relativistically generalized forms of the plasma frequency and electron collision frequency in plasmas. The coupled differential equations describing the propagation variations of laser beam are derived and numerically solved. The obtained simulation results present the similar variation tendency with experiments. By changing the plasma density, we theoretically analyze the feasibility of using a plasmas slab of a fixed thickness to compress the laser beam-width and acquire the focused laser intensity. The present work complements the relativistic correction of the electron collision frequency with reasonable derivations, promotes the theoretical approaching to experiments and provides effective instructions to the practical laser-plasma interactions.
Goossens, Bart; Aelterman, Jan; Luong, Hiep; Pizurica, Aleksandra; Philips, Wilfried
2013-02-01
In digital cameras and mobile phones, there is an ongoing trend to increase the image resolution, decrease the sensor size and to use lower exposure times. Because smaller sensors inherently lead to more noise and a worse spatial resolution, digital post-processing techniques are required to resolve many of the artifacts. Color filter arrays (CFAs), which use alternating patterns of color filters, are very popular because of price and power consumption reasons. However, color filter arrays require the use of a post-processing technique such as demosaicing to recover full resolution RGB images. Recently, there has been some interest in techniques that jointly perform the demosaicing and denoising. This has the advantage that the demosaicing and denoising can be performed optimally (e.g. in the MSE sense) for the considered noise model, while avoiding artifacts introduced when using demosaicing and denoising sequentially. In this paper, we will continue the research line of the wavelet-based demosaicing techniques. These approaches are computationally simple and very suited for combination with denoising. Therefore, we will derive Bayesian Minimum Squared Error (MMSE) joint demosaicing and denoising rules in the complex wavelet packet domain, taking local adaptivity into account. As an image model, we will use Gaussian Scale Mixtures, thereby taking advantage of the directionality of the complex wavelets. Our results show that this technique is well capable of reconstructing fine details in the image, while removing all of the noise, at a relatively low computational cost. In particular, the complete reconstruction (including color correction, white balancing etc) of a 12 megapixel RAW image takes 3.5 sec on a recent mid-range GPU.
Heggeseth, Brianna C; Jewell, Nicholas P
2013-07-20
Multivariate Gaussian mixtures are a class of models that provide a flexible parametric approach for the representation of heterogeneous multivariate outcomes. When the outcome is a vector of repeated measurements taken on the same subject, there is often inherent dependence between observations. However, a common covariance assumption is conditional independence-that is, given the mixture component label, the outcomes for subjects are independent. In this paper, we study, through asymptotic bias calculations and simulation, the impact of covariance misspecification in multivariate Gaussian mixtures. Although maximum likelihood estimators of regression and mixing probability parameters are not consistent under misspecification, they have little asymptotic bias when mixture components are well separated or if the assumed correlation is close to the truth even when the covariance is misspecified. We also present a robust standard error estimator and show that it outperforms conventional estimators in simulations and can indicate that the model is misspecified. Body mass index data from a national longitudinal study are used to demonstrate the effects of misspecification on potential inferences made in practice. Copyright © 2013 John Wiley & Sons, Ltd.
Rabbani, Hossein; Sonka, Milan; Abramoff, Michael D
2013-01-01
In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture the heavy-tailed property and inter- and intrascale dependencies of coefficients. In addition, based on the special structure of OCT images, we use an anisotropic windowing procedure for local parameters estimation that results in visual quality improvement. On this base, several OCT despeckling algorithms are obtained based on using Gaussian/two-sided Rayleigh noise distribution and homomorphic/nonhomomorphic model. In order to evaluate the performance of the proposed algorithm, we use 156 selected ROIs from 650 × 512 × 128 OCT dataset in the presence of wet AMD pathology. Our simulations show that the best MMSE estimator using local bivariate mixture prior is for the nonhomomorphic model in the presence of Gaussian noise which results in an improvement of 7.8 ± 1.7 in CNR.
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Hossein Rabbani
2013-01-01
Full Text Available In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture the heavy-tailed property and inter- and intrascale dependencies of coefficients. In addition, based on the special structure of OCT images, we use an anisotropic windowing procedure for local parameters estimation that results in visual quality improvement. On this base, several OCT despeckling algorithms are obtained based on using Gaussian/two-sided Rayleigh noise distribution and homomorphic/nonhomomorphic model. In order to evaluate the performance of the proposed algorithm, we use 156 selected ROIs from 650 × 512 × 128 OCT dataset in the presence of wet AMD pathology. Our simulations show that the best MMSE estimator using local bivariate mixture prior is for the nonhomomorphic model in the presence of Gaussian noise which results in an improvement of 7.8 ± 1.7 in CNR.
Avendaño-Valencia, Luis David; Fassois, Spilios D.
2017-12-01
The problem of vibration-based damage diagnosis in structures characterized by time-dependent dynamics under significant environmental and/or operational uncertainty is considered. A stochastic framework consisting of a Gaussian Mixture Random Coefficient model of the uncertain time-dependent dynamics under each structural health state, proper estimation methods, and Bayesian or minimum distance type decision making, is postulated. The Random Coefficient (RC) time-dependent stochastic model with coefficients following a multivariate Gaussian Mixture Model (GMM) allows for significant flexibility in uncertainty representation. Certain of the model parameters are estimated via a simple procedure which is founded on the related Multiple Model (MM) concept, while the GMM weights are explicitly estimated for optimizing damage diagnostic performance. The postulated framework is demonstrated via damage detection in a simple simulated model of a quarter-car active suspension with time-dependent dynamics and considerable uncertainty on the payload. Comparisons with a simpler Gaussian RC model based method are also presented, with the postulated framework shown to be capable of offering considerable improvement in diagnostic performance.
Gu, Wenjun; Zhang, Weizhi; Wang, Jin; Amini Kashani, M. R.; Kavehrad, Mohsen
2015-01-01
Over the past decade, location based services (LBS) have found their wide applications in indoor environments, such as large shopping malls, hospitals, warehouses, airports, etc. Current technologies provide wide choices of available solutions, which include Radio-frequency identification (RFID), Ultra wideband (UWB), wireless local area network (WLAN) and Bluetooth. With the rapid development of light-emitting-diodes (LED) technology, visible light communications (VLC) also bring a practical approach to LBS. As visible light has a better immunity against multipath effect than radio waves, higher positioning accuracy is achieved. LEDs are utilized both for illumination and positioning purpose to realize relatively lower infrastructure cost. In this paper, an indoor positioning system using VLC is proposed, with LEDs as transmitters and photo diodes as receivers. The algorithm for estimation is based on received-signalstrength (RSS) information collected from photo diodes and trilateration technique. By appropriately making use of the characteristics of receiver movements and the property of trilateration, estimation on three-dimensional (3-D) coordinates is attained. Filtering technique is applied to enable tracking capability of the algorithm, and a higher accuracy is reached compare to raw estimates. Gaussian mixture Sigma-point particle filter (GM-SPPF) is proposed for this 3-D system, which introduces the notion of Gaussian Mixture Model (GMM). The number of particles in the filter is reduced by approximating the probability distribution with Gaussian components.
Flexible Mixture-Amount Models for Business and Industry Using Gaussian Processes
A. Ruseckaite (Aiste); D. Fok (Dennis); P.P. Goos (Peter)
2016-01-01
markdownabstractMany products and services can be described as mixtures of ingredients whose proportions sum to one. Specialized models have been developed for linking the mixture proportions to outcome variables, such as preference, quality and liking. In many scenarios, only the mixture
Directory of Open Access Journals (Sweden)
Feng Lian
2012-01-01
Full Text Available The convergence of the Gaussian mixture extended-target probability hypothesis density (GM-EPHD filter and its extended Kalman (EK filtering approximation in mildly nonlinear condition, namely, the EK-GM-EPHD filter, is studied here. This paper proves that both the GM-EPHD filter and the EK-GM-EPHD filter converge uniformly to the true EPHD filter. The significance of this paper is in theory to present the convergence results of the GM-EPHD and EK-GM-EPHD filters and the conditions under which the two filters satisfy uniform convergence.
Rabbani, Hossein; Sonka, Milan; Abramoff, Michael D.
2013-01-01
In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture th...
Directory of Open Access Journals (Sweden)
Douglas Scott C
2007-01-01
Full Text Available We derive new fixed-point algorithms for the blind separation of complex-valued mixtures of independent, noncircularly symmetric, and non-Gaussian source signals. Leveraging recently developed results on the separability of complex-valued signal mixtures, we systematically construct iterative procedures on a kurtosis-based contrast whose evolutionary characteristics are identical to those of the FastICA algorithm of Hyvarinen and Oja in the real-valued mixture case. Thus, our methods inherit the fast convergence properties, computational simplicity, and ease of use of the FastICA algorithm while at the same time extending this class of techniques to complex signal mixtures. For extracting multiple sources, symmetric and asymmetric signal deflation procedures can be employed. Simulations for both noiseless and noisy mixtures indicate that the proposed algorithms have superior finite-sample performance in data-starved scenarios as compared to existing complex ICA methods while performing about as well as the best of these techniques for larger data-record lengths.
Del Pozzo, W.; Berry, C. P. L.; Ghosh, A.; Haines, T. S. F.; Singer, L. P.; Vecchio, A.
2018-06-01
We reconstruct posterior distributions for the position (sky area and distance) of a simulated set of binary neutron-star gravitational-waves signals observed with Advanced LIGO and Advanced Virgo. We use a Dirichlet Process Gaussian-mixture model, a fully Bayesian non-parametric method that can be used to estimate probability density functions with a flexible set of assumptions. The ability to reliably reconstruct the source position is important for multimessenger astronomy, as recently demonstrated with GW170817. We show that for detector networks comparable to the early operation of Advanced LIGO and Advanced Virgo, typical localization volumes are ˜104-105 Mpc3 corresponding to ˜102-103 potential host galaxies. The localization volume is a strong function of the network signal-to-noise ratio, scaling roughly ∝ϱnet-6. Fractional localizations improve with the addition of further detectors to the network. Our Dirichlet Process Gaussian-mixture model can be adopted for localizing events detected during future gravitational-wave observing runs, and used to facilitate prompt multimessenger follow-up.
Energy Technology Data Exchange (ETDEWEB)
Holoien, Thomas W.-S.; /Ohio State U., Dept. Astron. /Ohio State U., CCAPP /KIPAC, Menlo Park /SLAC; Marshall, Philip J.; Wechsler, Risa H.; /KIPAC, Menlo Park /SLAC
2017-05-11
We describe two new open-source tools written in Python for performing extreme deconvolution Gaussian mixture modeling (XDGMM) and using a conditioned model to re-sample observed supernova and host galaxy populations. XDGMM is new program that uses Gaussian mixtures to perform density estimation of noisy data using extreme deconvolution (XD) algorithms. Additionally, it has functionality not available in other XD tools. It allows the user to select between the AstroML and Bovy et al. fitting methods and is compatible with scikit-learn machine learning algorithms. Most crucially, it allows the user to condition a model based on the known values of a subset of parameters. This gives the user the ability to produce a tool that can predict unknown parameters based on a model that is conditioned on known values of other parameters. EmpiriciSN is an exemplary application of this functionality, which can be used to fit an XDGMM model to observed supernova/host data sets and predict likely supernova parameters using a model conditioned on observed host properties. It is primarily intended to simulate realistic supernovae for LSST data simulations based on empirical galaxy properties.
Holoien, Thomas W.-S.; Marshall, Philip J.; Wechsler, Risa H.
2017-06-01
We describe two new open-source tools written in Python for performing extreme deconvolution Gaussian mixture modeling (XDGMM) and using a conditioned model to re-sample observed supernova and host galaxy populations. XDGMM is new program that uses Gaussian mixtures to perform density estimation of noisy data using extreme deconvolution (XD) algorithms. Additionally, it has functionality not available in other XD tools. It allows the user to select between the AstroML and Bovy et al. fitting methods and is compatible with scikit-learn machine learning algorithms. Most crucially, it allows the user to condition a model based on the known values of a subset of parameters. This gives the user the ability to produce a tool that can predict unknown parameters based on a model that is conditioned on known values of other parameters. EmpiriciSN is an exemplary application of this functionality, which can be used to fit an XDGMM model to observed supernova/host data sets and predict likely supernova parameters using a model conditioned on observed host properties. It is primarily intended to simulate realistic supernovae for LSST data simulations based on empirical galaxy properties.
Directory of Open Access Journals (Sweden)
Milad eLankarany
2013-09-01
Full Text Available Time-varying excitatory and inhibitory synaptic inputs govern activity of neurons and process information in the brain. The importance of trial-to-trial fluctuations of synaptic inputs has recently been investigated in neuroscience. Such fluctuations are ignored in the most conventional techniques because they are removed when trials are averaged during linear regression techniques. Here, we propose a novel recursive algorithm based on Gaussian mixture Kalman filtering for estimating time-varying excitatory and inhibitory synaptic inputs from single trials of noisy membrane potential in current clamp recordings. The Kalman filtering is followed by an expectation maximization algorithm to infer the statistical parameters (time-varying mean and variance of the synaptic inputs in a non-parametric manner. As our proposed algorithm is repeated recursively, the inferred parameters of the mixtures are used to initiate the next iteration. Unlike other recent algorithms, our algorithm does not assume an a priori distribution from which the synaptic inputs are generated. Instead, the algorithm recursively estimates such a distribution by fitting a Gaussian mixture model. The performance of the proposed algorithms is compared to a previously proposed PF-based algorithm (Paninski et al., 2012 with several illustrative examples, assuming that the distribution of synaptic input is unknown. If noise is small, the performance of our algorithms is similar to that of the previous one. However, if noise is large, they can significantly outperform the previous proposal. These promising results suggest that our algorithm is a robust and efficient technique for estimating time varying excitatory and inhibitory synaptic conductances from single trials of membrane potential recordings.
International Nuclear Information System (INIS)
Woulache, R.L.; Kofane, T.C.; Yemele, D.
2005-08-01
Thermal nucleation of kink-antikink pairs in a nonlinear Klein- Gordon model with Remoissenet-Peyrard substrate potential coupled to an applied field is analyzed in the limits of moderate temperature and strong damping. We derive analytically the non- Gaussian correction to the nucleation rate formula of kink- antikink pairs previously calculated by Yemele and Kofane and show that the correction factor depends on the intensity of the applied field, the temperature of the system and the shape of the substrate potential. (author)
FPGA Implementation of Gaussian Mixture Model Algorithm for 47 fps Segmentation of 1080p Video
Directory of Open Access Journals (Sweden)
Mariangela Genovese
2013-01-01
Full Text Available Circuits and systems able to process high quality video in real time are fundamental in nowadays imaging systems. The circuit proposed in the paper, aimed at the robust identification of the background in video streams, implements the improved formulation of the Gaussian Mixture Model (GMM algorithm that is included in the OpenCV library. An innovative, hardware oriented, formulation of the GMM equations, the use of truncated binary multipliers, and ROM compression techniques allow reduced hardware complexity and increased processing capability. The proposed circuit has been designed having commercial FPGA devices as target and provides speed and logic resources occupation that overcome previously proposed implementations. The circuit, when implemented on Virtex6 or StratixIV, processes more than 45 frame per second in 1080p format and uses few percent of FPGA logic resources.
Directory of Open Access Journals (Sweden)
Li Yao
2014-01-01
Full Text Available Modeling background and segmenting moving objects are significant techniques for computer vision applications. Mixture-of-Gaussians (MoG background model is commonly used in foreground extraction in video steam. However considering the case that the objects enter the scenery and stay for a while, the foreground extraction would fail as the objects stay still and gradually merge into the background. In this paper, we adopt a blob tracking method to cope with this situation. To construct the MoG model more quickly, we add frame difference method to the foreground extracted from MoG for very crowded situations. What is more, a new shadow removal method based on RGB color space is proposed.
Qiu, Lei; Yuan, Shenfang; Mei, Hanfei; Fang, Fang
2016-01-01
Structural Health Monitoring (SHM) technology is considered to be a key technology to reduce the maintenance cost and meanwhile ensure the operational safety of aircraft structures. It has gradually developed from theoretic and fundamental research to real-world engineering applications in recent decades. The problem of reliable damage monitoring under time-varying conditions is a main issue for the aerospace engineering applications of SHM technology. Among the existing SHM methods, Guided Wave (GW) and piezoelectric sensor-based SHM technique is a promising method due to its high damage sensitivity and long monitoring range. Nevertheless the reliability problem should be addressed. Several methods including environmental parameter compensation, baseline signal dependency reduction and data normalization, have been well studied but limitations remain. This paper proposes a damage propagation monitoring method based on an improved Gaussian Mixture Model (GMM). It can be used on-line without any structural mechanical model and a priori knowledge of damage and time-varying conditions. With this method, a baseline GMM is constructed first based on the GW features obtained under time-varying conditions when the structure under monitoring is in the healthy state. When a new GW feature is obtained during the on-line damage monitoring process, the GMM can be updated by an adaptive migration mechanism including dynamic learning and Gaussian components split-merge. The mixture probability distribution structure of the GMM and the number of Gaussian components can be optimized adaptively. Then an on-line GMM can be obtained. Finally, a best match based Kullback-Leibler (KL) divergence is studied to measure the migration degree between the baseline GMM and the on-line GMM to reveal the weak cumulative changes of the damage propagation mixed in the time-varying influence. A wing spar of an aircraft is used to validate the proposed method. The results indicate that the crack
Li, Zheng; Jiang, Yi-han; Duan, Lian; Zhu, Chao-zhe
2017-08-01
Objective. Functional near infra-red spectroscopy (fNIRS) is a promising brain imaging technology for brain-computer interfaces (BCI). Future clinical uses of fNIRS will likely require operation over long time spans, during which neural activation patterns may change. However, current decoders for fNIRS signals are not designed to handle changing activation patterns. The objective of this study is to test via simulations a new adaptive decoder for fNIRS signals, the Gaussian mixture model adaptive classifier (GMMAC). Approach. GMMAC can simultaneously classify and track activation pattern changes without the need for ground-truth labels. This adaptive classifier uses computationally efficient variational Bayesian inference to label new data points and update mixture model parameters, using the previous model parameters as priors. We test GMMAC in simulations in which neural activation patterns change over time and compare to static decoders and unsupervised adaptive linear discriminant analysis classifiers. Main results. Our simulation experiments show GMMAC can accurately decode under time-varying activation patterns: shifts of activation region, expansions of activation region, and combined contractions and shifts of activation region. Furthermore, the experiments show the proposed method can track the changing shape of the activation region. Compared to prior work, GMMAC performed significantly better than the other unsupervised adaptive classifiers on a difficult activation pattern change simulation: 99% versus brain-computer interfaces, including neurofeedback training systems, where operation over long time spans is required.
Mazoyer, Bernard; Zago, Laure; Jobard, Gaël; Crivello, Fabrice; Joliot, Marc; Perchey, Guy; Mellet, Emmanuel; Petit, Laurent; Tzourio-Mazoyer, Nathalie
2014-01-01
Hemispheric lateralization for language production and its relationships with manual preference and manual preference strength were studied in a sample of 297 subjects, including 153 left-handers (LH). A hemispheric functional lateralization index (HFLI) for language was derived from fMRI acquired during a covert sentence generation task as compared with a covert word list recitation. The multimodal HFLI distribution was optimally modeled using a mixture of 3 and 4 Gaussian functions in right-handers (RH) and LH, respectively. Gaussian function parameters helped to define 3 types of language hemispheric lateralization, namely "Typical" (left hemisphere dominance with clear positive HFLI values, 88% of RH, 78% of LH), "Ambilateral" (no dominant hemisphere with HFLI values close to 0, 12% of RH, 15% of LH) and "Strongly-atypical" (right-hemisphere dominance with clear negative HFLI values, 7% of LH). Concordance between dominant hemispheres for hand and for language did not exceed chance level, and most of the association between handedness and language lateralization was explained by the fact that all Strongly-atypical individuals were left-handed. Similarly, most of the relationship between language lateralization and manual preference strength was explained by the fact that Strongly-atypical individuals exhibited a strong preference for their left hand. These results indicate that concordance of hemispheric dominance for hand and for language occurs barely above the chance level, except in a group of rare individuals (less than 1% in the general population) who exhibit strong right hemisphere dominance for both language and their preferred hand. They call for a revisit of models hypothesizing common determinants for handedness and for language dominance.
Directory of Open Access Journals (Sweden)
Bernard Mazoyer
Full Text Available Hemispheric lateralization for language production and its relationships with manual preference and manual preference strength were studied in a sample of 297 subjects, including 153 left-handers (LH. A hemispheric functional lateralization index (HFLI for language was derived from fMRI acquired during a covert sentence generation task as compared with a covert word list recitation. The multimodal HFLI distribution was optimally modeled using a mixture of 3 and 4 Gaussian functions in right-handers (RH and LH, respectively. Gaussian function parameters helped to define 3 types of language hemispheric lateralization, namely "Typical" (left hemisphere dominance with clear positive HFLI values, 88% of RH, 78% of LH, "Ambilateral" (no dominant hemisphere with HFLI values close to 0, 12% of RH, 15% of LH and "Strongly-atypical" (right-hemisphere dominance with clear negative HFLI values, 7% of LH. Concordance between dominant hemispheres for hand and for language did not exceed chance level, and most of the association between handedness and language lateralization was explained by the fact that all Strongly-atypical individuals were left-handed. Similarly, most of the relationship between language lateralization and manual preference strength was explained by the fact that Strongly-atypical individuals exhibited a strong preference for their left hand. These results indicate that concordance of hemispheric dominance for hand and for language occurs barely above the chance level, except in a group of rare individuals (less than 1% in the general population who exhibit strong right hemisphere dominance for both language and their preferred hand. They call for a revisit of models hypothesizing common determinants for handedness and for language dominance.
Modification of Gaussian mixture models for data classification in high energy physics
Štěpánek, Michal; Franc, Jiří; Kůs, Václav
2015-01-01
In high energy physics, we deal with demanding task of signal separation from background. The Model Based Clustering method involves the estimation of distribution mixture parameters via the Expectation-Maximization algorithm in the training phase and application of Bayes' rule in the testing phase. Modifications of the algorithm such as weighting, missing data processing, and overtraining avoidance will be discussed. Due to the strong dependence of the algorithm on initialization, genetic optimization techniques such as mutation, elitism, parasitism, and the rank selection of individuals will be mentioned. Data pre-processing plays a significant role for the subsequent combination of final discriminants in order to improve signal separation efficiency. Moreover, the results of the top quark separation from the Tevatron collider will be compared with those of standard multivariate techniques in high energy physics. Results from this study has been used in the measurement of the inclusive top pair production cross section employing DØ Tevatron full Runll data (9.7 fb-1).
International Nuclear Information System (INIS)
Tabuchi, Motohiro; Yamane, Nobumoto; Morikawa, Yoshitaka
2008-01-01
In recent decades, X-ray CT imaging has become more important as a result of its high-resolution performance. However, it is well known that the X-ray dose is insufficient in the techniques that use low-dose imaging in health screening or thin-slice imaging in work-up. Therefore, the degradation of CT images caused by the streak artifact frequently becomes problematic. In this study, we applied a Wiener filter (WF) using the universal Gaussian mixture distribution model (UNI-GMM) as a statistical model to remove streak artifact. In designing the WF, it is necessary to estimate the statistical model and the precise co-variances of the original image. In the proposed method, we obtained a variety of chest X-ray CT images using a phantom simulating a chest organ, and we estimated the statistical information using the images for training. The results of simulation showed that it is possible to fit the UNI-GMM to the chest X-ray CT images and reduce the specific noise. (author)
Genovese, Mariangela; Napoli, Ettore
2013-05-01
The identification of moving objects is a fundamental step in computer vision processing chains. The development of low cost and lightweight smart cameras steadily increases the request of efficient and high performance circuits able to process high definition video in real time. The paper proposes two processor cores aimed to perform the real time background identification on High Definition (HD, 1920 1080 pixel) video streams. The implemented algorithm is the OpenCV version of the Gaussian Mixture Model (GMM), an high performance probabilistic algorithm for the segmentation of the background that is however computationally intensive and impossible to implement on general purpose CPU with the constraint of real time processing. In the proposed paper, the equations of the OpenCV GMM algorithm are optimized in such a way that a lightweight and low power implementation of the algorithm is obtained. The reported performances are also the result of the use of state of the art truncated binary multipliers and ROM compression techniques for the implementation of the non-linear functions. The first circuit has commercial FPGA devices as a target and provides speed and logic resource occupation that overcome previously proposed implementations. The second circuit is oriented to an ASIC (UMC-90nm) standard cell implementation. Both implementations are able to process more than 60 frames per second in 1080p format, a frame rate compatible with HD television.
Cecinati, F.; Wani, O.; Rico-Ramirez, M. A.
2016-12-01
It is widely recognised that merging radar rainfall estimates (RRE) with rain gauge data can improve the RRE and provide areal and temporal coverage that rain gauges cannot offer. Many methods to merge radar and rain gauge data are based on kriging and require an assumption of Gaussianity on the variable of interest. In particular, this work looks at kriging with external drift (KED), because it is an efficient, widely used, and well performing merging method. Rainfall, especially at finer temporal scale, does not have a normal distribution and presents a bi-modal skewed distribution. In some applications a Gaussianity assumption is made, without any correction. In other cases, variables are transformed in order to obtain a distribution closer to Gaussian. This work has two objectives: 1) compare different transformation methods in merging applications; 2) evaluate the uncertainty arising when untransformed rainfall data is used in KED. The comparison of transformation methods is addressed under two points of view. On the one hand, the ability to reproduce the original probability distribution after back-transformation of merged products is evaluated with qq-plots, on the other hand the rainfall estimates are compared with an independent set of rain gauge measurements. The tested methods are 1) no transformation, 2) Box-Cox transformations with parameter equal to λ=0.5 (square root), 3) λ=0.25 (square root - square root), and 4) λ=0.1 (almost logarithmic), 5) normal quantile transformation, and 6) singularity analysis. The uncertainty associated with the use of non-transformed data in KED is evaluated in comparison with the best performing product. The methods are tested on a case study in Northern England, using hourly data from 211 tipping bucket rain gauges from the Environment Agency and radar rainfall data at 1 km/5-min resolutions from the UK Met Office. In addition, 25 independent rain gauges from the UK Met Office were used to assess the merged products.
Li, Rui; Perneczky, Robert; Drzezga, Alexander; Kramer, Stefan; Initiative, for the Alzheimer's Disease Neuroimaging
2015-01-01
We present a method to discover interesting brain regions in [18F] fluorodeoxyglucose positron emission tomography (PET) scans, showing also the benefits when PET scans are in combined use with non-imaging variables. The discriminative brain regions facilitate a better understanding of Alzheimer's disease (AD) progression, and they can also be used for predicting conversion from mild cognitive impairment (MCI) to AD. A survival analysis(Cox regression) and infinite Gaussian mixture model (IGM...
Jin, S.; Tamura, M.; Susaki, J.
2014-09-01
Leaf area index (LAI) is one of the most important structural parameters of forestry studies which manifests the ability of the green vegetation interacted with the solar illumination. Classic understanding about LAI is to consider the green canopy as integration of horizontal leaf layers. Since multi-angle remote sensing technique developed, LAI obliged to be deliberated according to the observation geometry. Effective LAI could formulate the leaf-light interaction virtually and precisely. To retrieve the LAI/effective LAI from remotely sensed data therefore becomes a challenge during the past decades. Laser scanning technique can provide accurate surface echoed coordinates with densely scanned intervals. To utilize the density based statistical algorithm for analyzing the voluminous amount of the 3-D points data is one of the subjects of the laser scanning applications. Computational geometry also provides some mature applications for point cloud data (PCD) processing and analysing. In this paper, authors investigated the feasibility of a new application for retrieving the effective LAI of an isolated broad leaf tree. Simplified curvature was calculated for each point in order to remove those non-photosynthetic tissues. Then PCD were discretized into voxel, and clustered by using Gaussian mixture model. Subsequently the area of each cluster was calculated by employing the computational geometry applications. In order to validate our application, we chose an indoor plant to estimate the leaf area, the correlation coefficient between calculation and measurement was 98.28 %. We finally calculated the effective LAI of the tree with 6 × 6 assumed observation directions.
Griesbach, J.; Wetterer, C.; Sydney, P.; Gerber, J.
Photometric processing of non-resolved Electro-Optical (EO) images has commonly required the use of dark and flat calibration frames that are obtained to correct for charge coupled device (CCD) dark (thermal) noise and CCD quantum efficiency/optical path vignetting effects respectively. It is necessary to account/calibrate for these effects so that the brightness of objects of interest (e.g. stars or resident space objects (RSOs)) may be measured in a consistent manner across the CCD field of view. Detected objects typically require further calibration using aperture photometry to compensate for sky background (shot noise). For this, annuluses are measured around each detected object whose contained pixels are used to estimate an average background level that is subtracted from the detected pixel measurements. In a new photometric calibration software tool developed for AFRL/RD, called Efficient Photometry In-Frame Calibration (EPIC), an automated background normalization technique is proposed that eliminates the requirement to capture dark and flat calibration images. The proposed technique simultaneously corrects for dark noise, shot noise, and CCD quantum efficiency/optical path vignetting effects. With this, a constant detection threshold may be applied for constant false alarm rate (CFAR) object detection without the need for aperture photometry corrections. The detected pixels may be simply summed (without further correction) for an accurate instrumental magnitude estimate. The noise distribution associated with each pixel is assumed to be sampled from a Poisson distribution. Since Poisson distributed data closely resembles Gaussian data for parameterized means greater than 10, the data may be corrected by applying bias subtraction and standard-deviation division. EPIC performs automated background normalization on rate-tracked satellite images using the following technique. A deck of approximately 50-100 images is combined by performing an independent median
Fujitani, Youhei
2017-11-01
Suppose a spherical colloidal particle surrounded by a near-critical binary fluid mixture in the homogeneous phase. The particle surface usually preferentially attracts one component of the mixture, and the resultant concentration gradient, which causes the osmotic pressure, becomes significant in the ambient near-criticality. The concentration profile is deformed by the particle motion, and can generate a nonzero force exerted on the moving particle. This link was previously shown to slightly suppress the positional equal-time correlation of a particle trapped by a harmonic potential. This previous study presupposed a small fluctuation amplitude of a particle much larger than the correlation length, a weak preferential attraction, and the Gaussian model for the free-energy functional of the mixture. In the present study, we calculate the equal-time correlation without assuming the weak preferential attraction and show that the suppression becomes much more distinct in some range of the trap stiffness because of the increased induced mass. This suggests the possible experimental usage of a trapped particle as a probe for local environments of a near-critical binary fluid mixture.
DEFF Research Database (Denmark)
Bak, N.; Ebdrup, B.H.; Oranje, B
2017-01-01
Deficits in information processing and cognition are among the most robust findings in schizophrenia patients. Previous efforts to translate group-level deficits into clinically relevant and individualized information have, however, been non-successful, which is possibly explained by biologically...... and sixty-five healthy controls underwent extensive electrophysiological and neurocognitive test batteries. Patients were assessed on the Positive and Negative Syndrome Scale (PANSS) before and after 6 weeks of monotherapy with the relatively selective D2 receptor antagonist, amisulpride (280.3±159 mg per...... day). A reduced principal component space based on 19 electrophysiological variables and 26 cognitive variables was used as input for a Gaussian mixture model to identify subgroups of patients. With support vector machines, we explored the relation between PANSS subscores and the identified subgroups...
Song, Jong-Won; Hirao, Kimihiko
2015-10-14
Since the advent of hybrid functional in 1993, it has become a main quantum chemical tool for the calculation of energies and properties of molecular systems. Following the introduction of long-range corrected hybrid scheme for density functional theory a decade later, the applicability of the hybrid functional has been further amplified due to the resulting increased performance on orbital energy, excitation energy, non-linear optical property, barrier height, and so on. Nevertheless, the high cost associated with the evaluation of Hartree-Fock (HF) exchange integrals remains a bottleneck for the broader and more active applications of hybrid functionals to large molecular and periodic systems. Here, we propose a very simple yet efficient method for the computation of long-range corrected hybrid scheme. It uses a modified two-Gaussian attenuating operator instead of the error function for the long-range HF exchange integral. As a result, the two-Gaussian HF operator, which mimics the shape of the error function operator, reduces computational time dramatically (e.g., about 14 times acceleration in C diamond calculation using periodic boundary condition) and enables lower scaling with system size, while maintaining the improved features of the long-range corrected density functional theory.
Directory of Open Access Journals (Sweden)
Silva-Aguilar Martín
2011-01-01
Full Text Available Metals are ubiquitous pollutants present as mixtures. In particular, mixture of arsenic-cadmium-lead is among the leading toxic agents detected in the environment. These metals have carcinogenic and cell-transforming potential. In this study, we used a two step cell transformation model, to determine the role of oxidative stress in transformation induced by a mixture of arsenic-cadmium-lead. Oxidative damage and antioxidant response were determined. Metal mixture treatment induces the increase of damage markers and the antioxidant response. Loss of cell viability and increased transforming potential were observed during the promotion phase. This finding correlated significantly with generation of reactive oxygen species. Cotreatment with N-acetyl-cysteine induces effect on the transforming capacity; while a diminution was found in initiation, in promotion phase a total block of the transforming capacity was observed. Our results suggest that oxidative stress generated by metal mixture plays an important role only in promotion phase promoting transforming capacity.
Stanke, Monika; Bralin, Amir; Bubin, Sergiy; Adamowicz, Ludwik
2018-01-01
In this work we report progress in the development and implementation of quantum-mechanical methods for calculating bound ground and excited states of small atomic systems. The work concerns singlet states with the L =1 total orbital angular momentum (P states). The method is based on the finite-nuclear-mass (non-Born-Oppenheimer; non-BO) approach and the use of all-particle explicitly correlated Gaussian functions for expanding the nonrelativistic wave function of the system. The development presented here includes derivation and implementation of algorithms for calculating the leading relativistic corrections for singlet states. The corrections are determined in the framework of the perturbation theory as expectation values of the corresponding effective operators using the non-BO wave functions. The method is tested in the calculations of the ten lowest 1P states of the helium atom and the four lowest 1P states of the beryllium atom.
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.
Gilthorpe, M S; Dahly, D L; Tu, Y K; Kubzansky, L D; Goodman, E
2014-06-01
Lifecourse trajectories of clinical or anthropological attributes are useful for identifying how our early-life experiences influence later-life morbidity and mortality. Researchers often use growth mixture models (GMMs) to estimate such phenomena. It is common to place constrains on the random part of the GMM to improve parsimony or to aid convergence, but this can lead to an autoregressive structure that distorts the nature of the mixtures and subsequent model interpretation. This is especially true if changes in the outcome within individuals are gradual compared with the magnitude of differences between individuals. This is not widely appreciated, nor is its impact well understood. Using repeat measures of body mass index (BMI) for 1528 US adolescents, we estimated GMMs that required variance-covariance constraints to attain convergence. We contrasted constrained models with and without an autocorrelation structure to assess the impact this had on the ideal number of latent classes, their size and composition. We also contrasted model options using simulations. When the GMM variance-covariance structure was constrained, a within-class autocorrelation structure emerged. When not modelled explicitly, this led to poorer model fit and models that differed substantially in the ideal number of latent classes, as well as class size and composition. Failure to carefully consider the random structure of data within a GMM framework may lead to erroneous model inferences, especially for outcomes with greater within-person than between-person homogeneity, such as BMI. It is crucial to reflect on the underlying data generation processes when building such models.
Skakun, Sergii; Franch, Belen; Vermote, Eric; Roger, Jean-Claude; Becker-Reshef, Inbal; Justice, Christopher; Kussul, Nataliia
2017-01-01
Knowledge on geographical location and distribution of crops at global, national and regional scales is an extremely valuable source of information applications. Traditional approaches to crop mapping using remote sensing data rely heavily on reference or ground truth data in order to train/calibrate classification models. As a rule, such models are only applicable to a single vegetation season and should be recalibrated to be applicable for other seasons. This paper addresses the problem of early season large-area winter crop mapping using Moderate Resolution Imaging Spectroradiometer (MODIS) derived Normalized Difference Vegetation Index (NDVI) time-series and growing degree days (GDD) information derived from the Modern-Era Retrospective analysis for Research and Applications (MERRA-2) product. The model is based on the assumption that winter crops have developed biomass during early spring while other crops (spring and summer) have no biomass. As winter crop development is temporally and spatially non-uniform due to the presence of different agro-climatic zones, we use GDD to account for such discrepancies. A Gaussian mixture model (GMM) is applied to discriminate winter crops from other crops (spring and summer). The proposed method has the following advantages: low input data requirements, robustness, applicability to global scale application and can provide winter crop maps 1.5-2 months before harvest. The model is applied to two study regions, the State of Kansas in the US and Ukraine, and for multiple seasons (2001-2014). Validation using the US Department of Agriculture (USDA) Crop Data Layer (CDL) for Kansas and ground measurements for Ukraine shows that accuracies of greater than 90% can be achieved in mapping winter crops 1.5-2 months before harvest. Results also show good correspondence to official statistics with average coefficients of determination R(exp. 2) greater than 0.85.
Energy Technology Data Exchange (ETDEWEB)
Cogollo, Heiner R S; Rodriguez, Yeinzon; Valenzuela-Toledo, Cesar A, E-mail: heiner.sarmiento@ciencias.uis.edu.co, E-mail: yeinzon.rodriguez@uan.edu.co, E-mail: cavalto@ciencias.uis.edu.co [Escuela de Fisica, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga (Colombia)
2008-08-15
We show in this paper that it is possible to attain very high, including observable, values for the level of non-Gaussianity f{sub NL} associated with the bispectrum B{sub {zeta}} of the primordial curvature perturbation {zeta}, in a subclass of small-field slow-roll models of inflation with canonical kinetic terms. Such a result is obtained by taking care of loop corrections both in the spectrum P{sub {zeta}} and in the bispectrum B{sub {zeta}}. Sizable values for f{sub NL} arise even if {zeta} is generated during inflation. Five issues are considered when constraining the available parameter space: (1) We must ensure that we are in a perturbative regime so that the {zeta} series expansion, and its truncation, are valid. (2) We must apply the correct condition for the (possible) loop dominance in B{sub {zeta}} and/or P{sub {zeta}}. (3) We must satisfy the spectrum normalization condition. (4) We must satisfy the spectral tilt constraint. (5) We must have enough inflation to solve the horizon problem.
International Nuclear Information System (INIS)
Cogollo, Heiner R S; Rodríguez, Yeinzon; Valenzuela-Toledo, César A
2008-01-01
We show in this paper that it is possible to attain very high, including observable, values for the level of non-Gaussianity f NL associated with the bispectrum B ζ of the primordial curvature perturbation ζ, in a subclass of small-field slow-roll models of inflation with canonical kinetic terms. Such a result is obtained by taking care of loop corrections both in the spectrum P ζ and in the bispectrum B ζ . Sizable values for f NL arise even if ζ is generated during inflation. Five issues are considered when constraining the available parameter space: (1) We must ensure that we are in a perturbative regime so that the ζ series expansion, and its truncation, are valid. (2) We must apply the correct condition for the (possible) loop dominance in B ζ and/or P ζ . (3) We must satisfy the spectrum normalization condition. (4) We must satisfy the spectral tilt constraint. (5) We must have enough inflation to solve the horizon problem
International Nuclear Information System (INIS)
Smith, Mark F.; Daube-Witherspoon, Margaret E.; Plascjak, Paul S.; Szajek, Lawrence P.; Carson, Richard E.; Everett, James R.; Green, Shielah L.; Territo, Paul R.; Balaban, Robert S.; Bacharach, Stephen L.; Eckelman, William C.
2001-01-01
Multi-instrument activity estimation and decay correction techniques were developed for radionuclide mixtures, motivated by the desire for accurate quantitation of Tc-94m positron emission tomography (PET) studies. Tc-94m and byproduct Tc isotopes were produced by proton irradiation of enriched Mo-94 and natural Mo targets. Mixture activities at the end of bombardment were determined with a calibrated high purity germanium detector. The activity fractions of the greatest mixture impurities relative to 100% for Tc-94m averaged 10.0% (Tc-94g) and 3.3% (Tc-93) for enriched targets and 10.1% (Tc-94g), 11.0% (Tc-95), 255.8% (Tc-96m), and 7.2% (Tc-99m) for natural targets. These radioisotopes have different half-lives (e.g., 52.5 min for Tc-94m, 293 min for Tc-94g), positron branching ratios (e.g., 0.72 for Tc-94m, 0.11 for Tc-94g) and gamma ray emissions for themselves and their short-lived, excited Mo daughters. This complicates estimation of injected activity with a dose calibrator, in vivo activity with PET and blood sample activity with a gamma counter. Decay correction using only the Tc-94m half-life overestimates activity and is inadequate. For this reason analytic formulas for activity estimation and decay correction of radionuclide mixtures were developed. Isotope-dependent sensitivity factors for a PET scanner, dose calibrator, and gamma counter were determined using theoretical sensitivity models and fits of experimental decay curves to sums of exponentials with fixed decay rates. For up to 8 h after the end of bombardment with activity from enriched and natural Mo targets, decay-corrected activities were within 3% of the mean for three PET studies of a uniform cylinder, within 3% of the mean for six dose calibrator decay studies, and within 6% of the mean for four gamma counter decay studies. Activity estimation and decay correction for Tc-94m mixtures enable routine use of Tc-94m in quantitative PET, as illustrated by application to a canine Tc-94m sestamibi
Energy Technology Data Exchange (ETDEWEB)
Liu, T [Department of Radiation Oncology and Winship Cancer Institute, Emory Univ, Atlanta, GA (United States); Yu, D; Beitler, J; Curran, W; Yang, X [Department of Radiation Oncology and Winship Cancer Institute, Emory University, Atlanta, GA (United States); Tridandapani, S [Department of Radiology and Imaging Sciences and Winship Cancer Institute, Emory University, Atlanta, GA (United States); Bruner, D [School of Nursing and Winship Cancer Institute, Emory Univesity, Atlanta, GA (United States)
2014-06-15
Purpose: Xerostomia (dry mouth), secondary to parotid-gland injury, is a distressing side-effect in head-and-neck radiotherapy (RT). This study's purpose is to develop a novel ultrasound technique to quantitatively evaluate post-RT parotid-gland injury. Methods: Recent ultrasound studies have shown that healthy parotid glands exhibit homogeneous echotexture, whereas post-RT parotid glands are often heterogeneous, with multiple hypoechoic (inflammation) or hyperechoic (fibrosis) regions. We propose to use a Gaussian mixture model to analyze the ultrasonic echo-histogram of the parotid glands. An IRB-approved clinical study was conducted: (1) control-group: 13 healthy-volunteers, served as the control; (2) acutetoxicity group − 20 patients (mean age: 62.5 ± 8.9 years, follow-up: 2.0±0.8 months); and (3) late-toxicity group − 18 patients (mean age: 60.7 ± 7.3 years, follow-up: 20.1±10.4 months). All patients experienced RTOG grade 1 or 2 salivary-gland toxicity. Each participant underwent an ultrasound scan (10 MHz) of the bilateral parotid glands. An echo-intensity histogram was derived for each parotid and a Gaussian mixture model was used to fit the histogram using expectation maximization (EM) algorithm. The quality of the fitting was evaluated with the R-squared value. Results: (1) Controlgroup: all parotid glands fitted well with one Gaussian component, with a mean intensity of 79.8±4.9 (R-squared>0.96). (2) Acute-toxicity group: 37 of the 40 post-RT parotid glands fitted well with two Gaussian components, with a mean intensity of 42.9±7.4, 73.3±12.2 (R-squared>0.95). (3) Latetoxicity group: 32 of the 36 post-RT parotid fitted well with 3 Gaussian components, with mean intensities of 49.7±7.6, 77.2±8.7, and 118.6±11.8 (R-squared>0.98). Conclusion: RT-associated parotid-gland injury is common in head-and-neck RT, but challenging to assess. This work has demonstrated that the Gaussian mixture model of the echo-histogram could quantify acute and
International Nuclear Information System (INIS)
Liu, T; Yu, D; Beitler, J; Curran, W; Yang, X; Tridandapani, S; Bruner, D
2014-01-01
Purpose: Xerostomia (dry mouth), secondary to parotid-gland injury, is a distressing side-effect in head-and-neck radiotherapy (RT). This study's purpose is to develop a novel ultrasound technique to quantitatively evaluate post-RT parotid-gland injury. Methods: Recent ultrasound studies have shown that healthy parotid glands exhibit homogeneous echotexture, whereas post-RT parotid glands are often heterogeneous, with multiple hypoechoic (inflammation) or hyperechoic (fibrosis) regions. We propose to use a Gaussian mixture model to analyze the ultrasonic echo-histogram of the parotid glands. An IRB-approved clinical study was conducted: (1) control-group: 13 healthy-volunteers, served as the control; (2) acutetoxicity group − 20 patients (mean age: 62.5 ± 8.9 years, follow-up: 2.0±0.8 months); and (3) late-toxicity group − 18 patients (mean age: 60.7 ± 7.3 years, follow-up: 20.1±10.4 months). All patients experienced RTOG grade 1 or 2 salivary-gland toxicity. Each participant underwent an ultrasound scan (10 MHz) of the bilateral parotid glands. An echo-intensity histogram was derived for each parotid and a Gaussian mixture model was used to fit the histogram using expectation maximization (EM) algorithm. The quality of the fitting was evaluated with the R-squared value. Results: (1) Controlgroup: all parotid glands fitted well with one Gaussian component, with a mean intensity of 79.8±4.9 (R-squared>0.96). (2) Acute-toxicity group: 37 of the 40 post-RT parotid glands fitted well with two Gaussian components, with a mean intensity of 42.9±7.4, 73.3±12.2 (R-squared>0.95). (3) Latetoxicity group: 32 of the 36 post-RT parotid fitted well with 3 Gaussian components, with mean intensities of 49.7±7.6, 77.2±8.7, and 118.6±11.8 (R-squared>0.98). Conclusion: RT-associated parotid-gland injury is common in head-and-neck RT, but challenging to assess. This work has demonstrated that the Gaussian mixture model of the echo-histogram could quantify acute and
Self-consistent field theory of protein adsorption in a non-Gaussian polyelectrolyte brush
Biesheuvel, P.M.; Leermakers, F.A.M.; Stuart, M.A.C.
2006-01-01
To describe adsorption of globular protein molecules in a polyelectrolyte brush we use the strong-stretching approximation of the Edwards self-consistent field equation, combined with corrections for a non-Gaussian brush. To describe chemical potentials in this mixture of (globular) species of
Energy Technology Data Exchange (ETDEWEB)
Wang, Feng; Chen, Junlong; Liu, Jueping, E-mail: jpliu@whu.edu.cn [Department of Physics, School of Physics Science and Technology, Wuhan University, 430072, Wuhan (China)
2015-09-28
Based on a correction from instanton–gluon interference to the correlation function, the properties of the 0{sup -+} pseudoscalar glueball are investigated in a family of finite-width Gaussian sum rules. In the framework of a semiclassical expansion for quantum chromodynamics in the instanton liquid background, the contribution arising from the interference between instantons and the quantum gluon fields is calculated, and it is included in the correlation function together with a pure-classical contribution from instantons and the perturbative one. The interference contribution turns out to be gauge-invariant, to be free from an infrared divergence, and to have a great role to play in restoring the positivity of the spectra of the full correlation function. The negligible contribution from vacuum condensates is excluded in our correlation function to avoid double counting. Instead of the usual zero-width approximation for the resonances, the usual Breit–Wigner form with a suitable threshold behavior for the spectral function of the finite-width resonances is adopted. Consistency between the subtracted and unsubtracted sum rules is very well justified. The values of the mass, decay width, and coupling constants for the 0{sup -+} resonance in which the glueball fraction is dominant are obtained, and they agree with the phenomenological analysis.
Energy Technology Data Exchange (ETDEWEB)
Wang, Feng; Chen, Junlong; Liu, Jueping [Wuhan University, Department of Physics, School of Physics Science and Technology, Wuhan (China)
2015-09-15
Based on a correction from instanton-gluon interference to the correlation function, the properties of the 0{sup -+} pseudoscalar glueball are investigated in a family of finite-width Gaussian sum rules. In the framework of a semiclassical expansion for quantum chromodynamics in the instanton liquid background, the contribution arising from the interference between instantons and the quantum gluon fields is calculated, and it is included in the correlation function together with a pure-classical contribution from instantons and the perturbative one. The interference contribution turns out to be gauge-invariant, to be free from an infrared divergence, and to have a great role to play in restoring the positivity of the spectra of the full correlation function. The negligible contribution from vacuum condensates is excluded in our correlation function to avoid double counting. Instead of the usual zero-width approximation for the resonances, the usual Breit-Wigner form with a suitable threshold behavior for the spectral function of the finite-width resonances is adopted. Consistency between the subtracted and unsubtracted sum rules is very well justified. The values of the mass, decay width, and coupling constants for the 0{sup -+} resonance in which the glueball fraction is dominant are obtained, and they agree with the phenomenological analysis. (orig.)
DEFF Research Database (Denmark)
Pinkevych, Mykola; Cromer, Deborah; Tolstrup, Martin
2016-01-01
[This corrects the article DOI: 10.1371/journal.ppat.1005000.][This corrects the article DOI: 10.1371/journal.ppat.1005740.][This corrects the article DOI: 10.1371/journal.ppat.1005679.].......[This corrects the article DOI: 10.1371/journal.ppat.1005000.][This corrects the article DOI: 10.1371/journal.ppat.1005740.][This corrects the article DOI: 10.1371/journal.ppat.1005679.]....
Statistically tuned Gaussian background subtraction technique for ...
Indian Academy of Sciences (India)
temporal median method and mixture of Gaussian model and performance evaluation ... to process the videos captured by unmanned aerial vehicle (UAV). ..... The output is obtained by simulation using MATLAB 2010 in a standalone PC with ...
International Nuclear Information System (INIS)
Rodriguez, Yeinzon; Valenzuela-Toledo, Cesar A.
2010-01-01
We calculate the trispectrum T ζ of the primordial curvature perturbation ζ, generated during a slow-roll inflationary epoch by considering a two-field quadratic model of inflation with canonical kinetic terms. We consider loop contributions as well as tree-level terms, and show that it is possible to attain very high, including observable, values for the level of non-Gaussianity τ NL if T ζ is dominated by the one-loop contribution. Special attention is paid to the claim in J. Cosmol. Astropart. Phys. 02 (2009) 017 that, in the model studied in this paper and for the specific inflationary trajectory we choose, the quantum fluctuations of the fields overwhelm the classical evolution. We argue that such a claim actually does not apply to our model, although more research is needed in order to understand the role of quantum diffusion. We also consider the probability that an observer in an ensemble of realizations of the density field sees a non-Gaussian distribution. In that respect, we show that the probability associated to the chosen inflationary trajectory is non-negligible. Finally, the levels of non-Gaussianity f NL and τ NL in the bispectrum B ζ and trispectrum T ζ of ζ, respectively, are also studied for the case in which ζ is not generated during inflation.
2002-01-01
Tile Calorimeter modules stored at CERN. The larger modules belong to the Barrel, whereas the smaller ones are for the two Extended Barrels. (The article was about the completion of the 64 modules for one of the latter.) The photo on the first page of the Bulletin n°26/2002, from 24 July 2002, illustrating the article «The ATLAS Tile Calorimeter gets into shape» was published with a wrong caption. We would like to apologise for this mistake and so publish it again with the correct caption.
Directory of Open Access Journals (Sweden)
2012-01-01
Full Text Available Regarding Gorelik, G., & Shackelford, T.K. (2011. Human sexual conflict from molecules to culture. Evolutionary Psychology, 9, 564–587: The authors wish to correct an omission in citation to the existing literature. In the final paragraph on p. 570, we neglected to cite Burch and Gallup (2006 [Burch, R. L., & Gallup, G. G., Jr. (2006. The psychobiology of human semen. In S. M. Platek & T. K. Shackelford (Eds., Female infidelity and paternal uncertainty (pp. 141–172. New York: Cambridge University Press.]. Burch and Gallup (2006 reviewed the relevant literature on FSH and LH discussed in this paragraph, and should have been cited accordingly. In addition, Burch and Gallup (2006 should have been cited as the originators of the hypothesis regarding the role of FSH and LH in the semen of rapists. The authors apologize for this oversight.
2002-01-01
The photo on the second page of the Bulletin n°48/2002, from 25 November 2002, illustrating the article «Spanish Visit to CERN» was published with a wrong caption. We would like to apologise for this mistake and so publish it again with the correct caption. The Spanish delegation, accompanied by Spanish scientists at CERN, also visited the LHC superconducting magnet test hall (photo). From left to right: Felix Rodriguez Mateos of CERN LHC Division, Josep Piqué i Camps, Spanish Minister of Science and Technology, César Dopazo, Director-General of CIEMAT (Spanish Research Centre for Energy, Environment and Technology), Juan Antonio Rubio, ETT Division Leader at CERN, Manuel Aguilar-Benitez, Spanish Delegate to Council, Manuel Delfino, IT Division Leader at CERN, and Gonzalo León, Secretary-General of Scientific Policy to the Minister.
Directory of Open Access Journals (Sweden)
2014-01-01
Full Text Available Regarding Tagler, M. J., and Jeffers, H. M. (2013. Sex differences in attitudes toward partner infidelity. Evolutionary Psychology, 11, 821–832: The authors wish to correct values in the originally published manuscript. Specifically, incorrect 95% confidence intervals around the Cohen's d values were reported on page 826 of the manuscript where we reported the within-sex simple effects for the significant Participant Sex × Infidelity Type interaction (first paragraph, and for attitudes toward partner infidelity (second paragraph. Corrected values are presented in bold below. The authors would like to thank Dr. Bernard Beins at Ithaca College for bringing these errors to our attention. Men rated sexual infidelity significantly more distressing (M = 4.69, SD = 0.74 than they rated emotional infidelity (M = 4.32, SD = 0.92, F(1, 322 = 23.96, p < .001, d = 0.44, 95% CI [0.23, 0.65], but there was little difference between women's ratings of sexual (M = 4.80, SD = 0.48 and emotional infidelity (M = 4.76, SD = 0.57, F(1, 322 = 0.48, p = .29, d = 0.08, 95% CI [−0.10, 0.26]. As expected, men rated sexual infidelity (M = 1.44, SD = 0.70 more negatively than they rated emotional infidelity (M = 2.66, SD = 1.37, F(1, 322 = 120.00, p < .001, d = 1.12, 95% CI [0.85, 1.39]. Although women also rated sexual infidelity (M = 1.40, SD = 0.62 more negatively than they rated emotional infidelity (M = 2.09, SD = 1.10, this difference was not as large and thus in the evolutionary theory supportive direction, F(1, 322 = 72.03, p < .001, d = 0.77, 95% CI [0.60, 0.94].
Dirichlet Process Parsimonious Mixtures for clustering
Chamroukhi, Faicel; Bartcus, Marius; Glotin, Hervé
2015-01-01
The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general performed by maximum likelihood estimation and has also been considered from a parametric Bayesian prospective. We propose new Dirichlet Process Parsimonious mixtures (DPPM) which represent a Bayesian nonparametric formulation of these parsimonious Gaussian mixtur...
Tien Bui, Dieu; Hoang, Nhat-Duc
2017-09-01
In this study, a probabilistic model, named as BayGmmKda, is proposed for flood susceptibility assessment in a study area in central Vietnam. The new model is a Bayesian framework constructed by a combination of a Gaussian mixture model (GMM), radial-basis-function Fisher discriminant analysis (RBFDA), and a geographic information system (GIS) database. In the Bayesian framework, GMM is used for modeling the data distribution of flood-influencing factors in the GIS database, whereas RBFDA is utilized to construct a latent variable that aims at enhancing the model performance. As a result, the posterior probabilistic output of the BayGmmKda model is used as flood susceptibility index. Experiment results showed that the proposed hybrid framework is superior to other benchmark models, including the adaptive neuro-fuzzy inference system and the support vector machine. To facilitate the model implementation, a software program of BayGmmKda has been developed in MATLAB. The BayGmmKda program can accurately establish a flood susceptibility map for the study region. Accordingly, local authorities can overlay this susceptibility map onto various land-use maps for the purpose of land-use planning or management.
Directory of Open Access Journals (Sweden)
D. Tien Bui
2017-09-01
Full Text Available In this study, a probabilistic model, named as BayGmmKda, is proposed for flood susceptibility assessment in a study area in central Vietnam. The new model is a Bayesian framework constructed by a combination of a Gaussian mixture model (GMM, radial-basis-function Fisher discriminant analysis (RBFDA, and a geographic information system (GIS database. In the Bayesian framework, GMM is used for modeling the data distribution of flood-influencing factors in the GIS database, whereas RBFDA is utilized to construct a latent variable that aims at enhancing the model performance. As a result, the posterior probabilistic output of the BayGmmKda model is used as flood susceptibility index. Experiment results showed that the proposed hybrid framework is superior to other benchmark models, including the adaptive neuro-fuzzy inference system and the support vector machine. To facilitate the model implementation, a software program of BayGmmKda has been developed in MATLAB. The BayGmmKda program can accurately establish a flood susceptibility map for the study region. Accordingly, local authorities can overlay this susceptibility map onto various land-use maps for the purpose of land-use planning or management.
Directory of Open Access Journals (Sweden)
César Soto-Valero
2017-07-01
Full Text Available The generation and availability of football data has increased considerably last decades, mostly due to its popularity and also because of technological advances. Gaussian mixture clustering models represents a novel approach to exploring and analyzing performance data in sports. In this paper, we use principal components analysis in conjunction with a model-based Gaussian clustering method with the purpose of characterizing professional football players. Our model approach is tested using 40 attributes from EA Sports' FIFA video game series system, corresponding to 7705 European players. Clustering results reveal a clear distinction among different performance indicators, representing four different roles in the team. Players were labeled according to these roles and a gradient tree boosting model was used for ranking attributes regarding to its importance. We found that the dribbling skill is the most discriminating variable among the different clustered players’ profiles. Resumen En las últimas décadas se ha visto un incremento considerable en la generación y disponibilidad de datos de fútbol, esto se debe fundamentalmente a la popularidad de este deporte así como a los avances tecnológicos realizados en este campo. Los modelos de agrupamiento basados en mixturas Gaussianas representan un enfoque novedoso para explorar y analizar datos de desempeño deportivo. En el presente trabajo, se lleva a cabo una caracterización de jugadores profesionales de fútbol utilizando técnicas de análisis de componentes principales y agrupamiento basados en mixturas Gaussianas. El modelo presentado es comprobado utilizando datos del sistema de videojuegos FIFA de EA Sports, dichos datos representan 40 atributos correspondientes a 7705 futbolistas europeos. Los resultados del agrupamiento revelan una clara distinción entre algunos indicadores de desempeño, los cuales corresponden a cuatro roles diferentes en el equipo. Consecuentemente, los
Directory of Open Access Journals (Sweden)
Hafiz Azhar Ali Khan
Full Text Available House flies, Musca domestica L., are important pests of dairy operations worldwide, with the ability to adapt wide range of environmental conditions. There are a number of insecticides used for their management, but development of resistance is a serious problem. Insecticide mixtures could enhance the toxicity of insecticides in resistant insect pests, thus resulting as a potential resistance management tool. The toxicity of bifenthrin, cypermethrin, deltamethrin, chlorpyrifos, profenofos, emamectin benzoate and fipronil were assessed separately, and in mixtures against house flies. A field-collected population was significantly resistant to all the insecticides under investigation when compared with a laboratory susceptible strain. Most of the insecticide mixtures like one pyrethroid with other compounds evaluated under two conditions (1∶1-"A" and LC50: LC50-"B" significantly increased the toxicity of pyrethroids in the field population. Under both conditions, the combination indices of pyrethroids with other compounds, in most of the cases, were significantly below 1, suggesting synergism. The enzyme inhibitors, PBO and DEF, when used in combination with insecticides against the resistant population, toxicities of bifenthrin, cypermethrin, deltamethrin and emamectin were significantly increased, suggesting esterase and monooxygenase based resistance mechanism. The toxicities of bifenthrin, cypermethrin and deltamethrin in the resistant population of house flies could be enhanced by the combination with chlorpyrifos, profenofos, emamectin and fipronil. The findings of the present study might have practical significance for resistance management in house flies.
Energy Technology Data Exchange (ETDEWEB)
Hoejstrup, J [NEG Micon Project Development A/S, Randers (Denmark); Hansen, K S [Denmarks Technical Univ., Dept. of Energy Engineering, Lyngby (Denmark); Pedersen, B J [VESTAS Wind Systems A/S, Lem (Denmark); Nielsen, M [Risoe National Lab., Wind Energy and Atmospheric Physics, Roskilde (Denmark)
1999-03-01
The pdf`s of atmospheric turbulence have somewhat wider tails than a Gaussian, especially regarding accelerations, whereas velocities are close to Gaussian. This behaviour is being investigated using data from a large WEB-database in order to quantify the amount of non-Gaussianity. Models for non-Gaussian turbulence have been developed, by which artificial turbulence can be generated with specified distributions, spectra and cross-correlations. The artificial time series will then be used in load models and the resulting loads in the Gaussian and the non-Gaussian cases will be compared. (au)
Improved Denoising via Poisson Mixture Modeling of Image Sensor Noise.
Zhang, Jiachao; Hirakawa, Keigo
2017-04-01
This paper describes a study aimed at comparing the real image sensor noise distribution to the models of noise often assumed in image denoising designs. A quantile analysis in pixel, wavelet transform, and variance stabilization domains reveal that the tails of Poisson, signal-dependent Gaussian, and Poisson-Gaussian models are too short to capture real sensor noise behavior. A new Poisson mixture noise model is proposed to correct the mismatch of tail behavior. Based on the fact that noise model mismatch results in image denoising that undersmoothes real sensor data, we propose a mixture of Poisson denoising method to remove the denoising artifacts without affecting image details, such as edge and textures. Experiments with real sensor data verify that denoising for real image sensor data is indeed improved by this new technique.
Gaussian entanglement revisited
Lami, Ludovico; Serafini, Alessio; Adesso, Gerardo
2018-02-01
We present a novel approach to the separability problem for Gaussian quantum states of bosonic continuous variable systems. We derive a simplified necessary and sufficient separability criterion for arbitrary Gaussian states of m versus n modes, which relies on convex optimisation over marginal covariance matrices on one subsystem only. We further revisit the currently known results stating the equivalence between separability and positive partial transposition (PPT) for specific classes of Gaussian states. Using techniques based on matrix analysis, such as Schur complements and matrix means, we then provide a unified treatment and compact proofs of all these results. In particular, we recover the PPT-separability equivalence for: (i) Gaussian states of 1 versus n modes; and (ii) isotropic Gaussian states. In passing, we also retrieve (iii) the recently established equivalence between separability of a Gaussian state and and its complete Gaussian extendability. Our techniques are then applied to progress beyond the state of the art. We prove that: (iv) Gaussian states that are invariant under partial transposition are necessarily separable; (v) the PPT criterion is necessary and sufficient for separability for Gaussian states of m versus n modes that are symmetric under the exchange of any two modes belonging to one of the parties; and (vi) Gaussian states which remain PPT under passive optical operations can not be entangled by them either. This is not a foregone conclusion per se (since Gaussian bound entangled states do exist) and settles a question that had been left unanswered in the existing literature on the subject. This paper, enjoyable by both the quantum optics and the matrix analysis communities, overall delivers technical and conceptual advances which are likely to be useful for further applications in continuous variable quantum information theory, beyond the separability problem.
DEFF Research Database (Denmark)
Jacobsen, Christian Robert Dahl; Møller, Jesper
2017-01-01
We introduce new estimation methods for a subclass of the Gaussian scale mixture models for wavelet trees by Wainwright, Simoncelli and Willsky that rely on modern results for composite likelihoods and approximate Bayesian inference. Our methodology is illustrated for denoising and edge detection...
International Nuclear Information System (INIS)
Van Zon, Ramses; Ashwin, S S; Cohen, E G D
2008-01-01
To describe short time (picosecond) and small scale (nanometre) transport in fluids, a Green's function approach was recently developed. This approach relies on an expansion of the distribution of single particle displacements around a Gaussian function, yielding an infinite series of correction terms. Applying a recent theorem (van Zon and Cohen 2006 J. Stat. Phys. 123 1–37) shows that for sufficiently small times the terms in this series become successively smaller, so that truncating the series near or at the Gaussian level might provide a good approximation. In this paper, we derive a theoretical estimate for the time scale at which truncating the series at or near the Gaussian level could be supposed to be accurate for equilibrium nanoscale systems. In order to numerically estimate this time scale, the coefficients for the first few terms in the series are determined in computer simulations for a Lennard-Jones (LJ) fluid, an isotopic LJ mixture and a suspension of a LJ-based model of nanoparticles in a LJ fluid. The results suggest that for LJ fluids an expansion around a Gaussian is accurate at time scales up to a picosecond, while for nanoparticles in suspension (a nanofluid), the characteristic time scale up to which the Gaussian is accurate becomes of the order of 5–10 ps. (invited article)
Non-Gaussian halo assembly bias
International Nuclear Information System (INIS)
Reid, Beth A.; Verde, Licia; Dolag, Klaus; Matarrese, Sabino; Moscardini, Lauro
2010-01-01
The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f NL , offers a promising avenue towards constraining primordial non-Gaussianity with large-scale structure surveys. In this paper, we present the first detection of the dependence of the non-Gaussian halo bias on halo formation history using N-body simulations. We also present an analytic derivation of the expected signal based on the extended Press-Schechter formalism. In excellent agreement with our analytic prediction, we find that the halo formation history-dependent contribution to the non-Gaussian halo bias (which we call non-Gaussian halo assembly bias) can be factorized in a form approximately independent of redshift and halo mass. The correction to the non-Gaussian halo bias due to the halo formation history can be as large as 100%, with a suppression of the signal for recently formed halos and enhancement for old halos. This could in principle be a problem for realistic galaxy surveys if observational selection effects were to pick galaxies occupying only recently formed halos. Current semi-analytic galaxy formation models, for example, imply an enhancement in the expected signal of ∼ 23% and ∼ 48% for galaxies at z = 1 selected by stellar mass and star formation rate, respectively
CSIR Research Space (South Africa)
Roux, FS
2009-01-01
Full Text Available , t0)} = P(du, dv) {FR{g(u, v, t0)}} Replacement: u→ du = t− t0 i2 ∂ ∂u′ v → dv = t− t0 i2 ∂ ∂v′ CSIR National Laser Centre – p.13/30 Differentiation i.s.o integration Evaluate the integral over the Gaussian beam (once and for all). Then, instead... . Gaussian beams with vortex dipoles CSIR National Laser Centre – p.2/30 Gaussian beam notation Gaussian beam in normalised coordinates: g(u, v, t) = exp ( −u 2 + v2 1− it ) u = xω0 v = yω0 t = zρ ρ = piω20 λ ω0 — 1/e2 beam waist radius; ρ— Rayleigh range ω ω...
Gaussian operations and privacy
International Nuclear Information System (INIS)
Navascues, Miguel; Acin, Antonio
2005-01-01
We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in [Navascues et al. Phys. Rev. Lett. 94, 010502 (2005)]. Then, we prove that a generalized version of this protocol does not allow one to distill a secret key out of bound entangled Gaussian states
Ultrawide Bandwidth Receiver Based on a Multivariate Generalized Gaussian Distribution
Ahmed, Qasim Zeeshan
2015-04-01
Multivariate generalized Gaussian density (MGGD) is used to approximate the multiple access interference (MAI) and additive white Gaussian noise in pulse-based ultrawide bandwidth (UWB) system. The MGGD probability density function (pdf) is shown to be a better approximation of a UWB system as compared to multivariate Gaussian, multivariate Laplacian and multivariate Gaussian-Laplacian mixture (GLM). The similarity between the simulated and the approximated pdf is measured with the help of modified Kullback-Leibler distance (KLD). It is also shown that MGGD has the smallest KLD as compared to Gaussian, Laplacian and GLM densities. A receiver based on the principles of minimum bit error rate is designed for the MGGD pdf. As the requirement is stringent, the adaptive implementation of the receiver is also carried out in this paper. Training sequence of the desired user is the only requirement when implementing the detector adaptively. © 2002-2012 IEEE.
Nonclassicality by Local Gaussian Unitary Operations for Gaussian States
Directory of Open Access Journals (Sweden)
Yangyang Wang
2018-04-01
Full Text Available A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 -mode Gaussian states and an estimate of N for ( n + m -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.
Generalized Gaussian Error Calculus
Grabe, Michael
2010-01-01
For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...
Learning conditional Gaussian networks
DEFF Research Database (Denmark)
Bøttcher, Susanne Gammelgaard
This paper considers conditional Gaussian networks. The parameters in the network are learned by using conjugate Bayesian analysis. As conjugate local priors, we apply the Dirichlet distribution for discrete variables and the Gaussian-inverse gamma distribution for continuous variables, given...... a configuration of the discrete parents. We assume parameter independence and complete data. Further, to learn the structure of the network, the network score is deduced. We then develop a local master prior procedure, for deriving parameter priors in these networks. This procedure satisfies parameter...... independence, parameter modularity and likelihood equivalence. Bayes factors to be used in model search are introduced. Finally the methods derived are illustrated by a simple example....
Quantum beamstrahlung from gaussian bunches
International Nuclear Information System (INIS)
Chen, P.
1987-08-01
The method of Baier and Katkov is applied to calculate the correction terms to the Sokolov-Ternov radiation formula due to the variation of the magnetic field strength along the trajectory of a radiating particle. We carry the calculation up to the second order in the power expansion of B tau/B, where tau is the formation time of radiation. The expression is then used to estimate the quantum beamstrahlung average energy loss from e + e - bunches with gaussian distribution in bunch currents. We show that the effect of the field variation is to reduce the average energy loss from previous calculations based on the Sokolov-Ternov formula or its equivalent. Due to the limitation of our method, only an upper bound of the reduction is obtained. 18 refs
AUTONOMOUS GAUSSIAN DECOMPOSITION
Energy Technology Data Exchange (ETDEWEB)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Heiles, Carl [Radio Astronomy Lab, UC Berkeley, 601 Campbell Hall, Berkeley, CA 94720 (United States); Hennebelle, Patrick [Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp-CNRS-Université Paris Diderot, F-91191 Gif-sur Yvette Cedex (France); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville, Socorro, NM 87801 (United States); Dickey, John, E-mail: rlindner@astro.wisc.edu [University of Tasmania, School of Maths and Physics, Private Bag 37, Hobart, TAS 7001 (Australia)
2015-04-15
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
Bounded Gaussian process regression
DEFF Research Database (Denmark)
Jensen, Bjørn Sand; Nielsen, Jens Brehm; Larsen, Jan
2013-01-01
We extend the Gaussian process (GP) framework for bounded regression by introducing two bounded likelihood functions that model the noise on the dependent variable explicitly. This is fundamentally different from the implicit noise assumption in the previously suggested warped GP framework. We...... with the proposed explicit noise-model extension....
AUTONOMOUS GAUSSIAN DECOMPOSITION
International Nuclear Information System (INIS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-01-01
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes
Quantum information with Gaussian states
International Nuclear Information System (INIS)
Wang Xiangbin; Hiroshima, Tohya; Tomita, Akihisa; Hayashi, Masahito
2007-01-01
Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright Gaussian light and weak Gaussian light. Extending the existing results of quantum information with discrete quantum states to the case of continuous variable quantum states is an interesting theoretical job. The quantum Gaussian states play a central role in such a case. We review the properties and applications of Gaussian states in quantum information with emphasis on the fundamental concepts, the calculation techniques and the effects of imperfections of the real-life experimental setups. Topics here include the elementary properties of Gaussian states and relevant quantum information device, entanglement-based quantum tasks such as quantum teleportation, quantum cryptography with weak and strong Gaussian states and the quantum channel capacity, mathematical theory of quantum entanglement and state estimation for Gaussian states
Gaussian discriminating strength
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.
Interconversion of pure Gaussian states requiring non-Gaussian operations
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2015-01-01
We analyze the conditions under which local operations and classical communication enable entanglement transformations between bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found [G. Giedke et al., Quant. Inf. Comput. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 ×2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other.
International Nuclear Information System (INIS)
Strandlie, A.; Wroldsen, J.
2006-01-01
If any of the probability densities involved in track fitting deviate from the Gaussian assumption, it is plausible that a non-linear estimator which better takes the actual shape of the distribution into account can do better. One such non-linear estimator is the Gaussian-sum filter, which is adequate if the distributions under consideration can be approximated by Gaussian mixtures. The main purpose of this paper is to present a Gaussian-sum filter for track fitting, based on a two-component approximation of the distribution of angular deflections due to multiple scattering. In a simulation study within a linear track model the Gaussian-sum filter is shown to be a competitive alternative to the Kalman filter. Scenarios at various momenta and with various maximum number of components in the Gaussian-sum filter are considered. Particularly at low momenta the Gaussian-sum filter yields a better estimate of the uncertainties than the Kalman filter, and it is also slightly more precise than the latter
Yurinsky, Vadim Vladimirovich
1995-01-01
Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
Non-Gaussianity in a quasiclassical electronic circuit
Suzuki, Takafumi J.; Hayakawa, Hisao
2017-05-01
We study the non-Gaussian dynamics of a quasiclassical electronic circuit coupled to a mesoscopic conductor. Non-Gaussian noise accompanying the nonequilibrium transport through the conductor significantly modifies the stationary probability density function (PDF) of the flux in the dissipative circuit. We incorporate weak quantum fluctuation of the dissipative LC circuit with a stochastic method and evaluate the quantum correction of the stationary PDF. Furthermore, an inverse formula to infer the statistical properties of the non-Gaussian noise from the stationary PDF is derived in the classical-quantum crossover regime. The quantum correction is indispensable to correctly estimate the microscopic transfer events in the QPC with the quasiclassical inverse formula.
Estimators for local non-Gaussianities
International Nuclear Information System (INIS)
Creminelli, P.; Senatore, L.; Zaldarriaga, M.
2006-05-01
We study the Likelihood function of data given f NL for the so-called local type of non-Gaussianity. In this case the curvature perturbation is a non-linear function, local in real space, of a Gaussian random field. We compute the Cramer-Rao bound for f NL and show that for small values of f NL the 3- point function estimator saturates the bound and is equivalent to calculating the full Likelihood of the data. However, for sufficiently large f NL , the naive 3-point function estimator has a much larger variance than previously thought. In the limit in which the departure from Gaussianity is detected with high confidence, error bars on f NL only decrease as 1/ln N pix rather than N pix -1/2 as the size of the data set increases. We identify the physical origin of this behavior and explain why it only affects the local type of non- Gaussianity, where the contribution of the first multipoles is always relevant. We find a simple improvement to the 3-point function estimator that makes the square root of its variance decrease as N pix -1/2 even for large f NL , asymptotically approaching the Cramer-Rao bound. We show that using the modified estimator is practically equivalent to computing the full Likelihood of f NL given the data. Thus other statistics of the data, such as the 4-point function and Minkowski functionals, contain no additional information on f NL . In particular, we explicitly show that the recent claims about the relevance of the 4-point function are not correct. By direct inspection of the Likelihood, we show that the data do not contain enough information for any statistic to be able to constrain higher order terms in the relation between the Gaussian field and the curvature perturbation, unless these are orders of magnitude larger than the size suggested by the current limits on f NL . (author)
Detectability of the effect of Inflationary non-Gaussianity on halo bias
Verde, Licia
2009-01-01
We consider the description of the clustering of halos for physically-motivated types of non-Gaussian initial conditions. In particular we include non-Gaussianity of the type arising from single field slow-roll, multi fields, curvaton (local type), higher-order derivative-type (equilateral), vacuum-state modifications (enfolded-type) and horizon-scale GR corrections type. We show that large-scale halo bias is a very sensitive tool to probe non-Gaussianity, potentially leading, for some planned surveys, to a detection of non-Gaussianity arising from horizon-scale GR corrections.
Rotating quantum Gaussian packets
International Nuclear Information System (INIS)
Dodonov, V V
2015-01-01
We study two-dimensional quantum Gaussian packets with a fixed value of mean angular momentum. This value is the sum of two independent parts: the ‘external’ momentum related to the motion of the packet center and the ‘internal’ momentum due to quantum fluctuations. The packets minimizing the mean energy of an isotropic oscillator with the fixed mean angular momentum are found. They exist for ‘co-rotating’ external and internal motions, and they have nonzero correlation coefficients between coordinates and momenta, together with some (moderate) amount of quadrature squeezing. Variances of angular momentum and energy are calculated, too. Differences in the behavior of ‘co-rotating’ and ‘anti-rotating’ packets are shown. The time evolution of rotating Gaussian packets is analyzed, including the cases of a charge in a homogeneous magnetic field and a free particle. In the latter case, the effect of initial shrinking of packets with big enough coordinate-momentum correlation coefficients (followed by the well known expansion) is discovered. This happens due to a competition of ‘focusing’ and ‘de-focusing’ in the orthogonal directions. (paper)
International Nuclear Information System (INIS)
McFadden, Paul; Skenderis, Kostas
2011-01-01
We investigate the non-Gaussianity of primordial cosmological perturbations within our recently proposed holographic description of inflationary universes. We derive a holographic formula that determines the bispectrum of cosmological curvature perturbations in terms of correlation functions of a holographically dual three-dimensional non-gravitational quantum field theory (QFT). This allows us to compute the primordial bispectrum for a universe which started in a non-geometric holographic phase, using perturbative QFT calculations. Strikingly, for a class of models specified by a three-dimensional super-renormalisable QFT, the primordial bispectrum is of exactly the factorisable equilateral form with f NL equil. = 5/36, irrespective of the details of the dual QFT. A by-product of this investigation is a holographic formula for the three-point function of the trace of the stress-energy tensor along general holographic RG flows, which should have applications outside the remit of this work
Palm distributions for log Gaussian Cox processes
DEFF Research Database (Denmark)
Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus Plenge
2017-01-01
This paper establishes a remarkable result regarding Palm distributions for a log Gaussian Cox process: the reduced Palm distribution for a log Gaussian Cox process is itself a log Gaussian Cox process that only differs from the original log Gaussian Cox process in the intensity function. This new...... result is used to study functional summaries for log Gaussian Cox processes....
Geometry of Gaussian quantum states
International Nuclear Information System (INIS)
Link, Valentin; Strunz, Walter T
2015-01-01
We study the Hilbert–Schmidt measure on the manifold of mixed Gaussian states in multi-mode continuous variable quantum systems. An analytical expression for the Hilbert–Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert–Schmidt measure. (paper)
Scaled unscented transform Gaussian sum filter: Theory and application
Luo, Xiaodong
2010-05-01
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]). In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel. As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to
Resource theory of non-Gaussian operations
Zhuang, Quntao; Shor, Peter W.; Shapiro, Jeffrey H.
2018-05-01
Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.
Efficient Kernel-Based Ensemble Gaussian Mixture Filtering
Liu, Bo; Ait-El-Fquih, Boujemaa; Hoteit, Ibrahim
2015-01-01
(KF)-like update of the ensemble members and a particle filter (PF)-like update of the weights, followed by a resampling step to start a new forecast cycle. After formulating EnGMF for any observational operator, we analyze the influence
Missing data reconstruction using Gaussian mixture models for fingerprint images
Agaian, Sos S.; Yeole, Rushikesh D.; Rao, Shishir P.; Mulawka, Marzena; Troy, Mike; Reinecke, Gary
2016-05-01
Publisher's Note: This paper, originally published on 25 May 2016, was replaced with a revised version on 16 June 2016. If you downloaded the original PDF, but are unable to access the revision, please contact SPIE Digital Library Customer Service for assistance. One of the most important areas in biometrics is matching partial fingerprints in fingerprint databases. Recently, significant progress has been made in designing fingerprint identification systems for missing fingerprint information. However, a dependable reconstruction of fingerprint images still remains challenging due to the complexity and the ill-posed nature of the problem. In this article, both binary and gray-level images are reconstructed. This paper also presents a new similarity score to evaluate the performance of the reconstructed binary image. The offered fingerprint image identification system can be automated and extended to numerous other security applications such as postmortem fingerprints, forensic science, investigations, artificial intelligence, robotics, all-access control, and financial security, as well as for the verification of firearm purchasers, driver license applicants, etc.
Protein local conformations arise from a mixture of Gaussian ...
Indian Academy of Sciences (India)
PRAKASH KUMAR
structure prediction methods are of significant value to ... 1Kanwal Rekhi School of Information Technology, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India ..... the tolerance to perturbations around the average structure.
Factoring variations in natural images with deep Gaussian mixture models
van den Oord, Aäron; Schrauwen, Benjamin
2014-01-01
Generative models can be seen as the swiss army knives of machine learning, as many problems can be written probabilistically in terms of the distribution of the data, including prediction, reconstruction, imputation and simulation. One of the most promising directions for unsupervised learning may lie in Deep Learning methods, given their success in supervised learning. However, one of the cur- rent problems with deep unsupervised learning methods, is that they often are harder to scale. As ...
Handbook of Gaussian basis sets
International Nuclear Information System (INIS)
Poirier, R.; Kari, R.; Csizmadia, I.G.
1985-01-01
A collection of a large body of information is presented useful for chemists involved in molecular Gaussian computations. Every effort has been made by the authors to collect all available data for cartesian Gaussian as found in the literature up to July of 1984. The data in this text includes a large collection of polarization function exponents but in this case the collection is not complete. Exponents for Slater type orbitals (STO) were included for completeness. This text offers a collection of Gaussian exponents primarily without criticism. (Auth.)
Overlay Spectrum Sharing using Improper Gaussian Signaling
Amin, Osama
2016-11-30
Improper Gaussian signaling (IGS) scheme has been recently shown to provide performance improvements in interference limited networks as opposed to the conventional proper Gaussian signaling (PGS) scheme. In this paper, we implement the IGS scheme in overlay cognitive radio system, where the secondary transmitter broadcasts a mixture of two different signals. The first signal is selected from the PGS scheme to match the primary message transmission. On the other hand, the second signal is chosen to be from the IGS scheme in order to reduce the interference effect on the primary receiver. We then optimally design the overlay cognitive radio to maximize the secondary link achievable rate while satisfying the primary network quality of service requirements. In particular, we consider full and partial channel knowledge scenarios and derive the feasibility conditions of operating the overlay cognitive radio systems. Moreover, we derive the superiority conditions of the IGS schemes over the PGS schemes supported with closed form expressions for the corresponding power distribution and the circularity coefficient and parameters. Simulation results are provided to support our theoretical derivations.
Imprint of primordial non-Gaussianity on dark matter halo profiles
Energy Technology Data Exchange (ETDEWEB)
Dizgah, Azadeh Moradinezhad; Dodelson, Scott; Riotto, Antonio
2013-09-01
We study the impact of primordial non-Gaussianity on the density profile of dark matter halos by using the semi-analytical model introduced recently by Dalal {\\it et al.} which relates the peaks of the initial linear density field to the final density profile of dark matter halos. Models with primordial non-Gaussianity typically produce an initial density field that differs from that produced in Gaussian models. We use the path-integral formulation of excursion set theory to calculate the non-Gaussian corrections to the peak profile and derive the statistics of the peaks of non-Gaussian density field. In the context of the semi-analytic model for halo profiles, currently allowed values for primordial non-Gaussianity would increase the shapes of the inner dark matter profiles, but only at the sub-percent level except in the very innermost regions.
Xiang, Yu; Xu, Buqing; Mišta, Ladislav; Tufarelli, Tommaso; He, Qiongyi; Adesso, Gerardo
2017-10-01
Einstein-Podolsky-Rosen (EPR) steering is an asymmetric form of correlations which is intermediate between quantum entanglement and Bell nonlocality, and can be exploited as a resource for quantum communication with one untrusted party. In particular, steering of continuous-variable Gaussian states has been extensively studied theoretically and experimentally, as a fundamental manifestation of the EPR paradox. While most of these studies focused on quadrature measurements for steering detection, two recent works revealed that there exist Gaussian states which are only steerable by suitable non-Gaussian measurements. In this paper we perform a systematic investigation of EPR steering of bipartite Gaussian states by pseudospin measurements, complementing and extending previous findings. We first derive the density-matrix elements of two-mode squeezed thermal Gaussian states in the Fock basis, which may be of independent interest. We then use such a representation to investigate steering of these states as detected by a simple nonlinear criterion, based on second moments of the correlation matrix constructed from pseudospin operators. This analysis reveals previously unexplored regimes where non-Gaussian measurements are shown to be more effective than Gaussian ones to witness steering of Gaussian states in the presence of local noise. We further consider an alternative set of pseudospin observables, whose expectation value can be expressed more compactly in terms of Wigner functions for all two-mode Gaussian states. However, according to the adopted criterion, these observables are found to be always less sensitive than conventional Gaussian observables for steering detection. Finally, we investigate continuous-variable Werner states, which are non-Gaussian mixtures of Gaussian states, and find that pseudospin measurements are always more effective than Gaussian ones to reveal their steerability. Our results provide useful insights on the role of non-Gaussian
Non-Gaussianity from tachyonic preheating in hybrid inflation
International Nuclear Information System (INIS)
Barnaby, Neil; Cline, James M.
2007-01-01
In a previous work we showed that large non-Gaussianities and nonscale-invariant distortions in the cosmic microwave background power spectrum can be generated in hybrid inflation models, due to the contributions of the tachyon (waterfall) field to the second order curvature perturbation. Here we clarify, correct, and extend those results. We show that large non-Gaussianity occurs only when the tachyon remains light throughout inflation, whereas n=4 contamination to the spectrum is the dominant effect when the tachyon is heavy. We find constraints on the parameters of warped-throat brane-antibrane inflation from non-Gaussianity. For F-term and D-term inflation models from supergravity, we obtain nontrivial constraints from the spectral distortion effect. We also establish that our analysis applies to complex tachyon fields
Information geometry of Gaussian channels
International Nuclear Information System (INIS)
Monras, Alex; Illuminati, Fabrizio
2010-01-01
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).
Reconstruction of electrons with the Gaussian-sum filter in the CMS tracker at the LHC
International Nuclear Information System (INIS)
Adam, W; Fruehwirth, R; Strandlie, A; Todorov, T
2005-01-01
The bremsstrahlung energy loss distribution of electrons propagating in matter is highly non-Gaussian. Because the Kalman filter relies solely on Gaussian probability density functions, it is not necessarily the optimal reconstruction algorithm for electron tracks. A Gaussian-sum filter (GSF) algorithm for electron reconstruction in the CMS tracker has therefore been developed and implemented. The basic idea is to model the bremsstrahlung energy loss distribution by a Gaussian mixture rather than by a single Gaussian. It is shown that the GSF is able to improve the momentum resolution of electrons compared to the standard Kalman filter. The momentum resolution and the quality of the error estimate are studied both with a fast simulation, modelling the radiative energy loss in a simplified detector, and the full CMS tracker simulation. (research note from collaboration)
Reconstruction of Electrons with the Gaussian-Sum Filter in the CMS Tracker at the LHC
Adam, Wolfgang; Strandlie, Are; Todor, T
2005-01-01
The bremsstrahlung energy loss distribution of electrons propagating in matter is highly non-Gaussian. Because the Kalman filter relies solely on Gaussian probability density functions, it is not necessarily the optimal reconstruction algorithm for electron tracks. A Gaussian-sum filter (GSF) algorithm for electron reconstruction in the CMS tracker has therefore been developed and implemented. The basic idea is to model the bremsstrahlung energy loss distribution by a Gaussian mixture rather than by a single Gaussian. It is shown that the GSF is able to improve the momentum resolution of electrons compared to the standard Kalman filter. The momentum resolution and the quality of he error estimate are studied both with a fast simulation, modelling the radiative energy loss in a simplified detector, and the full CMS tracker simulation.
Gaussian entanglement distribution via satellite
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.
Skewness and kurtosis analysis for non-Gaussian distributions
Celikoglu, Ahmet; Tirnakli, Ugur
2018-06-01
In this paper we address a number of pitfalls regarding the use of kurtosis as a measure of deviations from the Gaussian. We treat kurtosis in both its standard definition and that which arises in q-statistics, namely q-kurtosis. We have recently shown that the relation proposed by Cristelli et al. (2012) between skewness and kurtosis can only be verified for relatively small data sets, independently of the type of statistics chosen; however it fails for sufficiently large data sets, if the fourth moment of the distribution is finite. For infinite fourth moments, kurtosis is not defined as the size of the data set tends to infinity. For distributions with finite fourth moments, the size, N, of the data set for which the standard kurtosis saturates to a fixed value, depends on the deviation of the original distribution from the Gaussian. Nevertheless, using kurtosis as a criterion for deciding which distribution deviates further from the Gaussian can be misleading for small data sets, even for finite fourth moment distributions. Going over to q-statistics, we find that although the value of q-kurtosis is finite in the range of 0 < q < 3, this quantity is not useful for comparing different non-Gaussian distributed data sets, unless the appropriate q value, which truly characterizes the data set of interest, is chosen. Finally, we propose a method to determine the correct q value and thereby to compute the q-kurtosis of q-Gaussian distributed data sets.
A Monte Carlo simulation model for stationary non-Gaussian processes
DEFF Research Database (Denmark)
Grigoriu, M.; Ditlevsen, Ove Dalager; Arwade, S. R.
2003-01-01
includes translation processes and is useful for both Monte Carlo simulation and analytical studies. As for translation processes, the mixture of translation processes can have a wide range of marginal distributions and correlation functions. Moreover, these processes can match a broader range of second...... athe proposed Monte Carlo algorithm and compare features of translation processes and mixture of translation processes. Keywords: Monte Carlo simulation, non-Gaussian processes, sampling theorem, stochastic processes, translation processes......A class of stationary non-Gaussian processes, referred to as the class of mixtures of translation processes, is defined by their finite dimensional distributions consisting of mixtures of finite dimensional distributions of translation processes. The class of mixtures of translation processes...
Tachyon mediated non-Gaussianity
International Nuclear Information System (INIS)
Dutta, Bhaskar; Leblond, Louis; Kumar, Jason
2008-01-01
We describe a general scenario where primordial non-Gaussian curvature perturbations are generated in models with extra scalar fields. The extra scalars communicate to the inflaton sector mainly through the tachyonic (waterfall) field condensing at the end of hybrid inflation. These models can yield significant non-Gaussianity of the local shape, and both signs of the bispectrum can be obtained. These models have cosmic strings and a nearly flat power spectrum, which together have been recently shown to be a good fit to WMAP data. We illustrate with a model of inflation inspired from intersecting brane models.
Bayesian Kernel Mixtures for Counts.
Canale, Antonio; Dunson, David B
2011-12-01
Although Bayesian nonparametric mixture models for continuous data are well developed, there is a limited literature on related approaches for count data. A common strategy is to use a mixture of Poissons, which unfortunately is quite restrictive in not accounting for distributions having variance less than the mean. Other approaches include mixing multinomials, which requires finite support, and using a Dirichlet process prior with a Poisson base measure, which does not allow smooth deviations from the Poisson. As a broad class of alternative models, we propose to use nonparametric mixtures of rounded continuous kernels. An efficient Gibbs sampler is developed for posterior computation, and a simulation study is performed to assess performance. Focusing on the rounded Gaussian case, we generalize the modeling framework to account for multivariate count data, joint modeling with continuous and categorical variables, and other complications. The methods are illustrated through applications to a developmental toxicity study and marketing data. This article has supplementary material online.
The Multivariate Gaussian Probability Distribution
DEFF Research Database (Denmark)
Ahrendt, Peter
2005-01-01
This technical report intends to gather information about the multivariate gaussian distribution, that was previously not (at least to my knowledge) to be found in one place and written as a reference manual. Additionally, some useful tips and tricks are collected that may be useful in practical ...
On Gaussian conditional independence structures
Czech Academy of Sciences Publication Activity Database
Lněnička, Radim; Matúš, František
2007-01-01
Roč. 43, č. 3 (2007), s. 327-342 ISSN 0023-5954 R&D Projects: GA AV ČR IAA100750603 Institutional research plan: CEZ:AV0Z10750506 Keywords : multivariate Gaussian distribution * positive definite matrices * determinants * gaussoids * covariance selection models * Markov perfectness Subject RIV: BA - General Mathematics Impact factor: 0.552, year: 2007
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.
Energy Technology Data Exchange (ETDEWEB)
Klyusov, A A; Bakshutov, V S; Kulyavtsev, V A
1980-10-23
A grouting mixture is proposed for low-temperature boreholes. The mixture contains cement, beta gypsum polyhydrate, and calcium chloride, so as to increase the water resistance and strength properties of expanding brick at conditions from 20 to -5/sup 0/ C, the components are in the following ratios: (by wt.-%): cement, 77.45-88.06; beta gypsum polyhydrate, 9.79-19.36; calcium chloride, 2.15-3.19. Grouting mortar for cold boreholes serves as the cement.
Laguerre Gaussian beam multiplexing through turbulence
CSIR Research Space (South Africa)
Trichili, A
2014-08-17
Full Text Available We analyze the effect of atmospheric turbulence on the propagation of multiplexed Laguerre Gaussian modes. We present a method to multiplex Laguerre Gaussian modes using digital holograms and decompose the resulting field after encountering a...
Probabilistic mixture-based image modelling
Czech Academy of Sciences Publication Activity Database
Haindl, Michal; Havlíček, Vojtěch; Grim, Jiří
2011-01-01
Roč. 47, č. 3 (2011), s. 482-500 ISSN 0023-5954 R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/0593 Grant - others:CESNET(CZ) 387/2010; GA MŠk(CZ) 2C06019; GA ČR(CZ) GA103/11/0335 Institutional research plan: CEZ:AV0Z10750506 Keywords : BTF texture modelling * discrete distribution mixtures * Bernoulli mixture * Gaussian mixture * multi-spectral texture modelling Subject RIV: BD - Theory of Information Impact factor: 0.454, year: 2011 http://library.utia.cas.cz/separaty/2011/RO/haindl-0360244.pdf
Analytic matrix elements with shifted correlated Gaussians
DEFF Research Database (Denmark)
Fedorov, D. V.
2017-01-01
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.......Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics....
Gaussian process regression analysis for functional data
Shi, Jian Qing
2011-01-01
Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dime
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 statistics for palaeomagnetic vectors
Love, J. J.; Constable, C. G.
2003-03-01
With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimodal) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to
Reproducing kernel Hilbert spaces of Gaussian priors
Vaart, van der A.W.; Zanten, van J.H.; Clarke, B.; Ghosal, S.
2008-01-01
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described
The properties of the dark matter halo distribution in non-Gaussian scenarios
International Nuclear Information System (INIS)
Carbone, C.; Branchini, E.; Dolag, K.; Grossi, M.; Iannuzzi, F.; Matarrese, S.; Moscardini, L.; Verde, L.
2009-01-01
The description of halo abundance and clustering for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys, which can potentially detect primordial non-Gaussianity of the local form with a non-Gaussianity parameter |f NL | of order unity. This is particularly exciting because, while the simplest single-field slow-roll models of inflation predict a primordial |f NL | NL of large-scale structures that are expected to be above the predicted detection threshold [C. Carbone, L. Verde, and S. Matarrese, ApJL 684 (2008) L1]. We present tests on N-body simulations of analytical formulae describing the halo abundance and clustering for non-Gaussian initial conditions. In particular, when we calibrate the analytic non-Gaussian mass function of [S. Matarrese, L. Verde, L. and R. Jimenez, ApJL 541 (2000) 10] and [M. LoVerde, A. Miller, S. Shandera and L. Verde, JCAP 04 (2008) 014] and the analytic description of halo clustering for non-Gaussian initial conditions on N-body simulations, we find excellent agreement between the simulations and the analytic predictions if we make the substitutions δ c →δ c x√(q) and δ c →δ c xq where q≅0.75, in the density threshold for gravitational collapse and in the non-Gaussian fractional correction to the halo bias, respectively. We discuss the implications of these corrections on present and forecasted primordial non-Gaussianity constraints. We confirm that the non-Gaussian halo bias offers a robust and highly competitive test of primordial non-Gaussianity.
Inflation in random Gaussian landscapes
Energy Technology Data Exchange (ETDEWEB)
Masoumi, Ali; Vilenkin, Alexander; Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2017-05-01
We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations n {sub s} and its running α {sub s} . These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.
Infinite von Mises-Fisher Mixture Modeling of Whole Brain fMRI Data
DEFF Research Database (Denmark)
Røge, Rasmus; Madsen, Kristoffer Hougaard; Schmidt, Mikkel Nørgaard
2017-01-01
spherical manifold are rarely analyzed, in part due to the computational challenges imposed by directional statistics. In this letter, we discuss a Bayesian von Mises-Fisher (vMF) mixture model for data on the unit hypersphere and present an efficient inference procedure based on collapsed Markov chain...... Monte Carlo sampling. Comparing the vMF and gaussian mixture models on synthetic data, we demonstrate that the vMF model has a slight advantage inferring the true underlying clustering when compared to gaussian-based models on data generated from both a mixture of vMFs and a mixture of gaussians......Cluster analysis of functional magnetic resonance imaging (fMRI) data is often performed using gaussian mixture models, but when the time series are standardized such that the data reside on a hypersphere, this modeling assumption is questionable. The consequences of ignoring the underlying...
General Galilei Covariant Gaussian Maps
Gasbarri, Giulio; Toroš, Marko; Bassi, Angelo
2017-09-01
We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we consider translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined by Nimmrichter and Hornberger [Phys. Rev. Lett. 110, 16 (2013)].
Gaussian Embeddings for Collaborative Filtering
Dos Santos , Ludovic; Piwowarski , Benjamin; Gallinari , Patrick
2017-01-01
International audience; Most collaborative ltering systems, such as matrix factorization, use vector representations for items and users. Those representations are deterministic, and do not allow modeling the uncertainty of the learned representation, which can be useful when a user has a small number of rated items (cold start), or when there is connict-ing information about the behavior of a user or the ratings of an item. In this paper, we leverage recent works in learning Gaussian embeddi...
The halo bispectrum in N-body simulations with non-Gaussian initial conditions
Sefusatti, E.; Crocce, M.; Desjacques, V.
2012-10-01
We present measurements of the bispectrum of dark matter haloes in numerical simulations with non-Gaussian initial conditions of local type. We show, in the first place, that the overall effect of primordial non-Gaussianity on the halo bispectrum is larger than on the halo power spectrum when all measurable configurations are taken into account. We then compare our measurements with a tree-level perturbative prediction, finding good agreement at large scales when the constant Gaussian bias parameter, both linear and quadratic, and their constant non-Gaussian corrections are fitted for. The best-fitting values of the Gaussian bias factors and their non-Gaussian, scale-independent corrections are in qualitative agreement with the peak-background split expectations. In particular, we show that the effect of non-Gaussian initial conditions on squeezed configurations is fairly large (up to 30 per cent for fNL = 100 at redshift z = 0.5) and results from contributions of similar amplitude induced by the initial matter bispectrum, scale-dependent bias corrections as well as from non-linear matter bispectrum corrections. We show, in addition, that effects at second order in fNL are irrelevant for the range of values allowed by cosmic microwave background and galaxy power spectrum measurements, at least on the scales probed by our simulations (k > 0.01 h Mpc-1). Finally, we present a Fisher matrix analysis to assess the possibility of constraining primordial non-Gaussianity with future measurements of the galaxy bispectrum. We find that a survey with a volume of about 10 h-3 Gpc3 at mean redshift z ≃ 1 could provide an error on fNL of the order of a few. This shows the relevance of a joint analysis of galaxy power spectrum and bispectrum in future redshift surveys.
The Matter Bispectrum in N-body Simulations with non-Gaussian Initial Conditions
Sefusatti, Emiliano; Crocce, Martin; Desjacques, Vincent
2010-01-01
We present measurements of the dark matter bispectrum in N-body simulations with non-Gaussian initial conditions of the local kind for a large variety of triangular configurations and compare them with predictions from Eulerian perturbation theory up to one-loop corrections. We find that the effects of primordial non-Gaussianity at large scales, when compared to perturbation theory, are well described by the initial component of the matter bispectrum, linearly extrapolated at the redshift of ...
A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models
Directory of Open Access Journals (Sweden)
Elias D. Nino-Ruiz
2018-03-01
Full Text Available In this paper, we propose an efficient EnKF implementation for non-Gaussian data assimilation based on Gaussian Mixture Models and Markov-Chain-Monte-Carlo (MCMC methods. The proposed method works as follows: based on an ensemble of model realizations, prior errors are estimated via a Gaussian Mixture density whose parameters are approximated by means of an Expectation Maximization method. Then, by using an iterative method, observation operators are linearized about current solutions and posterior modes are estimated via a MCMC implementation. The acceptance/rejection criterion is similar to that of the Metropolis-Hastings rule. Experimental tests are performed on the Lorenz 96 model. The results show that the proposed method can decrease prior errors by several order of magnitudes in a root-mean-square-error sense for nearly sparse or dense observational networks.
DEFF Research Database (Denmark)
Andersen, Jens S.; Søgaard, M; Svensson, B
1994-01-01
Matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) of peptide mixtures was used to characterize recombinant barley alpha-amylase 1, produced in yeast. Three peptide mixtures were generated by cleavage with CNBr, digestion with endoproteinase Lys-C and Asp-N, respectively...
Large non-Gaussianity from two-component hybrid inflation
International Nuclear Information System (INIS)
Byrnes, Christian T.; Choi, Ki-Young; Hall, Lisa M.H.
2009-01-01
We study the generation of non-Gaussianity in models of hybrid inflation with two inflaton fields, (2-brid inflation). We analyse the region in the parameter and the initial condition space where a large non-Gaussianity may be generated during slow-roll inflation which is generally characterised by a large f NL , τ NL and a small g NL . For certain parameter values we can satisfy τ NL >> f NL 2 . The bispectrum is of the local type but may have a significant scale dependence. We show that the loop corrections to the power spectrum and bispectrum are suppressed during inflation, if one assume that the fields follow a classical background trajectory. We also include the effect of the waterfall field, which can lead to a significant change in the observables after the waterfall field is destabilised, depending on the couplings between the waterfall and inflaton fields
Weighted Feature Gaussian Kernel SVM for Emotion Recognition.
Wei, Wei; Jia, Qingxuan
2016-01-01
Emotion recognition with weighted feature based on facial expression is a challenging research topic and has attracted great attention in the past few years. This paper presents a novel method, utilizing subregion recognition rate to weight kernel function. First, we divide the facial expression image into some uniform subregions and calculate corresponding recognition rate and weight. Then, we get a weighted feature Gaussian kernel function and construct a classifier based on Support Vector Machine (SVM). At last, the experimental results suggest that the approach based on weighted feature Gaussian kernel function has good performance on the correct rate in emotion recognition. The experiments on the extended Cohn-Kanade (CK+) dataset show that our method has achieved encouraging recognition results compared to the state-of-the-art methods.
Detecting periodicities with Gaussian processes
Directory of Open Access Journals (Sweden)
Nicolas Durrande
2016-04-01
Full Text Available We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression, which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in the arabidopsis genome.
Monogamy inequality for distributed gaussian entanglement.
Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio
2007-02-02
We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.
Breaking Gaussian incompatibility on continuous variable quantum systems
Energy Technology Data Exchange (ETDEWEB)
Heinosaari, Teiko, E-mail: teiko.heinosaari@utu.fi [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Kiukas, Jukka, E-mail: jukka.kiukas@aber.ac.uk [Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, SY23 3BZ (United Kingdom); Schultz, Jussi, E-mail: jussi.schultz@gmail.com [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy)
2015-08-15
We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.
Bootstrapping realized volatility and realized beta under a local Gaussianity assumption
DEFF Research Database (Denmark)
Hounyo, Ulrich
The main contribution of this paper is to propose a new bootstrap method for statistics based on high frequency returns. The new method exploits the local Gaussianity and the local constancy of volatility of high frequency returns, two assumptions that can simplify inference in the high frequency...... context, as recently explained by Mykland and Zhang (2009). Our main contributions are as follows. First, we show that the local Gaussian bootstrap is firstorder consistent when used to estimate the distributions of realized volatility and ealized betas. Second, we show that the local Gaussian bootstrap...... matches accurately the first four cumulants of realized volatility, implying that this method provides third-order refinements. This is in contrast with the wild bootstrap of Gonçalves and Meddahi (2009), which is only second-order correct. Third, we show that the local Gaussian bootstrap is able...
Direct Reconstruction of CT-based Attenuation Correction Images for PET with Cluster-Based Penalties
Kim, Soo Mee; Alessio, Adam M.; De Man, Bruno; Asma, Evren; Kinahan, Paul E.
2015-01-01
Extremely low-dose CT acquisitions for the purpose of PET attenuation correction will have a high level of noise and biasing artifacts due to factors such as photon starvation. This work explores a priori knowledge appropriate for CT iterative image reconstruction for PET attenuation correction. We investigate the maximum a posteriori (MAP) framework with cluster-based, multinomial priors for the direct reconstruction of the PET attenuation map. The objective function for direct iterative attenuation map reconstruction was modeled as a Poisson log-likelihood with prior terms consisting of quadratic (Q) and mixture (M) distributions. The attenuation map is assumed to have values in 4 clusters: air+background, lung, soft tissue, and bone. Under this assumption, the MP was a mixture probability density function consisting of one exponential and three Gaussian distributions. The relative proportion of each cluster was jointly estimated during each voxel update of direct iterative coordinate decent (dICD) method. Noise-free data were generated from NCAT phantom and Poisson noise was added. Reconstruction with FBP (ramp filter) was performed on the noise-free (ground truth) and noisy data. For the noisy data, dICD reconstruction was performed with the combination of different prior strength parameters (β and γ) of Q- and M-penalties. The combined quadratic and mixture penalties reduces the RMSE by 18.7% compared to post-smoothed iterative reconstruction and only 0.7% compared to quadratic alone. For direct PET attenuation map reconstruction from ultra-low dose CT acquisitions, the combination of quadratic and mixture priors offers regularization of both variance and bias and is a potential method to derive attenuation maps with negligible patient dose. However, the small improvement in quantitative accuracy relative to the substantial increase in algorithm complexity does not currently justify the use of mixture-based PET attenuation priors for reconstruction of CT
International Nuclear Information System (INIS)
McHugh, Derek; Buzek, Vladimir; Ziman, Mario
2006-01-01
We present a class of non-Gaussian two-mode continuous-variable states for which the separability criterion for Gaussian states can be employed to detect whether they are separable or not. These states reduce to the two-mode Gaussian states as a special case
Limit theorems for functionals of Gaussian vectors
Institute of Scientific and Technical Information of China (English)
Hongshuai DAI; Guangjun SHEN; Lingtao KONG
2017-01-01
Operator self-similar processes,as an extension of self-similar processes,have been studied extensively.In this work,we study limit theorems for functionals of Gaussian vectors.Under some conditions,we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.
Palm distributions for log Gaussian Cox processes
DEFF Research Database (Denmark)
Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus
This paper reviews useful results related to Palm distributions of spatial point processes and provides a new result regarding the characterization of Palm distributions for the class of log Gaussian Cox processes. This result is used to study functional summary statistics for a log Gaussian Cox...
Gaussian limit of compact spin systems
International Nuclear Information System (INIS)
Bellissard, J.; Angelis, G.F. de
1981-01-01
It is shown that the Wilson and Wilson-Villain U(1) models reproduce, in the low coupling limit, the gaussian lattice approximation of the Euclidean electromagnetic field. By the same methods it is also possible to prove that the plane rotator and the Villain model share a common gaussian behaviour in the low temperature limit. (Auth.)
On the dependence structure of Gaussian queues
Es-Saghouani, A.; Mandjes, M.R.H.
2009-01-01
In this article we study Gaussian queues (that is, queues fed by Gaussian processes, such as fractional Brownian motion (fBm) and the integrated Ornstein-Uhlenbeck (iOU) process), with a focus on the dependence structure of the workload process. The main question is to what extent does the workload
Shedding new light on Gaussian harmonic analysis
Teuwen, J.J.B.
2016-01-01
This dissertation consists out of two rather disjoint parts. One part concerns some results on Gaussian harmonic analysis and the other on an optimization problem in optics. In the first part we study the Ornstein–Uhlenbeck process with respect to the Gaussian measure. We focus on two areas. One is
Nuclear collective flow from gaussian fits to triple differential distributions
International Nuclear Information System (INIS)
Gosset, J.; Demoulins, M.; Babinet, R.; Cavata, C.; Fanet, H.; L'Hote, D.; Lucas, B.; Poitou, J.; Valette, O.; Alard, J.P.; Augerat, J.; Bastid, N.; Charmensat, P.; Dupieux, P.; Fraysse, L.; Marroncle, J.; Montarou, G.; Parizet, M.J.; Qassoud, D.; Rahmani, A.; Brochard, F.; Gorodetzky, P.; Racca, C.
1990-01-01
In order to study the nuclear collective flow, the triple differential momentum distributions of charged baryons are fitted to a simple anisotropic gaussian distribution, within an acceptance which removes most of the spectator contribution. The adjusted flow angle and aspect ratios are corrected for systematic errors in the determination of the reaction plane. This method has been tested with Monte Carlo simulations and applied to experimental results and intranuclear cascade simulations of argon-nucleus collisions at 400 MeV per nucleon. (orig.)
Entanglement in Gaussian matrix-product states
International Nuclear Information System (INIS)
Adesso, Gerardo; Ericsson, Marie
2006-01-01
Gaussian matrix-product states are obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of N sites of a harmonic chain. Replacing the projections by associated Gaussian states, the building blocks, we show that the entanglement range in translationally invariant Gaussian matrix-product states depends on how entangled the building blocks are. In particular, infinite entanglement in the building blocks produces fully symmetric Gaussian states with maximum entanglement range. From their peculiar properties of entanglement sharing, a basic difference with spin chains is revealed: Gaussian matrix-product states can possess unlimited, long-range entanglement even with minimum number of ancillary bonds (M=1). Finally we discuss how these states can be experimentally engineered from N copies of a three-mode building block and N two-mode finitely squeezed states
Gaussian vs non-Gaussian turbulence: impact on wind turbine loads
DEFF Research Database (Denmark)
Berg, Jacob; Natarajan, Anand; Mann, Jakob
2016-01-01
taking into account the safety factor for extreme moments. Other extreme load moments as well as the fatigue loads are not affected because of the use of non-Gaussian turbulent inflow. It is suggested that the turbine thus acts like a low-pass filter that averages out the non-Gaussian behaviour, which......From large-eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non-Gaussian counterpart. Time series from the two...
s -wave scattering length of a Gaussian potential
Jeszenszki, Peter; Cherny, Alexander Yu.; Brand, Joachim
2018-04-01
We provide accurate expressions for the s -wave scattering length for a Gaussian potential well in one, two, and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of ultracold-atomic gases, where the s -wave scattering length is a physically relevant parameter. We first describe a numerical procedure to compute the value of the s -wave scattering length from the parameters of the Gaussian, but find that its accuracy is limited in the vicinity of singularities that result from the formation of new bound states. We then derive simple analytical expressions that capture the correct asymptotic behavior of the s -wave scattering length near the bound states. Expressions that are increasingly accurate in wide parameter regimes are found by a hierarchy of approximations that capture an increasing number of bound states. The small number of numerical coefficients that enter these expressions is determined from accurate numerical calculations. The approximate formulas combine the advantages of the numerical and approximate expressions, yielding an accurate and simple description from the weakly to the strongly interacting limit.
Non-Gaussian bias: insights from discrete density peaks
Desjacques, Vincent; Riotto, Antonio
2013-01-01
Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastly simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out tha...
The Modified Enskog Equation for Mixtures
Beijeren, H. van; Ernst, M.H.
1973-01-01
In a previous paper it was shown that a modified form of the Enskog equation, applied to mixtures of hard spheres, should be considered as the correct extension of the usual Enskog equation to the case of mixtures. The main argument was that the modified Enskog equation leads to linear transport
Increasing Entanglement between Gaussian States by Coherent Photon Subtraction
DEFF Research Database (Denmark)
Ourjoumtsev, Alexei; Dantan, Aurelien Romain; Tualle Brouri, Rosa
2007-01-01
We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states...
Representation of Gaussian semimartingales with applications to the covariance function
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2010-01-01
stationary Gaussian semimartingales and their canonical decomposition. Thirdly, we give a new characterization of the covariance function of Gaussian semimartingales, which enable us to characterize the class of martingales and the processes of bounded variation among the Gaussian semimartingales. We...
Some continual integrals from gaussian forms
International Nuclear Information System (INIS)
Mazmanishvili, A.S.
1985-01-01
The result summary of continual integration of gaussian functional type is given. The summary contains 124 continual integrals which are the mathematical expectation of the corresponding gaussian form by the continuum of random trajectories of four types: real-valued Ornstein-Uhlenbeck process, Wiener process, complex-valued Ornstein-Uhlenbeck process and the stochastic harmonic one. The summary includes both the known continual integrals and the unpublished before integrals. Mathematical results of the continual integration carried in the work may be applied in the problem of the theory of stochastic process, approaching to the finding of mean from gaussian forms by measures generated by the pointed stochastic processes
Non-Gaussianity from isocurvature perturbations
Energy Technology Data Exchange (ETDEWEB)
Kawasaki, Masahiro; Nakayama, Kazunori; Sekiguchi, Toyokazu; Suyama, Teruaki [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582 (Japan); Takahashi, Fuminobu, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: nakayama@icrr.u-tokyo.ac.jp, E-mail: sekiguti@icrr.u-tokyo.ac.jp, E-mail: suyama@icrr.u-tokyo.ac.jp, E-mail: fuminobu.takahashi@ipmu.jp [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan)
2008-11-15
We develop a formalism for studying non-Gaussianity in both curvature and isocurvature perturbations. It is shown that non-Gaussianity in the isocurvature perturbation between dark matter and photons leaves distinct signatures in the cosmic microwave background temperature fluctuations, which may be confirmed in future experiments, or possibly even in the currently available observational data. As an explicit example, we consider the quantum chromodynamics axion and show that it can actually induce sizable non-Gaussianity for the inflationary scale, H{sub inf} = O(10{sup 9}-10{sup 11}) GeV.
Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states
International Nuclear Information System (INIS)
Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
We study the entanglement of general (pure or mixed) two-mode Gaussian states of continuous-variable systems by comparing the two available classes of computable measures of entanglement: entropy-inspired Gaussian convex-roof measures and positive partial transposition-inspired measures (negativity and logarithmic negativity). We first review the formalism of Gaussian measures of entanglement, adopting the framework introduced in M. M. Wolf et al., Phys. Rev. A 69, 052320 (2004), where the Gaussian entanglement of formation was defined. We compute explicitly Gaussian measures of entanglement for two important families of nonsymmetric two-mode Gaussian state: namely, the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in G. Adesso et al., Phys. Rev. Lett. 92, 087901 (2004). This analysis allows us to compare the different orderings induced on the set of entangled two-mode Gaussian states by the negativities and by the Gaussian measures of entanglement. We find that in a certain range of values of the global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement of formation than states of maximum negativity. Consequently, Gaussian measures and negativities are definitely inequivalent measures of entanglement on nonsymmetric two-mode Gaussian states, even when restricted to a class of extremal states. On the other hand, the two families of entanglement measures are completely equivalent on symmetric states, for which the Gaussian entanglement of formation coincides with the true entanglement of formation. Finally, we show that the inequivalence between the two families of continuous-variable entanglement measures is somehow limited. Namely, we rigorously prove that, at fixed negativities, the Gaussian measures of entanglement are bounded from below. Moreover, we provide some strong evidence suggesting that they
Optimal unitary dilation for bosonic Gaussian channels
International Nuclear Information System (INIS)
Caruso, Filippo; Eisert, Jens; Giovannetti, Vittorio; Holevo, Alexander S.
2011-01-01
A general quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. In this paper the minimal number of quantum Gaussian environmental modes required to provide a unitary dilation of a multimode bosonic Gaussian channel is analyzed for both pure and mixed environments. We compute this quantity in the case of pure environment corresponding to the Stinespring representation and give an improved estimate in the case of mixed environment. The computations rely, on one hand, on the properties of the generalized Choi-Jamiolkowski state and, on the other hand, on an explicit construction of the minimal dilation for arbitrary bosonic Gaussian channel. These results introduce a new quantity reflecting ''noisiness'' of bosonic Gaussian channels and can be applied to address some issues concerning transmission of information in continuous variables systems.
Phase statistics in non-Gaussian scattering
International Nuclear Information System (INIS)
Watson, Stephen M; Jakeman, Eric; Ridley, Kevin D
2006-01-01
Amplitude weighting can improve the accuracy of frequency measurements in signals corrupted by multiplicative speckle noise. When the speckle field constitutes a circular complex Gaussian process, the optimal function of amplitude weighting is provided by the field intensity, corresponding to the intensity-weighted phase derivative statistic. In this paper, we investigate the phase derivative and intensity-weighted phase derivative returned from a two-dimensional random walk, which constitutes a generic scattering model capable of producing both Gaussian and non-Gaussian fluctuations. Analytical results are developed for the correlation properties of the intensity-weighted phase derivative, as well as limiting probability densities of the scattered field. Numerical simulation is used to generate further probability densities and determine optimal weighting criteria from non-Gaussian fields. The results are relevant to frequency retrieval in radiation scattered from random media
Galaxy bias and primordial non-Gaussianity
Energy Technology Data Exchange (ETDEWEB)
Assassi, Valentin; Baumann, Daniel [DAMTP, Cambridge University, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Schmidt, Fabian, E-mail: assassi@ias.edu, E-mail: D.D.Baumann@uva.nl, E-mail: fabians@MPA-Garching.MPG.DE [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching (Germany)
2015-12-01
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation.
Optimal cloning of mixed Gaussian states
International Nuclear Information System (INIS)
Guta, Madalin; Matsumoto, Keiji
2006-01-01
We construct the optimal one to two cloning transformation for the family of displaced thermal equilibrium states of a harmonic oscillator, with a fixed and known temperature. The transformation is Gaussian and it is optimal with respect to the figure of merit based on the joint output state and norm distance. The proof of the result is based on the equivalence between the optimal cloning problem and that of optimal amplification of Gaussian states which is then reduced to an optimization problem for diagonal states of a quantum oscillator. A key concept in finding the optimum is that of stochastic ordering which plays a similar role in the purely classical problem of Gaussian cloning. The result is then extended to the case of n to m cloning of mixed Gaussian states
Encoding information using laguerre gaussian modes
CSIR Research Space (South Africa)
Trichili, A
2015-08-01
Full Text Available The authors experimentally demonstrate an information encoding protocol using the two degrees of freedom of Laguerre Gaussian modes having different radial and azimuthal components. A novel method, based on digital holography, for information...
Interweave Cognitive Radio with Improper Gaussian Signaling
Hedhly, Wafa; Amin, Osama; Alouini, Mohamed-Slim
2018-01-01
Improper Gaussian signaling (IGS) has proven its ability in improving the performance of underlay and overlay cognitive radio paradigms. In this paper, the interweave cognitive radio paradigm is studied when the cognitive user employs IGS
Galaxy bias and primordial non-Gaussianity
International Nuclear Information System (INIS)
Assassi, Valentin; Baumann, Daniel; Schmidt, Fabian
2015-01-01
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation
A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families
Dutta, Subhajit
2014-07-28
Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.
A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families
Dutta, Subhajit; Genton, Marc G.
2014-01-01
Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.
Analytic Treatment of Deep Neural Networks Under Additive Gaussian Noise
Alfadly, Modar
2018-01-01
Despite the impressive performance of deep neural networks (DNNs) on numerous vision tasks, they still exhibit yet-to-understand uncouth behaviours. One puzzling behaviour is the reaction of DNNs to various noise attacks, where it has been shown that there exist small adversarial noise that can result in a severe degradation in the performance of DNNs. To rigorously treat this, we derive exact analytic expressions for the first and second moments (mean and variance) of a small piecewise linear (PL) network with a single rectified linear unit (ReLU) layer subject to general Gaussian input. We experimentally show that these expressions are tight under simple linearizations of deeper PL-DNNs, especially popular architectures in the literature (e.g. LeNet and AlexNet). Extensive experiments on image classification show that these expressions can be used to study the behaviour of the output mean of the logits for each class, the inter-class confusion and the pixel-level spatial noise sensitivity of the network. Moreover, we show how these expressions can be used to systematically construct targeted and non-targeted adversarial attacks. Then, we proposed a special estimator DNN, named mixture of linearizations (MoL), and derived the analytic expressions for its output mean and variance, as well. We employed these expressions to train the model to be particularly robust against Gaussian attacks without the need for data augmentation. Upon training this network on a loss that is consolidated with the derived output probabilistic moments, the network is not only robust under very high variance Gaussian attacks but is also as robust as networks that are trained with 20 fold data augmentation.
Analytic Treatment of Deep Neural Networks Under Additive Gaussian Noise
Alfadly, Modar M.
2018-04-12
Despite the impressive performance of deep neural networks (DNNs) on numerous vision tasks, they still exhibit yet-to-understand uncouth behaviours. One puzzling behaviour is the reaction of DNNs to various noise attacks, where it has been shown that there exist small adversarial noise that can result in a severe degradation in the performance of DNNs. To rigorously treat this, we derive exact analytic expressions for the first and second moments (mean and variance) of a small piecewise linear (PL) network with a single rectified linear unit (ReLU) layer subject to general Gaussian input. We experimentally show that these expressions are tight under simple linearizations of deeper PL-DNNs, especially popular architectures in the literature (e.g. LeNet and AlexNet). Extensive experiments on image classification show that these expressions can be used to study the behaviour of the output mean of the logits for each class, the inter-class confusion and the pixel-level spatial noise sensitivity of the network. Moreover, we show how these expressions can be used to systematically construct targeted and non-targeted adversarial attacks. Then, we proposed a special estimator DNN, named mixture of linearizations (MoL), and derived the analytic expressions for its output mean and variance, as well. We employed these expressions to train the model to be particularly robust against Gaussian attacks without the need for data augmentation. Upon training this network on a loss that is consolidated with the derived output probabilistic moments, the network is not only robust under very high variance Gaussian attacks but is also as robust as networks that are trained with 20 fold data augmentation.
DCMDN: Deep Convolutional Mixture Density Network
D'Isanto, Antonio; Polsterer, Kai Lars
2017-09-01
Deep Convolutional Mixture Density Network (DCMDN) estimates probabilistic photometric redshift directly from multi-band imaging data by combining a version of a deep convolutional network with a mixture density network. The estimates are expressed as Gaussian mixture models representing the probability density functions (PDFs) in the redshift space. In addition to the traditional scores, the continuous ranked probability score (CRPS) and the probability integral transform (PIT) are applied as performance criteria. DCMDN is able to predict redshift PDFs independently from the type of source, e.g. galaxies, quasars or stars and renders pre-classification of objects and feature extraction unnecessary; the method is extremely general and allows the solving of any kind of probabilistic regression problems based on imaging data, such as estimating metallicity or star formation rate in galaxies.
Gaussian sum rules for optical functions
International Nuclear Information System (INIS)
Kimel, I.
1981-12-01
A new (Gaussian) type of sum rules (GSR) for several optical functions, is presented. The functions considered are: dielectric permeability, refractive index, energy loss function, rotatory power and ellipticity (circular dichroism). While reducing to the usual type of sum rules in a certain limit, the GSR contain in general, a Gaussian factor that serves to improve convergence. GSR might be useful in analysing experimental data. (Author) [pt
Gaussian maximally multipartite-entangled states
Facchi, Paolo; Florio, Giuseppe; Lupo, Cosmo; Mancini, Stefano; Pascazio, Saverio
2009-12-01
We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n≤7 .
Gaussian maximally multipartite-entangled states
International Nuclear Information System (INIS)
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Lupo, Cosmo; Mancini, Stefano
2009-01-01
We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n≤7.
Bose, S
2002-01-01
The robust statistic proposed by Creighton (Creighton J D E 1999 Phys. Rev. D 60 021101) and Allen et al (Allen et al 2001 Preprint gr-gc/010500) for the detection of stationary non-Gaussian noise is briefly reviewed. We compute the robust statistic for generic weak gravitational-wave signals in the mixture-Gaussian noise model to an accuracy higher than in those analyses, and reinterpret its role. Specifically, we obtain the coherent statistic for detecting gravitational-wave signals from inspiralling compact binaries with an arbitrary network of earth-based interferometers. Finally, we show that excess computational costs incurred owing to non-Gaussianity is negligible compared to the cost of detection in Gaussian noise.
Combinatorial bounds on the α-divergence of univariate mixture models
Nielsen, Frank
2017-06-20
We derive lower- and upper-bounds of α-divergence between univariate mixture models with components in the exponential family. Three pairs of bounds are presented in order with increasing quality and increasing computational cost. They are verified empirically through simulated Gaussian mixture models. The presented methodology generalizes to other divergence families relying on Hellinger-type integrals.
Position Error Covariance Matrix Validation and Correction
Frisbee, Joe, Jr.
2016-01-01
In order to calculate operationally accurate collision probabilities, the position error covariance matrices predicted at times of closest approach must be sufficiently accurate representations of the position uncertainties. This presentation will discuss why the Gaussian distribution is a reasonable expectation for the position uncertainty and how this assumed distribution type is used in the validation and correction of position error covariance matrices.
Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.
Cagniot, Emmanuel; Fromager, Michael; Ait-Ameur, Kamel
2009-11-01
A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.
A Non-Gaussian Spatial Generalized Linear Latent Variable Model
Irincheeva, Irina
2012-08-03
We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents. © 2012 International Biometric Society.
A Non-Gaussian Spatial Generalized Linear Latent Variable Model
Irincheeva, Irina; Cantoni, Eva; Genton, Marc G.
2012-01-01
We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents. © 2012 International Biometric Society.
Stochastic cluster algorithms for discrete Gaussian (SOS) models
International Nuclear Information System (INIS)
Evertz, H.G.; Hamburg Univ.; Hasenbusch, M.; Marcu, M.; Tel Aviv Univ.; Pinn, K.; Muenster Univ.; Solomon, S.
1990-10-01
We present new Monte Carlo cluster algorithms which eliminate critical slowing down in the simulation of solid-on-solid models. In this letter we focus on the two-dimensional discrete Gaussian model. The algorithms are based on reflecting the integer valued spin variables with respect to appropriately chosen reflection planes. The proper choice of the reflection plane turns out to be crucial in order to obtain a small dynamical exponent z. Actually, the successful versions of our algorithm are a mixture of two different procedures for choosing the reflection plane, one of them ergodic but slow, the other one non-ergodic and also slow when combined with a Metropolis algorithm. (orig.)
International Nuclear Information System (INIS)
Crenn, J.P.
1981-07-01
It is proposed to draw up an approximate formula directly giving the attenuation of a gaussian beam penetrating into a superdimensioned dielectric circular wave guide. This formula is derived from optical laws, i.e. Fresnel's formulae of the reflexion of a wave on a dielectric to which a correcting term due to diffraction has been added. The results given by this formula are compared with the existing results, based on the breakdown of a gaussian beam into propagation modes, thereby enabling their validity and the field of use to be checked. An application is then made to the wave guides that will be employed in the infrared interferometer fitted in JET [fr
New gaussian points for the solution of first order ordinary ...
African Journals Online (AJOL)
Numerical experiments carried out using the new Gaussian points revealed there efficiency on stiff differential equations. The results also reveal that methods using the new Gaussian points are more accurate than those using the standard Gaussian points on non-stiff initial value problems. Keywords: Gaussian points ...
DEFF Research Database (Denmark)
Bennedsen, Mikkel
Using theory on (conditionally) Gaussian processes with stationary increments developed in Barndorff-Nielsen et al. (2009, 2011), this paper presents a general semiparametric approach to conducting inference on the fractal index, α, of a time series. Our setup encompasses a large class of Gaussian...
Non-Gaussian initial conditions in ΛCDM: Newtonian, relativistic, and primordial contributions
International Nuclear Information System (INIS)
Bruni, Marco; Hidalgo, Juan Carlos; Meures, Nikolai; Wands, David
2014-01-01
The goal of the present paper is to set initial conditions for structure formation at nonlinear order, consistent with general relativity, while also allowing for primordial non-Gaussianity. We use the nonlinear continuity and Raychaudhuri equations, which together with the nonlinear energy constraint, determine the evolution of the matter density fluctuation in general relativity. We solve this equations at first and second order in a perturbative expansion, recovering and extending previous results derived in the matter-dominated limit and in the Newtonian regime. We present a second-order solution for the comoving density contrast in a ΛCDM universe, identifying nonlinear contributions coming from the Newtonian growing mode, primordial non-Gaussianity and intrinsic non-Gaussianity, due to the essential nonlinearity of the relativistic constraint equations. We discuss the application of these results to initial conditions in N-body simulations, showing that relativistic corrections mimic a non-zero nonlinear parameter f NL
Graphical calculus for Gaussian pure states
International Nuclear Information System (INIS)
Menicucci, Nicolas C.; Flammia, Steven T.; Loock, Peter van
2011-01-01
We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.
Variational Gaussian approximation for Poisson data
Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen
2018-02-01
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.
Mode entanglement of Gaussian fermionic states
Spee, C.; Schwaiger, K.; Giedke, G.; Kraus, B.
2018-04-01
We investigate the entanglement of n -mode n -partite Gaussian fermionic states (GFS). First, we identify a reasonable definition of separability for GFS and derive a standard form for mixed states, to which any state can be mapped via Gaussian local unitaries (GLU). As the standard form is unique, two GFS are equivalent under GLU if and only if their standard forms coincide. Then, we investigate the important class of local operations assisted by classical communication (LOCC). These are central in entanglement theory as they allow one to partially order the entanglement contained in states. We show, however, that there are no nontrivial Gaussian LOCC (GLOCC) among pure n -partite (fully entangled) states. That is, any such GLOCC transformation can also be accomplished via GLU. To obtain further insight into the entanglement properties of such GFS, we investigate the richer class of Gaussian stochastic local operations assisted by classical communication (SLOCC). We characterize Gaussian SLOCC classes of pure n -mode n -partite states and derive them explicitly for few-mode states. Furthermore, we consider certain fermionic LOCC and show how to identify the maximally entangled set of pure n -mode n -partite GFS, i.e., the minimal set of states having the property that any other state can be obtained from one state inside this set via fermionic LOCC. We generalize these findings also to the pure m -mode n -partite (for m >n ) case.
Non-Gaussianity in island cosmology
International Nuclear Information System (INIS)
Piao Yunsong
2009-01-01
In this paper we fully calculate the non-Gaussianity of primordial curvature perturbation of the island universe by using the second order perturbation equation. We find that for the spectral index n s ≅0.96, which is favored by current observations, the non-Gaussianity level f NL seen in an island will generally lie between 30 and 60, which may be tested by the coming observations. In the landscape, the island universe is one of anthropically acceptable cosmological histories. Thus the results obtained in some sense mean the coming observations, especially the measurement of non-Gaussianity, will be significant to clarify how our position in the landscape is populated.
Entanglement negativity bounds for fermionic Gaussian states
Eisert, Jens; Eisler, Viktor; Zimborás, Zoltán
2018-04-01
The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for noninteracting bosonic systems, one can compute the negativity efficiently in the number of modes. However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian. To provide a remedy for this state of affairs, in this work, we introduce efficiently computable and rigorous upper and lower bounds to the negativity, making use of techniques of semidefinite programming, building upon the Lagrangian formulation of fermionic linear optics, and exploiting suitable products of Gaussian operators. We discuss examples in quantum many-body theory and hint at applications in the study of topological properties at finite temperature.
The Gaussian streaming model and convolution Lagrangian effective field theory
Energy Technology Data Exchange (ETDEWEB)
Vlah, Zvonimir [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94306 (United States); Castorina, Emanuele; White, Martin, E-mail: zvlah@stanford.edu, E-mail: ecastorina@berkeley.edu, E-mail: mwhite@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States)
2016-12-01
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.
DEFF Research Database (Denmark)
Turcot, Valérie; Lu, Yingchang; Highland, Heather M
2018-01-01
In the published version of this paper, the name of author Emanuele Di Angelantonio was misspelled. This error has now been corrected in the HTML and PDF versions of the article.......In the published version of this paper, the name of author Emanuele Di Angelantonio was misspelled. This error has now been corrected in the HTML and PDF versions of the article....
DEFF Research Database (Denmark)
Grundle, D S; Löscher, C R; Krahmann, G
2018-01-01
A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.......A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper....
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-12-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
International Nuclear Information System (INIS)
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-01-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
Energy Technology Data Exchange (ETDEWEB)
Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)
2012-12-15
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Construction of Capacity Achieving Lattice Gaussian Codes
Alghamdi, Wael
2016-04-01
We propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3].
Gaussian processes and constructive scalar field theory
International Nuclear Information System (INIS)
Benfatto, G.; Nicolo, F.
1981-01-01
The last years have seen a very deep progress of constructive euclidean field theory, with many implications in the area of the random fields theory. The authors discuss an approach to super-renormalizable scalar field theories, which puts in particular evidence the connections with the theory of the Gaussian processes associated to the elliptic operators. The paper consists of two parts. Part I treats some problems in the theory of Gaussian processes which arise in the approach to the PHI 3 4 theory. Part II is devoted to the discussion of the ultraviolet stability in the PHI 3 4 theory. (Auth.)
Integration of non-Gaussian fields
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Mohr, Gunnar; Hoffmeyer, Pernille
1996-01-01
The limitations of the validity of the central limit theorem argument as applied to definite integrals of non-Gaussian random fields are empirically explored by way of examples. The purpose is to investigate in specific cases whether the asymptotic convergence to the Gaussian distribution is fast....... and Randrup-Thomsen, S. Reliability of silo ring under lognormal stochastic pressure using stochastic interpolation. Proc. IUTAM Symp., Probabilistic Structural Mechanics: Advances in Structural Reliability Methods, San Antonio, TX, USA, June 1993 (eds.: P. D. Spanos & Y.-T. Wu) pp. 134-162. Springer, Berlin...
Quantum information theory with Gaussian systems
Energy Technology Data Exchange (ETDEWEB)
Krueger, O.
2006-04-06
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Quantum information theory with Gaussian systems
International Nuclear Information System (INIS)
Krueger, O.
2006-01-01
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Model selection for Gaussian kernel PCA denoising
DEFF Research Database (Denmark)
Jørgensen, Kasper Winther; Hansen, Lars Kai
2012-01-01
We propose kernel Parallel Analysis (kPA) for automatic kernel scale and model order selection in Gaussian kernel PCA. Parallel Analysis [1] is based on a permutation test for covariance and has previously been applied for model order selection in linear PCA, we here augment the procedure to also...... tune the Gaussian kernel scale of radial basis function based kernel PCA.We evaluate kPA for denoising of simulated data and the US Postal data set of handwritten digits. We find that kPA outperforms other heuristics to choose the model order and kernel scale in terms of signal-to-noise ratio (SNR...
International Nuclear Information System (INIS)
Ji, Se-Wan; Nha, Hyunchul; Kim, M S
2015-01-01
It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous manner is relevant to study it under certain circumstances and here we address quantum steerability of Gaussian states to this aim. In particular, we attempt to reformulate the criterion for Gaussian steering in terms of local and global purities and show that it is sufficient and necessary for the case of steering a 1-mode system by an N-mode system. It subsequently enables us to reinforce a strong monogamy relation under which only one party can steer a local system of 1-mode. Moreover, we show that only a negative partial-transpose state can manifest quantum steerability by Gaussian measurements in relation to the Peres conjecture. We also discuss our formulation for the case of distributing a two-mode squeezed state via one-way quantum channels making dissipation and amplification effects, respectively. Finally, we extend our approach to include non-Gaussian measurements, more precisely, all orders of higher-order squeezing measurements, and find that this broad set of non-Gaussian measurements is not useful to demonstrate steering for Gaussian states beyond Gaussian measurements. (paper)
International Nuclear Information System (INIS)
Guo-Ping, Ru; Rong, Yu; Yu-Long, Jiang; Gang, Ruan
2010-01-01
This paper investigates the thermal activation behaviour of current in an inhomogeneous Schottky diode with a Gaussian distribution of barrier height by numerical simulation. The analytical Gaussian distribution model predicted that the I-V-T curves may intersect with the possibility of the negative thermal activation of current, but may be contradictory to the thermionic emission mechanism in a Schottky diode. It shows that the cause of the unphysical phenomenon is related to the incorrect calculation of current across very low barriers. It proposes that junction voltage V j , excluding the voltage drop across series resistance from the external bias, is a crucial parameter for correct calculation of the current across very low barriers. For correctly employing the thermionic emission model, V j needs to be smaller than the barrier height ø. With proper scheme of series resistance connection where the condition of V j > ø is guaranteed, I-V-T curves of an inhomogeneous Schottky diode with a Gaussian distribution of barrier height have been simulated, which demonstrate normal thermal activation. Although the calculated results exclude the intersecting possibility of I-V-T curves with an assumption of temperature-independent series resistance, it shows that the intersecting is possible when the series resistance has a positive temperature coefficient. Finally, the comparison of our numerical and analytical results indicates that the analytical Gaussian distribution model is valid and accurate in analysing I-V-T curves only for small barrier height inhomogeneity. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Lifting primordial non-Gaussianity above the noise
International Nuclear Information System (INIS)
Welling, Yvette; Woude, Drian van der; Pajer, Enrico
2016-01-01
Primordial non-Gaussianity (PNG) in Large Scale Structures is obfuscated by the many additional sources of non-linearity. Within the Effective Field Theory approach to Standard Perturbation Theory, we show that matter non-linearities in the bispectrum can be modeled sufficiently well to strengthen current bounds with near future surveys, such as Euclid. We find that the EFT corrections are crucial to this improvement in sensitivity. Yet, our understanding of non-linearities is still insufficient to reach important theoretical benchmarks for equilateral PNG, while, for local PNG, our forecast is more optimistic. We consistently account for the theoretical error intrinsic to the perturbative approach and discuss the details of its implementation in Fisher forecasts.
Gaussian-2 theory using reduced Moller--Plesset orders
International Nuclear Information System (INIS)
Curtiss, L.A.; Raghavachari, K.; Pople, J.A.
1993-01-01
Two variations of Gaussian-2 (G2) theory are presented. In the first, referred to as G2 (MP2) theory, the basis-set-extension energy corrections are obtained at the 2nd order Moller--Plesset (MP2) level and in the second, referred to as G2(MP3) theory, they are obtained at the MP3 level. The methods are tested out on the set of 125 systems used for validation of G2 theory [J. Chem Phys. 94, 7221 (1991)]. The average absolute deviation of the G2(MP2) and G2(MP3) theories from experiment are 1.58 and 1.52 kcal/mol, respectively, compared to 1.21 kcal/mol for G2 theory. The new methods provide significant savings in computational time and disk storage
The correct "ball bearings" data.
Caroni, C
2002-12-01
The famous data on fatigue failure times of ball bearings have been quoted incorrectly from Lieblein and Zelen's original paper. The correct data include censored values, as well as non-fatigue failures that must be handled appropriately. They could be described by a mixture of Weibull distributions, corresponding to different modes of failure.
How Gaussian can our Universe be?
Cabass, G.; Pajer, E.; Schmidt, F.
2017-01-01
Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of kl2/ks2, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × (ns-1).
Gaussian vector fields on triangulated surfaces
DEFF Research Database (Denmark)
Ipsen, John H
2016-01-01
proven to be very useful to resolve the complex interplay between in-plane ordering of membranes and membrane conformations. In the present work we have developed a procedure for realistic representations of Gaussian models with in-plane vector degrees of freedoms on a triangulated surface. The method...
The Wehrl entropy has Gaussian optimizers
DEFF Research Database (Denmark)
De Palma, Giacomo
2018-01-01
We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel...
How Gaussian can our Universe be?
Energy Technology Data Exchange (ETDEWEB)
Cabass, G. [Physics Department and INFN, Università di Roma ' ' La Sapienza' ' , P.le Aldo Moro 2, 00185, Rome (Italy); Pajer, E. [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); Schmidt, F., E-mail: giovanni.cabass@roma1.infn.it, E-mail: e.pajer@uu.nl, E-mail: fabians@mpa-garching.mpg.de [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)
2017-01-01
Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of k {sub ℓ}{sup 2}/ k {sub s} {sup 2}, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × ( n {sub s}−1).
Gaussian shaping filter for nuclear spectrometry
International Nuclear Information System (INIS)
Menezes, A.S.C. de.
1980-01-01
A theorical study of a gaussian shaping filter, using Pade approximation, for using in gamma spectroscopy is presented. This approximation has proved superior to the classical cascade RC integrators approximation in therms of signal-to-noise ratio and pulse simmetry. An experimental filter was designed, simulated in computer, constructed, and tested in the laboratory. (author) [pt
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian U...
Chimera states in Gaussian coupled map lattices
Li, Xiao-Wen; Bi, Ran; Sun, Yue-Xiang; Zhang, Shuo; Song, Qian-Qian
2018-04-01
We study chimera states in one-dimensional and two-dimensional Gaussian coupled map lattices through simulations and experiments. Similar to the case of global coupling oscillators, individual lattices can be regarded as being controlled by a common mean field. A space-dependent order parameter is derived from a self-consistency condition in order to represent the collective state.
Gaussian curvature on hyperelliptic Riemann surfaces
Indian Academy of Sciences (India)
Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 2, May 2014, pp. 155–167. c Indian Academy of Sciences. Gaussian curvature on hyperelliptic Riemann surfaces. ABEL CASTORENA. Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México,. Campus Morelia) Apdo. Postal 61-3 Xangari, C.P. 58089 Morelia,.
Additivity properties of a Gaussian channel
International Nuclear Information System (INIS)
Giovannetti, Vittorio; Lloyd, Seth
2004-01-01
The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Renyi entropies at the output of a channel. The conjecture is proven true for all Renyi entropies of integer order greater than two in a class of Gaussian bosonic channel where the input signal is randomly displaced or where it is coupled linearly to an external environment
Improving the gaussian effective potential: quantum mechanics
International Nuclear Information System (INIS)
Eboli, O.J.P.; Thomaz, M.T.; Lemos, N.A.
1990-08-01
In order to gain intuition for variational problems in field theory, we analyze variationally the quantum-mechanical anharmonic oscillator [(V(x)sup(k) - sub(2) x sup(2) + sup(λ) - sub(4) λ sup(4)]. Special attention is paid to improvements to the Gaussian effective potential. (author)
Open problems in Gaussian fluid queueing theory
Dȩbicki, K.; Mandjes, M.
2011-01-01
We present three challenging open problems that originate from the analysis of the asymptotic behavior of Gaussian fluid queueing models. In particular, we address the problem of characterizing the correlation structure of the stationary buffer content process, the speed of convergence to
Oracle Wiener filtering of a Gaussian signal
Babenko, A.; Belitser, E.
2011-01-01
We study the problem of filtering a Gaussian process whose trajectories, in some sense, have an unknown smoothness ß0 from the white noise of small intensity e. If we knew the parameter ß0, we would use the Wiener filter which has the meaning of oracle. Our goal is now to mimic the oracle, i.e.,
Oracle Wiener filtering of a Gaussian signal
Babenko, A.; Belitser, E.N.
2011-01-01
We study the problem of filtering a Gaussian process whose trajectories, in some sense, have an unknown smoothness β0 from the white noise of small intensity . If we knew the parameter β0, we would use the Wiener filter which has the meaning of oracle. Our goal is now to mimic the oracle, i.e.,
Perfusion Quantification Using Gaussian Process Deconvolution
DEFF Research Database (Denmark)
Andersen, Irene Klærke; Have, Anna Szynkowiak; Rasmussen, Carl Edward
2002-01-01
The quantification of perfusion using dynamic susceptibility contrast MRI (DSC-MRI) requires deconvolution to obtain the residual impulse response function (IRF). In this work, a method using the Gaussian process for deconvolution (GPD) is proposed. The fact that the IRF is smooth is incorporated...
Sinha, B K; Pal, Manisha; Das, P
2014-01-01
The book dwells mainly on the optimality aspects of mixture designs. As mixture models are a special case of regression models, a general discussion on regression designs has been presented, which includes topics like continuous designs, de la Garza phenomenon, Loewner order domination, Equivalence theorems for different optimality criteria and standard optimality results for single variable polynomial regression and multivariate linear and quadratic regression models. This is followed by a review of the available literature on estimation of parameters in mixture models. Based on recent research findings, the volume also introduces optimal mixture designs for estimation of optimum mixing proportions in different mixture models, which include Scheffé’s quadratic model, Darroch-Waller model, log- contrast model, mixture-amount models, random coefficient models and multi-response model. Robust mixture designs and mixture designs in blocks have been also reviewed. Moreover, some applications of mixture desig...
Sufficient condition for a quantum state to be genuinely quantum non-Gaussian
Happ, L.; Efremov, M. A.; Nha, H.; Schleich, W. P.
2018-02-01
We show that the expectation value of the operator \\hat{{ \\mathcal O }}\\equiv \\exp (-c{\\hat{x}}2)+\\exp (-c{\\hat{p}}2) defined by the position and momentum operators \\hat{x} and \\hat{p} with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states that cannot be represented as a mixture of Gaussian states. Our condition can be readily tested employing a highly efficient homodyne detection which unlike quantum-state tomography requires the measurements of only two orthogonal quadratures. We demonstrate that our method is even able to detect quantum non-Gaussian states with positive–definite Wigner functions. This situation cannot be addressed in terms of the negativity of the phase-space distribution. Moreover, we demonstrate that our condition can characterize quantum non-Gaussianity for the class of superposition states consisting of a vacuum and integer multiples of four photons under more than 50 % signal attenuation.
Nonlinear Bayesian Estimation of BOLD Signal under Non-Gaussian Noise
Directory of Open Access Journals (Sweden)
Ali Fahim Khan
2015-01-01
Full Text Available Modeling the blood oxygenation level dependent (BOLD signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF.
Cosmological information in Gaussianized weak lensing signals
Joachimi, B.; Taylor, A. N.; Kiessling, A.
2011-11-01
Gaussianizing the one-point distribution of the weak gravitational lensing convergence has recently been shown to increase the signal-to-noise ratio contained in two-point statistics. We investigate the information on cosmology that can be extracted from the transformed convergence fields. Employing Box-Cox transformations to determine optimal transformations to Gaussianity, we develop analytical models for the transformed power spectrum, including effects of noise and smoothing. We find that optimized Box-Cox transformations perform substantially better than an offset logarithmic transformation in Gaussianizing the convergence, but both yield very similar results for the signal-to-noise ratio. None of the transformations is capable of eliminating correlations of the power spectra between different angular frequencies, which we demonstrate to have a significant impact on the errors in cosmology. Analytic models of the Gaussianized power spectrum yield good fits to the simulations and produce unbiased parameter estimates in the majority of cases, where the exceptions can be traced back to the limitations in modelling the higher order correlations of the original convergence. In the ideal case, without galaxy shape noise, we find an increase in the cumulative signal-to-noise ratio by a factor of 2.6 for angular frequencies up to ℓ= 1500, and a decrease in the area of the confidence region in the Ωm-σ8 plane, measured in terms of q-values, by a factor of 4.4 for the best performing transformation. When adding a realistic level of shape noise, all transformations perform poorly with little decorrelation of angular frequencies, a maximum increase in signal-to-noise ratio of 34 per cent, and even slightly degraded errors on cosmological parameters. We argue that to find Gaussianizing transformations of practical use, it will be necessary to go beyond transformations of the one-point distribution of the convergence, extend the analysis deeper into the non
Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach
Directory of Open Access Journals (Sweden)
Javier Amezcua
2014-09-01
Full Text Available The analysis step of the (ensemble Kalman filter is optimal when (1 the distribution of the background is Gaussian, (2 state variables and observations are related via a linear operator, and (3 the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state-variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1–(3 are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.
International Nuclear Information System (INIS)
Valentine, J.D.; Rana, A.E.
1996-01-01
The effect of approximating a continuous Gaussian distribution with histogrammed data are studied. The expressions for theoretical uncertainties in centroid and full-width at half maximum (FWHM), as determined by calculation of moments, are derived using the error propagation method for a histogrammed Gaussian distribution. The results are compared with the corresponding pseudo-experimental uncertainties for computer-generated histogrammed Gaussian peaks to demonstrate the effect of binning the data. It is shown that increasing the number of bins in the histogram improves the continuous distribution approximation. For example, a FWHM ≥ 9 and FWHM ≥ 12 bins are needed to reduce the pseudo-experimental standard deviation of FWHM to within ≥5% and ≥1%, respectively, of the theoretical value for a peak containing 10,000 counts. In addition, the uncertainties in the centroid and FWHM as a function of peak area are studied. Finally, Sheppard's correction is applied to partially correct for the binning effect
Learning non-Gaussian Time Series using the Box-Cox Gaussian Process
Rios, Gonzalo; Tobar, Felipe
2018-01-01
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model general non-Gaussian data with complex correlation structure, GPs can be paired with an expressive covariance kernel and then fed into a nonlinear transformation (or warping). However, overparametrising the kernel and the warping is known to, respectively, hin...
MCEM algorithm for the log-Gaussian Cox process
Delmas, Celine; Dubois-Peyrard, Nathalie; Sabbadin, Regis
2014-01-01
Log-Gaussian Cox processes are an important class of models for aggregated point patterns. They have been largely used in spatial epidemiology (Diggle et al., 2005), in agronomy (Bourgeois et al., 2012), in forestry (Moller et al.), in ecology (sightings of wild animals) or in environmental sciences (radioactivity counts). A log-Gaussian Cox process is a Poisson process with a stochastic intensity depending on a Gaussian random eld. We consider the case where this Gaussian random eld is ...
Impact of Improper Gaussian Signaling on the Achievable Rate of Overlay Cognitive Radio
Amin, Osama
2017-05-12
Improper Gaussian signaling (IGS) has been recently shown to provide performance improvements in underlay cognitive radio systems as opposed to the conventional proper Gaussian signaling (PGS) scheme. For the first time, this paper implements IGS scheme in overlay cognitive radio system, where the secondary transmitter broadcasts a mixture of two different signals. The first signal is selected from the PGS scheme to support the primary message transmission. On the other hand, the second signal is chosen to be from the IGS scheme in order to reduce the interference effect on the primary receiver. We then optimally design the overlay cognitive radio that employs IGS to maximize the secondary link achievable rate while satisfying the minimum rate requirement of the primary network. In particular, we derive closed form expressions for the circularity coefficient used in the IGS scheme and the power distribution parameters. Simulation results are provided to support our theoretical derivations.
Impact of Improper Gaussian Signaling on the Achievable Rate of Overlay Cognitive Radio
Amin, Osama; Abediseid, Walid; Alouini, Mohamed-Slim
2017-01-01
Improper Gaussian signaling (IGS) has been recently shown to provide performance improvements in underlay cognitive radio systems as opposed to the conventional proper Gaussian signaling (PGS) scheme. For the first time, this paper implements IGS scheme in overlay cognitive radio system, where the secondary transmitter broadcasts a mixture of two different signals. The first signal is selected from the PGS scheme to support the primary message transmission. On the other hand, the second signal is chosen to be from the IGS scheme in order to reduce the interference effect on the primary receiver. We then optimally design the overlay cognitive radio that employs IGS to maximize the secondary link achievable rate while satisfying the minimum rate requirement of the primary network. In particular, we derive closed form expressions for the circularity coefficient used in the IGS scheme and the power distribution parameters. Simulation results are provided to support our theoretical derivations.
Large deviations for Gaussian processes in Hoelder norm
International Nuclear Information System (INIS)
Fatalov, V R
2003-01-01
Some results are proved on the exact asymptotic representation of large deviation probabilities for Gaussian processes in the Hoeder norm. The following classes of processes are considered: the Wiener process, the Brownian bridge, fractional Brownian motion, and stationary Gaussian processes with power-law covariance function. The investigation uses the method of double sums for Gaussian fields
Phase space structure of generalized Gaussian cat states
International Nuclear Information System (INIS)
Nicacio, Fernando; Maia, Raphael N.P.; Toscano, Fabricio; Vallejos, Raul O.
2010-01-01
We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states. The structure of the interference term of the Wigner function is always hyperbolic, surviving the action of a thermal reservoir. We also consider certain superpositions of mixed Gaussian states. An application to semiclassical dynamics is discussed.
Linking network usage patterns to traffic Gaussianity fit
de Oliveira Schmidt, R.; Sadre, R.; Melnikov, Nikolay; Schönwälder, Jürgen; Pras, Aiko
Gaussian traffic models are widely used in the domain of network traffic modeling. The central assumption is that traffic aggregates are Gaussian distributed. Due to its importance, the Gaussian character of network traffic has been extensively assessed by researchers in the past years. In 2001,
Amplitude calculations for 3D Gaussian beam migration using complex-valued traveltimes
International Nuclear Information System (INIS)
Bleistein, Norman; Gray, Samuel H
2010-01-01
Gaussian beams are often used to represent Green's functions in three-dimensional Kirchhoff-type true-amplitude migrations because such migrations made using Gaussian beams yield superior images to similar migrations using classical ray-theoretic Green's functions. Typically, the integrand of a migration formula consists of two Green's functions—each describing propagation to the image point—one from the source and the other from the receiver position. The use of Gaussian beams to represent each of these Green's functions in 3D introduces two additional double integrals when compared to a Kirchhoff migration using ray-theoretic Green's functions, thereby adding a significant computational burden. Hill (2001 Geophysics 66 1240–50) proposed a method for reducing those four integrals to two, compromising slightly on the full potential quality of the Gaussian beam representations for the sake of more efficient computation. That approach requires a two-dimensional steepest descent analysis for the asymptotic evaluation of a double integral. The method requires evaluation of the complex traveltimes of the Gaussian beams as well as the amplitudes of the integrands at the determined saddle points. In addition, it is necessary to evaluate the determinant of a certain (Hessian) matrix of second derivatives. Hill (2001 Geophysics 66 1240–50) did not report on this last part; thus, his proposed migration formula is kinematically correct but lacks correct amplitude behavior. In this paper, we derive a formula for that Hessian matrix in terms of dynamic ray tracing quantities. We also show in a simple example how the integral that we analyze here arises in a true amplitude migration formula
On Alternate Relaying with Improper Gaussian Signaling
Gaafar, Mohamed
2016-06-06
In this letter, we investigate the potential benefits of adopting improper Gaussian signaling (IGS) in a two-hop alternate relaying (AR) system. Given the known benefits of using IGS in interference-limited networks, we propose to use IGS to relieve the inter-relay interference (IRI) impact on the AR system assuming no channel state information is available at the source. In this regard, we assume that the two relays use IGS and the source uses proper Gaussian signaling (PGS). Then, we optimize the degree of impropriety of the relays signal, measured by the circularity coefficient, to maximize the total achievable rate. Simulation results show that using IGS yields a significant performance improvement over PGS, especially when the first hop is a bottleneck due to weak source-relay channel gains and/or strong IRI.
On Alternate Relaying with Improper Gaussian Signaling
Gaafar, Mohamed; Amin, Osama; Ikhlef, Aissa; Chaaban, Anas; Alouini, Mohamed-Slim
2016-01-01
In this letter, we investigate the potential benefits of adopting improper Gaussian signaling (IGS) in a two-hop alternate relaying (AR) system. Given the known benefits of using IGS in interference-limited networks, we propose to use IGS to relieve the inter-relay interference (IRI) impact on the AR system assuming no channel state information is available at the source. In this regard, we assume that the two relays use IGS and the source uses proper Gaussian signaling (PGS). Then, we optimize the degree of impropriety of the relays signal, measured by the circularity coefficient, to maximize the total achievable rate. Simulation results show that using IGS yields a significant performance improvement over PGS, especially when the first hop is a bottleneck due to weak source-relay channel gains and/or strong IRI.
Fractional Diffusion in Gaussian Noisy Environment
Directory of Open Access Journals (Sweden)
Guannan Hu
2015-03-01
Full Text Available We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: \\(D_t^{(\\alpha} u(t, x=\\textit{B}u+u\\cdot \\dot W^H\\, where \\(D_t^{(\\alpha}\\ is the Caputo fractional derivative of order \\(\\alpha\\in (0,1\\ with respect to the time variable \\(t\\, \\(\\textit{B}\\ is a second order elliptic operator with respect to the space variable \\(x\\in\\mathbb{R}^d\\ and \\(\\dot W^H\\ a time homogeneous fractional Gaussian noise of Hurst parameter \\(H=(H_1, \\cdots, H_d\\. We obtain conditions satisfied by \\(\\alpha\\ and \\(H\\, so that the square integrable solution \\(u\\ exists uniquely.
Extended Linear Models with Gaussian Priors
DEFF Research Database (Denmark)
Quinonero, Joaquin
2002-01-01
In extended linear models the input space is projected onto a feature space by means of an arbitrary non-linear transformation. A linear model is then applied to the feature space to construct the model output. The dimension of the feature space can be very large, or even infinite, giving the model...... a very big flexibility. Support Vector Machines (SVM's) and Gaussian processes are two examples of such models. In this technical report I present a model in which the dimension of the feature space remains finite, and where a Bayesian approach is used to train the model with Gaussian priors...... on the parameters. The Relevance Vector Machine, introduced by Tipping, is a particular case of such a model. I give the detailed derivations of the expectation-maximisation (EM) algorithm used in the training. These derivations are not found in the literature, and might be helpful for newcomers....
Interweave Cognitive Radio with Improper Gaussian Signaling
Hedhly, Wafa
2018-01-15
Improper Gaussian signaling (IGS) has proven its ability in improving the performance of underlay and overlay cognitive radio paradigms. In this paper, the interweave cognitive radio paradigm is studied when the cognitive user employs IGS. The instantaneous achievable rate performance of both the primary and secondary users are analyzed for specific secondary user sensing and detection capabilities. Next, the IGS scheme is optimized to maximize the achievable rate secondary user while satisfying a target minimum rate requirement for the primary user. Proper Gaussian signaling (PGS) scheme design is also derived to be used as benchmark of the IGS scheme design. Finally, different numerical results are introduced to show the gain reaped from adopting IGS over PGS under different system parameters. The main advantage of employing IGS is observed at low sensing and detection capabilities of the SU, lower PU direct link and higher SU interference on the PU side.
Image reconstruction under non-Gaussian noise
DEFF Research Database (Denmark)
Sciacchitano, Federica
During acquisition and transmission, images are often blurred and corrupted by noise. One of the fundamental tasks of image processing is to reconstruct the clean image from a degraded version. The process of recovering the original image from the data is an example of inverse problem. Due...... to the ill-posedness of the problem, the simple inversion of the degradation model does not give any good reconstructions. Therefore, to deal with the ill-posedness it is necessary to use some prior information on the solution or the model and the Bayesian approach. Additive Gaussian noise has been......D thesis intends to solve some of the many open questions for image restoration under non-Gaussian noise. The two main kinds of noise studied in this PhD project are the impulse noise and the Cauchy noise. Impulse noise is due to for instance the malfunctioning pixel elements in the camera sensors, errors...
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.
Log Gaussian Cox processes on the sphere
DEFF Research Database (Denmark)
Pacheco, Francisco Andrés Cuevas; Møller, Jesper
We define and study the existence of log Gaussian Cox processes (LGCPs) for the description of inhomogeneous and aggregated/clustered point patterns on the d-dimensional sphere, with d = 2 of primary interest. Useful theoretical properties of LGCPs are studied and applied for the description of sky...... positions of galaxies, in comparison with previous analysis using a Thomas process. We focus on simple estimation procedures and model checking based on functional summary statistics and the global envelope test....
Recognition of Images Degraded by Gaussian Blur
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Farokhi, Sajad; Höschl, Cyril; Suk, Tomáš; Zitová, Barbara; Pedone, M.
2016-01-01
Roč. 25, č. 2 (2016), s. 790-806 ISSN 1057-7149 R&D Projects: GA ČR(CZ) GA15-16928S Institutional support: RVO:67985556 Keywords : Blurred image * object recognition * blur invariant comparison * Gaussian blur * projection operators * image moments * moment invariants Subject RIV: JD - Computer Applications, Robotics Impact factor: 4.828, year: 2016 http://library.utia.cas.cz/separaty/2016/ZOI/flusser-0454335.pdf
Adaptive multiple importance sampling for Gaussian processes
Czech Academy of Sciences Publication Activity Database
Xiong, X.; Šmídl, Václav; Filippone, M.
2017-01-01
Roč. 87, č. 8 (2017), s. 1644-1665 ISSN 0094-9655 R&D Projects: GA MŠk(CZ) 7F14287 Institutional support: RVO:67985556 Keywords : Gaussian Process * Bayesian estimation * Adaptive importance sampling Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability Impact factor: 0.757, year: 2016 http://library.utia.cas.cz/separaty/2017/AS/smidl-0469804.pdf
International Nuclear Information System (INIS)
Bachoc, F.
2013-01-01
The parametric estimation of the covariance function of a Gaussian process is studied, in the framework of the Kriging model. Maximum Likelihood and Cross Validation estimators are considered. The correctly specified case, in which the covariance function of the Gaussian process does belong to the parametric set used for estimation, is first studied in an increasing-domain asymptotic framework. The sampling considered is a randomly perturbed multidimensional regular grid. Consistency and asymptotic normality are proved for the two estimators. It is then put into evidence that strong perturbations of the regular grid are always beneficial to Maximum Likelihood estimation. The incorrectly specified case, in which the covariance function of the Gaussian process does not belong to the parametric set used for estimation, is then studied. It is shown that Cross Validation is more robust than Maximum Likelihood in this case. Finally, two applications of the Kriging model with Gaussian processes are carried out on industrial data. For a validation problem of the friction model of the thermal-hydraulic code FLICA 4, where experimental results are available, it is shown that Gaussian process modeling of the FLICA 4 code model error enables to considerably improve its predictions. Finally, for a meta modeling problem of the GERMINAL thermal-mechanical code, the interest of the Kriging model with Gaussian processes, compared to neural network methods, is shown. (author) [fr
Rowlinson, J S; Baldwin, J E; Buckingham, A D; Danishefsky, S
2013-01-01
Liquids and Liquid Mixtures, Third Edition explores the equilibrium properties of liquids and liquid mixtures and relates them to the properties of the constituent molecules using the methods of statistical thermodynamics. Topics covered include the critical state, fluid mixtures at high pressures, and the statistical thermodynamics of fluids and mixtures. This book consists of eight chapters and begins with an overview of the liquid state and the thermodynamic properties of liquids and liquid mixtures, including vapor pressure and heat capacities. The discussion then turns to the thermodynami
DEFF Research Database (Denmark)
Stokholm, Jakob; Blaser, Martin J.; Thorsen, Jonathan
2018-01-01
The originally published version of this Article contained an incorrect version of Figure 3 that was introduced following peer review and inadvertently not corrected during the production process. Both versions contain the same set of abundance data, but the incorrect version has the children...
DEFF Research Database (Denmark)
Flachsbart, Friederike; Dose, Janina; Gentschew, Liljana
2018-01-01
The original version of this Article contained an error in the spelling of the author Robert Häsler, which was incorrectly given as Robert Häesler. This has now been corrected in both the PDF and HTML versions of the Article....
DEFF Research Database (Denmark)
Roehle, Robert; Wieske, Viktoria; Schuetz, Georg M
2018-01-01
The original version of this article, published on 19 March 2018, unfortunately contained a mistake. The following correction has therefore been made in the original: The names of the authors Philipp A. Kaufmann, Ronny Ralf Buechel and Bernhard A. Herzog were presented incorrectly....
Neutron inverse kinetics via Gaussian Processes
International Nuclear Information System (INIS)
Picca, Paolo; Furfaro, Roberto
2012-01-01
Highlights: ► A novel technique for the interpretation of experiments in ADS is presented. ► The technique is based on Bayesian regression, implemented via Gaussian Processes. ► GPs overcome the limits of classical methods, based on PK approximation. ► Results compares GPs and ANN performance, underlining similarities and differences. - Abstract: The paper introduces the application of Gaussian Processes (GPs) to determine the subcriticality level in accelerator-driven systems (ADSs) through the interpretation of pulsed experiment data. ADSs have peculiar kinetic properties due to their special core design. For this reason, classical – inversion techniques based on point kinetic (PK) generally fail to generate an accurate estimate of reactor subcriticality. Similarly to Artificial Neural Networks (ANNs), Gaussian Processes can be successfully trained to learn the underlying inverse neutron kinetic model and, as such, they are not limited to the model choice. Importantly, GPs are strongly rooted into the Bayes’ theorem which makes them a powerful tool for statistical inference. Here, GPs have been designed and trained on a set of kinetics models (e.g. point kinetics and multi-point kinetics) for homogeneous and heterogeneous settings. The results presented in the paper show that GPs are very efficient and accurate in predicting the reactivity for ADS-like systems. The variance computed via GPs may provide an indication on how to generate additional data as function of the desired accuracy.
Resonant non-Gaussianity with equilateral properties
International Nuclear Information System (INIS)
Gwyn, Rhiannon; Rummel, Markus
2012-11-01
We discuss the effect of superimposing multiple sources of resonant non-Gaussianity, which arise for instance in models of axion inflation. The resulting sum of oscillating shape contributions can be used to ''Fourier synthesize'' different non-oscillating shapes in the bispectrum. As an example we reproduce an approximately equilateral shape from the superposition of O(10) oscillatory contributions with resonant shape. This implies a possible degeneracy between the equilateral-type non-Gaussianity typical of models with non-canonical kinetic terms, such as DBI inflation, and an equilateral-type shape arising from a superposition of resonant-type contributions in theories with canonical kinetic terms. The absence of oscillations in the 2-point function together with the structure of the resonant N-point functions, imply that detection of equilateral non-Gaussianity at a level greater than the PLANCK sensitivity of f NL ∝O(5) will rule out a resonant origin. We comment on the questions arising from possible embeddings of this idea in a string theory setting.
Unitarily localizable entanglement of Gaussian states
International Nuclear Information System (INIS)
Serafini, Alessio; Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
We consider generic (mxn)-mode bipartitions of continuous-variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as (m+n)-mode Gaussian states invariant under local mode permutations on the m-mode and n-mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of m+n-2 uncorrelated single-mode states. The entanglement between the m-mode and the n-mode blocks can then be completely concentrated on a single pair of modes by means of local unitary operations alone. This result allows us to prove that the PPT (positivity of the partial transpose) condition is necessary and sufficient for the separability of (m+n)-mode bisymmetric Gaussian states. We determine exactly their negativity and identify a subset of bisymmetric states whose multimode entanglement of formation can be computed analytically. We consider explicit examples of pure and mixed bisymmetric states and study their entanglement scaling with the number of modes
Gaussian Hypothesis Testing and Quantum Illumination.
Wilde, Mark M; Tomamichel, Marco; Lloyd, Seth; Berta, Mario
2017-09-22
Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of the minimal type-II error probability in a quantum hypothesis test of two Gaussian states given a fixed constraint on the type-I error probability. This formula is a direct function of the mean vectors and covariance matrices of the quantum Gaussian states in question. We give an application to quantum illumination, which is the task of determining whether there is a low-reflectivity object embedded in a target region with a bright thermal-noise bath. For the asymmetric-error setting, we find that a quantum illumination transmitter can achieve an error probability exponent stronger than a coherent-state transmitter of the same mean photon number, and furthermore, that it requires far fewer trials to do so. This occurs when the background thermal noise is either low or bright, which means that a quantum advantage is even easier to witness than in the symmetric-error setting because it occurs for a larger range of parameters. Going forward from here, we expect our formula to have applications in settings well beyond those considered in this paper, especially to quantum communication tasks involving quantum Gaussian channels.
Resonant non-Gaussianity with equilateral properties
Energy Technology Data Exchange (ETDEWEB)
Gwyn, Rhiannon [Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut), Potsdam (Germany); Rummel, Markus [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-11-15
We discuss the effect of superimposing multiple sources of resonant non-Gaussianity, which arise for instance in models of axion inflation. The resulting sum of oscillating shape contributions can be used to ''Fourier synthesize'' different non-oscillating shapes in the bispectrum. As an example we reproduce an approximately equilateral shape from the superposition of O(10) oscillatory contributions with resonant shape. This implies a possible degeneracy between the equilateral-type non-Gaussianity typical of models with non-canonical kinetic terms, such as DBI inflation, and an equilateral-type shape arising from a superposition of resonant-type contributions in theories with canonical kinetic terms. The absence of oscillations in the 2-point function together with the structure of the resonant N-point functions, imply that detection of equilateral non-Gaussianity at a level greater than the PLANCK sensitivity of f{sub NL} {proportional_to}O(5) will rule out a resonant origin. We comment on the questions arising from possible embeddings of this idea in a string theory setting.
Non-Gaussian conductivity fluctuations in semiconductors
International Nuclear Information System (INIS)
Melkonyan, S.V.
2010-01-01
A theoretical study is presented on the statistical properties of conductivity fluctuations caused by concentration and mobility fluctuations of the current carriers. It is established that mobility fluctuations result from random deviations in the thermal equilibrium distribution of the carriers. It is shown that mobility fluctuations have generation-recombination and shot components which do not satisfy the requirements of the central limit theorem, in contrast to the current carrier's concentration fluctuation and intraband component of the mobility fluctuation. It is shown that in general the mobility fluctuation consist of thermal (or intraband) Gaussian and non-thermal (or generation-recombination, shot, etc.) non-Gaussian components. The analyses of theoretical results and experimental data from literature show that the statistical properties of mobility fluctuation and of 1/f-noise fully coincide. The deviation from Gaussian statistics of the mobility or 1/f fluctuations goes hand in hand with the magnitude of non-thermal noise (generation-recombination, shot, burst, pulse noises, etc.).
Perturbative Gaussianizing transforms for cosmological fields
Hall, Alex; Mead, Alexander
2018-01-01
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.
Accuracy of dynamical-decoupling-based spectroscopy of Gaussian noise
Szańkowski, Piotr; Cywiński, Łukasz
2018-03-01
The fundamental assumption of dynamical-decoupling-based noise spectroscopy is that the coherence decay rate of qubit (or qubits) driven with a sequence of many pulses, is well approximated by the environmental noise spectrum spanned on frequency comb defined by the sequence. Here we investigate the precise conditions under which this commonly used spectroscopic approach is quantitatively correct. To this end we focus on two representative examples of spectral densities: the long-tailed Lorentzian, and finite-ranged Gaussian—both expected to be encountered when using the qubit for nanoscale nuclear resonance imaging. We have found that, in contrast to Lorentz spectrum, for which the corrections to the standard spectroscopic formulas can easily be made negligible, the spectra with finite range are more challenging to reconstruct accurately. For Gaussian line shape of environmental spectral density, direct application of the standard dynamical-decoupling-based spectroscopy leads to erroneous attribution of long-tail behavior to the reconstructed spectrum. Fortunately, artifacts such as this, can be completely avoided with the simple extension to standard reconstruction method.
Enhancement of force patterns classification based on Gaussian distributions.
Ertelt, Thomas; Solomonovs, Ilja; Gronwald, Thomas
2018-01-23
Description of the patterns of ground reaction force is a standard method in areas such as medicine, biomechanics and robotics. The fundamental parameter is the time course of the force, which is classified visually in particular in the field of clinical diagnostics. Here, the knowledge and experience of the diagnostician is relevant for its assessment. For an objective and valid discrimination of the ground reaction force pattern, a generic method, especially in the medical field, is absolutely necessary to describe the qualities of the time-course. The aim of the presented method was to combine the approaches of two existing procedures from the fields of machine learning and the Gauss approximation in order to take advantages of both methods for the classification of ground reaction force patterns. The current limitations of both methods could be eliminated by an overarching method. Twenty-nine male athletes from different sports were examined. Each participant was given the task of performing a one-legged stopping maneuver on a force plate from the maximum possible starting speed. The individual time course of the ground reaction force of each subject was registered and approximated on the basis of eight Gaussian distributions. The descriptive coefficients were then classified using Bayesian regulated neural networks. The different sports served as the distinguishing feature. Although the athletes were all given the same task, all sports referred to a different quality in the time course of ground reaction force. Meanwhile within each sport, the athletes were homogeneous. With an overall prediction (R = 0.938) all subjects/sports were classified correctly with 94.29% accuracy. The combination of the two methods: the mathematical description of the time course of ground reaction forces on the basis of Gaussian distributions and their classification by means of Bayesian regulated neural networks, seems an adequate and promising method to discriminate the
Zhu, Tao; Wang, Anzhong; Kirsten, Klaus; Cleaver, Gerald; Sheng, Qin
2018-02-01
Loop quantum cosmology provides a resolution of the classical big bang singularity in the deep Planck era. The evolution, prior to the usual slow-roll inflation, naturally generates excited states at the onset of the slow-roll inflation. It is expected that these quantum gravitational effects could leave its fingerprints on the primordial perturbation spectrum and non-Gaussianity, and lead to some observational evidences in the cosmic microwave background. While the impact of the quantum effects on the primordial perturbation spectrum has been already studied and constrained by current data, in this paper we continue to study such effects but now on the non-Gaussianity of the primordial curvature perturbations. We present detailed and analytical calculations of the non-Gaussianity and show explicitly that the corrections due to the quantum effects are at the same magnitude of the slow-roll parameters in the observable scales and thus are well within current observational constraints. Despite this, we show that the non-Gaussianity in the squeezed limit can be enhanced at superhorizon scales and it is these effects that can yield a large statistical anisotropy on the power spectrum through the Erickcek-Kamionkowski-Carroll mechanism.
Searching for non-Gaussianity in the WMAP data
International Nuclear Information System (INIS)
Bernui, A.; Reboucas, M. J.
2009-01-01
Some analyses of recent cosmic microwave background (CMB) data have provided hints that there are deviations from Gaussianity in the WMAP CMB temperature fluctuations. Given the far-reaching consequences of such a non-Gaussianity for our understanding of the physics of the early universe, it is important to employ alternative indicators in order to determine whether the reported non-Gaussianity is of cosmological origin, and/or extract further information that may be helpful for identifying its causes. We propose two new non-Gaussianity indicators, based on skewness and kurtosis of large-angle patches of CMB maps, which provide a measure of departure from Gaussianity on large angular scales. A distinctive feature of these indicators is that they provide sky maps of non-Gaussianity of the CMB temperature data, thus allowing a possible additional window into their origins. Using these indicators, we find no significant deviation from Gaussianity in the three and five-year WMAP Internal Linear Combination (ILC) map with KQ75 mask, while the ILC unmasked map exhibits deviation from Gaussianity, quantifying therefore the WMAP team recommendation to employ the new mask KQ75 for tests of Gaussianity. We also use our indicators to test for Gaussianity the single frequency foreground unremoved WMAP three and five-year maps, and show that the K and Ka maps exhibit a clear indication of deviation from Gaussianity even with the KQ75 mask. We show that our findings are robust with respect to the details of the method.
A Variational approach to thin film hydrodynamics of binary mixtures
Xu, Xinpeng; Thiele, Uwe; Qian, Tiezheng
2015-01-01
In order to model the dynamics of thin films of mixtures, solutions, and suspensions, a thermodynamically consistent formulation is needed such that various coexisting dissipative processes with cross couplings can be correctly described
A simple approach to polymer mixture miscibility.
Higgins, Julia S; Lipson, Jane E G; White, Ronald P
2010-03-13
Polymeric mixtures are important materials, but the control and understanding of mixing behaviour poses problems. The original Flory-Huggins theoretical approach, using a lattice model to compute the statistical thermodynamics, provides the basic understanding of the thermodynamic processes involved but is deficient in describing most real systems, and has little or no predictive capability. We have developed an approach using a lattice integral equation theory, and in this paper we demonstrate that this not only describes well the literature data on polymer mixtures but allows new insights into the behaviour of polymers and their mixtures. The characteristic parameters obtained by fitting the data have been successfully shown to be transferable from one dataset to another, to be able to correctly predict behaviour outside the experimental range of the original data and to allow meaningful comparisons to be made between different polymer mixtures.
Gaussian capacity of the quantum bosonic memory channel with additive correlated Gaussian noise
International Nuclear Information System (INIS)
Schaefer, Joachim; Karpov, Evgueni; Cerf, Nicolas J.
2011-01-01
We present an algorithm for calculation of the Gaussian classical capacity of a quantum bosonic memory channel with additive Gaussian noise. The algorithm, restricted to Gaussian input states, is applicable to all channels with noise correlations obeying certain conditions and works in the full input energy domain, beyond previous treatments of this problem. As an illustration, we study the optimal input states and capacity of a quantum memory channel with Gauss-Markov noise [J. Schaefer, Phys. Rev. A 80, 062313 (2009)]. We evaluate the enhancement of the transmission rate when using these optimal entangled input states by comparison with a product coherent-state encoding and find out that such a simple coherent-state encoding achieves not less than 90% of the capacity.
Full Text Available ... out more. Corrective Jaw Surgery Corrective Jaw Surgery Orthognathic surgery is performed to correct the misalignment of jaws ... out more. Corrective Jaw Surgery Corrective Jaw Surgery Orthognathic surgery is performed to correct the misalignment of jaws ...
Overlay Spectrum Sharing using Improper Gaussian Signaling
Amin, Osama; Abediseid, Walid; Alouini, Mohamed-Slim
2016-01-01
in overlay cognitive radio system, where the secondary transmitter broadcasts a mixture of two different signals. The first signal is selected from the PGS scheme to match the primary message transmission. On the other hand, the second signal is chosen
High-Order Local Pooling and Encoding Gaussians Over a Dictionary of Gaussians.
Li, Peihua; Zeng, Hui; Wang, Qilong; Shiu, Simon C K; Zhang, Lei
2017-07-01
Local pooling (LP) in configuration (feature) space proposed by Boureau et al. explicitly restricts similar features to be aggregated, which can preserve as much discriminative information as possible. At the time it appeared, this method combined with sparse coding achieved competitive classification results with only a small dictionary. However, its performance lags far behind the state-of-the-art results as only the zero-order information is exploited. Inspired by the success of high-order statistical information in existing advanced feature coding or pooling methods, we make an attempt to address the limitation of LP. To this end, we present a novel method called high-order LP (HO-LP) to leverage the information higher than the zero-order one. Our idea is intuitively simple: we compute the first- and second-order statistics per configuration bin and model them as a Gaussian. Accordingly, we employ a collection of Gaussians as visual words to represent the universal probability distribution of features from all classes. Our problem is naturally formulated as encoding Gaussians over a dictionary of Gaussians as visual words. This problem, however, is challenging since the space of Gaussians is not a Euclidean space but forms a Riemannian manifold. We address this challenge by mapping Gaussians into the Euclidean space, which enables us to perform coding with common Euclidean operations rather than complex and often expensive Riemannian operations. Our HO-LP preserves the advantages of the original LP: pooling only similar features and using a small dictionary. Meanwhile, it achieves very promising performance on standard benchmarks, with either conventional, hand-engineered features or deep learning-based features.
Area of isodensity contours in Gaussian and non-Gaussian fields
International Nuclear Information System (INIS)
Ryden, B.S.
1988-01-01
The area of isodensity contours in a smoothed density field can be measured by the contour-crossing statistic N1, the number of times per unit length that a line drawn through the density field pierces an isodensity contour. The contour-crossing statistic distinguishes between Gaussian and non-Gaussian fields and provides a measure of the effective slope of the power spectrum. The statistic is easy to apply and can be used on pencil beams and slices as well as on a three-dimensional field. 10 references
Stochastic differential calculus for Gaussian and non-Gaussian noises: A critical review
Falsone, G.
2018-03-01
In this paper a review of the literature works devoted to the study of stochastic differential equations (SDEs) subjected to Gaussian and non-Gaussian white noises and to fractional Brownian noises is given. In these cases, particular attention must be paid in treating the SDEs because the classical rules of the differential calculus, as the Newton-Leibnitz one, cannot be applied or are applicable with many difficulties. Here all the principal approaches solving the SDEs are reported for any kind of noise, highlighting the negative and positive properties of each one and making the comparisons, where it is possible.
International Nuclear Information System (INIS)
Liu Shixiong; Guo Hong; Liu Mingwei; Wu Guohua
2004-01-01
Propagation characteristics of focused Gaussian beam (FoGB) and fundamental Gaussian beam (FuGB) propagating in vacuum are investigated. Based on the Fourier transform and the angular spectral analysis, the transverse component and the second-order approximate longitudinal component of the electric field are obtained in the paraxial approximation. The electric field components, the phase velocity and the group velocity of FoGB are compared with those of FuGB. The spot size of FoGB is also discussed
International Nuclear Information System (INIS)
Tan, Cheng-Yang; Fermilab
2006-01-01
One common way for measuring the emittance of an electron beam is with the slits method. The usual approach for analyzing the data is to calculate an emittance that is a subset of the parent emittance. This paper shows an alternative way by using the method of correlations which ties the parameters derived from the beamlets to the actual parameters of the parent emittance. For parent distributions that are Gaussian, this method yields exact results. For non-Gaussian beam distributions, this method yields an effective emittance that can serve as a yardstick for emittance comparisons
Non-Gaussian statistics, classical field theory, and realizable Langevin models
International Nuclear Information System (INIS)
Krommes, J.A.
1995-11-01
The direct-interaction approximation (DIA) to the fourth-order statistic Z ∼ left-angle λψ 2 ) 2 right-angle, where λ is a specified operator and ψ is a random field, is discussed from several points of view distinct from that of Chen et al. [Phys. Fluids A 1, 1844 (1989)]. It is shown that the formula for Z DIA already appeared in the seminal work of Martin, Siggia, and Rose (Phys. Rev. A 8, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sd. 28, 145 (1971)] and Kraichnan [J. Fluid Mech. 41, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections (''spurious vertices'') is described. It is shown how to derive an improved representation, that realizes cumulants through O(ψ 4 ), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation Z DIA M to Z DIA is derived. Both Z DIA and Z DIA M incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example
Non-Gaussianity from Broken Symmetries
Kolb, Edward W; Vallinotto, A; Kolb, Edward W.; Riotto, Antonio; Vallinotto, Alberto
2006-01-01
Recently we studied inflation models in which the inflaton potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, $f_{NL}$, can be as large as 10^2.
First Passage Time Intervals of Gaussian Processes
Perez, Hector; Kawabata, Tsutomu; Mimaki, Tadashi
1987-08-01
The first passage time problem of a stationary Guassian process is theretically and experimentally studied. Renewal functions are derived for a time-dependent boundary and numerically calculated for a Gaussian process having a seventh-order Butterworth spectrum. The results show a multipeak property not only for the constant boundary but also for a linearly increasing boundary. The first passage time distribution densities were experimentally determined for a constant boundary. The renewal functions were shown to be a fairly good approximation to the distribution density over a limited range.
CMB constraints on running non-Gaussianity
Oppizzi, Filippo; Liguori, Michele; Renzi, Alessandro; Arroja, Frederico; Bartolo, Nicola
2017-01-01
We develop a complete set of tools for CMB forecasting, simulation and estimation of primordial running bispectra, arising from a variety of curvaton and single-field (DBI) models of Inflation. We validate our pipeline using mock CMB running non-Gaussianity realizations and test it on real data by obtaining experimental constraints on the $f_{\\rm NL}$ running spectral index, $n_{\\rm NG}$, using WMAP 9-year data. Our final bounds (68\\% C.L.) read $-0.3< n_{\\rm NG}
Turbo Equalization Using Partial Gaussian Approximation
DEFF Research Database (Denmark)
Zhang, Chuanzong; Wang, Zhongyong; Manchón, Carles Navarro
2016-01-01
This letter deals with turbo equalization for coded data transmission over intersymbol interference (ISI) channels. We propose a message-passing algorithm that uses the expectation propagation rule to convert messages passed from the demodulator and decoder to the equalizer and computes messages...... returned by the equalizer by using a partial Gaussian approximation (PGA). We exploit the specific structure of the ISI channel model to compute the latter messages from the beliefs obtained using a Kalman smoother/equalizer. Doing so leads to a significant complexity reduction compared to the initial PGA...
Optical trapping with Super-Gaussian beams
CSIR Research Space (South Africa)
Mc
2013-04-01
Full Text Available stream_source_info McLaren1_2013.pdf.txt stream_content_type text/plain stream_size 2236 Content-Encoding UTF-8 stream_name McLaren1_2013.pdf.txt Content-Type text/plain; charset=UTF-8 JT2A.34.pdf Optics in the Life... Sciences Congress Technical Digest © 2013 The Optical Society (OSA) Optical trapping with Super-Gaussian beams Melanie McLaren, Thulile Khanyile, Patience Mthunzi and Andrew Forbes* National Laser Centre, Council for Scientific and Industrial Research...
Bregman Cost for Non-Gaussian Noise
DEFF Research Database (Denmark)
Burger, Martin; Dong, Yiqiu; Sciacchitano, Federica
estimator for the Bregman cost if the image is corrupted by Gaussian noise. In this work we extend this result to other noise models with log-concave likelihood density, by introducing two related Bregman cost functions for which the CM and the MAP estimates are proper Bayes estima-tors. Moreover, we also....... From a theoretical point of view it has been argued that the MAP estimate is only in an asymptotic sense a Bayes estimator for the uniform cost function, while the CM estimate is a Bayes estimator for the means squared cost function. Recently, it has been proven that the MAP estimate is a proper Bayes...
Non-Gaussian covariance of CMB B modes of polarization and parameter degradation
International Nuclear Information System (INIS)
Li Chao; Smith, Tristan L.; Cooray, Asantha
2007-01-01
The B-mode polarization lensing signal is a useful probe of the neutrino mass and to a lesser extent the dark energy equation of state as the signal depends on the integrated mass power spectrum between us and the last scattering surface. This lensing B-mode signal, however, is non-Gaussian and the resulting non-Gaussian covariance to the power spectrum could impact cosmological parameter measurements, as correlations between B-mode bins are at a level of 0.1. On the other hand, for temperature and E-mode polarization power spectra, the non-Gaussian covariance is not significant, where we find correlations at the 10 -5 level even for adjacent bins. When the power spectrum is estimated with roughly 5 uniformly spaced bins from l=5 to l=100 and 13 logarithmic uniformly spaced bins from l=100 to l=2000, the resulting degradation on neutrino mass and dark energy equation of state is about a factor of 2 to 3 when compared to the case where statistics are simply considered to be Gaussian. If we increase the total number of bins between l=5 and l=2000 to be about 100, we find that the non-Gaussianities only make a minor difference with less than a few percent correction to uncertainties of most cosmological parameters determined from the data. For Planck, the resulting constraints on the sum of the neutrino masses is σ Σm ν ∼0.2 eV and on the dark energy equation of state parameter we find that σ w ∼0.5. A post-Planck experiment can improve the neutrino mass measurement by a factor of 3 to 4
Missing Value Imputation Based on Gaussian Mixture Model for the Internet of Things
Yan, Xiaobo; Xiong, Weiqing; Hu, Liang; Wang, Feng; Zhao, Kuo
2015-01-01
This paper addresses missing value imputation for the Internet of Things (IoT). Nowadays, the IoT has been used widely and commonly by a variety of domains, such as transportation and logistics domain and healthcare domain. However, missing values are very common in the IoT for a variety of reasons, which results in the fact that the experimental data are incomplete. As a result of this, some work, which is related to the data of the IoT, can’t be carried out normally. And it leads to the red...
A univocal definition of the neuronal soma morphology using Gaussian mixture models
Directory of Open Access Journals (Sweden)
Sergio eLuengo-Sanchez
2015-11-01
Full Text Available The definition of the soma is fuzzy, as there is no clear line demarcating the soma of the labeled neurons and the origin of the dendrites and axon. Thus, the morphometric analysis of the neuronal soma is highly subjective. In this paper, we provide a mathematical definition and an automatic segmentation method to delimit the neuronal soma. We applied this method to the characterization of pyramidal cells, which are the most abundant neurons in the cerebral cortex. Since there are no benchmarks with which to compare the proposed procedure, we validated the goodness of this automatic segmentation method against manual segmentation by experts in neuroanatomy to set up a framework for comparison. We concluded that there were no significant differences between automatically and manually segmented somata, i.e., the proposed procedure segments the neurons more or less as an expert does. It also provides univocal, justifiable and objective cutoffs. Thus, this study is a means of characterizing pyramidal neurons in order to objectively compare the morphometry of the somata of these neurons in different cortical areas and species.
A univocal definition of the neuronal soma morphology using Gaussian mixture models.
Luengo-Sanchez, Sergio; Bielza, Concha; Benavides-Piccione, Ruth; Fernaud-Espinosa, Isabel; DeFelipe, Javier; Larrañaga, Pedro
2015-01-01
The definition of the soma is fuzzy, as there is no clear line demarcating the soma of the labeled neurons and the origin of the dendrites and axon. Thus, the morphometric analysis of the neuronal soma is highly subjective. In this paper, we provide a mathematical definition and an automatic segmentation method to delimit the neuronal soma. We applied this method to the characterization of pyramidal cells, which are the most abundant neurons in the cerebral cortex. Since there are no benchmarks with which to compare the proposed procedure, we validated the goodness of this automatic segmentation method against manual segmentation by neuroanatomists to set up a framework for comparison. We concluded that there were no significant differences between automatically and manually segmented somata, i.e., the proposed procedure segments the neurons similarly to how a neuroanatomist does. It also provides univocal, justifiable and objective cutoffs. Thus, this study is a means of characterizing pyramidal neurons in order to objectively compare the morphometry of the somata of these neurons in different cortical areas and species.
Single-step emulation of nonlinear fiber-optic link with gaussian mixture model
DEFF Research Database (Denmark)
Borkowski, Robert; Doberstein, Andy; Haisch, Hansjörg
2015-01-01
We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission.......We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission....
On-line signature verification using Gaussian Mixture Models and small-sample learning strategies
Directory of Open Access Journals (Sweden)
Gabriel Jaime Zapata-Zapata
2016-01-01
Full Text Available El artículo aborda el problema de entrenamiento de sistemas de verificación de firmas en línea cuando el número de muestras disponibles para el entrenamiento es bajo, debido a que en la mayoría de situaciones reales el número de firmas disponibles por usuario es muy limitado. El artículo evalúa nueve diferentes estrategias de clasificación basadas en modelos de mezclas de Gaussianas (GMM por sus siglas en inglés y la estrategia conocida como modelo histórico universal (UBM por sus siglas en inglés, la cual está diseñada con el objetivo de trabajar bajo condiciones de menor número de muestras. Las estrategias de aprendizaje de los GMM incluyen el algoritmo convencional de Esperanza y Maximización, y una aproximación Bayesiana basada en aprendizaje variacional. Las firmas son caracterizadas principalmente en términos de velocidades y aceleraciones de los patrones de escritura a mano de los usuarios. Los resultados muestran que cuando se evalúa el sistema en una configuración genuino vs. impostor, el método GMM-UBM es capaz de mantener una precisión por encima del 93%, incluso en casos en los que únicamente se usa para entrenamiento el 20% de las muestras disponibles (equivalente a 5 firmas, mientras que la combinación de un modelo Bayesiano UBM con una Máquina de Soporte Vectorial (SVM por sus siglas en inglés, modelo conocido como GMM-Supervector, logra un 99% de acierto cuando las muestras de entrenamiento exceden las 20. Por otro lado, cuando se simula un ambiente real en el que no están disponibles muestras impostoras y se usa
Dirichlet Process Gaussian Mixture Model for Activity Discovery in Smart Homes with Ambient Sensors
Nguyen, Thuong; Le Viet Duc, Duc Viet; Zhang, Quing; Karunanithi, Mohan
2017-01-01
Most of the existing approaches to activity recognition in smart homes rely on supervised learning with well annotated sensor data. However obtaining such labeled data is not only challenging but sometimes also an unobtainable task, especially for senior citizens who may suffer various mental health
Mixtures of Gaussians for uncertainty description in bivariate latent heat flux proxies
Wójcik, R.; Troch, P.A.A.; Stricker, J.N.M.; Torfs, P.J.J.F.
2006-01-01
This paper proposes a new probabilistic approach for describing uncertainty in the ensembles of latent heat flux proxies. The proxies are obtained from hourly Bowen ratio and satellite-derived measurements, respectively, at several locations in the southern Great Plains region in the United States.
A univocal definition of the neuronal soma morphology using Gaussian mixture models
Luengo-Sanchez, Sergio; Bielza, Concha; Benavides-Piccione, Ruth; Fernaud-Espinosa, Isabel; DeFelipe, Javier; Larrañaga, Pedro
2015-01-01
The definition of the soma is fuzzy, as there is no clear line demarcating the soma of the labeled neurons and the origin of the dendrites and axon. Thus, the morphometric analysis of the neuronal soma is highly subjective. In this paper, we provide a mathematical definition and an automatic segmentation method to delimit the neuronal soma. We applied this method to the characterization of pyramidal cells, which are the most abundant neurons in the cerebral cortex. Since there are no benchmarks with which to compare the proposed procedure, we validated the goodness of this automatic segmentation method against manual segmentation by neuroanatomists to set up a framework for comparison. We concluded that there were no significant differences between automatically and manually segmented somata, i.e., the proposed procedure segments the neurons similarly to how a neuroanatomist does. It also provides univocal, justifiable and objective cutoffs. Thus, this study is a means of characterizing pyramidal neurons in order to objectively compare the morphometry of the somata of these neurons in different cortical areas and species. PMID:26578898
Rings, J.; Vrugt, J.A.; Schoups, G.; Huisman, J.A.; Vereecken, H.
2012-01-01
Bayesian model averaging (BMA) is a standard method for combining predictive distributions from different models. In recent years, this method has enjoyed widespread application and use in many fields of study to improve the spread-skill relationship of forecast ensembles. The BMA predictive
International Nuclear Information System (INIS)
Beenakker, W.J.P.
1989-01-01
The prospect of high accuracy measurements investigating the weak interactions, which are expected to take place at the electron-positron storage ring LEP at CERN and the linear collider SCL at SLAC, offers the possibility to study also the weak quantum effects. In order to distinguish if the measured weak quantum effects lie within the margins set by the standard model and those bearing traces of new physics one had to go beyond the lowest order and also include electroweak radiative corrections (EWRC) in theoretical calculations. These higher-order corrections also can offer the possibility of getting information about two particles present in the Glashow-Salam-Weinberg model (GSW), but not discovered up till now, the top quark and the Higgs boson. In ch. 2 the GSW standard model of electroweak interactions is described. In ch. 3 some special techniques are described for determination of integrals which are responsible for numerical instabilities caused by large canceling terms encountered in the calculation of EWRC effects, and methods necessary to get hold of the extensive algebra typical for EWRC. In ch. 4 various aspects related to EWRC effects are discussed, in particular the dependence of the unknown model parameters which are the masses of the top quark and the Higgs boson. The processes which are discussed are production of heavy fermions from electron-positron annihilation and those of the fermionic decay of the Z gauge boson. (H.W.). 106 refs.; 30 figs.; 6 tabs.; schemes
Characterisation of random Gaussian and non-Gaussian stress processes in terms of extreme responses
Directory of Open Access Journals (Sweden)
Colin Bruno
2015-01-01
Full Text Available In the field of military land vehicles, random vibration processes generated by all-terrain wheeled vehicles in motion are not classical stochastic processes with a stationary and Gaussian nature. Non-stationarity of processes induced by the variability of the vehicle speed does not form a major difficulty because the designer can have good control over the vehicle speed by characterising the histogram of instantaneous speed of the vehicle during an operational situation. Beyond this non-stationarity problem, the hard point clearly lies in the fact that the random processes are not Gaussian and are generated mainly by the non-linear behaviour of the undercarriage and the strong occurrence of shocks generated by roughness of the terrain. This non-Gaussian nature is expressed particularly by very high flattening levels that can affect the design of structures under extreme stresses conventionally acquired by spectral approaches, inherent to Gaussian processes and based essentially on spectral moments of stress processes. Due to these technical considerations, techniques for characterisation of random excitation processes generated by this type of carrier need to be changed, by proposing innovative characterisation methods based on time domain approaches as described in the body of the text rather than spectral domain approaches.
DEFF Research Database (Denmark)
Møller, Jesper; Jacobsen, Robert Dahl
We introduce a promising alternative to the usual hidden Markov tree model for Gaussian wavelet coefficients, where their variances are specified by the hidden states and take values in a finite set. In our new model, the hidden states have a similar dependence structure but they are jointly Gaus...
Approximation problems with the divergence criterion for Gaussian variablesand Gaussian processes
A.A. Stoorvogel; J.H. van Schuppen (Jan)
1996-01-01
textabstractSystem identification for stationary Gaussian processes includes an approximation problem. Currently the subspace algorithm for this problem enjoys much attention. This algorithm is based on a transformation of a finite time series to canonical variable form followed by a truncation.
Comparison of Gaussian and non-Gaussian Atmospheric Profile Retrievals from Satellite Microwave Data
Kliewer, A.; Forsythe, J. M.; Fletcher, S. J.; Jones, A. S.
2017-12-01
The Cooperative Institute for Research in the Atmosphere at Colorado State University has recently developed two different versions of a mixed-distribution (lognormal combined with a Gaussian) based microwave temperature and mixing ratio retrieval system as well as the original Gaussian-based approach. These retrieval systems are based upon 1DVAR theory but have been adapted to use different descriptive statistics of the lognormal distribution to minimize the background errors. The input radiance data is from the AMSU-A and MHS instruments on the NOAA series of spacecraft. To help illustrate how the three retrievals are affected by the change in the distribution we are in the process of creating a new website to show the output from the different retrievals. Here we present initial results from different dynamical situations to show how the tool could be used by forecasters as well as for educators. However, as the new retrieved values are from a non-Gaussian based 1DVAR then they will display non-Gaussian behaviors that need to pass a quality control measure that is consistent with this distribution, and these new measures are presented here along with initial results for checking the retrievals.
Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies.
Savitsky, Terrance; Vannucci, Marina; Sha, Naijun
2011-02-01
This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori unknown form of possibly nonlinear associations to the response. The modeling approach we describe incorporates Gaussian processes in a generalized linear model framework to obtain a class of nonparametric regression models where the covariance matrix depends on the predictors. We consider, in particular, continuous, categorical and count responses. We also look into models that account for survival outcomes. We explore alternative covariance formulations for the Gaussian process prior and demonstrate the flexibility of the construction. Next, we focus on the important problem of selecting variables from the set of possible predictors and describe a general framework that employs mixture priors. We compare alternative MCMC strategies for posterior inference and achieve a computationally efficient and practical approach. We demonstrate performances on simulated and benchmark data sets.
Directory of Open Access Journals (Sweden)
Yun Wang
2016-01-01
Full Text Available Gamma Gaussian inverse Wishart cardinalized probability hypothesis density (GGIW-CPHD algorithm was always used to track group targets in the presence of cluttered measurements and missing detections. A multiple models GGIW-CPHD algorithm based on best-fitting Gaussian approximation method (BFG and strong tracking filter (STF is proposed aiming at the defect that the tracking error of GGIW-CPHD algorithm will increase when the group targets are maneuvering. The best-fitting Gaussian approximation method is proposed to implement the fusion of multiple models using the strong tracking filter to correct the predicted covariance matrix of the GGIW component. The corresponding likelihood functions are deduced to update the probability of multiple tracking models. From the simulation results we can see that the proposed tracking algorithm MM-GGIW-CPHD can effectively deal with the combination/spawning of groups and the tracking error of group targets in the maneuvering stage is decreased.
Functional Dual Adaptive Control with Recursive Gaussian Process Model
International Nuclear Information System (INIS)
Prüher, Jakub; Král, Ladislav
2015-01-01
The paper deals with dual adaptive control problem, where the functional uncertainties in the system description are modelled by a non-parametric Gaussian process regression model. Current approaches to adaptive control based on Gaussian process models are severely limited in their practical applicability, because the model is re-adjusted using all the currently available data, which keeps growing with every time step. We propose the use of recursive Gaussian process regression algorithm for significant reduction in computational requirements, thus bringing the Gaussian process-based adaptive controllers closer to their practical applicability. In this work, we design a bi-criterial dual controller based on recursive Gaussian process model for discrete-time stochastic dynamic systems given in an affine-in-control form. Using Monte Carlo simulations, we show that the proposed controller achieves comparable performance with the full Gaussian process-based controller in terms of control quality while keeping the computational demands bounded. (paper)
A Gaussian Approximation Potential for Silicon
Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor
We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.
Statistics of peaks of Gaussian random fields
International Nuclear Information System (INIS)
Bardeen, J.M.; Bond, J.R.; Kaiser, N.; Szalay, A.S.; Stanford Univ., CA; California Univ., Berkeley; Cambridge Univ., England; Fermi National Accelerator Lab., Batavia, IL)
1986-01-01
A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of upcrossing points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima. 67 references
Versatile Gaussian probes for squeezing estimation
Rigovacca, Luca; Farace, Alessandro; Souza, Leonardo A. M.; De Pasquale, Antonella; Giovannetti, Vittorio; Adesso, Gerardo
2017-05-01
We consider an instance of "black-box" quantum metrology in the Gaussian framework, where we aim to estimate the amount of squeezing applied on an input probe, without previous knowledge on the phase of the applied squeezing. By taking the quantum Fisher information (QFI) as the figure of merit, we evaluate its average and variance with respect to this phase in order to identify probe states that yield good precision for many different squeezing directions. We first consider the case of single-mode Gaussian probes with the same energy, and find that pure squeezed states maximize the average quantum Fisher information (AvQFI) at the cost of a performance that oscillates strongly as the squeezing direction is changed. Although the variance can be brought to zero by correlating the probing system with a reference mode, the maximum AvQFI cannot be increased in the same way. A different scenario opens if one takes into account the effects of photon losses: coherent states represent the optimal single-mode choice when losses exceed a certain threshold and, moreover, correlated probes can now yield larger AvQFI values than all single-mode states, on top of having zero variance.
Finite Range Decomposition of Gaussian Processes
Brydges, C D; Mitter, P K
2003-01-01
Let $D$ be the finite difference Laplacian associated to the lattice $bZ^{d}$. For dimension $dge 3$, $age 0$ and $L$ a sufficiently large positive dyadic integer, we prove that the integral kernel of the resolvent $G^{a}:=(a-D)^{-1}$ can be decomposed as an infinite sum of positive semi-definite functions $ V_{n} $ of finite range, $ V_{n} (x-y) = 0$ for $|x-y|ge O(L)^{n}$. Equivalently, the Gaussian process on the lattice with covariance $G^{a}$ admits a decomposition into independent Gaussian processes with finite range covariances. For $a=0$, $ V_{n} $ has a limiting scaling form $L^{-n(d-2)}Gamma_{ c,ast }{bigl (frac{x-y}{ L^{n}}bigr )}$ as $nrightarrow infty$. As a corollary, such decompositions also exist for fractional powers $(-D)^{-alpha/2}$, $0
Directory of Open Access Journals (Sweden)
Georgios C Manikis
Full Text Available The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer.Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2 at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG and non-Gaussian (MNG and BNG were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE. To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC and F-ratio.All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area.No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.
Relative entropy as a measure of entanglement for Gaussian states
Institute of Scientific and Technical Information of China (English)
Lu Huai-Xin; Zhao Bo
2006-01-01
In this paper, we derive an explicit analytic expression of the relative entropy between two general Gaussian states. In the restriction of the set for Gaussian states and with the help of relative entropy formula and Peres-Simon separability criterion, one can conveniently obtain the relative entropy entanglement for Gaussian states. As an example,the relative entanglement for a two-mode squeezed thermal state has been obtained.
Meat mixture detection in Iberian pork sausages.
Ortiz-Somovilla, V; España-España, F; De Pedro-Sanz, E J; Gaitán-Jurado, A J
2005-11-01
Five homogenized meat mixture treatments of Iberian (I) and/or Standard (S) pork were set up. Each treatment was analyzed by NIRS as a fresh product (N=75) and as dry-cured sausage (N=75). Spectra acquisition was carried out using DA 7000 equipment (Perten Instruments), obtaining a total of 750 spectra. Several absorption peaks and bands were selected as the most representative for homogenized dry-cured and fresh sausages. Discriminant analysis and mixture prediction equations were carried out based on the spectral data gathered. The best results using discriminant models were for fresh products, with 98.3% (calibration) and 60% (validation) correct classification. For dry-cured sausages 91.7% (calibration) and 80% (validation) of the samples were correctly classified. Models developed using mixture prediction equations showed SECV=4.7, r(2)=0.98 (calibration) and 73.3% of validation set were correctly classified for the fresh product. These values for dry-cured sausages were SECV=5.9, r(2)=0.99 (calibration) and 93.3% correctly classified for validation.
Prediction and retrodiction with continuously monitored Gaussian states
DEFF Research Database (Denmark)
Zhang, Jinglei; Mølmer, Klaus
2017-01-01
Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and continuous probing which maintain their Gaussian state property......(t)$ to Gaussian states implies that the matrix $E(t)$ is also fully characterized by a vector of mean values and a covariance matrix. We derive the dynamical equations for these quantities and we illustrate their use in the retrodiction of measurements on Gaussian systems....
Geometry of perturbed Gaussian states and quantum estimation
International Nuclear Information System (INIS)
Genoni, Marco G; Giorda, Paolo; Paris, Matteo G A
2011-01-01
We address the non-Gaussianity (nG) of states obtained by weakly perturbing a Gaussian state and investigate the relationships with quantum estimation. For classical perturbations, i.e. perturbations to eigenvalues, we found that the nG of the perturbed state may be written as the quantum Fisher information (QFI) distance minus a term depending on the infinitesimal energy change, i.e. it provides a lower bound to statistical distinguishability. Upon moving on isoenergetic surfaces in a neighbourhood of a Gaussian state, nG thus coincides with a proper distance in the Hilbert space and exactly quantifies the statistical distinguishability of the perturbations. On the other hand, for perturbations leaving the covariance matrix unperturbed, we show that nG provides an upper bound to the QFI. Our results show that the geometry of non-Gaussian states in the neighbourhood of a Gaussian state is definitely not trivial and cannot be subsumed by a differential structure. Nevertheless, the analysis of perturbations to a Gaussian state reveals that nG may be a resource for quantum estimation. The nG of specific families of perturbed Gaussian states is analysed in some detail with the aim of finding the maximally non-Gaussian state obtainable from a given Gaussian one. (fast track communication)
Gaussian polynomials and content ideal in trivial extensions
International Nuclear Information System (INIS)
Bakkari, C.; Mahdou, N.
2006-12-01
The goal of this paper is to exhibit a class of Gaussian non-coherent rings R (with zero-divisors) such that wdim(R) = ∞ and fPdim(R) is always at most one and also exhibits a new class of rings (with zerodivisors) which are neither locally Noetherian nor locally domain where Gaussian polynomials have a locally principal content. For this purpose, we study the possible transfer of the 'Gaussian' property and the property 'the content ideal of a Gaussian polynomial is locally principal' to various trivial extension contexts. This article includes a brief discussion of the scopes and limits of our result. (author)
International Nuclear Information System (INIS)
Sisovic, N. M.; Konjevic, N.
2008-01-01
The results of Doppler spectroscopy of hydrogen Balmer lines from a stainless steel (SS) and copper (Cu) hollow cathode (HC) glow discharge in ammonia and argon-ammonia mixture are reported. The experimental profiles in ammonia discharge are fitted well by superposing three Gaussian profiles. The half widths, in energy units, of narrow and medium Gaussians are in the ranges 0.3-0.4 eV and 3-4 eV, respectively, for both hollow cathodes what is expected on the basis of earlier electron beam→NH 3 experiments. The half widths of the largest Gaussian in ammonia are 46 and 55 eV for SS and Cu HC, respectively. In argon-ammonia discharge, three Gaussians are also required to fit experimental profiles. While half widths of narrow and medium Gaussians are similar to those in ammonia, the half widths of the largest Gaussians are 35 and 42 eV for SS and Cu HC, respectively. The half widths of the largest Gaussians in ammonia and in argon-ammonia mixture indicate the presence of excessive Doppler broadening.
Energy Technology Data Exchange (ETDEWEB)
Wang, Yuan-Mei; Li, Jun-Gang, E-mail: jungl@bit.edu.cn; Zou, Jian
2017-06-15
Highlights: • Adaptive measurement strategy is used to detect the presence of a magnetic field. • Gaussian Ornstein–Uhlenbeck noise and non-Gaussian noise have been considered. • Weaker magnetic fields may be more easily detected than some stronger ones. - Abstract: By using the adaptive measurement method we study how to detect whether a weak magnetic field is actually present or not under Gaussian noise and non-Gaussian noise. We find that the adaptive measurement method can effectively improve the detection accuracy. For the case of Gaussian noise, we find the stronger the magnetic field strength, the easier for us to detect the magnetic field. Counterintuitively, for non-Gaussian noise, some weaker magnetic fields are more likely to be detected rather than some stronger ones. Finally, we give a reasonable physical interpretation.
Gaussian process regression for sensor networks under localization uncertainty
Jadaliha, M.; Xu, Yunfei; Choi, Jongeun; Johnson, N.S.; Li, Weiming
2013-01-01
In this paper, we formulate Gaussian process regression with observations under the localization uncertainty due to the resource-constrained sensor networks. In our formulation, effects of observations, measurement noise, localization uncertainty, and prior distributions are all correctly incorporated in the posterior predictive statistics. The analytically intractable posterior predictive statistics are proposed to be approximated by two techniques, viz., Monte Carlo sampling and Laplace's method. Such approximation techniques have been carefully tailored to our problems and their approximation error and complexity are analyzed. Simulation study demonstrates that the proposed approaches perform much better than approaches without considering the localization uncertainty properly. Finally, we have applied the proposed approaches on the experimentally collected real data from a dye concentration field over a section of a river and a temperature field of an outdoor swimming pool to provide proof of concept tests and evaluate the proposed schemes in real situations. In both simulation and experimental results, the proposed methods outperform the quick-and-dirty solutions often used in practice.
Nuclear collective flow from gaussian fits to triple differential distributions
International Nuclear Information System (INIS)
Gosset, J.; Babinet, R.; Cavata, C.; Marco, M. de; Demoulins, M.; Fanet, H.; Fodor, Z.; L'Hote, D.; Lucas, B.
1990-01-01
A simple characterization of triple differential cross sections is needed for a systematic study of the nuclear matter collective flow in relativistic nucleus-nucleus collisions. Our analysis is based upon a fitting procedure, so that the triple differential distributions need not be measured in the whole momentum space. If the detector acceptance eliminates most spectator particles or if it is artificially restricted for doing so, this method leads to a flow characterization of the participant nuclear matter. The center-of-mass triple-differential momentum distributions are fitted to a simple analytical shape, namely an anisotropic Gaussian distribution. The adjusted parameters (flow angle and aspect ratios) are corrected for uncertainty in the event-by-event determination of the reaction plane azimuth (finite-number effects). Results are presented for neon-nucleus and argon-nucleus collisions at incident energy between 400 and 800 MeV per nucleon. Flow is already significant for light systems, and depends clearly upon the impact parameter
Thermodiffusion in multicomponent n-alkane mixtures.
Galliero, Guillaume; Bataller, Henri; Bazile, Jean-Patrick; Diaz, Joseph; Croccolo, Fabrizio; Hoang, Hai; Vermorel, Romain; Artola, Pierre-Arnaud; Rousseau, Bernard; Vesovic, Velisa; Bou-Ali, M Mounir; Ortiz de Zárate, José M; Xu, Shenghua; Zhang, Ke; Montel, François; Verga, Antonio; Minster, Olivier
2017-01-01
Compositional grading within a mixture has a strong impact on the evaluation of the pre-exploitation distribution of hydrocarbons in underground layers and sediments. Thermodiffusion, which leads to a partial diffusive separation of species in a mixture due to the geothermal gradient, is thought to play an important role in determining the distribution of species in a reservoir. However, despite recent progress, thermodiffusion is still difficult to measure and model in multicomponent mixtures. In this work, we report on experimental investigations of the thermodiffusion of multicomponent n -alkane mixtures at pressure above 30 MPa. The experiments have been conducted in space onboard the Shi Jian 10 spacecraft so as to isolate the studied phenomena from convection. For the two exploitable cells, containing a ternary liquid mixture and a condensate gas, measurements have shown that the lightest and heaviest species had a tendency to migrate, relatively to the rest of the species, to the hot and cold region, respectively. These trends have been confirmed by molecular dynamics simulations. The measured condensate gas data have been used to quantify the influence of thermodiffusion on the initial fluid distribution of an idealised one dimension reservoir. The results obtained indicate that thermodiffusion tends to noticeably counteract the influence of gravitational segregation on the vertical distribution of species, which could result in an unstable fluid column. This confirms that, in oil and gas reservoirs, the availability of thermodiffusion data for multicomponent mixtures is crucial for a correct evaluation of the initial state fluid distribution.
Perception of trigeminal mixtures.
Filiou, Renée-Pier; Lepore, Franco; Bryant, Bruce; Lundström, Johan N; Frasnelli, Johannes
2015-01-01
The trigeminal system is a chemical sense allowing for the perception of chemosensory information in our environment. However, contrary to smell and taste, we lack a thorough understanding of the trigeminal processing of mixtures. We, therefore, investigated trigeminal perception using mixtures of 3 relatively receptor-specific agonists together with one control odor in different proportions to determine basic perceptual dimensions of trigeminal perception. We found that 4 main dimensions were linked to trigeminal perception: sensations of intensity, warmth, coldness, and pain. We subsequently investigated perception of binary mixtures of trigeminal stimuli by means of these 4 perceptual dimensions using different concentrations of a cooling stimulus (eucalyptol) mixed with a stimulus that evokes warmth perception (cinnamaldehyde). To determine if sensory interactions are mainly of central or peripheral origin, we presented stimuli in a physical "mixture" or as a "combination" presented separately to individual nostrils. Results showed that mixtures generally yielded higher ratings than combinations on the trigeminal dimensions "intensity," "warm," and "painful," whereas combinations yielded higher ratings than mixtures on the trigeminal dimension "cold." These results suggest dimension-specific interactions in the perception of trigeminal mixtures, which may be explained by particular interactions that may take place on peripheral or central levels. © The Author 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Yan, Yuan
2017-07-13
Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.
Yan, Yuan; Genton, Marc G.
2017-01-01
Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.
IBS for non-gaussian distributions
International Nuclear Information System (INIS)
Fedotov, A.; Sidorin, A.O.; Smirnov, A.V.
2010-01-01
In many situations distribution can significantly deviate from Gaussian which requires accurate treatment of IBS. Our original interest in this problem was motivated by the need to have an accurate description of beam evolution due to IBS while distribution is strongly affected by the external electron cooling force. A variety of models with various degrees of approximation were developed and implemented in BETACOOL in the past to address this topic. A more complete treatment based on the friction coefficient and full 3-D diffusion tensor was introduced in BETACOOL at the end of 2007 under the name 'local IBS model'. Such a model allowed us calculation of IBS for an arbitrary beam distribution. The numerical benchmarking of this local IBS algorithm and its comparison with other models was reported before. In this paper, after briefly describing the model and its limitations, they present its comparison with available experimental data.
Optical vortex scanning inside the Gaussian beam
International Nuclear Information System (INIS)
Masajada, J; Leniec, M; Augustyniak, I
2011-01-01
We discussed a new scanning method for optical vortex-based scanning microscopy. The optical vortex is introduced into the incident Gaussian beam by a vortex lens. Then the beam with the optical vortex is focused by an objective and illuminates the sample. By changing the position of the vortex lens we can shift the optical vortex position at the sample plane. By adjusting system parameters we can get 30 times smaller shift at the sample plane compared to the vortex lens shift. Moreover, if the range of vortex shifts is smaller than 3% of the beam radius in the sample plane the amplitude and phase distribution around the phase dislocation remains practically unchanged. Thus we can scan the sample topography precisely with an optical vortex
White Gaussian Noise - Models for Engineers
Jondral, Friedrich K.
2018-04-01
This paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.
Gaussian process regression for geometry optimization
Denzel, Alexander; Kästner, Johannes
2018-03-01
We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Matérn kernel and the squared exponential kernel. The Matérn kernel performs much better. We give a detailed description of the optimization procedures. These include overshooting the step resulting from GPR in order to obtain a higher degree of interpolation vs. extrapolation. In a benchmark against the Limited-memory Broyden-Fletcher-Goldfarb-Shanno optimizer of the DL-FIND library on 26 test systems, we found the new optimizer to generally reduce the number of required optimization steps.
Gaussian elimination is not optimal, revisited
DEFF Research Database (Denmark)
Macedo, Hugo Daniel
2016-01-01
We refactor the universal law for the tensor product to express matrix multiplication as the product . MN of two matrices . M and . N thus making possible to use such matrix product to encode and transform algorithms performing matrix multiplication using techniques from linear algebra. We explore...... the end results are equations involving matrix products, our exposition builds upon previous works on the category of matrices (and the related category of finite vector spaces) which we extend by showing: why the direct sum . (⊕,0) monoid is not closed, a biproduct encoding of Gaussian elimination...... such possibility and show two stepwise refinements transforming the composition . MN into the Naïve and Strassen's matrix multiplication algorithms. The inspection of the stepwise transformation of the composition of matrices . MN into the Naïve matrix multiplication algorithm evidences that the steps...
Tunnelling through a Gaussian random barrier
International Nuclear Information System (INIS)
Bezak, Viktor
2008-01-01
A thorough analysis of the tunnelling of electrons through a laterally inhomogeneous rectangular barrier is presented. The barrier height is defined as a statistically homogeneous Gaussian random function. In order to simplify calculations, we assume that the electron energy is low enough in comparison with the mean value of the barrier height. The randomness of the barrier height is defined vertically by a constant variance and horizontally by a finite correlation length. We present detailed calculations of the angular probability density for the tunnelled electrons (i.e. for the scattering forwards). The tunnelling manifests a remarkably diffusive character if the wavelength of the electrons is comparable with the correlation length of the barrier
International Nuclear Information System (INIS)
Desjacques, Vincent; Jeong, Donghui; Schmidt, Fabian
2011-01-01
Recent results of N-body simulations have shown that current theoretical models are not able to correctly predict the amplitude of the scale-dependent halo bias induced by primordial non-Gaussianity, for models going beyond the simplest, local quadratic case. Motivated by these discrepancies, we carefully examine three theoretical approaches based on (1) the statistics of thresholded regions, (2) a peak-background split method based on separation of scales, and (3) a peak-background split method using the conditional mass function. We first demonstrate that the statistics of thresholded regions, which is shown to be equivalent at leading order to a local bias expansion, cannot explain the mass-dependent deviation between theory and N-body simulations. In the two formulations of the peak-background split on the other hand, we identify an important, but previously overlooked, correction to the non-Gaussian bias that strongly depends on halo mass. This new term is in general significant for any primordial non-Gaussianity going beyond the simplest local f NL model. In a separate paper (to be published in PRD rapid communication), the authors compare these new theoretical predictions with N-body simulations, showing good agreement for all simulated types of non-Gaussianity.
Gaussian process regression for tool wear prediction
Kong, Dongdong; Chen, Yongjie; Li, Ning
2018-05-01
To realize and accelerate the pace of intelligent manufacturing, this paper presents a novel tool wear assessment technique based on the integrated radial basis function based kernel principal component analysis (KPCA_IRBF) and Gaussian process regression (GPR) for real-timely and accurately monitoring the in-process tool wear parameters (flank wear width). The KPCA_IRBF is a kind of new nonlinear dimension-increment technique and firstly proposed for feature fusion. The tool wear predictive value and the corresponding confidence interval are both provided by utilizing the GPR model. Besides, GPR performs better than artificial neural networks (ANN) and support vector machines (SVM) in prediction accuracy since the Gaussian noises can be modeled quantitatively in the GPR model. However, the existence of noises will affect the stability of the confidence interval seriously. In this work, the proposed KPCA_IRBF technique helps to remove the noises and weaken its negative effects so as to make the confidence interval compressed greatly and more smoothed, which is conducive for monitoring the tool wear accurately. Moreover, the selection of kernel parameter in KPCA_IRBF can be easily carried out in a much larger selectable region in comparison with the conventional KPCA_RBF technique, which helps to improve the efficiency of model construction. Ten sets of cutting tests are conducted to validate the effectiveness of the presented tool wear assessment technique. The experimental results show that the in-process flank wear width of tool inserts can be monitored accurately by utilizing the presented tool wear assessment technique which is robust under a variety of cutting conditions. This study lays the foundation for tool wear monitoring in real industrial settings.
Higher-Order Hybrid Gaussian Kernel in Meshsize Boosting Algorithm
African Journals Online (AJOL)
In this paper, we shall use higher-order hybrid Gaussian kernel in a meshsize boosting algorithm in kernel density estimation. Bias reduction is guaranteed in this scheme like other existing schemes but uses the higher-order hybrid Gaussian kernel instead of the regular fixed kernels. A numerical verification of this scheme ...
Convergence of posteriors for discretized log Gaussian Cox processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus Plenge
2004-01-01
In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations...... when the cell sizes of the discretization tends to zero. The effect of discretization is studied in a data example....
Comparing Fixed and Variable-Width Gaussian Networks
Czech Academy of Sciences Publication Activity Database
Kůrková, Věra; Kainen, P.C.
2014-01-01
Roč. 57, September (2014), s. 23-28 ISSN 0893-6080 R&D Projects: GA MŠk(CZ) LD13002 Institutional support: RVO:67985807 Keywords : Gaussian radial and kernel networks * Functionally equivalent networks * Universal approximators * Stabilizers defined by Gaussian kernels * Argminima of error functionals Subject RIV: IN - Informatics, Computer Science Impact factor: 2.708, year: 2014
Two-photon optics of Bessel-Gaussian modes
CSIR Research Space (South Africa)
McLaren, M
2013-09-01
Full Text Available In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum...
Application Of Shared Gamma And Inverse-Gaussian Frailty Models ...
African Journals Online (AJOL)
Shared Gamma and Inverse-Gaussian Frailty models are used to analyze the survival times of patients who are clustered according to cancer/tumor types under Parametric Proportional Hazard framework. The result of the ... However, no evidence is strong enough for preference of either Gamma or Inverse Gaussian Frailty.
Optimality of Gaussian attacks in continuous-variable quantum cryptography.
Navascués, Miguel; Grosshans, Frédéric; Acín, Antonio
2006-11-10
We analyze the asymptotic security of the family of Gaussian modulated quantum key distribution protocols for continuous-variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.
Degeneracy of energy levels of pseudo-Gaussian oscillators
International Nuclear Information System (INIS)
Iacob, Theodor-Felix; Iacob, Felix; Lute, Marina
2015-01-01
We study the main features of the isotropic radial pseudo-Gaussian oscillators spectral properties. This study is made upon the energy levels degeneracy with respect to orbital angular momentum quantum number. In a previous work [6] we have shown that the pseudo-Gaussian oscillators belong to the class of quasi-exactly solvable models and an exact solution has been found
Post-Gaussian Effective Potential of Double sine-Gordon Field
International Nuclear Information System (INIS)
Cai Weiran; Lou Senyue
2005-01-01
In the framework of the functional integral formalism, we calculate the effective potential of the double sine-Gordon (DsG) model up to the second order with an optimized expansion and the Coleman's normal-ordering prescription. Within the range of convergence, we make a comparison among the classical and the effective potential of the first and second order. The numerical analysis shows that the DsG post-Gaussian EP possesses some fine global properties and makes a substantial and a concordant quantum correction to the features of the classical potential.
Gaussian cloning of coherent states with known phases
International Nuclear Information System (INIS)
Alexanian, Moorad
2006-01-01
The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of 2/3. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of 4/5. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier
Forecasts of non-Gaussian parameter spaces using Box-Cox transformations
Joachimi, B.; Taylor, A. N.
2011-09-01
Forecasts of statistical constraints on model parameters using the Fisher matrix abound in many fields of astrophysics. The Fisher matrix formalism involves the assumption of Gaussianity in parameter space and hence fails to predict complex features of posterior probability distributions. Combining the standard Fisher matrix with Box-Cox transformations, we propose a novel method that accurately predicts arbitrary posterior shapes. The Box-Cox transformations are applied to parameter space to render it approximately multivariate Gaussian, performing the Fisher matrix calculation on the transformed parameters. We demonstrate that, after the Box-Cox parameters have been determined from an initial likelihood evaluation, the method correctly predicts changes in the posterior when varying various parameters of the experimental setup and the data analysis, with marginally higher computational cost than a standard Fisher matrix calculation. We apply the Box-Cox-Fisher formalism to forecast cosmological parameter constraints by future weak gravitational lensing surveys. The characteristic non-linear degeneracy between matter density parameter and normalization of matter density fluctuations is reproduced for several cases, and the capabilities of breaking this degeneracy by weak-lensing three-point statistics is investigated. Possible applications of Box-Cox transformations of posterior distributions are discussed, including the prospects for performing statistical data analysis steps in the transformed Gaussianized parameter space.
International Nuclear Information System (INIS)
Allen, Bruce; Creighton, Jolien D.E.; Flanagan, Eanna E.; Romano, Joseph D.
2003-01-01
In a previous paper (paper I), we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by truncating or clipping sample values which lie in those non-Gaussian tails. The methods were derived, in the frequentist framework, by minimizing false alarm probabilities at fixed false detection probability in the limit of weak signals. For stochastic signals, the resulting statistic consisted of a sum of an autocorrelation term and a cross-correlation term; it was necessary to discard 'by hand' the autocorrelation term in order to arrive at the correct, generalized cross-correlation statistic. In the present paper, we present an alternative derivation of the same signal detection techniques from within the Bayesian framework. We compute, for both deterministic and stochastic signals, the probability that a signal is present in the data, in the limit where the signal-to-noise ratio squared per frequency bin is small, where the signal is nevertheless strong enough to be detected (integrated signal-to-noise ratio large compared to 1), and where the total probability in the non-Gaussian tail part of the noise distribution is small. We show that, for each model considered, the resulting probability is to a good approximation a monotonic function of the detection statistic derived in paper I. Moreover, for stochastic signals, the new Bayesian derivation automatically eliminates the problematic autocorrelation term
Analysis of regularized inversion of data corrupted by white Gaussian noise
International Nuclear Information System (INIS)
Kekkonen, Hanne; Lassas, Matti; Siltanen, Samuli
2014-01-01
Tikhonov regularization is studied in the case of linear pseudodifferential operator as the forward map and additive white Gaussian noise as the measurement error. The measurement model for an unknown function u(x) is m(x) = Au(x) + δ ε (x), where δ > 0 is the noise magnitude. If ε was an L 2 -function, Tikhonov regularization gives an estimate T α (m) = u∈H r arg min { ||Au-m|| L 2 2 + α||u|| H r 2 } for u where α = α(δ) is the regularization parameter. Here penalization of the Sobolev norm ||u|| H r covers the cases of standard Tikhonov regularization (r = 0) and first derivative penalty (r = 1). Realizations of white Gaussian noise are almost never in L 2 , but do belong to H s with probability one if s < 0 is small enough. A modification of Tikhonov regularization theory is presented, covering the case of white Gaussian measurement noise. Furthermore, the convergence of regularized reconstructions to the correct solution as δ → 0 is proven in appropriate function spaces using microlocal analysis. The convergence of the related finite-dimensional problems to the infinite-dimensional problem is also analysed. (paper)
International Nuclear Information System (INIS)
Tsuchida, Takahiro; Kimura, Koji
2015-01-01
Equivalent non-Gaussian excitation method is proposed to obtain the moments up to the fourth order of the response of systems under non-Gaussian random excitation. The excitation is prescribed by the probability density and power spectrum. Moment equations for the response can be derived from the stochastic differential equations for the excitation and the system. However, the moment equations are not closed due to the nonlinearity of the diffusion coefficient in the equation for the excitation. In the proposed method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by the second-order polynomial. In order to demonstrate the validity of the method, a linear system to non-Gaussian excitation with generalized Gaussian distribution is analyzed. The results show the method is applicable to non-Gaussian excitation with the widely different kurtosis and bandwidth. (author)
Capeans, M; Mandelli, B
2012-01-01
The importance of the correct gas mixture for the Resistive Plate Chamber (RPC) detector systems is fundamental for their correct and safe operation. A small change in the percentages of the gas mixture components can alter the RPC performance and this will rebound on the data quality in the ALICE, ATLAS and CMS experiments at CERN. A constant monitoring of the gas mixture injected in the RPCs would avoid such kind of problems. A systematic study has been performed to understand RPC performances with several gas mixture compositions and in the presence of common gas impurities. The systematic analysis of several RPC performance parameters in different gas mixtures allows the rapid identification of any variation in the RPC gas mixture. A set-up for the online monitoring of the RPC gas mixture in the LHC gas systems is also proposed.
Primordial non-Gaussianity from LAMOST surveys
International Nuclear Information System (INIS)
Gong Yan; Wang Xin; Chen Xuelei; Zheng Zheng
2010-01-01
The primordial non-Gaussianity (PNG) in the matter density perturbation is a very powerful probe of the physics of the very early Universe. The local PNG can induce a distinct scale-dependent bias on the large scale structure distribution of galaxies and quasars, which could be used for constraining it. We study the detection limits of PNG from the surveys of the LAMOST telescope. The cases of the main galaxy survey, the luminous red galaxy (LRG) survey, and the quasar survey of different magnitude limits are considered. We find that the Main1 sample (i.e. the main galaxy survey which is one magnitude deeper than the SDSS main galaxy survey, or r NL are |f NL | NL | NL | is between 50 and 103, depending on the magnitude limit of the survey. With Planck-like priors on cosmological parameters, the quasar survey with g NL | < 43 (2σ). We also discuss the possibility of further tightening the constraint by using the relative bias method proposed by Seljak.
A Decentralized Receiver in Gaussian Interference
Directory of Open Access Journals (Sweden)
Christian D. Chapman
2018-04-01
Full Text Available Bounds are developed on the maximum communications rate between a transmitter and a fusion node aided by a cluster of distributed receivers with limited resources for cooperation, all in the presence of an additive Gaussian interferer. The receivers cannot communicate with one another and can only convey processed versions of their observations to the fusion center through a Local Array Network (LAN with limited total throughput. The effectiveness of each bound’s approach for mitigating a strong interferer is assessed over a wide range of channels. It is seen that, if resources are shared effectively, even a simple quantize-and-forward strategy can mitigate an interferer 20 dB stronger than the signal in a diverse range of spatially Ricean channels. Monte-Carlo experiments for the bounds reveal that, while achievable rates are stable when varying the receiver’s observed scattered-path to line-of-sight signal power, the receivers must adapt how they share resources in response to this change. The bounds analyzed are proven to be achievable and are seen to be tight with capacity when LAN resources are either ample or limited.
Bayesian nonparametric adaptive control using Gaussian processes.
Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A
2015-03-01
Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.
Gaussian Error Correction of Quantum States in a Correlated Noisy Channel
DEFF Research Database (Denmark)
Lassen, Mikael Østergaard; Berni, Adriano; Madsen, Lars Skovgaard
2013-01-01
Noise is the main obstacle for the realization of fault-tolerant quantum information processing and secure communication over long distances. In this work, we propose a communication protocol relying on simple linear optics that optimally protects quantum states from non-Markovian or correlated...... noise. We implement the protocol experimentally and demonstrate the near-ideal protection of coherent and entangled states in an extremely noisy channel. Since all real-life channels are exhibiting pronounced non-Markovian behavior, the proposed protocol will have immediate implications in improving...... the performance of various quantum information protocols....
Mixtures Estimation and Applications
Mengersen, Kerrie; Titterington, Mike
2011-01-01
This book uses the EM (expectation maximization) algorithm to simultaneously estimate the missing data and unknown parameter(s) associated with a data set. The parameters describe the component distributions of the mixture; the distributions may be continuous or discrete. The editors provide a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions along with MCMC computational methods, together with a range of detailed discussions covering the applications of the methods and features chapters from the leading experts on the subject
Constrained Fisher Scoring for a Mixture of Factor Analyzers
2016-09-01
where ω ∈ [0, 4π). Each observation of the spiral is corrupted by additive white Gaussian noise with unit variance. This model was used in previous works...that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information...from different aspects and then learn a joint statistical model for the object manifold. We employ a mixture of factor analyzers model and derive a
Boltzmann-Gaussian transition under specific noise effect
International Nuclear Information System (INIS)
Anh, Chu Thuy; Lan, Nguyen Tri; Viet, Nguyen Ai
2014-01-01
It is observed that a short time data set of market returns presents almost symmetric Boltzmann distribution whereas a long time data set tends to show a Gaussian distribution. To understand this universal phenomenon, many hypotheses which are spreading in a wide range of interdisciplinary research were proposed. In current work, the effects of background fluctuations on symmetric Boltzmann distribution is investigated. The numerical calculation is performed to show that the Gaussian noise may cause the transition from initial Boltzmann distribution to Gaussian one. The obtained results would reflect non-dynamic nature of the transition under consideration.
Legendre Duality of Spherical and Gaussian Spin Glasses
International Nuclear Information System (INIS)
Genovese, Giuseppe; Tantari, Daniele
2015-01-01
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model
Controllable gaussian-qubit interface for extremal quantum state engineering.
Adesso, Gerardo; Campbell, Steve; Illuminati, Fabrizio; Paternostro, Mauro
2010-06-18
We study state engineering through bilinear interactions between two remote qubits and two-mode gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.
Legendre Duality of Spherical and Gaussian Spin Glasses
Energy Technology Data Exchange (ETDEWEB)
Genovese, Giuseppe, E-mail: giuseppe.genovese@math.uzh.ch [Universität Zürich, Institut für Mathematik (Switzerland); Tantari, Daniele, E-mail: daniele.tantari@sns.it [Scuola Normale Superiore di Pisa, Centro Ennio de Giorgi (Italy)
2015-12-15
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.
Methods to characterize non-Gaussian noise in TAMA
International Nuclear Information System (INIS)
Ando, Masaki; Arai, K; Takahashi, R; Tatsumi, D; Beyersdorf, P; Kawamura, S; Miyoki, S; Mio, N; Moriwaki, S; Numata, K; Kanda, N; Aso, Y; Fujimoto, M-K; Tsubono, K; Kuroda, K
2003-01-01
We present a data characterization method for the main output signal of the interferometric gravitational-wave detector, in particular targeting at effective detection of burst gravitational waves from stellar core collapse. The time scale of non-Gaussian events is evaluated in this method, and events with longer time scale than real signals are rejected as non-Gaussian noises. As a result of data analysis using 1000 h of real data with the interferometric gravitational-wave detector TAMA300, the false-alarm rate was improved 10 3 times with this non-Gaussian noise evaluation and rejection method
Coincidence Imaging and interference with coherent Gaussian beams
Institute of Scientific and Technical Information of China (English)
CAI Yang-jian; ZHU Shi-yao
2006-01-01
we present a theoretical study of coincidence imaging and interference with coherent Gaussian beams The equations for the coincidence image formation and interference fringes are derived,from which it is clear that the imaging is due to the corresponding focusing in the two paths .The quality and visibility of the images and fringes can be high simultaneously.The nature of the coincidence imaging and interference between quantum entangled photon pairs and coherent Gaussian beams are different .The coincidence image with coherent Gaussian beams is due to intensity-intensity correspondence,a classical nature,while that with entangled photon pairs is due to the amplitude correlation a quantum nature.
Quantum Teamwork for Unconditional Multiparty Communication with Gaussian States
Zhang, Jing; Adesso, Gerardo; Xie, Changde; Peng, Kunchi
2009-08-01
We demonstrate the capability of continuous variable Gaussian states to communicate multipartite quantum information. A quantum teamwork protocol is presented according to which an arbitrary possibly entangled multimode state can be faithfully teleported between two teams each comprising many cooperative users. We prove that N-mode Gaussian weighted graph states exist for arbitrary N that enable unconditional quantum teamwork implementations for any arrangement of the teams. These perfect continuous variable maximally multipartite entangled resources are typical among pure Gaussian states and are unaffected by the entanglement frustration occurring in multiqubit states.
A note on moving average models for Gaussian random fields
DEFF Research Database (Denmark)
Hansen, Linda Vadgård; Thorarinsdottir, Thordis L.
The class of moving average models offers a flexible modeling framework for Gaussian random fields with many well known models such as the Matérn covariance family and the Gaussian covariance falling under this framework. Moving average models may also be viewed as a kernel smoothing of a Lévy...... basis, a general modeling framework which includes several types of non-Gaussian models. We propose a new one-parameter spatial correlation model which arises from a power kernel and show that the associated Hausdorff dimension of the sample paths can take any value between 2 and 3. As a result...
Nielsen, Frank
2016-12-09
Information-theoreticmeasures, such as the entropy, the cross-entropy and the Kullback-Leibler divergence between two mixture models, are core primitives in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using costly Monte Carlo stochastic integration, approximated or bounded using various techniques. We present a fast and generic method that builds algorithmically closed-form lower and upper bounds on the entropy, the cross-entropy, the Kullback-Leibler and the α-divergences of mixtures. We illustrate the versatile method by reporting our experiments for approximating the Kullback-Leibler and the α-divergences between univariate exponential mixtures, Gaussian mixtures, Rayleigh mixtures and Gamma mixtures.
International Nuclear Information System (INIS)
Tsuchida, Takahiro; Kimura, Koji
2016-01-01
Equivalent non-Gaussian excitation method is proposed to obtain the response moments up to the 4th order of dynamic systems under non-Gaussian random excitation. The non-Gaussian excitation is prescribed by the probability density and the power spectrum, and is described by an Ito stochastic differential equation. Generally, moment equations for the response, which are derived from the governing equations for the excitation and the system, are not closed due to the nonlinearity of the diffusion coefficient in the equation for the excitation even though the system is linear. In the equivalent non-Gaussian excitation method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by a quadratic polynomial. In numerical examples, a linear system subjected to nonGaussian excitations with bimodal and Rayleigh distributions is analyzed by using the present method. The results show that the method yields the variance, skewness and kurtosis of the response with high accuracy for non-Gaussian excitation with the widely different probability densities and bandwidth. The statistical moments of the equivalent non-Gaussian excitation are also investigated to describe the feature of the method. (paper)
Feature Matching for SAR and Optical Images Based on Gaussian-Gamma-shaped Edge Strength Map
Directory of Open Access Journals (Sweden)
CHEN Min
2016-03-01
Full Text Available A matching method for SAR and optical images, robust to pixel noise and nonlinear grayscale differences, is presented. Firstly, a rough correction to eliminate rotation and scale change between images is performed. Secondly, features robust to speckle noise of SAR image are detected by improving the original phase congruency based method. Then, feature descriptors are constructed on the Gaussian-Gamma-shaped edge strength map according to the histogram of oriented gradient pattern. Finally, descriptor similarity and geometrical relationship are combined to constrain the matching processing.The experimental results demonstrate that the proposed method provides significant improvement in correct matches number and image registration accuracy compared with other traditional methods.
GOOS, Peter; JONES, Bradley; SYAFITRI, Utami
2013-01-01
In mixture experiments, the factors under study are proportions of the ingredients of a mixture. The special nature of the factors in a mixture experiment necessitates specific types of regression models, and specific types of experimental designs. Although mixture experiments usually are intended to predict the response(s) for all possible formulations of the mixture and to identify optimal proportions for each of the ingredients, little research has been done concerning their I-optimal desi...
Groten, J.P.
2000-01-01
Drinking water can be considered as a complex mixture that consists of tens, hundreds or thousands of chemicals of which the composition is qualitatively and quantitatively not fully known. From a public health point of view it is most relevant to answer the question of whether chemicals in drinking
Optimal multicopy asymmetric Gaussian cloning of coherent states
Fiurášek, Jaromír; Cerf, Nicolas J.
2007-05-01
We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward.
Making tensor factorizations robust to non-gaussian noise.
Energy Technology Data Exchange (ETDEWEB)
Chi, Eric C. (Rice University, Houston, TX); Kolda, Tamara Gibson
2011-03-01
Tensors are multi-way arrays, and the CANDECOMP/PARAFAC (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of independent and identically distributed (i.i.d.) Gaussian noise. We demonstrate that this loss function can be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization (MM) algorithm for fitting a CP model using our proposed loss function (CPAL1) and compare its performance to the workhorse algorithm for fitting CP models, CP alternating least squares (CPALS).
Simple form for the Gaussian equations in curved space
International Nuclear Information System (INIS)
Mazzitelli, F.D.; Paz, J.P.
1988-01-01
We show that the variational Gaussian equations for λphi 4 theory in an arbitrary background gravitational field admit a simple form, which allows the use of a Schwinger-DeWitt-type expansion in order to renormalize them
Optimal multicopy asymmetric Gaussian cloning of coherent states
International Nuclear Information System (INIS)
Fiurasek, Jaromir; Cerf, Nicolas J.
2007-01-01
We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward
Quantifying entanglement in two-mode Gaussian states
Tserkis, Spyros; Ralph, Timothy C.
2017-12-01
Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography, and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure that is straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.
Super-resolving random-Gaussian apodized photon sieve.
Sabatyan, Arash; Roshaninejad, Parisa
2012-09-10
A novel apodized photon sieve is presented in which random dense Gaussian distribution is implemented to modulate the pinhole density in each zone. The random distribution in dense Gaussian distribution causes intrazone discontinuities. Also, the dense Gaussian distribution generates a substantial number of pinholes in order to form a large degree of overlap between the holes in a few innermost zones of the photon sieve; thereby, clear zones are formed. The role of the discontinuities on the focusing properties of the photon sieve is examined as well. Analysis shows that secondary maxima have evidently been suppressed, transmission has increased enormously, and the central maxima width is approximately unchanged in comparison to the dense Gaussian distribution. Theoretical results have been completely verified by experiment.
Mimicking an amplitude damping channel for Laguerre Gaussian Modes
CSIR Research Space (South Africa)
Dudley, Angela L
2010-10-01
Full Text Available An amplitude damping channel for Laguerre-Gaussian (LG) modes is presented. Experimentally the action of the channel on LG modes is in good agreement with that predicted theoretically....
Scalable Gaussian Processes and the search for exoplanets
CERN. Geneva
2015-01-01
Gaussian Processes are a class of non-parametric models that are often used to model stochastic behavior in time series or spatial data. A major limitation for the application of these models to large datasets is the computational cost. The cost of a single evaluation of the model likelihood scales as the third power of the number of data points. In the search for transiting exoplanets, the datasets of interest have tens of thousands to millions of measurements with uneven sampling, rendering naive application of a Gaussian Process model impractical. To attack this problem, we have developed robust approximate methods for Gaussian Process regression that can be applied at this scale. I will describe the general problem of Gaussian Process regression and offer several applicable use cases. Finally, I will present our work on scaling this model to the exciting field of exoplanet discovery and introduce a well-tested open source implementation of these new methods.
Schweiner, Frank; Laturner, Jeanine; Main, Jörg; Wunner, Günter
2017-11-01
Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) have analytical formulas for the level spacing distribution function been derived within random matrix theory. We investigate arbitrary crossovers in the triangle between all three statistics. To this aim we propose an according formula for the level spacing distribution function depending on two parameters. Comparing the behavior of our formula for the special cases of P→GUE, P→GOE, and GOE→GUE with the results from random matrix theory, we prove that these crossovers are described reasonably. Recent investigations by F. Schweiner et al. [Phys. Rev. E 95, 062205 (2017)2470-004510.1103/PhysRevE.95.062205] have shown that the Hamiltonian of magnetoexcitons in cubic semiconductors can exhibit all three statistics in dependence on the system parameters. Evaluating the numerical results for magnetoexcitons in dependence on the excitation energy and on a parameter connected with the cubic valence band structure and comparing the results with the formula proposed allows us to distinguish between regular and chaotic behavior as well as between existent or broken antiunitary symmetries. Increasing one of the two parameters, transitions between different crossovers, e.g., from the P→GOE to the P→GUE crossover, are observed and discussed.
Energy Technology Data Exchange (ETDEWEB)
Kenfack, Lionel Tenemeza, E-mail: kenfacklionel300@gmail.com [Mesoscopic and Multilayer Structure Laboratory, Department of Physics, Faculty of Science, University of Dschang, PO Box: 67 Dschang (Cameroon); Tchoffo, Martin; Fai, Lukong Cornelius [Mesoscopic and Multilayer Structure Laboratory, Department of Physics, Faculty of Science, University of Dschang, PO Box: 67 Dschang (Cameroon); Fouokeng, Georges Collince [Mesoscopic and Multilayer Structure Laboratory, Department of Physics, Faculty of Science, University of Dschang, PO Box: 67 Dschang (Cameroon); Laboratoire de Génie des Matériaux, Pôle Recherche-Innovation-Entrepreneuriat (PRIE), Institut Universitaire de la Côte, BP 3001 Douala (Cameroon)
2017-04-15
We address the entanglement dynamics of a three-qubit system interacting with a classical fluctuating environment described either by a Gaussian or non-Gaussian noise in three different configurations namely: common, independent and mixed environments. Specifically, we focus on the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise (RTN). The qubits are prepared in a state composed of a Greenberger-Horne-Zeilinger (GHZ) and a W state. With the help of the tripartite negativity, we show that the entanglement evolution is not only affected by the type of system-environment coupling but also by the kind and the memory properties of the considered noise. We also compared the dynamics induced by the two kinds of noise and we find that even if both noises have a Lorentzian spectrum, the effects of the OU noise cannot be in a simple way deduced from those of the RTN and vice-versa. In addition, we show that the entanglement can be indefinitely preserved when the qubits are coupled to the environmental noise in a common environment (CE). Finally, the presence or absence of peculiar phenomena such as entanglement revivals (ER) and entanglement sudden death (ESD) is observed.
International Nuclear Information System (INIS)
Kenfack, Lionel Tenemeza; Tchoffo, Martin; Fai, Lukong Cornelius; Fouokeng, Georges Collince
2017-01-01
We address the entanglement dynamics of a three-qubit system interacting with a classical fluctuating environment described either by a Gaussian or non-Gaussian noise in three different configurations namely: common, independent and mixed environments. Specifically, we focus on the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise (RTN). The qubits are prepared in a state composed of a Greenberger-Horne-Zeilinger (GHZ) and a W state. With the help of the tripartite negativity, we show that the entanglement evolution is not only affected by the type of system-environment coupling but also by the kind and the memory properties of the considered noise. We also compared the dynamics induced by the two kinds of noise and we find that even if both noises have a Lorentzian spectrum, the effects of the OU noise cannot be in a simple way deduced from those of the RTN and vice-versa. In addition, we show that the entanglement can be indefinitely preserved when the qubits are coupled to the environmental noise in a common environment (CE). Finally, the presence or absence of peculiar phenomena such as entanglement revivals (ER) and entanglement sudden death (ESD) is observed.
Non-gaussianity versus nonlinearity of cosmological perturbations.
Verde, L
2001-06-01
Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.
GAUSSIAN 76: an ab initio molecular orbital program
International Nuclear Information System (INIS)
Binkley, J.S.; Whiteside, R.; Hariharan, P.C.; Seeger, R.; Hehre, W.J.; Lathan, W.A.; Newton, M.D.; Ditchfield, R.; Pople, J.A.
Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally for easy use. Closed shell (RHF) or unrestricted open shell (UHF) wave functions can be obtained. Facilities are provided for geometry optimization to potential minima and for limited potential surface scans
Gaussian Process Regression for WDM System Performance Prediction
DEFF Research Database (Denmark)
Wass, Jesper; Thrane, Jakob; Piels, Molly
2017-01-01
Gaussian process regression is numerically and experimentally investigated to predict the bit error rate of a 24 x 28 CiBd QPSK WDM system. The proposed method produces accurate predictions from multi-dimensional and sparse measurement data.......Gaussian process regression is numerically and experimentally investigated to predict the bit error rate of a 24 x 28 CiBd QPSK WDM system. The proposed method produces accurate predictions from multi-dimensional and sparse measurement data....
Revisiting non-Gaussianity from non-attractor inflation models
Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei
2018-05-01
Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition—such as in the case of smooth transition or some sharp transition scenarios—the Script O(1) local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.
Identification and estimation of non-Gaussian structural vector autoregressions
DEFF Research Database (Denmark)
Lanne, Markku; Meitz, Mika; Saikkonen, Pentti
-Gaussian components is, without any additional restrictions, identified and leads to (essentially) unique impulse responses. We also introduce an identification scheme under which the maximum likelihood estimator of the non-Gaussian SVAR model is consistent and asymptotically normally distributed. As a consequence......, additional economic identifying restrictions can be tested. In an empirical application, we find a negative impact of a contractionary monetary policy shock on financial markets, and clearly reject the commonly employed recursive identifying restrictions....
Current inversion induced by colored non-Gaussian noise
International Nuclear Information System (INIS)
Bag, Bidhan Chandra; Hu, Chin-Kung
2009-01-01
We study a stochastic process driven by colored non-Gaussian noises. For the flashing ratchet model we find that there is a current inversion in the variation of the current with the half-cycle period which accounts for the potential on–off operation. The current inversion almost disappears if one switches from non-Gaussian (NG) to Gaussian (G) noise. We also find that at low value of the asymmetry parameter of the potential the mobility controlled current is more negative for NG noise as compared to G noise. But at large magnitude of the parameter the diffusion controlled positive current is higher for the former than for the latter. On increasing the noise correlation time (τ), keeping the noise strength fixed, the mean velocity of a particle first increases and then decreases after passing through a maximum if the noise is non-Gaussian. For Gaussian noise, the current monotonically decreases. The current increases with the noise parameter p, 0< p<5/3, which is 1 for Gaussian noise
Passivity and practical work extraction using Gaussian operations
International Nuclear Information System (INIS)
Brown, Eric G; Huber, Marcus; Friis, Nicolai
2016-01-01
Quantum states that can yield work in a cyclical Hamiltonian process form one of the primary resources in the context of quantum thermodynamics. Conversely, states whose average energy cannot be lowered by unitary transformations are called passive. However, while work may be extracted from non-passive states using arbitrary unitaries, the latter may be hard to realize in practice. It is therefore pertinent to consider the passivity of states under restricted classes of operations that can be feasibly implemented. Here, we ask how restrictive the class of Gaussian unitaries is for the task of work extraction. We investigate the notion of Gaussian passivity, that is, we present necessary and sufficient criteria identifying all states whose energy cannot be lowered by Gaussian unitaries. For all other states we give a prescription for the Gaussian operations that extract the maximal amount of energy. Finally, we show that the gap between passivity and Gaussian passivity is maximal, i.e., Gaussian-passive states may still have a maximal amount of energy that is extractable by arbitrary unitaries, even under entropy constraints. (paper)
Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin
2018-02-01
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.
Non-Gaussianity from inflation: theory and observations
Bartolo, N.; Komatsu, E.; Matarrese, S.; Riotto, A.
2004-11-01
This is a review of models of inflation and of their predictions for the primordial non-Gaussianity in the density perturbations which are thought to be at the origin of structures in the Universe. Non-Gaussianity emerges as a key observable to discriminate among competing scenarios for the generation of cosmological perturbations and is one of the primary targets of present and future Cosmic Microwave Background satellite missions. We give a detailed presentation of the state-of-the-art of the subject of non-Gaussianity, both from the theoretical and the observational point of view, and provide all the tools necessary to compute at second order in perturbation theory the level of non-Gaussianity in any model of cosmological perturbations. We discuss the new wave of models of inflation, which are firmly rooted in modern particle physics theory and predict a significant amount of non-Gaussianity. The review is addressed to both astrophysicists and particle physicists and contains useful tables which summarize the theoretical and observational results regarding non-Gaussianity.
Back to Normal! Gaussianizing posterior distributions for cosmological probes
Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.
2014-05-01
We present a method to map multivariate non-Gaussian posterior probability densities into Gaussian ones via nonlinear Box-Cox transformations, and generalizations thereof. This is analogous to the search for normal parameters in the CMB, but can in principle be applied to any probability density that is continuous and unimodal. The search for the optimally Gaussianizing transformation amongst the Box-Cox family is performed via a maximum likelihood formalism. We can judge the quality of the found transformation a posteriori: qualitatively via statistical tests of Gaussianity, and more illustratively by how well it reproduces the credible regions. The method permits an analytical reconstruction of the posterior from a sample, e.g. a Markov chain, and simplifies the subsequent joint analysis with other experiments. Furthermore, it permits the characterization of a non-Gaussian posterior in a compact and efficient way. The expression for the non-Gaussian posterior can be employed to find analytic formulae for the Bayesian evidence, and consequently be used for model comparison.
Merging Mixture Components for Cell Population Identification in Flow Cytometry
Directory of Open Access Journals (Sweden)
Greg Finak
2009-01-01
Full Text Available We present a framework for the identification of cell subpopulations in flow cytometry data based on merging mixture components using the flowClust methodology. We show that the cluster merging algorithm under our framework improves model fit and provides a better estimate of the number of distinct cell subpopulations than either Gaussian mixture models or flowClust, especially for complicated flow cytometry data distributions. Our framework allows the automated selection of the number of distinct cell subpopulations and we are able to identify cases where the algorithm fails, thus making it suitable for application in a high throughput FCM analysis pipeline. Furthermore, we demonstrate a method for summarizing complex merged cell subpopulations in a simple manner that integrates with the existing flowClust framework and enables downstream data analysis. We demonstrate the performance of our framework on simulated and real FCM data. The software is available in the flowMerge package through the Bioconductor project.
Statistical-mechanics analysis of Gaussian labeled-unlabeled classification problems
International Nuclear Information System (INIS)
Tanaka, Toshiyuki
2013-01-01
The labeled-unlabeled classification problem in semi-supervised learning is studied via statistical-mechanics approach. We analytically investigate performance of a learner with an equal-weight mixture of two symmetrically-located Gaussians, performing posterior mean estimation of the parameter vector on the basis of a dataset consisting of labeled and unlabeled data generated from the same probability model as that assumed by the learner. Under the assumption of replica symmetry, we have analytically obtained a set of saddle-point equations, which allows us to numerically evaluate performance of the learner. On the basis of the analytical result we have observed interesting phenomena, in particular the coexistence of good and bad solutions, which may happen when the number of unlabeled data is relatively large compared with that of labeled data
Collective dynamics in dense fluid mixtures
International Nuclear Information System (INIS)
Sinha, S.
1992-01-01
This thesis deals with the short wavelength collective dynamics of dense binary fluid mixtures. The analysis shows that at the level of linearized generalized hydrodynamics, the longitudinal modes of the system separates essentially into two parts - one involves the coupling of partial density fluctuations of the two species and the other involves coupling of longitudinal momentum and temperature fluctuations. The authors have shown that the coupling of longitudinal momentum and temperature fluctuations leads to an adequate description of sound propagation in such systems. In particular, they show that structural disorder controls the trapping of sound waves in dense mixtures. The coupling of the partial density fluctuations of the two species leads to a simple description of the partial dynamic structure factors. The results are in agreement with the molecular dynamics simulations of soft sphere mixtures. The partial density fluctuations are the slowest decaying fluctuations on molecular length scales and it turns out that nonlinear coupling of these slow modes leads to important corrections to the long time behavior of the time correlation functions determining the shear viscosity in dense mixtures
Predicting diffusivities in dense fluid mixtures
Directory of Open Access Journals (Sweden)
C. DARIVA
1999-09-01
Full Text Available In this work the Enskog solution of the Boltzmann equation, as corrected by Speedy, together with the Weeks-Chandler-Andersen (WCA perturbation theory of liquids is employed in correlating and predicting self-diffusivities of dense fluids. Afterwards this theory is used to estimate mutual diffusion coefficients of solutes at infinite dilution in sub and supercritical solvents. We have also investigated the behavior of Fick diffusion coefficients in the proximity of a binary vapor-liquid critical point since this subject is of great interest for extraction purposes. The approach presented here, which makes use of a density and temperature dependent hard-sphere diameter, is shown to be excellent for predicting diffusivities in dense pure fluids and fluid mixtures. The calculations involved highly nonideal mixtures as well as systems with high molecular asymmetry. The predicted diffusivities are in good agreement with the experimental data for the pure and binary systems. The methodology proposed here makes only use of pure component information and density of mixtures. The simple algebraic relations are proposed without any binary adjustable parameters and can be readily used for estimating diffusivities in multicomponent mixtures.
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Mixture based outlier filtration
Czech Academy of Sciences Publication Activity Database
Pecherková, Pavla; Nagy, Ivan
2006-01-01
Roč. 46, č. 2 (2006), s. 30-35 ISSN 1210-2709 R&D Projects: GA MŠk 1M0572; GA MDS 1F43A/003/120 Institutional research plan: CEZ:AV0Z10750506 Keywords : data filtration * system modelling * mixture models Subject RIV: BD - Theory of Information http://library.utia.cas.cz/prace/20060165.pdf
International Nuclear Information System (INIS)
Chu, Jun-Uk; Song, Kang-Il; Han, Sungmin; Suh, Jun-Kyo Francis; Choi, Kuiwon; Youn, Inchan; Lee, Soo Hyun; Kang, Ji Yoon; Hwang, Dosik
2013-01-01
Cutaneous afferent activities recorded by a nerve cuff electrode have been used to detect the stance phase in a functional electrical stimulation system for foot drop correction. However, the implantation procedure was difficult, as the cuff electrode had to be located on the distal branches of a multi-fascicular nerve to exclude muscle afferent and efferent activities. This paper proposes a new gait phase detection scheme that can be applied to a proximal nerve root that includes cutaneous afferent fibers as well as muscle afferent and efferent fibers. To test the feasibility of this scheme, electroneurogram (ENG) signals were measured from the rat sciatic nerve during treadmill walking at several speeds, and the signal properties of the sciatic nerve were analyzed for a comparison with kinematic data from the ankle joint. On the basis of these experiments, a wavelet packet transform was tested to define a feature vector from the sciatic ENG signals according to the gait phases. We also propose a Gaussian mixture model (GMM) classifier and investigate whether it could be used successfully to discriminate feature vectors into the stance and swing phases. In spite of no significant differences in the rectified bin-integrated values between the stance and swing phases, the sciatic ENG signals could be reliably classified using the proposed wavelet packet transform and GMM classification methods. (paper)
Wen, Xian-Huan; Gómez-Hernández, J. Jaime
1998-03-01
The macrodispersion of an inert solute in a 2-D heterogeneous porous media is estimated numerically in a series of fields of varying heterogeneity. Four different random function (RF) models are used to model log-transmissivity (ln T) spatial variability, and for each of these models, ln T variance is varied from 0.1 to 2.0. The four RF models share the same univariate Gaussian histogram and the same isotropic covariance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme values (both high and low) are spatially uncorrelated. The other three models are non-multi-Gaussian: model B with high connectivity of high extreme values, model C with high connectivity of low extreme values, and model D with high connectivities of both high and low extreme values. Residence time distributions (RTDs) and macrodispersivities (longitudinal and transverse) are computed on ln T fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RTDs and macrodispersivities for the multi-Gaussian model are in good agreement with analytically derived values using first-order theories for log-transmissivity variance up to 2.0. The results from the non-multi-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when ln T variance is small. RTDs in non-multi-Gaussian realizations with high connectivity at high extreme values display earlier breakthrough than in multi-Gaussian realizations, whereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian realizations are, in general, larger than
Mixture for plugging absorption zones
Energy Technology Data Exchange (ETDEWEB)
Sitinkov, G V; Kovalenko, N G; Makarov, L V; Zinnatulchin, Ts Kh
1981-01-17
A mixture is proposed for plugging absorption zones. The mixture contains synthetic polymer and a solvent. So as to increase the penetrability of the mixture through a reduction in its viscosity and an increase in insulation properties, the compound contains either Capron or Neilon as the synthetic polyamide resin polmyer, and concentrated chloride as the solvent. The mixture is prepared in a special AzINMASh-30 unit (acid cart). After the mixture has been produced, it is injected into the borehole by means of an acid cart pump. So as to prevent coaggulation at the point when the mixture in injected into the stratum through tubes, the mixture is placed betwen chemically inert fluids, for example, a clay mortar. The inert and compressed fluids are injected by means of a cementing unit. The entire process of production and application of the mixture is simple and fully automated through the use of well-known equipment.
Bianchi, Davide; Chiesa, Matteo; Guzzo, Luigi
2015-01-01
As a step towards a more accurate modelling of redshift-space distortions (RSD) in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation r, such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean μ and dispersion σ. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distortions on all scales, fully capturing the overall linear and non-linear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of RSD is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. We also show how this description naturally allows for the Taylor expansion of 1 + ξS(s) around 1 + ξR(r), which leads to the Kaiser linear formula when truncated to second order, explicating its connection with the moments of the velocity distribution functions. More work is needed, but these results indicate a very promising path to make definitive progress in our programme to improve RSD estimators.
Cecinati, F.; Wani, O.; Rico-Ramirez, M. A.
2017-11-01
Merging radar and rain gauge rainfall data is a technique used to improve the quality of spatial rainfall estimates and in particular the use of Kriging with External Drift (KED) is a very effective radar-rain gauge rainfall merging technique. However, kriging interpolations assume Gaussianity of the process. Rainfall has a strongly skewed, positive, probability distribution, characterized by a discontinuity due to intermittency. In KED rainfall residuals are used, implicitly calculated as the difference between rain gauge data and a linear function of the radar estimates. Rainfall residuals are non-Gaussian as well. The aim of this work is to evaluate the impact of applying KED to non-Gaussian rainfall residuals, and to assess the best techniques to improve Gaussianity. We compare Box-Cox transformations with λ parameters equal to 0.5, 0.25, and 0.1, Box-Cox with time-variant optimization of λ, normal score transformation, and a singularity analysis technique. The results suggest that Box-Cox with λ = 0.1 and the singularity analysis is not suitable for KED. Normal score transformation and Box-Cox with optimized λ, or λ = 0.25 produce satisfactory results in terms of Gaussianity of the residuals, probability distribution of the merged rainfall products, and rainfall estimate quality, when validated through cross-validation. However, it is observed that Box-Cox transformations are strongly dependent on the temporal and spatial variability of rainfall and on the units used for the rainfall intensity. Overall, applying transformations results in a quantitative improvement of the rainfall estimates only if the correct transformations for the specific data set are used.
International Nuclear Information System (INIS)
Li Zhe; Liu Min; Shi Rui; Wu Xuemei; Tuo Xianguo
2012-01-01
Background: Non-standard analysis (NSA) technique is one of the most important development directions of energy dispersive X-ray fluorescence (EDXRF). Purpose: This NSA technique is mainly based on Monte Carlo (MC) simulation and full energy peak broadening, which were studied preliminarily in this paper. Methods: A kind of MC model was established for Si-PIN based EDXRF setup, and the flux spectra were obtained for iron ore sample. Finally, the flux spectra were broadened by Gaussian broaden parameters calculated by a new method proposed in this paper, and the broadened spectra were compared with measured energy spectra. Results: MC method can be used to simulate EDXRF measurement, and can correct the matrix effects among elements automatically. Peak intensities can be obtained accurately by using the proposed Gaussian broaden technique. Conclusions: This study provided a key technique for EDXRF to achieve advanced NSA technology. (authors)
Separating Underdetermined Convolutive Speech Mixtures
DEFF Research Database (Denmark)
Pedersen, Michael Syskind; Wang, DeLiang; Larsen, Jan
2006-01-01
a method for underdetermined blind source separation of convolutive mixtures. The proposed framework is applicable for separation of instantaneous as well as convolutive speech mixtures. It is possible to iteratively extract each speech signal from the mixture by combining blind source separation...
Mixtures of truncated basis functions
DEFF Research Database (Denmark)
Langseth, Helge; Nielsen, Thomas Dyhre; Rumí, Rafael
2012-01-01
In this paper we propose a framework, called mixtures of truncated basis functions (MoTBFs), for representing general hybrid Bayesian networks. The proposed framework generalizes both the mixture of truncated exponentials (MTEs) framework and the mixture of polynomials (MoPs) framework. Similar t...
Poisson–Gaussian Noise Analysis and Estimation for Low-Dose X-ray Images in the NSCT Domain
Lee, Sangyoon; Lee, Min Seok; Kang, Moon Gi
2018-01-01
The noise distribution of images obtained by X-ray sensors in low-dosage situations can be analyzed using the Poisson and Gaussian mixture model. Multiscale conversion is one of the most popular noise reduction methods used in recent years. Estimation of the noise distribution of each subband in the multiscale domain is the most important factor in performing noise reduction, with non-subsampled contourlet transform (NSCT) representing an effective method for scale and direction decomposition. In this study, we use artificially generated noise to analyze and estimate the Poisson–Gaussian noise of low-dose X-ray images in the NSCT domain. The noise distribution of the subband coefficients is analyzed using the noiseless low-band coefficients and the variance of the noisy subband coefficients. The noise-after-transform also follows a Poisson–Gaussian distribution, and the relationship between the noise parameters of the subband and the full-band image is identified. We then analyze noise of actual images to validate the theoretical analysis. Comparison of the proposed noise estimation method with an existing noise reduction method confirms that the proposed method outperforms traditional methods. PMID:29596335
Poisson-Gaussian Noise Analysis and Estimation for Low-Dose X-ray Images in the NSCT Domain.
Lee, Sangyoon; Lee, Min Seok; Kang, Moon Gi
2018-03-29
The noise distribution of images obtained by X-ray sensors in low-dosage situations can be analyzed using the Poisson and Gaussian mixture model. Multiscale conversion is one of the most popular noise reduction methods used in recent years. Estimation of the noise distribution of each subband in the multiscale domain is the most important factor in performing noise reduction, with non-subsampled contourlet transform (NSCT) representing an effective method for scale and direction decomposition. In this study, we use artificially generated noise to analyze and estimate the Poisson-Gaussian noise of low-dose X-ray images in the NSCT domain. The noise distribution of the subband coefficients is analyzed using the noiseless low-band coefficients and the variance of the noisy subband coefficients. The noise-after-transform also follows a Poisson-Gaussian distribution, and the relationship between the noise parameters of the subband and the full-band image is identified. We then analyze noise of actual images to validate the theoretical analysis. Comparison of the proposed noise estimation method with an existing noise reduction method confirms that the proposed method outperforms traditional methods.
Capacity and optimal collusion attack channels for Gaussian fingerprinting games
Wang, Ying; Moulin, Pierre
2007-02-01
In content fingerprinting, the same media covertext - image, video, audio, or text - is distributed to many users. A fingerprint, a mark unique to each user, is embedded into each copy of the distributed covertext. In a collusion attack, two or more users may combine their copies in an attempt to "remove" their fingerprints and forge a pirated copy. To trace the forgery back to members of the coalition, we need fingerprinting codes that can reliably identify the fingerprints of those members. Researchers have been focusing on designing or testing fingerprints for Gaussian host signals and the mean square error (MSE) distortion under some classes of collusion attacks, in terms of the detector's error probability in detecting collusion members. For example, under the assumptions of Gaussian fingerprints and Gaussian attacks (the fingerprinted signals are averaged and then the result is passed through a Gaussian test channel), Moulin and Briassouli1 derived optimal strategies in a game-theoretic framework that uses the detector's error probability as the performance measure for a binary decision problem (whether a user participates in the collusion attack or not); Stone2 and Zhao et al. 3 studied average and other non-linear collusion attacks for Gaussian-like fingerprints; Wang et al. 4 stated that the average collusion attack is the most efficient one for orthogonal fingerprints; Kiyavash and Moulin 5 derived a mathematical proof of the optimality of the average collusion attack under some assumptions. In this paper, we also consider Gaussian cover signals, the MSE distortion, and memoryless collusion attacks. We do not make any assumption about the fingerprinting codes used other than an embedding distortion constraint. Also, our only assumptions about the attack channel are an expected distortion constraint, a memoryless constraint, and a fairness constraint. That is, the colluders are allowed to use any arbitrary nonlinear strategy subject to the above
Generation of Quasi-Gaussian Pulses Based on Correlation Techniques
Directory of Open Access Journals (Sweden)
POHOATA, S.
2012-02-01
Full Text Available The Gaussian pulses have been mostly used within communications, where some applications can be emphasized: mobile telephony (GSM, where GMSK signals are used, as well as the UWB communications, where short-period pulses based on Gaussian waveform are generated. Since the Gaussian function signifies a theoretical concept, which cannot be accomplished from the physical point of view, this should be expressed by using various functions, able to determine physical implementations. New techniques of generating the Gaussian pulse responses of good precision are approached, proposed and researched in this paper. The second and third order derivatives with regard to the Gaussian pulse response are accurately generated. The third order derivates is composed of four individual rectangular pulses of fixed amplitudes, being easily to be generated by standard techniques. In order to generate pulses able to satisfy the spectral mask requirements, an adequate filter is necessary to be applied. This paper emphasizes a comparative analysis based on the relative error and the energy spectra of the proposed pulses.
Gaussianization for fast and accurate inference from cosmological data
Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.
2016-06-01
We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box-Cox transformations and generalizations thereof. This permits an analytical reconstruction of the posterior from a point sample, like a Markov chain, and simplifies the subsequent joint analysis with other experiments. This way, a multivariate posterior density can be reported efficiently, by compressing the information contained in Markov Chain Monte Carlo samples. Further, the model evidence integral (I.e. the marginal likelihood) can be computed analytically. This method is analogous to the search for normal parameters in the cosmic microwave background, but is more general. The search for the optimally Gaussianizing transformation is performed computationally through a maximum-likelihood formalism; its quality can be judged by how well the credible regions of the posterior are reproduced. We demonstrate that our method outperforms kernel density estimates in this objective. Further, we select marginal posterior samples from Planck data with several distinct strongly non-Gaussian features, and verify the reproduction of the marginal contours. To demonstrate evidence computation, we Gaussianize the joint distribution of data from weak lensing and baryon acoustic oscillations, for different cosmological models, and find a preference for flat Λcold dark matter. Comparing to values computed with the Savage-Dickey density ratio, and Population Monte Carlo, we find good agreement of our method within the spread of the other two.
Non-Gaussian Methods for Causal Structure Learning.
Shimizu, Shohei
2018-05-22
Causal structure learning is one of the most exciting new topics in the fields of machine learning and statistics. In many empirical sciences including prevention science, the causal mechanisms underlying various phenomena need to be studied. Nevertheless, in many cases, classical methods for causal structure learning are not capable of estimating the causal structure of variables. This is because it explicitly or implicitly assumes Gaussianity of data and typically utilizes only the covariance structure. In many applications, however, non-Gaussian data are often obtained, which means that more information may be contained in the data distribution than the covariance matrix is capable of containing. Thus, many new methods have recently been proposed for using the non-Gaussian structure of data and inferring the causal structure of variables. This paper introduces prevention scientists to such causal structure learning methods, particularly those based on the linear, non-Gaussian, acyclic model known as LiNGAM. These non-Gaussian data analysis tools can fully estimate the underlying causal structures of variables under assumptions even in the presence of unobserved common causes. This feature is in contrast to other approaches. A simulated example is also provided.
Consistency relations for sharp inflationary non-Gaussian features
Energy Technology Data Exchange (ETDEWEB)
Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Blanco Encalada 2008, Santiago (Chile); Soto, Alex, E-mail: sander.mooij@ing.uchile.cl, E-mail: gpalmaquilod@ing.uchile.cl, E-mail: gpanotop@ing.uchile.cl, E-mail: gatogeno@gmail.com [Departamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago (Chile)
2016-09-01
If cosmic inflation suffered tiny time-dependent deviations from the slow-roll regime, these would induce the existence of small scale-dependent features imprinted in the primordial spectra, with their shapes and sizes revealing information about the physics that produced them. Small sharp features could be suppressed at the level of the two-point correlation function, making them undetectable in the power spectrum, but could be amplified at the level of the three-point correlation function, offering us a window of opportunity to uncover them in the non-Gaussian bispectrum. In this article, we show that sharp features may be analyzed using only data coming from the three point correlation function parametrizing primordial non-Gaussianity. More precisely, we show that if features appear in a particular non-Gaussian triangle configuration (e.g. equilateral, folded, squeezed), these must reappear in every other configuration according to a specific relation allowing us to correlate features across the non-Gaussian bispectrum. As a result, we offer a method to study scale-dependent features generated during inflation that depends only on data coming from measurements of non-Gaussianity, allowing us to omit data from the power spectrum.
Consistency relations for sharp inflationary non-Gaussian features
International Nuclear Information System (INIS)
Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris; Soto, Alex
2016-01-01
If cosmic inflation suffered tiny time-dependent deviations from the slow-roll regime, these would induce the existence of small scale-dependent features imprinted in the primordial spectra, with their shapes and sizes revealing information about the physics that produced them. Small sharp features could be suppressed at the level of the two-point correlation function, making them undetectable in the power spectrum, but could be amplified at the level of the three-point correlation function, offering us a window of opportunity to uncover them in the non-Gaussian bispectrum. In this article, we show that sharp features may be analyzed using only data coming from the three point correlation function parametrizing primordial non-Gaussianity. More precisely, we show that if features appear in a particular non-Gaussian triangle configuration (e.g. equilateral, folded, squeezed), these must reappear in every other configuration according to a specific relation allowing us to correlate features across the non-Gaussian bispectrum. As a result, we offer a method to study scale-dependent features generated during inflation that depends only on data coming from measurements of non-Gaussianity, allowing us to omit data from the power spectrum.
Prevalence Incidence Mixture Models
The R package and webtool fits Prevalence Incidence Mixture models to left-censored and irregularly interval-censored time to event data that is commonly found in screening cohorts assembled from electronic health records. Absolute and relative risk can be estimated for simple random sampling, and stratified sampling (the two approaches of superpopulation and a finite population are supported for target populations). Non-parametric (absolute risks only), semi-parametric, weakly-parametric (using B-splines), and some fully parametric (such as the logistic-Weibull) models are supported.
Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes.
Hougaard, P; Lee, M L; Whitmore, G A
1997-12-01
Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.
Finite mixture models for sub-pixel coastal land cover classification
CSIR Research Space (South Africa)
Ritchie, Michaela C
2017-05-01
Full Text Available Models for Sub- pixel Coastal Land Cover Classification M. Ritchie Dr. M. Lück-Vogel Dr. P. Debba Dr. V. Goodall ISRSE - 37 Tshwane, South Africa 10 May 2017 2Study Area Africa South Africa FALSE BAY 3Strand Gordon’s Bay Study Area WorldView-2 Image.../Urban 1 10 10 Herbaceous Vegetation 1 5 5 Shadow 1 8 8 Sparse Vegetation 1 3 3 Water 1 10 10 Woody Vegetation 1 5 5 11 Maximum Likelihood Classification (MLC) 12 Gaussian Mixture Discriminant Analysis (GMDA) 13 A B C t-distribution Mixture Discriminant...
Continuous-variable quantum teleportation with non-Gaussian resources
International Nuclear Information System (INIS)
Dell'Anno, F.; De Siena, S.; Albano, L.; Illuminati, F.
2007-01-01
We investigate continuous variable quantum teleportation using non-Gaussian states of the radiation field as entangled resources. We compare the performance of different classes of degaussified resources, including two-mode photon-added and two-mode photon-subtracted squeezed states. We then introduce a class of two-mode squeezed Bell-like states with one-parameter dependence for optimization. These states interpolate between and include as subcases different classes of degaussified resources. We show that optimized squeezed Bell-like resources yield a remarkable improvement in the fidelity of teleportation both for coherent and nonclassical input states. The investigation reveals that the optimal non-Gaussian resources for continuous variable teleportation are those that most closely realize the simultaneous maximization of the content of entanglement, the degree of affinity with the two-mode squeezed vacuum, and the, suitably measured, amount of non-Gaussianity
Generation of correlated finite alphabet waveforms using gaussian random variables
Ahmed, Sajid
2016-01-13
Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.
Outage performance of cognitive radio systems with Improper Gaussian signaling
Amin, Osama
2015-06-14
Improper Gaussian signaling has proved its ability to improve the achievable rate of the systems that suffer from interference compared with proper Gaussian signaling. In this paper, we first study impact of improper Gaussian signaling on the performance of the cognitive radio system by analyzing the outage probability of both the primary user (PU) and the secondary user (SU). We derive exact expression of the SU outage probability and upper and lower bounds for the PU outage probability. Then, we design the SU signal by adjusting its transmitted power and the circularity coefficient to minimize the SU outage probability while maintaining a certain PU quality-of-service. Finally, we evaluate the proposed bounds and adaptive algorithms by numerical results.
Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.
García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G
2017-08-01
The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.
Topological recursion for Gaussian means and cohomological field theories
Andersen, J. E.; Chekhov, L. O.; Norbury, P.; Penner, R. C.
2015-12-01
We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich-Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M g,s disc (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M g,1 for all g in three ways: using the refined Harer-Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.
Standard sirens and dark sector with Gaussian process*
Directory of Open Access Journals (Sweden)
Cai Rong-Gen
2018-01-01
Full Text Available The gravitational waves from compact binary systems are viewed as a standard siren to probe the evolution of the universe. This paper summarizes the potential and ability to use the gravitational waves to constrain the cosmological parameters and the dark sector interaction in the Gaussian process methodology. After briefly introducing the method to reconstruct the dark sector interaction by the Gaussian process, the concept of standard sirens and the analysis of reconstructing the dark sector interaction with LISA are outlined. Furthermore, we estimate the constraint ability of the gravitational waves on cosmological parameters with ET. The numerical methods we use are Gaussian process and the Markov-Chain Monte-Carlo. Finally, we also forecast the improvements of the abilities to constrain the cosmological parameters with ET and LISA combined with the Planck.
Cosmic microwave background power asymmetry from non-Gaussian modulation.
Schmidt, Fabian; Hui, Lam
2013-01-04
Non-Gaussianity in the inflationary perturbations can couple observable scales to modes of much longer wavelength (even superhorizon), leaving as a signature a large-angle modulation of the observed cosmic microwave background power spectrum. This provides an alternative origin for a power asymmetry that is otherwise often ascribed to a breaking of statistical isotropy. The non-Gaussian modulation effect can be significant even for typical ~10(-5) perturbations while respecting current constraints on non-Gaussianity if the squeezed limit of the bispectrum is sufficiently infrared divergent. Just such a strongly infrared-divergent bispectrum has been claimed for inflation models with a non-Bunch-Davies initial state, for instance. Upper limits on the observed cosmic microwave background power asymmetry place stringent constraints on the duration of inflation in such models.
Generation of correlated finite alphabet waveforms using gaussian random variables
Ahmed, Sajid; Alouini, Mohamed-Slim; Jardak, Seifallah
2016-01-01
Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.
Gaussian Process Interpolation for Uncertainty Estimation in Image Registration
Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William
2014-01-01
Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127
Primordial non-Gaussian features from DBI Galileon inflation
International Nuclear Information System (INIS)
Choudhury, Sayantan; Pal, Supratik
2015-01-01
We have studied primordial non-Gaussian features of a model of potential-driven single field DBI Galileon inflation. We have computed the bispectrum from the three-point correlation function considering all possible cross correlations between the scalar and tensor modes of the proposed setup. Further, we have computed the trispectrum from a four-point correlation function considering the contribution from contact interaction, and scalar and graviton exchange diagrams in the in-in picture. Finally we have obtained the non-Gaussian consistency conditions from the four-point correlator, which results in partial violation of the Suyama-Yamaguchi four-point consistency relation. This further leads to the conclusion that sufficient primordial non-Gaussianities can be obtained from DBI Galileon inflation. (orig.)
Non-Gaussian diffusion in static disordered media
Luo, Liang; Yi, Ming
2018-04-01
Non-Gaussian diffusion is commonly considered as a result of fluctuating diffusivity, which is correlated in time or in space or both. In this work, we investigate the non-Gaussian diffusion in static disordered media via a quenched trap model, where the diffusivity is spatially correlated. Several unique effects due to quenched disorder are reported. We analytically estimate the diffusion coefficient Ddis and its fluctuation over samples of finite size. We show a mechanism of population splitting in the non-Gaussian diffusion. It results in a sharp peak in the distribution of displacement P (x ,t ) around x =0 , that has frequently been observed in experiments. We examine the fidelity of the coarse-grained diffusion map, which is reconstructed from particle trajectories. Finally, we propose a procedure to estimate the correlation length in static disordered environments, where the information stored in the sample-to-sample fluctuation has been utilized.
Self-assembled structures of Gaussian nematic particles.
Nikoubashman, Arash; Likos, Christos N
2010-03-17
We investigate the stable crystalline configurations of a nematic liquid crystal made of soft parallel ellipsoidal particles interacting via a repulsive, anisotropic Gaussian potential. For this purpose, we use genetic algorithms (GA) in order to predict all relevant and possible solid phase candidates into which this fluid can freeze. Subsequently we present and discuss the emerging novel structures and the resulting zero-temperature phase diagram of this system. The latter features a variety of crystalline arrangements, in which the elongated Gaussian particles in general do not align with any one of the high-symmetry crystallographic directions, a compromise arising from the interplay and competition between anisotropic repulsions and crystal ordering. Only at very strong degrees of elongation does a tendency of the Gaussian nematics to align with the longest axis of the elementary unit cell emerge.
Gaussian white noise as a resource for work extraction.
Dechant, Andreas; Baule, Adrian; Sasa, Shin-Ichi
2017-03-01
We show that uncorrelated Gaussian noise can drive a system out of equilibrium and can serve as a resource from which work can be extracted. We consider an overdamped particle in a periodic potential with an internal degree of freedom and a state-dependent friction, coupled to an equilibrium bath. Applying additional Gaussian white noise drives the system into a nonequilibrium steady state and causes a finite current if the potential is spatially asymmetric. The model thus operates as a Brownian ratchet, whose current we calculate explicitly in three complementary limits. Since the particle current is driven solely by additive Gaussian white noise, this shows that the latter can potentially perform work against an external load. By comparing the extracted power to the energy injection due to the noise, we discuss the efficiency of such a ratchet.
Approximate thermodynamic state relations in partially ionized gas mixtures
International Nuclear Information System (INIS)
Ramshaw, John D.
2004-01-01
Thermodynamic state relations for mixtures of partially ionized nonideal gases are often approximated by artificially partitioning the mixture into compartments or subvolumes occupied by the pure partially ionized constituent gases, and requiring these subvolumes to be in temperature and pressure equilibrium. This intuitively reasonable procedure is easily shown to reproduce the correct thermal and caloric state equations for a mixture of neutral (nonionized) ideal gases. The purpose of this paper is to point out that (a) this procedure leads to incorrect state equations for a mixture of partially ionized ideal gases, whereas (b) the alternative procedure of requiring that the subvolumes all have the same temperature and free electron density reproduces the correct thermal and caloric state equations for such a mixture. These results readily generalize to the case of partially degenerate and/or relativistic electrons, to a common approximation used to represent pressure ionization effects, and to two-temperature plasmas. This suggests that equating the subvolume electron number densities or chemical potentials instead of pressures is likely to provide a more accurate approximation in nonideal plasma mixtures
International Nuclear Information System (INIS)
1981-01-01
Apparatus is described for the separation of a gaseous plasma mixture into components in some of which the original concentration of a specific ion has been greatly increased or decreased, comprising: a source for converting the gaseous mixture into a train of plasma packets; an open-ended vessel with a main section and at least one branch section, adapted to enclose along predetermined tracks the original plasma packets in the main section, and the separated plasma components in the branch sections; drive means for generating travelling magnetic waves along the predetermined tracks with the magnetic flux vector of the waves transverse to each of the tracks; and means for maintaining phase coherence between the plasma packets and the magnetic waves at a value needed for accelerating the components of the packets to different velocities and in such different directions that the plasma of each packet is divided into distinctly separate packets in some of which the original concentration of a specific ion has been greatly increased or decreased, and which plasma packets are collected from the branch sections of the vessels. (author)
Concept of planetary gear system to control fluid mixture ratio
Mcgroarty, J. D.
1966-01-01
Mechanical device senses and corrects for fluid flow departures from the selected flow ratio of two fluids. This system has been considered for control of rocket engine propellant mixture control but could find use wherever control of the flow ratio of any two fluids is desired.
International Nuclear Information System (INIS)
Fields, D.E.; Miller, C.W.
1980-05-01
The most commonly used approach for estimating the atmospheric concentration and deposition of material downwind from its point of release is the Gaussian plume atmospheric dispersion model. Two of the critical parameters in this model are sigma/sub y/ and sigma/sub z/, the horizontal and vertical dispersion parameters, respectively. A number of different sets of values for sigma/sub y/ and sigma/sub z/ have been determined empirically for different release heights and meteorological and terrain conditions. The computer code DWNWND, described in this report, is an interactive implementation of the Gaussian plume model. This code allows the user to specify any one of eight different sets of the empirically determined dispersion paramters. Using the selected dispersion paramters, ground-level normalized exposure estimates are made at any specified downwind distance. Computed values may be corrected for plume depletion due to deposition and for plume settling due to gravitational fall. With this interactive code, the user chooses values for ten parameters which define the source, the dispersion and deposition process, and the sampling point. DWNWND is written in FORTRAN for execution on a PDP-10 computer, requiring less than one second of central processor unit time for each simulation
Fast and Scalable Gaussian Process Modeling with Applications to Astronomical Time Series
Foreman-Mackey, Daniel; Agol, Eric; Ambikasaran, Sivaram; Angus, Ruth
2017-12-01
The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large data sets. Gaussian processes (GPs) are a popular class of models used for this purpose, but since the computational cost scales, in general, as the cube of the number of data points, their application has been limited to small data sets. In this paper, we present a novel method for GPs modeling in one dimension where the computational requirements scale linearly with the size of the data set. We demonstrate the method by applying it to simulated and real astronomical time series data sets. These demonstrations are examples of probabilistic inference of stellar rotation periods, asteroseismic oscillation spectra, and transiting planet parameters. The method exploits structure in the problem when the covariance function is expressed as a mixture of complex exponentials, without requiring evenly spaced observations or uniform noise. This form of covariance arises naturally when the process is a mixture of stochastically driven damped harmonic oscillators—providing a physical motivation for and interpretation of this choice—but we also demonstrate that it can be a useful effective model in some other cases. We present a mathematical description of the method and compare it to existing scalable GP methods. The method is fast and interpretable, with a range of potential applications within astronomical data analysis and beyond. We provide well-tested and documented open-source implementations of this method in C++, Python, and Julia.
Gaussian-3 theory using scaled energies
International Nuclear Information System (INIS)
Curtiss, Larry A.; Raghavachari, Krishnan; Redfern, Paul C.; Pople, John A.
2000-01-01
A modification of Guassian-3 (G3) theory using multiplicative scale factors, instead of the additive higher level correction, is presented. In this method, referred to as G3S, the correlation energy is scaled by five parameters and the Hartree-Fock energy by one parameter. The six parameters are fitted to the G2/97 test set of 299 energies and the resulting mean absolute deviation from experiment is 0.99 kcal/mol compared to 1.01 kcal/mol for G3 theory. The G3S method has the advantage compared to G3 theory in that it can be used for studying potential energy surfaces where the products and reactants have a different number of paired electrons. In addition, versions of the computationally less intensive G3(MP3) and G3(MP2) methods that use scaled energies are also presented. These methods, referred to as G3S(MP3) and G3S(MP2), have mean absolute deviations of 1.16 and 1.35 kcal/mol, respectively. (c) 2000 American Institute of Physics
Bayesian analysis of log Gaussian Cox processes for disease mapping
DEFF Research Database (Denmark)
Benes, Viktor; Bodlák, Karel; Møller, Jesper
We consider a data set of locations where people in Central Bohemia have been infected by tick-borne encephalitis, and where population census data and covariates concerning vegetation and altitude are available. The aims are to estimate the risk map of the disease and to study the dependence...... of the risk on the covariates. Instead of using the common area level approaches we consider a Bayesian analysis for a log Gaussian Cox point process with covariates. Posterior characteristics for a discretized version of the log Gaussian Cox process are computed using markov chain Monte Carlo methods...
Polarization coupling of vector Bessel–Gaussian beams
International Nuclear Information System (INIS)
Takeuchi, Ryushi; Kozawa, Yuichi; Sato, Shunichi
2013-01-01
We report polarization coupling of radial and azimuthal electric field components of a vector light beam as predicted by the fact that the vector Helmholtz equation is expressed as coupled differential equations in cylindrical coordinates. To clearly observe the polarization variation of a beam as it propagates, higher order transverse modes of a vector Bessel–Gaussian beam were generated by a gain distribution modulation technique, which created a narrow ring-shaped gain region in a Nd:YVO 4 crystal. The polarization coupling was confirmed by the observation that the major polarization component of a vector Bessel–Gaussian beam alternates between radial and azimuthal components along with the propagation. (paper)
Gaussian-state entanglement in a quantum beat laser
International Nuclear Information System (INIS)
Tahira, Rabia; Ikram, Manzoor; Nha, Hyunchul; Zubairy, M. Suhail
2011-01-01
Recently quantum beat lasers have been considered as a source of entangled radiation [S. Qamar, F. Ghafoor, M. Hillery, and M. S. Zubairy, Phys. Rev. A 77, 062308 (2008)]. We investigate and quantify the entanglement of this system when the initial cavity modes are prepared in a Gaussian two-mode state, one being a nonclassical state and the other a thermal state. It is investigated how the output entanglement varies with the nonclassicality of the input Gaussian state, thermal noise, and the strength of the driving field.
Neural pulse frequency modulation of an exponentially correlated Gaussian process
Hutchinson, C. E.; Chon, Y.-T.
1976-01-01
The effect of NPFM (Neural Pulse Frequency Modulation) on a stationary Gaussian input, namely an exponentially correlated Gaussian input, is investigated with special emphasis on the determination of the average number of pulses in unit time, known also as the average frequency of pulse occurrence. For some classes of stationary input processes where the formulation of the appropriate multidimensional Markov diffusion model of the input-plus-NPFM system is possible, the average impulse frequency may be obtained by a generalization of the approach adopted. The results are approximate and numerical, but are in close agreement with Monte Carlo computer simulation results.
Local features with large spiky non-Gaussianities during inflation
International Nuclear Information System (INIS)
Abolhasani, Ali Akbar; Firouzjahi, Hassan; Khosravi, Shahram; Sasaki, Misao
2012-01-01
We provide a dynamical mechanism to generate localized features during inflation. The local feature is due to a sharp waterfall phase transition which is coupled to the inflaton field. The key effect is the contributions of waterfall quantum fluctuations which induce a sharp peak on the curvature perturbation which can be as large as the background curvature perturbation from inflaton field. Due to non-Gaussian nature of waterfall quantum fluctuations a large spike non-Gaussianity is produced which is narrowly peaked at modes which leave the Hubble radius at the time of phase transition. The large localized peaks in power spectrum and bispectrum can have interesting consequences on CMB anisotropies
Coulomb Final State Interactions for Gaussian Wave Packets
Wiedemann, Urs Achim; Heinz, Ulrich W
1999-01-01
Two-particle like-sign and unlike-sign correlations including Coulomb final state interactions are calculated for Gaussian wave packets emitted from a Gaussian source. We show that the width of the wave packets can be fully absorbed into the spatial and momentum space widths of an effective emission function for plane wave states, and that Coulomb final state interaction effects are sensitive only to the latter, but not to the wave packet width itself. Results from analytical and numerical calculations are compared with recently published work by other authors.
Permutation entropy of fractional Brownian motion and fractional Gaussian noise
International Nuclear Information System (INIS)
Zunino, L.; Perez, D.G.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.
2008-01-01
We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays
Power variation for Gaussian processes with stationary increments
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Corcuera, J.M.; Podolskij, Mark
2009-01-01
We develop the asymptotic theory for the realised power variation of the processes X=•G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity conditions on the path of the pr......We develop the asymptotic theory for the realised power variation of the processes X=•G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity conditions on the path...... a chaos representation....
Pulsed homodyne Gaussian quantum tomography with low detection efficiency
Esposito, M.; Benatti, F.; Floreanini, R.; Olivares, S.; Randi, F.; Titimbo, K.; Pividori, M.; Novelli, F.; Cilento, F.; Parmigiani, F.; Fausti, D.
2014-04-01
Pulsed homodyne quantum tomography usually requires a high detection efficiency, limiting its applicability in quantum optics. Here, it is shown that the presence of low detection efficiency (<50%) does not prevent the tomographic reconstruction of quantum states of light, specifically, of Gaussian states. This result is obtained by applying the so-called ‘minimax’ adaptive reconstruction of the Wigner function to pulsed homodyne detection. In particular, we prove, by both numerical and real experiments, that an effective discrimination of different Gaussian quantum states can be achieved. Our finding paves the way to a more extensive use of quantum tomographic methods, even in physical situations in which high detection efficiency is unattainable.
Pulsed homodyne Gaussian quantum tomography with low detection efficiency
International Nuclear Information System (INIS)
Esposito, M; Benatti, F; Randi, F; Titimbo, K; Pividori, M; Parmigiani, F; Fausti, D; Floreanini, R; Olivares, S; Novelli, F; Cilento, F
2014-01-01
Pulsed homodyne quantum tomography usually requires a high detection efficiency, limiting its applicability in quantum optics. Here, it is shown that the presence of low detection efficiency (<50) does not prevent the tomographic reconstruction of quantum states of light, specifically, of Gaussian states. This result is obtained by applying the so-called ‘minimax’ adaptive reconstruction of the Wigner function to pulsed homodyne detection. In particular, we prove, by both numerical and real experiments, that an effective discrimination of different Gaussian quantum states can be achieved. Our finding paves the way to a more extensive use of quantum tomographic methods, even in physical situations in which high detection efficiency is unattainable
Propagation of Gaussian Beams through Active GRIN Materials
International Nuclear Information System (INIS)
Gomez-Varela, A I; Flores-Arias, M T; Bao-Varela, C; Gomez-Reino, C; De la Fuente, X
2011-01-01
We discussed light propagation through an active GRIN material that exhibits loss or gain. Effects of gain or loss in GRIN materials can be phenomenologically taken into account by using a complex refractive index in the wave equation. This work examines the implication of using a complex refractive index on light propagation in an active GRIN material illuminated by a non-uniform monochromatic wave described by a Gaussian beam. We analyze how a Gaussian beam is propagated through the active material in order to characterize it by the beam parameters and the transverse irradiance distribution.
Modulation depth of Michelson interferometer with Gaussian beam.
Välikylä, Tuomas; Kauppinen, Jyrki
2011-12-20
Mirror misalignment or the tilt angle of the Michelson interferometer can be estimated from the modulation depth measured with collimated monochromatic light. The intensity of the light beam is usually assumed to be uniform, but, for example, with gas lasers it generally has a Gaussian distribution, which makes the modulation depth less sensitive to the tilt angle. With this assumption, the tilt angle may be underestimated by about 50%. We have derived a mathematical model for modulation depth with a circular aperture and Gaussian beam. The model reduces the error of the tilt angle estimate to below 1%. The results of the model have been verified experimentally.
Pedagogical introduction to the entropy of entanglement for Gaussian states
Demarie, Tommaso F.
2018-05-01
In quantum information theory, the entropy of entanglement is a standard measure of bipartite entanglement between two partitions of a composite system. For a particular class of continuous variable quantum states, the Gaussian states, the entropy of entanglement can be expressed elegantly in terms of symplectic eigenvalues, elements that characterise a Gaussian state and depend on the correlations of the canonical variables. We give a rigorous step-by-step derivation of this result and provide physical insights, together with an example that can be useful in practice for calculations.
Gaussian basis functions for highly oscillatory scattering wavefunctions
Mant, B. P.; Law, M. M.
2018-04-01
We have applied a basis set of distributed Gaussian functions within the S-matrix version of the Kohn variational method to scattering problems involving deep potential energy wells. The Gaussian positions and widths are tailored to the potential using the procedure of Bačić and Light (1986 J. Chem. Phys. 85 4594) which has previously been applied to bound-state problems. The placement procedure is shown to be very efficient and gives scattering wavefunctions and observables in agreement with direct numerical solutions. We demonstrate the basis function placement method with applications to hydrogen atom–hydrogen atom scattering and antihydrogen atom–hydrogen atom scattering.
An optical tweezer in asymmetrical vortex Bessel-Gaussian beams
Energy Technology Data Exchange (ETDEWEB)
Kotlyar, V. V.; Kovalev, A. A., E-mail: alexeysmr@mail.ru; Porfirev, A. P. [Image Processing Systems Institute, 151 Molodogvardeiskaya St., 443001 Samara (Russian Federation); Department of Technical cybernetics, Samara State Aerospace University, Samara 443086 (Russian Federation)
2016-07-14
We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.