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.
Gaussian-mixture umbrella sampling
Maragakis, Paul; van der Vaart, Arjan; Karplus, Martin
2009-01-01
We introduce the Gaussian-mixture umbrella sampling method (GAMUS), a biased molecular dynamics technique based on adaptive umbrella sampling that efficiently escapes free energy minima in multi-dimensional problems. The prior simulation data are reweighted with a maximum likelihood formulation, and the new approximate probability density is fit to a Gaussian-mixture model, augmented by information about the unsampled areas. The method can be used to identify free energy minima in multi-dimen...
Gaussian mixture model of heart rate variability.
Directory of Open Access Journals (Sweden)
Tommaso Costa
Full Text Available 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.
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...
The Supervised Learning Gaussian Mixture Model
Institute of Scientific and Technical Information of China (English)
马继涌; 高文
1998-01-01
The traditional Gaussian Mixture Model(GMM)for pattern recognition is an unsupervised learning method.The parameters in the model are derived only by the training samples in one class without taking into account the effect of sample distributions of other classes,hence,its recognition accuracy is not ideal sometimes.This paper introduces an approach for estimating the parameters in GMM in a supervising way.The Supervised Learning Gaussian Mixture Model(SLGMM)improves the recognition accuracy of the GMM.An experimental example has shown its effectiveness.The experimental results have shown that the recognition accuracy derived by the approach is higher than those obtained by the Vector Quantization(VQ)approach,the Radial Basis Function (RBF) network model,the Learning Vector Quantization (LVQ) approach and the GMM.In addition,the training time of the approach is less than that of Multilayer Perceptrom(MLP).
Video compressive sensing using Gaussian mixture models.
Yang, Jianbo; Yuan, Xin; Liao, Xuejun; Llull, Patrick; Brady, David J; Sapiro, Guillermo; Carin, Lawrence
2014-11-01
A Gaussian mixture model (GMM)-based algorithm is proposed for video reconstruction from temporally compressed video measurements. The GMM is used to model spatio-temporal video patches, and the reconstruction can be efficiently computed based on analytic expressions. The GMM-based inversion method benefits from online adaptive learning and parallel computation. We demonstrate the efficacy of the proposed inversion method with videos reconstructed from simulated compressive video measurements, and from a real compressive video camera. We also use the GMM as a tool to investigate adaptive video compressive sensing, i.e., adaptive rate of temporal compression.
Statistical Compressed Sensing of Gaussian Mixture Models
Yu, Guoshen
2011-01-01
A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is introduced. SCS based on Gaussian models is investigated in depth. For signals that follow a single Gaussian model, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS based on sparse models, where N is the signal dimension, and with an optimal decoder implemented via linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the best k-term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional sparsity-oriented CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is u...
Statistical Compressive Sensing of Gaussian Mixture Models
Yu, Guoshen
2010-01-01
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is introduced. For signals following a Gaussian distribution, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS, where N is the signal dimension, and with an optimal decoder implemented with linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the k-best term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is upper bounded by a constant times the k-best term approximation with probability one, and the ...
Tails assumptions and posterior concentration rates for mixtures of Gaussians
Naulet, Zacharie; Rousseau, Judith
2016-01-01
Nowadays in density estimation, posterior rates of convergence for location and location-scale mixtures of Gaussians are only known under light-tail assumptions; with better rates achieved by location mixtures. It is conjectured, but not proved, that the situation should be reversed under heavy tails assumptions. The conjecture is based on the feeling that there is no need to achieve a good order of approximation in regions with few data (say, in the tails), favoring location-scale mixtures w...
Gaussian mixture models as flux prediction method for central receivers
Grobler, Annemarie; Gauché, Paul; Smit, Willie
2016-05-01
Flux prediction methods are crucial to the design and operation of central receiver systems. Current methods such as the circular and elliptical (bivariate) Gaussian prediction methods are often used in field layout design and aiming strategies. For experimental or small central receiver systems, the flux profile of a single heliostat often deviates significantly from the circular and elliptical Gaussian models. Therefore a novel method of flux prediction was developed by incorporating the fitting of Gaussian mixture models onto flux profiles produced by flux measurement or ray tracing. A method was also developed to predict the Gaussian mixture model parameters of a single heliostat for a given time using image processing. Recording the predicted parameters in a database ensures that more accurate predictions are made in a shorter time frame.
Minimum Mean Square Error Estimation Under Gaussian Mixture Statistics
Flam, John T; Kansanen, Kimmo; Ekman, Torbjorn
2011-01-01
This paper investigates the minimum mean square error (MMSE) estimation of x, given the observation y = Hx+n, when x and n are independent and Gaussian Mixture (GM) distributed. The introduction of GM distributions, represents a generalization of the more familiar and simpler Gaussian signal and Gaussian noise instance. We present the necessary theoretical foundation and derive the MMSE estimator for x in a closed form. Furthermore, we provide upper and lower bounds for its mean square error (MSE). These bounds are validated through Monte Carlo simulations.
Improved Gaussian Mixture Models for Adaptive Foreground Segmentation
DEFF Research Database (Denmark)
Katsarakis, Nikolaos; Pnevmatikakis, Aristodemos; Tan, Zheng-Hua
2016-01-01
Adaptive foreground segmentation is traditionally performed using Stauffer & Grimson’s algorithm that models every pixel of the frame by a mixture of Gaussian distributions with continuously adapted parameters. In this paper we provide an enhancement of the algorithm by adding two important dynamic...... elements to the baseline algorithm: The learning rate can change across space and time, while the Gaussian distributions can be merged together if they become similar due to their adaptation process. We quantify the importance of our enhancements and the effect of parameter tuning using an annotated...
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 the norma......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...... the normalized L2 distance was slightly inferior to the Kullback-Leibler distance with respect to classification performance, it has the advantage of obeying the triangle inequality, which allows for efficient searching....
Detecting Clusters in Atom Probe Data with Gaussian Mixture Models.
Zelenty, Jennifer; Dahl, Andrew; Hyde, Jonathan; Smith, George D W; Moody, Michael P
2017-04-01
Accurately identifying and extracting clusters from atom probe tomography (APT) reconstructions is extremely challenging, yet critical to many applications. Currently, the most prevalent approach to detect clusters is the maximum separation method, a heuristic that relies heavily upon parameters manually chosen by the user. In this work, a new clustering algorithm, Gaussian mixture model Expectation Maximization Algorithm (GEMA), was developed. GEMA utilizes a Gaussian mixture model to probabilistically distinguish clusters from random fluctuations in the matrix. This machine learning approach maximizes the data likelihood via expectation maximization: given atomic positions, the algorithm learns the position, size, and width of each cluster. A key advantage of GEMA is that atoms are probabilistically assigned to clusters, thus reflecting scientifically meaningful uncertainty regarding atoms located near precipitate/matrix interfaces. GEMA outperforms the maximum separation method in cluster detection accuracy when applied to several realistically simulated data sets. Lastly, GEMA was successfully applied to real APT data.
Invariant image object recognition using Gaussian mixture densities
Dahmen, Jörg
2002-01-01
In this work, a statistical image object recognition system is presented, which is based on the use of Gaussian mixture densities in the context of the Bayesian decision rule. Optionally, to reduce the number of free model parameters, a linear discriminant analysis is applied. This baseline system is then extended with respect to the incorporation of invariances. To do so, we start by suitably multiplying the available reference images. This idea is then applied to the observations to be clas...
Hidden Markov Models with Factored Gaussian Mixtures Densities
Institute of Scientific and Technical Information of China (English)
LI Hao-zheng; LIU Zhi-qiang; ZHU Xiang-hua
2004-01-01
We present a factorial representation of Gaussian mixture models for observation densities in Hidden Markov Models(HMMs), which uses the factorial learning in the HMM framework. We derive the reestimation formulas for estimating the factorized parameters by the Expectation Maximization (EM) algorithm. We conduct several experiments to compare the performance of this model structure with Factorial Hidden Markov Models(FHMMs) and HMMs, some conclusions and promising empirical results are presented.
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.
General relativistic corrections and non-Gaussianity
Villa, Eleonora; Matarrese, Sabino
2014-01-01
General relativistic cosmology cannot be reduced to linear relativistic perturbations superposed on an isotropic and homogeneous (Friedmann-Robertson-Walker) background, even though such a simple scheme has been successfully applied to analyse a large variety of phenomena (such as Cosmic Microwave Background primary anisotropies, matter clustering on large scales, weak gravitational lensing, etc.). The general idea of going beyond this simple paradigm is what characterises most of the efforts made in recent years: the study of second and higher-order cosmological perturbations including all general relativistic contributions -- also in connection with primordial non-Gaussianities -- the idea of defining large-scale structure observables directly from a general relativistic perspective, the various attempts to go beyond the Newtonian approximation in the study of non-linear gravitational dynamics, by using e.g., Post-Newtonian treatments, are all examples of this general trend. Here we summarise some of these ...
Multi-resolution image segmentation based on Gaussian mixture model
Institute of Scientific and Technical Information of China (English)
Tang Yinggan; Liu Dong; Guan Xinping
2006-01-01
Mixture model based image segmentation method, which assumes that image pixels are independent and do not consider the position relationship between pixels, is not robust to noise and usually leads to misclassification. A new segmentation method, called multi-resolution Gaussian mixture model method, is proposed. First, an image pyramid is constructed and son-father link relationship is built between each level of pyramid. Then the mixture model segmentation method is applied to the top level. The segmentation result on the top level is passed top-down to the bottom level according to the son-father link relationship between levels. The proposed method considers not only local but also global information of image, it overcomes the effect of noise and can obtain better segmentation result. Experimental result demonstrates its effectiveness.
Classifying Gamma-Ray Bursts with Gaussian Mixture Model
Yang, En-Bo; Choi, Chul-Sung; Chang, Heon-Young
2016-01-01
Using Gaussian Mixture Model (GMM) and Expectation Maximization Algorithm, we perform an analysis of time duration ($T_{90}$) for \\textit{CGRO}/BATSE, \\textit{Swift}/BAT and \\textit{Fermi}/GBM Gamma-Ray Bursts. The $T_{90}$ distributions of 298 redshift-known \\textit{Swift}/BAT GRBs have also been studied in both observer and rest frames. Bayesian Information Criterion has been used to compare between different GMM models. We find that two Gaussian components are better to describe the \\textit{CGRO}/BATSE and \\textit{Fermi}/GBM GRBs in the observer frame. Also, we caution that two groups are expected for the \\textit{Swift}/BAT bursts in the rest frame, which is consistent with some previous results. However, \\textit{Swift} GRBs in the observer frame seem to show a trimodal distribution, of which the superficial intermediate class may result from the selection effect of \\textit{Swift}/BAT.
Classifying gamma-ray bursts with Gaussian Mixture Model
Zhang, Zhi-Bin; Yang, En-Bo; Choi, Chul-Sung; Chang, Heon-Young
2016-11-01
Using Gaussian Mixture Model (GMM) and expectation-maximization algorithm, we perform an analysis of time duration (T90) for Compton Gamma Ray Observatory (CGRO)/BATSE, Swift/BAT and Fermi/GBM gamma-ray bursts (GRBs). The T90 distributions of 298 redshift-known Swift/BAT GRBs have also been studied in both observer and rest frames. Bayesian information criterion has been used to compare between different GMM models. We find that two Gaussian components are better to describe the CGRO/BATSE and Fermi/GBM GRBs in the observer frame. Also, we caution that two groups are expected for the Swift/BAT bursts in the rest frame, which is consistent with some previous results. However, Swift GRBs in the observer frame seem to show a trimodal distribution, of which the superficial intermediate class may result from the selection effect of Swift/BAT.
Novel blind source separation algorithm using Gaussian mixture density function
Institute of Scientific and Technical Information of China (English)
孔薇; 杨杰; 周越
2004-01-01
The blind source separation (BSS) is an important task for numerous applications in signal processing, communications and array processing. But for many complex sources blind separation algorithms are not efficient because the probability distribution of the sources cannot be estimated accurately. So in this paper, to justify the ME(maximum enteropy) approach, the relation between the ME and the MMI(minimum mutual information) is elucidated first. Then a novel algorithm that uses Gaussian mixture density to approximate the probability distribution of the sources is presented based on the ME approach. The experiment of the BSS of ship-radiated noise demonstrates that the proposed algorithm is valid and efficient.
Molecular Code Division Multiple Access: Gaussian Mixture Modeling
Zamiri-Jafarian, Yeganeh
Communications between nano-devices is an emerging research field in nanotechnology. Molecular Communication (MC), which is a bio-inspired paradigm, is a promising technique for communication in nano-network. In MC, molecules are administered to exchange information among nano-devices. Due to the nature of molecular signals, traditional communication methods can't be directly applied to the MC framework. The objective of this thesis is to present novel diffusion-based MC methods when multi nano-devices communicate with each other in the same environment. A new channel model and detection technique, along with a molecular-based access method, are proposed in here for communication between asynchronous users. In this work, the received molecular signal is modeled as a Gaussian mixture distribution when the MC system undergoes Brownian noise and inter-symbol interference (ISI). This novel approach demonstrates a suitable modeling for diffusion-based MC system. Using the proposed Gaussian mixture model, a simple receiver is designed by minimizing the error probability. To determine an optimum detection threshold, an iterative algorithm is derived which minimizes a linear approximation of the error probability function. Also, a memory-based receiver is proposed to improve the performance of the MC system by considering previously detected symbols in obtaining the threshold value. Numerical evaluations reveal that theoretical analysis of the bit error rate (BER) performance based on the Gaussian mixture model match simulation results very closely. Furthermore, in this thesis, molecular code division multiple access (MCDMA) is proposed to overcome the inter-user interference (IUI) caused by asynchronous users communicating in a shared propagation environment. Based on the selected molecular codes, a chip detection scheme with an adaptable threshold value is developed for the MCDMA system when the proposed Gaussian mixture model is considered. Results indicate that the
Immune adaptive Gaussian mixture par ticle filter for state estimation
Institute of Scientific and Technical Information of China (English)
Wenlong Huang; Xiaodan Wang; Yi Wang; Guohong Li
2015-01-01
The particle filter (PF) is a flexible and powerful sequen-tial Monte Carlo (SMC) technique capable of modeling nonlinear, non-Gaussian, and nonstationary dynamical systems. However, the generic PF suffers from particle degeneracy and sample im-poverishment, which greatly affects its performance for nonlinear, non-Gaussian tracking problems. To deal with those issues, an improved PF is proposed. The algorithm consists of a PF that uses an immune adaptive Gaussian mixture model (IAGM) based immune algorithm to re-approximate the posterior density. At the same time, three immune antibody operators are embed in the new filter. Instead of using a resample strategy, the newest obser-vation and conditional likelihood are integrated into those immune antibody operators to update the particles, which can further im-prove the diversity of particles, and drive particles toward their close local maximum of the posterior probability. The improved PF algorithm can produce a closed-form expression for the posterior state distribution. Simulation results show the proposed algorithm can maintain the effectiveness and diversity of particles and avoid sample impoverishment, and its performance is superior to several PFs and Kalman filters.
Relativistic corrections and non-Gaussianity in radio continuum surveys
Energy Technology Data Exchange (ETDEWEB)
Maartens, Roy [Physics Department, University of the Western Cape, Cape Town 7535 (South Africa); Zhao, Gong-Bo; Bacon, David; Koyama, Kazuya [Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom); Raccanelli, Alvise, E-mail: Roy.Maartens@port.ac.uk, E-mail: Gong-bo.Zhao@port.ac.uk, E-mail: David.Bacon@port.ac.uk, E-mail: Kazuya.Koyama@port.ac.uk, E-mail: alvise@caltech.edu [Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA 91109 (United States)
2013-02-01
Forthcoming radio continuum surveys will cover large volumes of the observable Universe and will reach to high redshifts, making them potentially powerful probes of dark energy, modified gravity and non-Gaussianity. We consider the continuum surveys with LOFAR, WSRT and ASKAP, and examples of continuum surveys with the SKA. We extend recent work on these surveys by including redshift space distortions and lensing convergence in the radio source auto-correlation. In addition we compute the general relativistic (GR) corrections to the angular power spectrum. These GR corrections to the standard Newtonian analysis of the power spectrum become significant on scales near and beyond the Hubble scale at each redshift. We find that the GR corrections are at most percent-level in LOFAR, WODAN and EMU surveys, but they can produce O(10%) changes for high enough sensitivity SKA continuum surveys. The signal is however dominated by cosmic variance, and multiple-tracer techniques will be needed to overcome this problem. The GR corrections are suppressed in continuum surveys because of the integration over redshift — we expect that GR corrections will be enhanced for future SKA HI surveys in which the source redshifts will be known. We also provide predictions for the angular power spectra in the case where the primordial perturbations have local non-Gaussianity. We find that non-Gaussianity dominates over GR corrections, and rises above cosmic variance when f{sub NL}∼>5 for SKA continuum surveys.
Efficient speaker verification using Gaussian mixture model component clustering.
Energy Technology Data Exchange (ETDEWEB)
De Leon, Phillip L. (New Mexico State University, Las Cruces, NM); McClanahan, Richard D.
2012-04-01
In speaker verification (SV) systems that employ a support vector machine (SVM) classifier to make decisions on a supervector derived from Gaussian mixture model (GMM) component mean vectors, a significant portion of the computational load is involved in the calculation of the a posteriori probability of the feature vectors of the speaker under test with respect to the individual component densities of the universal background model (UBM). Further, the calculation of the sufficient statistics for the weight, mean, and covariance parameters derived from these same feature vectors also contribute a substantial amount of processing load to the SV system. In this paper, we propose a method that utilizes clusters of GMM-UBM mixture component densities in order to reduce the computational load required. In the adaptation step we score the feature vectors against the clusters and calculate the a posteriori probabilities and update the statistics exclusively for mixture components belonging to appropriate clusters. Each cluster is a grouping of multivariate normal distributions and is modeled by a single multivariate distribution. As such, the set of multivariate normal distributions representing the different clusters also form a GMM. This GMM is referred to as a hash GMM which can be considered to a lower resolution representation of the GMM-UBM. The mapping that associates the components of the hash GMM with components of the original GMM-UBM is referred to as a shortlist. This research investigates various methods of clustering the components of the GMM-UBM and forming hash GMMs. Of five different methods that are presented one method, Gaussian mixture reduction as proposed by Runnall's, easily outperformed the other methods. This method of Gaussian reduction iteratively reduces the size of a GMM by successively merging pairs of component densities. Pairs are selected for merger by using a Kullback-Leibler based metric. Using Runnal's method of reduction, we
Leading non-Gaussian corrections for diffusion orientation distribution function.
Jensen, Jens H; Helpern, Joseph A; Tabesh, Ali
2014-02-01
An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed from the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves on the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common.
Fuzzy local Gaussian mixture model for brain MR image segmentation.
Ji, Zexuan; Xia, Yong; Sun, Quansen; Chen, Qiang; Xia, Deshen; Feng, David Dagan
2012-05-01
Accurate brain tissue segmentation from magnetic resonance (MR) images is an essential step in quantitative brain image analysis. However, due to the existence of noise and intensity inhomogeneity in brain MR images, many segmentation algorithms suffer from limited accuracy. In this paper, we assume that the local image data within each voxel's neighborhood satisfy the Gaussian mixture model (GMM), and thus propose the fuzzy local GMM (FLGMM) algorithm for automated brain MR image segmentation. This algorithm estimates the segmentation result that maximizes the posterior probability by minimizing an objective energy function, in which a truncated Gaussian kernel function is used to impose the spatial constraint and fuzzy memberships are employed to balance the contribution of each GMM. We compared our algorithm to state-of-the-art segmentation approaches in both synthetic and clinical data. Our results show that the proposed algorithm can largely overcome the difficulties raised by noise, low contrast, and bias field, and substantially improve the accuracy of brain MR image segmentation.
Protein local conformations arise from a mixture of Gaussian distributions
Indian Academy of Sciences (India)
Ashish V Tendulkar; Babatunde Ogunnaike; Pramod P Wangikar
2007-08-01
The classical approaches for protein structure prediction rely either on homology of the protein sequence with a template structure or on ab initio calculations for energy minimization. These methods suffer from disadvantages such as the lack of availability of homologous template structures or intractably large conformational search space, respectively. The recently proposed fragment library based approaches first predict the local structures, which can be used in conjunction with the classical approaches of protein structure prediction. The accuracy of the predictions is dependent on the quality of the fragment library. In this work, we have constructed a library of local conformation classes purely based on geometric similarity. The local conformations are represented using Geometric Invariants, properties that remain unchanged under transformations such as translation and rotation, followed by dimension reduction via principal component analysis. The local conformations are then modeled as a mixture of Gaussian probability distribution functions (PDF). Each one of the Gaussian PDF’s corresponds to a conformational class with the centroid representing the average structure of that class. We find 46 classes when we use an octapeptide as a unit of local conformation. The protein 3-D structure can now be described as a sequence of local conformational classes. Further, it was of interest to see whether the local conformations can be predicted from the amino acid sequences. To that end, we have analyzed the correlation between sequence features and the conformational classes.
Decision Based Uncertainty Propagation Using Adaptive Gaussian Mixtures
Terejanu, Gabriel; Singh, Tarunraj; Scott, Peter D
2011-01-01
Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the information held by the decision maker into the data assimilation process. Here the information held by the decision maker is a loss function at a decision time which maps the state space onto real numbers which represent the threat associated with different possible outcomes or states. The new probability density function obtained will address the region of interest, the area in the state space with the highest threat, and will provide overall a better approximation to the true conditional probability density function within it. The approximation used for the probability density function is a Gaussian mixture and a numerical example is presented to illustrate the concept.
Gaussian Mixture Model and Rjmcmc Based RS Image Segmentation
Shi, X.; Zhao, Q. H.
2017-09-01
For the image segmentation method based on Gaussian Mixture Model (GMM), there are some problems: 1) The number of component was usually a fixed number, i.e., fixed class and 2) GMM is sensitive to image noise. This paper proposed a RS image segmentation method that combining GMM with reversible jump Markov Chain Monte Carlo (RJMCMC). In proposed algorithm, GMM was designed to model the distribution of pixel intensity in RS image. Assume that the number of component was a random variable. Respectively build the prior distribution of each parameter. In order to improve noise resistance, used Gibbs function to model the prior distribution of GMM weight coefficient. According to Bayes' theorem, build posterior distribution. RJMCMC was used to simulate the posterior distribution and estimate its parameters. Finally, an optimal segmentation is obtained on RS image. Experimental results show that the proposed algorithm can converge to the optimal number of class and get an ideal segmentation results.
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.
Replacing standard galaxy profiles with mixtures of Gaussians
Hogg, David W
2012-01-01
Exponential, de Vaucouleurs, and S\\'ersic profiles are simple and successful models for fitting two-dimensional images of galaxies. One numerical issue encountered in this kind of fitting is the pixel rendering and convolution (or correlation) of the models with the telescope point-spread function (PSF); these operations are slow, and easy to get slightly wrong at small radii. Here we exploit the realization that these models can be approximated to arbitrary accuracy with a mixture (linear superposition) of two-dimensional Gaussians (MoGs). MoGs are fast to render and fast to affine-transform. Most importantly, if you have a MoG model for the pixel-convolved PSF, the PSF-convolved, affine-transformed galaxy models are themselves MoGs and therefore very fast to compute, integrate, and render precisely. We present worked examples that can be directly used in image fitting; we are using them ourselves. The MoG profiles we provide can be swapped in to replace the standard models in any image-fitting code; they sp...
Compressive sensing by learning a Gaussian mixture model from measurements.
Yang, Jianbo; Liao, Xuejun; Yuan, Xin; Llull, Patrick; Brady, David J; Sapiro, Guillermo; Carin, Lawrence
2015-01-01
Compressive sensing of signals drawn from a Gaussian mixture model (GMM) admits closed-form minimum mean squared error reconstruction from incomplete linear measurements. An accurate GMM signal model is usually not available a priori, because it is difficult to obtain training signals that match the statistics of the signals being sensed. We propose to solve that problem by learning the signal model in situ, based directly on the compressive measurements of the signals, without resorting to other signals to train a model. A key feature of our method is that the signals being sensed are treated as random variables and are integrated out in the likelihood. We derive a maximum marginal likelihood estimator (MMLE) that maximizes the likelihood of the GMM of the underlying signals given only their linear compressive measurements. We extend the MMLE to a GMM with dominantly low-rank covariance matrices, to gain computational speedup. We report extensive experimental results on image inpainting, compressive sensing of high-speed video, and compressive hyperspectral imaging (the latter two based on real compressive cameras). The results demonstrate that the proposed methods outperform state-of-the-art methods by significant margins.
Orbit-product representation and correction of Gaussian belief propagation
Energy Technology Data Exchange (ETDEWEB)
Johnson, Jason K [Los Alamos National Laboratory; Chertkov, Michael [Los Alamos National Laboratory; Chernyak, Vladimir [WAYNE STATE UNIV
2009-01-01
We present a new interpretation of Gaussian belief propagation (GaBP) based on the 'zeta function' representation of the determinant as a product over orbits of a graph. We show that GaBP captures back-tracking orbits of the graph and consider how to correct this estimate by accounting for non-backtracking orbits. We show that the product over non-backtracking orbits may be interpreted as the determinant of the non-backtracking adjacency matrix of the graph with edge weights based on the solution of GaBP. An efficient method is proposed to compute a truncated correction factor including all non-backtracking orbits up to a specified length.
Mixtures of conditional Gaussian scale mixtures applied to multiscale image representations.
Directory of Open Access Journals (Sweden)
Lucas Theis
Full Text Available We present a probabilistic model for natural images that is based on mixtures of Gaussian scale mixtures and a simple multiscale representation. We show that it is able to generate images with interesting higher-order correlations when trained on natural images or samples from an occlusion-based model. More importantly, our multiscale model allows for a principled evaluation. While it is easy to generate visually appealing images, we demonstrate that our model also yields the best performance reported to date when evaluated with respect to the cross-entropy rate, a measure tightly linked to the average log-likelihood. The ability to quantitatively evaluate our model differentiates it from other multiscale models, for which evaluation of these kinds of measures is usually intractable.
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.
Overlapping Mixtures of Gaussian Processes for the Data Association Problem
Lázaro-Gredilla, Miguel; Lawrence, Neil
2011-01-01
In this work we introduce a mixture of GPs to address the data association problem, i.e. to label a group of observations according to the sources that generated them. Unlike several previously proposed GP mixtures, the novel mixture has the distinct characteristic of using no gating function to determine the association of samples and mixture components. Instead, all the GPs in the mixture are global and samples are clustered following "trajectories" across input space. We use a non-standard variational Bayesian algorithm to efficiently recover sample labels and learn the hyperparameters. We show how multi-object tracking problems can be disambiguated and also explore the characteristics of the model in traditional regression settings.
Directory of Open Access Journals (Sweden)
Shih-Sian Cheng
2004-12-01
Full Text Available We propose a self-splitting Gaussian mixture learning (SGML algorithm for Gaussian mixture modelling. The SGML algorithm is deterministic and is able to find an appropriate number of components of the Gaussian mixture model (GMM based on a self-splitting validity measure, Bayesian information criterion (BIC. It starts with a single component in the feature space and splits adaptively during the learning process until the most appropriate number of components is found. The SGML algorithm also performs well in learning the GMM with a given component number. In our experiments on clustering of a synthetic data set and the text-independent speaker identification task, we have observed the ability of the SGML for model-based clustering and automatically determining the model complexity of the speaker GMMs for speaker identification.
Infrared image segmentation based on region of interest extraction with Gaussian mixture modeling
Yeom, Seokwon
2017-05-01
Infrared (IR) imaging has the capability to detect thermal characteristics of objects under low-light conditions. This paper addresses IR image segmentation with Gaussian mixture modeling. An IR image is segmented with Expectation Maximization (EM) method assuming the image histogram follows the Gaussian mixture distribution. Multi-level segmentation is applied to extract the region of interest (ROI). Each level of the multi-level segmentation is composed of the k-means clustering, the EM algorithm, and a decision process. The foreground objects are individually segmented from the ROI windows. In the experiments, various methods are applied to the IR image capturing several humans at night.
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.
Directory of Open Access Journals (Sweden)
Nsiri Benayad
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.
Iterative Diffusion-Based Distributed Cubature Gaussian Mixture Filter for Multisensor Estimation
Directory of Open Access Journals (Sweden)
Bin Jia
2016-10-01
Full Text Available In this paper, a distributed cubature Gaussian mixture filter (DCGMF based on an iterative diffusion strategy (DCGMF-ID is proposed for multisensor estimation and information fusion. The uncertainties are represented as Gaussian mixtures at each sensor node. A high-degree cubature Kalman filter provides accurate estimation of each Gaussian mixture component. An iterative diffusion scheme is utilized to fuse the mean and covariance of each Gaussian component obtained from each sensor node. The DCGMF-ID extends the conventional diffusion-based fusion strategy by using multiple iterative information exchanges among neighboring sensor nodes. The convergence property of the iterative diffusion is analyzed. In addition, it is shown that the convergence of the iterative diffusion can be interpreted from the information-theoretic perspective as minimization of the Kullback–Leibler divergence. The performance of the DCGMF-ID is compared with the DCGMF based on the average consensus (DCGMF-AC and the DCGMF based on the iterative covariance intersection (DCGMF-ICI via a maneuvering target-tracking problem using multiple sensors. The simulation results show that the DCGMF-ID has better performance than the DCGMF based on noniterative diffusion, which validates the benefit of iterative information exchanges. In addition, the DCGMF-ID outperforms the DCGMF-ICI and DCGMF-AC when the number of iterations is limited.
An efficient approach for shadow detection based on Gaussian mixture model
Institute of Scientific and Technical Information of China (English)
韩延祥; 张志胜; 陈芳; 陈恺
2014-01-01
An efficient approach was proposed for discriminating shadows from moving objects. In the background subtraction stage, moving objects were extracted. Then, the initial classification for moving shadow pixels and foreground object pixels was performed by using color invariant features. In the shadow model learning stage, instead of a single Gaussian distribution, it was assumed that the density function computed on the values of chromaticity difference or bright difference, can be modeled as a mixture of Gaussian consisting of two density functions. Meanwhile, the Gaussian parameter estimation was performed by using EM algorithm. The estimates were used to obtain shadow mask according to two constraints. Finally, experiments were carried out. The visual experiment results confirm the effectiveness of proposed method. Quantitative results in terms of the shadow detection rate and the shadow discrimination rate (the maximum values are 85.79%and 97.56%, respectively) show that the proposed approach achieves a satisfying result with post-processing step.
Directory of Open Access Journals (Sweden)
Cohen S.X.
2014-03-01
Full Text Available In this article, we describe a novel unsupervised spectral image segmentation algorithm. This algorithm extends the classical Gaussian Mixture Model-based unsupervised classification technique by incorporating a spatial flavor into the model: the spectra are modelized by a mixture of K classes, each with a Gaussian distribution, whose mixing proportions depend on the position. Using a piecewise constant structure for those mixing proportions, we are able to construct a penalized maximum likelihood procedure that estimates the optimal partition as well as all the other parameters, including the number of classes. We provide a theoretical guarantee for this estimation, even when the generating model is not within the tested set, and describe an efficient implementation. Finally, we conduct some numerical experiments of unsupervised segmentation from a real dataset.
Automated sleep spindle detection using IIR filters and a Gaussian Mixture Model.
Patti, Chanakya Reddy; Penzel, Thomas; Cvetkovic, Dean
2015-08-01
Sleep spindle detection using modern signal processing techniques such as the Short-Time Fourier Transform and Wavelet Analysis are common research methods. These methods are computationally intensive, especially when analysing data from overnight sleep recordings. The authors of this paper propose an alternative using pre-designed IIR filters and a multivariate Gaussian Mixture Model. Features extracted with IIR filters are clustered using a Gaussian Mixture Model without the use of any subject independent thresholds. The Algorithm was tested on a database consisting of overnight sleep PSG of 5 subjects and an online public spindles database consisting of six 30 minute sleep excerpts. An overall sensitivity of 57% and a specificity of 98.24% was achieved in the overnight database group and a sensitivity of 65.19% at a 16.9% False Positive proportion for the 6 sleep excerpts.
Filling the gaps: Gaussian mixture models from noisy, truncated or incomplete samples
Melchior, Peter
2016-01-01
We extend the common mixtures-of-Gaussians density estimation approach to account for a known sample incompleteness by simultaneous imputation from the current model. The method called GMMis generalizes existing Expectation-Maximization techniques for truncated data to arbitrary truncation geometries and probabilistic rejection. It can incorporate an uniform background distribution as well as independent multivariate normal measurement errors for each of the observed samples, and recovers an estimate of the error-free distribution from which both observed and unobserved samples are drawn. We compare GMMis to the standard Gaussian mixture model for simple test cases with different types of incompleteness, and apply it to observational data from the NASA Chandra X-ray telescope. The python code is capable of performing density estimation with millions of samples and thousands of model components and is released as an open-source package at https://github.com/pmelchior/pyGMMis
Perturbative corrections for approximate inference in gaussian latent variable models
DEFF Research Database (Denmark)
Opper, Manfred; Paquet, Ulrich; Winther, Ole
2013-01-01
but intractable correction, and can be applied to the model's partition function and other moments of interest. The correction is expressed over the higher-order cumulants which are neglected by EP's local matching of moments. Through the expansion, we see that EP is correct to first order. By considering higher...... 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....
Directory of Open Access Journals (Sweden)
Yli-Harja Olli
2009-05-01
Full Text Available Abstract Background Cluster analysis has become a standard computational method for gene function discovery as well as for more general explanatory data analysis. A number of different approaches have been proposed for that purpose, out of which different mixture models provide a principled probabilistic framework. Cluster analysis is increasingly often supplemented with multiple data sources nowadays, and these heterogeneous information sources should be made as efficient use of as possible. Results This paper presents a novel Beta-Gaussian mixture model (BGMM for clustering genes based on Gaussian distributed and beta distributed data. The proposed BGMM can be viewed as a natural extension of the beta mixture model (BMM and the Gaussian mixture model (GMM. The proposed BGMM method differs from other mixture model based methods in its integration of two different data types into a single and unified probabilistic modeling framework, which provides a more efficient use of multiple data sources than methods that analyze different data sources separately. Moreover, BGMM provides an exceedingly flexible modeling framework since many data sources can be modeled as Gaussian or beta distributed random variables, and it can also be extended to integrate data that have other parametric distributions as well, which adds even more flexibility to this model-based clustering framework. We developed three types of estimation algorithms for BGMM, the standard expectation maximization (EM algorithm, an approximated EM and a hybrid EM, and propose to tackle the model selection problem by well-known model selection criteria, for which we test the Akaike information criterion (AIC, a modified AIC (AIC3, the Bayesian information criterion (BIC, and the integrated classification likelihood-BIC (ICL-BIC. Conclusion Performance tests with simulated data show that combining two different data sources into a single mixture joint model greatly improves the clustering
A Rough Set Bounded Spatially Constrained Asymmetric Gaussian Mixture Model for Image Segmentation.
Ji, Zexuan; Huang, Yubo; Sun, Quansen; Cao, Guo; Zheng, Yuhui
2017-01-01
Accurate image segmentation is an important issue in image processing, where Gaussian mixture models play an important part and have been proven effective. However, most Gaussian mixture model (GMM) based methods suffer from one or more limitations, such as limited noise robustness, over-smoothness for segmentations, and lack of flexibility to fit data. In order to address these issues, in this paper, we propose a rough set bounded asymmetric Gaussian mixture model with spatial constraint for image segmentation. First, based on our previous work where each cluster is characterized by three automatically determined rough-fuzzy regions, we partition the target image into three rough regions with two adaptively computed thresholds. Second, a new bounded indicator function is proposed to determine the bounded support regions of the observed data. The bounded indicator and posterior probability of a pixel that belongs to each sub-region is estimated with respect to the rough region where the pixel lies. Third, to further reduce over-smoothness for segmentations, two novel prior factors are proposed that incorporate the spatial information among neighborhood pixels, which are constructed based on the prior and posterior probabilities of the within- and between-clusters, and considers the spatial direction. We compare our algorithm to state-of-the-art segmentation approaches in both synthetic and real images to demonstrate the superior performance of the proposed algorithm.
CSIR Research Space (South Africa)
Miya, WS
2008-10-01
Full Text Available In this paper, a comparison between Extension Neural Network (ENN), Gaussian Mixture Model (GMM) and Hidden Markov model (HMM) is conducted for bushing condition monitoring. The monitoring process is a two-stage implementation of a classification...
On the non-Gaussian corrections in the self dynamics of semi-quantum fluids
Energy Technology Data Exchange (ETDEWEB)
Colognesi, D., E-mail: daniele.colognesi@isc.cnr.it [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Bafile, U.; Celli, M. [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Neumann, M. [Fakultät für Physik der Universität Wien, Strudlhofgasse 4, A-1090 Wien (Austria)
2015-01-13
Highlights: • We study the Gaussian approximation in the self dynamics of semi-quantum liquids. • Correction scheme for the self intermediate scattering function is proposed. • Deviations from the Gaussian approximation are calculated in liquid H{sub 2}. • Experimental data confirm our approach and show that corrections are necessary. - Abstract: This paper is devoted to the study of the limits of the well-known Gaussian approximation in the self dynamics of quantum systems. After introducing the basic formalism and shortly reviewing the methods used in classical systems to apply corrections to the Gaussian approximation, an extension to quantum fluids is devised, with a particular interest in the so-called semi-quantum fluids, i.e. those in which the single particle momentum distribution approximately retains its Maxwellian form (but not its classical width). In this case a detailed correction scheme for both the short- and the long-time behaviors of the intermediate scattering function is proposed. Subsequently, a practical test of this approach is performed on a high resolution neutron scattering spectrum derived from liquid parahydrogen at T=14.1 K. Extracting the spectral deviations from the Gaussian approximation with the help of an accurate centroid molecular dynamics simulation, we are able to describe them precisely and to derive the first two correction coefficients in this system by means of a simple fitting procedure. These experimental findings confirm the validity of our approach and show that a description of the self dynamics beyond the Gaussian approximation is necessary even in simple liquids affected by mild quantum effects.
Novel Methods for Surface EMG Analysis and Exploration Based on Multi-Modal Gaussian Mixture Models.
Directory of Open Access Journals (Sweden)
Anna Magdalena Vögele
Full Text Available This paper introduces a new method for data analysis of animal muscle activation during locomotion. It is based on fitting Gaussian mixture models (GMMs to surface EMG data (sEMG. This approach enables researchers/users to isolate parts of the overall muscle activation within locomotion EMG data. Furthermore, it provides new opportunities for analysis and exploration of sEMG data by using the resulting Gaussian modes as atomic building blocks for a hierarchical clustering. In our experiments, composite peak models representing the general activation pattern per sensor location (one sensor on the long back muscle, three sensors on the gluteus muscle on each body side were identified per individual for all 14 horses during walk and trot in the present study. Hereby we show the applicability of the method to identify composite peak models, which describe activation of different muscles throughout cycles of locomotion.
Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures
Energy Technology Data Exchange (ETDEWEB)
Procacci, Piero [Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy and Centro Interdipartimentale per lo Studio delle Dinamiche Complesse (CSDC), Via Sansone 1, I-50019 Sesto Fiorentino (Italy)
2015-04-21
In this paper, we present an improved method for obtaining unbiased estimates of the free energy difference between two thermodynamic states using the work distribution measured in nonequilibrium driven experiments connecting these states. The method is based on the assumption that any observed work distribution is given by a mixture of Gaussian distributions, whose normal components are identical in either direction of the nonequilibrium process, with weights regulated by the Crooks theorem. Using the prototypical example for the driven unfolding/folding of deca-alanine, we show that the predicted behavior of the forward and reverse work distributions, assuming a combination of only two Gaussian components with Crooks derived weights, explains surprisingly well the striking asymmetry in the observed distributions at fast pulling speeds. The proposed methodology opens the way for a perfectly parallel implementation of Jarzynski-based free energy calculations in complex systems.
The Shape of Solar Cycles Described by a Simplified Binary Mixture of Gaussian Functions
Li, F. Y.; Xiang, N. B.; Kong, D. F.; Xie, J. L.
2017-01-01
Sunspot cycles usually present a double-peak structure. This work is devoted to using a function to describe the shape of sunspot cycles, including bimodal cycles, and we find that the shape of sunspot cycles can be described by a binary mixture of Gaussian functions with six parameters, two amplitudes, two gradients of curve, and two rising times, and the parameters could be reduced to three. The fitting result of this binary mixture of Gaussian functions is compared with some other functions used previously in the literature, and this function works pretty well, especially at cycle peaks. It is worth mentioning that the function can describe well the shape of those sunspot cycles that show double peaks, and it is superior to the binary mixture of the Laplace functions that was once utilized. The Solar Influences Data Analysis Center, on behalf of the World Data Center, recently issued a new version (version 2) of sunspot number. The characteristics of sunspot cycles are investigated, based on the function description of the new version.
Energy Technology Data Exchange (ETDEWEB)
Fouque, A.L.; Ciuciu, Ph.; Risser, L. [NeuroSpin/CEA, F-91191 Gif-sur-Yvette (France); Fouque, A.L.; Ciuciu, Ph.; Risser, L. [IFR 49, Institut d' Imagerie Neurofonctionnelle, Paris (France)
2009-07-01
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)
Semi-Supervised Classification based on Gaussian Mixture Model for remote imagery
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Semi-Supervised Classification (SSC),which makes use of both labeled and unlabeled data to determine classification borders in feature space,has great advantages in extracting classification information from mass data.In this paper,a novel SSC method based on Gaussian Mixture Model (GMM) is proposed,in which each class’s feature space is described by one GMM.Experiments show the proposed method can achieve high classification accuracy with small amount of labeled data.However,for the same accuracy,supervised classification methods such as Support Vector Machine,Object Oriented Classification,etc.should be provided with much more labeled data.
Novel pseudo-divergence of Gaussian mixture models based speaker clustering method
Institute of Scientific and Technical Information of China (English)
Wang Bo; Xu Yiqiong; Li Bicheng
2006-01-01
Serial structure is applied to speaker recognition to reduce the algorithm delay and computational complexity. The speech is first classified into speaker class, and then searches the most likely one inside the class.Difference between Gaussian Mixture Models (GMMs) is widely applied in speaker classification. The paper proposes a novel mean of pseudo-divergence, the ratio of Inter-Model dispersion to Intra-Model dispersion, to present the difference between GMMs, to perform speaker cluster. Weight, mean and variance, GMM's components, are involved in the dispersion. Experiments indicate that the measurement can well present the difference of GMMs and has improved performance of speaker clustering.
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...... are considered to be Gaussian. Conventional FORM analysis yields the linearization point of the idealized limit-state surface. A model correction factor is then introduced to push the idealized limit-state surface onto the actual limit-state surface. A few iterations yield a good approximation of the reliability...... reliability method; Model correction factor method; Nataf field integration; Non-Gaussion random field; Random field integration; Structural reliability; Pile foundation reliability...
A Novel Robust Scene Change Detection Algorithm for Autonomous Robots Using Mixtures of Gaussians
Directory of Open Access Journals (Sweden)
Luis J. Manso
2014-02-01
Full Text Available Interest in change detection techniques has considerably increased during recent years in the field of autonomous robotics. This is partly because changes in a robot's working environment are useful for several robotic skills (e.g., spatial cognition, modelling or navigation and applications (e.g., surveillance or guidance robots. Changes are usually detected by comparing current data provided by the robot's sensors with a previously known map or model of the environment. When the data consists of a large point cloud, dealing with it is a computationally expensive task, mainly due to the amount of points and the redundancy. Using Gaussian Mixture Models (GMM instead of raw point clouds leads to a more compact feature space that can be used to efficiently process the input data. This allows us to successfully segment the set of 3D points acquired by the sensor and reduce the computational load of the change detection algorithm. However, the segmentation of the environment as a Mixture of Gaussians has some problems that need to be properly addressed. In this paper, a novel change detection algorithm is described in order to improve the robustness and computational cost of previous approaches. The proposal is based on the classic Expectation Maximization (EM algorithm, for which different selection criteria are evaluated. As demonstrated in the experimental results section, the proposed change detection algorithm achieves the detection of changes in the robot's working environment faster and more accurately than similar approaches.
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.
Chen, Yunjie; Zhan, Tianming; Zhang, Ji; Wang, Hongyuan
2016-01-01
We propose a novel segmentation method based on regional and nonlocal information to overcome the impact of image intensity inhomogeneities and noise in human brain magnetic resonance images. With the consideration of the spatial distribution of different tissues in brain images, our method does not need preestimation or precorrection procedures for intensity inhomogeneities and noise. A nonlocal information based Gaussian mixture model (NGMM) is proposed to reduce the effect of noise. To reduce the effect of intensity inhomogeneity, the multigrid nonlocal Gaussian mixture model (MNGMM) is proposed to segment brain MR images in each nonoverlapping multigrid generated by using a new multigrid generation method. Therefore the proposed model can simultaneously overcome the impact of noise and intensity inhomogeneity and automatically classify 2D and 3D MR data into tissues of white matter, gray matter, and cerebral spinal fluid. To maintain the statistical reliability and spatial continuity of the segmentation, a fusion strategy is adopted to integrate the clustering results from different grid. The experiments on synthetic and clinical brain MR images demonstrate the superior performance of the proposed model comparing with several state-of-the-art algorithms.
A Novel Robust Scene Change Detection Algorithm for Autonomous Robots Using Mixtures of Gaussians
Directory of Open Access Journals (Sweden)
Luis J. Manso
2014-02-01
Full Text Available Interest in change detection techniques has considerably increased during recent years in the field of autonomous robotics. This is partly because changes in a robot’s working environment are useful for several robotic skills (e.g., spatial cognition, modelling or navigation and applications (e.g., surveillance or guidance robots. Changes are usually detected by comparing current data provided by the robot’s sensors with a previously known map or model of the environment. When the data consists of a large point cloud, dealing with it is a computationally expensive task, mainly due to the amount of points and the redundancy. Using Gaussian Mixture Models (GMM instead of raw point clouds leads to a more compact feature space that can be used to efficiently process the input data. This allows us to successfully segment the set of 3D points acquired by the sensor and reduce the computational load of the change detection algorithm. However, the segmentation of the environment as a Mixture of Gaussians has some problems that need to be properly addressed. In this paper, a novel change detection algorithm is described in order to improve the robustness and computational cost of previous approaches. The proposal is based on the classic Expectation Maximization (EM algorithm, for which different selection criteria are evaluated. As demonstrated in the experimental results section, the proposed change detection algorithm achieves the detection of changes in the robot’s working environment faster and more accurately than similar approaches.
Tests for, origins of, and corrections to non-Gaussian statistics. The dipole-flip model.
Schile, Addison J; Thompson, Ward H
2017-04-21
Linear response approximations are central to our understanding and simulations of nonequilibrium statistical mechanics. Despite the success of these approaches in predicting nonequilibrium dynamics, open questions remain. Laird and Thompson [J. Chem. Phys. 126, 211104 (2007)] previously formalized, in the context of solvation dynamics, the connection between the static linear-response approximation and the assumption of Gaussian statistics. The Gaussian statistics perspective is useful in understanding why linear response approximations are still accurate for perturbations much larger than thermal energies. In this paper, we use this approach to address three outstanding issues in the context of the "dipole-flip" model, which is known to exhibit nonlinear response. First, we demonstrate how non-Gaussian statistics can be predicted from purely equilibrium molecular dynamics (MD) simulations (i.e., without resort to a full nonequilibrium MD as is the current practice). Second, we show that the Gaussian statistics approximation may also be used to identify the physical origins of nonlinear response residing in a small number of coordinates. Third, we explore an approach for correcting the Gaussian statistics approximation for nonlinear response effects using the same equilibrium simulation. The results are discussed in the context of several other examples of nonlinear responses throughout the literature.
ADAPTIVE BACKGROUND DENGAN METODE GAUSSIAN MIXTURE MODELS UNTUK REAL-TIME TRACKING
Directory of Open Access Journals (Sweden)
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.
2016-02-01
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
Directory of Open Access Journals (Sweden)
Qunyi Xie
2016-01-01
Full Text Available Content-based image retrieval has recently become an important research topic and has been widely used for managing images from repertories. In this article, we address an efficient technique, called MNGS, which integrates multiview constrained nonnegative matrix factorization (NMF and Gaussian mixture model- (GMM- based spectral clustering for image retrieval. In the proposed methodology, the multiview NMF scheme provides competitive sparse representations of underlying images through decomposition of a similarity-preserving matrix that is formed by fusing multiple features from different visual aspects. In particular, the proposed method merges manifold constraints into the standard NMF objective function to impose an orthogonality constraint on the basis matrix and satisfy the structure preservation requirement of the coefficient matrix. To manipulate the clustering method on sparse representations, this paper has developed a GMM-based spectral clustering method in which the Gaussian components are regrouped in spectral space, which significantly improves the retrieval effectiveness. In this way, image retrieval of the whole database translates to a nearest-neighbour search in the cluster containing the query image. Simultaneously, this study investigates the proof of convergence of the objective function and the analysis of the computational complexity. Experimental results on three standard image datasets reveal the advantages that can be achieved with the proposed retrieval scheme.
Xiao, Yiming; Shah, Mohak; Francis, Simon; Arnold, Douglas L.; Arbel, Tal; Collins, D. Louis
Brain tissue segmentation is important in studying markers in human brain Magnetic Resonance Images (MRI) of patients with diseases such as Multiple Sclerosis (MS). Parametric segmentation approaches typically assume unimodal Gaussian distributions on MRI intensities of individual tissue classes, even in applications on multi-spectral images. However, this assumption has not been rigorously verified especially in the context of MS. In this work, we evaluate the local MRI intensities of both healthy and diseased brain tissues of 21 multi-spectral MRIs (63 volumes in total) of MS patients for adherence to this assumption. We show that the tissue intensities are not uniform across the brain and vary across (anatomical) regions of the brain. Consequently, we show that Gaussian mixtures can better model the multi-spectral intensities. We utilize an Expectation Maximization (EM) based approach to learn the models along with a symmetric Jeffreys divergence criterion to study differences in intensity distributions. The effects of these findings are also empirically verified on automatic segmentation of brains with MS.
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.
Approximating Gaussian mixture model or radial basis function network with multilayer perceptron.
Patrikar, Ajay M
2013-07-01
Gaussian mixture models (GMMs) and multilayer perceptron (MLP) are both popular pattern classification techniques. This brief shows that a multilayer perceptron with quadratic inputs (MLPQ) can accurately approximate GMMs with diagonal covariance matrices. The mapping equations between the parameters of GMM and the weights of MLPQ are presented. A similar approach is applied to radial basis function networks (RBFNs) to show that RBFNs with Gaussian basis functions and Euclidean norm can be approximated accurately with MLPQ. The mapping equations between RBFN and MLPQ weights are presented. There are well-established training procedures for GMMs, such as the expectation maximization (EM) algorithm. The GMM parameters obtained by the EM algorithm can be used to generate a set of initial weights of MLPQ. Similarly, a trained RBFN can be used to generate a set of initial weights of MLPQ. MLPQ training can be continued further with gradient-descent based methods, which can lead to improvement in performance compared to the GMM or RBFN from which it is initialized. Thus, the MLPQ can always perform as well as or better than the GMM or RBFN.
Mixture subclass discriminant analysis link to restricted Gaussian model and other generalizations.
Gkalelis, Nikolaos; Mezaris, Vasileios; Kompatsiaris, Ioannis; Stathaki, Tania
2013-01-01
In this paper, a theoretical link between mixture subclass discriminant analysis (MSDA) and a restricted Gaussian model is first presented. Then, two further discriminant analysis (DA) methods, i.e., fractional step MSDA (FSMSDA) and kernel MSDA (KMSDA) are proposed. Linking MSDA to an appropriate Gaussian model allows the derivation of a new DA method under the expectation maximization (EM) framework (EM-MSDA), which simultaneously derives the discriminant subspace and the maximum likelihood estimates. The two other proposed methods generalize MSDA in order to solve problems inherited from conventional DA. FSMSDA solves the subclass separation problem, that is, the situation in which the dimensionality of the discriminant subspace is strictly smaller than the rank of the inter-between-subclass scatter matrix. This is done by an appropriate weighting scheme and the utilization of an iterative algorithm for preserving useful discriminant directions. On the other hand, KMSDA uses the kernel trick to separate data with nonlinearly separable subclass structure. Extensive experimentation shows that the proposed methods outperform conventional MSDA and other linear discriminant analysis variants.
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
GAUSSIAN MIXTURE MODEL BASED LEVEL SET TECHNIQUE FOR AUTOMATED SEGMENTATION OF CARDIAC MR IMAGES
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G. Dharanibai,
2011-04-01
Full Text Available In this paper we propose a Gaussian Mixture Model (GMM integrated level set method for automated segmentation of left ventricle (LV, right ventricle (RV and myocardium from short axis views of cardiacmagnetic resonance image. By fitting GMM to the image histogram, global pixel intensity characteristics of the blood pool, myocardium and background are estimated. GMM provides initial segmentation andthe segmentation solution is regularized using level set. Parameters for controlling the level set evolution are automatically estimated from the Bayesian inference classification of pixels. We propose a new speed function that combines edge and region information that stops the evolving level set at the myocardial boundary. Segmentation efficacy is analyzed qualitatively via visual inspection. Results show the improved performance of our of proposed speed function over the conventional Bayesian driven adaptive speed function in automatic segmentation of myocardium
Mixed Platoon Flow Dispersion Model Based on Speed-Truncated Gaussian Mixture Distribution
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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.
Color-texture segmentation using JSEG based on Gaussian mixture modeling
Institute of Scientific and Technical Information of China (English)
Wang Yuzhong; Yang Jie; Zhou Yue
2006-01-01
An improved approach for J-value segmentation (JSEG) is presented for unsupervised color image segmentation. Instead of color quantization algorithm, an automatic classification method based on adaptive mean shift (AMS)based clustering is used for nonparametric clustering of image data set. The clustering results are used to construct Gaussian mixture modelling (GMM) of image data for the calculation of soft J value. The region growing algorithm used in JSEG is then applied in segmenting the image based on the multiscale soft J-images. Experiments show that the synergism of JSEG and the soft classification based on AMS based clustering and GMM overcomes the limitations of JSEG successfully and is more robust.
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.
Wang, Chuanyun; Song, Fei; Qin, Shiyin
2017-02-01
Addressing the problems of infrared small target tracking in forward looking infrared (FLIR) system, a new infrared small target tracking method is presented, in which features binding of both target gray intensity and spatial relationship is implemented by compressive sensing so as to construct the Gaussian mixture model of compressive appearance distribution. Subsequently, naive Bayesian classification is carried out over testing samples acquired with non-uniform sampling probability to identify the most credible location of targets from background scene. A series of experiments are carried out over four infrared small target image sequences with more than 200 images for each sequence, the results demonstrate the effectiveness and advantages of the proposed method in both success rate and precision rate.
Non-Gaussianities due to Relativistic Corrections to the Observed Galaxy Bispectrum
Di Dio, E; Durrer, R; Marozzi, G; Dizgah, A Moradinezhad; Noreña, J; Riotto, A
2016-01-01
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 $f_{\\rm NL}$ 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 contributio...
Loukas, Constantinos; Georgiou, Evangelos
2013-01-01
There is currently great interest in analyzing the workflow of minimally invasive operations performed in a physical or simulation setting, with the aim of extracting important information that can be used for skills improvement, optimization of intraoperative processes, and comparison of different interventional strategies. The first step in achieving this goal is to segment the operation into its key interventional phases, which is currently approached by modeling a multivariate signal that describes the temporal usage of a predefined set of tools. Although this technique has shown promising results, it is challenged by the manual extraction of the tool usage sequence and the inability to simultaneously evaluate the surgeon's skills. In this paper we describe an alternative methodology for surgical phase segmentation and performance analysis based on Gaussian mixture multivariate autoregressive (GMMAR) models of the hand kinematics. Unlike previous work in this area, our technique employs signals from orientation sensors, attached to the endoscopic instruments of a virtual reality simulator, without considering which tools are employed at each time-step of the operation. First, based on pre-segmented hand motion signals, a training set of regression coefficients is created for each surgical phase using multivariate autoregressive (MAR) models. Then, a signal from a new operation is processed with GMMAR, wherein each phase is modeled by a Gaussian component of regression coefficients. These coefficients are compared to those of the training set. The operation is segmented according to the prior probabilities of the surgical phases estimated via GMMAR. The method also allows for the study of motor behavior and hand motion synchronization demonstrated in each phase, a quality that can be incorporated into modern laparoscopic simulators for skills assessment.
Kamiya, Ryo; Ogawa, Koichi
2013-08-01
The aim of the study is to improve the spatial resolution of 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.
A Gaussian mixture model for definition of lung tumor volumes in positron emission tomography.
Aristophanous, Michalis; Penney, Bill C; Martel, Mary K; Pelizzari, Charles A
2007-11-01
The increased interest in 18F-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
On the Eavesdropper's Correct Decision in Gaussian and Fading Wiretap Channels Using Lattice Codes
Ernvall-Hytönen, Anne-Maria
2011-01-01
In this paper, the probability of Eve the Eavesdropper's correct decision is considered both in the Gaussian and Rayleigh fading wiretap channels when using lattice codes for the transmission. First, it is proved that the secrecy function determining Eve's performance attains its maximum at y=1 on all known extremal even unimodular lattices. This is a special case of a conjecture by Belfiore and Sol\\'e. Further, a very simple method to verify or disprove the conjecture on any given unimodular lattice is given. Second, preliminary analysis on the behavior of Eve's probability of correct decision in the fast fading wiretap channel is provided. More specifically, we compute the truncated inverse norm power sum factors in Eve's probability expression. The analysis reveals a performance-secrecy-complexity tradeoff: relaxing on the legitimate user's performance can significantly increase the security of transmission. The confusion experienced by the eavesdropper may be further increased by using skewed lattices, bu...
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.
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.
Gaussian Mixture Model and Deep Neural Network based Vehicle Detection and Classification
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S Sri Harsha
2016-09-01
Full Text Available The exponential rise in the demand of vision based traffic surveillance systems have motivated academia-industries to develop optimal vehicle detection and classification scheme. In this paper, an adaptive learning rate based Gaussian mixture model (GMM algorithm has been developed for background subtraction of multilane traffic data. Here, vehicle rear information and road dash-markings have been used for vehicle detection. Performing background subtraction, connected component analysis has been applied to retrieve vehicle region. A multilayered AlexNet deep neural network (DNN has been applied to extract higher layer features. Furthermore, scale invariant feature transform (SIFT based vehicle feature extraction has been performed. The extracted 4096-dimensional features have been processed for dimensional reduction using principle component analysis (PCA and linear discriminant analysis (LDA. The features have been mapped for SVM-based classification. The classification results have exhibited that AlexNet-FC6 features with LDA give the accuracy of 97.80%, followed by AlexNet-FC6 with PCA (96.75%. AlexNet-FC7 feature with LDA and PCA algorithms has exhibited classification accuracy of 91.40% and 96.30%, respectively. On the contrary, SIFT features with LDA algorithm has exhibited 96.46% classification accuracy. The results revealed that enhanced GMM with AlexNet DNN at FC6 and FC7 can be significant for optimal vehicle detection and classification.
Gaussian mixture sigma-point particle filter for optical indoor navigation system
Zhang, Weizhi; Gu, Wenjun; Chen, Chunyi; Chowdhury, M. I. S.; Kavehrad, Mohsen
2013-12-01
With the fast growing and popularization of smart computing devices, there is a rise in demand for accurate and reliable indoor positioning. Recently, systems using visible light communications (VLC) technology have been considered as candidates for indoor positioning applications. A number of researchers have reported that VLC-based positioning systems could achieve position estimation accuracy in the order of centimeter. This paper proposes an Indoors navigation environment, based on visible light communications (VLC) technology. Light-emitting-diodes (LEDs), which are essentially semiconductor devices, can be easily modulated and used as transmitters within the proposed system. Positioning is realized by collecting received-signal-strength (RSS) information on the receiver side, following which least square estimation is performed to obtain the receiver position. To enable tracking of user's trajectory and reduce the effect of wild values in raw measurements, different filters are employed. In this paper, by computer simulations we have shown that Gaussian mixture Sigma-point particle filter (GM-SPPF) outperforms other filters such as basic Kalman filter and sequential importance-resampling particle filter (SIR-PF), at a reasonable computational cost.
Remote sensing image fusion based on Gaussian mixture model and multiresolution analysis
Xiao, Moyan; He, Zhibiao
2013-10-01
A novel image fusion algorithm based on region segmentation and multiresolution analysis(MRA) is proposed to make full use of advantages of different multiscale transform. Nonsubsampled contourlet transform(NSCT) processes edges better than wavelet transform does. While wavelet transform handles smooth area and singularities better than NSCT does. As an image often includes more than one feature, the proposed method is conducted on the basis of Gaussian mixture model(GMM) based region segmentation. Firstly, transform the multispectral(MS) image into intensity, hue and saturation component. Secondly, segment intensity component into dense contour and smooth regions according to GMM and NSCT. And then gain new intensity component by fusing intensity component and high resolution image with Àtrous wavelet transform(ATWT) fusion in smooth areas and NSCT fusion in dense contour areas. Finally transform the new intensity together with hue component, saturation component back into RGB space and obtain the fused image. Multisource remote sensing images are tested to assess this proposed algorithm. Visual evaluation and statistics analysis are employed to evaluate the quality of fused images of different methods. The proposed improved algorithm demonstrates excellent spectrum information and high resolution. Experiment results show that the new proposed fusion algorithm incorporating with region segmentation based improved GMM and MRA outperforms those algorithms based on single multiscale transform.
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
2015-03-17
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.
Shahrabi, Mohammad Ali; Hashemi, Hosein; Hafizi, Mohammad Kazem
2016-02-01
Seismic and magnetotelluric (MT) methods are the most applicable geophysical methods in exploration of hydrocarbon resources. In this paper, mixture of Gaussian clustering is used to combine seismic and MT images under the scheme of Expectation/Maximization (EM) algorithm. Pre-Stack Depth Migration (PSDM) velocity, Root Mean Square (RMS) velocity and vertical gradient of RMS velocity of seismic and resistivity model of MT along 19.3 km MUN-21 profile in Munir Block that has been located in Southwest of Iran in Dezful embayment over the Seh-Qanat anticline are applied. The anticline is the most important oil trap of this area. The Expectation/Maximization (EM) method that has been applied includes: (1) creation of data vectors from the seismic and MT images using image processing techniques, (2) normalizing and mapping using Principal Component Analysis (PCA) procedure (3) unsupervised learning of dataset matrix, (4) setting the matrix in Expectation/Maximization (EM) iteration algorithm (5) remapping to physical space. The final model consists fof six classes which could be given to eight formations that belong to Eocene to Neocomian geological age. Pre-Stack Depth Migration (PSDM) velocity model obtained from seismic study on Seh-Qanat anticline only detected 2 horizons of formations, Asmari and Sarvak Formations; however, the current methodology introduces subdivision anticline into six classes by matching it to the log information of Seh-Qanat Deep-1 (SQD-1) borehole where it was excavated over the anticline with total depth of 2876 m.
Directory of Open Access Journals (Sweden)
Uttam Mande
2012-06-01
Full Text Available Lot of research is projected to map the criminal with that of crime and it is observed that there is still a huge increase in the crime rate due to the gap between the optimal usage of technologies and investigation. This has given scope for the development of new methodologies in the area of crime investigation using the techniques based on data mining, image processing, forensic, and social mining. In this paper, presents a model using new methodology for mapping the criminal with the crime. This model clusters the criminal data basing on the type crime. When a crime occurs, based on the eye witness specified features, the criminal is mapped. Here we propose a novel methodology that uses Generalized Gaussian Mixture Model to map the features specified by the eyewitness with that of the features of the criminal who have committed the same type of the crime, if the criminal is not mapped, the suspect table is checked and the reports are generated
Short-term traffic safety forecasting using Gaussian mixture model and Kalman filter
Institute of Scientific and Technical Information of China (English)
Sheng JIN; Dian-hai WANG; Cheng XU; Dong-fang MA
2013-01-01
In this paper; a prediction model is developed that combines a Gaussian mixture model (GMM) and a Kalman filter for online forecasting of traffic safety on expressways.Raw time-to-collision (TTC) samples are divided into two categories:those representing vehicles in risky situations and those in safe situations.Then,the GMM is used to model the bimodal distribution of the TTC samples,and the maximum likelihood (ML) estimation parameters of the TTC distribution are obtained using the expectation-maximization (EM) algorithm.We propose a new traffic safety indicator,named the proportion of exposure to traffic conflicts (PETTC),for assessing the risk and predicting the safety of expressway traffic.A Kalman filter is applied to forecast the short-term safety indicator,PETTC,and solves the online safety prediction problem.A dataset collected from four different expressway locations is used for performance estimation.The test results demonstrate the precision and robustness of the prediction model under different traffic conditions and using different datasets.These results could help decision-makers to improve their online traffic safety forecasting and enable the optimal operation of expressway traffic management systems.
A Grasp-pose Generation Method Based on Gaussian Mixture Models
Directory of Open Access Journals (Sweden)
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.
Scale factor correction for Gaussian beam truncation in second moment beam radius measurements
Hofer, Lucas R.; Dragone, Rocco V.; MacGregor, Andrew D.
2017-04-01
Charged-couple devices (CCD) and complementary metal oxide semiconductor (CMOS) image sensors, in conjunction with the second moment radius analysis method, are effective tools for determining the radius of a laser beam. However, the second moment method heavily weights sensor noise, which must be dealt with using a thresholding algorithm and a software aperture. While these noise reduction methods lower the random error due to noise, they simultaneously generate systematic error by truncating the Gaussian beam's edges. A scale factor that is invariant to beam ellipticity and corrects for the truncation of the Gaussian beam due to thresholding and the software aperture has been derived. In particular, simulations showed an order of magnitude reduction in measured beam radius error when using the scale factor-irrespective of beam ellipticity-and further testing with real beam data demonstrated that radii corrected by the scale factor are independent of the noise reduction parameters. Thus, through use of the scale factor, the accuracy of beam radius measurements made with a CCD or CMOS sensor and the second moment are significantly improved.
Adaptive Gaussian mixture models for pre-screening in GPR data
Torrione, Peter; Morton, Kenneth, Jr.; Besaw, Lance E.
2011-06-01
Due to the large amount of data generated by vehicle-mounted ground penetrating radar (GPR) antennae arrays, advanced feature extraction and classification can only be performed on a small subset of data during real-time operation. As a result, most GPR based landmine detection systems implement "pre-screening" algorithms to processes all of the data generated by the antennae array and identify locations with anomalous signatures for more advanced processing. These pre-screening algorithms must be computationally efficient and obtain high probability of detection, but can permit a false alarm rate which might be higher than the total system requirements. Many approaches to prescreening have previously been proposed, including linear prediction coefficients, the LMS algorithm, and CFAR-based approaches. Similar pre-screening techniques have also been developed in the field of video processing to identify anomalous behavior or anomalous objects. One such algorithm, an online k-means approximation to an adaptive Gaussian mixture model (GMM), is particularly well-suited to application for pre-screening in GPR data due to its computational efficiency, non-linear nature, and relevance of the logic underlying the algorithm to GPR processing. In this work we explore the application of an adaptive GMM-based approach for anomaly detection from the video processing literature to pre-screening in GPR data. Results with the ARA Nemesis landmine detection system demonstrate significant pre-screening performance improvements compared to alternative approaches, and indicate that the proposed algorithm is a complimentary technique to existing methods.
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.
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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.
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.
Carena, A; Curri, V; Poggiolini, P; Jiang, Y; Forghieri, F
2014-01-01
The GN-model has been shown to overestimate the variance of non-linearity due to the signal Gaussianity approximation, leading to realistic system maximum reach predictions which may be pessimistic by about 5% to 15%, depending on fiber type and system set-up. Analytical corrections have been proposed, which however substantially increase the model complexity. In this paper we provide a closed-form simple GN-model correction which we show to be very effective in correcting for the GN-model tendency to overestimate non-linearity. Our formula also allows to clearly identify the correction dependence on key system parameters, such as the span length and loss.
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
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 proportion
Zhang, Ruoqiao; Pal, Debashish; Thibault, Jean-Baptiste; Sauer, Ken D; Bouman, Charles A
2016-01-01
Markov random fields (MRFs) have been widely used as prior models in various inverse problems such as tomographic reconstruction. While MRFs provide a simple and often effective way to model the spatial dependencies in images, they suffer from the fact that parameter estimation is difficult. In practice, this means that MRFs typically have very simple structure that cannot completely capture the subtle characteristics of complex images. In this paper, we present a novel Gaussian mixture Markov random field model (GM-MRF) that can be used as a very expressive prior model for inverse problems such as denoising and reconstruction. The GM-MRF forms a global image model by merging together individual Gaussian-mixture models (GMMs) for image patches. In addition, we present a novel analytical framework for computing MAP estimates using the GM-MRF prior model through the construction of surrogate functions that result in a sequence of quadratic optimizations. We also introduce a simple but effective method to adjust...
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.
Yang, Y.; Liu, W.
2017-09-01
To solve the problems of existing method of change detection using fully polarimetric SAR which not takes full advantage of polarimetric information and the result of false alarm rate of which is high, a method is proposed based on test statistic and Gaussian mixture model in this paper. In the case of the flood disaster in Wuhan city in 2016, difference image is obtained by the likelihoodratio parameter which is built using coherency matrix C3 or covariance matrix T3 of fully polarimetric SAR based on test statistic, and it becomes a reality that the change information is automatic extracted by the parameter of Gaussian mixture model (GMM) of difference image based on the expectation maximization (EM) iterative algorithm. The experimental results show that the overall accuracy of change detection results can be improved and false alarm rate can be reduced using this method by comparison with traditional constant false alarm rate (CFAR) method. Thus the validity and feasibility of the method is demonstrated.
Holoien, Thomas W -S; Wechsler, Risa H
2016-01-01
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 for using Gaussian mixtures to do density estimation of noisy data using extreme deconvolution (XD) algorithms that has functionality not available in other XD tools. It allows the user to select between the AstroML (Vanderplas et al. 2012; Ivezic et al. 2015) and Bovy et al. (2011) fitting methods and is compatible with scikit-learn machine learning algorithms (Pedregosa et al. 2011). 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 conditioned on known values of other parameters. EmpiriciSN is an example application of this functionality that can be used for fitting an XDGMM model to observed supernova/host datas...
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.
Hazarika, Deepika; Nath, Vijay Kumar; Bhuyan, Manbendra
2016-12-01
A new Lapped transform domain SAR image despeckling algorithm using a two-state Gaussian mixture probability density function that uses local parameters for the mixture model, is proposed. The use of lapped orthogonal transform (LOT) is motivated by its low computational complexity and robustness to oversmoothing. It is shown that the dyadic rearranged LOT coefficients of logarithmically transformed SAR images can be well approximated using two-state Gaussian mixture distribution compared to Laplacian, Gamma, generalized Gaussian and Cauchy distributions, based on the Kolmogorov-Smirnov (KS) goodness of fit test. The LOT coefficients of speckle noise are modeled using zero mean Gaussian distributions. A maximum a posteriori (MAP) estimator within Bayesian framework is developed using this proposed prior distribution and is used to restore the noisy LOT coefficients. The parameters of mixture distribution are estimated using the expectation-maximization algorithm. This paper presents a new technique to identify LOT modulus maxima which allows us to classify LOT coefficients into the edge and non edge coefficients. The classified edge coefficients are kept unmodified by the proposed algorithm whereas the noise-free estimates of non-edge coefficients are obtained using Bayesian MAP estimator developed using two state Gaussian mixture distribution with local parameters. Finally the proposed technique is combined with the cycle spinning scheme to further improve the despeckling performance. Experimental results show that the proposed method very efficiently reduces speckle in homogeneous regions while preserving more edge structures compared to some recent well known methods.
Correction Factor for Gaussian Deconvolution of Optically Thick Linewidths in Homogeneous Sources
Kastner, S. O.; Bhatia, A. K.
1999-01-01
Profiles of optically thick, non-Gaussian emission line profiles convoluted with Gaussian instrumental profiles are constructed, and are deconvoluted on the usual Gaussian basis to examine the departure from accuracy thereby caused in "measured" linewidths. It is found that "measured" linewidths underestimate the true linewidths of optically thick lines, by a factor which depends on the resolution factor r congruent to Doppler width/instrumental width and on the optical thickness tau(sub 0). An approximating expression is obtained for this factor, applicable in the range of at least 0 tau(sub 0) estimates of the true linewidth and optical thickness.
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.
Lankarany, M; Zhu, W-P; Swamy, M N S; Toyoizumi, Taro
2013-01-01
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 (GMKF) for estimating time-varying excitatory and inhibitory synaptic inputs from single trials of noisy membrane potential in current clamp recordings. The KF is followed by an expectation maximization (EM) 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 (GMM). 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.
Bubin, Sergiy; Stanke, Monika; Adamowicz, Ludwik
2017-06-01
In our previous work S. Bubin et al., Chem. Phys. Lett. 647, 122 (2016), 10.1016/j.cplett.2016.01.056, it was established that complex explicitly correlated one-center all-particle Gaussian functions (CECGs) provide effective basis functions for very accurate nonrelativistic molecular non-Born-Oppenheimer calculations. In this work, we advance the molecular CECGs approach further by deriving and implementing algorithms for calculating the leading relativistic corrections within this approach. The algorithms are tested in the calculations of the corrections for all 23 bound pure vibrational states of the HD+ ion.
Stanke, Monika; Palikot, Ewa; Adamowicz, Ludwik
2016-05-01
Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H2 and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.
Institute of Scientific and Technical Information of China (English)
Zhang Zhi; Li Jianxun; Liu Liu; Liu Zhaolei; Han Shan
2015-01-01
Since the features of low energy consumption and limited power supply are very impor-tant for wireless sensor networks (WSNs), the problems of distributed state estimation with quan-tized innovations are investigated in this paper. In the first place, the assumptions of prior and posterior probability density function (PDF) with quantized innovations in the previous papers are analyzed. After that, an innovative Gaussian mixture estimator is proposed. On this basis, this paper presents a Gaussian mixture state estimation algorithm based on quantized innovations for WSNs. In order to evaluate and compare the performance of this kind of state estimation algo-rithms for WSNs, the posterior Cramer–Rao lower bound (CRLB) with quantized innovations is put forward. Performance analysis and simulations show that the proposed Gaussian mixture state estimation algorithm is efficient than the others under the same number of quantization levels and the performance of these algorithms can be benchmarked by the theoretical lower bound.
Directory of Open Access Journals (Sweden)
Zhang Zhi
2015-12-01
Full Text Available Since the features of low energy consumption and limited power supply are very important for wireless sensor networks (WSNs, the problems of distributed state estimation with quantized innovations are investigated in this paper. In the first place, the assumptions of prior and posterior probability density function (PDF with quantized innovations in the previous papers are analyzed. After that, an innovative Gaussian mixture estimator is proposed. On this basis, this paper presents a Gaussian mixture state estimation algorithm based on quantized innovations for WSNs. In order to evaluate and compare the performance of this kind of state estimation algorithms for WSNs, the posterior Cramér–Rao lower bound (CRLB with quantized innovations is put forward. Performance analysis and simulations show that the proposed Gaussian mixture state estimation algorithm is efficient than the others under the same number of quantization levels and the performance of these algorithms can be benchmarked by the theoretical lower bound.
Garrido, M C; Ruiz, A; 10.1613/jair.533
2011-01-01
This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard prob...
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.
Fifth-order corrected field descriptions of the Hermite-Gaussian (0,0) and (0,1) mode laser beam.
Wang, J X; Scheid, W; Hoelss, M; Ho, Y K
2001-12-01
In this paper, we extend the work of Barton and Alexander [J. App. Phys. 66, 2800 (1989)] on the fifth-order corrected field expressions for a Hermite-Gaussian (0,0) mode laser beam to more general cases with adjustable parameters. The parametric dependence of the electron dynamics is investigated by numerical methods. Finally, the fifth-order corrected field equations for the Hermite-Gaussian (0,1) mode are also presented.
Chen, Jian; Yuan, Shenfang; Qiu, Lei; Wang, Hui; Yang, Weibo
2017-07-25
Accurate on-line prognosis of fatigue crack propagation is of great meaning for prognostics and health management (PHM) technologies to ensure structural integrity, which is a challenging task because of uncertainties which arise from sources such as intrinsic material properties, loading, and environmental factors. The particle filter algorithm has been proved to be a powerful tool to deal with prognostic problems those are affected by uncertainties. However, most studies adopted the basic particle filter algorithm, which uses the transition probability density function as the importance density and may suffer from serious particle degeneracy problem. This paper proposes an on-line fatigue crack propagation prognosis method based on a novel Gaussian weight-mixture proposal particle filter and the active guided wave based on-line crack monitoring. Based on the on-line crack measurement, the mixture of the measurement probability density function and the transition probability density function is proposed to be the importance density. In addition, an on-line dynamic update procedure is proposed to adjust the parameter of the state equation. The proposed method is verified on the fatigue test of attachment lugs which are a kind of important joint components in aircraft structures. Copyright © 2017 Elsevier B.V. All rights reserved.
Bridging the ensemble Kalman filter and particle filters: the adaptive Gaussian mixture filter
Stordal, Andreas Størksen; Karlsen, Hans A.; Nævdal, Geir; Hans J. Skaug; Vallès, Brice
2010-01-01
The nonlinear filtering problem occurs in many scientific areas. Sequential Monte Carlo solutions with the correct asymptotic behavior such as particle filters exist, but they are computationally too expensive when working with high-dimensional systems. The ensemble Kalman filter (EnKF) is a more robust method that has shown promising results with a small sample size, but the samples are not guaranteed to come from the true posterior distribution. By approximating the model error with a Gauss...
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.
Vargas Cardona, Hernán Darío; Orozco, Álvaro Ángel; Álvarez, Mauricio A
2013-01-01
Automatic identification of biosignals is one of the more studied fields in biomedical engineering. In this paper, we present an approach for the unsupervised recognition of biomedical signals: Microelectrode Recordings (MER) and Electrocardiography signals (ECG). The unsupervised learning is based in classic and bayesian estimation theory. We employ gaussian mixtures models with two estimation methods. The first is derived from the frequentist estimation theory, known as Expectation-Maximization (EM) algorithm. The second is obtained from bayesian probabilistic estimation and it is called variational inference. In this framework, both methods are used for parameters estimation of Gaussian mixtures. The mixtures models are used for unsupervised pattern classification, through the responsibility matrix. The algorithms are applied in two real databases acquired in Parkinson's disease surgeries and electrocardiograms. The results show an accuracy over 85% in MER and 90% in ECG for identification of two classes. These results are statistically equal or even better than parametric (Naive Bayes) and nonparametric classifiers (K-nearest neighbor).
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 <54% in two-choice classification accuracy. Significance. We believe GMMAC will be useful for clinical fNIRS-based brain-computer interfaces, including neurofeedback training systems, where operation over long time spans is required.
Qiu, Lei; Yuan, Shenfang; Bao, Qiao; Mei, Hanfei; Ren, Yuanqiang
2016-05-01
For aerospace application of structural health monitoring (SHM) technology, the problem of reliable damage monitoring under time-varying conditions must be addressed and the SHM technology has to be fully validated on real aircraft structures under realistic load conditions on ground before it can reach the status of flight test. In this paper, the guided wave (GW) based SHM method is applied to a full-scale aircraft fatigue test which is one of the most similar test status to the flight test. To deal with the time-varying problem, a GW-Gaussian mixture model (GW-GMM) is proposed. The probability characteristic of GW features, which is introduced by time-varying conditions is modeled by GW-GMM. The weak cumulative variation trend of the crack propagation, which is mixed in time-varying influence can be tracked by the GW-GMM migration during on-line damage monitoring process. A best match based Kullback-Leibler divergence is proposed to measure the GW-GMM migration degree to reveal the crack propagation. The method is validated in the full-scale aircraft fatigue test. The validation results indicate that the reliable crack propagation monitoring of the left landing gear spar and the right wing panel under realistic load conditions are achieved.
Ortiz-Rosario, Alexis; Adeli, Hojjat; Buford, John A
2017-01-15
Researchers often rely on simple methods to identify involvement of neurons in a particular motor task. The historical approach has been to inspect large groups of neurons and subjectively separate neurons into groups based on the expertise of the investigator. In cases where neuron populations are small it is reasonable to inspect these neuronal recordings and their firing rates carefully to avoid data omissions. In this paper, a new methodology is presented for automatic objective classification of neurons recorded in association with behavioral tasks into groups. By identifying characteristics of neurons in a particular group, the investigator can then identify functional classes of neurons based on their relationship to the task. The methodology is based on integration of a multiple signal classification (MUSIC) algorithm to extract relevant features from the firing rate and an expectation-maximization Gaussian mixture algorithm (EM-GMM) to cluster the extracted features. The methodology is capable of identifying and clustering similar firing rate profiles automatically based on specific signal features. An empirical wavelet transform (EWT) was used to validate the features found in the MUSIC pseudospectrum and the resulting signal features captured by the methodology. Additionally, this methodology was used to inspect behavioral elements of neurons to physiologically validate the model. This methodology was tested using a set of data collected from awake behaving non-human primates. Copyright © 2016 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Rui Li
Full Text Available We present a method to discover discriminative brain metabolism patterns in [18F] fluorodeoxyglucose positron emission tomography (PET scans, facilitating the clinical diagnosis of Alzheimer's disease. In the work, the term "pattern" stands for a certain brain region that characterizes a target group of patients and can be used for a classification as well as interpretation purposes. Thus, it can be understood as a so-called "region of interest (ROI". In the literature, an ROI is often found by a given brain atlas that defines a number of brain regions, which corresponds to an anatomical approach. The present work introduces a semi-data-driven approach that is based on learning the characteristics of the given data, given some prior anatomical knowledge. A Gaussian Mixture Model (GMM and model selection are combined to return a clustering of voxels that may serve for the definition of ROIs. Experiments on both an in-house dataset and data of the Alzheimer's Disease Neuroimaging Initiative (ADNI suggest that the proposed approach arrives at a better diagnosis than a merely anatomical approach or conventional statistical hypothesis testing.
Chattopadhyay, Souradeep; Maitra, Ranjan
2017-08-01
Clustering methods are an important tool to enumerate and describe the different coherent kind of gamma-ray bursts (GRBs). But their performance can be affected by a number of factors such as the choice of clustering algorithm and inherent associated assumptions, the inclusion of variables in clustering, nature of initialization methods used or the iterative algorithm or the criterion used to judge the optimal number of groups supported by the data. We analysed GRBs from the Burst and Transient Source Experiment (BATSE) 4Br Catalog using k-means and Gaussian-mixture-models-based clustering methods and found that after accounting for all the above factors, all six variables - different subsets of which have been used in the literature - that are, namely, the flux duration variables (T50, T90), the peak flux (P256) measured in 256 ms bins, the total fluence (Ft) and the spectral hardness ratios (H32 and H321) contain information on clustering. Further, our analysis found evidence of five different kinds of GRBs and that these groups have different kinds of dispersions in terms of shape, size and orientation. In terms of duration, fluence and spectrum, the five types of GRBs were characterized as intermediate/faint/intermediate, long/intermediate/soft, intermediate/intermediate/intermediate, short/faint/hard and long/bright/intermediate.
Directory of Open Access Journals (Sweden)
Ronghui Zhang
2013-01-01
Full Text Available Vehicle-flow detection and tracking by digital image are one of the most important technologies in the traffic monitoring system. Gaussian mixture distribution method is used to eliminate the influence of moving vehicle firstly in this text, and then we built the background images for vehicle flow. Combining the advantages of background difference algorithm with inter frame difference operator, the real-time background is segmented integrally and dynamically updated accurately by matching the reconstructed image with current background. In order to ensure the robustness of vehicle detection, three by three window templates are adopted to remove the isolated noise spot in the image of vehicle contour. The template structural element is used to do some graphical morphological filtering. So, the corrosion and expansion sets are obtained. To narrow the target search scope and improve the calculation speed and precision of the algorithm, Kalman filtering model is used to realize the tracking of fast moving vehicles. Experimental results show that the method has good real-time and reliable performance.
Qiu, Lei; Yuan, Shenfang; Chang, Fu-Kuo; Bao, Qiao; Mei, Hanfei
2014-12-01
Structural health monitoring technology for aerospace structures has gradually turned from fundamental research to practical implementations. However, real aerospace structures work under time-varying conditions that introduce uncertainties to signal features that are extracted from sensor signals, giving rise to difficulty in reliably evaluating the damage. This paper proposes an online updating Gaussian Mixture Model (GMM)-based damage evaluation method to improve damage evaluation reliability under time-varying conditions. In this method, Lamb-wave-signal variation indexes and principle component analysis (PCA) are adopted to obtain the signal features. A baseline GMM is constructed on the signal features acquired under time-varying conditions when the structure is in a healthy state. By adopting the online updating mechanism based on a moving feature sample set and inner probability structural reconstruction, the probability structures of the GMM can be updated over time with new monitoring signal features to track the damage progress online continuously under time-varying conditions. This method can be implemented without any physical model of damage or structure. A real aircraft wing spar, which is an important load-bearing structure of an aircraft, is adopted to validate the proposed method. The validation results show that the method is effective for edge crack growth monitoring of the wing spar bolts holes under the time-varying changes in the tightness degree of the bolts.
Spain, Christopher J.; Anderson, Derek T.; Keller, James M.; Popescu, Mihail; Stone, Kevin E.
2011-06-01
Burying objects below the ground can potentially alter their thermal properties. Moreover, there is often soil disturbance associated with recently buried objects. An intensity video frame image generated by an infrared camera in the medium and long wavelengths often locally varies in the presence of buried explosive hazards. Our approach to automatically detecting these anomalies is to estimate a background model of the image sequence. Pixel values that do not conform to the background model may represent local changes in thermal or soil signature caused by buried objects. Herein, we present a Gaussian mixture model-based technique to estimate the statistical model of background pixel values. The background model is used to detect anomalous pixel values on the road while a vehicle is moving. Foreground pixel confidence values are projected into the UTM coordinate system and a UTM confidence map is built. Different operating levels are explored and the connected component algorithm is then used to extract islands that are subjected to size, shape and orientation filters. We are currently using this approach as a feature in a larger multi-algorithm fusion system. However, in this article we also present results for using this algorithm as a stand-alone detector algorithm in order to further explore its value in detecting buried explosive hazards.
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.
Kusmakar, Shitanshu; Muthuganapathy, Ramanathan; Yan, Bernard; O'Brien, Terence J; Palaniswami, Marimuthu
2016-08-01
Any abnormal hypersynchronus activity of neurons can be characterized as an epileptic seizure (ES). A broad class of non-epileptic seizures is comprised of Psychogenic non-epileptic seizures (PNES). PNES are paroxysmal events, which mimics epileptic seizures and pose a diagnostic challenge with epileptic seizures due to their clinical similarities. The diagnosis of PNES is done using video-electroencephalography (VEM) monitoring. VEM being a resource intensive process calls for alternative methods for detection of PNES. There is now an emerging interest in the use of accelerometer based devices for the detection of seizures. In this work, we present an algorithm based on Gaussian mixture model (GMM's) for the identification of PNES, ES and normal movements using a wrist-worn accelerometer device. Features in time, frequency and wavelet domain are extracted from the norm of accelerometry signal. All events are then classified into three classes i.e normal, PNES and ES using a parametric estimate of the multivariate normal probability density function. An algorithm based on GMM's allows us to accurately model the non-epileptic and epileptic movements, thus enhancing the overall predictive accuracy of the system. The new algorithm was tested on data collected from 16 patients and showed an overall detection accuracy of 91% with 25 false alarms.
Boberg, Owen M.; Friel, Eileen D.; Vesperini, Enrico
2016-06-01
We present the results of an analysis using Gaussian mixture models (GMM) to separate multiple populations in Milky Way globular clusters based on the Na and O abundances of their members. Recent studies have shown that the method used to separate the populations in globular clusters (e.g. photometry, molecular band strengths, light element abundances) can result in different fractions of primordial and second generation stars. These fractions have important implications on the mass lost by globular clusters during their evolution, and the mechanism responsible for creating the second generation. For many previous studies, the first generation (FG) stars, with primordial Na and O, were classified as such by falling below a maximum [Na/Fe] abundance based on the estimated [Na/Fe] of the Milky Way field population most similar to a given cluster. Stars that were above this [Na/Fe] threshold were classified as second generation (SG) stars, representing the Na enhanced and O depleted population in the cluster. The method we present here is based on separating these populations in the [Na/Fe] vs [O/Fe] plane by constructing a multi-component, and multi-dimensional, GMM. The dataset provided by Carretta et al. 2009 provides a homogeneous sample of [Na/Fe] and [O/Fe] abundances in ~1,000 stars in southern globular clusters. Using all of the stars available in this sample, we created a general GMM that was subsequently used to classify the stars in individual clusters as FG or SG. To perform this classification, the stars in each cluster are assigned a probability of belonging to each of the Gaussian components in the GMM calculated from the entire Carretta sample. Based on these probabilities, we can assign a given star to the FG or SG. Here we present how the fractions of FG and SG stars present in a given globular cluster, as calculated by our GMM, compare to those determined from a single [Na/Fe] threshold. We will also characterize how the fractions of FG and SG stars
Directory of Open Access Journals (Sweden)
Shanmugapriya. K
2014-01-01
Full Text Available The human action recognition system first gathers images by simply querying the name of the action on a web image search engine like Google or Yahoo. Based on the assumption that the set of retrieved images contains relevant images of the queried action, we construct a dataset of action images in an incremental manner. This yields a large image set, which includes images of actions taken from multiple viewpoints in a range of environments, performed by people who have varying body proportions and different clothing. The images mostly present the “key poses” since these images try to convey the action with a single pose. In existing system to support this they first used an incremental image retrieval procedure to collect and clean up the necessary training set for building the human pose classifiers. There are challenges that come at the expense of this broad and representative data. First, the retrieved images are very noisy, since the Web is very diverse. Second, detecting and estimating the pose of humans in still images is more difficult than in videos, partly due to the background clutter and the lack of a foreground mask. In videos, foreground segmentation can exploit motion cues to great benefit. In still images, the only cue at hand is the appearance information and therefore, our model must address various challenges associated with different forms of appearance. Therefore for robust separation, in proposed work a segmentation algorithm based on Gaussian Mixture Models is proposed which is adaptive to light illuminations, shadow and white balance is proposed here. This segmentation algorithm processes the video with or without noise and sets up adaptive background models based on the characteristics also this method is a very effective technique for background modeling which classifies the pixels of a video frame either background or foreground based on probability distribution.
Dai, Peishan; Luo, Hanyuan; Sheng, Hanwei; Zhao, Yali; Li, Ling; Wu, Jing; Zhao, Yuqian; Suzuki, Kenji
2015-01-01
Vessel segmentation in retinal fundus images is a preliminary step to clinical diagnosis for some systemic diseases and some eye diseases. The performances of existing methods for segmenting small vessels which are usually of more importance than the main vessels in a clinical diagnosis are not satisfactory in clinical use. In this paper, we present a method for both main and peripheral vessel segmentation. A local gray-level change enhancement algorithm called gray-voting is used to enhance the small vessels, while a two-dimensional Gabor wavelet is used to extract the main vessels. We fuse the gray-voting results with the 2D-Gabor filter results as pre-processing outcome. A Gaussian mixture model is then used to extract vessel clusters from the pre-processing outcome, while small vessels fragments are obtained using another gray-voting process, which complements the vessel cluster extraction already performed. At the last step, we eliminate the fragments that do not belong to the vessels based on the shape of the fragments. We evaluated the approach with two publicly available DRIVE (Staal et al., 2004) and STARE (Hoover et at., 2000) datasets with manually segmented results. For the STARE dataset, when using the second manually segmented results which include much more small vessels than the first manually segmented results as the "gold standard," this approach achieved an average sensitivity, accuracy and specificity of 65.0%, 92.1% and 97.0%, respectively. The sensitivities of this approach were much higher than those of the other existing methods, with comparable specificities; these results thus demonstrated that this approach was sensitive to detection of small vessels.
Directory of Open Access Journals (Sweden)
Peishan Dai
Full Text Available Vessel segmentation in retinal fundus images is a preliminary step to clinical diagnosis for some systemic diseases and some eye diseases. The performances of existing methods for segmenting small vessels which are usually of more importance than the main vessels in a clinical diagnosis are not satisfactory in clinical use. In this paper, we present a method for both main and peripheral vessel segmentation. A local gray-level change enhancement algorithm called gray-voting is used to enhance the small vessels, while a two-dimensional Gabor wavelet is used to extract the main vessels. We fuse the gray-voting results with the 2D-Gabor filter results as pre-processing outcome. A Gaussian mixture model is then used to extract vessel clusters from the pre-processing outcome, while small vessels fragments are obtained using another gray-voting process, which complements the vessel cluster extraction already performed. At the last step, we eliminate the fragments that do not belong to the vessels based on the shape of the fragments. We evaluated the approach with two publicly available DRIVE (Staal et al., 2004 and STARE (Hoover et at., 2000 datasets with manually segmented results. For the STARE dataset, when using the second manually segmented results which include much more small vessels than the first manually segmented results as the "gold standard," this approach achieved an average sensitivity, accuracy and specificity of 65.0%, 92.1% and 97.0%, respectively. The sensitivities of this approach were much higher than those of the other existing methods, with comparable specificities; these results thus demonstrated that this approach was sensitive to detection of small vessels.
基于高斯混合模型的腹主动脉图像分割%Image Segmentation of Abdominal Aorta Based on Gaussian Mixture Model
Institute of Scientific and Technical Information of China (English)
刘海华; 郭杰龙
2015-01-01
为了有效地分割腹主动脉图像，提出了基于适度空间约束的高斯混合模型分割算法。该算法将三维空间邻域信息融入高斯混合模型中，利用最大期望算法（ EM）获取腹部血管灰度图像的估计参数，从而分割出血管图像。实验结果表明：所提出的方法不仅能准确地分割腹主动脉的血管分支图像，而且对于图像噪声的抑制有较好的效果。%To segment the abdominal aorta from CT images effectively, a improved segmentation algorithm based on Gaussian mixture model with space constraints is proposed.This algorithm integrates 3D neighborhood information into Gaussian mixture model, then estimates the parameters of Gaussian mixture model by using EM algorithm to segment the aorta from gray image of abdominal aorta.The experiments demonstrate that the proposed not only achieves the better segmentation of aortic branches, but also inhibits noise in images by considering the spatial neighborhood information.
Aigrain, Suzanne; Pope, Benjamin
2016-01-01
We present K2SC (K2 Systematics Correction), a Python pipeline to model instrumental systematics and astrophysical variability in light curves from the K2 mission. K2SC uses Gaussian process regression to model position-dependent systematics and time-dependent variability simultaneously, enabling the user to remove both (e.g., for transit searches) or to remove systematics while preserving variability (for variability studies). For periodic variables, K2SC automatically computes estimates of the period, amplitude and evolution timescale of the variability. We apply K2SC to publicly available K2 data from campaigns 3--5, showing that we obtain photometric precision approaching that of the original Kepler mission. We compare our results to other publicly available K2 pipelines, showing that we obtain similar or better results, on average. We use transit injection and recovery tests to evaluate the impact of K2SC on planetary transit searches in K2 PDC (Pre-search Data Conditioning) data, for planet-to-star radi...
Majka, M.; Góra, P. F.
2015-05-01
The Gaussian chain model is the classical description of a polymeric chain, which provides analytical results regarding end-to-end distance, the distribution of segments around the mass center of a chain, coarse-grained interactions between two chains and effective interactions in binary mixtures. This hierarchy of results can be calculated thanks to the α stability of the Gaussian distribution. In this paper we show that it is possible to generalize the model of Gaussian chain to the entire class of α -stable distributions, obtaining the analogous hierarchy of results expressed by the analytical closed-form formulas in the Fourier space. This allows us to establish the α -stable chain model. We begin with reviewing the applications of Levy flights in the context of polymer sciences, which include: chains described by the heavy-tailed distributions of persistence length; polymers adsorbed to the surface; and the chains driven by a noise with power-law spatial correlations. Further, we derive the distribution of segments around the mass center of the α -stable chain and construct the coarse-grained interaction potential between two chains. These results are employed to discuss the model of binary mixture consisting of the α -stable chains. In what follows, we establish the spinodal decomposition condition generalized to the mixtures of the α -stable polymers. This condition is further applied to compare the on-surface phase separation of adsorbed polymers (which are known to be described with heavy-tailed statistics) with the phase separation condition in the bulk. Finally, we predict the four different scenarios of simultaneous mixing and demixing in the two- and three-dimensional systems.
Aigrain, S.; Parviainen, H.; Pope, B. J. S.
2016-07-01
We present K2SC (K2 Systematics Correction), a PYTHON pipeline to model instrumental systematics and astrophysical variability in light curves from the K2 mission. K2SC uses Gaussian Process regression to model position-dependent systematics and time-dependent variability simultaneously, enabling the user to remove both (e.g. for transit searches) or to remove systematics while preserving variability (for variability studies). For periodic variables, K2SC automatically computes estimates of the period, amplitude and evolution time-scale of the variability. We apply K2SC to publicly available K2 data from Campaigns 3-5 showing that we obtain photometric precision approaching that of the original Kepler mission. We compare our results to other publicly available K2 pipelines, showing that we obtain similar or better results, on average. We use transit injection and recovery tests to evaluate the impact of K2SC on planetary transit searches in K2 Pre-search Data Conditioning data, for planet-to-star radius ratios down to Rp/R* = 0.01 and periods up to P = 40 d, and show that K2SC significantly improves the ability to distinguish between true and false detections, particularly for small planets. K2SC can be run automatically on many light curves, or manually tailored for specific objects such as pulsating stars or large amplitude eclipsing binaries. It can be run on ASCII and FITS light-curve files, regardless of their origin. Both the code and the processed light curves are publicly available, and we provide instructions for downloading and using them. The methodology used by K2SC will be applicable to future transit search missions such as TESS and PLATO.
A robust vector field correction method via a mixture statistical model of PIV signal
Lee, Yong; Yang, Hua; Yin, Zhouping
2016-03-01
Outlier (spurious vector) is a common problem in practical velocity field measurement using particle image velocimetry technology (PIV), and it should be validated and replaced by a reliable value. One of the most challenging problems is to correctly label the outliers under the circumstance that measurement noise exists or the flow becomes turbulent. Moreover, the outlier's cluster occurrence makes it difficult to pick out all the outliers. Most of current methods validate and correct the outliers using local statistical models in a single pass. In this work, a vector field correction (VFC) method is proposed directly from a mixture statistical model of PIV signal. Actually, this problem is formulated as a maximum a posteriori (MAP) estimation of a Bayesian model with hidden/latent variables, labeling the outliers in the original field. The solution of this MAP estimation, i.e., the outlier set and the restored flow field, is optimized iteratively using an expectation-maximization algorithm. We illustrated this VFC method on two kinds of synthetic velocity fields and two kinds of experimental data and demonstrated that it is robust to a very large number of outliers (even up to 60 %). Besides, the proposed VFC method has high accuracy and excellent compatibility for clustered outliers, compared with the state-of-the-art methods. Our VFC algorithm is computationally efficient, and corresponding Matlab code is provided for others to use it. In addition, our approach is general and can be seamlessly extended to three-dimensional-three-component (3D3C) PIV data.
Yu, Kai; Chen, Xinjian; Shi, Fei; Zhu, Weifang; Zhang, Bin; Xiang, Dehui
2016-03-01
Positron Emission Tomography (PET) and Computed Tomography (CT) have been widely used in clinical practice for radiation therapy. Most existing methods only used one image modality, either PET or CT, which suffers from the low spatial resolution in PET or low contrast in CT. In this paper, a novel 3D graph cut method is proposed, which integrated Gaussian Mixture Models (GMMs) into the graph cut method. We also employed the random walk method as an initialization step to provide object seeds for the improvement of the graph cut based segmentation on PET and CT images. The constructed graph consists of two sub-graphs and a special link between the sub-graphs which penalize the difference segmentation between the two modalities. Finally, the segmentation problem is solved by the max-flow/min-cut method. The proposed method was tested on 20 patients' PET-CT images, and the experimental results demonstrated the accuracy and efficiency of the proposed algorithm.
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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.
基于谱修正方法的非高斯风场模拟%Non-Gaussian Wind Field Simulation Based on Spectral Correction Method
Institute of Scientific and Technical Information of China (English)
孙芳锦; 张爱社
2012-01-01
To overcome disadvantages of Hermite-based spectral correction method, and to eliminate large consumption of the simulation due to computing coefficients of Hermite polynomial, a new method for simulating non-Gaussian wind field is proposed. Non-Gaussian cumulative distribution function (CDF) is employed to replace Hermit-based probability density function correction. Selecting arbitrary marginal PDF model as probability target model, and targeting power spectral density as sample function, the sample function is converged to the target probability density function and power spectral density through iteration correction. The method is applied to simulate non-Gaussian wind field of a real-life structure. The results compare well with the target spectrum. The method proposed here has fairly high accuracy and efficiency.%为克服基于Hermite谱修正方法的缺点,减少该方法中计算Hermite多项式系数所需耗费的大量机时,提出了一种模拟非高斯风压场的新方法,采用非高斯7积分布函数(CDF)映射技术来代替基于Hermite的概率密度函数(PDF)修正.选择任意边缘PDF模型作为概率目标模型,采用目标功率谱密度(PSD)作为样本函数,通过迭代修正该样本函数,使其收敛于目标概率密度函数和目标功率谱密度.将该方法应用于实际结构的非高斯风场模拟,模拟结果与目标谱符合良好,表明本文方法模拟非高斯风场具有较高的精确度和计算效率.
Trajectory Prediction Algorithm Based on Gaussian Mixture Model%一种基于高斯混合模型的轨迹预测算法
Institute of Scientific and Technical Information of China (English)
乔少杰; 金琨; 韩楠; 唐常杰; 格桑多吉; Louis Alberto GUTIERREZ
2015-01-01
For intelligent transportation systems, digital military battlefield and driver assistance systems, it is of great practical value to predict the trajectories of moving objects with uncertainty in a real-time, accurate and reliable fashion. Intelligent trajectory prediction can not only provide accurate location-based services, but also monitor and estimate traffic to suggest the best path, and as such becomes an active research direction. Aiming to overcome the drawbacks of the existing methods, a new trajectory prediction model based on Gaussian mixture models called GMTP is proposed. The new model contains the following essential phases: (1) modeling the complex motion patterns based on Gaussian mixture models, (2) calculating the probability distribution of different types of motion patterns by using Gaussian mixture model in order to partition trajectory data into distinct components, and (3) inferring the most possible trajectories of moving objects via Gaussian process regression. The GMTP algorithm is naturally a Gaussian nonlinear statistical probability model and the advantage of the proposed model is that the result is not only a predicted value, but also a whole distribution beyond the future trajectories, therefore making it possible to infer the location in regard to some motion patterns, e.g., uniformly accelerated motion, by using statistical probability distribution. Extensive experiments are conducted on real trajectory data sets and the results show that the prediction accuracy of the GMTP algorithm is improved by 22.2% and 23.8%, and the runtime can be reduced by 92.7% and 95.9% on average, respectively, when compared to the Gaussian process regression model and Kalman filter prediction algorithm with similar parameter setting.%在智能交通控制系统、军事数字化战场、辅助驾驶系统中,实时、精确、可靠的移动对象不确定性轨迹预测具有极高的应用价值.智能轨迹预测不仅可以提供精准的基
Institute of Scientific and Technical Information of China (English)
程红伟; 陶俊勇; 蒋瑜; 陈循
2014-01-01
Aiming at the difficulty in deriving mathematical expressions of amplitude probability density functions of non-Gaussian vibrations,a Gaussian mixture model-based probability density function (PDF ) was proposed for non-Gaussian vibration signals.The estimation of higher-order moments of a non-Gaussian vibration process was obtained with sample time histories.Based on the quantitative relations between the even order moments of a given Gaussian process, combining with a secorld order Gaussian mixture model,an equation set for achieving the parameters of each Gaussian component in the Gaussian mixture model was established.Based on the obtained weighting factors and variances of Gaussian components,the mathematical model of non-Gaussian probability density function was then achieved.The examples of simulated signals and measured signals verified the validity of the presented method.%针对非高斯振动信号的幅值概率密度函数难以用数学模型表述的问题，提出了基于高斯混合模型的非高斯概率密度函数表示方法。首先，基于时域样本信号得到非高斯振动信号的高阶矩估计值。其次，基于高斯随机过程偶次高阶矩之间的定量关系，结合二阶高斯混合模型建立方程组，求解得到混合模型中每个高斯分量的方差和权值。然后，将各高斯分量的权值和方差代入高斯混合模型，得到适用于对称非高斯振动信号的幅值概率密度函数。最后，通过仿真信号和实测振动信号，验证了该方法的有效性和适用性。
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.
Avendaño-Valencia, Luis David; Fassois, Spilios D.
2017-07-01
The study focuses on vibration response based health monitoring for an operating wind turbine, which features time-dependent dynamics under environmental and operational uncertainty. A Gaussian Mixture Model Random Coefficient (GMM-RC) model based Structural Health Monitoring framework postulated in a companion paper is adopted and assessed. The assessment is based on vibration response signals obtained from a simulated offshore 5 MW wind turbine. The non-stationarity in the vibration signals originates from the continually evolving, due to blade rotation, inertial properties, as well as the wind characteristics, while uncertainty is introduced by random variations of the wind speed within the range of 10-20 m/s. Monte Carlo simulations are performed using six distinct structural states, including the healthy state and five types of damage/fault in the tower, the blades, and the transmission, with each one of them characterized by four distinct levels. Random vibration response modeling and damage diagnosis are illustrated, along with pertinent comparisons with state-of-the-art diagnosis methods. The results demonstrate consistently good performance of the GMM-RC model based framework, offering significant performance improvements over state-of-the-art methods. Most damage types and levels are shown to be properly diagnosed using a single vibration sensor.
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
Hammouda, Boualem
2014-01-01
It is common practice to assume that Bragg scattering peaks have Gaussian shape. The Gaussian shape function is used to perform most instrumental smearing corrections. Using Monte Carlo ray tracing simulation, the resolution of a realistic small-angle neutron scattering (SANS) instrument is generated reliably. Including a single-crystal sample with large d-spacing, Bragg peaks are produced. Bragg peaks contain contributions from the resolution function and from spread in the sample structure. Results show that Bragg peaks are Gaussian in the resolution-limited condition (with negligible sample spread) while this is not the case when spread in the sample structure is non-negligible. When sample spread contributes, the exponentially modified Gaussian function is a better account of the Bragg peak shape. This function is characterized by a non-zero third moment (skewness) which makes Bragg peaks asymmetric for broad neutron wavelength spreads. PMID:26601025
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.]....
基于Davinei-DM6467的高斯混合模型算法的实现%Realization of gaussian mixture model algorithm based on Davinci-DM6467
Institute of Scientific and Technical Information of China (English)
刘德方; 王戴木; 邓明; 陈静; 赵正平
2012-01-01
针对智能监控中运动目标检测的问题，提出了基于Davinci—DM6467的高斯混合模型像素级的背景分割策略。对彩色图像建立高斯混合模型，根据场景中象素点的稳定性来调整模型参数的更新速率；通过和马氏阈值进行对比来判断是不是要更新背景模型；通过和背景阈值进行对比来判断哪几个模型是属于背景区域。经验证性实验测试，结果表明，高斯混合模型在运动检测中实时性好，对环境有较强的鲁棒性。%In the light of movement target detection during intelligence monitoring, the author put forward Gaussian mixture model of pixel level background segmentation strategy based on Davinei-DM6467. Firstly establishing Gaussian mixture model for colorful images and then adjusting the updating velocity of model parameters according to the stability of each pixels in frames ; secondly comparing them with Markov threshold to judge whether to update the background model; finally comparing them with back-ground threshold to judge which several models belong to background region. Experimental results show that Gaussian mixture model in motion detection is possessed of good real-time and strong robustness to environment.
Error correction and diversity analysis of population mixtures determined by NGS.
Wood, Graham R; Burroughs, Nigel J; Evans, David J; Ryabov, Eugene V
2014-01-01
The impetus for this work was the need to analyse nucleotide diversity in a viral mix taken from honeybees. The paper has two findings. First, a method for correction of next generation sequencing error in the distribution of nucleotides at a site is developed. Second, a package of methods for assessment of nucleotide diversity is assembled. The error correction method is statistically based and works at the level of the nucleotide distribution rather than the level of individual nucleotides. The method relies on an error model and a sample of known viral genotypes that is used for model calibration. A compendium of existing and new diversity analysis tools is also presented, allowing hypotheses about diversity and mean diversity to be tested and associated confidence intervals to be calculated. The methods are illustrated using honeybee viral samples. Software in both Excel and Matlab and a guide are available at http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software/, the Warwick University Systems Biology Centre software download site.
Permutation Correction in the Frequency Domain in Blind Separation of Speech Mixtures
Directory of Open Access Journals (Sweden)
Pham DT
2006-01-01
Full Text Available This paper presents a method for blind separation of convolutive mixtures of speech signals, based on the joint diagonalization of the time varying spectral matrices of the observation records. The main and still largely open problem in a frequency domain approach is permutation ambiguity. In an earlier paper of the authors, the continuity of the frequency response of the unmixing filters is exploited, but it leaves some frequency permutation jumps. This paper therefore proposes a new method based on two assumptions. The frequency continuity of the unmixing filters is still used in the initialization of the diagonalization algorithm. Then, the paper introduces a new method based on the time-frequency representations of the sources. They are assumed to vary smoothly with frequency. This hypothesis of the continuity of the time variation of the source energy is exploited on a sliding frequency bandwidth. It allows us to detect the remaining frequency permutation jumps. The method is compared with other approaches and results on real world recordings demonstrate superior performances of the proposed algorithm.
Directory of Open Access Journals (Sweden)
Sojitra Rajanit
2015-03-01
Full Text Available A new simple, economical, precise and accurate method are described for the simultaneous determination of Nifedipine (NIF and Metoprolol Succinate (MET in combined tablet dosage form. The proposed method was applied for the determination of Nifedipine and Metoprolol Succinate in synthetic mixture, for determination of sampling wavelength, 10μg/ml of each of NIF and MET were scanned in 200-400 nm range and sampling wavelengths were 313nm for NIF and 275.40nm for MET are selected for development and validation of absorption correction method. For this method linearity observed in the range of 5-25μg/ml for NIF and 25- 125μg/ml for MET, and in their pharmaceutical formulation with mean percentage recoveries 100.68 and 100.33, respectively. The method was validated according to ICH guidelines and can be applied for routine quality control testing.
Institute of Scientific and Technical Information of China (English)
孔晨燕; 谢从华; 苏剑峰; 于丹
2012-01-01
To remove the trailing noise, histogram fuzzy based filter denoising methods often have the problems of image blurring and residual noisy. To address this problem, the authors of this paper propose a new image de⁃noising method based on Generalized Gaussian Mixture (GGM) model and weighted average image filter. Firstly, the generalized Gaussian mixture model for image is constructed. Secondly, the noise data is determined accord⁃ing to the feature differences between this point and its neighbors. Finally, a weighted average filter is construct⁃ed by the GGM to build an image denoising. Histogram based filter and classical partial differential equation method are compared with the proposed method. Experimental results show that the method has a better denois⁃ing effect than the other methods.% 基于直方图的模糊滤波方法对图像的拖尾噪声去噪会导致图像模糊、残留的噪声较多等问题，本文提出一种新的基于广义高斯混合模型的图像去噪方法。首先，建立图像的广义高斯分布及其有限混合模型；其次，通过像素周围点特征值的变化范围确定噪声数据；最后，利用广义高斯函数构建一个加权平均滤波器进行图像去噪。对基于直方图的滤波方法、经典的偏微分方程和本文方法进行比较实验，结果表明本文方法具有更好的去噪效果。
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.
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)
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.
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].
2015-10-01
In the article by Quintavalle et al (Quintavalle C, Anselmi CV, De Micco F, Roscigno G, Visconti G, Golia B, Focaccio A, Ricciardelli B, Perna E, Papa L, Donnarumma E, Condorelli G, Briguori C. Neutrophil gelatinase–associated lipocalin and contrast-induced acute kidney injury. Circ Cardiovasc Interv. 2015;8:e002673. DOI: 10.1161/CIRCINTERVENTIONS.115.002673.), which published online September 2, 2015, and appears in the September 2015 issue of the journal, a correction was needed. On page 1, the institutional affiliation for Elvira Donnarumma, PhD, “SDN Foundation,” has been changed to read, “IRCCS SDN, Naples, Italy.” The institutional affiliation for Laura Papa, PhD, “Institute for Endocrinology and Experimental Oncology, National Research Council, Naples, Italy,” has been changed to read, “Institute of Genetics and Biomedical Research, Milan Unit, Milan, Italy” and “Humanitas Research Hospital, Rozzano, Italy.” The authors regret this error.
Gaussian Sum PHD Filtering Algorithm for Nonlinear Non-Gaussian Models
Institute of Scientific and Technical Information of China (English)
Yin Jianjun; Zhang Jianqiu; Zhuang Zesen
2008-01-01
A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density (GSPHD) filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussiaa sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaassian mixture probability hypothesis density (GMPHD) filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special ease of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.
Institute of Scientific and Technical Information of China (English)
奚玲; 平西建; 张昊
2012-01-01
Aiming at the security problem of adaptive steganography, the analysis method based on Gaussian mixture model(GMM) of real image is proposed. Compared the stego random characteristic function of probability density function between the adaptive Spread Spectrum Image Steganography(SSIS) and the general non adaptive one under the condition that the total embedding intensity is equal, it demonstrates that the security of adaptive SSIS is higher than that of non-adaptive schemes. Analysis result shows that the method provides theoretical evidence for using adaptive scheme to improve statistical imperceptibility of steganography.%对自适应隐写的安全性问题进行分析,提出一种基于自然图像的高斯混合模型分析方法.在总嵌入强度相同的条件下,比较自适应和非自适应扩频隐写载密随机变量概率密度函数的特征函数,验证自适应扩频隐写的统计安全性高于等嵌入强度下非自适应扩频隐写.分析结果表明,该方法能为提升信息隐藏系统的抗统计分析性能提供理论依据.
Cluster Sampling Filters for Non-Gaussian Data Assimilation
2016-01-01
This paper presents a fully non-Gaussian version of the Hamiltonian Monte Carlo (HMC) sampling filter. The Gaussian prior assumption in the original HMC filter is relaxed. Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a Gaussian Mixture Model (GMM) to the prior ensemble. Using the data likelihood function, the posterior density is then formulated as a mixture density, and is sampled using a HMC appr...
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
Allodji, Rodrigue S; Thiébaut, Anne C M; Leuraud, Klervi; Rage, Estelle; Henry, Stéphane; Laurier, Dominique; Bénichou, Jacques
2012-12-30
A broad variety of methods for measurement error (ME) correction have been developed, but these methods have rarely been applied possibly because their ability to correct ME is poorly understood. We carried out a simulation study to assess the performance of three error-correction methods: two variants of regression calibration (the substitution method and the estimation calibration method) and the simulation extrapolation (SIMEX) method. Features of the simulated cohorts were borrowed from the French Uranium Miners' Cohort in which exposure to radon had been documented from 1946 to 1999. In the absence of ME correction, we observed a severe attenuation of the true effect of radon exposure, with a negative relative bias of the order of 60% on the excess relative risk of lung cancer death. In the main scenario considered, that is, when ME characteristics previously determined as most plausible from the French Uranium Miners' Cohort were used both to generate exposure data and to correct for ME at the analysis stage, all three error-correction methods showed a noticeable but partial reduction of the attenuation bias, with a slight advantage for the SIMEX method. However, the performance of the three correction methods highly depended on the accurate determination of the characteristics of ME. In particular, we encountered severe overestimation in some scenarios with the SIMEX method, and we observed lack of correction with the three methods in some other scenarios. For illustration, we also applied and compared the proposed methods on the real data set from the French Uranium Miners' Cohort study.
Institute of Scientific and Technical Information of China (English)
肖涵; 李友荣; 吕勇
2011-01-01
In order to overcome the shortcoming of recurrence plot that can only supply the qualitative analysis to signals, the recurrence quantification analysis is used to analysis different fault modes gear's vibration signal. The gear fault pattern recognition method that combined the gaussian mixture model with the feature vector that consists of determinism and laminarity is proposed. Based on the signals that acquired form gear fault experiment table, the proposed method is compared with RBF artificial neural network classification method by Re-substitution test, Jackknife test and Independent data set test respectively. The classification results show that the higher discrimination can be achieved by the proposed method.%针对递归图只能对信号进行定性分析,不利于其深入应用的缺点,应用递归定量分析方法对各种故障模式振动信号进行定量分析.采用确定率和层流率组成齿轮故障识别的特征向量,并结合高斯混合模型实现齿轮故障模式识别.以齿轮故障实验台上所测取的实验数据为对象,分别采用Re-substitution检验法,Jackknife检验法和Independent dataset检验法对提出的方法和RBF人工神经网络分类算法进行检验.结果表明,递归定量分析与高斯混合模型相结合应用于齿轮故障模式识别具有更高的识别率.
Music Emotion Four Classification Research Based on Gaussian Mixture Model%基于高斯混合模型的音乐情绪四分类研究
Institute of Scientific and Technical Information of China (English)
陆阳; 郭滨; 白雪梅
2015-01-01
针对音乐情感复杂难以归类的问题,提出了一种在四分类坐标下建立高斯混合模型进行音乐信号归类的研究方法.在建立模型的基础上,创新地为表示情绪特性的轴两端建立模型使其转换成二层分类器进行加权判别.结果表明,为表示情绪特性的轴建立模型且权值分配在0.7和0.3的条件下,音乐的分类工作可以取得最优结果,其结果明显优于直接为每类情绪建立模型的结果.%For the problem of music emotional complexity and difficult to categorize, we proposed a method to estab-lish Gaussian mixture models in four classifications. On the basis of establish models, we innovated established GMM for shaft at both ends of the emotional model and converted it into two-layer weighted classifier discrimination. The re-sults shows that the GMM for shaft models and weight distribution under the condition of 0.7 and 0.3, the musical work can obtain the best classification result, and the result is better than the result of directly establish models for each type of emotion.
Statistical Compressive Sensing of Gaussian Mixture Models
2010-10-01
the algorithm iterates [18] (refer to [18] Sec. 2 for more details). The dictionary for conventional CS is learned with K- SVD [1] from 720,000 image...framework for solving inverse problems. VII. REFERENCES [1] M. Aharon, M. Elad, and A. Bruckstein. K- SVD : An algorithm for designing overcomplete...In Proc. ICCV, 2001. [16] M. Talagrand. A new look at independence. Ann. Prob., 24:1, 1996. [17] G. Yu, S. Mallat, and E. Bacry. Audio denoising by
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)
Rebafka, Tabea; Roueff, François; Souloumiac, Antoine
2010-01-01
A fast and efficient estimation method is proposed that compensates the distortion in nonlinear transformation models. A likelihood-based estimator is developed that can be computed by an EM-type algorithm. The consistency of the estimator is shown and its limit distribution is provided. The new estimator is particularly well suited for fluorescence lifetime measurements, where only the shortest arrival time of a random number of emitted fluorescence photons can be detected and where arrival times are often modeled by a mixture of exponential distributions. The method is evaluated on real and synthetic data. Compared to currently used methods in fluorescence, the new estimator should allow a reduction of the acquisition time of an order of magnitude.
Institute of Scientific and Technical Information of China (English)
张虎; 方华; 李春贵
2014-01-01
There are often the cases in road video surveillance systems that the vehicles are slowly moving or in short stay.In view of the problems that the background subtraction method of traditional Gaussian mixture model is sensitive to abrupt changes in environment and has information loss on slow moving target,we propose an improved adaptive vehicle detection algorithm.First,in order to restrain the foreground of slow movement to be trained to the background,the present pixel-values are classified before updating the parameters,and the models are set different replacement rates according to classification results.Secondly,for removing the interference of environmental changes,a metric factor that tracks environmental changes is introduced to realise the adaptive switch between the background subtraction and the inter-frame difference algorithm when abrupt environmental change occurs.Finally the more accurate object is gotten by ecological filtering.Experiments show that this algorithm can get better detection effect for moving vehicles in daytime real-time traffic video.%道路视频监控中经常存在车辆缓慢运动或短暂停留的情况。针对传统混合高斯模型背景减除法对环境突变敏感和对缓慢运动目标丢失信息的问题，提出一种改进的自适应车辆检测方法。首先，在参数更新前对像素值分类并根据分类结果设置模型更新率，抑制缓慢运动前景被训练成背景；引入一个跟踪环境变化的度量因子，当环境突变时实现背景减除和帧差法的自适应切换，滤除环境变化的干扰；最后通过生态学滤波得到准确的运动目标。实验表明，该算法对白天实时路况视频中的运动车辆具有较好的检测效果。
DEFF Research Database (Denmark)
Højstrup, Jørgen; Hansen, Kurt S.; Pedersen, Bo Juul;
1999-01-01
The pdf's of atmosperic turbulence have somewhat wider tails than a Gaussian, especially regarding accelerations, whereas velocities are close to Gaussian. This behaviour has been investigated using data from a large WEB-database in order to quantify the amount of non-gaussianity. Models for non-...
Optimality of Gaussian discord.
Pirandola, Stefano; Spedalieri, Gaetana; Braunstein, Samuel L; Cerf, Nicolas J; Lloyd, Seth
2014-10-03
In this Letter we exploit the recently solved conjecture on the bosonic minimum output entropy to show the optimality of Gaussian discord, so that the computation of quantum discord for bipartite Gaussian states can be restricted to local Gaussian measurements. We prove such optimality for a large family of Gaussian states, including all two-mode squeezed thermal states, which are the most typical Gaussian states realized in experiments. Our family also includes other types of Gaussian states and spans their entire set in a suitable limit where they become Choi matrices of Gaussian channels. As a result, we completely characterize the quantum correlations possessed by some of the most important bosonic states in quantum optics and quantum information.
Gaussian Intrinsic Entanglement
Mišta, Ladislav; Tatham, Richard
2016-12-01
We introduce a cryptographically motivated quantifier of entanglement in bipartite Gaussian systems called Gaussian intrinsic entanglement (GIE). The GIE is defined as the optimized mutual information of a Gaussian distribution of outcomes of measurements on parts of a system, conditioned on the outcomes of a measurement on a purifying subsystem. We show that GIE vanishes only on separable states and exhibits monotonicity under Gaussian local trace-preserving operations and classical communication. In the two-mode case, we compute GIE for all pure states as well as for several important classes of symmetric and asymmetric mixed states. Surprisingly, in all of these cases, GIE is equal to Gaussian Rényi-2 entanglement. As GIE is operationally associated with the secret-key agreement protocol and can be computed for several important classes of states, it offers a compromise between computable and physically meaningful entanglement quantifiers.
CSIR Research Space (South Africa)
Roux, FS
2009-01-01
Full Text Available . 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...(z) 0 x z Rayleigh range Beam waist ρ ρ Rayleigh range CSIR National Laser Centre – p.3/30 Gaussian beam Gaussian beam in terms of amplitude and phase g(u, v, t) = exp ( −u 2 + v2 1 + t2 ) exp ( − it(u 2 + v2) 1 + t2 ) Normalised beam radius: √ 1 + t2...
On bosonic non-Gaussian processes: photon-added Gaussian channels
Sabapathy, Krishna Kumar
2016-01-01
We present a framework for systematically studying linear bosonic non-Gaussian channels. Our emphasis is on a class of channels that we call as photon-added Gaussian channels and these are experimentally viable with current quantum-optical technologies. These channels are obtained by extending Gaussian channels with photon addition applied to the environment state (in its respective Stinespring unitary representation) giving rise to a one-parameter family of non-Gaussian channels indexed by photon number $n$ with $n=0$ corresponding to the underlying Gaussian channel. We then derive the corresponding operator-sum representation and observe that these channels are Fock-preserving, i.e., coherence non-generating on incoherent states in the Fock basis. Furthermore, noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels analogous to the Fock basis representation of a thermal state. We then report examples of activation of nonclassicality, using this method of photon-addition, ...
Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
Sabapathy, Krishna Kumar; Winter, Andreas
2017-06-01
We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels, which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing such as entanglement distillation from Gaussian states and universal quantum computation. The single-mode photon-added channels we consider are obtained by using two-mode beam splitters and squeezing operators with photon addition applied to the ancilla ports giving rise to families of non-Gaussian channels. For each such channel, we derive its operator-sum representation, indispensable in the present context. We observe that these channels are Fock preserving (coherence nongenerating). We then report two examples of activation using our scheme of photon addition, that of quantum-optical nonclassicality at outputs of channels that would otherwise output only classical states and of both the quantum and private communication capacities, hinting at far-reaching applications for quantum-optical communication. Further, we see that noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We also present other physical and information-theoretic properties of these channels.
Review of Gaussian diffusion-deposition models
Energy Technology Data Exchange (ETDEWEB)
Horst, T.W.
1979-01-01
The assumptions and predictions of several Gaussian diffusion-deposition models are compared. A simple correction to the Chamberlain source depletion model is shown to predict ground-level airborne concentrations and dry deposition fluxes in close agreement with the exact solution of Horst.
Gaussian and Non-Gaussian operations on non-Gaussian state: engineering non-Gaussianity
Directory of Open Access Journals (Sweden)
Olivares Stefano
2014-03-01
Full Text Available Multiple photon subtraction applied to a displaced phase-averaged coherent state, which is a non-Gaussian classical state, produces conditional states with a non trivial (positive Glauber-Sudarshan Prepresentation. We theoretically and experimentally demonstrate that, despite its simplicity, this class of conditional states cannot be fully characterized by direct detection of photon numbers. In particular, the non-Gaussianity of the state is a characteristics that must be assessed by phase-sensitive measurements. We also show that the non-Gaussianity of conditional states can be manipulated by choosing suitable conditioning values and composition of phase-averaged states.
Autonomous Gaussian Decomposition
Lindner, Robert R; Murray, Claire E; Stanimirović, Snežana; Babler, Brian L; Heiles, Carl; Hennebelle, Patrick; Goss, W M; Dickey, John
2014-01-01
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 21cm absorption spectra from the 21cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the HI 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 up...
Broadcasting Correlated Gaussians
Bross, Shraga; Tinguely, Stephan
2007-01-01
We consider the transmission of a bi-variate Gaussian source over a one-to-two power-limited Gaussian broadcast channel. Receiver 1 observes the transmitted signal corrupted by Gaussian noise and wishes to estimate the first component of the source. Receiver 2 observes the transmitted signal in larger Gaussian noise and wishes to estimate the second component. We seek to characterize the pairs of mean squared-error distortions that are simultaneously achievable at the two receivers. Our result is that below a certain SNR-threshold an "uncoded scheme" that sends a linear combination of the source components is optimal. The SNR-theshold can be expressed as a function of the source correlation and the distortion at Receiver 1.
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...... 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....
On Gaussian random supergravity
Bachlechner, Thomas C.
2014-01-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial K\\"ahler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a nume...
Semiparametric Gaussian copula classification
Zhao, Yue; Wegkamp, Marten
2014-01-01
This paper studies the binary classification of two distributions with the same Gaussian copula in high dimensions. Under this semiparametric Gaussian copula setting, we derive an accurate semiparametric estimator of the log density ratio, which leads to our empirical decision rule and a bound on its associated excess risk. Our estimation procedure takes advantage of the potential sparsity as well as the low noise condition in the problem, which allows us to achieve faster convergence rate of...
Ferreira, P G; Ferreira, Pedro G.; Magueijo, Joao
1997-01-01
Gaussian cosmic microwave background skies are fully specified by the power spectrum. The conventional method of characterizing non-Gaussian skies is to evaluate higher order moments, the n-point functions and their Fourier transforms. We argue that this method is inefficient, due to the redundancy of information existing in the complete set of moments. In this paper we propose a set of new statistics or non-Gaussian spectra to be extracted out of the angular distribution of the Fourier transform of the temperature anisotropies in the small field limit. These statistics complement the power spectrum and act as localization, shape, and connectedness statistics. They quantify generic non-Gaussian structure, and may be used in more general image processing tasks. We concentrate on a subset of these statistics and argue that while they carry no information in Gaussian theories they may be the best arena for making predictions in some non-Gaussian theories. As examples of applications we consider superposed Gaussi...
Blind source separation based on generalized gaussian model
Institute of Scientific and Technical Information of China (English)
YANG Bin; KONG Wei; ZHOU Yue
2007-01-01
Since in most blind source separation (BSS) algorithms the estimations of probability density function (pdf) of sources are fixed or can only switch between one sup-Gaussian and other sub-Gaussian model,they may not be efficient to separate sources with different distributions. So to solve the problem of pdf mismatch and the separation of hybrid mixture in BSS, the generalized Gaussian model (GGM) is introduced to model the pdf of the sources since it can provide a general structure of univariate distributions. Its great advantage is that only one parameter needs to be determined in modeling the pdf of different sources, so it is less complex than Gaussian mixture model. By using maximum likelihood (ML) approach, the convergence of the proposed algorithm is improved. The computer simulations show that it is more efficient and valid than conventional methods with fixed pdf estimation.
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.
Institute of Scientific and Technical Information of China (English)
杨颖; 戴彬
2013-01-01
光照不匀会对字符图像检测带来极大的负面影响.基于高斯频域低通滤波和图像差分提出一个新的字符图像光照不均校正法,该方法首先根据照明光场和图像细节分别对应低频分量和高频分量的特点,设计高斯低通滤波器去除光照背景以获取照明光场,然后再以此为根据对字符图像进行校正.同时,针对高斯低通滤波器参数选择上的难点,提出了实验法确定参数σ加逐次滤波对照明光场进行逼近的方法,以确保最终校正结果的准确.实验结果表明该方法校正效果较好.%Uneven illumination can result in serious negative impact on character image detection, Based on Gaussian frequency low pass filtering and image difference, a new character image uneven illumination correction method was proposed. According to the characteristics which Lighting light field and image detail respectively corresponding to low-frequency components and high-frequency components, gaussian frequency low pass filtering was firstly designed to remove light background which aims to get lighting light field. And then, character image was corrected based on the designed gaussian frequency low pass filtering. Meanwhile, for the difficulty on choice of gaussian low-pass filter parameter, a method which obtains parameter σ based on experimentation and successive filtering on lighting light field was presented to ensure the end correction results. The experimental results show that the correction effect of the proposed method is better.
Deblured Gaussian Blurred Images
Al-amri, Salem Saleh; D, Khamitkar S
2010-01-01
This paper attempts to undertake the study of Restored Gaussian Blurred Images. by using four types of techniques of deblurring image as Wiener filter, Regularized filter, Lucy Richardson deconvlutin algorithm and Blind deconvlution algorithm with an information of the Point Spread Function (PSF) corrupted blurred image with Different values of Size and Alfa and then corrupted by Gaussian noise. The same is applied to the remote sensing image and they are compared with one another, So as to choose the base technique for restored or deblurring image.This paper also attempts to undertake the study of restored Gaussian blurred image with no any information about the Point Spread Function (PSF) by using same four techniques after execute the guess of the PSF, the number of iterations and the weight threshold of it. To choose the base guesses for restored or deblurring image of this techniques.
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...
Gaussian fluctuations in chaotic eigenstates
Srednicki, M A; Srednicki, Mark; Stiernelof, Frank
1996-01-01
We study the fluctuations that are predicted in the autocorrelation function of an energy eigenstate of a chaotic, two-dimensional billiard by the conjecture (due to Berry) that the eigenfunction is a gaussian random variable. We find an explicit formula for the root-mean-square amplitude of the expected fluctuations in the autocorrelation function. These fluctuations turn out to be O(\\hbar^{1/2}) in the small \\hbar (high energy) limit. For comparison, any corrections due to scars from isolated periodic orbits would also be O(\\hbar^{1/2}). The fluctuations take on a particularly simple form if the autocorrelation function is averaged over the direction of the separation vector. We compare our various predictions with recent numerical computations of Li and Robnik for the Robnik billiard, and find good agreement. We indicate how our results generalize to higher dimensions.
Trofimov, M Yu; Kozitskiy, S B
2015-01-01
An adiabatic mode Helmholtz equation for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the crosswedge benchmark and proved an excellent agreement with the source images method.
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.
Institute of Scientific and Technical Information of China (English)
陈阳; 杨绿溪; 何振亚
2000-01-01
The problem of blind separation of signals in post-nonlinear mixture is addressed in this paper.The post-nonlinear mixture is formed by a component wise nonlinear distortion after the linear mixture.Hence a nonlinear adjusting part placed in front of the linear separation structure is needed to compensate for the distortion in separating such signals.The learning rules for the post-nonlinear separation structure are derived by a maximum likelihood approach.An algorithm for blind separation of post-nonlinearly mixed sub- and super-Gaussian signals is proposed based on some previous work.Multilayer perceptrons are used in this algorithm to model the nonlinear part of the separation structure.The algorithm switches between sub- and super-Gaussian probability models during learning according to a stability condition and operates in a block-adaptive manner.The effectiveness of the algorithm is verified by experiments on simulated and real-world signals.%本文研究了后非线性混合信号的盲分离.后非线性混合信号是由线性混合的每一路信号分别经过一个非线性畸变产生的.因此分离这种信号需要在适用于线性混合的线性分离结构前放置一个用于补偿非线性畸变的非线性校正部分.本文用一种最大似然方法推导了一般后非线性分离结构的学习公式.在前人一些工作的基础上，提出了一种用于亚、超高斯信号后非线性混合的盲分离算法.该算法用多层感知器对分离结构的非线性校正部分进行建模，迭代过程中根据一稳定性条件在分别适用于亚、超高斯信号的概率模型间进行切换并以块自适应方式工作.通过对模拟信号及实际信号(图像和语音)的实验证明了该算法的有效性.
Structural first failure times under non-Gaussian stochastic behavior
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
An analytical moment-based method for calculating structural first failure times under non-Gaussian stochastic behavior is proposed. In the method, a power series that constants can be obtained from response moments (skewness, kurtosis, etc.) is used firstly to map a non-Gaussian structural response into a standard Gaussian process, then mean up-crossing rates, mean clump size and the initial passage probability of a critical barrier level by the original structural response are estimated, and finally, the formula for calculating first failure times is established on the assumption that corrected up-crossing rates are independent. An analysis of a nonlinear single-degree-of-freedom dynamical system excited by a Gaussian model of load not only demonstrates the usage of the proposed method but also shows the accuracy and efficiency of the proposed method by comparisons between the present method and other methods such as Monte Carlo simulation and the traditional Gaussian model.
Multipole invariants and non-Gaussianity
Land, K; Land, Kate; Magueijo, Joao
2004-01-01
We propose a framework for separating the information contained in the CMB multipoles, $a_{\\ell m}$, into its algebraically independent components. Thus we cleanly separate information pertaining to the power spectrum, non-Gaussianity and preferred axis effects. The formalism builds upon the recently proposed multipole vectors (Copi, Huterer & Starkman 2003; Schwarz & al 2004; Katz & Weeks 2004), and we elucidate a few features regarding these vectors, namely their lack of statistical independence for a Gaussian random process. In a few cases we explicitly relate our proposed invariants to components of the $n$-point correlation function (power spectrum, bispectrum). We find the invariants' distributions using a mixture of analytical and numerical methods. We also evaluate them for the co-added WMAP first year map.
Horner, Jonathan S
2013-01-01
The Hamilton-Jacobi (HJ) approach for exploring inflationary trajectories is employed in the generation of generalised inflationary non-Gaussian signals arising from single field inflation. Scale dependent solutions for $f_{NL}$ are determined via the numerical integration of the three--point function in the curvature perturbation. This allows the full exploration of single field inflationary dynamics in the out-of-slow-roll regime and opens up the possibility of using future observations of non-Gaussianity to constraint the inflationary potential using model-independent methods. The distribution of `equilateral' $f_{NL}$ arising from single field inflation with both canonical and non-canonical kinetic terms are show as an example of the application of this procedure.
Gaussian quantum marginal problem
Eisert, J; Sanders, B C; Tyc, T
2007-01-01
The quantum marginal problem asks what local spectra are consistent with a given state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn) and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of ...
On Gaussian random supergravity
Energy Technology Data Exchange (ETDEWEB)
Bachlechner, Thomas C. [Department of Physics, Cornell University,Physical Sciences Building 428, Ithaca, NY 14853 (United States)
2014-04-08
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kähler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with |F|≪M{sub susy} or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log (P)∝−N. We argue that random supergravities lead to potentially interesting inflationary dynamics.
On Gaussian random supergravity
Bachlechner, Thomas C.
2014-04-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kähler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with | F| ≪ M susy or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log( P ) ∝ - N. We argue that random supergravities lead to potentially interesting inflationary dynamics.
On Gaussian Random Supergravity
Bachlechner, Thomas C
2014-01-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kahler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with |F|<< M_{susy} or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log(P)\\propto -N. We argue that random supergravities lead to potentially interesting inflationary dynamics...
Scaled unscented transform Gaussian sum filter: theory and application
Luo, Xiaodong; Hoteit, Ibrahim
2010-01-01
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), 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 underlyi...
Trofimov, M. Yu.; Zakharenko, A. D.; Kozitskiy, S. B.
2016-10-01
A mode parabolic equation in the ray centered coordinates for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the ASA wedge benchmark and proved an excellent agreement with the source images method in the case of cross-slope propagation. But in the cases of wave propagation at some angles to the cross-slope direction an account of mode interaction becomes necessary.
Non-Gaussianity and Excursion Set Theory: Halo Bias
Energy Technology Data Exchange (ETDEWEB)
Adshead, Peter [Enrico Fermi Institute, Univ. of Chicago, IL (United States); Baxter, Eric J. [Univ. of Chicago, Chicago, IL (United States); Dodelson, Scott [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Lidz, Adam [Univ. of Pennsylvania, Philadelphia, PA (United States)
2012-09-01
We study the impact of primordial non-Gaussianity generated during inflation on the bias of halos using excursion set theory. We recapture the familiar result that the bias scales as $k^{-2}$ on large scales for local type non-Gaussianity but explicitly identify the approximations that go into this conclusion and the corrections to it. We solve the more complicated problem of non-spherical halos, for which the collapse threshold is scale dependent.
Bessel-Gaussian entanglement; presentation
CSIR Research Space (South Africa)
Mclaren, M
2013-07-01
Full Text Available GAUSSIAN BEAM LAGUERRE-GAUSSIAN BEAM 15 Page 5 Higher-order Bessel-Gaussian beams carry OAM Page 6 © CSIR 2013 www.csir.co.za Generating Bessel-Gaussian beams using spatial light modulators (SLMs) Blazed axicon Binary axicon... stream_source_info McLaren_2013.pdf.txt stream_content_type text/plain stream_size 2915 Content-Encoding UTF-8 stream_name McLaren_2013.pdf.txt Content-Type text/plain; charset=UTF-8 Bessel-Gaussian entanglement M. Mc...
Fixing convergence of Gaussian belief propagation
Energy Technology Data Exchange (ETDEWEB)
Johnson, Jason K [Los Alamos National Laboratory; Bickson, Danny [IBM RESEARCH LAB; Dolev, Danny [HEBREW UNIV
2009-01-01
Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm is linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanari's linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.
Non-Gaussian entanglement swapping
Dell'Anno, F; Nocerino, G; De Siena, S; Illuminati, F
2016-01-01
We investigate the continuous-variable entanglement swapping protocol in a non-Gaussian setting, with non- Gaussian states employed either as entangled inputs and/or as swapping resources. The quality of the swapping protocol is assessed in terms of the teleportation fidelity achievable when using the swapped states as shared entangled resources in a teleportation protocol. We thus introduce a two-step cascaded quantum communication scheme that includes a swapping protocol followed by a teleportation protocol. The swapping protocol is fed by a general class of tunable non-Gaussian states, the squeezed Bell states, which, by means of controllable free parameters, allows for a continuous morphing from Gaussian twin beams up to maximally non-Gaussian squeezed number states. In the realistic instance, taking into account the effects of losses and imperfections, we show that as the input two-mode squeezing increases, optimized non-Gaussian swapping resources allow for a monotonically increasing enhancement of the ...
Experimental Investigation of the Evolution of Gaussian Quantum Discord in an Open System
DEFF Research Database (Denmark)
Madsen, Lars S.; Berni, Adriano; Lassen, Mikael;
2012-01-01
Gaussian quantum discord is a measure of quantum correlations in Gaussian systems. Using Gaussian discord, we quantify the quantum correlations of a bipartite entangled state and a separable two-mode mixture of coherent states. We experimentally analyze the effect of noise addition and dissipatio...... on Gaussian discord and show that the former noise degrades the discord, while the latter noise for some states leads to an increase of the discord. In particular, we experimentally demonstrate the near death of discord by noisy evolution and its revival through dissipation....
Duvenaud, David; Rasmussen, Carl Edward
2011-01-01
We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks.
Multilevel Mixture Kalman Filter
Directory of Open Access Journals (Sweden)
Xiaodong Wang
2004-11-01
Full Text Available The mixture Kalman filter is a general sequential Monte Carlo technique for conditional linear dynamic systems. It generates samples of some indicator variables recursively based on sequential importance sampling (SIS and integrates out the linear and Gaussian state variables conditioned on these indicators. Due to the marginalization process, the complexity of the mixture Kalman filter is quite high if the dimension of the indicator sampling space is high. In this paper, we address this difficulty by developing a new Monte Carlo sampling scheme, namely, the multilevel mixture Kalman filter. The basic idea is to make use of the multilevel or hierarchical structure of the space from which the indicator variables take values. That is, we draw samples in a multilevel fashion, beginning with sampling from the highest-level sampling space and then draw samples from the associate subspace of the newly drawn samples in a lower-level sampling space, until reaching the desired sampling space. Such a multilevel sampling scheme can be used in conjunction with the delayed estimation method, such as the delayed-sample method, resulting in delayed multilevel mixture Kalman filter. Examples in wireless communication, specifically the coherent and noncoherent 16-QAM over flat-fading channels, are provided to demonstrate the performance of the proposed multilevel mixture Kalman filter.
Entangled Bessel-Gaussian beams
CSIR Research Space (South Africa)
McLaren, M
2012-10-01
Full Text Available Orbital angular momentum (OAM) entanglement is investigated in the Bessel-Gaussian (BG) basis. Having a readily adjustable radial scale, BG modes provide an alternative basis for OAM entanglement over Laguerre-Gaussian modes. We show that the OAM...
Gaussian Fibonacci Circulant Type Matrices
Directory of Open Access Journals (Sweden)
Zhaolin Jiang
2014-01-01
Full Text Available Circulant matrices have become important tools in solving integrable system, Hamiltonian structure, and integral equations. In this paper, we prove that Gaussian Fibonacci circulant type matrices are invertible matrices for n>2 and give the explicit determinants and the inverse matrices. Furthermore, the upper bounds for the spread on Gaussian Fibonacci circulant and left circulant matrices are presented, respectively.
Bandwidth of Gaussian weighted Chirp
DEFF Research Database (Denmark)
Wilhjelm, Jens E.
1993-01-01
Four major time duration and bandwidth expressions are calculated for a linearly frequency modulated sinusoid with Gaussian shaped envelope. This includes a Gaussian tone pulse. The bandwidth is found to be a nonlinear function of nominal time duration and nominal frequency excursion of the chirp...
Spectral representation of Gaussian semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2009-01-01
The aim of the present paper is to characterize the spectral representation of Gaussian semimartingales. That is, we provide necessary and sufficient conditions on the kernel K for X t =∫ K t (s) dN s to be a semimartingale. Here, N denotes an independently scattered Gaussian random measure...
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
Shandarin, S F; Xu, Y; Tegmark, M; Shandarin, Sergei F.; Feldman, Hume A.; Xu, Yongzhong; Tegmark, Max
2001-01-01
We test degree-scale cosmic microwave background (CMB) anisotropy for Gaussianity by studying the \\qmask map that was obtained from combining the QMAP and Saskatoon data. We compute seven morphological functions $M_i(\\dt)$, $i=1,...,7$: six \\mf and the number of regions $N_c$ at a hundred $\\dt$ levels. We also introduce a new parameterization of the morphological functions $M_i(A)$ in terms of the total area $A$ of the excursion set. We show that the latter considerably decorrelates the morphological statistics. We compare these results with those from 1000 Gaussian Monte Carlo maps with the same power spectrum, and conclude that the \\qmask map is neither a very typical nor a very exceptional realization of a Gaussian field. Roughly 20% of the 1000 Gaussian Monte Carlo maps differ more than the \\qmask map from the mean morphological parameters of the Gaussian fields.
Nonlinear Approximation Using Gaussian Kernels
Hangelbroek, Thomas
2009-01-01
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. Our scheme is sophisticated to a degree that it employs even locally Gaussians with varying tensions, and that it resolves local ...
Normal form decomposition for Gaussian-to-Gaussian superoperators
Energy Technology Data Exchange (ETDEWEB)
De Palma, Giacomo [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); INFN, Pisa (Italy); Mari, Andrea; Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Holevo, Alexander S. [Steklov Mathematical Institute, 119991 Moscow, Russia and National Research University Higher School of Economics (HSE), 101000 Moscow (Russian Federation)
2015-05-15
In this paper, we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non-positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings, we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.
Energy Technology Data Exchange (ETDEWEB)
Piepel, Gregory F.
2007-12-01
A mixture experiment involves combining two or more components in various proportions or amounts and then measuring one or more responses for the resulting end products. Other factors that affect the response(s), such as process variables and/or the total amount of the mixture, may also be studied in the experiment. A mixture experiment design specifies the combinations of mixture components and other experimental factors (if any) to be studied and the response variable(s) to be measured. Mixture experiment data analyses are then used to achieve the desired goals, which may include (i) understanding the effects of components and other factors on the response(s), (ii) identifying components and other factors with significant and nonsignificant effects on the response(s), (iii) developing models for predicting the response(s) as functions of the mixture components and any other factors, and (iv) developing end-products with desired values and uncertainties of the response(s). Given a mixture experiment problem, a practitioner must consider the possible approaches for designing the experiment and analyzing the data, and then select the approach best suited to the problem. Eight possible approaches include 1) component proportions, 2) mathematically independent variables, 3) slack variable, 4) mixture amount, 5) component amounts, 6) mixture process variable, 7) mixture of mixtures, and 8) multi-factor mixture. The article provides an overview of the mixture experiment designs, models, and data analyses for these approaches.
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.
Gaussian Mixture Reduction for Bayesian Target Tracking in Clutter
2005-12-22
IEEE Transactions on Automatic Control, AC-17(4):439–448, August 1972. 3. Arfken , George B. and Hans J. Weber. Mathematical Methods for Physicists...developed this method in a more formal mathematical manner. As their work popu- larized the method of maximum likelihood, it became commonly known as...Brooks/Cole Publish- ing Company, Belmont, CA, 1990. 10. Cramér, Harald. Mathematical Methods of Statistics. Princeton University Press, Princeton
Multiple extended target tracking algorithm based on Gaussian surface matrix
Institute of Scientific and Technical Information of China (English)
Jinlong Yang; Peng Li; Zhihua Li; Le Yang
2016-01-01
In this paper, we consider the problem of irregular shapes tracking for multiple extended targets by introducing the Gaussian surface matrix (GSM) into the framework of the random finite set (RFS) theory. The Gaussian surface function is constructed first by the measurements, and it is used to define the GSM via a mapping function. We then integrate the GSM with the probability hypothesis density (PHD) filter, the Bayesian recursion formulas of GSM-PHD are derived and the Gaussian mixture implementation is employed to obtain the closed-form solutions. Moreover, the estimated shapes are designed to guide the measurement set sub-partition, which can cope with the problem of the spatialy close target tracking. Simulation results show that the proposed algorithm can effectively estimate irregular target shapes and exhibit good robustness in cross extended target tracking.
Non-Gaussian errors of baryonic acoustic oscillations
Ngan, Wai-Hin Wayne; Pen, Ue-Li; McDonald, Patrick; MacDonald, Ilana
2011-01-01
We revisit the uncertainty in baryon acoustic oscillation (BAO) forecasts and data analyses. In particular, we study how much the error on the measured mean and uncertainty on the dilation scale are affected by the non-Gaussianity of the non-linear density field. We examine two possible impacts of non-Gaussian analysis: 1. we derive the distance estimators from Gaussian theory, but use 1000 N-Body simulations to measure the actual errors, and compare this to the Gaussian prediction, and 2. we compute new optimal estimators, which requires the inverse of the non-Gaussian covariance matrix of the matter power spectrum. Obtaining an accurate and precise inversion is challenging, and we opted for a noise reduction technique applied on the covariance matrices. By measuring the bootstrap error on the inverted matrix, this work quantifies for the first time the significance of the non-Gaussian error corrections on the BAO dilation scale. We find that the variance (error squared) on distance measurements can deviate ...
Quantification of Gaussian quantum steering
Kogias, Ioannis; Ragy, Sammy; Adesso, Gerardo
2014-01-01
Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits in-between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that steering bound entangled Gaussian states by Gaussian measurements is impossible.
Gaussian maximally multipartite entangled states
Facchi, Paolo; Lupo, Cosmo; Mancini, Stefano; Pascazio, Saverio
2009-01-01
We introduce the notion of maximally multipartite entangled states (MMES) in the context of Gaussian continuous variable quantum systems. These are bosonic multipartite states that are maximally entangled over all possible bipartitions of the system. By considering multimode Gaussian states with constrained energy, we show that perfect MMESs, 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 MMESs and their frustration for n <= 7.
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.
Statistically tuned Gaussian background subtraction technique for UAV videos
Indian Academy of Sciences (India)
R Athi Lingam; K Senthil Kumar
2014-08-01
Background subtraction is one of the efficient techniques to segment the targets from non-informative background of a video. The traditional background subtraction technique suits for videos with static background whereas the video obtained from unmanned aerial vehicle has dynamic background. Here, we propose an algorithm with tuning factor and Gaussian update for surveillance videos that suits effectively for aerial videos. The tuning factor is optimized by extracting the statistical features of the input frames.With the optimized tuning factor and Gaussian update an adaptive Gaussian-based background subtraction technique is proposed. The algorithm involves modelling, update and subtraction phases. This running Gaussian average based background subtraction technique uses updation at both model generation phase and subtraction phase. The resultant video extracts the moving objects from the dynamic background. Sample videos of various properties such as cluttered background, small objects, moving background and multiple objects are considered for evaluation. The technique is statistically compared with frame differencing technique, temporal median method and mixture of Gaussian model and performance evaluation is done to check the effectiveness of the proposed technique after optimization for both static and dynamic videos.
Elegant Ince-Gaussian breathers in strongly nonlocal nonlinear media
Institute of Scientific and Technical Information of China (English)
Bai Zhi-Yong; Deng Dong-Mei; Guo Qi
2012-01-01
A novel class of optical breathers,called elegant Ince-Gaussian breathers,are presented in this paper.They are exact analytical solutions to Snyder and Mitchell's mode in an elliptic coordinate system,and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function.We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schr(o)dinger equation.
Non-classical Gaussian states in noisy environments
Scheel, S; Scheel, Stefan; Welsch, Dirk-Gunnar
2002-01-01
In this article we review properties of Gaussian states and describe operations on them. The interaction of the electromagnetic field with an absorbing dielectric as a special type of environmental interaction will serve as the basis for the understanding of decoherence and entanglement degradation of Gaussian states of light propagating through fibers. The main part of the article is devoted to the study of quantum teleportation in noisy environments. Special emphasis is put onto the question of choosing the correct displacement on the receiver's side.
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.
Higher moments of weighted integrals of non-Gaussian fields
DEFF Research Database (Denmark)
Mohr, Gunnar
1999-01-01
In general, the exact probability distribution of a definite integral of a given non-Gaussian random field is not known. Some information about this unknown distribution can be obtained from the 3rd and 4th moment of the integral. Approximations to these moments can be calculated by discretizing...... the integral and replacing the integrand by third-degree polynomials of correlated Gaussian Variables which reproduce the first four moments and the correlation function of the field correctly. The method described (see Ditlevsen O, Mohr G, Hoffmeyer P. Integration of non-Gaussian fields. Probabilistic...... engineering mechanics, 1996) based on these ideas is discussed and further developed and used in a computer program which produces fairly accurate approximations to the mentioned moments with no restrictions put on the weight function applied to the field and the correlation function of the field...
Wave propagation in non-Gaussian random media
Franco, Mariano; Calzetta, Esteban
2015-01-01
We develop a compact perturbative series for acoustic wave propagation in a medium with a non-Gaussian stochastic speed of sound. We use Martin-Siggia and Rose auxiliary field techniques to render the classical wave propagation problem into a ‘quantum’ field theory one, and then frame this problem within the so-called Schwinger-Keldysh of closed time-path (CTP) formalism. Variation of the so-called two-particle irreducible (2PI) effective action (EA), whose arguments are both the mean fields and the irreducible two point correlations, yields the Schwinger-Dyson and the Bethe-Salpeter equations. We work out the loop expansion of the 2PI CTP EA and show that, in the paradigmatic problem of overlapping spherical intrusions in an otherwise homogeneous medium, non-Gaussian corrections might be much larger than Gaussian ones at the same order of loops.
Some aspects of symmetric Gamma process mixtures
Naulet, Zacharie; Barat, Eric
2015-01-01
In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. We propose a new Gibbs sampler for simulating the posterior and we establish adaptive posterior rates of convergence related to the Gaussian mean regression problem.
Gaussian Entanglement Distribution via Satellite
Hosseinidehaj, Nedasadat
2014-01-01
In this work we analyse 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 trade-off between space-based engineering complexity and the rate of ground-station entanglement generation...
Equi-Gaussian Curvature Folding
Indian Academy of Sciences (India)
E M El-Kholy; El-Said R Lashin; Salama N Daoud
2007-08-01
In this paper we introduce a new type of folding called equi-Gaussian curvature folding of connected Riemannian 2-manifolds. We prove that the composition and the cartesian product of such foldings is again an equi-Gaussian curvature folding. In case of equi-Gaussian curvature foldings, $f:M→ P_n$, of an orientable surface onto a polygon $P_n$ we prove that (i) $f\\in\\mathcal{F}_{EG}(S^2)\\Leftrightarrow n=3$ (ii) $f\\in\\mathcal{F}_{EG}(T^2)\\Rightarrow n=4$ (iii) $f\\in\\mathcal{F}_{EG}(\\# 2T^2)\\Rightarrow n=5, 6$ and we generalize (iii) for $\\# nT^2$.
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...
Analytic model of the effect of poly-Gaussian roughness on rarefied gas flow near the surface
Aksenova, Olga A.; Khalidov, Iskander A.
2016-11-01
The dependence of the macro-parameters of the flow on surface roughness of the walls and on geometrical shape of the surface is investigated asymptotically and numerically in a rarefied gas molecular flow at high Knudsen numbers. Surface roughness is approximated in statistical simulation by the model of poly-Gaussian (with probability density as the mixture of Gaussian densities [1]) random process. Substantial difference is detected for considered models of the roughness (Gaussian, poly-Gaussian and simple models applied by other researchers), as well in asymptotical expressions [3], as in numerical results. For instance, the influence of surface roughness on momentum and energy exchange coefficients increases noticeably for poly-Gaussian model compared to Gaussian one (although the main properties of poly-Gaussian random processes and fields are similar to corresponding properties of Gaussian processes and fields). Main advantage of the model is based on relative simple relations between the parameters of the model and the basic statistical characteristics of random field. Considered statistical approach permits to apply not only diffuse-specular model of the local scattering function V0 of reflected gas atoms, but also Cercignani-Lampis scattering kernel or phenomenological models of scattering function. Thus, the comparison between poly-Gaussian and Gaussian models shows more significant effect of roughness in aerodynamic values for poly-Gaussian model.
ChemXSeer Digital Library Gaussian Search
Lahiri, Shibamouli; Nangia, Shikha; Mitra, Prasenjit; Giles, C Lee; Mueller, Karl T
2011-01-01
We report on the Gaussian file search system designed as part of the ChemXSeer digital library. Gaussian files are produced by the Gaussian software [4], a software package used for calculating molecular electronic structure and properties. The output files are semi-structured, allowing relatively easy access to the Gaussian attributes and metadata. Our system is currently capable of searching Gaussian documents using a boolean combination of atoms (chemical elements) and attributes. We have also implemented a faceted browsing feature on three important Gaussian attribute types - Basis Set, Job Type and Method Used. The faceted browsing feature enables a user to view and process a smaller, filtered subset of documents.
Betti Numbers of Gaussian Fields
Park, Changbom; Pranav, Pratyush; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A.
2013-01-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be
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...
Relics of spatial curvature in the primordial non-gaussianity
Energy Technology Data Exchange (ETDEWEB)
Clunan, Tim; Seery, David, E-mail: T.P.Clunan@damtp.cam.ac.uk, E-mail: D.Seery@damtp.cam.ac.uk [Centre for Theoretical Cosmology, Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)
2010-01-01
We study signatures in the Cosmic Microwave Background (CMB) induced by the presence of strong spatial curvature prior to the epoch of inflation which generated our present universe. If inflation does not last sufficiently long to drive the large-scale spatial curvature to zero, then presently observable scales may have left the horizon while spatial slices could not be approximated by a flat, Euclidean geometry. We compute corrections to the power spectrum and non-gaussianity of the CMB temperature anisotropy in this scenario. The power spectrum does not receive significant corrections and is a weak diagnostic of the presence of curvature in the initial conditions, unless its running can be determined with high accuracy. However, the bispectral non-gaussianity parameter f{sub NL} receives modifications on the largest observable scales. We estimate that the maximum signal would correspond to f{sub NL} ∼ 0.3, which is out of reach for present-day microwave background experiments.
Scheme for adding electron-nucleus cusps to Gaussian orbitals
Ma, A.; Towler, M. D.; Drummond, N. D.; Needs, R. J.
2008-01-01
A simple scheme is described for introducing the correct cusps at nuclei into orbitals obtained from Gaussian basis set electronic structure calculations. The scheme is tested with all-electron variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods for the Ne atom, the H2 molecule, and 55 molecules from a standard benchmark set. It greatly reduces the variance of the local energy in all cases and slightly improves the variational energy. This scheme yields a gen...
A non-Gaussian Ensemble Filter for Assimilating Infrequent Noisy Observations
Harlim, John; Hunt, Brian R.
2007-03-01
We present a modified ensemble Kalman filter that allows a non-Gaussian background error distribution. Using a distribution that decays more slowly than a Gaussian allows the filter to make a larger correction to the background state in cases where it deviates significantly from the truth. For high-dimensional systems, this approach can be used locally. We compare this non-Gaussian filter to its Gaussian counterpart (with multiplicative variance inflation) with the three-dimensional Lorenz-63 model, the 40-dimensional Lorenz-96 model, and Molteni's SPEEDY model, a global model with ~105 state variables. When observations are sufficiently infrequent and noisy, the non-Gaussian filter yields a significant improvement in analysis and forecast errors.
Hierarchy in Sampling Gaussian-correlated Bosons
Huh, Joonsuk
2016-01-01
Boson Sampling represents a class of physical processes potentially intractable for classical devices to simulate. The Gaussian extension of Boson Sampling remains a computationally hard problem, where the input state is a product of uncorrelated Gaussian modes. Besides, motivated by molecular spectroscopy, Vibronic Boson Sampling involves operations that can generate Gaussian correlation among different Boson modes. Therefore, Gaussian Boson Sampling is a special case of Vibronic Boson Sampling. However, this does not necessarily mean that Vibronic Boson Sampling is more complex than Gaussian Boson Sampling. Here we develop a hierarchical structure to show how the initial correlation in Vibronic Boson Sampling can be absorbed in Gaussian Boson Sampling with ancillary modes and in a scattershot fashion. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling ...
Stable and Efficient Gaussian Process Calculations
National Aeronautics and Space Administration — The use of Gaussian processes can be an effective approach to prediction in a supervised learning environment. For large data sets, the standard Gaussian process...
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...
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....
Mixture Based Outlier Filtration
Directory of Open Access Journals (Sweden)
P. Pecherková
2006-01-01
Full Text Available Success/failure of adaptive control algorithms – especially those designed using the Linear Quadratic Gaussian criterion – depends on the quality of the process data used for model identification. One of the most harmful types of process data corruptions are outliers, i.e. ‘wrong data’ lying far away from the range of real data. The presence of outliers in the data negatively affects an estimation of the dynamics of the system. This effect is magnified when the outliers are grouped into blocks. In this paper, we propose an algorithm for outlier detection and removal. It is based on modelling the corrupted data by a two-component probabilistic mixture. The first component of the mixture models uncorrupted process data, while the second models outliers. When the outlier component is detected to be active, a prediction from the uncorrupted data component is computed and used as a reconstruction of the observed data. The resulting reconstruction filter is compared to standard methods on simulated and real data. The filter exhibits excellent properties, especially in the case of blocks of outliers.
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...
Optical trapping with Super-Gaussian beams
CSIR Research Space (South Africa)
McLaren, M
2013-04-01
Full Text Available We outline the possibility of optical trapping and tweezing with Super-Gaussian beam profiles. We show that the trapping strength can be tuned continuously by adjusting the order of a Super-Gaussian beam, approaching that of a perfect Gaussian...
Minimum output entropy of Gaussian channels
Lloyd, S; Maccone, L; Pirandola, S; Garcia-Patron, R
2009-01-01
We show that the minimum output entropy for all single-mode Gaussian channels is additive and is attained for Gaussian inputs. This allows the derivation of the channel capacity for a number of Gaussian channels, including that of the channel with linear loss, thermal noise, and linear amplification.
Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2015-01-01
One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechnics remains as non-local as quantum mechanics itself.
Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2016-05-01
We examine putative corrections to the Bell operator due to the noncommutativity in the phase space. Starting from a Gaussian squeezed envelope whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics, respectively, we conclude that although the time-evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechanics remain as nonlocal as quantum mechanics itself.
Information geometry of Gaussian channels
Monras, Alex
2009-01-01
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 from distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under some restriction on the available resources. We prove that optimal states are always pure and bounded in the number of ancillary modes that are needed. This has experimental and computational advantages: 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 computing the metric. We provide explicit formulae for computing the multiparametric quantum F...
The Halo Bispectrum in N-body Simulations with non-Gaussian Initial Conditions
Sefusatti, Emiliano; Desjacques, Vincent
2011-01-01
We present measurements of the bispectrum of dark matter halos in numerical simulations with non-Gaussian initial conditions of the 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 scale when the constant Gaussian bias parameter, both linear and quadratic, and their constant non-Gaussian corrections are fitted for. The best-fit 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% for f_NL=100 at redshift z=0.5) and results from contributions of similar amplitude induced by the initial matter bispectrum,...
Non-Gaussian Stochastic Gravity
Bates, Jason D.
2013-01-01
This paper presents a new, non-Gaussian formulation of stochastic gravity by incorporating the higher moments of the fluctuations of the quantum stress energy tensor for a free quantum scalar field in a consistent way. A scheme is developed for obtaining realizations of these fluctuations in terms of the Wightman function, and the behavior of the fluctuations is investigated. The resulting probability distribution for fluctuations of the energy density in Minkowski spacetime is found to be si...
Optical coherence tomography image denoising using Gaussianization transform
Amini, Zahra; Rabbani, Hossein
2017-08-01
We demonstrate the power of the Gaussianization transform (GT) for modeling image content by applying GT for optical coherence tomography (OCT) denoising. The proposed method is a developed version of the spatially constrained Gaussian mixture model (SC-GMM) method, which assumes that each cluster of similar patches in an image has a Gaussian distribution. SC-GMM tries to find some clusters of similar patches in the image using a spatially constrained patch clustering and then denoise each cluster by the Wiener filter. Although in this method GMM distribution is assumed for the noisy image, holding this assumption on a dataset is not investigated. We illustrate that making a Gaussian assumption on a noisy dataset has a significant effect on denoising results. For this purpose, a suitable distribution for OCT images is first obtained and then GT is employed to map this original distribution of OCT images to a GMM distribution. Then, this Gaussianized image is used as the input of the SC-GMM algorithm. This method, which is a combination of GT and SC-GMM, remarkably improves the results of OCT denoising compared with earlier version of SC-GMM and even produces better visual and numerical results than the state-of-the art works in this field. Indeed, the main advantage of the proposed OCT despeckling method is texture preservation, which is important for main image processing tasks like OCT inter- and intraretinal layer analysis. Thus, to prove the efficacy of the proposed method for this analysis, an improvement in the segmentation of intraretinal layers using the proposed method as a preprocessing step is investigated. Furthermore, the proposed method can achieve the best expert ranking between other contending methods, and the results show the helpfulness and usefulness of the proposed method in clinical applications.
Gaussian Functions, Γ-Functions and Wavelets
Institute of Scientific and Technical Information of China (English)
蔡涛; 许天周
2003-01-01
The relations between Gaussian function and Γ-function is revealed first at one-dimensional situation. Then, the Fourier transformation of n-dimensional Gaussian function is deduced by a lemma. Following the train of thought in one-dimensional situation, the relation between n-dimensional Gaussian function and Γ-function is given. By these, the possibility of arbitrary derivative of an n-dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ-function as well as in finding high-dimensional mother wavelets.
One-mode quantum-limited Gaussian channels have Gaussian maximizers
2016-01-01
We prove that Gaussian states saturate the p->q norms of the one-mode quantum-limited attenuator and amplifier. The proof starts from the majorization result of De Palma et al., IEEE Trans. Inf. Theory 62, 2895 (2016), and is based on a new logarithmic Sobolev inequality. Our result extends to noncommutative probability the seminal theorem "Gaussian kernels have only Gaussian maximizers" (Lieb, Invent. Math. 102, 179 (1990)), stating that Gaussian operators saturate the p->q norms of Gaussian...
Non Gaussian Minkowski functionals and extrema counts for CMB maps
Pogosyan, Dmitri; Codis, Sandrine; Pichon, Christophe
2016-10-01
In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky was suggested, but never rigorously developed. In this paper we present such development treating the effects of the curvature and finiteness of the spherical space $S_2$ exactly, without relying on flat-sky approximation. We present Minkowski functionals, including Euler characteristic and extrema counts to the first non-Gaussian correction, suitable for weakly non-Gaussian fields on a sphere, of which CMB is the prime example.
Blind source separation of ship-radiated noise based on generalized Gaussian model
Institute of Scientific and Technical Information of China (English)
Kong Wei; Yang Bin
2006-01-01
When the distribution of the sources cannot be estimated accurately, the ICA algorithms failed to separate the mixtures blindly. The generalized Gaussian model (GGM) is presented in ICA algorithm since it can model nonGaussian statistical structure of different source signals easily. By inferring only one parameter, a wide class of statistical distributions can be characterized. By using maximum likelihood (ML) approach and natural gradient descent, the learning rules of blind source separation (BSS) based on GGM are presented. The experiment of the ship-radiated noise demonstrates that the GGM can model the distributions of the ship-radiated noise and sea noise efficiently, and the learning rules based on GGM gives more successful separation results after comparing it with several conventional methods such as high order cumulants and Gaussian mixture density function.
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, an...
Improved estimation in a non-Gaussian parametric regression
Pchelintsev, Evgeny
2011-01-01
The paper considers the problem of estimating the parameters in a continuous time regression model with a non-Gaussian noise of pulse type. The noise is specified by the Ornstein-Uhlenbeck process driven by the mixture of a Brownian motion and a compound Poisson process. Improved estimates for the unknown regression parameters, based on a special modification of the James-Stein procedure with smaller quadratic risk than the usual least squares estimates, are proposed. The developed estimation scheme is applied for the improved parameter estimation in the discrete time regression with the autoregressive noise depending on unknown nuisance parameters.
A Gaussian Mixed Model for Learning Discrete Bayesian Networks.
Balov, Nikolay
2011-02-01
In this paper we address the problem of learning discrete Bayesian networks from noisy data. Considered is a graphical model based on mixture of Gaussian distributions with categorical mixing structure coming from a discrete Bayesian network. The network learning is formulated as a Maximum Likelihood estimation problem and performed by employing an EM algorithm. The proposed approach is relevant to a variety of statistical problems for which Bayesian network models are suitable - from simple regression analysis to learning gene/protein regulatory networks from microarray data.
FPGA design and implementation of Gaussian filter
Yang, Zhihui; Zhou, Gang
2015-12-01
In this paper , we choose four different variances of 1,3,6 and 12 to conduct FPGA design with three kinds of Gaussian filtering algorithm ,they are implementing Gaussian filter with a Gaussian filter template, Gaussian filter approximation with mean filtering and Gaussian filter approximation with IIR filtering. By waveform simulation and synthesis, we get the processing results on the experimental image and the consumption of FPGA resources of the three methods. We set the result of Gaussian filter used in matlab as standard to get the result error. By comparing the FPGA resources and the error of FPGA implementation methods, we get the best FPGA design to achieve a Gaussian filter. Conclusions can be drawn based on the results we have already got. When the variance is small, the FPGA resources is enough for the algorithm to implement Gaussian filter with a Gaussian filter template which is the best choice. But when the variance is so large that there is no more FPGA resources, we can chose the mean to approximate Gaussian filter with IIR filtering.
Gaussian free fields for mathematicians
Sheffield, Scott
2003-01-01
The d-dimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a d-dimensional-time analog of Brownian motion. Just as Brownian motion is the limit of the simple random walk (when time and space are appropriately scaled), the GFF is the limit of many incrementally varying random functions on d-dimensional grids. We present an overview of the GFF and some of the properties that are useful in light of recent connections between the GFF and the Schramm-L...
Gaussian moving averages and semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2008-01-01
In the present paper we study moving averages (also known as stochastic convolutions) driven by a Wiener process and with a deterministic kernel. Necessary and sufficient conditions on the kernel are provided for the moving average to be a semimartingale in its natural filtration. Our results...... are constructive - meaning that they provide a simple method to obtain kernels for which the moving average is a semimartingale or a Wiener process. Several examples are considered. In the last part of the paper we study general Gaussian processes with stationary increments. We provide necessary and sufficient...
Non-Gaussian Stochastic Processes.
1986-02-28
Underwriting Risk and Return Paradox Revisited," J. Risk and Insurance .24.L 621-627 (1982). P. Brockett and B. Arnold, "Identifiability for Dependent...Some Ruin Calculations," J. Risk and Insurance 5DIAL 727-731 (1983). P. Brockett, S. Cox, and R. Witt, "Self-Insurance and the Probability of...Financial Regret," J. Risk and Insurance 51(4) 720-729 (1984). P. Brockett, "The Likelihood Ratio Detector for Non-Gaussian Infinitely Divisible and Linear
Kasai, Seiya; Tadokoro, Yukihiro; Ichiki, Akihisa
2013-12-01
We design nonlinear functions for the transmission of a small signal with non-Gaussian noise and perform experiments to characterize their responses. Using statistical design theory [A. Ichiki and Y. Tadokoro, Phys. Rev. E 87, 012124 (2013), 10.1103/PhysRevE.87.012124], a static nonlinear function is estimated from the probability density function of the given noise in order to maximize the signal-to-noise ratio of the output. Using an electronic system that implements the optimized nonlinear function, we confirm the recovery of a small signal from a signal with non-Gaussian noise. In our experiment, the non-Gaussian noise is a mixture of Gaussian noises. A similar technique is also applied to the optimization of the threshold value of the function. We find that, for non-Gaussian noise, the response of the optimized nonlinear systems is better than that of the linear system.
Gaussian process based recursive system identification
Prüher, Jakub; Šimandl, Miroslav
2014-12-01
This paper is concerned with the problem of recursive system identification using nonparametric Gaussian process model. Non-linear stochastic system in consideration is affine in control and given in the input-output form. The use of recursive Gaussian process algorithm for non-linear system identification is proposed to alleviate the computational burden of full Gaussian process. The problem of an online hyper-parameter estimation is handled using proposed ad-hoc procedure. The approach to system identification using recursive Gaussian process is compared with full Gaussian process in terms of model error and uncertainty as well as computational demands. Using Monte Carlo simulations it is shown, that the use of recursive Gaussian process with an ad-hoc learning procedure offers converging estimates of hyper-parameters and constant computational demands.
Bipartite and Multipartite Entanglement of Gaussian States
Adesso, G; Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global and local amounts of mixedness, and efficiently estimated by direct measurements of the associated purities. For multimode Gaussian states endowed with local symmetry with respect to a given bipartition, we show how the multimode block entanglement can be completely and reversibly localized onto a single pair of modes by local, unitary operations. We then analyze the distribution of entanglement among multiple parties in multimode Gaussian states. We introduce the continuous-variable tangle to quantify entanglement sharing in Gaussian states and we prove that it satisfies the Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure, symmetric three-mode Gaussian states, at variance with their discrete-variable counterparts, allow a promiscuous sharing of ...
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.
Dissipation-induced pure Gaussian state
Koga, Kei
2011-01-01
This paper provides some necessary and sufficient conditions for a general Markovian Gaussian master equation to have a unique pure steady state. The conditions are described by simple matrix equations, thus they can be easily applied to the so-called environment engineering for pure Gaussian state preparation. In particular, it is shown that for any given pure Gaussian state we can actually construct a dissipative process yielding that state as the unique steady state.
D'Amico, Guido
2014-01-01
We analyze primordial non-Gaussianity in single field inflationary models when the tensor/scalar ratio is large, $r \\sim 0.2$. Our results show that detectable levels of non-Gaussianity $f_{NL} \\sim 50$ are still possible in the simplest class of models described by the effective theory of inflation. However, the \\emph{shape} is very tightly constrained, making a sharp prediction that could be confirmed or falsified by a future detection of non-Gaussianity.
Strongly Scale-dependent Non-Gaussianity
Riotto, Antonio
2011-01-01
We discuss models of primordial density perturbations where the non-Gaussianity is strongly scale-dependent. In particular, the non-Gaussianity may have a sharp cut-off and be very suppressed on large cosmological scales, but sizeable on small scales. This may have an impact on probes of non-Gaussianity in the large-scale structure and in the cosmic microwave background radiation anisotropies.
Computing an Exact Gaussian Scale-Space
Ives Rey Otero; Mauricio Delbracio
2016-01-01
Gaussian convolution is one of the most important algorithms in image processing. The present work focuses on the computation of the Gaussian scale-space, a family of increasingly blurred images, responsible, among other things, for the scale-invariance of SIFT, a popular image matching algorithm. We discuss and numerically analyze the precision of three different alternatives for defining a discrete counterpart to the continuous Gaussian operator. This study is focused on low blur levels, th...
A Family of Non-Gaussian Martingales with Gaussian Marginals
Directory of Open Access Journals (Sweden)
Kais Hamza
2007-08-01
Full Text Available We construct a family of martingales with Gaussian marginal distributions. We give a weak construction as Markov, inhomogeneous in time processes, and compute their infinitesimal generators. We give the predictable quadratic variation and show that the paths are not continuous. The construction uses distributions GÃÂƒ having a log-convolution semigroup property. Further, we categorize these processes as belonging to one of two classes, one of which is made up of piecewise deterministic pure jump processes. This class includes the case where GÃÂƒ is an inverse log-Poisson distribution. The processes in the second class include the case where GÃÂƒ is an inverse log-gamma distribution. The richness of the family has the potential to allow for the imposition of specifications other than the marginal distributions.
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.
Gaussian measures of entanglement versus negativities and the ordering of two-mode Gaussian states
Adesso, G; Adesso, Gerardo; Illuminati, Fabrizio
2005-01-01
In this work we focus on entanglement of two--mode Gaussian states of continuous variable systems. We introduce the formalism of Gaussian entanglement measures, adopting the framework developed in [M. M. Wolf {\\em et al.}, Phys. Rev. A {\\bf 69}, 052320 (2004)], where the Gaussian entanglement of formation was defined. We compute Gaussian measures explicitely for two important families of nonsymmetric two--mode Gaussian states, namely the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in [G. Adesso {\\em et al.}, Phys. Rev. Lett. {\\bf 92}, 087901 (2004)]. This allows us to compare the {\\em orderings} induced on the set of entangled two--mode Gaussian states by the negativities and by the Gaussian entanglement measures. We find that in a certain range of global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement than states of maximum negativity. Thus ...
Nuclear collective flow from gaussian fits to triple differential distributions
Energy Technology Data Exchange (ETDEWEB)
Gosset, J.; Demoulins, M.; Babinet, R.; Cavata, C.; Fanet, H.; L' Hote, D.; Lucas, B.; Poitou, J.; Valette, O. (CEA Centre d' Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Dept. de Physique Nucleaire); Lemaire, M.C. (Laboratoire National Saturne, Centre d' Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France)); Alard, J.P.; Augerat, J.; Bastid, N.; Charmensat, P.; Dupieux, P.; Fraysse, L.; Marroncle, J.; Montarou, G.; Parizet, M.J.; Qassoud, D.; Rahmani, A. (Clermont-Ferrand-2 Univ., 63 - Aubiere (France). Lab. de Physique Corpusculaire); Brochard, F.; Gorodetzky, P.; Racca, C. (Strasbourg-1 Univ., 67 (France). Centre de Recherches Nucleaires)
1990-09-13
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.).
Strongly Scale-dependent Non-Gaussianity
DEFF Research Database (Denmark)
Riotto, Antonio; Sloth, Martin Snoager
2010-01-01
We discuss models of primordial density perturbations where the non-Gaussianity is strongly scale-dependent. In particular, the non-Gaussianity may have a sharp cut-off and be very suppressed on large cosmological scales, but sizeable on small scales. This may have an impact on probes of non...
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...
Conditional and unconditional Gaussian quantum dynamics
Genoni, Marco G.; Lami, Ludovico; Serafini, Alessio
2016-07-01
This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as 'general-dyne') quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.
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...
Helical apodizers for tunable hyper Gaussian masks
Ojeda-Castañeda, J.; Ledesma, Sergio; Gómez-Sarabia, Cristina M.
2013-09-01
We discuss an optical method for controlling the half-width of Gaussian like transmittance windows, by using a pair of absorption masks that have both radial and helical amplitude variations. For describing the radial part of the proposed masks, we employ amplitude transmittance profiles of the form T(ρ) = exp(- ρ s ). For s = 2, one has an amplitude transmittance that is proportional to a Gaussian function. A sub Gaussian mask is defined by a value of s 2, one has super Gaussian masks. Our discussion considers that any of these radially varying masks has also helical modulations. We show that by using a suitable pair of this type of masks, one can control the halfwidth of Gaussian like windows.
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 w...
Fuzzy C-Means Clustering Based Phonetic Tied-Mixture HMM in Speech Recognition
Institute of Scientific and Technical Information of China (English)
XU Xiang-hua; ZHU Jie; GUO Qiang
2005-01-01
A fuzzy clustering analysis based phonetic tied-mixture HMM(FPTM) was presented to decrease parameter size and improve robustness of parameter training. FPTM was synthesized from state-tied HMMs by a modified fuzzy C-means clustering algorithm. Each Gaussian codebook of FPTM was built from Gaussian components within the same root node in phonetic decision tree. The experimental results on large vocabulary Mandarin speech recognition show that compared with conventional phonetic tied-mixture HMM and state-tied HMM with approximately the same number of Gaussian mixtures, FPTM achieves word error rate reductions by 4.84% and 13.02 % respectively. Combining the two schemes of mixing weights pruning and Gaussian centers fuzzy merging, a significantly parameter size reduction was achieved with little impact on recognition accuracy.
Betti numbers of Gaussian fields
Park, Changbom; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A
2013-01-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be used to distinguish topological spaces. In the case of the excursion sets of a three-dimensional field there are three possibly non-zero Betti numbers; $\\beta_0$ is the number of connected regions, $\\beta_1$ is the number of circular holes, and $\\beta_2$ is the number of three-dimensional voids. Their sum with alternating signs is the genus of the surface of excursion regions. It is found that each Betti number has a dominant contribution to the genus in a specific threshold range. $\\beta_0$ dominates the high-threshold part of the genus curve measuring the abundance of high density regions (clusters). $\\beta_1$ dominates the genus near the median thresholds which measures the topology of negatively curved iso-den...
Asymmetric Laguerre-Gaussian beams
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-06-01
We introduce a family of asymmetric Laguerre-Gaussian (aLG) laser beams. The beams have been derived via a complex-valued shift of conventional LG beams in the Cartesian plane. While propagating in a uniform medium, the first bright ring of the aLG beam becomes less asymmetric and the energy is redistributed toward peripheral diffraction rings. The projection of the orbital angular momentum (OAM) onto the optical axis is calculated. The OAM is shown to grow quadratically with increasing asymmetry parameter of the aLG beam, which equals the ratio of the shift to the waist radius. Conditions for the OAM becoming equal to the topological charge have been derived. For aLG beams with zero radial index, we have deduced an expression to define the intensity maximum coordinates and shown the crescent-shaped intensity pattern to rotate during propagation. Results of the experimental generation and rotation of aLG beams agree well with theoretical predictions.
On Gaussian Beams Described by Jacobi's Equation
Smith, Steven Thomas
2013-01-01
Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) It is shown that the \\v{C}erven\\'y equations for the amplitude and phase are equivalent to the classical Jacobi Equation of differential geometry. The \\v{C}erven\\'y equations describe Gaussian beams using Hamilton-Jacobi theory, whereas the Jacobi Equation expresses how Gaussian and Riemannian curvature determine geodesic flow on a Riemannian manifold. Thus the paper makes a fundamental connection between Gaussian beams and an acoustic channel's so-called intrinsic Gaussian curvature from differential geometry. (2) A new formula $\\pi(c/c")^{1/2}$ for the distance between convergence zones is derived and applied to several well-known profiles. (3) A class of "model spaces" are introduced that connect the acoustics of ducting/divergence zones with the channel's Gaussian curvature $K=cc"-(c')^2$. The "model" SSPs yield constant Gauss...
Gaussian Sum-Rule Analysis of Scalar Gluonium and Quark Mesons
Steele, T G; Orlandini, G
2003-01-01
Gaussian sum-rules, which are related to a two-parameter Gaussian-weighted integral of a hadronic spectral function, are able to examine the possibility that more than one resonance makes a significant contribution to the spectral function. The Gaussian sum-rules, including instanton effects, for scalar gluonic and non-strange scalar quark currents clearly indicate a distribution of the resonance strength in their respective spectral functions. Furthermore, analysis of a two narrow resonance model leads to excellent agreement between theory and phenomenology in both channels. The scalar quark and gluonic sum-rules are remarkably consistent in their prediction of masses of approximately 1.0 GeV and 1.4 GeV within this model. Such a similarity would be expected from hadronic states which are mixtures of gluonium and quark mesons.
A fuzzy-clustering analysis based phonetic tied-mixture HMM
Institute of Scientific and Technical Information of China (English)
XU Xianghua; ZHU Jie; GUO Qiang
2005-01-01
To efficiently decrease the size of parameters and improve the robustness of parameters training, a fuzzy clustering based phonetic tied-mixture model, FPTM, is presented.The Gaussian codebook of FPTM is synthesized from Gaussian components belonging to the same root node in phonetic decision tree. Fuzzy clustering method is further used for FPTM covariance sharing. Experimental results show that compared with the conventional PTM with approximately the same parameters size, FPTM decrease the size of Gaussian weights by 77.59% and increases word accuracy by 7.92%, which proves Gaussian fuzzy clustering is efficient. Compared with FPTM, covariance-shared FPTM decreases word error rate by 1.14% , which proves the combined fuzzy clustering for both Gaussian and covariance is superior to Gaussian fuzzy clustering alone.
BER of flat-topped Gaussian beam in slant path turbulent atmosphere
Lu, Fang; Han, Yanyan; Han, Xiang-e.; Yang, Rui-ke
2013-08-01
Based on the theory of optical wave propagation in the slant path and the ITU-R turbulence structure constant model which is dependent on altitude, the on-axis scintillation index of the flat-topped Gaussian beam at the receiver plane in slant path turbulence was given by using Kolmogorov atmospheric turbulence power spectrum model. The influences of the link altitudes, atmospheric refractive index structure constant C0 at the ground，the source size and the beam order on scintillation index of the flat-topped Gaussian beam are discussed in detail. The result shows that the scintillation index increased first and then decreased with the increase of the beam order. The advantage of a flat-topped Gaussian beam over a single Gaussian beam is restricted to small source sizes, which is consistent with the case of the horizontal path. To find the average bit error rate under weak slant path turbulence, the log-normal distribution model of the intensity fluctuation was used. The influence of beam order and source size on BER was discussed. The result indicates that the smaller sized flat-topped Gaussian beam will bring average bit error rate advantage over the same size Gaussian beam. Our results correctly reduce to the result of the horizontal path with atmospheric structure constant fixed.
Non-Gaussian signatures of tachyacoustic cosmology
Energy Technology Data Exchange (ETDEWEB)
Bessada, Dennis, E-mail: dennis.bessada@unifesp.br [UNIFESP — Universidade Federal de São Paulo, Laboratório de Física Teórica e Computação Científica, Rua São Nicolau, 210, 09913-030, Diadema, SP (Brazil)
2012-09-01
I investigate non-Gaussian signatures in the context of tachyacoustic cosmology, that is, a noninflationary model with superluminal speed of sound. I calculate the full non-Gaussian amplitude A, its size f{sub NL}, and corresponding shapes for a red-tilted spectrum of primordial scalar perturbations. Specifically, for cuscuton-like models I show that f{sub NL} ∼ O(1), and the shape of its non-Gaussian amplitude peaks for both equilateral and local configurations, the latter being dominant. These results, albeit similar, are quantitatively distinct from the corresponding ones obtained by Magueijo et al. in the context of superluminal bimetric models.
Computing an Exact Gaussian Scale-Space
Directory of Open Access Journals (Sweden)
Ives Rey Otero
2016-02-01
Full Text Available Gaussian convolution is one of the most important algorithms in image processing. The present work focuses on the computation of the Gaussian scale-space, a family of increasingly blurred images, responsible, among other things, for the scale-invariance of SIFT, a popular image matching algorithm. We discuss and numerically analyze the precision of three different alternatives for defining a discrete counterpart to the continuous Gaussian operator. This study is focused on low blur levels, that are crucial for the scale-space accuracy.
Computer simulation of rod-sphere mixtures
Antypov, D
2003-01-01
Results are presented from a series of simulations undertaken to investigate the effect of adding small spherical particles to a fluid of rods which would otherwise represent a liquid crystalline (LC) substance. Firstly, a bulk mixture of Hard Gaussian Overlap particles with an aspect ratio of 3:1 and hard spheres with diameters equal to the breadth of the rods is simulated at various sphere concentrations. Both mixing-demixing and isotropic-nematic transition are studied using Monte Carlo techniques. Secondly, the effect of adding Lennard-Jones particles to an LC system modelled using the well established Gay-Berne potential is investigated. These rod-sphere mixtures are simulated using both the original set of interaction parameters and a modified version of the rod-sphere potential proposed in this work. The subject of interest is the internal structure of the binary mixture and its dependence on density, temperature, concentration and various parameters characterising the intermolecular interactions. Both...
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.
Phase Correlations in Non-Gaussian Fields
Matsubara, T
2003-01-01
A breakthrough in understanding the phase information of Fourier modes in non-Gaussian fields is presented, discovering the general relation between phase correlations and the hierarchy of polyspectra. Although the exact relations involve the expansions of infinite series, one can truncate these expansions in weakly non-Gaussian fields. The phase sum, $\\theta_{\\sbfm{k}_1} + >... + \\theta_{\\sbfm{k}_N}$, satisfying $\\bfm{k}_1 + ... + \\bfm{k}_N = 0$, is found to be non-uniformly distributed in non-Gaussian fields, and the non-uniformness is represented by the polyspectra. A numerical demonstration proves that the distribution of the phase sum is the robust estimator of the non-Gaussianity.
Parity Violation in Graviton Non-gaussianity
Soda, Jiro; Nozawa, Masato
2011-01-01
We study parity violation in graviton non-gaussianity generated during inflation. We develop a useful formalism to calculate graviton non-gaussianity. Using this formalism, we explicitly calculate the parity violating part of the bispectrum for primordial gravitational waves in the exact de Sitter spacetime and prove that no parity violation appears in the non-gaussianity. We also extend the analysis to slow-roll inflation and find that the parity violation of the bispectrum is proportional to the slow-roll parameter. We argue that parity violating non-gaussianity can be tested by the CMB. Our results are also useful for calculating three-point function of the stress tensor in the non-conformal field theory through the gravity/field theory correspondence.
The curious nonexistence of Gaussian 2-designs
Blume-Kohout, Robin
2011-01-01
2-designs -- ensembles of quantum pure states whose 2nd moments equal those of the uniform Haar ensemble -- are optimal solutions for several tasks in quantum information science, especially state and process tomography. We show that Gaussian states cannot form a 2-design for the continuous-variable (quantum optical) Hilbert space L2(R). This is surprising because the affine symplectic group HWSp (the natural symmetry group of Gaussian states) is irreducible on the symmetric subspace of two copies. In finite dimensional Hilbert spaces, irreducibility guarantees that HWSp-covariant ensembles (such as mutually unbiased bases in prime dimensions) are always 2-designs. This property is violated by continuous variables, for a subtle reason: the (well-defined) HWSp-invariant ensemble of Gaussian states does not have an average state because the averaging integral does not converge. In fact, no Gaussian ensemble is even close (in a precise sense) to being a 2-design. This surprising difference between discrete and c...
GPstuff: Bayesian Modeling with Gaussian Processes
Vanhatalo, J.; Riihimaki, J.; Hartikainen, J.; Jylänki, P.P.; Tolvanen, V.; Vehtari, A.
2013-01-01
The GPstuff toolbox is a versatile collection of Gaussian process models and computational tools required for Bayesian inference. The tools include, among others, various inference methods, sparse approximations and model assessment methods.
Lecture notes on non-Gaussianity
Byrnes, Christian T
2014-01-01
We discuss how primordial non-Gaussianity of the curvature perturbation helps to constrain models of the early universe. Observations are consistent with Gaussian initial conditions, compatible with the predictions of the simplest models of inflation. Deviations are constrained to be at the sub percent level, constraining alternative models such as those with multiple fields, non-canonical kinetic terms or breaking the slow-roll conditions. We introduce some of the most important models of inflation which generate non-Gaussian perturbations and provide practical tools on how to calculate the three-point correlation function for a popular class of non-Gaussian models. The current state of the field is summarised and an outlook is given.
Uniform dimension results for Gaussian random fields
Institute of Scientific and Technical Information of China (English)
2009-01-01
Let X = {X(t),t ∈ RN} be a Gaussian random field with values in Rd defined by X(t) =(X1(t),...,Xd(t)), t ∈ RN.(1) The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed.It is shown that in general the uniform Hausdorff dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.When X is an(N,d)-Gaussian random field as in(1),where X1,...,Xd are independent copies of a real valued,centered Gaussian random field X0 which is anisotropic in the time variable.We establish uniform Hausdorff dimension results for the image sets of X.These results extend the corresponding results on one-dimensional Brownian motion,fractional Brownian motion and the Brownian sheet.
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.
Gas distribution, metal enrichment, and baryon fraction in Gaussian and non-Gaussian universes
Maio, Umberto
2011-01-01
We study the cosmological evolution of baryons in universes with and without primordial non-Gaussianities via (large scale) N-body/hydrodynamical simulations, including gas cooling, star formation, stellar evolution, chemical enrichment from both population III and population II regimes, and feedback effects. We find that large fnl values for non-Gaussianities can alter the gas probability distribution functions, the metal pollution history, the halo baryon, gas and stellar fractions, mostly at early times. More precisely: (i) non-Gaussianities lead to an earlier evolution of primordial gas, structures, and star formation; (ii) metal enrichment starts earlier (with respect to the Gaussian scenario) in non-Gaussian models with larger fnl; (iii) gas fractions within the haloes are not significantly affected by the different values of fnl, with deviations of ~1-10%; (iv) the stellar fraction is quite sensitive to non-Gaussianities at early times, with discrepancies reaching up to a factor of ~10 at very high z, ...
A Neural-Network based estimator to search for primordial non-Gaussianity in Planck CMB maps
Novaes, C P; Ferreira, I S; Wuensche, C A
2014-01-01
We present an upgraded combined estimator, based on Minkowski Functionals and a Neural Network, with excellent performance in detecting primordial non-Gaussianity in simulated maps that also contain a weighted mixture of Galactic contaminations, besides real pixel's noise from Planck cosmic microwave background radiation data. We rigorously test the ef\\/ficiency of our estimator considering several plausible scenarios for for residual non-Gaussianities in the foreground-cleaned Planck maps, with the intuition to optimize the training procedure of the Neural Network to discriminate between contaminations with primordial and secondary non-Gaussian signatures. With a validated estimator's performance, showing more than $97 \\%$ of hits in a variety of cases, we look for constraining the primordial non-Gaussianity in large angular scales analyses of the Planck maps. For the $\\mathtt{SMICA}$ map we found that ${f}_{\\rm \\,NL} = 44 \\pm 14$, at $2\\sigma$ confidence level, which is in excellent agreement with the WMAP-...
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.
Integrability Estimates for Gaussian Rough Differential Equations
Cass, Thomas; Lyons, Terry
2011-01-01
We derive explicit tail-estimates for the Jacobian of the solution flow of stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameter H>1/4. We remark on the relevance of such estimates to a number of significant open problems.
Homodyne estimation of Gaussian quantum discord.
Blandino, Rémi; Genoni, Marco G; Etesse, Jean; Barbieri, Marco; Paris, Matteo G A; Grangier, Philippe; Tualle-Brouri, Rosa
2012-11-02
We address the experimental estimation of Gaussian quantum discord for a two-mode squeezed thermal state, and demonstrate a measurement scheme based on a pair of homodyne detectors assisted by Bayesian analysis, which provides nearly optimal estimation for small value of discord. In addition, though homodyne detection is not optimal for Gaussian discord, the noise ratio to the ultimate quantum limit, as dictated by the quantum Cramer-Rao bound, is limited to about 10 dB.
GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION
Institute of Scientific and Technical Information of China (English)
陈泽乾
2002-01-01
A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators (e)t and its dual, creation operators (e)*t.
TURBO EQUALIZATION WITH JOINTLY GAUSSIAN EQUALIZER
Institute of Scientific and Technical Information of China (English)
Jiang Sen; Sun Hong; Li Ping
2005-01-01
A Jointly Gaussian (JG) equalizer is derived for turbo equalization based on an augmented real matrix representation of channel model and a Gaussian approximation of the received symbol sequence. Using matrix inversion lemma and Cholesky decomposition, a lowcomplexity implementation of JG equalizer is also presented. The simulation results and complexity comparison confirm that turbo equalization with JG equalizer has a better performance and a lower complexity than the existing turbo equalization with linear minimum mean squared error equalizer.
Approximate Capacity of Gaussian Relay Networks
Avestimehr, Amir Salman; Tse, David N C
2008-01-01
We present an achievable rate for general Gaussian relay networks. We show that the achievable rate is within a constant number of bits from the information-theoretic cut-set upper bound on the capacity of these networks. This constant depends on the topology of the network, but not the values of the channel gains. Therefore, we uniformly characterize the capacity of Gaussian relay networks within a constant number of bits, for all channel parameters.
Gaussian Process Techniques for Wireless Communications
Han, Mr Chong; Peters, Dr Gareth; Yuan, Prof Jinhong
2010-01-01
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as a non-parametric technique for system estimation from supervision learning. For the thesis project, we intend to propose a new, general methodology for inference and learning in non-linear state-space models probabilistically incorporating with the Gaussian process model estimation.
Gaussian expansion approach to Coulomb breakup
Egami, T; Matsumoto, T; Iseri, Y; Kamimura, M; Yahiro, M
2004-01-01
An accurate treatment of Coulomb breakup reactions is presented by using both the Gaussian expansion method and the method of continuum discretized coupled channels. As $L^2$-type basis functions for describing Coulomb breakup processes, we take complex-range Gaussian functions, which form in good approximation a complete set in a large configuration space being important for the processes. Accuracy of the method is tested quantitatively for $^{8}{\\rm B}+^{58}$Ni scattering at 25.8 MeV.
On-line EM algorithm for the normalized gaussian network.
Sato, M; Ishii, S
2000-02-01
A normalized gaussian network (NGnet) (Moody & Darken, 1989) is a network of local linear regression units. The model softly partitions the input space by normalized gaussian functions, and each local unit linearly approximates the output within the partition. In this article, we propose a new on-line EMalgorithm for the NGnet, which is derived from the batch EMalgorithm (Xu, Jordan, &Hinton 1995), by introducing a discount factor. We show that the on-line EM algorithm is equivalent to the batch EM algorithm if a specific scheduling of the discount factor is employed. In addition, we show that the on-line EM algorithm can be considered as a stochastic approximation method to find the maximum likelihood estimator. A new regularization method is proposed in order to deal with a singular input distribution. In order to manage dynamic environments, where the input-output distribution of data changes over time, unit manipulation mechanisms such as unit production, unit deletion, and unit division are also introduced based on probabilistic interpretation. Experimental results show that our approach is suitable for function approximation problems in dynamic environments. We also apply our on-line EM algorithm to robot dynamics problems and compare our algorithm with the mixtures-of-experts family.
Mashiku, Alinda; Garrison, James L.; Carpenter, J. Russell
2012-01-01
The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.
Nonparaxial Propagation of Vectorial Elliptical Gaussian Beams
Directory of Open Access Journals (Sweden)
Wang Xun
2016-01-01
Full Text Available Based on the vectorial Rayleigh-Sommerfeld diffraction integral formulae, analytical expressions for a vectorial elliptical Gaussian beam’s nonparaxial propagating in free space are derived and used to investigate target beam’s propagation properties. As a special case of nonparaxial propagation, the target beam’s paraxial propagation has also been examined. The relationship of vectorial elliptical Gaussian beam’s intensity distribution and nonparaxial effect with elliptic coefficient α and waist width related parameter fω has been analyzed. Results show that no matter what value of elliptic coefficient α is, when parameter fω is large, nonparaxial conclusions of elliptical Gaussian beam should be adopted; while parameter fω is small, the paraxial approximation of elliptical Gaussian beam is effective. In addition, the peak intensity value of elliptical Gaussian beam decreases with increasing the propagation distance whether parameter fω is large or small, and the larger the elliptic coefficient α is, the faster the peak intensity value decreases. These characteristics of vectorial elliptical Gaussian beam might find applications in modern optics.
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.
Mixture Density Mercer Kernels
National Aeronautics and Space Administration — We present a method of generating Mercer Kernels from an ensemble of probabilistic mixture models, where each mixture model is generated from a Bayesian mixture...
Wang, Li; Chen, Yunjie; Pan, Xiaohua; Hong, Xunning; Xia, Deshen
2010-05-15
This paper presents a variational level set approach in a multi-phase formulation to segmentation of brain magnetic resonance (MR) images with intensity inhomogeneity. In our model, the local image intensities are characterized by Gaussian distributions with different means and variances. We define a local Gaussian distribution fitting energy with level set functions and local means and variances as variables. The means and variances of local intensities are considered as spatially varying functions. Therefore, our method is able to deal with intensity inhomogeneity without inhomogeneity correction. Our method has been applied to 3T and 7T MR images with promising results.
Continuous-variable quantum key distribution protocols with a non-Gaussian modulation
Leverrier, Anthony
2011-01-01
In this paper, we consider continuous-variable quantum key distribution (QKD) protocols which use non-Gaussian modulations. These specific modulation schemes are compatible with very efficient error correction procedures, hence allowing the protocols to outperform previous protocols in terms of achievable range. In their simplest implementation, these protocols are secure for any linear quantum channels (hence against Gaussian attacks). We also show how the use of decoy states makes the protocols secure against arbitrary collective attacks, which implies their unconditional security in the asymptotic limit.
Gaussian vs non-Gaussian turbulence: impact on wind turbine loads
DEFF Research Database (Denmark)
Berg, Jacob; Natarajan, Anand; Mann, Jakob;
2016-01-01
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...... types of turbulence are then used as input to wind turbine load simulations under normal operations with the HAWC2 software package. A slight increase in the extreme loads of the tower base fore-aft moment is observed for high wind speeds when using non-Gaussian turbulence but is insignificant when...
Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
Serafini, A; Wolf, M M
2005-01-01
We address the question of the multiplicativity of the maximal p-norm output purities of bosonic Gaussian channels under Gaussian inputs. We focus on general Gaussian channels resulting from the reduction of unitary dynamics in larger Hilbert spaces. It is shown that the maximal output purity of tensor products of single-mode channels under Gaussian inputs is multiplicative for any p>1 for products of arbitrary identical channels as well as for a large class of products of different channels. In the case of p=2 multiplicativity is shown to be true for arbitrary products of generic channels acting on any number of modes.
Effect of lensing non-Gaussianity on the CMB power spectra
Lewis, Antony
2016-01-01
Observed CMB anisotropies are lensed, and the lensed power spectra can be calculated accurately assuming the lensing deflections are Gaussian. However, the lensing deflections are actually slightly non-Gaussian due to both non-linear large-scale structure growth and post-Born corrections. We calculate the leading correction to the lensed CMB power spectra from the non-Gaussianity, which is determined by the lensing bispectrum. The lowest-order result gives $\\sim 0.3\\%$ corrections to the BB and EE polarization spectra on small-scales, however we show that the effect on EE is reduced by about a factor of two by higher-order Gaussian lensing smoothing, rendering the total effect safely negligible for the foreseeable future. We give a simple analytic model for the signal expected from skewness of the large-scale lensing field; the effect is similar to a net demagnification and hence a small change in acoustic scale (and therefore out of phase with the dominant lensing smoothing that predominantly affects the pea...
Smith, David C.; Kornelson, Keri A.
2013-09-01
This research addresses the document vs. non-document image classification problem. The ability to select images containing text from an OCR processing stream that also includes images of scenes, people, faces, etc., will eliminate unnecessary computation and free up valuable computer resources for other tasks. This is particularly true for high volume OCR systems. Fisher vectors represent images as gradients of a global generative Gaussian Mixture Model (GMM) of low level image descriptors, and exhibit state-of-the-art performance for object categorization. Gaussian supervectors represent images by soft clustering low level image descriptors according to posterior GMM mixture probabilities, optionally using MAP adaptation, and have demonstrated state-of-the-art performance for scene categorization. We compare results obtained by applying linear SVMs to Fisher vector and Gaussian supervector representations to categorize images as having only text, no text, or a mixture of text and non-text. We also report the performance of GMM-based soft versions of vectors of locally aggregated descriptors (VLAD) and Bag of Visual words (BOV).
Evolution of CMB spectral distortion anisotropies and tests of primordial non-Gaussianity
Chluba, Jens; Amin, Mustafa A; Kamionkowski, Marc
2016-01-01
Anisotropies in distortions to the frequency spectrum of the cosmic microwave background (CMB) can be created through spatially varying heating processes in the early Universe. For instance, the dissipation of small-scale acoustic modes does create distortion anisotropies, in particular for non-Gaussian primordial perturbations. In this work, we derive approximations that allow describing the associated distortion field. We provide a systematic formulation of the problem using Fourier-space window functions, clarifying and generalizing previous approximations. Our expressions highlight the fact that the amplitudes of the spectral-distortion fluctuations induced by non-Gaussianity depend also on the homogeneous value of those distortions. Absolute measurements are thus required to obtain model-independent distortion constraints on primordial non-Gaussianity. We also include a simple description for the evolution of distortions through photon diffusion, showing that these corrections can usually be neglected. O...
First-order decomposition of thermal light in terms of a statistical mixture of pulses
Chenu, Aurélia; Brańczyk, Agata M.; J.E. Sipe
2014-01-01
We investigate the connection between thermal light and coherent pulses, constructing mixtures of single pulses that yield the same first-order, equal-space-point correlation function as thermal light. We present mixtures involving (i) pulses with a Gaussian lineshape and narrow bandwidths, and (ii) pulses with a coherence time that matches that of thermal light. We characterize the properties of the mixtures and pulses. Our results introduce an alternative description of thermal light in ter...
Morlock, Gertrud E; Brett, Neil
2015-04-17
The TLC-MS Interface, the successor of the ChromeXtract, has been available for elution head-based coupling of high-performance thin-layer chromatography with mass spectrometry (HPTLC-MS) since 2009, and is meanwhile widespread in use, mainly for compound confirmation. Until now, quantitative performance data has not been reported in detail and thus were investigated in this study. The performance data of HPTLC-electrospray ionization (ESI)-MS via the TLC-MS Interface showed good mean precisions (%RSD, n=5) for 6 dyes in a commercially available dye mixture investigated at two different concentrations (7.3% for the 1:8 dilution, and 10.1% for the 1:16 diluted) in a selected worst case scenario. The respective mean precisions of absorbance measurements were ≤1.3%. For calibrations by HPTLC-ESI-MS, the mean determination coefficient was 0.9975 for the 6 dyes (versus 0.9997 for absorbance measurement). HPTLC-MS analysis revealed the incorrect assignment of components in two commercially available dye mixtures. Using an additional software (MassWorks) that delivered a 100 times increased mass accuracy, the proposal of molecular formulae was shown to be obtainable under certain conditions with a low resolution single quadrupole mass spectrometer and in the case of helpful information such as the double bond equivalents. This enabled the identification of the incorrectly assigned unknown dyes and clearly demonstrated the benefit of using HPTLC-MS for zone confirmation. Copyright © 2015 Elsevier B.V. All rights reserved.
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...
The optimal pure Gaussian state canonically associated to a Gaussian quantum state
Energy Technology Data Exchange (ETDEWEB)
Gosson, Maurice de [Blekinge Institute of Technology, Karlskrona 371 79 (Sweden)]. E-mail: mdg@bth.se
2004-09-20
We show, using the symplectically invariant notion of 'quantum blob', that it is possible to attach a canonical optimal Gaussian pure state to an arbitrary quantum state. When at least one pair of conjugate variables satisfies the minimum uncertainty condition, then the associated Gaussian is uniquely determined up to an overall phase factor.
Generation of coherence via Gaussian measurements
Albarelli, Francesco; Genoni, Marco G.; Paris, Matteo G. A.
2017-07-01
We address measurement-based generation of quantum coherence in continuous variable systems. We consider Gaussian measurements performed on Gaussian states and focus on two scenarios: In the first one, we assume an initially correlated bipartite state shared by two parties and study how correlations may be exploited to remotely create quantum coherence via measurement back action. In particular, we focus on conditional states with zero first moments, so as to address coherence due to properties of the covariance matrix. We consider different classes of bipartite states with incoherent marginals and show that the larger the measurement squeezing, the larger the conditional coherence. Homodyne detection is thus the optimal Gaussian measurement to remotely generate coherence. We also show that for squeezed thermal states there exists a threshold value for the generated coherence which separates entangled and separable states at a fixed energy. Finally, we briefly discuss the tripartite case and the relationship between tripartite correlations and the conditional two-mode coherence. In the second scenario, we address the steady-state coherence of a system interacting with an environment which is continuously monitored. In particular, we discuss the dynamics of an optical parametric oscillator in order to investigate how the coherence of a Gaussian state may be increased by means of time-continuous Gaussian measurement on the interacting environment.
Trap split with Laguerre-Gaussian beams
Hamideh Kazemi, Seyedeh; Ghanbari, Saeed; Mahmoudi, Mohammad
2017-08-01
We present a convenient and effective way to generate a novel phenomenon of trapping, named ‘trap split’, in a conventional four-level double-Λ atomic system, driven by four femtosecond Laguerre-Gaussian laser pulses. We find that trap split can always be achieved when atoms are trapped by such laser pulses, as compared to Gaussian ones. This feature is enabled by the interaction of the atomic system and the Laguerre-Gaussian laser pulses with zero intensity in the center. A further advantage of using Laguerre-Gaussian laser pulses is the insensitivity to fluctuation in the intensity of the lasers in such a way that the separation between the traps remains constant. Moreover, it is demonstrated that the suggested scheme with Laguerre-Gaussian laser pulses can form optical traps with spatial sizes that are not limited by the wavelength of the laser, and can, in principle, become smaller than the wavelength of light. This work would greatly facilitate the trapping and manipulating of particles and the generation of trap split. It may also suggest the possibility of extension into new research fields, such as micro-machining and biophysics.
Induced focusing and conversion of a Gaussian beam into an elliptic Gaussian beam
Indian Academy of Sciences (India)
Manoj Mishra; Swapan Konar
2005-09-01
We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam, which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed to convert a circular Gaussian beam into an elliptic Gaussian beam.
Energy Efficient Estimation of Gaussian Sources Over Inhomogeneous Gaussian MAC Channels
Wei, Shuangqing; Iyengar, Sitharama; Rao, Nageswara S
2007-01-01
It has been shown lately the optimality of uncoded transmission in estimating Gaussian sources over homogeneous/symmetric Gaussian multiple access channels (MAC) using multiple sensors. It remains, however, unclear whether it still holds for any arbitrary networks and/or with high channel signal-to-noise ratio (SNR) and high signal-to-measurement-noise ratio (SMNR). In this paper, we first provide a joint source and channel coding approach in estimating Gaussian sources over Gaussian MAC channels, as well as its sufficient and necessary condition in restoring Gaussian sources with a prescribed distortion value. An interesting relationship between our proposed joint approach with a more straightforward separate source and channel coding scheme is then established. We then formulate constrained power minimization problems and transform them to relaxed convex geometric programming problems, whose numerical results exhibit that either separate or uncoded scheme becomes dominant over a linear topology network. In ...
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.
Institute of Scientific and Technical Information of China (English)
Li Wang(王丽); Jianhua Xue(薛建华)
2003-01-01
The conversion efficiency of THG on the flattened Gaussian and Gaussian beams is obtained in detail numerical stimulation for CsLiB6O10. The conversion efficiencies of 86.7% and 96% of the flattened Gaussian are larger than those of Gaussian beams of 72.6% and 88% under type I and type Ⅱ(1) phase matching. The efficiencies affected by the pump intensity, polarization rate, crystal lengths and orders of the flattened Gaussian beams were presented.
The series product for gaussian quantum input processes
Gough, John E.; James, Matthew R.
2017-02-01
We present a theory for connecting quantum Markov components into a network with quantum input processes in a Gaussian state (including thermal and squeezed). One would expect on physical grounds that the connection rules should be independent of the state of the input to the network. To compute statistical properties, we use a version of Wicks' theorem involving fictitious vacuum fields (Fock space based representation of the fields) and while this aids computation, and gives a rigorous formulation, the various representations need not be unitarily equivalent. In particular, a naive application of the connection rules would lead to the wrong answer. We establish the correct interconnection rules, and show that while the quantum stochastic differential equations of motion display explicitly the covariances (thermal and squeezing parameters) of the Gaussian input fields we introduce the Wick-Stratonovich form which leads to a way of writing these equations that does not depend on these covariances and so corresponds to the universal equations written in terms of formal quantum input processes. We show that a wholly consistent theory of quantum open systems in series can be developed in this way, and as required physically, is universal and in particular representation-free.
The Gaussian streaming model and Lagrangian effective field theory
Vlah, Zvonimir; White, Martin
2016-01-01
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 int...
The Gaussian streaming model and convolution Lagrangian effective field theory
Vlah, Zvonimir; Castorina, Emanuele; White, Martin
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.
Non-Gaussian Minkowski functionals & extrema counts in redshift space
Codis, Sandrine; Pogosyan, Dmitry; Bernardeau, Francis; Matsubara, Takahiko
2013-01-01
In the context of upcoming large-scale structure surveys such as Euclid, it is of prime importance to quantify the effect of peculiar velocities on geometric probes. Hence the formalism to compute in redshift space the geometrical and topological one-point statistics of mildly non-Gaussian 2D and 3D cosmic fields is developed. Leveraging the partial isotropy of the target statistics, the Gram-Charlier expansion of the joint probability distribution of the field and its derivatives is reformulated in terms of the corresponding anisotropic variables. In particular, the cosmic non-linear evolution of the Minkowski functionals, together with the statistics of extrema are investigated in turn for 3D catalogues and 2D slabs. The amplitude of the non-Gaussian redshift distortion correction is estimated for these geometric probes. In 3D, gravitational perturbation theory is implemented in redshift space to predict the cosmic evolution of all relevant Gram-Charlier coefficients. Applications to the estimation of the c...
Non-gaussianity and Statistical Anisotropy in Cosmological Inflationary Models
Valenzuela-Toledo, Cesar A
2010-01-01
We study the statistical descriptors for some cosmological inflationary models that allow us to get large levels of non-gaussianity and violations of statistical isotropy. Basically, we study two different class of models: a model that include only scalar field perturbations, specifically a subclass of small-field slow-roll models of inflation with canonical kinetic terms, and models that admit both vector and scalar field perturbations. We study the former to show that it is possible to attain very high, including observable, values for the levels of non-gaussianity f_{NL} and \\tao_{NL} in the bispectrum B_\\zeta and trispectrum T_\\zeta of the primordial curvature perturbation \\zeta respectively. Such a result is obtained by taking care of loop corrections in the spectrum P_\\zeta, the bispectrum B_\\zeta and the trispectrum T_\\zeta . Sizeable values for f_{NL} and \\tao_{NL} arise even if \\zeta is generated during inflation. For the latter we study the spectrum P_\\zeta, bispectrum B_\\zeta and trispectrum $T_\\ze...
Impact of Non-Gaussian Error Volumes on Conjunction Assessment Risk Analysis
Ghrist, Richard W.; Plakalovic, Dragan
2012-01-01
An understanding of how an initially Gaussian error volume becomes non-Gaussian over time is an important consideration for space-vehicle conjunction assessment. Traditional assumptions applied to the error volume artificially suppress the true non-Gaussian nature of the space-vehicle position uncertainties. For typical conjunction assessment objects, representation of the error volume by a state error covariance matrix in a Cartesian reference frame is a more significant limitation than is the assumption of linearized dynamics for propagating the error volume. In this study, the impact of each assumption is examined and isolated for each point in the volume. Limitations arising from representing the error volume in a Cartesian reference frame is corrected by employing a Monte Carlo approach to probability of collision (Pc), using equinoctial samples from the Cartesian position covariance at the time of closest approach (TCA) between the pair of space objects. A set of actual, higher risk (Pc >= 10 (exp -4)+) conjunction events in various low-Earth orbits using Monte Carlo methods are analyzed. The impact of non-Gaussian error volumes on Pc for these cases is minimal, even when the deviation from a Gaussian distribution is significant.
Spectra for the product of Gaussian noises
Kish, L B; Gingl, Z; Granqvist, C G
2012-01-01
Products of Gaussian noises often emerge as the result of non-linear detection techniques or as a parasitic effect, and their proper handling is important in many practical applications, including in fluctuation-enhanced sensing, indoor air or environmental quality monitoring, etc. We use Rice's random phase oscillator formalism to calculate the power density spectra variance for the product of two Gaussian band-limited white noises with zero-mean and the same bandwidth W. The ensuing noise spectrum is found to decrease linearly from zero frequency to 2W, and it is zero for frequencies greater than 2W. Analogous calculations performed for the square of a single Gaussian noise confirm earlier results. The spectrum at non-zero frequencies, and the variance of the square of a noise, is amplified by a factor two as a consequence of correlation effects between frequency products. Our analytic results is corroborated by computer simulations.
Gaussian entanglement in the turbulent atmosphere
Bohmann, M.; Semenov, A. A.; Sperling, J.; Vogel, W.
2016-07-01
We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a nontrivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.
MULTI-SCALE GAUSSIAN PROCESSES MODEL
Institute of Scientific and Technical Information of China (English)
Zhou Yatong; Zhang Taiyi; Li Xiaohe
2006-01-01
A novel model named Multi-scale Gaussian Processes (MGP) is proposed. Motivated by the ideas of multi-scale representations in the wavelet theory, in the new model, a Gaussian process is represented at a scale by a linear basis that is composed of a scale function and its different translations. Finally the distribution of the targets of the given samples can be obtained at different scales. Compared with the standard Gaussian Processes (GP) model, the MGP model can control its complexity conveniently just by adjusting the scale parameter. So it can trade-off the generalization ability and the empirical risk rapidly. Experiments verify the feasibility of the MGP model, and exhibit that its performance is superior to the GP model if appropriate scales are chosen.
Number Counts and Non-Gaussianity
Shandera, Sarah; Scott, Pat; Galarza, Jhon Yana
2013-01-01
We describe a general procedure for using number counts of any object to constrain the probability distribution of the primordial fluctuations, allowing for generic weak non-Gaussianity. We apply this procedure to use limits on the abundance of primordial black holes and dark matter ultracompact minihalos (UCMHs) to characterize the allowed statistics of primordial fluctuations on very small scales. We present constraints on the power spectrum and the amplitude of the skewness for two different families of non-Gaussian distributions, distinguished by the relative importance of higher moments. Although primordial black holes probe the smallest scales, ultracompact minihalos provide significantly stronger constraints on the power spectrum and so are more likely to eventually provide small-scale constraints on non-Gaussianity.
Rough interfaces beyond the Gaussian approximation
Caselle, M; Gliozzi, F; Hasenbusch, M; Pinn, K; Vinti, S; Caselle, M; Gliozzi, F; Fiore, R; Hasenbusch, M; Pinn, K; Vinti, S
1994-01-01
We compare predictions of the Capillary Wave Model beyond its Gaussian approximation with Monte Carlo results for the energy gap and the surface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two--loop order ( one order beyond the Gaussian approximation). We compare predictions of the Capillary Wave Model with Monte Carlo results for the energy gap and the interface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two-loop order (one order beyond the Gaussian approximation).
Non-Gaussianity of Racetrack Inflation Models
Institute of Scientific and Technical Information of China (English)
SUN Cheng-Yi; ZHANG De-Hai
2007-01-01
In this paper, we use the result in [C.Y. Sun and D.H. Zhang, arXiv:astro-ph/0510709] to calculate the non-Gaussianity of the racetrack models in[J.J. Blanco-Pillado, et al., JHEP 0411 (2004) 063; arXiv:hep-th/0406230]and [J.J. Blanco-Pillado, et al., arXiv:hep-th/0603129]. The two models give different non-Gaussianities. Both of them are reasonable. However, we find that, for multi-field inflationary models with the non-trivial metric of the field space,the condition of the slow-roll cannot guarantee small non-Gaussianities.
Majorization preservation of Gaussian bosonic channels
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2016-07-01
It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics.
Integration of non-Gaussian fields
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Mohr, Gunnar; Hoffmeyer, Pernille
1996-01-01
enough to justify that it is sufficiently accurate for the applications to shortcut the problem and just assume that the distribution of the relevant stochastic integral is Gaussian. An earlier published example exhibiting this problem concerns silo pressure fields. [Ditlevsen, O., Christensen, C......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...
Pires, Carlos A. L.; Ribeiro, Andreia F. S.
2017-02-01
We develop an expansion of space-distributed time series into statistically independent uncorrelated subspaces (statistical sources) of low-dimension and exhibiting enhanced non-Gaussian probability distributions with geometrically simple chosen shapes (projection pursuit rationale). The method relies upon a generalization of the principal component analysis that is optimal for Gaussian mixed signals and of the independent component analysis (ICA), optimized to split non-Gaussian scalar sources. The proposed method, supported by information theory concepts and methods, is the independent subspace analysis (ISA) that looks for multi-dimensional, intrinsically synergetic subspaces such as dyads (2D) and triads (3D), not separable by ICA. Basically, we optimize rotated variables maximizing certain nonlinear correlations (contrast functions) coming from the non-Gaussianity of the joint distribution. As a by-product, it provides nonlinear variable changes `unfolding' the subspaces into nearly Gaussian scalars of easier post-processing. Moreover, the new variables still work as nonlinear data exploratory indices of the non-Gaussian variability of the analysed climatic and geophysical fields. The method (ISA, followed by nonlinear unfolding) is tested into three datasets. The first one comes from the Lorenz'63 three-dimensional chaotic model, showing a clear separation into a non-Gaussian dyad plus an independent scalar. The second one is a mixture of propagating waves of random correlated phases in which the emergence of triadic wave resonances imprints a statistical signature in terms of a non-Gaussian non-separable triad. Finally the method is applied to the monthly variability of a high-dimensional quasi-geostrophic (QG) atmospheric model, applied to the Northern Hemispheric winter. We find that quite enhanced non-Gaussian dyads of parabolic shape, perform much better than the unrotated variables in which concerns the separation of the four model's centroid regimes
Semisupervised Gaussian Process for Automated Enzyme Search.
Mellor, Joseph; Grigoras, Ioana; Carbonell, Pablo; Faulon, Jean-Loup
2016-06-17
Synthetic biology is today harnessing the design of novel and greener biosynthesis routes for the production of added-value chemicals and natural products. The design of novel pathways often requires a detailed selection of enzyme sequences to import into the chassis at each of the reaction steps. To address such design requirements in an automated way, we present here a tool for exploring the space of enzymatic reactions. Given a reaction and an enzyme the tool provides a probability estimate that the enzyme catalyzes the reaction. Our tool first considers the similarity of a reaction to known biochemical reactions with respect to signatures around their reaction centers. Signatures are defined based on chemical transformation rules by using extended connectivity fingerprint descriptors. A semisupervised Gaussian process model associated with the similar known reactions then provides the probability estimate. The Gaussian process model uses information about both the reaction and the enzyme in providing the estimate. These estimates were validated experimentally by the application of the Gaussian process model to a newly identified metabolite in Escherichia coli in order to search for the enzymes catalyzing its associated reactions. Furthermore, we show with several pathway design examples how such ability to assign probability estimates to enzymatic reactions provides the potential to assist in bioengineering applications, providing experimental validation to our proposed approach. To the best of our knowledge, the proposed approach is the first application of Gaussian processes dealing with biological sequences and chemicals, the use of a semisupervised Gaussian process framework is also novel in the context of machine learning applied to bioinformatics. However, the ability of an enzyme to catalyze a reaction depends on the affinity between the substrates of the reaction and the enzyme. This affinity is generally quantified by the Michaelis constant KM
Donor Centers in a Gaussian Potential
Institute of Scientific and Technical Information of China (English)
XIE Wen-Fang
2007-01-01
We study a neutral donor center (D0) and a negatively charged donor center (D-) trapped by a quantum dot, which is subjected to a Gaussian potential confinement. Calculations are made by using the method of numerical diagonalization of Hamiltonian within the effective-mass approximation. The dependence of the ground state of the neutral shallow donor and the negatively charged donor on the dot size and the potential depth is investigated. The same calculations performed with the parabolic approximation of the Gaussian potential lead to the results that are qualitatively and quantitatively different from each other.
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
Lupo, C; 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 or 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.
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...
Homodyne estimation of Gaussian quantum discord
Blandino, Rémi; Jean, Etesse; Barbieri, Marco; Paris, Matteo G A; Grangier, Philippe; Tualle-Brouri, Rosa
2012-01-01
We address the experimental estimation of Gaussian quantum discord for two-mode squeezed state, and demonstrate a measurement scheme based on a pair of homodyne detectors assisted by Bayesian analysis. Our scheme provides nearly optimal estimation for small value of discord, where Bayesian analysis allows to greatly improves performances. Besides, though homodyne detection is not optimal for Gaussian discord, the noise ratio to the ultimate quantum limit is limited to about 10 dB. Our results illustrate how suitable data processing can decrease significantly the uncertainty when optimal detection schemes are not available.
Nonlinearities with Non-Gaussian Inputs.
1978-03-01
possessing a spectral density function . a constant. Then Jet arc tan [G(t)J be the input. By Theorem 3 this input is not bandlimited; and if The rando...such that the absolute ,,~~ovalue of any point in the spectrum is less than N. If the Gaussian process X(t) possesses a H ~ ) spectral density function (i.e...Gaussian process and th. series ii convergent pointvise as veil X(t ) possesses a spectral density function . as in an sense (51. Let z~( ) and g2
Cosine-Gaussian Schell-model sources.
Mei, Zhangrong; Korotkova, Olga
2013-07-15
We introduce a new class of partially coherent sources of Schell type with cosine-Gaussian spectral degree of coherence and confirm that such sources are physically genuine. Further, we derive the expression for the cross-spectral density function of a beam generated by the novel source propagating in free space and analyze the evolution of the spectral density and the spectral degree of coherence. It is shown that at sufficiently large distances from the source the degree of coherence of the propagating beam assumes Gaussian shape while the spectral density takes on the dark-hollow profile.
Ergodicity and Gaussianity for Spherical Random Fields
Marinucci, Domenico
2009-01-01
We investigate the relationship between ergodicity and asymptotic Gaussianity of isotropic spherical random fields, in the high-resolution (or high-frequency) limit. In particular, our results suggest that under a wide variety of circumstances the two conditions are equivalent, i.e. the sample angular power spectrum may converge to the population value if and only if the underlying field is asymptotically Gaussian, in the high frequency sense. These findings may shed some light on the role of Cosmic Variance in Cosmic Microwave Background (CMB) radiation data analysis.
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].
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.)
Measurement-induced disturbances and nonclassical correlations of Gaussian states
Mišta, Ladislav; Tatham, Richard; Girolami, Davide; Korolkova, Natalia; Adesso, Gerardo
2010-01-01
We study quantum correlations beyond entanglement in two--mode Gaussian states of continuous variable systems, by means of the measurement-induced disturbance (MID) and its ameliorated version (AMID). In analogy with the recent studies of the Gaussian quantum discord, we define a Gaussian AMID by constraining the optimization to all bi-local Gaussian positive operator valued measurements. We solve the optimization explicitly for relevant families of states, including squeezed thermal states. Remarkably, we find that there is a finite subset of two--mode Gaussian states, comprising pure states, where non-Gaussian measurements such as photon counting are globally optimal for the AMID and realize a strictly smaller state disturbance compared to the best Gaussian measurements. However, for the majority of two--mode Gaussian states the unoptimized MID provides a loose overestimation of the actual content of quantum correlations, as evidenced by its comparison with Gaussian discord. This feature displays strong sim...
A Gaussian-product stochastic Gent-McWilliams parameterization
Grooms, Ian
2016-10-01
The locally-averaged horizontal buoyancy flux by mesoscale eddies is computed from eddy-resolving quasigeostrophic simulations of ocean-mesoscale eddy dynamics. This flux has a very non-Gaussian distribution peaked at zero, not at the mean value. This non-Gaussian flux distribution arises because the flux is a product of zero-mean random variables: the eddy velocity and buoyancy. A framework for stochastic Gent-McWilliams (GM) parameterization is presented. Gaussian random field models for subgrid-scale velocity and buoyancy are developed. The product of these Gaussian random fields is used to construct a non-Gaussian stochastic parameterization of the horizontal subgrid-scale density flux, which leads to a non-Gaussian stochastic GM parameterization. This new non-Gaussian stochastic GM parameterization is tested in an idealized box ocean model, and compared to a Gaussian approach that simply multiplies the deterministic GM parameterization by a Gaussian random field. The non-Gaussian approach has a significant impact on both the mean and variability of the simulations, more so than the Gaussian approach; for example, the non-Gaussian simulation has a much larger net kinetic energy and a stronger overturning circulation than a comparable Gaussian simulation. Future directions for development of the stochastic GM parameterization and extensions of the Gaussian-product approach are discussed.
Directory of Open Access Journals (Sweden)
Sergey Haitun
2015-06-01
Full Text Available Statistical criteria used today in the analysis of radio signals suspected on reasonable extraterrestrial origin, are based on the assumption that all the radio signals of natural origin are described by a Gaussian distribution, which is traditionally understood as the Gauss distribution. Usually the normal (Gauss distribution is opposed to all the others. However, this is difficult to recognize the reasonable, because in nature there are many different distributions. The article offers a more realistic dichotomy: the Gaussian distributions, obeying the central limiting theorem, dominate in nature, while non-Gaussian ones, obeying the Gnedenko-Doeblin limiting theorem, are generated by intelligent beings. When identifying objects belonging to an extraterrestrial civilization described by a non-Gaussian distribution is preferable to use the rank form distributions. Using this criterion is associated with certain difficulties: (1 in nature there are also non-Gaussian distributions; (2 in their activities animals generate non-Gaussian distributions like humans; (3 the identification of non-Gaussian distributions in the rank form is hampered sometimes by the rank distortion effect of mathematical nature.
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...
Comparison of the Sachs-Wolfe Effect for Gaussian and Non-Gaussian Fluctuations
Kung, J H
1993-01-01
A consequence of non-Gaussian perturbations on the Sachs-Wolfe effect is studied. For a particular power spectrum, predicted Sachs-Wolfe effects are calculated for two cases: Gaussian (random phase) configuration, and a specific kind of non-Gaussian configuration. We obtain a result that the Sachs-Wolfe effect for the latter case is smaller when each temperature fluctuation is properly normalized with respect to the corresponding mass fluctuation ${\\delta M\\over M}(R)$. The physical explanation and the generality of the result are discussed.
Non-Gaussian spectra and the search for cosmic strings
Magueijo, Joao; Lewin, Alex
1997-01-01
We present a new tool for relating theory and experiment suited for non-Gaussian theories: non-Gaussian spectra. It does for non-Gaussian theories what the angular power spectrum $C_\\ell$ does for Gaussian theories. We then show how previous studies of cosmic strings have over rated their non-Gaussian signature. More realistic maps are not visually stringy. However non-Gaussian spectra will accuse their stringiness. We finally summarise the steps of an undergoing experimental project aiming a...
The Gaussian entropy of fermionic systems
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav, E-mail: T.Prokopec@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Schmidt, Michael G., E-mail: M.G.Schmidt@thphys.uni-heidelberg.de [Institut fuer Theoretische Physik, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany); Weenink, Jan, E-mail: J.G.Weenink@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands)
2012-12-15
We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of these correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence and classicalization. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields. - Highlights: Black-Right-Pointing-Pointer We construct the Gaussian density operator for relativistic fermionic systems. Black-Right-Pointing-Pointer The Gaussian entropy of relativistic fermionic systems is described in terms of 2-point correlators. Black-Right-Pointing-Pointer We explicitly show the growth of entropy for fermionic fields mixing with a thermal fermionic environment.
Transitional behavior of quantum Gaussian memory channels
Lupo, C.; Mancini, S.
2010-05-01
We address the question of optimality of entangled input states in quantum Gaussian memory channels. For a class of such channels, which can be traced back to the memoryless setting, we state a criterion which relates the optimality of entangled inputs to the symmetry properties of the channels’ action. Several examples of channel models belonging to this class are discussed.
Non-gaussian CMBR angular power spectra
Magueijo, J
1995-01-01
In this paper we show how the prediction of CMBR angular power spectra C_l in non-Gaussian theories is affected by a cosmic covariance problem, that is (C_l,C_{l'}) correlations impart features on any observed C_l spectrum which are absent from the average C^l spectrum. Therefore the average spectrum is rendered a bad observational prediction, and two new prediction strategies, better adjusted to these theories, are proposed. In one we search for hidden random indices conditional to which the theory is released from the correlations. Contact with experiment can then be made in the form of the conditional power spectra plus the random index distribution. In another approach we apply to the problem a principal component analysis. We discuss the effect of correlations on the predictivity of non-Gaussian theories. We finish by showing how correlations may be crucial in delineating the borderline between predictions made by non-Gaussian and Gaussian theories. In fact, in some particular theories, correlations may ...
How Gaussian can our universe be?
Cabass, Giovanni; Schmidt, Fabian
2016-01-01
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 ...
Gaussian mode selection with intracavity diffractive optics
CSIR Research Space (South Africa)
Litvin, IA
2009-10-01
Full Text Available element for mode shaping of a Nd:YAG laser,” Opt. Lett. 19, 108–110 (1994). 4. L. A. Romero, F. M. Dickey, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751–760 (1996). 5. F. Gori, “Flattened gaussian beams,” Opt. Commun. 107, 335–341 (1994...
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).
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.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., cons
Advanced LIGO: non-Gaussian beams
Energy Technology Data Exchange (ETDEWEB)
D' Ambrosio, Erika [California Institute of Technology, Pasadena, CA (United States); O' Shaugnessy, Richard [California Institute of Technology, Pasadena, CA (United States); Thorne, Kip [California Institute of Technology, Pasadena, CA (United States); Willems, Phil [California Institute of Technology, Pasadena, CA (United States); Strigin, Sergey [Moscow State University, Moscow (Russian Federation); Vyatchanin, Sergey [Moscow State University, Moscow (Russian Federation)
2004-03-07
By using non-Gaussian, flat-topped beams in the advanced gravitational wave interferometers currently being designed, one can reduce the impact on the interferometer sensitivity of a variety of fundamental disturbances (thermoelastic noise, noise in mirror coatings, thermal lensing, etc). This may make beating the standard quantum limit an achievable goal.
Advanced LIGO: non-Gaussian beams
D’Ambrosio, Erika; O’Shaugnessy, Richard; Thorne, Kip; Willems, Phil; Strigin, Sergey; Vyatchanin, Sergey
2004-01-01
By using non-Gaussian, flat-topped beams in the advanced gravitational wave interferometers currently being designed, one can reduce the impact on the interferometer sensitivity of a variety of fundamental disturbances (thermoelastic noise, noise in mirror coatings, thermal lensing, etc). This may make beating the standard quantum limit an achievable goal.
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...
Turbo Equalization Using Partial Gaussian Approximation
DEFF Research Database (Denmark)
Zhang, Chuanzong; Wang, Zhongyong; Manchón, Carles Navarro
2016-01-01
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...
Large-scale 3D galaxy correlation function and non-Gaussianity
Energy Technology Data Exchange (ETDEWEB)
Raccanelli, Alvise; Doré, Olivier [Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA 91109 (United States); Bertacca, Daniele; Maartens, Roy, E-mail: alvise@caltech.edu, E-mail: daniele.bertacca@gmail.com, E-mail: Olivier.P.Dore@jpl.nasa.gov, E-mail: roy.maartens@gmail.com [Physics Department, University of the Western Cape, Cape Town 7535 (South Africa)
2014-08-01
We investigate the properties of the 2-point galaxy correlation function at very large scales, including all geometric and local relativistic effects --- wide-angle effects, redshift space distortions, Doppler terms and Sachs-Wolfe type terms in the gravitational potentials. The general three-dimensional correlation function has a nonzero dipole and octupole, in addition to the even multipoles of the flat-sky limit. We study how corrections due to primordial non-Gaussianity and General Relativity affect the multipolar expansion, and we show that they are of similar magnitude (when f{sub NL} is small), so that a relativistic approach is needed. Furthermore, we look at how large-scale corrections depend on the model for the growth rate in the context of modified gravity, and we discuss how a modified growth can affect the non-Gaussian signal in the multipoles.
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.
Non-Gaussian and Clustering Behavior in One-Dimensional Polydisperse Granular Gas System
Institute of Scientific and Technical Information of China (English)
CHEN Zhi-Yuan; ZHANG Duan-Ming; ZHONG Zhi-Cheng; LI Rui
2007-01-01
We present a one-dimensional dynamic model of polydisperse granular mixture with the fractal characteristic of the particle size distribution, in which the particles are subject to inelastic mutual collisions and are driven by Gaussian white noise. The inhomogeneity of the particle size distribution is described by a fractal dimension D. The stationary state that the mixture reaches is the result of the balance between energy dissipation and energy injection. By molecular dynamics simulations, we have mainly studied how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the velocity distribution and distribution of interparticle spacing in the steady-state.The simulation results indicate that, in the inelasticity case, the velocity distribution strongly deviates from the Gaussian one and the system has a strong spatial clustering. Thus the inhomogeneity and the inelasticity have great effects on the velocity distribution and distribution of interparticle spacing. The quantitative information of the non-Gaussian velocity distribution and that of clustering are respectively represented.
a Distributed Gaussian Discrete Variable Representation
Karabulut, Hasan
In this work a discrete variable representation (DVR) is constructed from a distributed Gaussian basis (DGB). A DGB is a finite or infinite chain of uniformly distributed Gaussians g_{n}(x) = e^{-c^2(x/d-n)^2} where n takes integer values. There are three main parts of this thesis. In the first part (Chapter III) the finite chain distributed Gaussian DVR (Finite Chain DG-DVR) is derived. In order to accomplish this, the distributed Gaussian orthogonal polynomials are introduced. The connection of these polynomials to Stieltjes-Wigert polynomials is shown. The recurrence relation for these orthogonal polynomials is derived. Tested recipes are given to calculate the quadrature points and weights and to construct the corresponding Lagrange functions which are analogs of Lagrange interpolation polynomials. The symmetries of quadrature points, weights, and Lagrange functions are derived. Limit cases ctoinfty and cto 0 are studied. In the second part (Chapter IV)the infinite chain limit DG-DVR is derived from a limit of the finite chain DG-DVR. The quadrature points and weights and the Lagrange functions are found in this limit and kinetic energy operator is constructed. It is shown that in the limit c to 0 the infinite chain DG-DVR reduces to Colbert and Miller's DVR. A discussion of ability of a distributed Gaussian basis to represent an arbitrary function is given. The results of this treatment yield a possible explanation of surprising accuracy of Colbert-Miller DVR. In the third part construction of the DG-DVR is given when one point is chosen arbitrarily. Some interesting identities and integral representations for the b _{n} and sigma_ {n} coefficients that are introduced in the second part are found.
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.
Goos-H\\"anchen and Imbert-Fedorov shifts for astigmatic Gaussian beams
Ornigotti, Marco
2015-01-01
In this work we investigate the role of the beam astigmatism in the Goos-H\\"anchen and Imbert-Fedorov shift. As a case study, we consider a Gaussian beam focused by an astigmatic lens and we calculate explicitly the corrections to the standard formulas for beam shifts due to the astigmatism induced by the lens. Our results show that astigmatism may enhance the angular part of the shift.
Perturbative Expansion around the Gaussian Effective Potential of the Fermion Field Theory
Lee, G H; Yee, J H; Lee, Geon Hyoung; Lee, Tack Hwi; Yee, Jae Hyung
1998-01-01
We have extended the perturbative expansion method around the Gaussian effective action to the fermionic field theory, by taking the 2-dimensional Gross-Neveu model as an example. We have computed both the zero temperature and the finite temperature effective potentials of the Gross-Neveu model up to the first perturbative correction terms, and have found that the critical temperature, at which dynamically broken symmetry is restored, is significantly improved for small value of the flavour number.
Goos-Hänchen and Imbert-Fedorov shifts for astigmatic Gaussian beams
Ornigotti, Marco; Aiello, Andrea
2015-06-01
In this work we investigate the role of the beam astigmatism in the Goos-Hänchen and Imbert-Fedorov shift. As a case study, we consider a Gaussian beam focused by an astigmatic lens and we calculate explicitly the corrections to the standard formulas for beam shifts due to the astigmatism induced by the lens. Our results show that the different focusing in the longitudinal and transverse direction introduced by an astigmatic lens may enhance the angular part of the shift.
The Achievable Distortion Region of Bivariate Gaussian Source on Gaussian Broadcast Channel
Tian, Chao; Shamai, Shlomo
2010-01-01
We provide a complete characterization of the achievable distortion region for the problem of sending a bivariate Gaussian source over bandwidth-matched Gaussian broadcast channels, where each receiver is interested in only one component of the source. This setting naturally generalizes the simple single Gaussian source bandwidth-matched broadcast problem for which the uncoded scheme is known to be optimal. We show that a hybrid scheme can achieve the optimum for the bivariate case, but neither an uncoded scheme alone nor a separation-based scheme alone is sufficient. We further show that in this joint source channel coding setting, the Gaussian setting is the worst scenario among the sources and channel noises with the same covariances.
Low temperature asphalt mixtures
Modrijan, Damjan
2006-01-01
This thesis presents the problem of manufacturing and building in the asphalt mixtures produced by the classical hot procedure and the possibility of manufacturing low temperature asphalt mixtures.We will see the main advantages of low temperature asphalt mixtures prepared with bitumen with organic addition Sasobit and compare it to the classical asphalt mixtures. The advantages and disadvantages of that are valued in the practical example in the conclusion.
MR image intensity inhomogeneity correction
(Vişan Pungǎ, Mirela; Moldovanu, Simona; Moraru, Luminita
2015-01-01
MR technology is one of the best and most reliable ways of studying the brain. Its main drawback is the so-called intensity inhomogeneity or bias field which impairs the visual inspection and the medical proceedings for diagnosis and strongly affects the quantitative image analysis. Noise is yet another artifact in medical images. In order to accurately and effectively restore the original signal, reference is hereof made to filtering, bias correction and quantitative analysis of correction. In this report, two denoising algorithms are used; (i) Basis rotation fields of experts (BRFoE) and (ii) Anisotropic Diffusion (when Gaussian noise, the Perona-Malik and Tukey's biweight functions and the standard deviation of the noise of the input image are considered).
A mixture copula Bayesian network model for multimodal genomic data
Directory of Open Access Journals (Sweden)
Qingyang Zhang
2017-04-01
Full Text Available Gaussian Bayesian networks have become a widely used framework to estimate directed associations between joint Gaussian variables, where the network structure encodes the decomposition of multivariate normal density into local terms. However, the resulting estimates can be inaccurate when the normality assumption is moderately or severely violated, making it unsuitable for dealing with recent genomic data such as the Cancer Genome Atlas data. In the present paper, we propose a mixture copula Bayesian network model which provides great flexibility in modeling non-Gaussian and multimodal data for causal inference. The parameters in mixture copula functions can be efficiently estimated by a routine expectation–maximization algorithm. A heuristic search algorithm based on Bayesian information criterion is developed to estimate the network structure, and prediction can be further improved by the best-scoring network out of multiple predictions from random initial values. Our method outperforms Gaussian Bayesian networks and regular copula Bayesian networks in terms of modeling flexibility and prediction accuracy, as demonstrated using a cell signaling data set. We apply the proposed methods to the Cancer Genome Atlas data to study the genetic and epigenetic pathways that underlie serous ovarian cancer.
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...
Cumulant Based Harmonic Retrieval in Mixed Colored Gaussian and Non-Gaussian ARMA Noises
Institute of Scientific and Technical Information of China (English)
LI Shenghong; ZHU Hongwen
2001-01-01
This paper studies the problem of retrieving one-dimensional real harmonic signals in presence of mixed colored Gaussian and non-Gaussian autoregressive moving-average (ARMA) noises, and proposes a new approach to harmonic retrieval. In the approach, Hilbert transform is first used to transform the real noisy observed data into their complex form; and then, some kind of fourth-order cumulant,which is defined particularly, is employed to identify the autoregressive (AR) parameters of the colored non-Gaussian ARMA noise model; after the real noisy observed data are filtered with the identified AR parameters, cumulant based methods can be used to compute the frequencies and the amplitudes of the harmonics. The proposed new approach can be applied to retrieve one-dimensional real harmonic signals in mixed colored Gaussian and non-Gaussian ARMA noises, no matter whether there is quadratic phase coupling or not in the harmonic signals and no matter whether the distribution of the colored non-Gaussian ARMA noise is symmetrical or not. Simulation examples are presented to demonstrate its effectiveness.
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.
ITAC volume assessment through a Gaussian hidden Markov random field model-based algorithm.
Passera, Katia M; Potepan, Paolo; Brambilla, Luca; Mainardi, Luca T
2008-01-01
In this paper, a semi-automatic segmentation method for volume assessment of Intestinal-type adenocarcinoma (ITAC) is presented and validated. The method is based on a Gaussian hidden Markov random field (GHMRF) model that represents an advanced version of a finite Gaussian mixture (FGM) model as it encodes spatial information through the mutual influences of neighboring sites. To fit the GHMRF model an expectation maximization (EM) algorithm is used. We applied the method to a magnetic resonance data sets (each of them composed by T1-weighted, Contrast Enhanced T1-weighted and T2-weighted images) for a total of 49 tumor-contained slices. We tested GHMRF performances with respect to FGM by both a numerical and a clinical evaluation. Results show that the proposed method has a higher accuracy in quantifying lesion area than FGM and it can be applied in the evaluation of tumor response to therapy.
Robust Burg estimation of stationary autoregressive mixtures covariance
Decurninge, Alexis; Barbaresco, Frédéric
2015-01-01
Burg estimators are classically used for the estimation of the autocovariance of a stationary autoregressive process. We propose to consider scale mixtures of stationary autoregressive processes, a non-Gaussian extension of the latter. The traces of such processes are Spherically Invariant Random Vectors (SIRV) with a constraint on the scatter matrix due to the autoregressive model. We propose adaptations of the Burg estimators to the considered models and their associated robust versions based on geometrical considerations.
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
Level density for deformations of the Gaussian orthogonal ensemble
Bertuola, A C; Hussein, M S; Pato, M P; Sargeant, A J
2004-01-01
Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles we derive formulas for the average level density for (i) the transition from the Gaussian orthogonal ensemble (GOE) to the Poisson ensemble and (ii) the transition from the GOE to $m$ GOEs.
On the classical capacity of quantum Gaussian channels
Lupo, Cosmo; Pirandola, Stefano; Aniello, Paolo; Mancini, Stefano
2011-02-01
The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting the study to Gaussian encodings, for which we provide analytical expressions.
On the classical capacity of quantum Gaussian channels
Lupo, Cosmo; Aniello, Paolo; Mancini, Stefano
2010-01-01
The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting to Gaussian encodings, for which we provide analytical expressions.
On the classical capacity of quantum Gaussian channels
Energy Technology Data Exchange (ETDEWEB)
Lupo, Cosmo; Mancini, Stefano [School of Science and Technology, University of Camerino, I-62032 Camerino (Italy); Pirandola, Stefano [Department of Computer Science, University of York, York YO10 5GH (United Kingdom); Aniello, Paolo, E-mail: cosmo.lupo@unicam.it, E-mail: pirs@cs.york.ac.uk, E-mail: paolo.aniello@na.infn.it, E-mail: stefano.mancini@unicam.it [Dipartimento di Scienze Fisiche dell' Universita di Napoli Federico II, Complesso Universitario di Monte Sant' Angelo, Via Cintia, I-80126 Napoli (Italy)
2011-02-15
The set of quantum Gaussian channels acting on one bosonic mode can be classified according to the action of the group of Gaussian unitaries. We look for bounds on the classical capacity for channels belonging to such a classification. Lower bounds can be efficiently calculated by restricting the study to Gaussian encodings, for which we provide analytical expressions.
Linking network usage patterns to traffic Gaussianity fit
Oliveira Schmidt, de Ricardo; Sadre, Ramin; Melnikov, Nikolay; Schönwälder, Jürgen; Pras, Aiko
2014-01-01
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, res
Where is the COBE maps' non-Gaussianity?
Magueijo, Joao; Ferreira, Pedro G; Gorski, Krzysztof M.
1999-01-01
We review our recent claim that there is evidence of non-Gaussianity in the 4 Year COBE DMR data. We present some new results concerning the effect of the galactic cut upon the non-Gaussian signal. These findings imply a localization of the non-Gaussian signal on the Northern galactic hemisphere.
Primordial non-Gaussianity from the large scale structure
Desjacques, Vincent
2010-01-01
Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of non-Gaussianity would have profound implications for our understanding of cosmic structure formation. In this paper, we review past and current efforts in the search for primordial non-Gaussianity in the large scale structure of the Universe.
Asymptotics of high order noise corrections
Sondergaard, N; Pálla, G; Voros, A; Sondergaard, Niels; Vattay, Gabor; Palla, Gergely; Voros, Andre
1999-01-01
We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The leading contributions come from the period one orbits of the map. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.
Primordial Non-Gaussianity and Reionization
Lidz, Adam; Adshead, Peter; Dodelson, Scott
2013-01-01
The statistical properties of the primordial perturbations contain clues about the origins of those fluctuations. Although the Planck collaboration has recently obtained tight constraints on primordial non-gaussianity from cosmic microwave background measurements, it is still worthwhile to mine upcoming data sets in effort to place independent or competitive limits. The ionized bubbles that formed at redshift z~6-20 during the Epoch of Reionization are seeded by primordial overdensities, and so the statistics of the ionization field at high redshift are related to the statistics of the primordial field. Here we model the effect of primordial non-gaussianity on the reionization field. The epoch and duration of reionization are affected as are the sizes of the ionized bubbles, but these changes are degenerate with variations in the properties of the ionizing sources and the surrounding intergalactic medium. A more promising signature is the power spectrum of the spatial fluctuations in the ionization field, whi...
Entropic cosmology through non-gaussian statistics
Nunes, Rafael C; Abreu, Everton M C; Neto, Jorge Ananias
2015-01-01
Based on the relationship between thermodynamics and gravity, and with the aid of Verlinde's formalism, we propose an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe, which takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there through non-gaussian statistical theories proposed by Tsallis and Kaniadakis. We use the most recent data of type Ia supernovae, baryon acoustic oscillations, and the Hubble expansion rate function to constrain the free parameters on the $\\Lambda$CDM and $w$CDM models modified by the non-gaussian statistics. We evaluate the problem of age and we note that such modifications solve the problem at 1$\\sigma$ level confidence. Also we analyze the effects on the linear growth of matter density perturbations.
Large non-gaussianity in axion inflation.
Barnaby, Neil; Peloso, Marco
2011-05-06
The inflationary paradigm has enjoyed phenomenological success; however, a compelling particle physics realization is still lacking. Axions are among the best-motivated inflaton candidates, since the flatness of their potential is naturally protected by a shift symmetry. We reconsider the cosmological perturbations in axion inflation, consistently accounting for the coupling to gauge fields cΦFF, which is generically present in these models. This coupling leads to production of gauge quanta, which provide a new source of inflaton fluctuations, δΦ. For c≥10(2)M(p)(-1), these dominate over the vacuum fluctuations, and non-Gaussianity exceeds the current observational bound. This regime is typical for concrete realizations that admit a UV completion; hence, large non-Gaussianity is easily obtained in minimal and natural realizations of inflation.
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.
Bregman Cost for Non-Gaussian Noise
DEFF Research Database (Denmark)
Burger, Martin; Dong, Yiqiu; Sciacchitano, Federica
. 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...... 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...... prove that the CM estimate outperforms the MAP estimate, when the error is measured in a certain Bregman distance, a result previously unknown also in the case of additive Gaussian noise....
Edge Detection By Differences Of Gaussians
Marthon, Ph.; Thiesse, B.; Bruel, A.
1986-06-01
The Differences of Gaussians (DOGs) are of fundamental importance in edge detection. They belong to the human vision system as shown by Enroth-Cugell and Robson [ENR66]. The zero-crossings of their outputs mark the loci of the intensity changes. The set of descriptions from different operator sizes forms the input for later visual processes, such as stereopsis and motion analysis. We show that DOGs uniformly converge to the Laplacian of a Gaussian (ΔG2,σ) when both the inhibitory and excitatory variables converge to σ. Spatial and spectral properties of DOGs and ΔGs are compared: width and height of their central positive regions, bandiwidths... Finally, DOGs' responses to some features such as ideal edge, right angle corner, general corner..., are presented and magnitudes of error on edge position are given.
Fock expansion of multimode pure Gaussian states
Energy Technology Data Exchange (ETDEWEB)
Cariolaro, Gianfranco; Pierobon, Gianfranco, E-mail: gianfranco.pierobon@unipd.it [Università di Padova, Padova (Italy)
2015-12-15
The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, as shown for two-mode and three-mode Gaussian states.
Quantum fidelity for arbitrary Gaussian states
Banchi, Leonardo; Pirandola, Stefano
2015-01-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
Explicit Optimal Hardness via Gaussian stability results
De, Anindya
2012-01-01
The results of Raghavendra (2008) show that assuming Khot's Unique Games Conjecture (2002), for every constraint satisfaction problem there exists a generic semi-definite program that achieves the optimal approximation factor. This result is existential as it does not provide an explicit optimal rounding procedure nor does it allow to calculate exactly the Unique Games hardness of the problem. Obtaining an explicit optimal approximation scheme and the corresponding approximation factor is a difficult challenge for each specific approximation problem. An approach for determining the exact approximation factor and the corresponding optimal rounding was established in the analysis of MAX-CUT (KKMO 2004) and the use of the Invariance Principle (MOO 2005). However, this approach crucially relies on results explicitly proving optimal partitions in Gaussian space. Until recently, Borell's result (Borell 1985) was the only non-trivial Gaussian partition result known. In this paper we derive the first explicit optimal...
Trap split with Laguerre-Gaussian beams
Kazemi, Seyedeh Hamideh; Mahmoud, Mohammad
2016-01-01
The optical trapping techniques have been extensively used in physics, biophysics, micro-chemistry, and micro-mechanics to allow trapping and manipulation of materials ranging from particles, cells, biological substances, and polymers to DNA and RNA molecules. In this Letter, we present a convenient and effective way to generate a novel phenomenon of trapping, named trap split, in a conventional four-level double-$\\Lambda$ atomic system driven by four femtosecond Laguerre-Gaussian laser pulses. We find that trap split can be always achieved when atoms are trapped by such laser pulses, as compared to Gaussian ones. This work would greatly facilitate the trapping and manipulating the particles and generation of trap split. It may also suggest the possibility of extension into new research fields, such as micro-machining and biophysics.
Distributed Kalman Filter via Gaussian Belief Propagation
Bickson, Danny; Dolev, Danny
2008-01-01
Recent result shows how to compute distributively and efficiently the linear MMSE for the multiuser detection problem, using the Gaussian BP algorithm. In the current work, we extend this construction, and show that operating this algorithm twice on the matching inputs, has several interesting interpretations. First, we show equivalence to computing one iteration of the Kalman filter. Second, we show that the Kalman filter is a special case of the Gaussian information bottleneck algorithm, when the weight parameter $\\beta = 1$. Third, we discuss the relation to the Affine-scaling interior-point method and show it is a special case of Kalman filter. Besides of the theoretical interest of this linking estimation, compression/clustering and optimization, we allow a single distributed implementation of those algorithms, which is a highly practical and important task in sensor and mobile ad-hoc networks. Application to numerous problem domains includes collaborative signal processing and distributed allocation of ...
Gaussian Confinement in a Jkj Decay Model
da Silva, Mario L. L.; Hadjimichef, Dimiter; Vasconcellos, Cesar A. Z.
In microscopic decay models, one attempts to describe hadron strong decays in terms of quark and gluon degrees of freedom. We begin by assuming that strong decays are driven by the same interquark Hamiltonian which determines the spectrum, and that it incorporates gaussian confinement. An A → BC decay matrix element of the JKJ Hamiltonian involves a pair-production current matrix elements times a scatering matrix element. Diagrammatically this corresponds to an interaction between an initial line and produced pair.
Robust Filtering and Smoothing with Gaussian Processes
Deisenroth, Marc Peter; Turner, Ryan; Huber, Marco F.; Hanebeck, Uwe D.; Rasmussen, Carl Edward
2012-01-01
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of "system identification" is more robust than finding p...
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.
Power Spectrum of Generalized Fractional Gaussian Noise
Directory of Open Access Journals (Sweden)
Ming Li
2013-01-01
Full Text Available Recently, we introduced a type of autocorrelation function (ACF to describe a long-range dependent (LRD process indexed with two parameters, which takes standard fractional Gaussian noise (fGn for short as a special case. For simplicity, we call it the generalized fGn (GfGn. This short paper gives the power spectrum density function (PSD of GfGn.
Non-paraxial Elliptical Gaussian Beam
Institute of Scientific and Technical Information of China (English)
WANG Zhaoying; LIN Qiang; NI Jie
2001-01-01
By using the methods of Hertz vector and angular spectrum transormation, the exact solution of non-paraxial elliptical Gaussion beam with general astigmatism based on Maxwell′s equations is obtained. We discussed its propagation characteristics. The results show that the orientation of the elliptical beam spot changes continuously as the beam propagates through isotropic media. Splitting or coupling of beam spots may occur for different initial spot size. This is very different from that of paraxial elliptical Gaussian beam.
Bimetric structure formation: non-Gaussian predictions
Magueijo, Joao; Piazza, Federico
2010-01-01
The minimal bimetric theory employing a disformal transformation between matter and gravity metrics is known to produce exactly scale-invariant fluctuations. It has a purely equilateral non-Gaussian signal, with an amplitude smaller than that of DBI inflation (with opposite sign) but larger than standard inflation. We consider non-minimal bimetric models, where the coupling $B$ appearing in the disformal transformation ${\\hat g}_{\\mn}= g_{\\mn} -B\\partial_\\mu\\phi\\partial_\
Infinite Shift-invariant Grouped Multi-task Learning for Gaussian Processes
Wang, Yuyang; Protopapas, Pavlos
2012-01-01
Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we develop a novel Bayesian nonparametric model capturing a mixture of Gaussian processes where each task is a sum of a group-specific function and a component capturing individual variation, in addition to each task being phase shifted. We develop an efficient \\textsc{em} algorithm to learn the parameters of the model. As a special case we obtain the Gaussian mixture model and \\textsc{em} algorithm for phased-shifted periodic time series. Furthermore, we extend the proposed model by using a Dirichlet Process prior and thereby leading to an infinite mixture model that is capable of doing automatic model selection. A Variational Bayesian approach is developed for inference in this model. Experiments in regression, classification and class discovery demonstrate the performance of...
Least-squares Gaussian beam migration
Yuan, Maolin; Huang, Jianping; Liao, Wenyuan; Jiang, Fuyou
2017-02-01
A theory of least-squares Gaussian beam migration (LSGBM) is presented to optimally estimate a subsurface reflectivity. In the iterative inversion scheme, a Gaussian beam (GB) propagator is used as the kernel of linearized forward modeling (demigration) and its adjoint (migration). Born approximation based GB demigration relies on the calculation of Green’s function by a Gaussian-beam summation for the downward and upward wavefields. The adjoint operator of GB demigration accounts for GB prestack depth migration under the cross-correlation imaging condition, where seismic traces are processed one by one for each shot. A numerical test on the point diffractors model suggests that GB demigration can successfully simulate primary scattered data, while migration (adjoint) can yield a corresponding image. The GB demigration/migration algorithms are used for the least-squares migration scheme to deblur conventional migrated images. The proposed LSGBM is illustrated with two synthetic data for a four-layer model and the Marmousi2 model. Numerical results show that LSGBM, compared to migration (adjoint) with GBs, produces images with more balanced amplitude, higher resolution and even fewer artifacts. Additionally, the LSGBM shows a robust convergence rate.
Unitarily localizable entanglement of Gaussian states
Serafini, A; Illuminati, F; Serafini, Alessio; Adesso, Gerardo; Illuminati, Fabrizio
2004-01-01
We consider generic $m \\times n$-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 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 ...
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.
Further Notes on the Gaussian Beam Expansion
Institute of Scientific and Technical Information of China (English)
DAI Yu-Rong; DING De-Sheng
2012-01-01
We provide alternatively a simple way of computing the Fresnel field integral, a further extension to the Gaussian-beam expansion. With a known result that the circ function is approximately decomposed into a sum of Gaussian functions, the zero-order Bessel function of the first kind is similarly expanded by the Bessel-Fourior transform. Two expansions are together inserted in this integral, which is then expressible in terms of the simple algebraic functions. The approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics. As examples, the calculation results for the uniform and the simply supported piston sources are presented, in a good agreement with those evaluated by numerical integration.%We provide alternatively a simple way of computing the Fresnel field integral,a further extension to the Gaussianbeam expansion.With a known result that the circ function is approximately decomposed into a sum of Gaussian functions,the zero-order Bessel function of the first kind is similarly expanded by the Bessel-Fourior transform.Two expansions are together inserted in this integral,which is then expressible in terms of the simple algebraic functions.The approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics.As examples,the calculation results for the uniform and the simply supported piston sources are presented,in a good agreement with those evaluated by numerical integration.
Non-gaussianity from axion monodromy inflation
Energy Technology Data Exchange (ETDEWEB)
Hannestad, Steen; Haugbolle, Troels; Jarnhus, Philip R. [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark); Sloth, Martin S., E-mail: sth@phys.au.dk, E-mail: haugboel@nbi.ku.dk, E-mail: pjarn@phys.au.dk, E-mail: martin.sloth@cern.ch [CERN, Physics Department, Theory Unit, CH-1211 Geneva 23 (Switzerland)
2010-06-01
We study the primordial non-Gaussianity predicted from simple models of inflation with a linear potential and superimposed oscillations. This generic form of the potential is predicted by the axion monodromy inflation model, that has recently been proposed as a possible realisation of chaotic inflation in string theory, where the monodromy from wrapped branes extends the range of the closed string axions to beyond the Planck scale. The superimposed oscillations in the potential can lead to new signatures in the CMB spectrum and bispectrum. In particular the bispectrum will have a new distinct shape. We calculate the power spectrum and bispectrum of curvature perturbations in the model, as well as make analytic estimates in various limiting cases. From the numerical analysis we find that for a wide range of allowed parameters the model produces a feature in the bispectrum with f{sub NL} ∼ 5−50 or larger while the power spectrum is almost featureless. This model is therefore an example of a string inspired inflationary model which is testable mainly through its non-Gaussian features. Finally we provide a simple analytic fitting formula for the bispectrum which is accurate to approximately 5 % in all cases, and easily implementable in codes designed to provide non-Gaussian templates for CMB analyses.
Wave Period Distributions in Non-Gaussian Mixed Sea States
Institute of Scientific and Technical Information of China (English)
王迎光
2013-01-01
The wave period probability densities in non-Gaussian mixed sea states are calculated by utilizing a transformed Gaussian process method. The transformation relating the non-Gaussian process and the original Gaussian process is obtained based on the equivalence of the level up-crossing rates of the two processes. A saddle point approximation procedure is applied for calculating the level up-crossing rates in this study. The accuracy and efficiency of the transformed Gaussian process method are validated by comparing the results predicted by using the method with those predicted by the Monte Carlo simulation method.
Representation of Gaussian semimartingales with applications to the covariance function
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2010-01-01
The present paper is concerned with various aspects of Gaussian semimartingales. Firstly, generalizing a result of Stricker, we provide a convenient representation of Gaussian semimartingales as an -semimartingale plus a process of bounded variation which is independent of M. Secondly, we study...... 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...
Efficient calculation of integrals in mixed ramp-Gaussian basis sets
Energy Technology Data Exchange (ETDEWEB)
McKemmish, Laura K., E-mail: laura.mckemmish@gmail.com [Department of Physics and Astronomy, University College London, London (United Kingdom); Research School of Chemistry, Australian National University, Canberra (Australia)
2015-04-07
Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RAMPITUP. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or very large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.
Non Gaussian Minkowski functionals and extrema counts for 2D sky maps
Pogosyan, Dmitri; Pichon, Christophe
2016-01-01
In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for the 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post- Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky was suggested, but never rigorously developed. In this paper we present such development treating effects of the curvature and finiteness of the spherical space $S_2$ exactly, without relying on the flat-sky approximation. We present Minkowski functionals, including Euler characteristic and extrema counts to the first non-Gaussian correction, suitable for weakly non-Gaussian fields on a sphere, of which CMB is the prime e...
Modulated reheating and large non-gaussianity in string cosmology
Energy Technology Data Exchange (ETDEWEB)
Cicoli, M.; Quevedo, F. [Abdus Salam ICTP, Strada Costiera 11, Trieste 34014 (Italy); Tasinato, G. [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth, PO1 3FX (United Kingdom); Zavala, I. [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Burgess, C.P., E-mail: michele.cicoli@desy.de, E-mail: gianmassimo.tasinato@port.ac.uk, E-mail: e.i.zavala@rug.nl, E-mail: cburgess@perimeterinstitute.ca, E-mail: F.Quevedo@damtp.cam.ac.uk [Department of Physics and Astronomy, McMaster University, Hamilton ON (Canada)
2012-05-01
A generic feature of the known string inflationary models is that the same physics that makes the inflaton lighter than the Hubble scale during inflation often also makes other scalars this light. These scalars can acquire isocurvature fluctuations during inflation, and given that their VEVs determine the mass spectrum and the coupling constants of the effective low-energy field theory, these fluctuations give rise to couplings and masses that are modulated from one Hubble patch to another. These seem just what is required to obtain primordial adiabatic fluctuations through conversion into density perturbations through the 'modulation mechanism', wherein reheating takes place with different efficiency in different regions of our Universe. Fluctuations generated in this way can generically produce non-gaussianity larger than obtained in single-field slow-roll inflation; potentially observable in the near future. We provide here the first explicit example of the modulation mechanism at work in string cosmology, within the framework of LARGE Volume Type-IIB string flux compactifications. The inflationary dynamics involves two light Kähler moduli: a fibre divisor plays the rôle of the inflaton whose decay rate to visible sector degrees of freedom is modulated by the primordial fluctuations of a blow-up mode (which is made light by the use of poly-instanton corrections). We find the challenges of embedding the mechanism into a concrete UV completion constrains the properties of the non-gaussianity that is found, since for generic values of the underlying parameters, the model predicts a local bi-spectrum with f{sub NL} of order 'a few'. However, a moderate tuning of the parameters gives also rise to explicit examples with f{sub NL} ∼ O(20) potentially observable by the Planck satellite.
Modeling Sea-Level Change using Errors-in-Variables Integrated Gaussian Processes
Cahill, Niamh; Parnell, Andrew; Kemp, Andrew; Horton, Benjamin
2014-05-01
We perform Bayesian inference on historical and late Holocene (last 2000 years) rates of sea-level change. The data that form the input to our model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. To accurately estimate rates of sea-level change and reliably compare tide-gauge compilations with proxy reconstructions it is necessary to account for the uncertainties that characterize each dataset. Many previous studies used simple linear regression models (most commonly polynomial regression) resulting in overly precise rate estimates. The model we propose uses an integrated Gaussian process approach, where a Gaussian process prior is placed on the rate of sea-level change and the data itself is modeled as the integral of this rate process. The non-parametric Gaussian process model is known to be well suited to modeling time series data. The advantage of using an integrated Gaussian process is that it allows for the direct estimation of the derivative of a one dimensional curve. The derivative at a particular time point will be representative of the rate of sea level change at that time point. The tide gauge and proxy data are complicated by multiple sources of uncertainty, some of which arise as part of the data collection exercise. Most notably, the proxy reconstructions include temporal uncertainty from dating of the sediment core using techniques such as radiocarbon. As a result of this, the integrated Gaussian process model is set in an errors-in-variables (EIV) framework so as to take account of this temporal uncertainty. The data must be corrected for land-level change known as glacio-isostatic adjustment (GIA) as it is important to isolate the climate-related sea-level signal. The correction for GIA introduces covariance between individual age and sea level observations into the model. The proposed integrated Gaussian process model allows for the estimation of instantaneous rates of sea-level change and accounts for all
Post-selected von Neumann measurement with Hermite-Gaussian and Laguerre-Gaussian pointer states
Turek, Yusuf; Akutsu, Tomotada; Sun, Chang-Pu; Shikano, Yutaka
2015-01-01
Through the von Neumann interaction followed by post-selection, we can extract not only the eigenvalue of an observable of the measured system but also the weak value. In this post-selected von Neumann measurement, the initial pointer state of the measuring device is assumed to be a fundamental Gaussian wave function. By considering the optical implementation of the post-selected von Neumann measurement, higher-order Gaussian modes can be used. In this paper, we consider the Hermite--Gaussian (HG) and Laguerre--Gaussian (LG) modes as pointer states and calculate the average shift of the pointer states of the post-selected von Neumann measurement by assuming the system observable $\\hat{A}$ with $\\hat{A}^{2}=\\hat{I}$ and $\\hat{A}^{2}=\\hat{A}$ for an arbitrary interaction strength, where $\\hat{I}$ represents the identity operator. Our results show that the HG and LG pointer states for a given coupling direction have advantages and disadvantages over the fundamental Gaussian mode in improving the signal-to-noise ...
The bispectrum covariance beyond Gaussianity: A log-normal approach
Martin, Sandra; Simon, Patrick
2011-01-01
To investigate and specify the statistical properties of cosmological fields with particular attention to possible non-Gaussian features, accurate formulae for the bispectrum and the bispectrum covariance are required. The bispectrum is the lowest-order statistic providing an estimate for non-Gaussianities of a distribution, and the bispectrum covariance depicts the errors of the bispectrum measurement and their correlation on different scales. Currently, there do exist fitting formulae for the bispectrum and an analytical expression for the bispectrum covariance, but the former is not very accurate and the latter contains several intricate terms and only one of them can be readily evaluated from the power spectrum of the studied field. Neglecting all higher-order terms results in the Gaussian approximation of the bispectrum covariance. We study the range of validity of this Gaussian approximation for two-dimensional non-Gaussian random fields. For this purpose, we simulate Gaussian and non-Gaussian random fi...
Analytical structure of Hermite Gaussian beam in far field
Institute of Scientific and Technical Information of China (English)
Zhou Guo-Quan; Chen Liang; Chu Xiu-Xiang
2007-01-01
Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical structure of Hermite Gaussian beam in far field is presented. The structural energy flux distributions are also investigated in the far field. The structural pictures of some Hermite Gaussian beams are depicted in the far field. As the structure of Hermite Gaussian beam is dominated by the transverse mode numbers and the initial transverse Gaussian half width, it is more complex than that of Gaussian beam. The ratios of the structural energy fluxes to the whole energy flux are independent of the transverse mode numbers and the initial transverse Gaussian half width. The present research reveals the internal vectorial structure of Hermite Gaussian beam from other viewpoint.
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.
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...... Gaussian, and the wavelet coefficients have log-variances equal to the hidden states. We argue why this provides a flexible model where frequentist and Bayesian inference procedures become tractable for estimation of parameters and hidden states. Our methodology is illustrated for denoising and edge...
Computer simulation of rod-sphere mixtures
Energy Technology Data Exchange (ETDEWEB)
Antypov, Dmytro
2003-07-01
Results are presented from a series of simulations undertaken to investigate the effect of adding small spherical particles to a fluid of rods which would otherwise represent a liquid crystalline (LC) substance. Firstly, a bulk mixture of Hard Gaussian Overlap particles with an aspect ratio of 3:1 and hard spheres with diameters equal to the breadth of the rods is simulated at various sphere concentrations. Both mixing-demixing and isotropic-nematic transition are studied using Monte Carlo techniques. Secondly, the effect of adding Lennard-Jones particles to an LC system modelled using the well established Gay-Berne potential is investigated. These rod-sphere mixtures are simulated using both the original set of interaction parameters and a modified version of the rod-sphere potential proposed in this work. The subject of interest is the internal structure of the binary mixture and its dependence on density, temperature, concentration and various parameters characterising the intermolecular interactions. Both the mixing-demixing behaviour and the transitions between the isotropic and any LC phases have been studied for four systems which differ in the interaction potential between unlike particles. A range of contrasting microphase separated structures including bicontinuous, cubic, and micelle-like arrangement have been observed in bulk. Thirdly, the four types of mixtures previously studied in bulk are subjected to a static magnetic field. A variety of novel phases are observed for the cases of positive and negative anisotropy in the magnetic susceptibility. These include a lamellar structure, in which layers of rods are separated by layers of spheres, and a configuration with a self-assembling hexagonal array of spheres. Finally, two new models are presented to study liquid crystal mixtures in the presence of curved substrates. These are implemented for the cases of convex and concave spherical surfaces. The simulation results obtained in these geometries
Optimizing Electromagnetically Induced Transparency Signals with Laguerre-Gaussian Beams
Holtfrerich, Matthew; Akin, Tom; Krzyzewski, Sean; Marino, Alberto; Abraham, Eric
2016-05-01
We have performed electromagnetically induced transparency in ultracold Rubidium atoms using a Laguerre-Gaussian laser mode as the control beam. Laguerre-Gaussian modes are characterized by a ring type transverse intensity profile and carry intrinsic orbital angular momentum. This angular momentum carried by the control beam can be utilized in optical computing applications which is unavailable to the more common Gaussian laser field. Specifically, we use a Laguerre-Gaussian control beam with a Gaussian probe to show that the linewidth of the transmission spectrum can be narrowed when compared to a Gaussian control beam that has the same peak intensity. We present data extending this work to compare control fields in both the Gaussian and Laguerre-Gaussian modes with constant total power. We have made efforts to find the optical overlap that best minimizes the transmission linewidth while also maintaining signal contrast. This was done by changing the waist size of the control beam with respect to the probe. The best results were obtained when the waist of a Laguerre-Gaussian control beam is equal to the waist of the Gaussian probe resulting in narrow linewidth features.
An introduction to Gaussian Bayesian networks.
Grzegorczyk, Marco
2010-01-01
The extraction of regulatory networks and pathways from postgenomic data is important for drug -discovery and development, as the extracted pathways reveal how genes or proteins regulate each other. Following up on the seminal paper of Friedman et al. (J Comput Biol 7:601-620, 2000), Bayesian networks have been widely applied as a popular tool to this end in systems biology research. Their popularity stems from the tractability of the marginal likelihood of the network structure, which is a consistent scoring scheme in the Bayesian context. This score is based on an integration over the entire parameter space, for which highly expensive computational procedures have to be applied when using more complex -models based on differential equations; for example, see (Bioinformatics 24:833-839, 2008). This chapter gives an introduction to reverse engineering regulatory networks and pathways with Gaussian Bayesian networks, that is Bayesian networks with the probabilistic BGe scoring metric [see (Geiger and Heckerman 235-243, 1995)]. In the BGe model, the data are assumed to stem from a Gaussian distribution and a normal-Wishart prior is assigned to the unknown parameters. Gaussian Bayesian network methodology for analysing static observational, static interventional as well as dynamic (observational) time series data will be described in detail in this chapter. Finally, we apply these Bayesian network inference methods (1) to observational and interventional flow cytometry (protein) data from the well-known RAF pathway to evaluate the global network reconstruction accuracy of Bayesian network inference and (2) to dynamic gene expression time series data of nine circadian genes in Arabidopsis thaliana to reverse engineer the unknown regulatory network topology for this domain.
Non-Gaussianity as a Particle Detector
Lee, Hayden; Pimentel, Guilherme L
2016-01-01
We study the imprints of massive particles with spin on cosmological correlators. Using the framework of the effective field theory of inflation, we classify the couplings of these particles to the Goldstone boson of broken time translations and the graviton. We show that it is possible to generate observable non-Gaussianity within the regime of validity of the effective theory, as long as the masses of the particles are close to the Hubble scale and their interactions break the approximate conformal symmetry of the inflationary background. We derive explicit shape functions for the scalar and tensor bispectra that can serve as templates for future observational searches.
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...... optimized according to the noise level in each voxel. The comparison is carried out using artificial data as well as data from healthy volunteers. It is shown that GPD is comparable to SVD with a variable optimized threshold when determining the maximum of the IRF, which is directly related to the perfusion...
Non-Gaussianity from Axion Monodromy Inflation
DEFF Research Database (Denmark)
Hannestad, Steen; Haugboelle, Troels; R. Jarnhus, Philip;
2010-01-01
inflation in string theory, where the monodromy from wrapped branes extends the range of the closed string axions to beyond the Planck scale. The superimposed oscillations in the potential can lead to new signatures in the CMB spectrum and bispectrum. In particular the bispectrum will have a new distinct...... or larger while the power spectrum is almost featureless. This model is therefore an example of a string-inspired inflationary model which is testable mainly through its non-Gaussian features. Finally we provide a simple analytic fitting formula for the bispectrum which is accurate to approximately 5...
Boson sampling from a Gaussian state.
Lund, A P; Laing, A; Rahimi-Keshari, S; Rudolph, T; O'Brien, J L; Ralph, T C
2014-09-05
We pose a randomized boson-sampling problem. Strong evidence exists that such a problem becomes intractable on a classical computer as a function of the number of bosons. We describe a quantum optical processor that can solve this problem efficiently based on a Gaussian input state, a linear optical network, and nonadaptive photon counting measurements. All the elements required to build such a processor currently exist. The demonstration of such a device would provide empirical evidence that quantum computers can, indeed, outperform classical computers and could lead to applications.
Soft sensor modeling based on Gaussian processes
Institute of Scientific and Technical Information of China (English)
XIONG Zhi-hua; HUANG Guo-hong; SHAO Hui-he
2005-01-01
In order to meet the demand of online optimal running, a novel soft sensor modeling approach based on Gaussian processes was proposed. The approach is moderately simple to implement and use without loss of performance. It is trained by optimizing the hyperparameters using the scaled conjugate gradient algorithm with the squared exponential covariance function employed. Experimental simulations show that the soft sensor modeling approach has the advantage via a real-world example in a refinery. Meanwhile, the method opens new possibilities for application of kernel methods to potential fields.
Internal DLA and the Gaussian free field
Jerison, David; Sheffield, Scott
2011-01-01
In previous works, we showed that the internal DLA cluster on \\Z^d with t particles is a.s. spherical up to a maximal error of O(\\log t) if d=2 and O(\\sqrt{\\log t}) if d > 2. This paper addresses "average error": in a certain sense, the average deviation of internal DLA from its mean shape is of constant order when d=2 and of order r^{1-d/2} (for a radius r cluster) in general. Appropriately normalized, the fluctuations (taken over time and space) scale to a variant of the Gaussian free field.
Non-gaussianity from broken symmetries
Energy Technology Data Exchange (ETDEWEB)
Kolb, Edward W.; /Fermilab /Chicago U., Astron. Astrophys. Ctr. /Chicago U., EFI; Riotto, Antonio; /CERN; Vallinotto, Alberto; /Chicago U. /Fermilab
2005-11-01
Recently we studied inflation models in which the inflation potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, F{sub NL}, can be as large as 10{sup 2}.
Gaussian Markov random fields theory and applications
Rue, Havard
2005-01-01
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.
Gaussian Belief Propagation Based Multiuser Detection
Bickson, Danny; Shental, Ori; Siegel, Paul H; Wolf, Jack K
2008-01-01
In this work, we present a novel construction for solving the linear multiuser detection problem using the Gaussian Belief Propagation algorithm. Our algorithm yields an efficient, iterative and distributed implementation of the MMSE detector. We compare our algorithm's performance to a recent result and show an improved memory consumption, reduced computation steps and a reduction in the number of sent messages. We prove that recent work by Montanari et al. is an instance of our general algorithm, providing new convergence results for both algorithms.
Bayesian model selection in Gaussian regression
Abramovich, Felix
2009-01-01
We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized least squares estimation with a complexity penalty associated with a prior on the model size. We investigate the optimality properties of the resulting estimator. We establish the oracle inequality and specify conditions on the prior that imply its asymptotic minimaxity within a wide range of sparse and dense settings for "nearly-orthogonal" and "multicollinear" designs.
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...... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...
A Gaussian measure of quantum phase noise
Schleich, Wolfgang P.; Dowling, Jonathan P.
1992-01-01
We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.
Non-Gaussianity as a particle detector
Energy Technology Data Exchange (ETDEWEB)
Lee, Hayden [Department of Applied Mathematics and Theoretical Physics, Cambridge University,Cambridge, CB3 0WA (United Kingdom); Baumann, Daniel; Pimentel, Guilherme L. [Department of Applied Mathematics and Theoretical Physics, Cambridge University,Cambridge, CB3 0WA (United Kingdom); Institute of Physics, Universiteit van Amsterdam,Science Park, Amsterdam, 1090 GL (Netherlands)
2016-12-13
We study the imprints of massive particles with spin on cosmological correlators. Using the framework of the effective field theory of inflation, we classify the couplings of these particles to the Goldstone boson of broken time translations and the graviton. We show that it is possible to generate observable non-Gaussianity within the regime of validity of the effective theory, as long as the masses of the particles are close to the Hubble scale and their interactions break the approximate conformal symmetry of the inflationary background. We derive explicit shape functions for the scalar and tensor bispectra that can serve as templates for future observational searches.
Encoding information using laguerre gaussian modes
CSIR Research Space (South Africa)
Trichili, A
2015-08-01
Full Text Available Gaussian modes Abderrahmen Trichili1, Angela Dudley2,3, Amine Ben Salem1, Bienvenu Ndagano3, Mourad Zghal1,4 and Andrew Forbes2,3* 1University of Carthage, Engineering School of Communication of Tunis (Sup’Com), GreS’Com Laboratory, Ghazala Technopark, 2083..., Ariana, Tunisia 2CSIR National Laser Centre, P.O. Box 395, Pretoria 0001, South Africa 3School of Physics, University of the Witwatersrand, Johannesburg 2050, South Africa 4Institut Mines-Te´le´com/Te´le´com SudParis, 9 rue Charles Fourier, 91011 Evry...
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.
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.
Uttam Mande; Y. Srinivas; Murthy, J. V. R.
2012-01-01
Lot of research is projected to map the criminal with that of crime and it is observed that there is still a huge increase in the crime rate due to the gap between the optimal usage of technologies and investigation. This has given scope for the development of new methodologies in the area of crime investigation using the techniques based on data mining, image processing, forensic, and social mining. In this paper, presents a model using new methodology for mapping the criminal with the crime...
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
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
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....
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 probabi
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 probabi
Forecasts of non-Gaussian parameter spaces using Box-Cox transformations
Joachimi, B
2011-01-01
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 con...
First Passage Probability of Structures under Non-Gaussian Stochastic Behavior
Institute of Scientific and Technical Information of China (English)
HE Jun; ZHOU Rong-Jun; KOU Xin-Jian
2008-01-01
An analytical moment-based method was proposed for calculating first passage probability of structures under non-Ganssian stochastic behaviour. In the method, the third-moment standardization that constants can be obtained from first three-order response moments was used to map a non-Ganssian structural response into a standard Gaussian process; then the mean up-crossing rates, the mean clump size and the initial passage probability of some critical barrier level by the original structural response were estimated. Finally, the formula for calculating first passage probability was established on the assumption that the corrected up-crossing rates are independent. By a nonlinear single-degree-of-freedom system excited by a stationary Gaussian load,it is demonstrated how the procedure can be used for the type of structures considered. Further, comparisons between the results from the present procedure and those from Monte-Carlo simulation are performed.
On the impact of non-Gaussian wind statistics on wind turbines - an experimental approach
Schottler, Jannik; Reinke, Nico; Hoelling, Agnieszka; Whale, Jonathan; Peinke, Joachim; Hoelling, Michael
2016-11-01
The effect of intermittent and Gaussian inflow conditions on wind energy converters is studied experimentally. Two different flow situations were created in a wind tunnel using an active grid. Both flows exhibit nearly equal mean velocity values and turbulence intensities, but strongly differ in their two point uτ = u (t + τ) - u (t) on a variety of time scales τ, one being Gaussian distributed, the other one being strongly intermittent. A horizontal axis model wind turbine is exposed to both flows, isolating the effect of the differences not captured by mean values and turbulence intensities on the turbine. Thrust, torque and power data were recorded and analyzed, showing that the model turbine does not smooth out intermittency. Intermittent inflow is converted to similarly intermittent turbine data on all scales considered, reaching down to sub-rotor scales in space, indicating that it is not correct to assume a smoothing of wind speed fluctuations below the size of the rotor.
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.
A Mixture Innovation Heterogeneous Autoregressive Model for Structural Breaks and Long Memory
DEFF Research Database (Denmark)
Nonejad, Nima
We propose a flexible model to describe nonlinearities and long-range dependence in time series dynamics. Our model is an extension of the heterogeneous autoregressive model. Structural breaks occur through mixture distributions in state innovations of linear Gaussian state space models. Monte Ca...... forecasts compared to any single model specification. It provides further improvements when we average over nonlinear specifications....
Yun, Yuqi; Zevin, Michael; Sampson, Laura; Kalogera, Vassiliki
2017-01-01
With more observations from LIGO in the upcoming years, we will be able to construct an observed mass distribution of black holes to compare with binary evolution simulations. This will allow us to investigate the physics of binary evolution such as the effects of common envelope efficiency and wind strength, or the properties of the population such as the initial mass function.However, binary evolution codes become computationally expensive when running large populations of binaries over a multi-dimensional grid of input parameters, and may simulate accurately only for a limited combination of input parameter values. Therefore we developed a fast machine-learning method that utilizes Gaussian Mixture Model (GMM) and Gaussian Process (GP) regression, which together can predict distributions over the entire parameter space based on a limited number of simulated models. Furthermore, Gaussian Process regression naturally provides interpolation errors in addition to interpolation means, which could provide a means of targeting the most uncertain regions of parameter space for running further simulations.We also present a case study on applying this new method to predicting chirp mass distributions for binary black hole systems (BBHs) in Milky-way like galaxies of different metallicities.
DESIGN OF LDPC-CODED BICM USING A SEMI-GAUSSIAN APPROXIMATION
Institute of Scientific and Technical Information of China (English)
Huang Jie; Zhang Fan; Zhu Jinkang
2007-01-01
This paper investigates analysis and design of Low-Density Parity-Check (LDPC) coded BitInterleaved Coded Modulation (BICM) over Additive White Gaussian Noise (AWGN) channel. It focuses on Gray-labeled 8-ary Phase-Shift-Keying (8PSK) modulation and employs a Maximum A Posteriori (MAP) symbol-to-bit metric calculator at the receiver. An equivalent model of a BICM communication channel with ideal interleaving is presented. The probability distribution function of log-likelihood ratio messages from the MAP receiver can be approximated by a mixture of symmetric Gaussian densities. As a result semi-Gaussian approximation can be used to analyze the decoder.Extrinsic information transfer charts are employed to describe the convergence behavior of LDPC decoder. The design of irregular LDPC codes reduces to a linear programming problem on two-dimensional variable edge-degree distribution. This method allows irregular code design in a wider range of rates without any limit on the maximum node degree and can be used to design irregular codes having rates varying from 0.5275 to 0.9099. The designed convergence thresholds are only a few tenths,even a few hundredths of a decibel from the capacity limits. It is shown by Monte Carlo simulations that,when the block length is 30,000, these codes operate about 0.62-0.75 dB from the capacity limit at a bit error rate of 10-8.
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.
Directory of Open Access Journals (Sweden)
Madsen Per
2003-03-01
Full Text Available Abstract A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed.
Gaussian and non-Gaussian inverse modeling of groundwater flow using copulas and random mixing
Bárdossy, András.; Hörning, Sebastian
2016-06-01
This paper presents a new copula-based methodology for Gaussian and non-Gaussian inverse modeling of groundwater flow. The presented approach is embedded in a Monte Carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function. The target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields. The corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability, and honors all the observations of hydraulic transmissivities. The constraints related to hydraulic head observations are nonlinear. In order to fulfill these constraints, a connected domain in the weight space, inside which all linear constraints are fulfilled, is identified. This domain is defined analytically and includes an infinite number of conditional fields (i.e., conditioned on the observed hydraulic transmissivities), and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads. This procedure enables the simulation of a great number of solutions for the inverse problem, allowing a reasonable quantification of the associated uncertainties. The methodology can be used for fields with Gaussian copula dependence, and fields with specific non-Gaussian copula dependence. Further, arbitrary marginal distributions can be considered.
Korsgaard, Inge Riis; Lund, Mogens Sandø; Sorensen, Daniel; Gianola, Daniel; Madsen, Per; Jensen, Just
2003-01-01
A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed.
Non-Gaussianity vs. non-linearity of cosmological perturbations
Verde, L
2001-01-01
Following the discovery of the CMB, 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 towards 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, non-linear 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 these might not be faithful tr...
Continuous variable quantum information: Gaussian states and beyond
Adesso, Gerardo; Lee, Antony R
2014-01-01
The study of Gaussian states has arisen to a privileged position in continuous variable quantum information in recent years. This is due to vehemently pursued experimental realisations and a magnificently elegant mathematical framework. In this article, we provide a brief, and hopefully didactic, exposition of Gaussian state quantum information and its contemporary uses, including sometimes omitted crucial details. After introducing the subject material and outlining the essential toolbox of continuous variable systems, we define the basic notions needed to understand Gaussian states and Gaussian operations. In particular, emphasis is placed on the mathematical structure combining notions of algebra and symplectic geometry fundamental to a complete understanding of Gaussian informatics. Furthermore, we discuss the quantification of different forms of correlations (including entanglement and quantum discord) for Gaussian states, paying special attention to recently developed measures. The manuscript is conclud...
Compressive tracking with incremental multivariate Gaussian distribution
Li, Dongdong; Wen, Gongjian; Zhu, Gao; Zeng, Qiaoling
2016-09-01
Various approaches have been proposed for robust visual tracking, among which compressive tracking (CT) yields promising performance. In CT, Haar-like features are efficiently extracted with a very sparse measurement matrix and modeled as an online updated naïve Bayes classifier to account for target appearance change. The naïve Bayes classifier ignores overlap between Haar-like features and assumes that Haar-like features are independently distributed, which leads to drift in complex scenario. To address this problem, we present an extended CT algorithm, which assumes that all Haar-like features are correlated with each other and have multivariate Gaussian distribution. The mean vector and covariance matrix of multivariate normal distribution are incrementally updated with constant computational complexity to adapt to target appearance change. Each frame is associated with a temporal weight to expend less modeling power on old observation. Based on temporal weight, an update scheme with changing but convergent learning rate is derived with strict mathematic proof. Compared with CT, our extended algorithm achieves a richer representation of target appearance. The incremental multivariate Gaussian distribution is integrated into the particle filter framework to achieve better tracking performance. Extensive experiments on the CVPR2013 tracking benchmark demonstrate that our proposed tracker achieves superior performance both qualitatively and quantitatively over several state-of-the-art trackers.
Radiation damping in pulsed Gaussian beams
Harvey, Chris; Marklund, Mattias
2012-01-01
We consider the effects of radiation damping on the electron dynamics in a Gaussian-beam model of a laser field. For high intensities, i.e., with dimensionless intensity a0≫1, it is found that the dynamics divides into three regimes. For low-energy electrons (low initial γ factor, γ0) the radiation damping effects are negligible. At higher energies, but still at 2γ0a0 one is in a regime of radiation-reaction-induced electron capture. This capture is found to be stable with respect to the spatial properties of the electron beam and results in a significant energy loss of the electrons. In this regime the plane-wave model of the laser field provides a good description of the dynamics, whereas for lower energies the Gaussian-beam and plane-wave models differ significantly. Finally the dynamics is considered for the case of an x-ray free-electron laser field. It is found that the significantly lower intensities of such fields inhibit the damping effects.
Gravitational Wave Emulation Using Gaussian Process Regression
Doctor, Zoheyr; Farr, Ben; Holz, Daniel
2017-01-01
Parameter estimation (PE) for gravitational wave signals from compact binary coalescences (CBCs) requires reliable template waveforms which span the parameter space. Waveforms from numerical relativity are accurate but computationally expensive, so approximate templates are typically used for PE. These `approximants', while quick to compute, can introduce systematic errors and bias PE results. We describe a machine learning method for generating CBC waveforms and uncertainties using existing accurate waveforms as a training set. Coefficients of a reduced order waveform model are computed and each treated as arising from a Gaussian process. These coefficients and their uncertainties are then interpolated using Gaussian process regression (GPR). As a proof of concept, we construct a training set of approximant waveforms (rather than NR waveforms) in the two-dimensional space of chirp mass and mass ratio and interpolate new waveforms with GPR. We demonstrate that the mismatch between interpolated waveforms and approximants is below the 1% level for an appropriate choice of training set and GPR kernel hyperparameters.
Baseline correction of intraoperative electromyography using discrete wavelet transform.
Rampp, Stefan; Prell, Julian; Thielemann, Henning; Posch, Stefan; Strauss, Christian; Romstöck, Johann
2007-08-01
In intraoperative analysis of electromygraphic signals (EMG) for monitoring purposes, baseline artefacts frequently pose considerable problems. Since artefact sources in the operating room can only be reduced to a limited degree, signal-processing methods are needed to correct the registered data online without major changes to the relevant data itself. We describe a method for baseline correction based on "discrete wavelet transform" (DWT) and evaluate its performance compared to commonly used digital filters. EMG data from 10 patients who underwent removal of acoustic neuromas were processed. Effectiveness, preservation of relevant EMG patterns and processing speed of a DWT based correction method was assessed and compared to a range of commonly used Butterworth, Resistor-Capacitor and Gaussian filters. Butterworth and DWT filters showed better performance regarding artefact correction and pattern preservation compared to Resistor-Capacitor and Gaussian filters. Assuming equal weighting of both characteristics, DWT outperformed the other methods: While Butterworth, Resistor-Capacitor and Gaussian provided good pattern preservation, the effectiveness was low and vice versa, while DWT baseline correction at level 6 performed well in both characteristics. The DWT method allows reliable and efficient intraoperative baseline correction in real-time. It is superior to commonly used methods and may be crucial for intraoperative analysis of EMG data, for example for intraoperative assessment of facial nerve function.
A Note on Gaussian Distributions in $\\mathbb{R}^n$
Indian Academy of Sciences (India)
B G Manjunath; K R Parthasarathy
2012-11-01
Given any finite set $\\mathcal{F}$ of (-1)-dimensional subspaces of $\\mathbb{R}^n$ we give examples of nonGaussian probability measures in $\\mathbb{R}^n$ whose marginal distribution in each subspace from $\\mathcal{F}$ is Gaussian. However, if $\\mathcal{F}$ is an infinite family of such (-1)-dimensional subspaces then such a nonGaussian probability measure in $\\mathbb{R}^n$ does not exist.
Increasing entanglement between Gaussian states by coherent photon subtraction.
Ourjoumtsev, Alexei; Dantan, Aurélien; Tualle-Brouri, Rosa; Grangier, Philippe
2007-01-19
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 with negative Wigner functions and complex structures more entangled than the initial states in terms of negativity. The experimental results are in very good agreement with the theoretical predictions.
Increasing entanglement between Gaussian states by coherent photon subtraction
Ourjoumtsev, A; Tualle-Brouri, R; Grangier, P; Ourjoumtsev, Alexei; Dantan, Aurelien; Tualle-Brouri, Rosa; Grangier, Philippe
2006-01-01
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 non-degenerate parametric amplifier, produces delocalized "Schroedinger kitten" states with complex negative Wigner functions, more entangled than the initial states in terms of negativity. The experimental results are in very good agreement with the theoretical predictions.
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.
Relaxation oscillations in a laser with a Gaussian mirror.
Mossakowska-Wyszyńska, Agnieszka; Witoński, Piotr; Szczepański, Paweł
2002-03-20
We present an analysis of the relaxation oscillations in a laser with a Gaussian mirror by taking into account the three-dimensional spatial field distribution of the laser modes and the spatial hole burning effect. In particular, we discuss the influence of the Gaussian mirror peak reflectivity and a Gaussian parameter on the damping rate and frequency of the relaxation oscillation for two different laser structures, i.e., with a classically unstable resonator and a classically stable resonator.
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.
Novel mixture model for the representation of potential energy surfaces
Pham, Tien Lam; Kino, Hiori; Terakura, Kiyoyuki; Miyake, Takashi; Dam, Hieu Chi
2016-10-01
We demonstrate that knowledge of chemical physics on a materials system can be automatically extracted from first-principles calculations using a data mining technique; this information can then be utilized to construct a simple empirical atomic potential model. By using unsupervised learning of the generative Gaussian mixture model, physically meaningful patterns of atomic local chemical environments can be detected automatically. Based on the obtained information regarding these atomic patterns, we propose a chemical-structure-dependent linear mixture model for estimating the atomic potential energy. Our experiments show that the proposed mixture model significantly improves the accuracy of the prediction of the potential energy surface for complex systems that possess a large diversity in their local structures.
Identification and separation of DNA mixtures using peak area information
DEFF Research Database (Denmark)
Cowell, R.G.; Lauritzen, Steffen Lilholt; Mortera, J.
, whose profiles have been measured, have contributed to the mixture, but also to predict DNA profiles of unknown contributors by separating the mixture into its individual components. The potential of our methodology is illustrated on case data examples and compared with alternative approaces......We show how probabilistic expert systems can be used to analyse forensic identification problems involving DNA mixture traces using quantitative peak area information. Peak area is modelled with conditional Gaussian distributions. The expert system can be used for scertaining whether individuals....... The advantages are that identification and separation issues can be handled in a unified way within a single network model and the uncertainty associated with the analysis is quantified....
Testing large-angle deviation from Gaussianity in CMB maps
Bernui, A; Teixeira, A F F
2010-01-01
A detection of the level of non-Gaussianity in the CMB data is essential to discriminate among inflationary models and also to test alternative primordial scenarios. However, the extraction of primordial non-Gaussianity is a difficult endeavor since several effects of non-primordial nature can produce non-Gaussianity. On the other hand, different statistical tools can in principle provide information about distinct forms of non-Gaussianity. Thus, any single statistical estimator cannot be sensitive to all possible forms of non-Gaussianity. In this context, to shed some light in the potential sources of deviation from Gaussianity in CMB data it is important to use different statistical indicators. In a recent paper we proposed two new large-angle non-Gaussianity indicators which provide measures of the departure from Gaussianity on large angular scales. We used these indicators to carry out analyses of non-Gaussianity of the bands and of the foreground-reduced WMAP maps with and without the KQ75 mask. Here we ...
Making Tensor Factorizations Robust to Non-Gaussian Noise
Chi, Eric C
2010-01-01
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 i.i.d. Gaussian noise. We demonstrate that this loss function can actually 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 algorithm for fitting a CP model using our proposed loss function.
Think continuous: Markovian Gaussian models in spatial statistics
Simpson, Daniel; Rue, Håvard
2011-01-01
Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRFs with the more traditional Gaussian random field models as the Markov property is difficult to deploy in continuous space. Following the pioneering work of Lindgren et al. (2011), we expound on the link between Markovian Gaussian random fields and GMRFs. In particular, we discuss the theoretical and practical aspects of fast computation with continuously specified Markovian Gaussian random fields, as well as the clear advantages they offer in terms of clear, parsimonious and interpretable models of anisotropy and non-stationarity.
Saulquin, Bertrand; Fablet, Ronan; Bourg, Ludovic; Mercier, Gregoire; Fanton d'Andon, Odile
2016-08-01
From top-of-atmosphere (TOA) observations, atmospheric correction for ocean color inversion aims at distinguishing atmosphere and water contributions. From a methodological point of view, our approach relies on a Bayesian inference using Gaussian Mixture Model prior distributions and reference spectra of aerosol and water reflectance [1].We evaluate our estimates of the sea surface reflectance from the MERIS TOA observations. Using the MERMAID radiometric in-situ dataset, we obtain significant improvements in the estimation of the sea surface reflectance, especially for the 412, 442, 490 and 510 nm bands, compared with the standard ESA MEGS algorithm and the a state-of- the-art neural network approach (C2R). The mean gain value on the relative error for the 13 bands between 412 and 885 nm is of 57% compared with MEGS algorithm and 10% compared with the C2R. We further discuss the potential of MEETC2 for new ESA OLCI / Sentinel 3 mission.
Energy Technology Data Exchange (ETDEWEB)
Khayrullin, S.R.; Firsov, I.A.; Ongoyev, V.M.; Shekhtman, E.N.; Taskarin, B.T.
1983-01-01
A plugging mixture is proposed which contains triethanolamine, caustic soda, water and an additive. It is distinguished by the fact that in order to reduce the cost of the mixture while preserving its operational qualities, it additionally contains clay powder and as the additive, ground limestone with the following component ratio in percent by mass: ground limestone, 50 to 60; triethanolamine, 0.1 to 0.15; caustic soda, 2 to 3; clay powder, 8 to 10 and water the remainder. The mixture is distinguished by the fact that the ground limestone has a specific surface of 2,000 to 3,000 square centimeters per gram.
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.