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

Nunes, Rafael C.; Abreu, Everton M.C.; Neto, Jorge Ananias

Based on the relationship between thermodynamics and gravity we propose, with the aid of Verlinde's formalism, an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe. This description 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. The effect of these non-gaussian statistics in the cosmological context is to change the strength of the gravitational constant. In this paper, we consider the w CDM model modified by the non-gaussian statistics and investigate the compatibility of these non-gaussian modificationmore » with the cosmological observations. In order to analyze in which extend the cosmological data constrain these non-extensive statistics, we will use type Ia supernovae, baryon acoustic oscillations, Hubble expansion rate function and the linear growth of matter density perturbations data. We show that Tsallis' statistics is favored at 1σ confidence level.« less

Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system.

PubMed

Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C

2016-02-01

A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.

Rightfulness of Summation Cut-Offs in the Albedo Problem with Gaussian Fluctuations of the Density of Scatterers

NASA Astrophysics Data System (ADS)

Selim, M. M.; Bezák, V.

2003-06-01

The one-dimensional version of the radiative transfer problem (i.e. the so-called rod model) is analysed with a Gaussian random extinction function (x). Then the optical length X = 0 Ldx(x) is a Gaussian random variable. The transmission and reflection coefficients, T(X) and R(X), are taken as infinite series. When these series (and also when the series representing T 2(X), T 2(X), R(X)T(X), etc.) are averaged, term by term, according to the Gaussian statistics, the series become divergent after averaging. As it was shown in a former paper by the authors (in Acta Physica Slovaca (2003)), a rectification can be managed when a `modified' Gaussian probability density function is used, equal to zero for X > 0 and proportional to the standard Gaussian probability density for X > 0. In the present paper, the authors put forward an alternative, showing that if the m.s.r. of X is sufficiently small in comparison with & $bar X$ ; , the standard Gaussian averaging is well functional provided that the summation in the series representing the variable T m-j (X)R j (X) (m = 1,2,..., j = 1,...,m) is truncated at a well-chosen finite term. The authors exemplify their analysis by some numerical calculations.

Assessment of the non-Gaussianity and non-linearity levels of simulated sEMG signals on stationary segments.

PubMed

Messaoudi, Noureddine; Bekka, Raïs El'hadi; Ravier, Philippe; Harba, Rachid

2017-02-01

The purpose of this paper was to evaluate the effects of the longitudinal single differential (LSD), the longitudinal double differential (LDD) and the normal double differential (NDD) spatial filters, the electrode shape, the inter-electrode distance (IED) on non-Gaussianity and non-linearity levels of simulated surface EMG (sEMG) signals when the maximum voluntary contraction (MVC) varied from 10% to 100% by a step of 10%. The effects of recruitment range thresholds (RR), the firing rate (FR) strategy and the peak firing rate (PFR) of motor units were also considered. A cylindrical multilayer model of the volume conductor and a model of motor unit (MU) recruitment and firing rate were used to simulate sEMG signals in a pool of 120 MUs for 5s. Firstly, the stationarity of sEMG signals was tested by the runs, the reverse arrangements (RA) and the modified reverse arrangements (MRA) tests. Then the non-Gaussianity was characterised with bicoherence and kurtosis, and non-linearity levels was evaluated with linearity test. The kurtosis analysis showed that the sEMG signals detected by the LSD filter were the most Gaussian and those detected by the NDD filter were the least Gaussian. In addition, the sEMG signals detected by the LSD filter were the most linear. For a given filter, the sEMG signals detected by using rectangular electrodes were more Gaussian and more linear than that detected with circular electrodes. Moreover, the sEMG signals are less non-Gaussian and more linear with reverse onion-skin firing rate strategy than those with onion-skin strategy. The levels of sEMG signal Gaussianity and linearity increased with the increase of the IED, RR and PFR. Copyright © 2016 Elsevier Ltd. All rights reserved.

Chromatographic peak resolution using Microsoft Excel Solver. The merit of time shifting input arrays.

PubMed

Dasgupta, Purnendu K

2008-12-05

Resolution of overlapped chromatographic peaks is generally accomplished by modeling the peaks as Gaussian or modified Gaussian functions. It is possible, even preferable, to use actual single analyte input responses for this purpose and a nonlinear least squares minimization routine such as that provided by Microsoft Excel Solver can then provide the resolution. In practice, the quality of the results obtained varies greatly due to small shifts in retention time. I show here that such deconvolution can be considerably improved if one or more of the response arrays are iteratively shifted in time.

Study of sea-surface slope distribution and its effect on radar backscatter based on Global Precipitation Measurement Ku-band precipitation radar measurements

NASA Astrophysics Data System (ADS)

Yan, Qiushuang; Zhang, Jie; Fan, Chenqing; Wang, Jing; Meng, Junmin

2018-01-01

The collocated normalized radar backscattering cross-section measurements from the Global Precipitation Measurement (GPM) Ku-band precipitation radar (KuPR) and the winds from the moored buoys are used to study the effect of different sea-surface slope probability density functions (PDFs), including the Gaussian PDF, the Gram-Charlier PDF, and the Liu PDF, on the geometrical optics (GO) model predictions of the radar backscatter at low incidence angles (0 deg to 18 deg) at different sea states. First, the peakedness coefficient in the Liu distribution is determined using the collocations at the normal incidence angle, and the results indicate that the peakedness coefficient is a nonlinear function of the wind speed. Then, the performance of the modified Liu distribution, i.e., Liu distribution using the obtained peakedness coefficient estimate; the Gaussian distribution; and the Gram-Charlier distribution is analyzed. The results show that the GO model predictions with the modified Liu distribution agree best with the KuPR measurements, followed by the predictions with the Gaussian distribution, while the predictions with the Gram-Charlier distribution have larger differences as the total or the slick filtered, not the radar filtered, probability density is included in the distribution. The best-performing distribution changes with incidence angle and changes with wind speed.

A NEW METHOD OF PEAK DETECTION FOR ANALYSIS OF COMPREHENSIVE TWO-DIMENSIONAL GAS CHROMATOGRAPHY MASS SPECTROMETRY DATA.

PubMed

Kim, Seongho; Ouyang, Ming; Jeong, Jaesik; Shen, Changyu; Zhang, Xiang

2014-06-01

We develop a novel peak detection algorithm for the analysis of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (GC×GC-TOF MS) data using normal-exponential-Bernoulli (NEB) and mixture probability models. The algorithm first performs baseline correction and denoising simultaneously using the NEB model, which also defines peak regions. Peaks are then picked using a mixture of probability distribution to deal with the co-eluting peaks. Peak merging is further carried out based on the mass spectral similarities among the peaks within the same peak group. The algorithm is evaluated using experimental data to study the effect of different cut-offs of the conditional Bayes factors and the effect of different mixture models including Poisson, truncated Gaussian, Gaussian, Gamma, and exponentially modified Gaussian (EMG) distributions, and the optimal version is introduced using a trial-and-error approach. We then compare the new algorithm with two existing algorithms in terms of compound identification. Data analysis shows that the developed algorithm can detect the peaks with lower false discovery rates than the existing algorithms, and a less complicated peak picking model is a promising alternative to the more complicated and widely used EMG mixture models.

Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-04-15

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilizemore » the equilibrium and suppress the transition to drift-wave induced turbulence.« less

A study of atmospheric dispersion of radionuclides at a coastal site using a modified Gaussian model and a mesoscale sea breeze model

NASA Astrophysics Data System (ADS)

Venkatesan, R.; Mathiyarasu, R.; Somayaji, K. M.

Ground level concentration and sky-shine dose due to radioactive emissions from a nuclear power plant at a coastal site have been estimated using the standard Gaussian Plume Model (GPM) and the modified GPM suggested by Misra (Atmospheric Environment 14 (1980) 397), which incorporates fumigation effect under sea breeze condition. The difference in results between these two models is analysed in order to understand their significance and errors that would occur if proper choice were not made. Radioactive sky-shine dose from 41Ar, emitted from a 100 m stack of the nuclear plant is continuously recorded by environmental gamma dose monitors and the data is used to validate the modified GPM. It is observed that the dose values increase by a factor of about 2 times than those of the standard GPM estimates, up to a downwind distance of 6 km during sea breeze hours. In order to examine the dispersion of radioactive effluents in the mesoscale range, a sea breeze model coupled with a particle dispersion model is used. The deposited activity, thyroid dose and sky-shine radioactive dose are simulated for a range of 30 km. In this range, the plume is found to deviate from its straight-line trajectory, as otherwise assumed in GPM. A secondary maximum in the concentration and the sky-shine dose is also observed in the model results. These results are quite significant in realistically estimating the area affected under any unlikely event of an accidental release of radioactivity.

Sequential updating of multimodal hydrogeologic parameter fields using localization and clustering techniques

NASA Astrophysics Data System (ADS)

Sun, Alexander Y.; Morris, Alan P.; Mohanty, Sitakanta

2009-07-01

Estimated parameter distributions in groundwater models may contain significant uncertainties because of data insufficiency. Therefore, adaptive uncertainty reduction strategies are needed to continuously improve model accuracy by fusing new observations. In recent years, various ensemble Kalman filters have been introduced as viable tools for updating high-dimensional model parameters. However, their usefulness is largely limited by the inherent assumption of Gaussian error statistics. Hydraulic conductivity distributions in alluvial aquifers, for example, are usually non-Gaussian as a result of complex depositional and diagenetic processes. In this study, we combine an ensemble Kalman filter with grid-based localization and a Gaussian mixture model (GMM) clustering techniques for updating high-dimensional, multimodal parameter distributions via dynamic data assimilation. We introduce innovative strategies (e.g., block updating and dimension reduction) to effectively reduce the computational costs associated with these modified ensemble Kalman filter schemes. The developed data assimilation schemes are demonstrated numerically for identifying the multimodal heterogeneous hydraulic conductivity distributions in a binary facies alluvial aquifer. Our results show that localization and GMM clustering are very promising techniques for assimilating high-dimensional, multimodal parameter distributions, and they outperform the corresponding global ensemble Kalman filter analysis scheme in all scenarios considered.

A new peak detection algorithm for MALDI mass spectrometry data based on a modified Asymmetric Pseudo-Voigt model.

PubMed

Wijetunge, Chalini D; Saeed, Isaam; Boughton, Berin A; Roessner, Ute; Halgamuge, Saman K

2015-01-01

Mass Spectrometry (MS) is a ubiquitous analytical tool in biological research and is used to measure the mass-to-charge ratio of bio-molecules. Peak detection is the essential first step in MS data analysis. Precise estimation of peak parameters such as peak summit location and peak area are critical to identify underlying bio-molecules and to estimate their abundances accurately. We propose a new method to detect and quantify peaks in mass spectra. It uses dual-tree complex wavelet transformation along with Stein's unbiased risk estimator for spectra smoothing. Then, a new method, based on the modified Asymmetric Pseudo-Voigt (mAPV) model and hierarchical particle swarm optimization, is used for peak parameter estimation. Using simulated data, we demonstrated the benefit of using the mAPV model over Gaussian, Lorentz and Bi-Gaussian functions for MS peak modelling. The proposed mAPV model achieved the best fitting accuracy for asymmetric peaks, with lower percentage errors in peak summit location estimation, which were 0.17% to 4.46% less than that of the other models. It also outperformed the other models in peak area estimation, delivering lower percentage errors, which were about 0.7% less than its closest competitor - the Bi-Gaussian model. In addition, using data generated from a MALDI-TOF computer model, we showed that the proposed overall algorithm outperformed the existing methods mainly in terms of sensitivity. It achieved a sensitivity of 85%, compared to 77% and 71% of the two benchmark algorithms, continuous wavelet transformation based method and Cromwell respectively. The proposed algorithm is particularly useful for peak detection and parameter estimation in MS data with overlapping peak distributions and asymmetric peaks. The algorithm is implemented using MATLAB and the source code is freely available at http://mapv.sourceforge.net.

A new peak detection algorithm for MALDI mass spectrometry data based on a modified Asymmetric Pseudo-Voigt model

PubMed Central

2015-01-01

Background Mass Spectrometry (MS) is a ubiquitous analytical tool in biological research and is used to measure the mass-to-charge ratio of bio-molecules. Peak detection is the essential first step in MS data analysis. Precise estimation of peak parameters such as peak summit location and peak area are critical to identify underlying bio-molecules and to estimate their abundances accurately. We propose a new method to detect and quantify peaks in mass spectra. It uses dual-tree complex wavelet transformation along with Stein's unbiased risk estimator for spectra smoothing. Then, a new method, based on the modified Asymmetric Pseudo-Voigt (mAPV) model and hierarchical particle swarm optimization, is used for peak parameter estimation. Results Using simulated data, we demonstrated the benefit of using the mAPV model over Gaussian, Lorentz and Bi-Gaussian functions for MS peak modelling. The proposed mAPV model achieved the best fitting accuracy for asymmetric peaks, with lower percentage errors in peak summit location estimation, which were 0.17% to 4.46% less than that of the other models. It also outperformed the other models in peak area estimation, delivering lower percentage errors, which were about 0.7% less than its closest competitor - the Bi-Gaussian model. In addition, using data generated from a MALDI-TOF computer model, we showed that the proposed overall algorithm outperformed the existing methods mainly in terms of sensitivity. It achieved a sensitivity of 85%, compared to 77% and 71% of the two benchmark algorithms, continuous wavelet transformation based method and Cromwell respectively. Conclusions The proposed algorithm is particularly useful for peak detection and parameter estimation in MS data with overlapping peak distributions and asymmetric peaks. The algorithm is implemented using MATLAB and the source code is freely available at http://mapv.sourceforge.net. PMID:26680279

Data Dependent Peak Model Based Spectrum Deconvolution for Analysis of High Resolution LC-MS Data

PubMed Central

2015-01-01

A data dependent peak model (DDPM) based spectrum deconvolution method was developed for analysis of high resolution LC-MS data. To construct the selected ion chromatogram (XIC), a clustering method, the density based spatial clustering of applications with noise (DBSCAN), is applied to all m/z values of an LC-MS data set to group the m/z values into each XIC. The DBSCAN constructs XICs without the need for a user defined m/z variation window. After the XIC construction, the peaks of molecular ions in each XIC are detected using both the first and the second derivative tests, followed by an optimized chromatographic peak model selection method for peak deconvolution. A total of six chromatographic peak models are considered, including Gaussian, log-normal, Poisson, gamma, exponentially modified Gaussian, and hybrid of exponential and Gaussian models. The abundant nonoverlapping peaks are chosen to find the optimal peak models that are both data- and retention-time-dependent. Analysis of 18 spiked-in LC-MS data demonstrates that the proposed DDPM spectrum deconvolution method outperforms the traditional method. On average, the DDPM approach not only detected 58 more chromatographic peaks from each of the testing LC-MS data but also improved the retention time and peak area 3% and 6%, respectively. PMID:24533635

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

Bourdon, Christopher Jay; Olsen, Michael G.; Gorby, Allen D.

The analytical model for the depth of correlation (measurement depth) of a microscopic particle image velocimetry (micro-PIV) experiment derived by Olsen and Adrian (Exp. Fluids, 29, pp. S166-S174, 2000) has been modified to be applicable to experiments using high numerical aperture optics. A series of measurements are presented that experimentally quantify the depth of correlation of micro-PIV velocity measurements which employ high numerical aperture and magnification optics. These measurements demonstrate that the modified analytical model is quite accurate in estimating the depth of correlation in micro-PIV measurements using this class of optics. Additionally, it was found that the Gaussian particlemore » approximation made in this model does not significantly affect the model's performance. It is also demonstrated that this modified analytical model easily predicts the depth of correlation when viewing into a medium of a different index of refraction than the immersion medium.« less

Distillation and purification of symmetric entangled Gaussian states

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

Fiurasek, Jaromir

2010-10-15

We propose an entanglement distillation and purification scheme for symmetric two-mode entangled Gaussian states that allows to asymptotically extract a pure entangled Gaussian state from any input entangled symmetric Gaussian state. The proposed scheme is a modified and extended version of the entanglement distillation protocol originally developed by Browne et al. [Phys. Rev. A 67, 062320 (2003)]. A key feature of the present protocol is that it utilizes a two-copy degaussification procedure that involves a Mach-Zehnder interferometer with single-mode non-Gaussian filters inserted in its two arms. The required non-Gaussian filtering operations can be implemented by coherently combining two sequences ofmore » single-photon addition and subtraction operations.« less

A NEW METHOD OF PEAK DETECTION FOR ANALYSIS OF COMPREHENSIVE TWO-DIMENSIONAL GAS CHROMATOGRAPHY MASS SPECTROMETRY DATA*

PubMed Central

Kim, Seongho; Ouyang, Ming; Jeong, Jaesik; Shen, Changyu; Zhang, Xiang

2014-01-01

We develop a novel peak detection algorithm for the analysis of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (GC×GC-TOF MS) data using normal-exponential-Bernoulli (NEB) and mixture probability models. The algorithm first performs baseline correction and denoising simultaneously using the NEB model, which also defines peak regions. Peaks are then picked using a mixture of probability distribution to deal with the co-eluting peaks. Peak merging is further carried out based on the mass spectral similarities among the peaks within the same peak group. The algorithm is evaluated using experimental data to study the effect of different cut-offs of the conditional Bayes factors and the effect of different mixture models including Poisson, truncated Gaussian, Gaussian, Gamma, and exponentially modified Gaussian (EMG) distributions, and the optimal version is introduced using a trial-and-error approach. We then compare the new algorithm with two existing algorithms in terms of compound identification. Data analysis shows that the developed algorithm can detect the peaks with lower false discovery rates than the existing algorithms, and a less complicated peak picking model is a promising alternative to the more complicated and widely used EMG mixture models. PMID:25264474

Non-extensive entropy of modified Gaussian quantum dot under polaron effects

NASA Astrophysics Data System (ADS)

Bahramiyan, H.; Khordad, R.; Sedehi, H. R. Rastegar

2018-01-01

The effect of electron-phonon (e-p) interaction on the non-extensive Tsallis entropy of a modified Gaussian quantum dot has been investigated. In this work, the LO-phonons, SO-phonons and LO + SO-phonons have been considered. It is found that the entropy increases with enhancing the confinement potential range and depth. The entropy decreases with considering the electron-phonon interaction. The electron-LO + SO-phonon interaction has the largest contribution to the entropy.

Extended q -Gaussian and q -exponential distributions from gamma random variables

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2015-05-01

The family of q -Gaussian and q -exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q -Gaussian and q -exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q -Gaussian and modified q -exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.

Quantum steering of Gaussian states via non-Gaussian measurements

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

Offline handwritten word recognition using MQDF-HMMs

NASA Astrophysics Data System (ADS)

Ramachandrula, Sitaram; Hambarde, Mangesh; Patial, Ajay; Sahoo, Dushyant; Kochar, Shaivi

2015-01-01

We propose an improved HMM formulation for offline handwriting recognition (HWR). The main contribution of this work is using modified quadratic discriminant function (MQDF) [1] within HMM framework. In an MQDF-HMM the state observation likelihood is calculated by a weighted combination of MQDF likelihoods of individual Gaussians of GMM (Gaussian Mixture Model). The quadratic discriminant function (QDF) of a multivariate Gaussian can be rewritten by avoiding the inverse of covariance matrix by using the Eigen values and Eigen vectors of it. The MQDF is derived from QDF by substituting few of badly estimated lower-most Eigen values by an appropriate constant. The estimation errors of non-dominant Eigen vectors and Eigen values of covariance matrix for which the training data is insufficient can be controlled by this approach. MQDF has been successfully shown to improve the character recognition performance [1]. The usage of MQDF in HMM improves the computation, storage and modeling power of HMM when there is limited training data. We have got encouraging results on offline handwritten character (NIST database) and word recognition in English using MQDF HMMs.

Nonturbulent dispersion processes in complex terrain

Treesearch

Michael A. Fosberg; Douglas G. Fox; E.A. Howard; Jack D. Cohen

1976-01-01

Mass divergence influences on plume dispersion modify classic Gaussian calculations by as much as a factor of two in complex terrain. The Gaussian plume was derived in flux form to include this process.Authors' response to comments and criticism received following this publication:

A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-II beam

NASA Astrophysics Data System (ADS)

F, Khannous; A, A. A. Ebrahim; A, Belafhal

2016-04-01

Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric-Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre-Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.

Robust Alternatives to the Standard Deviation in Processing of Physics Experimental Data

NASA Astrophysics Data System (ADS)

Shulenin, V. P.

2016-10-01

Properties of robust estimations of the scale parameter are studied. It is noted that the median of absolute deviations and the modified estimation of the average Gini differences have asymptotically normal distributions and bounded influence functions, are B-robust estimations, and hence, unlike the estimation of the standard deviation, are protected from the presence of outliers in the sample. Results of comparison of estimations of the scale parameter are given for a Gaussian model with contamination. An adaptive variant of the modified estimation of the average Gini differences is considered.

Decomposition of mineral absorption bands using nonlinear least squares curve fitting: Application to Martian meteorites and CRISM data

NASA Astrophysics Data System (ADS)

Parente, Mario; Makarewicz, Heather D.; Bishop, Janice L.

2011-04-01

This study advances curve-fitting modeling of absorption bands of reflectance spectra and applies this new model to spectra of Martian meteorites ALH 84001 and EETA 79001 and data from the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM). This study also details a recently introduced automated parameter initialization technique. We assess the performance of this automated procedure by comparing it to the currently available initialization method and perform a sensitivity analysis of the fit results to variation in initial guesses. We explore the issues related to the removal of the continuum, offer guidelines for continuum removal when modeling the absorptions and explore different continuum-removal techniques. We further evaluate the suitability of curve fitting techniques using Gaussians/Modified Gaussians to decompose spectra into individual end-member bands. We show that nonlinear least squares techniques such as the Levenberg-Marquardt algorithm achieve comparable results to the MGM model ( Sunshine and Pieters, 1993; Sunshine et al., 1990) for meteorite spectra. Finally we use Gaussian modeling to fit CRISM spectra of pyroxene and olivine-rich terrains on Mars. Analysis of CRISM spectra of two regions show that the pyroxene-dominated rock spectra measured at Juventae Chasma were modeled well with low Ca pyroxene, while the pyroxene-rich spectra acquired at Libya Montes required both low-Ca and high-Ca pyroxene for a good fit.

Bayesian Analysis of Non-Gaussian Long-Range Dependent Processes

NASA Astrophysics Data System (ADS)

Graves, Timothy; Watkins, Nicholas; Franzke, Christian; Gramacy, Robert

2013-04-01

Recent studies [e.g. the Antarctic study of Franzke, J. Climate, 2010] have strongly suggested that surface temperatures exhibit long-range dependence (LRD). The presence of LRD would hamper the identification of deterministic trends and the quantification of their significance. It is well established that LRD processes exhibit stochastic trends over rather long periods of time. Thus, accurate methods for discriminating between physical processes that possess long memory and those that do not are an important adjunct to climate modeling. As we briefly review, the LRD idea originated at the same time as H-selfsimilarity, so it is often not realised that a model does not have to be H-self similar to show LRD [e.g. Watkins, GRL Frontiers, 2013]. We have used Markov Chain Monte Carlo algorithms to perform a Bayesian analysis of Auto-Regressive Fractionally-Integrated Moving-Average ARFIMA(p,d,q) processes, which are capable of modeling LRD. Our principal aim is to obtain inference about the long memory parameter, d, with secondary interest in the scale and location parameters. We have developed a reversible-jump method enabling us to integrate over different model forms for the short memory component. We initially assume Gaussianity, and have tested the method on both synthetic and physical time series. Many physical processes, for example the Faraday Antarctic time series, are significantly non-Gaussian. We have therefore extended this work by weakening the Gaussianity assumption, assuming an alpha-stable distribution for the innovations, and performing joint inference on d and alpha. Such a modified FARIMA(p,d,q) process is a flexible, initial model for non-Gaussian processes with long memory. We will present a study of the dependence of the posterior variance of the memory parameter d on the length of the time series considered. This will be compared with equivalent error diagnostics for other measures of d.

Computational Stimulation of the Basal Ganglia Neurons with Cost Effective Delayed Gaussian Waveforms

PubMed Central

Daneshzand, Mohammad; Faezipour, Miad; Barkana, Buket D.

2017-01-01

Deep brain stimulation (DBS) has compelling results in the desynchronization of the basal ganglia neuronal activities and thus, is used in treating the motor symptoms of Parkinson's disease (PD). Accurate definition of DBS waveform parameters could avert tissue or electrode damage, increase the neuronal activity and reduce energy cost which will prolong the battery life, hence avoiding device replacement surgeries. This study considers the use of a charge balanced Gaussian waveform pattern as a method to disrupt the firing patterns of neuronal cell activity. A computational model was created to simulate ganglia cells and their interactions with thalamic neurons. From the model, we investigated the effects of modified DBS pulse shapes and proposed a delay period between the cathodic and anodic parts of the charge balanced Gaussian waveform to desynchronize the firing patterns of the GPe and GPi cells. The results of the proposed Gaussian waveform with delay outperformed that of rectangular DBS waveforms used in in-vivo experiments. The Gaussian Delay Gaussian (GDG) waveforms achieved lower number of misses in eliciting action potential while having a lower amplitude and shorter length of delay compared to numerous different pulse shapes. The amount of energy consumed in the basal ganglia network due to GDG waveforms was dropped by 22% in comparison with charge balanced Gaussian waveforms without any delay between the cathodic and anodic parts and was also 60% lower than a rectangular charged balanced pulse with a delay between the cathodic and anodic parts of the waveform. Furthermore, by defining a Synchronization Level metric, we observed that the GDG waveform was able to reduce the synchronization of GPi neurons more effectively than any other waveform. The promising results of GDG waveforms in terms of eliciting action potential, desynchronization of the basal ganglia neurons and reduction of energy consumption can potentially enhance the performance of DBS devices. PMID:28848417

Computational Stimulation of the Basal Ganglia Neurons with Cost Effective Delayed Gaussian Waveforms.

PubMed

Daneshzand, Mohammad; Faezipour, Miad; Barkana, Buket D

2017-01-01

Deep brain stimulation (DBS) has compelling results in the desynchronization of the basal ganglia neuronal activities and thus, is used in treating the motor symptoms of Parkinson's disease (PD). Accurate definition of DBS waveform parameters could avert tissue or electrode damage, increase the neuronal activity and reduce energy cost which will prolong the battery life, hence avoiding device replacement surgeries. This study considers the use of a charge balanced Gaussian waveform pattern as a method to disrupt the firing patterns of neuronal cell activity. A computational model was created to simulate ganglia cells and their interactions with thalamic neurons. From the model, we investigated the effects of modified DBS pulse shapes and proposed a delay period between the cathodic and anodic parts of the charge balanced Gaussian waveform to desynchronize the firing patterns of the GPe and GPi cells. The results of the proposed Gaussian waveform with delay outperformed that of rectangular DBS waveforms used in in-vivo experiments. The Gaussian Delay Gaussian (GDG) waveforms achieved lower number of misses in eliciting action potential while having a lower amplitude and shorter length of delay compared to numerous different pulse shapes. The amount of energy consumed in the basal ganglia network due to GDG waveforms was dropped by 22% in comparison with charge balanced Gaussian waveforms without any delay between the cathodic and anodic parts and was also 60% lower than a rectangular charged balanced pulse with a delay between the cathodic and anodic parts of the waveform. Furthermore, by defining a Synchronization Level metric, we observed that the GDG waveform was able to reduce the synchronization of GPi neurons more effectively than any other waveform. The promising results of GDG waveforms in terms of eliciting action potential, desynchronization of the basal ganglia neurons and reduction of energy consumption can potentially enhance the performance of DBS devices.

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

PubMed

Spainhour, John Christian G; Janech, Michael G; Schwacke, John H; Velez, Juan Carlos Q; Ramakrishnan, Viswanathan

2014-01-01

Matrix assisted laser desorption/ionization time-of-flight (MALDI-TOF) coupled with stable isotope standards (SIS) has been used to quantify native peptides. This peptide quantification by MALDI-TOF approach has difficulties quantifying samples containing peptides with ion currents in overlapping spectra. In these overlapping spectra the currents sum together, which modify the peak heights and make normal SIS estimation problematic. An approach using Gaussian mixtures based on known physical constants to model the isotopic cluster of a known compound is proposed here. The characteristics of this approach are examined for single and overlapping compounds. The approach is compared to two commonly used SIS quantification methods for single compound, namely Peak Intensity method and Riemann sum area under the curve (AUC) method. For studying the characteristics of the Gaussian mixture method, Angiotensin II, Angiotensin-2-10, and Angiotenisn-1-9 and their associated SIS peptides were used. The findings suggest, Gaussian mixture method has similar characteristics as the two methods compared for estimating the quantity of isolated isotopic clusters for single compounds. All three methods were tested using MALDI-TOF mass spectra collected for peptides of the renin-angiotensin system. The Gaussian mixture method accurately estimated the native to labeled ratio of several isolated angiotensin peptides (5.2% error in ratio estimation) with similar estimation errors to those calculated using peak intensity and Riemann sum AUC methods (5.9% and 7.7%, respectively). For overlapping angiotensin peptides, (where the other two methods are not applicable) the estimation error of the Gaussian mixture was 6.8%, which is within the acceptable range. In summary, for single compounds the Gaussian mixture method is equivalent or marginally superior compared to the existing methods of peptide quantification and is capable of quantifying overlapping (convolved) peptides within the acceptable margin of error.

Comparison of microfacet BRDF model to modified Beckmann-Kirchhoff BRDF model for rough and smooth surfaces.

PubMed

Butler, Samuel D; Nauyoks, Stephen E; Marciniak, Michael A

2015-11-02

A popular class of BRDF models is the microfacet models, where geometric optics is assumed. In contrast, more complex physical optics models may more accurately predict the BRDF, but the calculation is more resource intensive. These seemingly disparate approaches are compared in detail for the rough and smooth surface approximations of the modified Beckmann-Kirchhoff BRDF model, assuming Gaussian surface statistics. An approximation relating standard Fresnel reflection with the semi-rough surface polarization term, Q, is presented for unpolarized light. For rough surfaces, the angular dependence of direction cosine space is shown to be identical to the angular dependence in the microfacet distribution function. For polished surfaces, the same comparison shows a breakdown in the microfacet models. Similarities and differences between microfacet BRDF models and the modified Beckmann-Kirchhoff model are identified. The rationale for the original Beckmann-Kirchhoff F(bk)(2) geometric term relative to both microfacet models and generalized Harvey-Shack model is presented. A modification to the geometric F(bk)(2) term in original Beckmann-Kirchhoff BRDF theory is proposed.

Application of Modified Particle Swarm Optimization Method for Parameter Extraction of 2-D TEC Mapping

NASA Astrophysics Data System (ADS)

Toker, C.; Gokdag, Y. E.; Arikan, F.; Arikan, O.

2012-04-01

Ionosphere is a very important part of Space Weather. Modeling and monitoring of ionospheric variability is a major part of satellite communication, navigation and positioning systems. Total Electron Content (TEC), which is defined as the line integral of the electron density along a ray path, is one of the parameters to investigate the ionospheric variability. Dual-frequency GPS receivers, with their world wide availability and efficiency in TEC estimation, have become a major source of global and regional TEC modeling. When Global Ionospheric Maps (GIM) of International GPS Service (IGS) centers (http://iono.jpl.nasa.gov/gim.html) are investigated, it can be observed that regional ionosphere along the midlatitude regions can be modeled as a constant, linear or a quadratic surface. Globally, especially around the magnetic equator, the TEC surfaces resemble twisted and dispersed single centered or double centered Gaussian functions. Particle Swarm Optimization (PSO) proved itself as a fast converging and an effective optimization tool in various diverse fields. Yet, in order to apply this optimization technique into TEC modeling, the method has to be modified for higher efficiency and accuracy in extraction of geophysical parameters such as model parameters of TEC surfaces. In this study, a modified PSO (mPSO) method is applied to regional and global synthetic TEC surfaces. The synthetic surfaces that represent the trend and small scale variability of various ionospheric states are necessary to compare the performance of mPSO over number of iterations, accuracy in parameter estimation and overall surface reconstruction. The Cramer-Rao bounds for each surface type and model are also investigated and performance of mPSO are tested with respect to these bounds. For global models, the sample points that are used in optimization are obtained using IGS receiver network. For regional TEC models, regional networks such as Turkish National Permanent GPS Network (TNPGN-Active) receiver sites are used. The regional TEC models are grouped into constant (one parameter), linear (two parameters), and quadratic (six parameters) surfaces which are functions of latitude and longitude. Global models require seven parameters for single centered Gaussian and 13 parameters for double centered Gaussian function. The error criterion is the normalized percentage error for both the surface and the parameters. It is observed that mPSO is very successful in parameter extraction of various regional and global models. The normalized reconstruction error varies from 10-4 for constant surfaces to 10-3 for quadratic surfaces in regional models, sampled with regional networks. Even for the cases of a severe geomagnetic storm that affects measurements globally, with IGS network, the reconstruction error is on the order of 10-1 even though individual parameters have higher normalized errors. The modified PSO technique proved itself to be a useful tool for parameter extraction of more complicated TEC models. This study is supported by TUBITAK EEEAG under Grant No: 109E055.

On the Pollutant Plume Dispersion in the Urban Canopy Layer over 2D Idealized Street Canyons: A Large-Eddy Simulation Approach

NASA Astrophysics Data System (ADS)

Wong, Colman C. C.; Liu, Chun-Ho

2010-05-01

Anthropogenic emissions are the major sources of air pollutants in urban areas. To improve the air quality in dense and mega cities, a simple but reliable prediction method is necessary. In the last five decades, the Gaussian pollutant plume model has been widely used for the estimation of air pollutant distribution in the atmospheric boundary layer (ABL) in an operational manner. Whereas, it was originally designed for rural areas with rather open and flat terrain. The recirculating flows below the urban canopy layer substantially modify the near-ground urban wind environment and so does the pollutant distribution. Though the plume height and dispersion are often adjusted empirically, the accuracy of applying the Gaussian pollutant plume model in urban areas, of which the bottom of the flow domain consists of numerous inhomogeneous buildings, is unclear. To elucidate the flow and pollutant transport, as well as to demystify the uncertainty of employing the Gaussian pollutant plume model over urban roughness, this study was performed to examine how the Gaussian-shape pollutant plume in the urban canopy layer is modified by the idealized two-dimensional (2D) street canyons at the bottom of the ABL. The specific objective is to develop a parameterization so that the geometric effects of urban morphology on the operational pollutant plume dispersion models could be taken into account. Because atmospheric turbulence is the major means of pollutant removal from street canyons to the ABL, the large-eddy simulation (LES) was adopted to calculate explicitly the flows and pollutant transport in the urban canopy layer. The subgrid-scale (SGS) turbulent kinetic energy (TKE) conservation was used to model the SGS processes in the incompressible, isothermal conditions. The computational domain consists of 12 identical idealized street canyons of unity aspect ratio which were placed evenly in the streamwise direction. Periodic boundary conditions (BCs) for the flow were applied in the horizontal and the spanwise directions. The prevalent wind was driven by a background pressure gradient in the roughness sublayer only, no background force was prescribed inside the street canyons. While the periodic BC of pollutant was used in the spanwise direction, zero pollutant and an open BC were applied, respectively, at the inflow and outflow of the streamwise extent to avoid pollutant being reflected back into the computational domain. The ground of the first street canyon was assigned as the pollutant source on which a BC of constant pollutant concentration was prescribed. The LES results showed that, in the neutrally stratified ABL, the pollutant distribution in the urban canopy layer resembled the Gaussian plume shape in general even recirculating flows were observed in the street canyons. The roof-level horizontal profile of pollutant concentration in the streamwise direction showed that the sharp drop on the leeward side of each street canyon was likely caused by the air and pollutant entrainments. On the windward side of each street canyon, a mild increase in pollutant concentration was observed that did not follow the Gaussian plume closely. Those deviations extended to a certain height over the roof level of the street canyons. It in turn suggests that the Gaussian pollutant plume model should be applied with caution in the urban canopy layer in the vicinity over urban roughness. To further analyze the effects of urban roughness on the plume dispersion in detail, a few LES calculations with different aspect ratios are currently being undertaken so as to compare with the current LES results.

Weak constrained localized ensemble transform Kalman filter for radar data assimilation

NASA Astrophysics Data System (ADS)

Janjic, Tijana; Lange, Heiner

2015-04-01

The applications on convective scales require data assimilation with a numerical model with single digit horizontal resolution in km and time evolving error covariances. The ensemble Kalman filter (EnKF) algorithm incorporates these two requirements. However, some challenges for the convective scale applications remain unresolved when using the EnKF approach. These include a need on convective scale to estimate fields that are nonnegative (as rain, graupel, snow) and use of data sets as radar reflectivity or cloud products that have the same property. What underlines these examples are errors that are non-Gaussian in nature causing a problem with EnKF, which uses Gaussian error assumptions to produce the estimates from the previous forecast and the incoming data. Since the proper estimates of hydrometeors are crucial for prediction on convective scales, question arises whether EnKF method can be modified to improve these estimates and whether there is a way of optimizing use of radar observations to initialize NWP models due to importance of this data set for prediction of connective storms. In order to deal with non-Gaussian errors different approaches can be taken in the EnKF framework. For example, variables can be transformed by assuming the relevant state variables follow an appropriate pre-specified non-Gaussian distribution, such as the lognormal and truncated Gaussian distribution or, more generally, by carrying out a parameterized change of state variables known as Gaussian anamorphosis. In a recent work by Janjic et al. 2014, it was shown on a simple example how conservation of mass could be beneficial for assimilation of positive variables. The method developed in the paper outperformed the EnKF as well as the EnKF with the lognormal change of variables. As argued in the paper the reason for this, is that each of these methods preserves mass (EnKF) or positivity (lognormal EnKF) but not both. Only once both positivity and mass were preserved in a new algorithm, the good estimates of the fields were obtained. The alternative to strong constraint formulation in Janjic et al. 2014 is to modify LETKF algorithm to take into the account physical properties only approximately. In this work we will include the weak constraints in the LETKF algorithm for estimation of hydrometers. The benefit on prediction is illustrated in an idealized setup (Lange and Craig, 2013). This setup uses the non hydrostatic COSMO model with a 2 km horizontal resolution, and the LETKF as implemented in KENDA (Km-scale Ensemble Data Assimilation) system of German Weather Service (Reich et al. 2011). Due to the Gaussian assumptions that underline the LETKF algorithm, the analyses of water species will become negative in some grid points of the COSMO model. These values are set to zero currently in KENDA after the LETKF analysis step. The tests done within this setup show that such a procedure introduces a bias in the analysis ensemble with respect to the true, that increases in time due to the cycled data assimilation. The benefits of including the constraints in LETKF are illustrated on the bias values during assimilation and the prediction.

Non-Gaussianity in a quasiclassical electronic circuit

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi J.; Hayakawa, Hisao

2017-05-01

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

Gaussian processes with optimal kernel construction for neuro-degenerative clinical onset prediction

NASA Astrophysics Data System (ADS)

Canas, Liane S.; Yvernault, Benjamin; Cash, David M.; Molteni, Erika; Veale, Tom; Benzinger, Tammie; Ourselin, Sébastien; Mead, Simon; Modat, Marc

2018-02-01

Gaussian Processes (GP) are a powerful tool to capture the complex time-variations of a dataset. In the context of medical imaging analysis, they allow a robust modelling even in case of highly uncertain or incomplete datasets. Predictions from GP are dependent of the covariance kernel function selected to explain the data variance. To overcome this limitation, we propose a framework to identify the optimal covariance kernel function to model the data.The optimal kernel is defined as a composition of base kernel functions used to identify correlation patterns between data points. Our approach includes a modified version of the Compositional Kernel Learning (CKL) algorithm, in which we score the kernel families using a new energy function that depends both the Bayesian Information Criterion (BIC) and the explained variance score. We applied the proposed framework to model the progression of neurodegenerative diseases over time, in particular the progression of autosomal dominantly-inherited Alzheimer's disease, and use it to predict the time to clinical onset of subjects carrying genetic mutation.

Stochastic transfer of polarized radiation in finite cloudy atmospheric media with reflective boundaries

NASA Astrophysics Data System (ADS)

Sallah, M.

2014-03-01

The problem of monoenergetic radiative transfer in a finite planar stochastic atmospheric medium with polarized (vector) Rayleigh scattering is proposed. The solution is presented for an arbitrary absorption and scattering cross sections. The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as reflectivity and transmissivity, for an arbitrary correlation function. A modified Gaussian probability distribution function is also used to average the solution in order to exclude the probable negative values of the optical variable. Pomraning-Eddington approximation is used, at first, to obtain the deterministic analytical solution for both the total intensity and the difference function used to describe the polarized radiation. The problem is treated with specular reflecting boundaries and angular-dependent externally incident flux upon the medium from one side and with no flux from the other side. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the average reflectivity and average transmissivity are obtained for both Gaussian and modified Gaussian probability density functions at the different degrees of polarization.

Construction of cosmic string induced temperature anisotropy maps with CMBFAST and statistical analysis

NASA Astrophysics Data System (ADS)

Simatos, N.; Perivolaropoulos, L.

2001-01-01

We use the publicly available code CMBFAST, as modified by Pogosian and Vachaspati, to simulate the effects of wiggly cosmic strings on the cosmic microwave background (CMB). Using the modified CMBFAST code, which takes into account vector modes and models wiggly cosmic strings by the one-scale model, we go beyond the angular power spectrum to construct CMB temperature maps with a resolution of a few degrees. The statistics of these maps are then studied using conventional and recently proposed statistical tests optimized for the detection of hidden temperature discontinuities induced by the Gott-Kaiser-Stebbins effect. We show, however, that these realistic maps cannot be distinguished in a statistically significant way from purely Gaussian maps with an identical power spectrum.

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

NASA Astrophysics Data System (ADS)

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

1995-06-01

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

Random wandering of laser beams with orbital angular momentum during propagation through atmospheric turbulence.

PubMed

Aksenov, Valerii P; Kolosov, Valeriy V; Pogutsa, Cheslav E

2014-06-10

The propagation of laser beams having orbital angular momenta (OAM) in the turbulent atmosphere is studied numerically. The variance of random wandering of these beams is investigated with the use of the Monte Carlo technique. It is found that, among various types of vortex laser beams, such as the Laguerre-Gaussian (LG) beam, modified Bessel-Gaussian beam, and hypergeometric Gaussian beam, having identical initial effective radii and OAM, the LG beam occupying the largest effective volume in space is the most stable one.

Black hole field theory with a firewall in two spacetime dimensions

NASA Astrophysics Data System (ADS)

Ho, C. T. Marco; Su, Daiqin; Mann, Robert B.; Ralph, Timothy C.

2016-10-01

We propose that the vacuum state of a scalar field around a black hole is a modified Unruh vacuum. In (1 +1 ) dimensions, we show that a free-faller close to such an horizon can be modeled as an inertial observer in a modified Minkowski vacuum. The modification allows for information-leaking correlations at high frequencies. Using a Gaussian detector centered at k0, we find that the expectation value of the number operator for a detector crossing the horizon is proportional to 1 /|k0|, implying that the free-faller will observe unbounded numbers of high-energy photons, i.e. a firewall.

Non-Gaussian analysis of diffusion weighted imaging in head and neck at 3T: a pilot study in patients with nasopharyngeal carcinoma.

PubMed

Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S P; Bhatia, Kunwar S; Wang, Yi-Xiang J; Ahuja, Anil T; King, Ann D

2014-01-01

To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm(2). DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization.

Design of a candidate flutter suppression control law for DAST ARW-2. [Drones for Aerodynamic and Structural Testing Aeroelastic Research Wing

NASA Technical Reports Server (NTRS)

Adams, W. M., Jr.; Tiffany, S. H.

1983-01-01

A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQG (linear quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.

A Gaussian Approximation Potential for Silicon

NASA Astrophysics Data System (ADS)

Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor

We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.

New Finger Biometric Method Using Near Infrared Imaging

PubMed Central

Lee, Eui Chul; Jung, Hyunwoo; Kim, Daeyeoul

2011-01-01

In this paper, we propose a new finger biometric method. Infrared finger images are first captured, and then feature extraction is performed using a modified Gaussian high-pass filter through binarization, local binary pattern (LBP), and local derivative pattern (LDP) methods. Infrared finger images include the multimodal features of finger veins and finger geometries. Instead of extracting each feature using different methods, the modified Gaussian high-pass filter is fully convolved. Therefore, the extracted binary patterns of finger images include the multimodal features of veins and finger geometries. Experimental results show that the proposed method has an error rate of 0.13%. PMID:22163741

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

NASA Astrophysics Data System (ADS)

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

1998-03-01

The macrodispersion of an inert solute in a 2-D heterogeneous porous media is estimated numerically in a series of fields of varying heterogeneity. Four different random function (RF) models are used to model log-transmissivity (ln T) spatial variability, and for each of these models, ln T variance is varied from 0.1 to 2.0. The four RF models share the same univariate Gaussian histogram and the same isotropic covariance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme values (both high and low) are spatially uncorrelated. The other three models are non-multi-Gaussian: model B with high connectivity of high extreme values, model C with high connectivity of low extreme values, and model D with high connectivities of both high and low extreme values. Residence time distributions (RTDs) and macrodispersivities (longitudinal and transverse) are computed on ln T fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RTDs and macrodispersivities for the multi-Gaussian model are in good agreement with analytically derived values using first-order theories for log-transmissivity variance up to 2.0. The results from the non-multi-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when ln T variance is small. RTDs in non-multi-Gaussian realizations with high connectivity at high extreme values display earlier breakthrough than in multi-Gaussian realizations, whereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian realizations are, in general, larger than in the multi-Gaussian ones, while transverse macrodispersivities in the non-multi-Gaussian realizations can be larger or smaller than in the multi-Gaussian ones depending on the type of connectivity at extreme values. Comparing the numerical results for different flow directions, it is confirmed that macrodispersivities in multi-Gaussian realizations with isotropic spatial correlation are not flow direction-dependent. Macrodispersivities in the non-multi-Gaussian realizations, however, are flow direction-dependent although the covariance of ln T is isotropic (the same for all four models). It is important to account for high connectivities at extreme transmissivity values, a likely situation in some geological formations. Some of the discrepancies between first-order-based analytical results and field-scale tracer test data may be due to the existence of highly connected paths of extreme conductivity values.

Non-Gaussian Analysis of Diffusion Weighted Imaging in Head and Neck at 3T: A Pilot Study in Patients with Nasopharyngeal Carcinoma

PubMed Central

Yuan, Jing; Yeung, David Ka Wai; Mok, Greta S. P.; Bhatia, Kunwar S.; Wang, Yi-Xiang J.; Ahuja, Anil T.; King, Ann D.

2014-01-01

Purpose To technically investigate the non-Gaussian diffusion of head and neck diffusion weighted imaging (DWI) at 3 Tesla and compare advanced non-Gaussian diffusion models, including diffusion kurtosis imaging (DKI), stretched-exponential model (SEM), intravoxel incoherent motion (IVIM) and statistical model in the patients with nasopharyngeal carcinoma (NPC). Materials and Methods After ethics approval was granted, 16 patients with NPC were examined using DWI performed at 3T employing an extended b-value range from 0 to 1500 s/mm2. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models on primary tumor, metastatic node, spinal cord and muscle. Non-Gaussian parameter maps were generated and compared to apparent diffusion coefficient (ADC) maps in NPC. Results Diffusion in NPC exhibited non-Gaussian behavior at the extended b-value range. Non-Gaussian models achieved significantly better fitting of DWI signal than the mono-exponential model. Non-Gaussian diffusion coefficients were substantially different from mono-exponential ADC both in magnitude and histogram distribution. Conclusion Non-Gaussian diffusivity in head and neck tissues and NPC lesions could be assessed by using non-Gaussian diffusion models. Non-Gaussian DWI analysis may reveal additional tissue properties beyond ADC and holds potentials to be used as a complementary tool for NPC characterization. PMID:24466318

Edgeworth streaming model for redshift space distortions

NASA Astrophysics Data System (ADS)

Uhlemann, Cora; Kopp, Michael; Haugg, Thomas

2015-09-01

We derive the Edgeworth streaming model (ESM) for the redshift space correlation function starting from an arbitrary distribution function for biased tracers of dark matter by considering its two-point statistics and show that it reduces to the Gaussian streaming model (GSM) when neglecting non-Gaussianities. We test the accuracy of the GSM and ESM independent of perturbation theory using the Horizon Run 2 N -body halo catalog. While the monopole of the redshift space halo correlation function is well described by the GSM, higher multipoles improve upon including the leading order non-Gaussian correction in the ESM: the GSM quadrupole breaks down on scales below 30 Mpc /h whereas the ESM stays accurate to 2% within statistical errors down to 10 Mpc /h . To predict the scale-dependent functions entering the streaming model we employ convolution Lagrangian perturbation theory (CLPT) based on the dust model and local Lagrangian bias. Since dark matter halos carry an intrinsic length scale given by their Lagrangian radius, we extend CLPT to the coarse-grained dust model and consider two different smoothing approaches operating in Eulerian and Lagrangian space, respectively. The coarse graining in Eulerian space features modified fluid dynamics different from dust while the coarse graining in Lagrangian space is performed in the initial conditions with subsequent single-streaming dust dynamics, implemented by smoothing the initial power spectrum in the spirit of the truncated Zel'dovich approximation. Finally, we compare the predictions of the different coarse-grained models for the streaming model ingredients to N -body measurements and comment on the proper choice of both the tracer distribution function and the smoothing scale. Since the perturbative methods we considered are not yet accurate enough on small scales, the GSM is sufficient when applied to perturbation theory.

MANCOVA for one way classification with homogeneity of regression coefficient vectors

NASA Astrophysics Data System (ADS)

Mokesh Rayalu, G.; Ravisankar, J.; Mythili, G. Y.

2017-11-01

The MANOVA and MANCOVA are the extensions of the univariate ANOVA and ANCOVA techniques to multidimensional or vector valued observations. The assumption of a Gaussian distribution has been replaced with the Multivariate Gaussian distribution for the vectors data and residual term variables in the statistical models of these techniques. The objective of MANCOVA is to determine if there are statistically reliable mean differences that can be demonstrated between groups later modifying the newly created variable. When randomization assignment of samples or subjects to groups is not possible, multivariate analysis of covariance (MANCOVA) provides statistical matching of groups by adjusting dependent variables as if all subjects scored the same on the covariates. In this research article, an extension has been made to the MANCOVA technique with more number of covariates and homogeneity of regression coefficient vectors is also tested.

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Stability of infinite derivative Abelian Higgs models

NASA Astrophysics Data System (ADS)

Ghoshal, Anish; Mazumdar, Anupam; Okada, Nobuchika; Villalba, Desmond

2018-04-01

Motivated by the stringy effects by modifying the local kinetic term of an Abelian Higgs field by the Gaussian kinetic term, we show that the Higgs field does not possess any instability; the Yukawa coupling between the scalar and the fermion, the gauge coupling, and the self interaction of the Higgs yields exponentially suppressed running at high energies, showing that such class of theory never suffers from vacuum instability. We briefly discuss its implications for the early Universe cosmology.

A deconvolution extraction method for 2D multi-object fibre spectroscopy based on the regularized least-squares QR-factorization algorithm

NASA Astrophysics Data System (ADS)

Yu, Jian; Yin, Qian; Guo, Ping; Luo, A.-li

2014-09-01

This paper presents an efficient method for the extraction of astronomical spectra from two-dimensional (2D) multifibre spectrographs based on the regularized least-squares QR-factorization (LSQR) algorithm. We address two issues: we propose a modified Gaussian point spread function (PSF) for modelling the 2D PSF from multi-emission-line gas-discharge lamp images (arc images), and we develop an efficient deconvolution method to extract spectra in real circumstances. The proposed modified 2D Gaussian PSF model can fit various types of 2D PSFs, including different radial distortion angles and ellipticities. We adopt the regularized LSQR algorithm to solve the sparse linear equations constructed from the sparse convolution matrix, which we designate the deconvolution spectrum extraction method. Furthermore, we implement a parallelized LSQR algorithm based on graphics processing unit programming in the Compute Unified Device Architecture to accelerate the computational processing. Experimental results illustrate that the proposed extraction method can greatly reduce the computational cost and memory use of the deconvolution method and, consequently, increase its efficiency and practicability. In addition, the proposed extraction method has a stronger noise tolerance than other methods, such as the boxcar (aperture) extraction and profile extraction methods. Finally, we present an analysis of the sensitivity of the extraction results to the radius and full width at half-maximum of the 2D PSF.

NGMIX: Gaussian mixture models for 2D images

NASA Astrophysics Data System (ADS)

Sheldon, Erin

2015-08-01

NGMIX implements Gaussian mixture models for 2D images. Both the PSF profile and the galaxy are modeled using mixtures of Gaussians. Convolutions are thus performed analytically, resulting in fast model generation as compared to methods that perform the convolution in Fourier space. For the galaxy model, NGMIX supports exponential disks and de Vaucouleurs and Sérsic profiles; these are implemented approximately as a sum of Gaussians using the fits from Hogg & Lang (2013). Additionally, any number of Gaussians can be fit, either completely free or constrained to be cocentric and co-elliptical.

Investigation of non-Gaussian effects in the Brazilian option market

NASA Astrophysics Data System (ADS)

Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.

2018-04-01

An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.

A non-gaussian model of continuous atmospheric turbulence for use in aircraft design

NASA Technical Reports Server (NTRS)

Reeves, P. M.; Joppa, R. G.; Ganzer, V. M.

1976-01-01

A non-Gaussian model of atmospheric turbulence is presented and analyzed. The model is restricted to the regions of the atmosphere where the turbulence is steady or continuous, and the assumptions of homogeneity and stationarity are justified. Also spatial distribution of turbulence is neglected, so the model consists of three independent, stationary stochastic processes which represent the vertical, lateral, and longitudinal gust components. The non-Gaussian and Gaussian models are compared with experimental data, and it is shown that the Gaussian model underestimates the number of high velocity gusts which occur in the atmosphere, while the non-Gaussian model can be adjusted to match the observed high velocity gusts more satisfactorily. Application of the proposed model to aircraft response is investigated, with particular attention to the response power spectral density, the probability distribution, and the level crossing frequency. A numerical example is presented which illustrates the application of the non-Gaussian model to the study of an aircraft autopilot system. Listings and sample results of a number of computer programs used in working with the model are included.

Truncated Gaussians as tolerance sets

NASA Technical Reports Server (NTRS)

Cozman, Fabio; Krotkov, Eric

1994-01-01

This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.

A general relativistic rotating evolutionary universe—Part II

NASA Astrophysics Data System (ADS)

Berman, Marcelo Samuel

2008-06-01

As a sequel to Berman (Astrophys. Space Sci., 2008b), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker’s metric has been employed with proper-time, in its standard applications; the generalised Gaussian metric implies in the use of a non-constant temporal metric coefficient modifying Robertson-Walker’s standard form. Experimental predictions are made.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals.

PubMed

Golze, Dorothea; Benedikter, Niels; Iannuzzi, Marcella; Wilhelm, Jan; Hutter, Jürg

2017-01-21

An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb, and Gaussian-type operators, which occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both integrals and their derivatives. In particular, our method is increasingly efficient for large angular momenta and highly contracted basis sets.

Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals

NASA Astrophysics Data System (ADS)

Golze, Dorothea; Benedikter, Niels; Iannuzzi, Marcella; Wilhelm, Jan; Hutter, Jürg

2017-01-01

An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb, and Gaussian-type operators, which occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both integrals and their derivatives. In particular, our method is increasingly efficient for large angular momenta and highly contracted basis sets.

The area of isodensity contours in cosmological models and galaxy surveys

NASA Technical Reports Server (NTRS)

Ryden, Barbara S.; Melott, Adrian L.; Craig, David A.; Gott, J. Richard, III; Weinberg, David H.

1989-01-01

The contour crossing statistic, defined as the mean number of times per unit length that a straight line drawn through the field crosses a given contour, is applied to model density fields and to smoothed samples of galaxies. Models in which the matter is in a bubble structure, in a filamentary net, or in clusters can be distinguished from Gaussian density distributions. The shape of the contour crossing curve in the initially Gaussian fields considered remains Gaussian after gravitational evolution and biasing, as long as the smoothing length is longer than the mass correlation length. With a smoothing length of 5/h Mpc, models containing cosmic strings are indistinguishable from Gaussian distributions. Cosmic explosion models are significantly non-Gaussian, having a bubbly structure. Samples from the CfA survey and the Haynes and Giovanelli (1986) survey are more strongly non-Gaussian at a smoothing length of 6/h Mpc than any of the models examined. At a smoothing length of 12/h Mpc, the Haynes and Giovanelli sample appears Gaussian.

Connections between Graphical Gaussian Models and Factor Analysis

ERIC Educational Resources Information Center

Salgueiro, M. Fatima; Smith, Peter W. F.; McDonald, John W.

2010-01-01

Connections between graphical Gaussian models and classical single-factor models are obtained by parameterizing the single-factor model as a graphical Gaussian model. Models are represented by independence graphs, and associations between each manifest variable and the latent factor are measured by factor partial correlations. Power calculations…

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

PubMed

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

2014-06-16

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

Comparisons of Non-Gaussian Statistical Models in DNA Methylation Analysis

PubMed Central

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

2014-01-01

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

Detailed noise statistics for an optically preamplified direct detection receiver

NASA Astrophysics Data System (ADS)

Danielsen, Soeren Lykke; Mikkelsen, Benny; Durhuus, Terji; Joergensen, Carsten; Stubkjaer, Kristian E.

We describe the exact statistics of an optically preamplified direct detection receiver by means of the moment generating function. The theory allows an arbitrary shaped electrical filter in the receiver circuit. The moment generating function (MGF) allows for a precise calculation of the error rate by using the inverse Fast Fourier transform (FFT). The exact results are compared with the usual Gaussian approximation (GA), the saddlepoint approximation (SAP) and the modified Chernoff bound (MCB). This comparison shows that the noise is not Gaussian distributed for all values of the optical amplifier gain. In the region from 20-30 dB gain, calculations shows that the GA underestimates the receiver sensitivity while the SAP is very close to the results of our exact model. Using the MGF derived in the article we then find the optimal bandwidth of the electrical filter in the receiver circuit and calculate the sensitivity degradation due to inter symbol interference (ISI).

Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-01-28

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modi ed Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in ow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then a modelbased feedback controller is designed for the reduced order model using linear quadratic regulators (LQR). Finally, a linear quadratic gaussian (LQG) controller, which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHWmore » equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.« less

A comparative assessment of preclinical chemotherapeutic response of tumors using quantitative non-Gaussian diffusion MRI

PubMed Central

Xu, Junzhong; Li, Ke; Smith, R. Adam; Waterton, John C.; Zhao, Ping; Ding, Zhaohua; Does, Mark D.; Manning, H. Charles; Gore, John C.

2016-01-01

Background Diffusion-weighted MRI (DWI) signal attenuation is often not mono-exponential (i.e. non-Gaussian diffusion) with stronger diffusion weighting. Several non-Gaussian diffusion models have been developed and may provide new information or higher sensitivity compared with the conventional apparent diffusion coefficient (ADC) method. However the relative merits of these models to detect tumor therapeutic response is not fully clear. Methods Conventional ADC, and three widely-used non-Gaussian models, (bi-exponential, stretched exponential, and statistical model), were implemented and compared for assessing SW620 human colon cancer xenografts responding to barasertib, an agent known to induce apoptosis via polyploidy. Bayesian Information Criterion (BIC) was used for model selection among all three non-Gaussian models. Results All of tumor volume, histology, conventional ADC, and three non-Gaussian DWI models could show significant differences between control and treatment groups after four days of treatment. However, only the non-Gaussian models detected significant changes after two days of treatment. For any treatment or control group, over 65.7% of tumor voxels indicate the bi-exponential model is strongly or very strongly preferred. Conclusion Non-Gaussian DWI model-derived biomarkers are capable of detecting tumor earlier chemotherapeutic response of tumors compared with conventional ADC and tumor volume. The bi-exponential model provides better fitting compared with statistical and stretched exponential models for the tumor and treatment models used in the current work. PMID:27919785

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

NASA Technical Reports Server (NTRS)

Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet

2015-01-01

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

A modified estimation distribution algorithm based on extreme elitism.

PubMed

Gao, Shujun; de Silva, Clarence W

2016-12-01

An existing estimation distribution algorithm (EDA) with univariate marginal Gaussian model was improved by designing and incorporating an extreme elitism selection method. This selection method highlighted the effect of a few top best solutions in the evolution and advanced EDA to form a primary evolution direction and obtain a fast convergence rate. Simultaneously, this selection can also keep the population diversity to make EDA avoid premature convergence. Then the modified EDA was tested by means of benchmark low-dimensional and high-dimensional optimization problems to illustrate the gains in using this extreme elitism selection. Besides, no-free-lunch theorem was implemented in the analysis of the effect of this new selection on EDAs. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Non-Gaussian Analysis of Turbulent Boundary Layer Fluctuating Pressure on Aircraft Skin Panels

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Steinwolf, Alexander

2005-01-01

The purpose of the study is to investigate the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the outer sidewall of a supersonic transport aircraft and to approximate these PDFs by analytical models. Experimental flight results show that the fluctuating pressure PDFs differ from the Gaussian distribution even for standard smooth surface conditions. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations in front of forward-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. There is a certain spatial pattern of the skewness and kurtosis behavior depending on the distance upstream from the step. All characteristics related to non-Gaussian behavior are highly dependent upon the distance from the step and the step height, less dependent on aircraft speed, and not dependent on the fuselage location. A Hermite polynomial transform model and a piecewise-Gaussian model fit the flight data well both for the smooth and stepped conditions. The piecewise-Gaussian approximation can be additionally regarded for convenience in usage after the model is constructed.

Short-term prediction of chaotic time series by using RBF network with regression weights.

PubMed

Rojas, I; Gonzalez, J; Cañas, A; Diaz, A F; Rojas, F J; Rodriguez, M

2000-10-01

We propose a framework for constructing and training a radial basis function (RBF) neural network. The structure of the gaussian functions is modified using a pseudo-gaussian function (PG) in which two scaling parameters sigma are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater flexibility with respect to function approximation. We propose a modified PG-BF (pseudo-gaussian basis function) network in which the regression weights are used to replace the constant weights in the output layer. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit and also to detect and remove inactive units. A salient feature of the network systems is that the method used for calculating the overall output is the weighted average of the output associated with each receptive field. The superior performance of the proposed PG-BF system over the standard RBF are illustrated using the problem of short-term prediction of chaotic time series.

Mechanical analysis of non-uniform bi-directional functionally graded intelligent micro-beams using modified couple stress theory

NASA Astrophysics Data System (ADS)

Bakhshi Khaniki, Hossein; Rajasekaran, Sundaramoorthy

2018-05-01

This study develops a comprehensive investigation on mechanical behavior of non-uniform bi-directional functionally graded beam sensors in the framework of modified couple stress theory. Material variation is modelled through both length and thickness directions using power-law, sigmoid and exponential functions. Moreover, beam is assumed with linear, exponential and parabolic cross-section variation through the length using power-law and sigmoid varying functions. Using these assumptions, a general model for microbeams is presented and formulated by employing Hamilton’s principle. Governing equations are solved using a mixed finite element method with Lagrangian interpolation technique, Gaussian quadrature method and Wilson’s Lagrangian multiplier method. It is shown that by using bi-directional functionally graded materials in nonuniform microbeams, mechanical behavior of such structures could be affected noticeably and scale parameter has a significant effect in changing the rigidity of nonuniform bi-directional functionally graded beams.

Optical trapping forces of a focused azimuthally polarized Bessel-Gaussian beam on a double-layered sphere

NASA Astrophysics Data System (ADS)

Wu, F. P.; Zhang, B.; Liu, Z. L.; Tang, Y.; Zhang, N.

2017-12-01

We calculate the trapping forces exerted by a highly focused Bessel-Gaussian beam on a double-layered sphere by means of vector diffraction integral, T-matrix method and Maxwell stress tensor integral. The Bessel-Gaussian beam is azimuthally polarized. Numerical results predicate that the double-layered sphere with air core can be stably trapped in three-dimensions. The trapping forces and efficiencies are dependent on the refraction index and size of the inner core. The trapping efficiency can be optimized by choosing the refraction indices of the inner core and outer layer. Our computational method can be easily modified for other laser beams and particles with arbitrary geometries and multilayers.

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

NASA Astrophysics Data System (ADS)

Song, Jong-Won; Hirao, Kimihiko

2015-07-01

We previously developed an efficient screened hybrid functional called Gaussian-Perdew-Burke-Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals. We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

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

Song, Jong-Won; Hirao, Kimihiko, E-mail: hirao@riken.jp

2015-07-14

We previously developed an efficient screened hybrid functional called Gaussian-Perdew–Burke–Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals.more » We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.« less

Temporal self-splitting of optical pulses

NASA Astrophysics Data System (ADS)

Ding, Chaoliang; Koivurova, Matias; Turunen, Jari; Pan, Liuzhan

2018-05-01

We present mathematical models for temporally and spectrally partially coherent pulse trains with Laguerre-Gaussian and Hermite-Gaussian Schell-model statistics as extensions of the standard Gaussian Schell model for pulse trains. We derive propagation formulas of both classes of pulsed fields in linearly dispersive media and in temporal optical systems. It is found that, in general, both types of fields exhibit time-domain self-splitting upon propagation. The Laguerre-Gaussian model leads to multiply peaked pulses, while the Hermite-Gaussian model leads to doubly peaked pulses, in the temporal far field (in dispersive media) or at the Fourier plane of a temporal system. In both model fields the character of the self-splitting phenomenon depends both on the degree of temporal and spectral coherence and on the power spectrum of the field.

Linear velocity fields in non-Gaussian models for large-scale structure

NASA Technical Reports Server (NTRS)

Scherrer, Robert J.

1992-01-01

Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.

Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

NASA Astrophysics Data System (ADS)

Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

2016-09-01

The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Arbitrage with fractional Gaussian processes

NASA Astrophysics Data System (ADS)

Zhang, Xili; Xiao, Weilin

2017-04-01

While the arbitrage opportunity in the Black-Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black-Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black-Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann-Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.

How Many Separable Sources? Model Selection In Independent Components Analysis

PubMed Central

Woods, Roger P.; Hansen, Lars Kai; Strother, Stephen

2015-01-01

Unlike mixtures consisting solely of non-Gaussian sources, mixtures including two or more Gaussian components cannot be separated using standard independent components analysis methods that are based on higher order statistics and independent observations. The mixed Independent Components Analysis/Principal Components Analysis (mixed ICA/PCA) model described here accommodates one or more Gaussian components in the independent components analysis model and uses principal components analysis to characterize contributions from this inseparable Gaussian subspace. Information theory can then be used to select from among potential model categories with differing numbers of Gaussian components. Based on simulation studies, the assumptions and approximations underlying the Akaike Information Criterion do not hold in this setting, even with a very large number of observations. Cross-validation is a suitable, though computationally intensive alternative for model selection. Application of the algorithm is illustrated using Fisher's iris data set and Howells' craniometric data set. Mixed ICA/PCA is of potential interest in any field of scientific investigation where the authenticity of blindly separated non-Gaussian sources might otherwise be questionable. Failure of the Akaike Information Criterion in model selection also has relevance in traditional independent components analysis where all sources are assumed non-Gaussian. PMID:25811988

Nonlinear estimation theory applied to the interplanetary orbit determination problem.

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Choe, C. Y.

1972-01-01

Martingale theory and appropriate smoothing properties of Loeve (1953) have been used to develop a modified Gaussian second-order filter. The performance of the filter is evaluated through numerical simulation of a Jupiter flyby mission. The observations used in the simulation are on-board measurements of the angle between Jupiter and a fixed star taken at discrete time intervals. In the numerical study, the influence of each of the second-order terms is evaluated. Five filter algorithms are used in the simulations. Four of the filters are the modified Gaussian second-order filter and three approximations derived by neglecting one or more of the second-order terms in the equations. The fifth filter is the extended Kalman-Bucy filter which is obtained by neglecting all of the second-order terms.

Gaussian fitting for carotid and radial artery pressure waveforms: comparison between normal subjects and heart failure patients.

PubMed

Liu, Chengyu; Zheng, Dingchang; Zhao, Lina; Liu, Changchun

2014-01-01

It has been reported that Gaussian functions could accurately and reliably model both carotid and radial artery pressure waveforms (CAPW and RAPW). However, the physiological relevance of the characteristic features from the modeled Gaussian functions has been little investigated. This study thus aimed to determine characteristic features from the Gaussian functions and to make comparisons of them between normal subjects and heart failure patients. Fifty-six normal subjects and 51 patients with heart failure were studied with the CAPW and RAPW signals recorded simultaneously. The two signals were normalized first and then modeled by three positive Gaussian functions, with their peak amplitude, peak time, and half-width determined. Comparisons of these features were finally made between the two groups. Results indicated that the peak amplitude of the first Gaussian curve was significantly decreased in heart failure patients compared with normal subjects (P<0.001). Significantly increased peak amplitude of the second Gaussian curves (P<0.001) and significantly shortened peak times of the second and third Gaussian curves (both P<0.001) were also presented in heart failure patients. These results were true for both CAPW and RAPW signals, indicating the clinical significance of the Gaussian modeling, which should provide essential tools for further understanding the underlying physiological mechanisms of the artery pressure waveform.

MSEE: Stochastic Cognitive Linguistic Behavior Models for Semantic Sensing

DTIC Science & Technology

2013-09-01

recognition, a Gaussian Process Dynamic Model with Social Network Analysis (GPDM-SNA) for a small human group action recognition, an extended GPDM-SNA...44  3.2. Small Human Group Activity Modeling Based on Gaussian Process Dynamic Model and Social Network Analysis (SN-GPDM...51  Approved for public release; distribution unlimited. 3 3.2.3. Gaussian Process Dynamical Model and

Some Modified Integrated Squared Error Procedures for Multivariate Normal Data.

DTIC Science & Technology

1982-06-01

p-dimensional Gaussian. There are a number of measures of qualitative robustness but the most important is the influence function . Most of the other...measures are derived from the influence function . The influence function is simply proportional to the score function (Huber, 1981, p. 45 ). The... influence function at the p-variate Gaussian distribution Np (UV) is as -1P IC(x; ,N) = IE&) ;-") sD=XV = (I+c) (p+2)(x-p) exp(- ! (x-p) TV-.1-)) (3.6

Effects of scale-dependent non-Gaussianity on cosmological structures

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

LoVerde, Marilena; Miller, Amber; Shandera, Sarah

2008-04-15

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

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

NASA Technical Reports Server (NTRS)

Kogut, A.; Banday, A. J.; Bennett, C. L.; Hinshaw, G.; Lubin, P. M.; Smoot, G. F.

1995-01-01

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

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

PubMed

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

2016-12-09

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

Evaluation of non-Gaussian diffusion in cardiac MRI.

PubMed

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

2017-09-01

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

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

PubMed

Hamby, D M

2002-01-01

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

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

PubMed

Liu, Xiong; Godbole, Ajit; Lu, Cheng; Michal, Guillaume; Venton, Philip

2015-11-01

The carbon capture and storage (CCS) and enhanced oil recovery (EOR) projects entail the possibility of accidental release of carbon dioxide (CO2) into the atmosphere. To quantify the spread of CO2 following such release, the 'Gaussian' dispersion model is often used to estimate the resulting CO2 concentration levels in the surroundings. The Gaussian model enables quick estimates of the concentration levels. However, the traditionally recommended values of the 'dispersion parameters' in the Gaussian model may not be directly applicable to CO2 dispersion. This paper presents an optimisation technique to obtain the dispersion parameters in order to achieve a quick estimation of CO2 concentration levels in the atmosphere following CO2 blowouts. The optimised dispersion parameters enable the Gaussian model to produce quick estimates of CO2 concentration levels, precluding the necessity to set up and run much more complicated models. Computational fluid dynamics (CFD) models were employed to produce reference CO2 dispersion profiles in various atmospheric stability classes (ASC), different 'source strengths' and degrees of ground roughness. The performance of the CFD models was validated against the 'Kit Fox' field measurements, involving dispersion over a flat horizontal terrain, both with low and high roughness regions. An optimisation model employing a genetic algorithm (GA) to determine the best dispersion parameters in the Gaussian plume model was set up. Optimum values of the dispersion parameters for different ASCs that can be used in the Gaussian plume model for predicting CO2 dispersion were obtained.

Generation of vector beams using a double-wedge depolarizer: Non-quantum entanglement

NASA Astrophysics Data System (ADS)

Samlan, C. T.; Viswanathan, Nirmal K.

2016-07-01

Propagation of horizontally polarized Gaussian beam through a double-wedge depolarizer generates vector beams with spatially varying state of polarization. Jones calculus is used to show that such beams are maximally nonseparable on the basis of even (Gaussian)-odd (Hermite-Gaussian) mode parity and horizontal-vertical polarization state. The maximum nonseparability in the two degrees of freedom of the vector beam at the double wedge depolarizer output is verified experimentally using a modified Sagnac interferometer and linear analyser projected interferograms to measure the concurrence 0.94±0.002 and violation of Clauser-Horne-Shimony-Holt form of Bell-like inequality 2.704±0.024. The investigation is carried out in the context of the use of vector beams for metrological applications.

Crossing statistics of laser light scattered through a nanofluid.

PubMed

Arshadi Pirlar, M; Movahed, S M S; Razzaghi, D; Karimzadeh, R

2017-09-01

In this paper, we investigate the crossing statistics of speckle patterns formed in the Fresnel diffraction region by a laser beam scattering through a nanofluid. We extend zero-crossing statistics to assess the dynamical properties of the nanofluid. According to the joint probability density function of laser beam fluctuation and its time derivative, the theoretical frameworks for Gaussian and non-Gaussian regimes are revisited. We count the number of crossings not only at zero level but also for all available thresholds to determine the average speed of moving particles. Using a probabilistic framework in determining crossing statistics, a priori Gaussianity is not essentially considered; therefore, even in the presence of deviation from Gaussian fluctuation, this modified approach is capable of computing relevant quantities, such as mean value of speed, more precisely. Generalized total crossing, which represents the weighted summation of crossings for all thresholds to quantify small deviation from Gaussian statistics, is introduced. This criterion can also manipulate the contribution of noises and trends to infer reliable physical quantities. The characteristic time scale for having successive crossings at a given threshold is defined. In our experimental setup, we find that increasing sample temperature leads to more consistency between Gaussian and perturbative non-Gaussian predictions. The maximum number of crossings does not necessarily occur at mean level, indicating that we should take into account other levels in addition to zero level to achieve more accurate assessments.

'A device for being able to book P&L': the organizational embedding of the Gaussian copula.

PubMed

MacKenzie, Donald; Spears, Taylor

2014-06-01

This article, the second of two articles on the Gaussian copula family of models, discusses the attitude of 'quants' (modellers) to these models, showing that contrary to some accounts, those quants were not 'model dopes' who uncritically accepted the outputs of the models. Although sometimes highly critical of Gaussian copulas - even 'othering' them as not really being models --they nevertheless nearly all kept using them, an outcome we explain with reference to the embedding of these models in inter- and intra-organizational processes: communication, risk control and especially the setting of bonuses. The article also examines the role of Gaussian copula models in the 2007-2008 global crisis and in a 2005 episode known as 'the correlation crisis'. We end with the speculation that all widely used derivatives models (and indeed the evaluation culture in which they are embedded) help generate inter-organizational co-ordination, and all that is special in this respect about the Gaussian copula is that its status as 'other' makes this role evident.

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

PubMed

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

2017-07-01

This work characterizes the effect of lipid and noise signals on muscle diffusion parameter estimation in several conventional and non-Gaussian models, the ultimate objectives being to characterize popular fat suppression approaches for human muscle diffusion studies, to provide simulations to inform experimental work and to report normative non-Gaussian parameter values. The models investigated in this work were the Gaussian monoexponential and intravoxel incoherent motion (IVIM) models, and the non-Gaussian kurtosis and stretched exponential models. These were evaluated via simulations, and in vitro and in vivo experiments. Simulations were performed using literature input values, modeling fat contamination as an additive baseline to data, whereas phantom studies used a phantom containing aliphatic and olefinic fats and muscle-like gel. Human imaging was performed in the hamstring muscles of 10 volunteers. Diffusion-weighted imaging was applied with spectral attenuated inversion recovery (SPAIR), slice-select gradient reversal and water-specific excitation fat suppression, alone and in combination. Measurement bias (accuracy) and dispersion (precision) were evaluated, together with intra- and inter-scan repeatability. Simulations indicated that noise in magnitude images resulted in <6% bias in diffusion coefficients and non-Gaussian parameters (α, K), whereas baseline fitting minimized fat bias for all models, except IVIM. In vivo, popular SPAIR fat suppression proved inadequate for accurate parameter estimation, producing non-physiological parameter estimates without baseline fitting and large biases when it was used. Combining all three fat suppression techniques and fitting data with a baseline offset gave the best results of all the methods studied for both Gaussian diffusion and, overall, for non-Gaussian diffusion. It produced consistent parameter estimates for all models, except IVIM, and highlighted non-Gaussian behavior perpendicular to muscle fibers (α ~ 0.95, K ~ 3.1). These results show that effective fat suppression is crucial for accurate measurement of non-Gaussian diffusion parameters, and will be an essential component of quantitative studies of human muscle quality. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.

Moving target detection method based on improved Gaussian mixture model

NASA Astrophysics Data System (ADS)

Ma, J. Y.; Jie, F. R.; Hu, Y. J.

2017-07-01

Gaussian Mixture Model is often employed to build background model in background difference methods for moving target detection. This paper puts forward an adaptive moving target detection algorithm based on improved Gaussian Mixture Model. According to the graylevel convergence for each pixel, adaptively choose the number of Gaussian distribution to learn and update background model. Morphological reconstruction method is adopted to eliminate the shadow.. Experiment proved that the proposed method not only has good robustness and detection effect, but also has good adaptability. Even for the special cases when the grayscale changes greatly and so on, the proposed method can also make outstanding performance.

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

NASA Astrophysics Data System (ADS)

Guo, Qin; Sun, Zhongkui; Xu, Wei

2016-05-01

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

Probability density and exceedance rate functions of locally Gaussian turbulence

NASA Technical Reports Server (NTRS)

Mark, W. D.

1989-01-01

A locally Gaussian model of turbulence velocities is postulated which consists of the superposition of a slowly varying strictly Gaussian component representing slow temporal changes in the mean wind speed and a more rapidly varying locally Gaussian turbulence component possessing a temporally fluctuating local variance. Series expansions of the probability density and exceedance rate functions of the turbulence velocity model, based on Taylor's series, are derived. Comparisons of the resulting two-term approximations with measured probability density and exceedance rate functions of atmospheric turbulence velocity records show encouraging agreement, thereby confirming the consistency of the measured records with the locally Gaussian model. Explicit formulas are derived for computing all required expansion coefficients from measured turbulence records.

Gaussian mixture models as flux prediction method for central receivers

NASA Astrophysics Data System (ADS)

Grobler, Annemarie; Gauché, Paul; Smit, Willie

2016-05-01

Flux prediction methods are crucial to the design and operation of central receiver systems. Current methods such as the circular and elliptical (bivariate) Gaussian prediction methods are often used in field layout design and aiming strategies. For experimental or small central receiver systems, the flux profile of a single heliostat often deviates significantly from the circular and elliptical Gaussian models. Therefore a novel method of flux prediction was developed by incorporating the fitting of Gaussian mixture models onto flux profiles produced by flux measurement or ray tracing. A method was also developed to predict the Gaussian mixture model parameters of a single heliostat for a given time using image processing. Recording the predicted parameters in a database ensures that more accurate predictions are made in a shorter time frame.

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

PubMed Central

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

2003-01-01

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

Gaussian Mixture Model of Heart Rate Variability

PubMed Central

Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

2012-01-01

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

Random medium model for cusping of plane waves.

PubMed

Li, Jia; Korotkova, Olga

2017-09-01

We introduce a model for a three-dimensional (3D) Schell-type stationary medium whose degree of potential's correlation satisfies the Fractional Multi-Gaussian (FMG) function. Compared with the scattered profile produced by the Gaussian Schell-model (GSM) medium, the Fractional Multi-Gaussian Schell-model (FMGSM) medium gives rise to a sharp concave intensity apex in the scattered field. This implies that the FMGSM medium also accounts for a larger than Gaussian's power in the bucket (PIB) in the forward scattering direction, hence being a better candidate than the GSM medium for generating highly-focused (cusp-like) scattered profiles in the far zone. Compared to other mathematical models for the medium's correlation function which can produce similar cusped scattered profiles the FMG function offers unprecedented tractability being the weighted superposition of Gaussian functions. Our results provide useful applications to energy counter problems and particle manipulation by weakly scattered fields.

Orthogonal Gaussian process models

DOE PAGES

Plumlee, Matthew; Joseph, V. Roshan

2017-01-01

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

Orthogonal Gaussian process models

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

Plumlee, Matthew; Joseph, V. Roshan

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

Distribution of Votes and a Model of Political Opinion Formation for Majority Elections

NASA Astrophysics Data System (ADS)

Prenga, Dode; Ifti, Margarita

We study the behavior of the number of votes cast for different electoral subjects in majority elections, and in particular, the Albanian elections of the last 10 years, as well as the British, Russian, and Canadian elections. We report the frequency of obtaining a certain percentage (fraction) of votes versus this fraction for the parliamentary elections. In the distribution of votes cast in majority elections we identify two regimes. In the low percentiles we see a power law distribution, with exponent about -1.7. In the power law regime we find over 80% of the data points, while they relate to 20% of the votes cast. Votes of the small electoral subjects are found in this regime. The other regime includes percentiles above 20%, and has Gaussian distribution. It corresponds to large electoral subjects. A similar pattern is observed in other first past the post (FPP) elections, such as British and Canadian, but here the Gaussian is reduced to an exponential. Finally we show that this distribution can not be reproduced by a modified "word of mouth" model of opinion formation. This behavior can be reproduced by a model that comprises different number of zealots, as well as different campaign strengths for different electoral subjects, in presence of preferential attachment of voters to candidates.

Gaussian mixture modeling of acoustic emissions for structural health monitoring of reinforced concrete structures

NASA Astrophysics Data System (ADS)

Farhidzadeh, Alireza; Dehghan-Niri, Ehsan; Salamone, Salvatore

2013-04-01

Reinforced Concrete (RC) has been widely used in construction of infrastructures for many decades. The cracking behavior in concrete is crucial due to the harmful effects on structural performance such as serviceability and durability requirements. In general, in loading such structures until failure, tensile cracks develop at the initial stages of loading, while shear cracks dominate later. Therefore, monitoring the cracking modes is of paramount importance as it can lead to the prediction of the structural performance. In the past two decades, significant efforts have been made toward the development of automated structural health monitoring (SHM) systems. Among them, a technique that shows promises for monitoring RC structures is the acoustic emission (AE). This paper introduces a novel probabilistic approach based on Gaussian Mixture Modeling (GMM) to classify AE signals related to each crack mode. The system provides an early warning by recognizing nucleation of numerous critical shear cracks. The algorithm is validated through an experimental study on a full-scale reinforced concrete shear wall subjected to a reversed cyclic loading. A modified conventional classification scheme and a new criterion for crack classification are also proposed.

Non-Gaussian PDF Modeling of Turbulent Boundary Layer Fluctuating Pressure Excitation

NASA Technical Reports Server (NTRS)

Steinwolf, Alexander; Rizzi, Stephen A.

2003-01-01

The purpose of the study is to investigate properties of the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the exterior of a supersonic transport aircraft. It is shown that fluctuating pressure PDFs differ from the Gaussian distribution even for surface conditions having no significant discontinuities. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations upstream of forward-facing step discontinuities and downstream of aft-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. Various analytical PDF distributions are used and further developed to model this behavior.

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

NASA Astrophysics Data System (ADS)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

Non-Gaussianities in multifield DBI inflation with a waterfall phase transition

NASA Astrophysics Data System (ADS)

Kidani, Taichi; Koyama, Kazuya; Mizuno, Shuntaro

2012-10-01

We study multifield Dirac-Born-Infeld (DBI) inflation models with a waterfall phase transition. This transition happens for a D3 brane moving in the warped conifold if there is an instability along angular directions. The transition converts the angular perturbations into the curvature perturbation. Thanks to this conversion, multifield models can evade the stringent constraints that strongly disfavor single field ultraviolet (UV) DBI inflation models in string theory. We explicitly demonstrate that our model satisfies current observational constraints on the spectral index and equilateral non-Gaussianity as well as the bound on the tensor to scalar ratio imposed in string theory models. In addition, we show that large local type non-Gaussianity is generated together with equilateral non-Gaussianity in this model.

Shear Melting of a Colloidal Glass

NASA Astrophysics Data System (ADS)

Eisenmann, Christoph; Kim, Chanjoong; Mattsson, Johan; Weitz, David A.

2010-01-01

We use confocal microscopy to explore shear melting of colloidal glasses, which occurs at strains of ˜0.08, coinciding with a strongly non-Gaussian step size distribution. For larger strains, the particle mean square displacement increases linearly with strain and the step size distribution becomes Gaussian. The effective diffusion coefficient varies approximately linearly with shear rate, consistent with a modified Stokes-Einstein relationship in which thermal energy is replaced by shear energy and the length scale is set by the size of cooperatively moving regions consisting of ˜3 particles.

The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

NASA Technical Reports Server (NTRS)

Campbell, Joel

2007-01-01

A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

The SMM model as a boundary value problem using the discrete diffusion equation.

PubMed

Campbell, Joel

2007-12-01

A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Multiview road sign detection via self-adaptive color model and shape context matching

NASA Astrophysics Data System (ADS)

Liu, Chunsheng; Chang, Faliang; Liu, Chengyun

2016-09-01

The multiview appearance of road signs in uncontrolled environments has made the detection of road signs a challenging problem in computer vision. We propose a road sign detection method to detect multiview road signs. This method is based on several algorithms, including the classical cascaded detector, the self-adaptive weighted Gaussian color model (SW-Gaussian model), and a shape context matching method. The classical cascaded detector is used to detect the frontal road signs in video sequences and obtain the parameters for the SW-Gaussian model. The proposed SW-Gaussian model combines the two-dimensional Gaussian model and the normalized red channel together, which can largely enhance the contrast between the red signs and background. The proposed shape context matching method can match shapes with big noise, which is utilized to detect road signs in different directions. The experimental results show that compared with previous detection methods, the proposed multiview detection method can reach higher detection rate in detecting signs with different directions.

Nonlinear estimation theory applied to orbit determination

NASA Technical Reports Server (NTRS)

Choe, C. Y.

1972-01-01

The development of an approximate nonlinear filter using the Martingale theory and appropriate smoothing properties is considered. Both the first order and the second order moments were estimated. The filter developed can be classified as a modified Gaussian second order filter. Its performance was evaluated in a simulated study of the problem of estimating the state of an interplanetary space vehicle during both a simulated Jupiter flyby and a simulated Jupiter orbiter mission. In addition to the modified Gaussian second order filter, the modified truncated second order filter was also evaluated in the simulated study. Results obtained with each of these filters were compared with numerical results obtained with the extended Kalman filter and the performance of each filter is determined by comparison with the actual estimation errors. The simulations were designed to determine the effects of the second order terms in the dynamic state relations, the observation state relations, and the Kalman gain compensation term. It is shown that the Kalman gain-compensated filter which includes only the Kalman gain compensation term is superior to all of the other filters.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Flat-top beam for laser-stimulated pain

NASA Astrophysics Data System (ADS)

McCaughey, Ryan; Nadeau, Valerie; Dickinson, Mark

2005-04-01

One of the main problems during laser stimulation in human pain research is the risk of tissue damage caused by excessive heating of the skin. This risk has been reduced by using a laser beam with a flattop (or superGaussian) intensity profile, instead of the conventional Gaussian beam. A finite difference approximation to the heat conduction equation has been applied to model the temperature distribution in skin as a result of irradiation by flattop and Gaussian profile CO2 laser beams. The model predicts that a 15 mm diameter, 15 W, 100 ms CO2 laser pulse with an order 6 superGaussian profile produces a maximum temperature 6 oC less than a Gaussian beam with the same energy density. A superGaussian profile was created by passing a Gaussian beam through a pair of zinc selenide aspheric lenses which refract the more intense central region of the beam towards the less intense periphery. The profiles of the lenses were determined by geometrical optics. In human pain trials the superGaussian beam required more power than the Gaussian beam to reach sensory and pain thresholds.

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

PubMed

Kawabata, Takeshi

2018-07-01

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

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

PubMed

MacKenzie, Donald; Spears, Taylor

2014-06-01

Drawing on documentary sources and 114 interviews with market participants, this and a companion article discuss the development and use in finance of the Gaussian copula family of models, which are employed to estimate the probability distribution of losses on a pool of loans or bonds, and which were centrally involved in the credit crisis. This article, which explores how and why the Gaussian copula family developed in the way it did, employs the concept of 'evaluation culture', a set of practices, preferences and beliefs concerning how to determine the economic value of financial instruments that is shared by members of multiple organizations. We identify an evaluation culture, dominant within the derivatives departments of investment banks, which we call the 'culture of no-arbitrage modelling', and explore its relation to the development of Gaussian copula models. The article suggests that two themes from the science and technology studies literature on models (modelling as 'impure' bricolage, and modelling as articulating with heterogeneous objectives and constraints) help elucidate the history of Gaussian copula models in finance.

De-blending deep Herschel surveys: A multi-wavelength approach

NASA Astrophysics Data System (ADS)

Pearson, W. J.; Wang, L.; van der Tak, F. F. S.; Hurley, P. D.; Burgarella, D.; Oliver, S. J.

2017-07-01

Aims: Cosmological surveys in the far-infrared are known to suffer from confusion. The Bayesian de-blending tool, XID+, currently provides one of the best ways to de-confuse deep Herschel SPIRE images, using a flat flux density prior. This work is to demonstrate that existing multi-wavelength data sets can be exploited to improve XID+ by providing an informed prior, resulting in more accurate and precise extracted flux densities. Methods: Photometric data for galaxies in the COSMOS field were used to constrain spectral energy distributions (SEDs) using the fitting tool CIGALE. These SEDs were used to create Gaussian prior estimates in the SPIRE bands for XID+. The multi-wavelength photometry and the extracted SPIRE flux densities were run through CIGALE again to allow us to compare the performance of the two priors. Inferred ALMA flux densities (FinferALMA), at 870 μm and 1250 μm, from the best fitting SEDs from the second CIGALE run were compared with measured ALMA flux densities (FmeasALMA) as an independent performance validation. Similar validations were conducted with the SED modelling and fitting tool MAGPHYS and modified black-body functions to test for model dependency. Results: We demonstrate a clear improvement in agreement between the flux densities extracted with XID+ and existing data at other wavelengths when using the new informed Gaussian prior over the original uninformed prior. The residuals between FmeasALMA and FinferALMA were calculated. For the Gaussian priors these residuals, expressed as a multiple of the ALMA error (σ), have a smaller standard deviation, 7.95σ for the Gaussian prior compared to 12.21σ for the flat prior; reduced mean, 1.83σ compared to 3.44σ; and have reduced skew to positive values, 7.97 compared to 11.50. These results were determined to not be significantly model dependent. This results in statistically more reliable SPIRE flux densities and hence statistically more reliable infrared luminosity estimates. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

Gaussian temporal modulation for the behavior of multi-sinc Schell-model pulses in dispersive media

NASA Astrophysics Data System (ADS)

Liu, Xiayin; Zhao, Daomu; Tian, Kehan; Pan, Weiqing; Zhang, Kouwen

2018-06-01

A new class of pulse source with correlation being modeled by the convolution operation of two legitimate temporal correlation function is proposed. Particularly, analytical formulas for the Gaussian temporally modulated multi-sinc Schell-model (MSSM) pulses generated by such pulse source propagating in dispersive media are derived. It is demonstrated that the average intensity of MSSM pulses on propagation are reshaped from flat profile or a train to a distribution with a Gaussian temporal envelope by adjusting the initial correlation width of the Gaussian pulse. The effects of the Gaussian temporal modulation on the temporal degree of coherence of the MSSM pulse are also analyzed. The results presented here show the potential of coherence modulation for pulse shaping and pulsed laser material processing.

The Non-Gaussian Nature of Prostate Motion Based on Real-Time Intrafraction Tracking

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

Lin, Yuting; Liu, Tian; Yang, Wells

2013-10-01

Purpose: The objective of this work is to test the validity of the Gaussian approximation for prostate motion through characterization of its spatial distribution. Methods and Materials: Real-time intrafraction prostate motion was observed using Calypso 4-dimensional (4D) nonradioactive electromagnetic tracking system. We report the results from a total of 1024 fractions from 31 prostate cancer patients. First, the correlation of prostate motion in right/left (RL), anteroposterior (AP), and superoinferior (SI) direction were determined using Pearson's correlation of coefficient. Then the spatial distribution of prostate motion was analyzed for individual fraction, individual patient including all fractions, and all patients including allmore » fractions. The displacement in RL, AP, SI, oblique, or total direction is fitted into a Gaussian distribution, and a Lilliefors test was used to evaluate the validity of the hypothesis that the displacement is normally distributed. Results: There is high correlation in AP/SI direction (61% of fractions with medium or strong correlation). This is consistent with the longitudinal oblique motion of the prostate, and likely the effect from respiration on an organ confined within the genitourinary diaphragm with the rectum sitting posteriorly and bladder sitting superiorly. In all directions, the non-Gaussian distribution is more common for individual fraction, individual patient including all fractions, and all patients including all fractions. The spatial distribution of prostate motion shows an elongated shape in oblique direction, indicating a higher range of motion in the AP and SI directions. Conclusions: Our results showed that the prostate motion is highly correlated in AP and SI direction, indicating an oblique motion preference. In addition, the spatial distribution of prostate motion is elongated in an oblique direction, indicating that the organ motion dosimetric modeling using Gaussian kernel may need to be modified to account for the particular organ motion character of prostate.« less

The non-Gaussian nature of prostate motion based on real-time intrafraction tracking.

PubMed

Lin, Yuting; Liu, Tian; Yang, Wells; Yang, Xiaofeng; Khan, Mohammad K

2013-10-01

The objective of this work is to test the validity of the Gaussian approximation for prostate motion through characterization of its spatial distribution. Real-time intrafraction prostate motion was observed using Calypso 4-dimensional (4D) nonradioactive electromagnetic tracking system. We report the results from a total of 1024 fractions from 31 prostate cancer patients. First, the correlation of prostate motion in right/left (RL), anteroposterior (AP), and superoinferior (SI) direction were determined using Pearson's correlation of coefficient. Then the spatial distribution of prostate motion was analyzed for individual fraction, individual patient including all fractions, and all patients including all fractions. The displacement in RL, AP, SI, oblique, or total direction is fitted into a Gaussian distribution, and a Lilliefors test was used to evaluate the validity of the hypothesis that the displacement is normally distributed. There is high correlation in AP/SI direction (61% of fractions with medium or strong correlation). This is consistent with the longitudinal oblique motion of the prostate, and likely the effect from respiration on an organ confined within the genitourinary diaphragm with the rectum sitting posteriorly and bladder sitting superiorly. In all directions, the non-Gaussian distribution is more common for individual fraction, individual patient including all fractions, and all patients including all fractions. The spatial distribution of prostate motion shows an elongated shape in oblique direction, indicating a higher range of motion in the AP and SI directions. Our results showed that the prostate motion is highly correlated in AP and SI direction, indicating an oblique motion preference. In addition, the spatial distribution of prostate motion is elongated in an oblique direction, indicating that the organ motion dosimetric modeling using Gaussian kernel may need to be modified to account for the particular organ motion character of prostate. Copyright © 2013 Elsevier Inc. All rights reserved.

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

PubMed Central

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

2017-01-01

Purpose The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Material and methods Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. Results All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. Conclusion No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior. PMID:28863161

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

PubMed

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

2017-01-01

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

Prediction of peak shape in hydro-organic and micellar-organic liquid chromatography as a function of mobile phase composition.

PubMed

Baeza-Baeza, J J; Ruiz-Angel, M J; García-Alvarez-Coque, M C

2007-09-07

A simple model is proposed that relates the parameters describing the peak width with the retention time, which can be easily predicted as a function of mobile phase composition. This allows the further prediction of peak shape with global errors below 5%, using a modified Gaussian model with a parabolic variance. The model is useful in the optimisation of chromatographic resolution to assess an eventual overlapping of close peaks. The dependence of peak shape with mobile phase composition was studied for mobile phases containing acetonitrile in the presence and absence of micellised surfactant (micellar-organic and hydro-organic reversed-phase liquid chromatography, RPLC). In micellar RPLC, both modifiers (surfactant and acetonitrile) were observed to decrease or improve the efficiencies in the same percentage, at least in the studied concentration ranges. The study also revealed that the problem of achieving smaller efficiencies in this chromatographic mode, compared to hydro-organic RPLC, is not only related to the presence of surfactant covering the stationary phase, but also to the smaller concentration of organic solvent in the mobile phase.

Gaussian processes: a method for automatic QSAR modeling of ADME properties.

PubMed

Obrezanova, Olga; Csanyi, Gabor; Gola, Joelle M R; Segall, Matthew D

2007-01-01

In this article, we discuss the application of the Gaussian Process method for the prediction of absorption, distribution, metabolism, and excretion (ADME) properties. On the basis of a Bayesian probabilistic approach, the method is widely used in the field of machine learning but has rarely been applied in quantitative structure-activity relationship and ADME modeling. The method is suitable for modeling nonlinear relationships, does not require subjective determination of the model parameters, works for a large number of descriptors, and is inherently resistant to overtraining. The performance of Gaussian Processes compares well with and often exceeds that of artificial neural networks. Due to these features, the Gaussian Processes technique is eminently suitable for automatic model generation-one of the demands of modern drug discovery. Here, we describe the basic concept of the method in the context of regression problems and illustrate its application to the modeling of several ADME properties: blood-brain barrier, hERG inhibition, and aqueous solubility at pH 7.4. We also compare Gaussian Processes with other modeling techniques.

Automatic image equalization and contrast enhancement using Gaussian mixture modeling.

PubMed

Celik, Turgay; Tjahjadi, Tardi

2012-01-01

In this paper, we propose an adaptive image equalization algorithm that automatically enhances the contrast in an input image. The algorithm uses the Gaussian mixture model to model the image gray-level distribution, and the intersection points of the Gaussian components in the model are used to partition the dynamic range of the image into input gray-level intervals. The contrast equalized image is generated by transforming the pixels' gray levels in each input interval to the appropriate output gray-level interval according to the dominant Gaussian component and the cumulative distribution function of the input interval. To take account of the hypothesis that homogeneous regions in the image represent homogeneous silences (or set of Gaussian components) in the image histogram, the Gaussian components with small variances are weighted with smaller values than the Gaussian components with larger variances, and the gray-level distribution is also used to weight the components in the mapping of the input interval to the output interval. Experimental results show that the proposed algorithm produces better or comparable enhanced images than several state-of-the-art algorithms. Unlike the other algorithms, the proposed algorithm is free of parameter setting for a given dynamic range of the enhanced image and can be applied to a wide range of image types.

Regional cardiac wall motion from gated myocardial perfusion SPECT studies

NASA Astrophysics Data System (ADS)

Smith, M. F.; Brigger, P.; Ferrand, S. K.; Dilsizian, V.; Bacharach, S. L.

1999-06-01

A method for estimating regional epicardial and endocardial wall motion from gated myocardial perfusion SPECT studies has been developed. The method uses epicardial and endocardial boundaries determined from four long-axis slices at each gate of the cardiac cycle. The epicardial and endocardial wall position at each time gate is computed with respect to stationary reference ellipsoids, and wall motion is measured along lines normal to these ellipsoids. An initial quantitative evaluation of the method was made using the beating heart from the dynamic mathematical cardiac torso (MCAT) phantom, with and without a 1.5-cm FWHM Gaussian blurring filter. Epicardial wall motion was generally well-estimated within a fraction of a 3.56-mm voxel, although apical motion was overestimated with the Gaussian filter. Endocardial wall motion was underestimated by about two voxels with and without the Gaussian filter. The MCAT heart phantom was modified to model hypokinetic and dyskinetic wall motion. The wall motion analysis method enabled this abnormal motion to be differentiated from normal motion. Regional cardiac wall motion also was analyzed for /sup 201/Tl patient studies. Estimated wall motion was consistent with a nuclear medicine physician's visual assessment of motion from gated long-axis slices for male and female study examples. Additional research is required for a comprehensive evaluation of the applicability of the method to patient studies with normal and abnormal wall motion.

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

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

Stein, Michael

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

A simple non-Markovian computational model of the statistics of soccer leagues: Emergence and scaling effects

NASA Astrophysics Data System (ADS)

da Silva, Roberto; Vainstein, Mendeli H.; Lamb, Luis C.; Prado, Sandra D.

2013-03-01

We propose a novel probabilistic model that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential (ability) which is updated during the tournament according to the results of previous games. The updated potential modifies a team future winning/losing probabilities. We show that this evolutionary game is able to reproduce the statistical properties of final standings of actual editions of the Brazilian tournament (Brasileirão) if the starting potential is the same for all teams. Other leagues such as the Italian (Calcio) and the Spanish (La Liga) tournaments have notoriously non-Gaussian traces and cannot be straightforwardly reproduced by this evolutionary non-Markovian model with simple initial conditions. However, we show that by setting the initial abilities based on data from previous tournaments, our model is able to capture the stylized statistical features of double round robin system (DRRS) tournaments in general. A complete understanding of these phenomena deserves much more attention, but we suggest a simple explanation based on data collected in Brazil: here several teams have been crowned champion in previous editions corroborating that the champion typically emerges from random fluctuations that partly preserve the Gaussian traces during the tournament. On the other hand, in the Italian and Spanish cases, only a few teams in recent history have won their league tournaments. These leagues are based on more robust and hierarchical structures established even before the beginning of the tournament. For the sake of completeness, we also elaborate a totally Gaussian model (which equalizes the winning, drawing, and losing probabilities) and we show that the scores of the Brazilian tournament “Brasileirão” cannot be reproduced. This shows that the evolutionary aspects are not superfluous and play an important role which must be considered in other alternative models. Finally, we analyze the distortions of our model in situations where a large number of teams is considered, showing the existence of a transition from a single to a double peaked histogram of the final classification scores. An interesting scaling is presented for different sized tournaments.

SU-C-BRC-04: Efficient Dose Calculation Algorithm for FFF IMRT with a Simplified Bivariate Gaussian Source Model

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

Li, F; Park, J; Barraclough, B

2016-06-15

Purpose: To develop an efficient and accurate independent dose calculation algorithm with a simplified analytical source model for the quality assurance and safe delivery of Flattening Filter Free (FFF)-IMRT on an Elekta Versa HD. Methods: The source model consisted of a point source and a 2D bivariate Gaussian source, respectively modeling the primary photons and the combined effect of head scatter, monitor chamber backscatter and collimator exchange effect. The in-air fluence was firstly calculated by back-projecting the edges of beam defining devices onto the source plane and integrating the visible source distribution. The effect of the rounded MLC leaf end,more » tongue-and-groove and interleaf transmission was taken into account in the back-projection. The in-air fluence was then modified with a fourth degree polynomial modeling the cone-shaped dose distribution of FFF beams. Planar dose distribution was obtained by convolving the in-air fluence with a dose deposition kernel (DDK) consisting of the sum of three 2D Gaussian functions. The parameters of the source model and the DDK were commissioned using measured in-air output factors (Sc) and cross beam profiles, respectively. A novel method was used to eliminate the volume averaging effect of ion chambers in determining the DDK. Planar dose distributions of five head-and-neck FFF-IMRT plans were calculated and compared against measurements performed with a 2D diode array (MapCHECK™) to validate the accuracy of the algorithm. Results: The proposed source model predicted Sc for both 6MV and 10MV with an accuracy better than 0.1%. With a stringent gamma criterion (2%/2mm/local difference), the passing rate of the FFF-IMRT dose calculation was 97.2±2.6%. Conclusion: The removal of the flattening filter represents a simplification of the head structure which allows the use of a simpler source model for very accurate dose calculation. The proposed algorithm offers an effective way to ensure the safe delivery of FFF-IMRT.« less

Topology of large-scale structure in seeded hot dark matter models

NASA Technical Reports Server (NTRS)

Beaky, Matthew M.; Scherrer, Robert J.; Villumsen, Jens V.

1992-01-01

The topology of the isodensity surfaces in seeded hot dark matter models, in which static seed masses provide the density perturbations in a universe dominated by massive neutrinos is examined. When smoothed with a Gaussian window, the linear initial conditions in these models show no trace of non-Gaussian behavior for r0 equal to or greater than 5 Mpc (h = 1/2), except for very low seed densities, which show a shift toward isolated peaks. An approximate analytic expression is given for the genus curve expected in linear density fields from randomly distributed seed masses. The evolved models have a Gaussian topology for r0 = 10 Mpc, but show a shift toward a cellular topology with r0 = 5 Mpc; Gaussian models with an identical power spectrum show the same behavior.

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

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

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

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

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

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

Non-gaussianity versus nonlinearity of cosmological perturbations.

PubMed

Verde, L

2001-06-01

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

Density Estimation with Mercer Kernels

NASA Technical Reports Server (NTRS)

Macready, William G.

2003-01-01

We present a new method for density estimation based on Mercer kernels. The density estimate can be understood as the density induced on a data manifold by a mixture of Gaussians fit in a feature space. As is usual, the feature space and data manifold are defined with any suitable positive-definite kernel function. We modify the standard EM algorithm for mixtures of Gaussians to infer the parameters of the density. One benefit of the approach is it's conceptual simplicity, and uniform applicability over many different types of data. Preliminary results are presented for a number of simple problems.

Analytical performance specifications for changes in assay bias (Δbias) for data with logarithmic distributions as assessed by effects on reference change values.

PubMed

Petersen, Per H; Lund, Flemming; Fraser, Callum G; Sölétormos, György

2016-11-01

Background The distributions of within-subject biological variation are usually described as coefficients of variation, as are analytical performance specifications for bias, imprecision and other characteristics. Estimation of specifications required for reference change values is traditionally done using relationship between the batch-related changes during routine performance, described as Δbias, and the coefficients of variation for analytical imprecision (CV A ): the original theory is based on standard deviations or coefficients of variation calculated as if distributions were Gaussian. Methods The distribution of between-subject biological variation can generally be described as log-Gaussian. Moreover, recent analyses of within-subject biological variation suggest that many measurands have log-Gaussian distributions. In consequence, we generated a model for the estimation of analytical performance specifications for reference change value, with combination of Δbias and CV A based on log-Gaussian distributions of CV I as natural logarithms. The model was tested using plasma prolactin and glucose as examples. Results Analytical performance specifications for reference change value generated using the new model based on log-Gaussian distributions were practically identical with the traditional model based on Gaussian distributions. Conclusion The traditional and simple to apply model used to generate analytical performance specifications for reference change value, based on the use of coefficients of variation and assuming Gaussian distributions for both CV I and CV A , is generally useful.

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

PubMed

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

2017-05-24

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

TH-C-BRD-04: Beam Modeling and Validation with Triple and Double Gaussian Dose Kernel for Spot Scanning Proton Beams

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

Hirayama, S; Takayanagi, T; Fujii, Y

2014-06-15

Purpose: To present the validity of our beam modeling with double and triple Gaussian dose kernels for spot scanning proton beams in Nagoya Proton Therapy Center. This study investigates the conformance between the measurements and calculation results in absolute dose with two types of beam kernel. Methods: A dose kernel is one of the important input data required for the treatment planning software. The dose kernel is the 3D dose distribution of an infinitesimal pencil beam of protons in water and consists of integral depth doses and lateral distributions. We have adopted double and triple Gaussian model as lateral distributionmore » in order to take account of the large angle scattering due to nuclear reaction by fitting simulated inwater lateral dose profile for needle proton beam at various depths. The fitted parameters were interpolated as a function of depth in water and were stored as a separate look-up table for the each beam energy. The process of beam modeling is based on the method of MDACC [X.R.Zhu 2013]. Results: From the comparison results between the absolute doses calculated by double Gaussian model and those measured at the center of SOBP, the difference is increased up to 3.5% in the high-energy region because the large angle scattering due to nuclear reaction is not sufficiently considered at intermediate depths in the double Gaussian model. In case of employing triple Gaussian dose kernels, the measured absolute dose at the center of SOBP agrees with calculation within ±1% regardless of the SOBP width and maximum range. Conclusion: We have demonstrated the beam modeling results of dose distribution employing double and triple Gaussian dose kernel. Treatment planning system with the triple Gaussian dose kernel has been successfully verified and applied to the patient treatment with a spot scanning technique in Nagoya Proton Therapy Center.« less

A perturbative approach to the redshift space correlation function: beyond the Standard Model

NASA Astrophysics Data System (ADS)

Bose, Benjamin; Koyama, Kazuya

2017-08-01

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model which is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with <= 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpch <= s <= 180Mpc/h. Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.

Analytical model of the optical vortex microscope.

PubMed

Płocinniczak, Łukasz; Popiołek-Masajada, Agnieszka; Masajada, Jan; Szatkowski, Mateusz

2016-04-20

This paper presents an analytical model of the optical vortex scanning microscope. In this microscope the Gaussian beam with an embedded optical vortex is focused into the sample plane. Additionally, the optical vortex can be moved inside the beam, which allows fine scanning of the sample. We provide an analytical solution of the whole path of the beam in the system (within paraxial approximation)-from the vortex lens to the observation plane situated on the CCD camera. The calculations are performed step by step from one optical element to the next. We show that at each step, the expression for light complex amplitude has the same form with only four coefficients modified. We also derive a simple expression for the vortex trajectory of small vortex displacements.

Analysis of Digital Communication Signals and Extraction of Parameters.

DTIC Science & Technology

1994-12-01

Fast Fourier Transform (FFT). The correlation methods utilize modified time-frequency distributions , where one of these is based on the Wigner - Ville ... Distribution ( WVD ). Gaussian white noise is added to the signal to simulate various signal-to-noise ratios (SNRs).

Variational Gaussian approximation for Poisson data

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

PubMed

Si, Weijian; Wang, Liwei; Qu, Zhiyu

2016-11-23

The cardinalized probability hypothesis density (CPHD) filter is an alternative approximation to the full multi-target Bayesian filter for tracking multiple targets. However, although the joint propagation of the posterior intensity and cardinality distribution in its recursion allows more reliable estimates of the target number than the PHD filter, the CPHD filter suffers from the spooky effect where there exists arbitrary PHD mass shifting in the presence of missed detections. To address this issue in the Gaussian mixture (GM) implementation of the CPHD filter, this paper presents an improved GM-CPHD filter, which incorporates a weight redistribution scheme into the filtering process to modify the updated weights of the Gaussian components when missed detections occur. In addition, an efficient gating strategy that can adaptively adjust the gate sizes according to the number of missed detections of each Gaussian component is also presented to further improve the computational efficiency of the proposed filter. Simulation results demonstrate that the proposed method offers favorable performance in terms of both estimation accuracy and robustness to clutter and detection uncertainty over the existing methods.

Extinction time of a stochastic predator-prey model by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao

2018-03-01

The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.

Modeling Multi-Variate Gaussian Distributions and Analysis of Higgs Boson Couplings with the ATLAS Detector

NASA Astrophysics Data System (ADS)

Krohn, Olivia; Armbruster, Aaron; Gao, Yongsheng; Atlas Collaboration

2017-01-01

Software tools developed for the purpose of modeling CERN LHC pp collision data to aid in its interpretation are presented. Some measurements are not adequately described by a Gaussian distribution; thus an interpretation assuming Gaussian uncertainties will inevitably introduce bias, necessitating analytical tools to recreate and evaluate non-Gaussian features. One example is the measurements of Higgs boson production rates in different decay channels, and the interpretation of these measurements. The ratios of data to Standard Model expectations (μ) for five arbitrary signals were modeled by building five Poisson distributions with mixed signal contributions such that the measured values of μ are correlated. Algorithms were designed to recreate probability distribution functions of μ as multi-variate Gaussians, where the standard deviation (σ) and correlation coefficients (ρ) are parametrized. There was good success with modeling 1-D likelihood contours of μ, and the multi-dimensional distributions were well modeled within 1- σ but the model began to diverge after 2- σ due to unmerited assumptions in developing ρ. Future plans to improve the algorithms and develop a user-friendly analysis package will also be discussed. NSF International Research Experiences for Students

Evaluation of the influence of double and triple Gaussian proton kernel models on accuracy of dose calculations for spot scanning technique.

PubMed

Hirayama, Shusuke; Takayanagi, Taisuke; Fujii, Yusuke; Fujimoto, Rintaro; Fujitaka, Shinichiro; Umezawa, Masumi; Nagamine, Yoshihiko; Hosaka, Masahiro; Yasui, Keisuke; Omachi, Chihiro; Toshito, Toshiyuki

2016-03-01

The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique. The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations. The authors investigated the difference between double and triple Gaussian kernel models. The authors found that the difference between the two studied kernel models appeared at mid-depths and the accuracy of predicting the double Gaussian model deteriorated at the low-dose bump that appeared at mid-depths. When the authors employed the double Gaussian kernel model, the accuracy of calculations for the absolute dose at the center of the SOBP varied with irradiation conditions and the maximum difference was 3.4%. In contrast, the results obtained from calculations with the triple Gaussian kernel model indicated good agreement with the measurements within ±1.1%, regardless of the irradiation conditions. The difference between the results obtained with the two types of studied kernel models was distinct in the high energy region. The accuracy of calculations with the double Gaussian kernel model varied with the field size and SOBP width because the accuracy of prediction with the double Gaussian model was insufficient at the low-dose bump. The evaluation was only qualitative under limited volumetric irradiation conditions. Further accumulation of measured data would be needed to quantitatively comprehend what influence the double and triple Gaussian kernel models had on the accuracy of dose calculations.

Effect of inhomogeneous Schottky barrier height of SnO2 nanowires device

NASA Astrophysics Data System (ADS)

Amorim, Cleber A.; Bernardo, Eric P.; Leite, Edson R.; Chiquito, Adenilson J.

2018-05-01

The current–voltage (I–V) characteristics of metal–semiconductor junction (Au–Ni/SnO2/Au–Ni) Schottky barrier in SnO2 nanowires were investigated over a wide temperature range. By using the Schottky–Mott model, the zero bias barrier height Φ B was estimated from I–V characteristics, and it was found to increase with increasing temperature; on the other hand the ideality factor (n) was found to decrease with increasing temperature. The variation in the Schottky barrier and n was attributed to the spatial inhomogeneity of the Schottky barrier height. The experimental I–V characteristics exhibited a Gaussian distribution having mean barrier heights {\\overline{{{Φ }}}}B of 0.30 eV and standard deviation σ s of 60 meV. Additionally, the Richardson modified constant was obtained to be 70 A cm‑2 K‑2, leading to an effective mass of 0.58m 0. Consequently, the temperature dependence of I–V characteristics of the SnO2 nanowire devices can be successfully explained on the Schottky–Mott theory framework taking into account a Gaussian distribution of barrier heights.

Laser amplification of incoherent radiation

NASA Technical Reports Server (NTRS)

Menegozzi, L. N.; Lamb, W. E., Jr.

1978-01-01

The amplification of noise in a laser amplifier is treated theoretically. The model for the active medium and its description using density-matrix techniques, are taken from the theory of laser operation. The spectral behavior of the radiation in the nonlinear regime is studied and the formalism is written from the onset in the frequency domain. The statistics of the light are gradually modified by the nonlinear amplification process, and expressions are derived for the rate of change of fluctuations in intensity as a measure of statistical changes. In addition, the range of validity of Litvak's Gaussian-statistics approximation is discussed. In the homogeneous-broadening case, the evolution of initially broadband Gaussian radiation toward quasimonochromatic oscillations with laserlike statistics is explored in several numerical examples. The connections of this study with the time-domain work on self-pulsing in a ring-laser configuration, are established. Finally, spectral-narrowing and -rebroadening effects in Doppler-broadened media are discussed both analytically and with numerical examples. These examples show the distinct contribution of pulsations in the population ('Raman-type terms'), and saturation phenomena.

Steady-state distributions of probability fluxes on complex networks

NASA Astrophysics Data System (ADS)

Chełminiak, Przemysław; Kurzyński, Michał

2017-02-01

We consider a simple model of the Markovian stochastic dynamics on complex networks to examine the statistical properties of the probability fluxes. The additional transition, called hereafter a gate, powered by the external constant force breaks a detailed balance in the network. We argue, using a theoretical approach and numerical simulations, that the stationary distributions of the probability fluxes emergent under such conditions converge to the Gaussian distribution. By virtue of the stationary fluctuation theorem, its standard deviation depends directly on the square root of the mean flux. In turn, the nonlinear relation between the mean flux and the external force, which provides the key result of the present study, allows us to calculate the two parameters that entirely characterize the Gaussian distribution of the probability fluxes both close to as well as far from the equilibrium state. Also, the other effects that modify these parameters, such as the addition of shortcuts to the tree-like network, the extension and configuration of the gate and a change in the network size studied by means of computer simulations are widely discussed in terms of the rigorous theoretical predictions.

Beyond Gaussians: a study of single spot modeling for scanning proton dose calculation

PubMed Central

Li, Yupeng; Zhu, Ronald X.; Sahoo, Narayan; Anand, Aman; Zhang, Xiaodong

2013-01-01

Active spot scanning proton therapy is becoming increasingly adopted by proton therapy centers worldwide. Unlike passive-scattering proton therapy, active spot scanning proton therapy, especially intensity-modulated proton therapy, requires proper modeling of each scanning spot to ensure accurate computation of the total dose distribution contributed from a large number of spots. During commissioning of the spot scanning gantry at the Proton Therapy Center in Houston, it was observed that the long-range scattering protons in a medium may have been inadequately modeled for high-energy beams by a commercial treatment planning system, which could lead to incorrect prediction of field-size effects on dose output. In the present study, we developed a pencil-beam algorithm for scanning-proton dose calculation by focusing on properly modeling individual scanning spots. All modeling parameters required by the pencil-beam algorithm can be generated based solely on a few sets of measured data. We demonstrated that low-dose halos in single-spot profiles in the medium could be adequately modeled with the addition of a modified Cauchy-Lorentz distribution function to a double-Gaussian function. The field-size effects were accurately computed at all depths and field sizes for all energies, and good dose accuracy was also achieved for patient dose verification. The implementation of the proposed pencil beam algorithm also enabled us to study the importance of different modeling components and parameters at various beam energies. The results of this study may be helpful in improving dose calculation accuracy and simplifying beam commissioning and treatment planning processes for spot scanning proton therapy. PMID:22297324

Bayesian sensitivity analysis of bifurcating nonlinear models

NASA Astrophysics Data System (ADS)

Becker, W.; Worden, K.; Rowson, J.

2013-01-01

Sensitivity analysis allows one to investigate how changes in input parameters to a system affect the output. When computational expense is a concern, metamodels such as Gaussian processes can offer considerable computational savings over Monte Carlo methods, albeit at the expense of introducing a data modelling problem. In particular, Gaussian processes assume a smooth, non-bifurcating response surface. This work highlights a recent extension to Gaussian processes which uses a decision tree to partition the input space into homogeneous regions, and then fits separate Gaussian processes to each region. In this way, bifurcations can be modelled at region boundaries and different regions can have different covariance properties. To test this method, both the treed and standard methods were applied to the bifurcating response of a Duffing oscillator and a bifurcating FE model of a heart valve. It was found that the treed Gaussian process provides a practical way of performing uncertainty and sensitivity analysis on large, potentially-bifurcating models, which cannot be dealt with by using a single GP, although an open problem remains how to manage bifurcation boundaries that are not parallel to coordinate axes.

A Gaussian framework for modeling effects of frequency-dependent attenuation, frequency-dependent scattering, and gating.

PubMed

Wear, Keith A

2002-11-01

For a wide range of applications in medical ultrasound, power spectra of received signals are approximately Gaussian. It has been established previously that an ultrasound beam with a Gaussian spectrum propagating through a medium with linear attenuation remains Gaussian. In this paper, Gaussian transformations are derived to model the effects of scattering (according to a power law, as is commonly applicable in soft tissues, especially over limited frequency ranges) and gating (with a Hamming window, a commonly used gate function). These approximations are shown to be quite accurate even for relatively broad band systems with fractional bandwidths approaching 100%. The theory is validated by experiments in phantoms consisting of glass particles suspended in agar.

Doubly self-consistent field theory of grafted polymers under simple shear in steady state.

PubMed

Suo, Tongchuan; Whitmore, Mark D

2014-03-21

We present a generalization of the numerical self-consistent mean-field theory of polymers to the case of grafted polymers under simple shear. The general theoretical framework is presented, and then applied to three different chain models: rods, Gaussian chains, and finitely extensible nonlinear elastic (FENE) chains. The approach is self-consistent at two levels. First, for any flow field, the polymer density profile and effective potential are calculated self-consistently in a manner similar to the usual self-consistent field theory of polymers, except that the calculation is inherently two-dimensional even for a laterally homogeneous system. Second, through the use of a modified Brinkman equation, the flow field and the polymer profile are made self-consistent with respect to each other. For all chain models, we find that reasonable levels of shear cause the chains to tilt, but it has very little effect on the overall thickness of the polymer layer, causing a small decrease for rods, and an increase of no more than a few percent for the Gaussian and FENE chains. Using the FENE model, we also probe the individual bond lengths, bond correlations, and bond angles along the chains, the effects of the shear on them, and the solvent and bonded stress profiles. We find that the approximations needed within the theory for the Brinkman equation affect the bonded stress, but none of the other quantities.

Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process

NASA Astrophysics Data System (ADS)

Turner, Douglas C.; Ladde, Gangaram S.

2018-03-01

Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.

Comparison of hypertabastic survival model with other unimodal hazard rate functions using a goodness-of-fit test.

PubMed

Tahir, M Ramzan; Tran, Quang X; Nikulin, Mikhail S

2017-05-30

We studied the problem of testing a hypothesized distribution in survival regression models when the data is right censored and survival times are influenced by covariates. A modified chi-squared type test, known as Nikulin-Rao-Robson statistic, is applied for the comparison of accelerated failure time models. This statistic is used to test the goodness-of-fit for hypertabastic survival model and four other unimodal hazard rate functions. The results of simulation study showed that the hypertabastic distribution can be used as an alternative to log-logistic and log-normal distribution. In statistical modeling, because of its flexible shape of hazard functions, this distribution can also be used as a competitor of Birnbaum-Saunders and inverse Gaussian distributions. The results for the real data application are shown. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

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

PubMed

Plechawska, Małgorzata; Polańska, Joanna

2009-01-01

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

Generalized energy measurements and modified transient quantum fluctuation theorems

NASA Astrophysics Data System (ADS)

Watanabe, Gentaro; Venkatesh, B. Prasanna; Talkner, Peter

2014-05-01

Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements and even yields a projective measurement in the limit of infinite repetitions.

Formation of doughnut and super-Gaussian intensity distributions of laser radiation in the far field using a bimorph mirror

NASA Astrophysics Data System (ADS)

Lylova, A. N.; Sheldakova, Yu. V.; Kudryashov, A. V.; Samarkin, V. V.

2018-01-01

We consider the methods for modelling doughnut and super-Gaussian intensity distributions in the far field by means of deformable bimorph mirrors. A method for the rapid formation of a specified intensity distribution using a Shack - Hartmann sensor is proposed, and the results of the modelling of doughnut and super-Gaussian intensity distributions are presented.

Revisiting non-Gaussianity from non-attractor inflation models

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

An Efficient and Robust Moving Shadow Removal Algorithm and Its Applications in ITS

NASA Astrophysics Data System (ADS)

Lin, Chin-Teng; Yang, Chien-Ting; Shou, Yu-Wen; Shen, Tzu-Kuei

2010-12-01

We propose an efficient algorithm for removing shadows of moving vehicles caused by non-uniform distributions of light reflections in the daytime. This paper presents a brand-new and complete structure in feature combination as well as analysis for orientating and labeling moving shadows so as to extract the defined objects in foregrounds more easily in each snapshot of the original files of videos which are acquired in the real traffic situations. Moreover, we make use of Gaussian Mixture Model (GMM) for background removal and detection of moving shadows in our tested images, and define two indices for characterizing non-shadowed regions where one indicates the characteristics of lines and the other index can be characterized by the information in gray scales of images which helps us to build a newly defined set of darkening ratios (modified darkening factors) based on Gaussian models. To prove the effectiveness of our moving shadow algorithm, we carry it out with a practical application of traffic flow detection in ITS (Intelligent Transportation System)—vehicle counting. Our algorithm shows the faster processing speed, 13.84 ms/frame, and can improve the accuracy rate in 4% ~ 10% for our three tested videos in the experimental results of vehicle counting.

In vitro tympanic membrane position identification with a co-axial fiber-optic otoscope

NASA Astrophysics Data System (ADS)

Sundberg, Mikael; Peebo, Markus; Strömberg, Tomas

2011-09-01

Otitis media diagnosis can be assisted by measuring the shape of the tympanic membrane. We have developed an ear speculum for an otoscope, including spatially distributed source and detector optical fibers, to generate source-detector intensity matrices (SDIMs), representing the curvature of surfaces. The surfaces measured were a model ear with a latex membrane and harvested temporal bones including intact tympanic membranes. The position of the tympanic membrane was shifted from retracted to bulging by air pressure and that of the latex membrane by water displacement. The SDIM was normalized utilizing both external (a sheared flat plastic cylinder) and internal references (neutral position of the membrane). Data was fitted to a two-dimensional Gaussian surface representing the shape by its amplitude and offset. Retracted and bulging surfaces were discriminated for the model ear by the sign of the Gaussian amplitude for both internal and external reference normalization. Tympanic membranes were separated after a two-step normalization: first to an external reference, adjusted for the distance between speculum and the surfaces, and second by comparison with an average normally positioned SDIM from tympanic membranes. In conclusion, we have shown that the modified otoscope can discriminate between bulging and retracted tympanic membranes in a single measurement, given a two-step normalization.

US-SOMO HPLC-SAXS module: dealing with capillary fouling and extraction of pure component patterns from poorly resolved SEC-SAXS data

PubMed Central

Brookes, Emre; Vachette, Patrice; Rocco, Mattia; Pérez, Javier

2016-01-01

Size-exclusion chromatography coupled with SAXS (small-angle X-ray scattering), often performed using a flow-through capillary, should allow direct collection of monodisperse sample data. However, capillary fouling issues and non-baseline-resolved peaks can hamper its efficacy. The UltraScan solution modeler (US-SOMO) HPLC-SAXS (high-performance liquid chromatography coupled with SAXS) module provides a comprehensive framework to analyze such data, starting with a simple linear baseline correction and symmetrical Gaussian decomposition tools [Brookes, Pérez, Cardinali, Profumo, Vachette & Rocco (2013 ▸). J. Appl. Cryst. 46, 1823–1833]. In addition to several new features, substantial improvements to both routines have now been implemented, comprising the evaluation of outcomes by advanced statistical tools. The novel integral baseline-correction procedure is based on the more sound assumption that the effect of capillary fouling on scattering increases monotonically with the intensity scattered by the material within the X-ray beam. Overlapping peaks, often skewed because of sample interaction with the column matrix, can now be accurately decomposed using non-symmetrical modified Gaussian functions. As an example, the case of a polydisperse solution of aldolase is analyzed: from heavily convoluted peaks, individual SAXS profiles of tetramers, octamers and dodecamers are extracted and reliably modeled. PMID:27738419

Evolution of the frequency chirp of Gaussian pulses and beams when passing through a pulse compressor.

PubMed

Li, Derong; Lv, Xiaohua; Bowlan, Pamela; Du, Rui; Zeng, Shaoqun; Luo, Qingming

2009-09-14

The evolution of the frequency chirp of a laser pulse inside a classical pulse compressor is very different for plane waves and Gaussian beams, although after propagating through the last (4th) dispersive element, the two models give the same results. In this paper, we have analyzed the evolution of the frequency chirp of Gaussian pulses and beams using a method which directly obtains the spectral phase acquired by the compressor. We found the spatiotemporal couplings in the phase to be the fundamental reason for the difference in the frequency chirp acquired by a Gaussian beam and a plane wave. When the Gaussian beam propagates, an additional frequency chirp will be introduced if any spatiotemporal couplings (i.e. angular dispersion, spatial chirp or pulse front tilt) are present. However, if there are no couplings present, the chirp of the Gaussian beam is the same as that of a plane wave. When the Gaussian beam is well collimated, the introduced frequency chirp predicted by the plane wave and Gaussian beam models are in closer agreement. This work improves our understanding of pulse compressors and should be helpful for optimizing dispersion compensation schemes in many applications of femtosecond laser pulses.

Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising.

PubMed

Zhang, Kai; Zuo, Wangmeng; Chen, Yunjin; Meng, Deyu; Zhang, Lei

2017-07-01

The discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm, and regularization method into image denoising. Specifically, residual learning and batch normalization are utilized to speed up the training process as well as boost the denoising performance. Different from the existing discriminative denoising models which usually train a specific model for additive white Gaussian noise at a certain noise level, our DnCNN model is able to handle Gaussian denoising with unknown noise level (i.e., blind Gaussian denoising). With the residual learning strategy, DnCNN implicitly removes the latent clean image in the hidden layers. This property motivates us to train a single DnCNN model to tackle with several general image denoising tasks, such as Gaussian denoising, single image super-resolution, and JPEG image deblocking. Our extensive experiments demonstrate that our DnCNN model can not only exhibit high effectiveness in several general image denoising tasks, but also be efficiently implemented by benefiting from GPU computing.

Diversity in the Visible-NIR Absorption Band Characteristics of Lunar and Asteroidal Plagioclase

NASA Technical Reports Server (NTRS)

Hiroi, T.; Kaiden, H.; Misawa, K.; Kojima, H.; Uemoto, K.; Ohtake, M.; Arai, T.; Sasaki, S.; Takeda, H.; Nyquist, L. E.;

Performance of a Diaphragmed Microlens for a Packaged Microspectrometer

PubMed Central

Lo, Joe; Chen, Shih-Jui; Fang, Qiyin; Papaioannou, Thanassis; Kim, Eun-Sok; Gundersen, Martin; Marcu, Laura

2009-01-01

This paper describes the design, fabrication, packaging and testing of a microlens integrated in a multi-layered MEMS microspectrometer. The microlens was fabricated using modified PDMS molding to form a suspended lens diaphragm. Gaussian beam propagation model was used to measure the focal length and quantify M2 value of the microlens. A tunable calibration source was set up to measure the response of the packaged device. Dual wavelength separation by the packaged device was demonstrated by CCD imaging and beam profiling of the spectroscopic output. We demonstrated specific techniques to measure critical parameters of microoptics systems for future optimization of spectroscopic devices. PMID:22399943

Effects of the interaction range on structural phases of flexible polymers.

PubMed

Gross, J; Neuhaus, T; Vogel, T; Bachmann, M

2013-02-21

We systematically investigate how the range of interaction between non-bonded monomers influences the formation of structural phases of elastic, flexible polymers. Massively parallel replica-exchange simulations of a generic, coarse-grained model, performed partly on graphics processing units and in multiple-gaussian modified ensembles, pave the way for the construction of the structural phase diagram, parametrized by interaction range and temperature. Conformational transitions between gas-like, liquid, and diverse solid (pseudo) phases are identified by microcanonical statistical inflection-point analysis. We find evidence for finite-size effects that cause the crossover of "collapse" and "freezing" transitions for very short interaction ranges.

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

NASA Astrophysics Data System (ADS)

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

2012-09-01

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

Robust radio interferometric calibration using the t-distribution

NASA Astrophysics Data System (ADS)

Kazemi, S.; Yatawatta, S.

2013-10-01

A major stage of radio interferometric data processing is calibration or the estimation of systematic errors in the data and the correction for such errors. A stochastic error (noise) model is assumed, and in most cases, this underlying model is assumed to be Gaussian. However, outliers in the data due to interference or due to errors in the sky model would have adverse effects on processing based on a Gaussian noise model. Most of the shortcomings of calibration such as the loss in flux or coherence, and the appearance of spurious sources, could be attributed to the deviations of the underlying noise model. In this paper, we propose to improve the robustness of calibration by using a noise model based on Student's t-distribution. Student's t-noise is a special case of Gaussian noise when the variance is unknown. Unlike Gaussian-noise-model-based calibration, traditional least-squares minimization would not directly extend to a case when we have a Student's t-noise model. Therefore, we use a variant of the expectation-maximization algorithm, called the expectation-conditional maximization either algorithm, when we have a Student's t-noise model and use the Levenberg-Marquardt algorithm in the maximization step. We give simulation results to show the robustness of the proposed calibration method as opposed to traditional Gaussian-noise-model-based calibration, especially in preserving the flux of weaker sources that are not included in the calibration model.

Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems.

PubMed

Sapsis, Themistoklis P; Majda, Andrew J

2013-08-20

A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems is developed here. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear nonnormal dynamics in the unperturbed system and energy-conserving nonlinear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. In the Lorenz 96 model, the ROMQG algorithm with just a single mode captures the transient response to random or deterministic forcing. For the baroclinic ocean turbulence models, the inexpensive ROMQG algorithm with 252 modes, less than 0.2% of the total, captures the nonlinear response of the energy, the heat flux, and even the one-dimensional energy and heat flux spectra.

Infrared maritime target detection using a probabilistic single Gaussian model of sea clutter in Fourier domain

NASA Astrophysics Data System (ADS)

Zhou, Anran; Xie, Weixin; Pei, Jihong; Chen, Yapei

2018-02-01

For ship targets detection in cluttered infrared image sequences, a robust detection method, based on the probabilistic single Gaussian model of sea background in Fourier domain, is put forward. The amplitude spectrum sequences at each frequency point of the pure seawater images in Fourier domain, being more stable than the gray value sequences of each background pixel in the spatial domain, are regarded as a Gaussian model. Next, a probability weighted matrix is built based on the stability of the pure seawater's total energy spectrum in the row direction, to make the Gaussian model more accurate. Then, the foreground frequency points are separated from the background frequency points by the model. Finally, the false-alarm points are removed utilizing ships' shape features. The performance of the proposed method is tested by visual and quantitative comparisons with others.

Modified fundamental Airy wave.

PubMed

Seshadri, S R

2014-01-01

The propagation characteristics of the fundamental Airy wave are obtained; the intensity distribution is the same as that for a point electric dipole situated at the origin and oriented normal to the propagation direction. The propagation characteristics of the modified fundamental Airy wave are determined. These characteristics are the same as those for the fundamental Gaussian wave provided that an equivalent waist is identified for the Airy wave. In general, the waves are localized spatially with the peak in the propagation direction.

A Heavy Tailed Expectation Maximization Hidden Markov Random Field Model with Applications to Segmentation of MRI

PubMed Central

Castillo-Barnes, Diego; Peis, Ignacio; Martínez-Murcia, Francisco J.; Segovia, Fermín; Illán, Ignacio A.; Górriz, Juan M.; Ramírez, Javier; Salas-Gonzalez, Diego

2017-01-01

A wide range of segmentation approaches assumes that intensity histograms extracted from magnetic resonance images (MRI) have a distribution for each brain tissue that can be modeled by a Gaussian distribution or a mixture of them. Nevertheless, intensity histograms of White Matter and Gray Matter are not symmetric and they exhibit heavy tails. In this work, we present a hidden Markov random field model with expectation maximization (EM-HMRF) modeling the components using the α-stable distribution. The proposed model is a generalization of the widely used EM-HMRF algorithm with Gaussian distributions. We test the α-stable EM-HMRF model in synthetic data and brain MRI data. The proposed methodology presents two main advantages: Firstly, it is more robust to outliers. Secondly, we obtain similar results than using Gaussian when the Gaussian assumption holds. This approach is able to model the spatial dependence between neighboring voxels in tomographic brain MRI. PMID:29209194

Improved Gaussian Beam-Scattering Algorithm

NASA Technical Reports Server (NTRS)

Lock, James A.

1995-01-01

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.

Modélisation de la viscoélasticité transverse du bois vert à l'aide d'une combinaison de deux éléments paraboliques

NASA Astrophysics Data System (ADS)

Bardet, Sandrine; Gril, Joseph

The rigidity in radial compression at different levels of temperature and strain rate have been measured on green Boco, with a drastic softening around 60 ∘ C attributed to the glassy transition of lignin. The representation of experimental results in an approximated complex diagram revealed a secondary viscoelastic process occurring at lower temperature. A multiparabolic model was used for the analysis. For convenience, each parabolic element was replaced by a generalised Maxwell model with a modified-Gaussian relaxation spectrum. This model fitted correctly the observed behaviour of wood in the time range of 0.05 to 50 sec and temperature between 10 to 90 ∘ C. To cite this article: S. Bardet, J. Gril, C. R. Mecanique 330 (2002) 549-556.

Emission wavelength tuning of fluorescence by fine structural control of optical metamaterials with Fano resonance

PubMed Central

Moritake, Y.; Kanamori, Y.; Hane, K.

2016-01-01

We demonstrated fine emission wavelength tuning of quantum dot (QD) fluorescence by fine structural control of optical metamaterials with Fano resonance. An asymmetric-double-bar (ADB), which was composed of only two bars with slightly different bar lengths, was used to obtain Fano resonance in the optical region. By changing the short bar length of ADB structures with high dimensional accuracy in the order of 10 nm, resonant wavelengths of Fano resonance were controlled from 1296 to 1416 nm. Fluorescence of QDs embedded in a polymer layer on ADB metamaterials were modified due to coupling to Fano resonance and fine tuning from 1350 to 1376 nm was observed. Wavelength tuning of modified fluorescence was reproduced by analysis using absorption peaks of Fano resonance. Tuning range of modified fluorescence became narrow, which was interpreted by a simple Gaussian model and resulted from comparable FWHM in QD fluorescence and Fano resonant peaks. The results will help the design and fabrication of metamaterial devices with fluorophores such as light sources and biomarkers. PMID:27622503

Calculation of exchange interaction for modified Gaussian coupled quantum dots

NASA Astrophysics Data System (ADS)

Khordad, R.

2017-08-01

A system of two laterally coupled quantum dots with modified Gaussian potential has been considered. Each quantum dot has an electron under electric and magnetic field. The quantum dots have been considered as hydrogen-like atoms. The physical picture has translated into the Heisenberg spin Hamiltonian. The Schrödinger equation using finite element method has been numerically solved. The exchange energy factor has been calculated as a functions of electric field, magnetic field, and the separation distance between the centers of the dots ( d). According to the results, it is found that there is the transition from anti-ferromagnetic to ferromagnetic for constant electric field. Also, the transition occurs from ferromagnetic to anti-ferromagnetic for constant magnetic field (B>1 T). With decreasing the distance between the centers of the dots and increasing magnetic field, the transition occurs from anti-ferromagnetic to ferromagnetic. It is found that a switching of exchange energy factor is presented without canceling the interactions of the electric and magnetic fields on the system.

Anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field: two-loop approximation.

PubMed

Adzhemyan, L Ts; Antonov, N V; Honkonen, J; Kim, T L

2005-01-01

The field theoretic renormalization group and operator-product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the Navier-Stokes equation, subject to an external random stirring force with the correlation function proportional to delta(t- t')k(4-d-2epsilon). It is shown that the scalar field is intermittent already for small epsilon, its structure functions display anomalous scaling behavior, and the corresponding exponents can be systematically calculated as series in epsilon. The practical calculation is accomplished to order epsilon2 (two-loop approximation), including anisotropic sectors. As for the well-known Kraichnan rapid-change model, the anomalous scaling results from the existence in the model of composite fields (operators) with negative scaling dimensions, identified with the anomalous exponents. Thus the mechanism of the origin of anomalous scaling appears similar for the Gaussian model with zero correlation time and the non-Gaussian model with finite correlation time. It should be emphasized that, in contrast to Gaussian velocity ensembles with finite correlation time, the model and the perturbation theory discussed here are manifestly Galilean covariant. The relevance of these results for real passive advection and comparison with the Gaussian models and experiments are briefly discussed.

Soft Mixer Assignment in a Hierarchical Generative Model of Natural Scene Statistics

PubMed Central

Schwartz, Odelia; Sejnowski, Terrence J.; Dayan, Peter

2010-01-01

Gaussian scale mixture models offer a top-down description of signal generation that captures key bottom-up statistical characteristics of filter responses to images. However, the pattern of dependence among the filters for this class of models is prespecified. We propose a novel extension to the gaussian scale mixture model that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs. Specifically, we propose that inputs are generated by gaussian variables (modeling local filter structure), multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers. We demonstrate inference of both components of the generative model, for synthesized data and for different classes of natural images, such as a generic ensemble and faces. For natural images, the mixer variable assignments show invariances resembling those of complex cells in visual cortex; the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models. We also show how our model helps interrelate a wide range of models of image statistics and cortical processing. PMID:16999575

Corneal changes induced by laser ablation: study of the visual-quality evolution by a customized eye model

NASA Astrophysics Data System (ADS)

Ortiz, D.; Anera, R. G.; Saiz, J. M.; Jiménez, J. R.; Moreno, F.; Jiménez Del Barco, L.; González, F.

2006-11-01

This study focuses on the changes induced in both the asphericity and homogeneity of the cornea for a group of myopic eyes undergoing LASIK surgery. Eyes were characterized by a Kooijman-based customized eye model in which changes were introduced in the form of Gaussian-distributed refractive-index variations of given correlation length for the inhomogeneities and in the form of an expression, based on the modified Munnerlyn's paraxial formula, for the post-LASIK asphericity. Visual quality was evaluated in terms of the Modulation Transfer Function and the Point-Spread Function. The results show that, on average, the evolution of visual acuity is consistent with the change in corneal asphericity, while the evolution of contrast sensitivity requires a loss in corneal homogeneity in order to be explained. By including both effects in the model, the overall model performance in predicting visual quality is improved.

Curvaton scenario within the minimal supersymmetric standard model and predictions for non-Gaussianity.

PubMed

Mazumdar, Anupam; Nadathur, Seshadri

2012-03-16

We provide a model in which both the inflaton and the curvaton are obtained from within the minimal supersymmetric standard model, with known gauge and Yukawa interactions. Since now both the inflaton and curvaton fields are successfully embedded within the same sector, their decay products thermalize very quickly before the electroweak scale. This results in two important features of the model: first, there will be no residual isocurvature perturbations, and second, observable non-Gaussianities can be generated with the non-Gaussianity parameter f(NL)~O(5-1000) being determined solely by the combination of weak-scale physics and the standard model Yukawa interactions.

An adaptive Hinfinity controller design for bank-to-turn missiles using ridge Gaussian neural networks.

PubMed

Lin, Chuan-Kai; Wang, Sheng-De

2004-11-01

A new autopilot design for bank-to-turn (BTT) missiles is presented. In the design of autopilot, a ridge Gaussian neural network with local learning capability and fewer tuning parameters than Gaussian neural networks is proposed to model the controlled nonlinear systems. We prove that the proposed ridge Gaussian neural network, which can be a universal approximator, equals the expansions of rotated and scaled Gaussian functions. Although ridge Gaussian neural networks can approximate the nonlinear and complex systems accurately, the small approximation errors may affect the tracking performance significantly. Therefore, by employing the Hinfinity control theory, it is easy to attenuate the effects of the approximation errors of the ridge Gaussian neural networks to a prescribed level. Computer simulation results confirm the effectiveness of the proposed ridge Gaussian neural networks-based autopilot with Hinfinity stabilization.

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.

PubMed

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Gaussian signal relaxation around spin echoes: Implications for precise reversible transverse relaxation quantification of pulmonary tissue at 1.5 and 3 Tesla.

PubMed

Zapp, Jascha; Domsch, Sebastian; Weingärtner, Sebastian; Schad, Lothar R

2017-05-01

To characterize the reversible transverse relaxation in pulmonary tissue and to study the benefit of a quadratic exponential (Gaussian) model over the commonly used linear exponential model for increased quantification precision. A point-resolved spectroscopy sequence was used for comprehensive sampling of the relaxation around spin echoes. Measurements were performed in an ex vivo tissue sample and in healthy volunteers at 1.5 Tesla (T) and 3 T. The goodness of fit using χred2 and the precision of the fitted relaxation time by means of its confidence interval were compared between the two relaxation models. The Gaussian model provides enhanced descriptions of pulmonary relaxation with lower χred2 by average factors of 4 ex vivo and 3 in volunteers. The Gaussian model indicates higher sensitivity to tissue structure alteration with increased precision of reversible transverse relaxation time measurements also by average factors of 4 ex vivo and 3 in volunteers. The mean relaxation times of the Gaussian model in volunteers are T2,G' = (1.97 ± 0.27) msec at 1.5 T and T2,G' = (0.83 ± 0.21) msec at 3 T. Pulmonary signal relaxation was found to be accurately modeled as Gaussian, providing a potential biomarker T2,G' with high sensitivity. Magn Reson Med 77:1938-1945, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Separation of the atmospheric variability into non-Gaussian multidimensional sources by projection pursuit techniques

NASA Astrophysics Data System (ADS)

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 (positive and negative phases of the Arctic Oscillation and of the North Atlantic Oscillation). Triads are also likely in the QG model but of weaker expression than dyads due to the imposed shape and dimension. The study emphasizes the existence of nonlinear dyadic and triadic nonlinear teleconnections.

Phenomenological Study of Interaction between Solar Acoustic Waves and Sunspots from Measured Scattered Wavefunctions

NASA Astrophysics Data System (ADS)

Yang, Ming-Hsu; Chou, Dean-Yi; Zhao, Hui; Liang, Zhi-Chao

2012-08-01

The solar acoustic waves around a sunspot are modified because of the interaction with the sunspot. The interaction can be viewed as that the sunspot, excited by the incident wave, generates the scattered wave, and the scattered wave is added to the incident wave to form the total wave around the sunspot. We define an interaction parameter, which could be complex, describing the interaction between the acoustic waves and the sunspot. The scattered wavefunction on the surface can be expressed as a two-dimensional integral of the product of the Green's function, the wavefunction, and the two-dimensional interaction parameter over the sunspot area for the Born approximation of different orders. We assume a simple model for the two-dimensional interaction parameter distribution: its absolute value is axisymmetric with a Gaussian distribution and its phase is a constant. The measured scattered wavefunctions of various modes for NOAAs 11084 and 11092 are fitted to the theoretical scattered wavefunctions to determine the three model parameters, magnitude, Gaussian radius, and phase, for the Born approximation of different orders. The three model parameters converge to some values at high-order Born approximations. The result of the first-order Born approximation is significantly different from the convergent value in some cases. The rate of convergence depends on the sunspot size and wavelength. It converges more rapidly for the smaller sunspot and longer wavelength. The magnitude increases with mode frequency and degree for each radial order. The Gaussian radius is insensitive to frequency and degree. The spatial range of the interaction parameter is greater than that of the continuum intensity deficit, but smaller than that of the acoustic power deficit of the sunspot. The phase versus phase speed falls into a small range. This suggests that the phase could be a function phase speed. NOAAs 11084 and 11092 have a similar magnitude and phase, although the ratio of their sizes is 0.75.

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

PubMed

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

2018-06-01

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

Analysis of low altitude atmospheric turbulence data measured in flight

NASA Technical Reports Server (NTRS)

Ganzer, V. M.; Joppa, R. G.; Vanderwees, G.

1977-01-01

All three components of turbulence were measured simultaneously in flight at each wing tip of a Beech D-18 aircraft. The flights were conducted at low altitude, 30.5 - 61.0 meters (100-200 ft.), over water in the presence of wind driven turbulence. Statistical properties of flight measured turbulence were compared with Gaussian and non-Gaussian turbulence models. Spatial characteristics of the turbulence were analyzed using the data from flight perpendicular and parallel to the wind. The probability density distributions of the vertical gusts show distinctly non-Gaussian characteristics. The distributions of the longitudinal and lateral gusts are generally Gaussian. The power spectra compare in the inertial subrange at some points better with the Dryden spectrum, while at other points the von Karman spectrum is a better approximation. In the low frequency range the data show peaks or dips in the power spectral density. The cross between vertical gusts in the direction of the mean wind were compared with a matched non-Gaussian model. The real component of the cross spectrum is in general close to the non-Gaussian model. The imaginary component, however, indicated a larger phase shift between these two gust components than was found in previous research.

Smoothing the Marmousi Model

NASA Astrophysics Data System (ADS)

Žáček, K.

Summary- The only way to make an excessively complex velocity model suitable for application of ray-based methods, such as the Gaussian beam or Gaussian packet methods, is to smooth it. We have smoothed the Marmousi model by choosing a coarser grid and by minimizing the second spatial derivatives of the slowness. This was done by minimizing the relevant Sobolev norm of slowness. We show that minimizing the relevant Sobolev norm of slowness is a suitable technique for preparing the optimum models for asymptotic ray theory methods. However, the price we pay for a model suitable for ray tracing is an increase of the difference between the smoothed and original model. Similarly, the estimated error in the travel time also increases due to the difference between the models. In smoothing the Marmousi model, we have found the estimated error of travel times at the verge of acceptability. Due to the low frequencies in the wavefield of the original Marmousi data set, we have found the Gaussian beams and Gaussian packets at the verge of applicability even in models sufficiently smoothed for ray tracing.

Topology in two dimensions. IV - CDM models with non-Gaussian initial conditions

NASA Astrophysics Data System (ADS)

Coles, Peter; Moscardini, Lauro; Plionis, Manolis; Lucchin, Francesco; Matarrese, Sabino; Messina, Antonio

1993-02-01

The results of N-body simulations with both Gaussian and non-Gaussian initial conditions are used here to generate projected galaxy catalogs with the same selection criteria as the Shane-Wirtanen counts of galaxies. The Euler-Poincare characteristic is used to compare the statistical nature of the projected galaxy clustering in these simulated data sets with that of the observed galaxy catalog. All the models produce a topology dominated by a meatball shift when normalized to the known small-scale clustering properties of galaxies. Models characterized by a positive skewness of the distribution of primordial density perturbations are inconsistent with the Lick data, suggesting problems in reconciling models based on cosmic textures with observations. Gaussian CDM models fit the distribution of cell counts only if they have a rather high normalization but possess too low a coherence length compared with the Lick counts. This suggests that a CDM model with extra large scale power would probably fit the available data.

Capacity of PPM on Gaussian and Webb Channels

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Receiver design for SPAD-based VLC systems under Poisson-Gaussian mixed noise model.

PubMed

Mao, Tianqi; Wang, Zhaocheng; Wang, Qi

2017-01-23

Single-photon avalanche diode (SPAD) is a promising photosensor because of its high sensitivity to optical signals in weak illuminance environment. Recently, it has drawn much attention from researchers in visible light communications (VLC). However, existing literature only deals with the simplified channel model, which only considers the effects of Poisson noise introduced by SPAD, but neglects other noise sources. Specifically, when an analog SPAD detector is applied, there exists Gaussian thermal noise generated by the transimpedance amplifier (TIA) and the digital-to-analog converter (D/A). Therefore, in this paper, we propose an SPAD-based VLC system with pulse-amplitude-modulation (PAM) under Poisson-Gaussian mixed noise model, where Gaussian-distributed thermal noise at the receiver is also investigated. The closed-form conditional likelihood of received signals is derived using the Laplace transform and the saddle-point approximation method, and the corresponding quasi-maximum-likelihood (quasi-ML) detector is proposed. Furthermore, the Poisson-Gaussian-distributed signals are converted to Gaussian variables with the aid of the generalized Anscombe transform (GAT), leading to an equivalent additive white Gaussian noise (AWGN) channel, and a hard-decision-based detector is invoked. Simulation results demonstrate that, the proposed GAT-based detector can reduce the computational complexity with marginal performance loss compared with the proposed quasi-ML detector, and both detectors are capable of accurately demodulating the SPAD-based PAM signals.

On the lorentzian versus Gaussian character of time-domain spin-echo signals from the brain as sampled by means of gradient-echoes: Implications for quantitative transverse relaxation studies.

PubMed

Mulkern, Robert V; Balasubramanian, Mukund; Mitsouras, Dimitrios

2014-07-30

To determine whether Lorentzian or Gaussian intra-voxel frequency distributions are better suited for modeling data acquired with gradient-echo sampling of single spin-echoes for the simultaneous characterization of irreversible and reversible relaxation rates. Clinical studies (e.g., of brain iron deposition) using such acquisition schemes have typically assumed Lorentzian distributions. Theoretical expressions of the time-domain spin-echo signal for intra-voxel Lorentzian and Gaussian distributions were used to fit data from a human brain scanned at both 1.5 Tesla (T) and 3T, resulting in maps of irreversible and reversible relaxation rates for each model. The relative merits of the Lorentzian versus Gaussian model were compared by means of quality of fit considerations. Lorentzian fits were equivalent to Gaussian fits primarily in regions of the brain where irreversible relaxation dominated. In the multiple brain regions where reversible relaxation effects become prominent, however, Gaussian fits were clearly superior. The widespread assumption that a Lorentzian distribution is suitable for quantitative transverse relaxation studies of the brain should be reconsidered, particularly at 3T and higher field strengths as reversible relaxation effects become more prominent. Gaussian distributions offer alternate fits of experimental data that should prove quite useful in general. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc. © 2014 Wiley Periodicals, Inc.

Interactive Gaussian Graphical Models for Discovering Depth Trends in ChemCam Data

NASA Astrophysics Data System (ADS)

Oyen, D. A.; Komurlu, C.; Lanza, N. L.

2018-04-01

Interactive Gaussian graphical models discover surface compositional features on rocks in ChemCam targets. Our approach visualizes shot-to-shot relationships among LIBS observations, and identifies the wavelengths involved in the trend.

Simulating the effect of non-linear mode coupling in cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Kiessling, A.; Taylor, A. N.; Heavens, A. F.

2011-09-01

Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment and to optimize the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimization it is usually assumed that the power-spectrum covariance matrix is diagonal in Fourier space. However, in the low-redshift Universe, non-linear mode coupling will tend to correlate small-scale power, moving information from lower to higher order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naïve Gaussian Fisher matrix forecasts with a maximum likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2D and tomographic shear analysis of a Euclid-like survey. In both cases, we find that the 68 per cent confidence area of the Ωm-σ8 plane increases by a factor of 5. However, the marginal errors increase by just 20-40 per cent. We propose a new method to model the effects of non-linear shear-power mode coupling in the Fisher matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68 per cent confidence regions of the full maximum likelihood analysis in the Ωm-σ8 plane to high accuracy for both 2D and tomographic weak lensing surveys. Finally, we perform a multiparameter analysis of Ωm, σ8, h, ns, w0 and wa to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The 6D volume of the 1σ error contours for the non-linear Fisher analysis is a factor of 3 larger than for the Gaussian case, and the shape of the 68 per cent confidence volume is modified. We propose that future Fisher matrix estimates of cosmological parameter accuracies should include mode-coupling effects.

Characterization of Adrenal Adenoma by Gaussian Model-Based Algorithm.

PubMed

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

2016-01-01

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

Assimilating every-30-second 100-m-mesh radar observations for convective weather: implications to non-Gaussian PDF

NASA Astrophysics Data System (ADS)

Miyoshi, T.; Teramura, T.; Ruiz, J.; Kondo, K.; Lien, G. Y.

2016-12-01

Convective weather is known to be highly nonlinear and chaotic, and it is hard to predict their location and timing precisely. Our Big Data Assimilation (BDA) effort has been exploring to use dense and frequent observations to avoid non-Gaussian probability density function (PDF) and to apply an ensemble Kalman filter under the Gaussian error assumption. The phased array weather radar (PAWR) can observe a dense three-dimensional volume scan with 100-m range resolution and 100 elevation angles in only 30 seconds. The BDA system assimilates the PAWR reflectivity and Doppler velocity observations every 30 seconds into 100 ensemble members of storm-scale numerical weather prediction (NWP) model at 100-m grid spacing. The 30-second-update, 100-m-mesh BDA system has been quite successful in multiple case studies of local severe rainfall events. However, with 1000 ensemble members, the reduced-resolution BDA system at 1-km grid spacing showed significant non-Gaussian PDF with every-30-second updates. With a 10240-member ensemble Kalman filter with a global NWP model at 112-km grid spacing, we found roughly 1000 members satisfactory to capture the non-Gaussian error structures. With these in mind, we explore how the density of observations in space and time affects the non-Gaussianity in an ensemble Kalman filter with a simple toy model. In this presentation, we will present the most up-to-date results of the BDA research, as well as the investigation with the toy model on the non-Gaussianity with dense and frequent observations.

Wind field near complex terrain using numerical weather prediction model

NASA Astrophysics Data System (ADS)

Chim, Kin-Sang

The PennState/NCAR MM5 model was modified to simulate an idealized flow pass through a 3D obstacle in the Micro- Alpha Scale domain. The obstacle used were the idealized Gaussian obstacle and the real topography of Lantau Island of Hong Kong. The Froude number under study is ranged from 0.22 to 1.5. Regime diagrams for both the idealized Gaussian obstacle and Lantau island were constructed. This work is divided into five parts. The first part is the problem definition and the literature review of the related publications. The second part briefly discuss as the PennState/NCAR MM5 model and a case study of long- range transport is included. The third part is devoted to the modification and the verification of the PennState/NCAR MM5 model on the Micro-Alpha Scale domain. The implementation of the Orlanski (1976) open boundary condition is included with the method of single sounding initialization of the model. Moreover, an upper dissipative layer, Klemp and Lilly (1978), is implemented on the model. The simulated result is verified by the Automatic Weather Station (AWS) data and the Wind Profiler data. Four different types of Planetary Boundary Layer (PBL) parameterization schemes have been investigated in order to find out the most suitable one for Micro-Alpha Scale domain in terms of both accuracy and efficiency. Bulk Aerodynamic type of PBL parameterization scheme is found to be the most suitable PBL parameterization scheme. Investigation of the free- slip lower boundary condition is performed and the simulated result is compared with that with friction. The fourth part is the use of the modified PennState/NCAR MM5 model for an idealized flow simulation. The idealized uniform flow used is nonhydrostatic and has constant Froude number. Sensitivity test is performed by varying the Froude number and the regime diagram is constructed. Moreover, nondimensional drag is found to be useful for regime identification. The model result is also compared with the analytic results by Miles (1969) and Smith (1980, 1985), and the numerical results of Stein (1992), Miranda and James (1992) and Olaffson and Bougeault (1997). It is found that the simulated result in the present study is comparable with others. The fifth part is the construction of the regime diagram for the Lantau island of Hong Kong. All eight major wind directions are discussed.

Experimental study of the focusing properties of a Gaussian Schell-model vortex beam

NASA Astrophysics Data System (ADS)

Wang, Fei; Zhu, Shijun; Cai, Yangjian

2011-08-01

We carry out an experimental and theoretical study of the focusing properties of a Gaussian Schell-model (GSM) vortex beam. It is found that we can shape the beam profile of the focused GSM vortex beam by varying its initial spatial coherence width. Focused dark hollow, flat-topped, and Gaussian beam spots can be obtained in our experiment, which will be useful for trapping particles. The experimental results agree well with the theoretical results.

A perturbative approach to the redshift space correlation function: beyond the Standard Model

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

Bose, Benjamin; Koyama, Kazuya, E-mail: benjamin.bose@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model whichmore » is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with ≤ 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpc h ≤ s ≤ 180Mpc/ h . Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.« less

Event rate and reaction time performance in ADHD: Testing predictions from the state regulation deficit hypothesis using an ex-Gaussian model.

PubMed

Metin, Baris; Wiersema, Jan R; Verguts, Tom; Gasthuys, Roos; van Der Meere, Jacob J; Roeyers, Herbert; Sonuga-Barke, Edmund

2016-01-01

According to the state regulation deficit (SRD) account, ADHD is associated with a problem using effort to maintain an optimal activation state under demanding task settings such as very fast or very slow event rates. This leads to a prediction of disrupted performance at event rate extremes reflected in higher Gaussian response variability that is a putative marker of activation during motor preparation. In the current study, we tested this hypothesis using ex-Gaussian modeling, which distinguishes Gaussian from non-Gaussian variability. Twenty-five children with ADHD and 29 typically developing controls performed a simple Go/No-Go task under four different event-rate conditions. There was an accentuated quadratic relationship between event rate and Gaussian variability in the ADHD group compared to the controls. The children with ADHD had greater Gaussian variability at very fast and very slow event rates but not at moderate event rates. The results provide evidence for the SRD account of ADHD. However, given that this effect did not explain all group differences (some of which were independent of event rate) other cognitive and/or motivational processes are also likely implicated in ADHD performance deficits.

INPUFF: A SINGLE SOURCE GAUSSIAN PUFF DISPERSION ALGORITHM. USER'S GUIDE

EPA Science Inventory

INPUFF is a Gaussian INtegrated PUFF model. The Gaussian puff diffusion equation is used to compute the contribution to the concentration at each receptor from each puff every time step. Computations in INPUFF can be made for a single point source at up to 25 receptor locations. ...

Sparse covariance estimation in heterogeneous samples*

PubMed Central

Rodríguez, Abel; Lenkoski, Alex; Dobra, Adrian

2015-01-01

Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to nonlinear relationships among variables. To address such situations we explore mixtures of Gaussian graphical models; in particular, we consider both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. As an illustration, we study the trends in foreign exchange rate fluctuations in the pre-Euro era. PMID:26925189

SU-F-T-158: Experimental Characterization of Field Size Dependence of Dose and Lateral Beam Profiles of Scanning Proton and Carbon Ion Beams for Empirical Model in Air

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

Li, Y; Hsi, W; Zhao, J

2016-06-15

Purpose: The Gaussian model for the lateral profiles in air is crucial for an accurate treatment planning system. The field size dependence of dose and the lateral beam profiles of scanning proton and carbon ion beams are due mainly to particles undergoing multiple Coulomb scattering in the beam line components and secondary particles produced by nuclear interactions in the target, both of which depend upon the energy and species of the beam. In this work, lateral profile shape parameters were fitted to measurements of field size dependence dose at the center of field size in air. Methods: Previous studies havemore » employed empirical fits to measured profile data to significantly reduce the QA time required for measurements. From this approach to derive the weight and sigma of lateral profiles in air, empirical model formulations were simulated for three selected energies for both proton and carbon beams. Results: The 20%–80% lateral penumbras predicted by the double model for proton and single model for carbon with the error functions agreed with the measurements within 1 mm. The standard deviation between measured and fitted field size dependence of dose for empirical model in air has a maximum accuracy of 0.74% for proton with double Gaussian, and of 0.57% for carbon with single Gaussian. Conclusion: We have demonstrated that the double Gaussian model of lateral beam profiles is significantly better than the single Gaussian model for proton while a single Gaussian model is sufficient for carbon. The empirical equation may be used to double check the separately obtained model that is currently used by the planning system. The empirical model in air for dose of spot scanning proton and carbon ion beams cannot be directly used for irregular shaped patient fields, but can be to provide reference values for clinical use and quality assurance.« less

On the numbers of images of two stochastic gravitational lensing models

NASA Astrophysics Data System (ADS)

Wei, Ang

2017-02-01

We study two gravitational lensing models with Gaussian randomness: the continuous mass fluctuation model and the floating black hole model. The lens equations of these models are related to certain random harmonic functions. Using Rice's formula and Gaussian techniques, we obtain the expected numbers of zeros of these functions, which indicate the amounts of images in the corresponding lens systems.

Solute Concentration at a Pumping Well in Non-Gaussian Random Aquifers under Time-Varying Operational Schedules

NASA Astrophysics Data System (ADS)

Libera, A.; de Barros, F.; Riva, M.; Guadagnini, A.

2016-12-01

Managing contaminated groundwater systems is an arduous task for multiple reasons. First, subsurface hydraulic properties are heterogeneous and the high costs associated with site characterization leads to data scarcity (therefore, model predictions are uncertain). Second, it is common for water agencies to schedule groundwater extraction through a temporal sequence of pumping rates to maximize the benefits to anthropogenic activities and minimize the environmental footprint of the withdrawal operations. The temporal variability in pumping rates and aquifer heterogeneity affect dilution rates of contaminant plumes and chemical concentration breakthrough curves (BTCs) at the well. While contaminant transport under steady-state pumping is widely studied, the manner in which a given time-varying pumping schedule affects contaminant plume behavior is tackled only marginally. At the same time, most studies focus on the impact of Gaussian random hydraulic conductivity (K) fields on transport. Here, we systematically analyze the significance of the random space function (RSF) model characterizing K in the presence of distinct pumping operations on the uncertainty of the concentration BTC at the operating well. We juxtapose Monte Carlo based numerical results associated with two models: (a) a recently proposed Generalized Sub-Gaussian model which allows capturing non-Gaussian statistical scaling features of RSFs such as hydraulic conductivity, and (b) the commonly used Gaussian field approximation. Our novel results include an appraisal of the coupled effect of (a) the model employed to depict the random spatial variability of K and (b) transient flow regime, as induced by a temporally varying pumping schedule, on the concentration BTC at the operating well. We systematically quantify the sensitivity of the uncertainty in the contaminant BTC to the RSF model adopted for K (non-Gaussian or Gaussian) in the presence of diverse well pumping schedules. Results contribute to determine conditions under which any of these two key factors prevails on the other.

Stochastic inflation lattice simulations - Ultra-large scale structure of the universe

NASA Technical Reports Server (NTRS)

Salopek, D. S.

1991-01-01

Non-Gaussian fluctuations for structure formation may arise in inflation from the nonlinear interaction of long wavelength gravitational and scalar fields. Long wavelength fields have spatial gradients, a (exp -1), small compared to the Hubble radius, and they are described in terms of classical random fields that are fed by short wavelength quantum noise. Lattice Langevin calculations are given for a toy model with a scalar field interacting with an exponential potential where one can obtain exact analytic solutions of the Fokker-Planck equation. For single scalar field models that are consistent with current microwave background fluctuations, the fluctuations are Gaussian. However, for scales much larger than our observable Universe, one expects large metric fluctuations that are non-Gaussian. This example illuminates non-Gaussian models involving multiple scalar fields which are consistent with current microwave background limits.

Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models

NASA Astrophysics Data System (ADS)

Yang, Linxiao; Fang, Jun; Duan, Huiping; Li, Hongbin; Zeng, Bing

2018-06-01

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.

EM in high-dimensional spaces.

PubMed

Draper, Bruce A; Elliott, Daniel L; Hayes, Jeremy; Baek, Kyungim

2005-06-01

This paper considers fitting a mixture of Gaussians model to high-dimensional data in scenarios where there are fewer data samples than feature dimensions. Issues that arise when using principal component analysis (PCA) to represent Gaussian distributions inside Expectation-Maximization (EM) are addressed, and a practical algorithm results. Unlike other algorithms that have been proposed, this algorithm does not try to compress the data to fit low-dimensional models. Instead, it models Gaussian distributions in the (N - 1)-dimensional space spanned by the N data samples. We are able to show that this algorithm converges on data sets where low-dimensional techniques do not.

Doubly self-consistent field theory of grafted polymers under simple shear in steady state

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

Suo, Tongchuan; Whitmore, Mark D., E-mail: mark-whitmore@umanitoba.ca

2014-03-21

We present a generalization of the numerical self-consistent mean-field theory of polymers to the case of grafted polymers under simple shear. The general theoretical framework is presented, and then applied to three different chain models: rods, Gaussian chains, and finitely extensible nonlinear elastic (FENE) chains. The approach is self-consistent at two levels. First, for any flow field, the polymer density profile and effective potential are calculated self-consistently in a manner similar to the usual self-consistent field theory of polymers, except that the calculation is inherently two-dimensional even for a laterally homogeneous system. Second, through the use of a modified Brinkmanmore » equation, the flow field and the polymer profile are made self-consistent with respect to each other. For all chain models, we find that reasonable levels of shear cause the chains to tilt, but it has very little effect on the overall thickness of the polymer layer, causing a small decrease for rods, and an increase of no more than a few percent for the Gaussian and FENE chains. Using the FENE model, we also probe the individual bond lengths, bond correlations, and bond angles along the chains, the effects of the shear on them, and the solvent and bonded stress profiles. We find that the approximations needed within the theory for the Brinkman equation affect the bonded stress, but none of the other quantities.« less

A two-scale roughness model for the gloss of coated paper

NASA Astrophysics Data System (ADS)

Elton, N. J.

2008-08-01

A model for gloss is developed for surfaces with two-scale random roughness where one scale lies in the wavelength region (microroughness) and the other in the geometrical optics limit (macroroughness). A number of important industrial materials such as coated and printed paper and some paints exhibit such two-scale rough surfaces. Scalar Kirchhoff theory is used to describe scattering in the wavelength region and a facet model used for roughness features much greater than the wavelength. Simple analytical expressions are presented for the gloss of surfaces with Gaussian, modified and intermediate Lorentzian distributions of surface slopes, valid for gloss at high angle of incidence. In the model, gloss depends only on refractive index, rms microroughness amplitude and the FWHM of the surface slope distribution, all of which may be obtained experimentally. Model predictions are compared with experimental results for a range of coated papers and gloss standards, and found to be in fair agreement within model limitations.

Experimental study of the focusing properties of a Gaussian Schell-model vortex beam.

PubMed

Wang, Fei; Zhu, Shijun; Cai, Yangjian

2011-08-15

We carry out an experimental and theoretical study of the focusing properties of a Gaussian Schell-model (GSM) vortex beam. It is found that we can shape the beam profile of the focused GSM vortex beam by varying its initial spatial coherence width. Focused dark hollow, flat-topped, and Gaussian beam spots can be obtained in our experiment, which will be useful for trapping particles. The experimental results agree well with the theoretical results. © 2011 Optical Society of America

Study of Gaussian Doped Double Gate JunctionLess (GD-DG-JL) transistor including source drain depletion length: Model for sub-threshold behavior

NASA Astrophysics Data System (ADS)

Kumari, Vandana; Kumar, Ayush; Saxena, Manoj; Gupta, Mridula

2018-01-01

The sub-threshold model formulation of Gaussian Doped Double Gate JunctionLess (GD-DG-JL) FET including source/drain depletion length is reported in the present work under the assumption that the ungated regions are fully depleted. To provide deeper insight into the device performance, the impact of gaussian straggle, channel length, oxide and channel thickness and high-k gate dielectric has been studied using extensive TCAD device simulation.

High-Performance Clock Synchronization Algorithms for Distributed Wireless Airborne Computer Networks with Applications to Localization and Tracking of Targets

DTIC Science & Technology

2010-06-01

GMKPF represents a better and more flexible alternative to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ...accurate results relative to GML and EML when the network delays are modeled in terms of a single non-Gaussian/non-exponential distribution or as a...to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ) estimators for clock offset estimation in non-Gaussian or non

Electric dipole moment of the deuteron in the standard model with NN - ΛN - ΣN coupling

NASA Astrophysics Data System (ADS)

Yamanaka, Nodoka

2017-07-01

We calculate the electric dipole moment (EDM) of the deuteron in the standard model with | ΔS | = 1 interactions by taking into account the NN - ΛN - ΣN channel coupling, which is an important nuclear level systematics. The two-body problem is solved with the Gaussian Expansion Method using the realistic Argonne v18 nuclear force and the YN potential which can reproduce the binding energies of Λ3H, Λ3He, and Λ4He. The | ΔS | = 1 interbaryon potential is modeled by the one-meson exchange process. It is found that the deuteron EDM is modified by less than 10%, and the main contribution to this deviation is due to the polarization of the hyperon-nucleon channels. The effect of the YN interaction is small, and treating ΛN and ΣN channels as free is a good approximation for the EDM of the deuteron.

Signal Partitioning Algorithm for Highly Efficient Gaussian Mixture Modeling in Mass Spectrometry

PubMed Central

Polanski, Andrzej; Marczyk, Michal; Pietrowska, Monika; Widlak, Piotr; Polanska, Joanna

2015-01-01

Mixture - modeling of mass spectra is an approach with many potential applications including peak detection and quantification, smoothing, de-noising, feature extraction and spectral signal compression. However, existing algorithms do not allow for automated analyses of whole spectra. Therefore, despite highlighting potential advantages of mixture modeling of mass spectra of peptide/protein mixtures and some preliminary results presented in several papers, the mixture modeling approach was so far not developed to the stage enabling systematic comparisons with existing software packages for proteomic mass spectra analyses. In this paper we present an efficient algorithm for Gaussian mixture modeling of proteomic mass spectra of different types (e.g., MALDI-ToF profiling, MALDI-IMS). The main idea is automated partitioning of protein mass spectral signal into fragments. The obtained fragments are separately decomposed into Gaussian mixture models. The parameters of the mixture models of fragments are then aggregated to form the mixture model of the whole spectrum. We compare the elaborated algorithm to existing algorithms for peak detection and we demonstrate improvements of peak detection efficiency obtained by using Gaussian mixture modeling. We also show applications of the elaborated algorithm to real proteomic datasets of low and high resolution. PMID:26230717

Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.

PubMed

Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi

2015-02-01

We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.

Partial-Wave Representations of Laser Beams for Use in Light-Scattering Calculations

NASA Technical Reports Server (NTRS)

Gouesbet, Gerard; Lock, James A.; Grehan, Gerard

1995-01-01

In the framework of generalized Lorenz-Mie theory, laser beams are described by sets of beam-shape coefficients. The modified localized approximation to evaluate these coefficients for a focused Gaussian beam is presented. A new description of Gaussian beams, called standard beams, is introduced. A comparison is made between the values of the beam-shape coefficients in the framework of the localized approximation and the beam-shape coefficients of standard beams. This comparison leads to new insights concerning the electromagnetic description of laser beams. The relevance of our discussion is enhanced by a demonstration that the localized approximation provides a very satisfactory description of top-hat beams as well.

The formation of cosmic structure in a texture-seeded cold dark matter cosmogony

NASA Technical Reports Server (NTRS)

Gooding, Andrew K.; Park, Changbom; Spergel, David N.; Turok, Neil; Gott, Richard, III

1992-01-01

The growth of density fluctuations induced by global texture in an Omega = 1 cold dark matter (CDM) cosmogony is calculated. The resulting power spectra are in good agreement with each other, with more power on large scales than in the standard inflation plus CDM model. Calculation of related statistics (two-point correlation functions, mass variances, cosmic Mach number) indicates that the texture plus CDM model compares more favorably than standard CDM with observations of large-scale structure. Texture produces coherent velocity fields on large scales, as observed. Excessive small-scale velocity dispersions, and voids less empty than those observed may be remedied by including baryonic physics. The topology of the cosmic structure agrees well with observation. The non-Gaussian texture induced density fluctuations lead to earlier nonlinear object formation than in Gaussian models and may also be more compatible with recent evidence that the galaxy density field is non-Gaussian on large scales. On smaller scales the density field is strongly non-Gaussian, but this appears to be primarily due to nonlinear gravitational clustering. The velocity field on smaller scales is surprisingly Gaussian.

Non-Gaussian microwave background fluctuations from nonlinear gravitational effects

NASA Technical Reports Server (NTRS)

Salopek, D. S.; Kunstatter, G. (Editor)

1991-01-01

Whether the statistics of primordial fluctuations for structure formation are Gaussian or otherwise may be determined if the Cosmic Background Explorer (COBE) Satellite makes a detection of the cosmic microwave-background temperature anisotropy delta T(sub CMB)/T(sub CMB). Non-Gaussian fluctuations may be generated in the chaotic inflationary model if two scalar fields interact nonlinearly with gravity. Theoretical contour maps are calculated for the resulting Sachs-Wolfe temperature fluctuations at large angular scales (greater than 3 degrees). In the long-wavelength approximation, one can confidently determine the nonlinear evolution of quantum noise with gravity during the inflationary epoch because: (1) different spatial points are no longer in causal contact; and (2) quantum gravity corrections are typically small-- it is sufficient to model the system using classical random fields. If the potential for two scalar fields V(phi sub 1, phi sub 2) possesses a sharp feature, then non-Gaussian fluctuations may arise. An explicit model is given where cold spots in delta T(sub CMB)/T(sub CMB) maps are suppressed as compared to the Gaussian case. The fluctuations are essentially scale-invariant.

Effects of non-Gaussian Brownian motion on direct force optical tweezers measurements of the electrostatic forces between pairs of colloidal particles.

PubMed

Raudsepp, Allan; A K Williams, Martin; B Hall, Simon

2016-07-01

Measurements of the electrostatic force with separation between a fixed and an optically trapped colloidal particle are examined with experiment, simulation and analytical calculation. Non-Gaussian Brownian motion is observed in the position of the optically trapped particle when particles are close and traps weak. As a consequence of this motion, a simple least squares parameterization of direct force measurements, in which force is inferred from the displacement of an optically trapped particle as separation is gradually decreased, contains forces generated by the rectification of thermal fluctuations in addition to those originating directly from the electrostatic interaction between the particles. Thus, when particles are close and traps weak, simply fitting the measured direct force measurement to DLVO theory extracts parameters with modified meanings when compared to the original formulation. In such cases, however, physically meaningful DLVO parameters can be recovered by comparing the measured non-Gaussian statistics to those predicted by solutions to Smoluchowski's equation for diffusion in a potential.

Computational thermochemistry: Automated generation of scale factors for vibrational frequencies calculated by electronic structure model chemistries

NASA Astrophysics Data System (ADS)

Yu, Haoyu S.; Fiedler, Lucas J.; Alecu, I. M.; Truhlar, Donald G.

2017-01-01

We present a Python program, FREQ, for calculating the optimal scale factors for calculating harmonic vibrational frequencies, fundamental vibrational frequencies, and zero-point vibrational energies from electronic structure calculations. The program utilizes a previously published scale factor optimization model (Alecu et al., 2010) to efficiently obtain all three scale factors from a set of computed vibrational harmonic frequencies. In order to obtain the three scale factors, the user only needs to provide zero-point energies of 15 or 6 selected molecules. If the user has access to the Gaussian 09 or Gaussian 03 program, we provide the option for the user to run the program by entering the keywords for a certain method and basis set in the Gaussian 09 or Gaussian 03 program. Four other Python programs, input.py, input6, pbs.py, and pbs6.py, are also provided for generating Gaussian 09 or Gaussian 03 input and PBS files. The program can also be used with data from any other electronic structure package. A manual of how to use this program is included in the code package.

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models

PubMed Central

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful. PMID:28626348

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models.

PubMed

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful.

Non-Gaussian spatiotemporal simulation of multisite daily precipitation: downscaling framework

NASA Astrophysics Data System (ADS)

Ben Alaya, M. A.; Ouarda, T. B. M. J.; Chebana, F.

2018-01-01

Probabilistic regression approaches for downscaling daily precipitation are very useful. They provide the whole conditional distribution at each forecast step to better represent the temporal variability. The question addressed in this paper is: how to simulate spatiotemporal characteristics of multisite daily precipitation from probabilistic regression models? Recent publications point out the complexity of multisite properties of daily precipitation and highlight the need for using a non-Gaussian flexible tool. This work proposes a reasonable compromise between simplicity and flexibility avoiding model misspecification. A suitable nonparametric bootstrapping (NB) technique is adopted. A downscaling model which merges a vector generalized linear model (VGLM as a probabilistic regression tool) and the proposed bootstrapping technique is introduced to simulate realistic multisite precipitation series. The model is applied to data sets from the southern part of the province of Quebec, Canada. It is shown that the model is capable of reproducing both at-site properties and the spatial structure of daily precipitations. Results indicate the superiority of the proposed NB technique, over a multivariate autoregressive Gaussian framework (i.e. Gaussian copula).

Infinite von Mises-Fisher Mixture Modeling of Whole Brain fMRI Data.

PubMed

Røge, Rasmus E; Madsen, Kristoffer H; Schmidt, Mikkel N; Mørup, Morten

2017-10-01

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 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 subsequently normalized. Thus, when performing model selection, the two models are not in agreement. Analyzing multisubject whole brain resting-state fMRI data from healthy adult subjects, we find that the vMF mixture model is considerably more reliable than the gaussian mixture model when comparing solutions across models trained on different groups of subjects, and again we find that the two models disagree on the optimal number of components. The analysis indicates that the fMRI data support more than a thousand clusters, and we confirm this is not a result of overfitting by demonstrating better prediction on data from held-out subjects. Our results highlight the utility of using directional statistics to model standardized fMRI data and demonstrate that whole brain segmentation of fMRI data requires a very large number of functional units in order to adequately account for the discernible statistical patterns in the data.

Fractional Brownian motion time-changed by gamma and inverse gamma process

NASA Astrophysics Data System (ADS)

Kumar, A.; Wyłomańska, A.; Połoczański, R.; Sundar, S.

2017-02-01

Many real time-series exhibit behavior adequate to long range dependent data. Additionally very often these time-series have constant time periods and also have characteristics similar to Gaussian processes although they are not Gaussian. Therefore there is need to consider new classes of systems to model these kinds of empirical behavior. Motivated by this fact in this paper we analyze two processes which exhibit long range dependence property and have additional interesting characteristics which may be observed in real phenomena. Both of them are constructed as the superposition of fractional Brownian motion (FBM) and other process. In the first case the internal process, which plays role of the time, is the gamma process while in the second case the internal process is its inverse. We present in detail their main properties paying main attention to the long range dependence property. Moreover, we show how to simulate these processes and estimate their parameters. We propose to use a novel method based on rescaled modified cumulative distribution function for estimation of parameters of the second considered process. This method is very useful in description of rounded data, like waiting times of subordinated processes delayed by inverse subordinators. By using the Monte Carlo method we show the effectiveness of proposed estimation procedures. Finally, we present the applications of proposed models to real time series.

Future constraints on angle-dependent non-Gaussianity from large radio surveys

NASA Astrophysics Data System (ADS)

Raccanelli, Alvise; Shiraishi, Maresuke; Bartolo, Nicola; Bertacca, Daniele; Liguori, Michele; Matarrese, Sabino; Norris, Ray P.; Parkinson, David

2017-03-01

We investigate how well future large-scale radio surveys could measure different shapes of primordial non-Gaussianity; in particular we focus on angle-dependent non-Gaussianity arising from primordial anisotropic sources, whose bispectrum has an angle dependence between the three wavevectors that is characterized by Legendre polynomials PL and expansion coefficients cL. We provide forecasts for measurements of galaxy power spectrum, finding that Large-Scale Structure (LSS) data could allow measurements of primordial non-Gaussianity that would be competitive with, or improve upon, current constraints set by CMB experiments, for all the shapes considered. We argue that the best constraints will come from the possibility to assign redshift information to radio galaxy surveys, and investigate a few possible scenarios for the EMU and SKA surveys. A realistic (futuristic) modeling could provide constraints of fNLloc ≈ 1(0 . 5) for the local shape, fNL of O(10) (O(1)) for the orthogonal, equilateral and folded shapes, and cL=1 ≈ 80(2) , cL=2 ≈ 400(10) for angle-dependent non-Gaussianity showing that only futuristic galaxy surveys will be able to set strong constraints on these models. Nevertheless, the more futuristic forecasts show the potential of LSS analyses to considerably improve current constraints on non-Gaussianity, and so on models of the primordial Universe. Finally, we find the minimum requirements that would be needed to reach σ(cL=1) = 10, which can be considered as a typical (lower) value predicted by some (inflationary) models.

Comparing fixed and variable-width Gaussian networks.

PubMed

Kůrková, Věra; Kainen, Paul C

2014-09-01

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

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

Lange, R.; Dickerson, M.A.; Peterson, K.R.

Two numerical models for the calculation of air concentration and ground deposition of airborne effluent releases are compared. The Particle-in-Cell (PIC) model and the Straight-Line Airflow Gaussian model were used for the simulation. Two sites were selected for comparison: the Hudson River Valley, New York, and the area around the Savannah River Plant, South Carolina. Input for the models was synthesized from meteorological data gathered in previous studies by various investigators. It was found that the PIC model more closely simulated the three-dimensional effects of the meteorology and topography. Overall, the Gaussian model calculated higher concentrations under stable conditions withmore » better agreement between the two methods during neutral to unstable conditions. In addition, because of its consideration of exposure from the returning plume after flow reversal, the PIC model calculated air concentrations over larger areas than did the Gaussian model.« less

New deconvolution method for microscopic images based on the continuous Gaussian radial basis function interpolation model.

PubMed

Chen, Zhaoxue; Chen, Hao

2014-01-01

A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution.

Bayesian spatial transformation models with applications in neuroimaging data

PubMed Central

Miranda, Michelle F.; Zhu, Hongtu; Ibrahim, Joseph G.

2013-01-01

Summary The aim of this paper is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. Our STMs include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov Random Field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder. PMID:24128143

Gaussian Finite Element Method for Description of Underwater Sound Diffraction

NASA Astrophysics Data System (ADS)

Huang, Dehua

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

Development and modification of a Gaussian and non-Gaussian noise exposure system

NASA Astrophysics Data System (ADS)

Schlag, Adam W.

Millions of people across the world currently have noise induced hearing loss, and many are working in conditions with both continuous Gaussian and non-Gaussian noises that could affect their hearing. It was hypothesized that the energy of the noise was the cause of the hearing loss and did not depend on temporal pattern of a noise. This was referred to as the equal energy hypothesis. This hypothesis has been shown to have limitations though. This means that there is a difference in the types of noise a person receives to induce hearing loss and it is necessary to build a system that can easily mimic various conditions to conduct research. This study builds a system that can produce both non-Gaussian impulse/impact noises and continuous Gaussian noise. It was found that the peak sound pressure level of the system could reach well above the needed 120 dB level to represent acoustic trauma and could replicate well above the 85 dB A-weighted sound pressure level to produce conditions of gradual developing hearing loss. The system reached a maximum of 150 dB sound peak pressure level and a maximum of 133 dB A-weighted sound pressure level. Various parameters could easily be adjusted to control the sound, such as the high and low cutoff frequency to center the sound at 4 kHz. The system build can easily be adjusted to create numerous sound conditions and will hopefully be modified and improved in hopes of eventually being used for animal studies to lead to the creation of a method to treat or prevent noise induced hearing loss.

Apparatus and method for measuring and imaging surface resistance

DOEpatents

Martens, Jon S.; Hietala, Vincent M.; Hohenwarter, Gert K. G.

1993-08-24

Apparatus and method for determining and imaging superconductor surface resistance. The apparatus comprises modified Gaussian confocal resonator structure with the sample remote from the radiating mirror. Surface resistance is determined by analyzing and imaging reflected microwaves; imaging reveals anomalies due to surface impurities, non-stoichiometry, and the like, in the surface of the superconductor.

Genetic algorithm driven spectral shaping of supercontinuum radiation in a photonic crystal fiber

NASA Astrophysics Data System (ADS)

Michaeli, Linor; Bahabad, Alon

2018-05-01

We employ a genetic algorithm to control a pulse-shaping system pumping a nonlinear photonic crystal with ultrashort pulses. With this system, we are able to modify the spectrum of the generated supercontinuum (SC) radiation to yield narrow Gaussian-like features around pre-selected wavelengths over the whole SC spectrum.

Weakly anomalous diffusion with non-Gaussian propagators

NASA Astrophysics Data System (ADS)

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

2012-08-01

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

Moving vehicles segmentation based on Gaussian motion model

NASA Astrophysics Data System (ADS)

Zhang, Wei; Fang, Xiang Z.; Lin, Wei Y.

2005-07-01

Moving objects segmentation is a challenge in computer vision. This paper focuses on the segmentation of moving vehicles in dynamic scene. We analyses the psychology of human vision and present a framework for segmenting moving vehicles in the highway. The proposed framework consists of two parts. Firstly, we propose an adaptive background update method in which the background is updated according to the change of illumination conditions and thus can adapt to the change of illumination sensitively. Secondly, we construct a Gaussian motion model to segment moving vehicles, in which the motion vectors of the moving pixels are modeled as a Gaussian model and an on-line EM algorithm is used to update the model. The Gaussian distribution of the adaptive model is elevated to determine which moving vectors result from moving vehicles and which from other moving objects such as waving trees. Finally, the pixels with motion vector result from the moving vehicles are segmented. Experimental results of several typical scenes show that the proposed model can detect the moving vehicles correctly and is immune from influence of the moving objects caused by the waving trees and the vibration of camera.

Diffusion of Super-Gaussian Profiles

ERIC Educational Resources Information Center

Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.

2007-01-01

The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…

Kinetic and energy production analysis of pyrolysis of lignocellulosic biomass using a three-parallel Gaussian reaction model.

PubMed

Chen, Tianju; Zhang, Jinzhi; Wu, Jinhu

2016-07-01

The kinetic and energy productions of pyrolysis of a lignocellulosic biomass were investigated using a three-parallel Gaussian distribution method in this work. The pyrolysis experiment of the pine sawdust was performed using a thermogravimetric-mass spectroscopy (TG-MS) analyzer. A three-parallel Gaussian distributed activation energy model (DAEM)-reaction model was used to describe thermal decomposition behaviors of the three components, hemicellulose, cellulose and lignin. The first, second and third pseudocomponents represent the fractions of hemicellulose, cellulose and lignin, respectively. It was found that the model is capable of predicting the pyrolysis behavior of the pine sawdust. The activation energy distribution peaks for the three pseudo-components were centered at 186.8, 197.5 and 203.9kJmol(-1) for the pine sawdust, respectively. The evolution profiles of H2, CH4, CO, and CO2 were well predicted using the three-parallel Gaussian distribution model. In addition, the chemical composition of bio-oil was also obtained by pyrolysis-gas chromatography/mass spectrometry instrument (Py-GC/MS). Copyright © 2016 Elsevier Ltd. All rights reserved.

Estimation of High-Dimensional Graphical Models Using Regularized Score Matching

PubMed Central

Lin, Lina; Drton, Mathias; Shojaie, Ali

2017-01-01

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

Geographically weighted regression model on poverty indicator

NASA Astrophysics Data System (ADS)

Slamet, I.; Nugroho, N. F. T. A.; Muslich

2017-12-01

In this research, we applied geographically weighted regression (GWR) for analyzing the poverty in Central Java. We consider Gaussian Kernel as weighted function. The GWR uses the diagonal matrix resulted from calculating kernel Gaussian function as a weighted function in the regression model. The kernel weights is used to handle spatial effects on the data so that a model can be obtained for each location. The purpose of this paper is to model of poverty percentage data in Central Java province using GWR with Gaussian kernel weighted function and to determine the influencing factors in each regency/city in Central Java province. Based on the research, we obtained geographically weighted regression model with Gaussian kernel weighted function on poverty percentage data in Central Java province. We found that percentage of population working as farmers, population growth rate, percentage of households with regular sanitation, and BPJS beneficiaries are the variables that affect the percentage of poverty in Central Java province. In this research, we found the determination coefficient R2 are 68.64%. There are two categories of district which are influenced by different of significance factors.

Robust Linear Models for Cis-eQTL Analysis.

PubMed

Rantalainen, Mattias; Lindgren, Cecilia M; Holmes, Christopher C

2015-01-01

Expression Quantitative Trait Loci (eQTL) analysis enables characterisation of functional genetic variation influencing expression levels of individual genes. In outbread populations, including humans, eQTLs are commonly analysed using the conventional linear model, adjusting for relevant covariates, assuming an allelic dosage model and a Gaussian error term. However, gene expression data generally have noise that induces heavy-tailed errors relative to the Gaussian distribution and often include atypical observations, or outliers. Such departures from modelling assumptions can lead to an increased rate of type II errors (false negatives), and to some extent also type I errors (false positives). Careful model checking can reduce the risk of type-I errors but often not type II errors, since it is generally too time-consuming to carefully check all models with a non-significant effect in large-scale and genome-wide studies. Here we propose the application of a robust linear model for eQTL analysis to reduce adverse effects of deviations from the assumption of Gaussian residuals. We present results from a simulation study as well as results from the analysis of real eQTL data sets. Our findings suggest that in many situations robust models have the potential to provide more reliable eQTL results compared to conventional linear models, particularly in respect to reducing type II errors due to non-Gaussian noise. Post-genomic data, such as that generated in genome-wide eQTL studies, are often noisy and frequently contain atypical observations. Robust statistical models have the potential to provide more reliable results and increased statistical power under non-Gaussian conditions. The results presented here suggest that robust models should be considered routinely alongside other commonly used methodologies for eQTL analysis.

Catadioptric optics for laser Doppler velocimeter applications

NASA Technical Reports Server (NTRS)

Dunagan, Stephen E.

1989-01-01

This paper examines the adaptation of low-cost Schmidt-Cassegrain astronomical telescopes to perform the laser-beam-focusing and scattered-light collection tasks associated with dual-beam laser Doppler velocimetry. A generic telescope design is analyzed using ray-tracing methods and Gaussian beam-propagation theory. A straightforward modification procedure to convert from infinite to near unity conjugate-ratio operation with very low residual aberration is identified and tested with a 200-mm-aperture telescope modified for f/10 operation. Performance data for this modified telescope configuration are near the diffraction limit and agree well with predictions.

Statistical description of turbulent transport for flux driven toroidal plasmas

NASA Astrophysics Data System (ADS)

Anderson, J.; Imadera, K.; Kishimoto, Y.; Li, J. Q.; Nordman, H.

2017-06-01

A novel methodology to analyze non-Gaussian probability distribution functions (PDFs) of intermittent turbulent transport in global full-f gyrokinetic simulations is presented. In this work, the auto-regressive integrated moving average (ARIMA) model is applied to time series data of intermittent turbulent heat transport to separate noise and oscillatory trends, allowing for the extraction of non-Gaussian features of the PDFs. It was shown that non-Gaussian tails of the PDFs from first principles based gyrokinetic simulations agree with an analytical estimation based on a two fluid model.

Speech Enhancement Using Gaussian Scale Mixture Models

PubMed Central

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

2011-01-01

This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress. PMID:21359139

Theory and generation of conditional, scalable sub-Gaussian random fields

NASA Astrophysics Data System (ADS)

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

2016-03-01

Many earth and environmental (as well as a host of other) variables, Y, and their spatial (or temporal) increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture key aspects of such non-Gaussian scaling by treating Y and/or ΔY as sub-Gaussian random fields (or processes). This however left unaddressed the empirical finding that whereas sample frequency distributions of Y tend to display relatively mild non-Gaussian peaks and tails, those of ΔY often reveal peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we proposed a generalized sub-Gaussian model (GSG) which resolves this apparent inconsistency between the statistical scaling behaviors of observed variables and their increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. Most importantly, we demonstrated the feasibility of estimating all parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments, ΔY. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random fields, introduce two approximate versions of this algorithm to reduce CPU time, and explore them on one and two-dimensional synthetic test cases.

Stable radiation pressure acceleration of ions by suppressing transverse Rayleigh-Taylor instability with multiple Gaussian pulses

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

Zhou, M. L.; Liu, B.; Hu, R. H.

In the case of a thin plasma slab accelerated by the radiation pressure of an ultra-intense laser pulse, the development of Rayleigh-Taylor instability (RTI) will destroy the acceleration structure and terminate the acceleration process much sooner than theoretical limit. In this paper, a new scheme using multiple Gaussian pulses for ion acceleration in a radiation pressure acceleration regime is investigated with particle-in-cell simulation. We found that with multiple Gaussian pulses, the instability could be efficiently suppressed and the divergence of the ion bunch is greatly reduced, resulting in a longer acceleration time and much more collimated ion bunch with highermore » energy than using a single Gaussian pulse. An analytical model is developed to describe the suppression of RTI at the laser-plasma interface. The model shows that the suppression of RTI is due to the introduction of the long wavelength mode RTI by the multiple Gaussian pulses.« less

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

PubMed

Le Montagner, Yoann; Angelini, Elsa D; Olivo-Marin, Jean-Christophe

2014-03-01

The behavior and performance of denoising algorithms are governed by one or several parameters, whose optimal settings depend on the content of the processed image and the characteristics of the noise, and are generally designed to minimize the mean squared error (MSE) between the denoised image returned by the algorithm and a virtual ground truth. In this paper, we introduce a new Poisson-Gaussian unbiased risk estimator (PG-URE) of the MSE applicable to a mixed Poisson-Gaussian noise model that unifies the widely used Gaussian and Poisson noise models in fluorescence bioimaging applications. We propose a stochastic methodology to evaluate this estimator in the case when little is known about the internal machinery of the considered denoising algorithm, and we analyze both theoretically and empirically the characteristics of the PG-URE estimator. Finally, we evaluate the PG-URE-driven parametrization for three standard denoising algorithms, with and without variance stabilizing transforms, and different characteristics of the Poisson-Gaussian noise mixture.

Leading non-Gaussian corrections for diffusion orientation distribution function.

PubMed

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

2014-02-01

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

Leading Non-Gaussian Corrections for Diffusion Orientation Distribution Function

PubMed Central

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

2014-01-01

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

Brownian motion under dynamic disorder: effects of memory on the decay of the non-Gaussianity parameter

NASA Astrophysics Data System (ADS)

Tyagi, Neha; Cherayil, Binny J.

2018-03-01

The increasingly widespread occurrence in complex fluids of particle motion that is both Brownian and non-Gaussian has recently been found to be successfully modeled by a process (frequently referred to as ‘diffusing diffusivity’) in which the white noise that governs Brownian diffusion is itself stochastically modulated by either Ornstein–Uhlenbeck dynamics or by two-state noise. But the model has so far not been able to account for an aspect of non-Gaussian Brownian motion that is also commonly observed: a non-monotonic decay of the parameter that quantifies the extent of deviation from Gaussian behavior. In this paper, we show that the inclusion of memory effects in the model—via a generalized Langevin equation—can rationalise this phenomenon.

Cosmic microwave background power asymmetry from non-Gaussian modulation.

PubMed

Schmidt, Fabian; Hui, Lam

2013-01-04

Non-Gaussianity in the inflationary perturbations can couple observable scales to modes of much longer wavelength (even superhorizon), leaving as a signature a large-angle modulation of the observed cosmic microwave background power spectrum. This provides an alternative origin for a power asymmetry that is otherwise often ascribed to a breaking of statistical isotropy. The non-Gaussian modulation effect can be significant even for typical ~10(-5) perturbations while respecting current constraints on non-Gaussianity if the squeezed limit of the bispectrum is sufficiently infrared divergent. Just such a strongly infrared-divergent bispectrum has been claimed for inflation models with a non-Bunch-Davies initial state, for instance. Upper limits on the observed cosmic microwave background power asymmetry place stringent constraints on the duration of inflation in such models.

Degeneracy of energy levels of pseudo-Gaussian oscillators

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

Iacob, Theodor-Felix; Iacob, Felix, E-mail: felix@physics.uvt.ro; Lute, Marina

2015-12-07

We study the main features of the isotropic radial pseudo-Gaussian oscillators spectral properties. This study is made upon the energy levels degeneracy with respect to orbital angular momentum quantum number. In a previous work [6] we have shown that the pseudo-Gaussian oscillators belong to the class of quasi-exactly solvable models and an exact solution has been found.

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

Bayesian spatial transformation models with applications in neuroimaging data.

PubMed

Miranda, Michelle F; Zhu, Hongtu; Ibrahim, Joseph G

2013-12-01

The aim of this article is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. The proposed STM include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov random field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder. © 2013, The International Biometric Society.

Testing for the Gaussian nature of cosmological density perturbations through the three-point temperature correlation function

NASA Technical Reports Server (NTRS)

Luo, Xiaochun; Schramm, David N.

1993-01-01

One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian where seeds produced by topological defects tend to be non-Gaussian. The three-point correlation function of the temperature anisotropy of the cosmic microwave background radiation (CBR) provides a sensitive test of this aspect of the primordial density field. In this paper, this function is calculated in the general context of various allowed non-Gaussian models. It is shown that the Cosmic Background Explorer and the forthcoming South Pole and balloon CBR anisotropy data may be able to provide a crucial test of the Gaussian nature of the perturbations.

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

NASA Astrophysics Data System (ADS)

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

2011-12-01

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

Poisson-Gaussian Noise Reduction Using the Hidden Markov Model in Contourlet Domain for Fluorescence Microscopy Images

PubMed Central

Yang, Sejung; Lee, Byung-Uk

2015-01-01

In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach. PMID:26352138

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2015-08-01

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

A Non-Gaussian Stock Price Model: Options, Credit and a Multi-Timescale Memory

NASA Astrophysics Data System (ADS)

Borland, L.

We review a recently proposed model of stock prices, based on astatistical feedback model that results in a non-Gaussian distribution of price changes. Applications to option pricing and the pricing of debt is discussed. A generalization to account for feedback effects over multiple timescales is also presented. This model reproduces most of the stylized facts (ie statistical anomalies) observed in real financial markets.

Mean First Passage Time and Stochastic Resonance in a Transcriptional Regulatory System with Non-Gaussian Noise

NASA Astrophysics Data System (ADS)

Kang, Yan-Mei; Chen, Xi; Lin, Xu-Dong; Tan, Ning

The mean first passage time (MFPT) in a phenomenological gene transcriptional regulatory model with non-Gaussian noise is analytically investigated based on the singular perturbation technique. The effect of the non-Gaussian noise on the phenomenon of stochastic resonance (SR) is then disclosed based on a new combination of adiabatic elimination and linear response approximation. Compared with the results in the Gaussian noise case, it is found that bounded non-Gaussian noise inhibits the transition between different concentrations of protein, while heavy-tailed non-Gaussian noise accelerates the transition. It is also found that the optimal noise intensity for SR in the heavy-tailed noise case is smaller, while the optimal noise intensity in the bounded noise case is larger. These observations can be explained by the heavy-tailed noise easing random transitions.

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

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

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

PubMed

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

2017-08-01

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

Influence of local inhomogeneities induced in corneal ablation on the evolution of contrast sensitivity

NASA Astrophysics Data System (ADS)

Ortiz, Dolores; Saiz, Jose M.; González, Francisco

2004-04-01

The presence of local inhomogeneities in corneal tissue after refractive surgery has an influence on visual performance. Here we focus on the corneal ablation associated with Lasik surgery and its effect on the modulation transfer function (MTF) that we obtained by modifying a personalized Kooijman model. Inhomogeneities induced by the ablation occur in the form of Gaussian-distributed refractive-index variations of a given correlation length. We show how variation of refractive-index deviation and correlation length (size) of the inhomogeneities allows us to obtain pairs of values that are able to achieve a MTF evolution similar to that observed for contrast sensitivity in the same patients. An estimate of the characteristics of the local effects is obtained.

Twisted waves and instabilities in a permeating dusty plasma

NASA Astrophysics Data System (ADS)

Bukhari, S.; Ali, S.; Khan, S. A.; Mendonca, J. T.

2018-04-01

New features of the twisted dusty plasma modes and associated instabilities are investigated in permeating plasmas. Using the Vlasov-Poisson model equations, a generalized dispersion relation is obtained for a Maxwellian distributed plasma to analyse the dust-acoustic and dust-ion-acoustic waves with finite orbital angular momentum (OAM) states. Existence conditions for damping/growth rates are discussed and showed significant modifications in twisted dusty modes as compared to straight propagating dusty modes. Numerically, the instability growth rate, which depends on particle streaming and twist effects in the wave potential, is significantly modified due to the Laguerre-Gaussian profiles. Relevance of the study to wave excitations due to penetration of solar wind into cometary clouds or interstellar dusty plasmas is discussed.

Back to Normal! Gaussianizing posterior distributions for cosmological probes

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

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

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

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

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

2013-06-01

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

Gaussian-Beam Laser-Resonator Program

NASA Technical Reports Server (NTRS)

Cross, Patricia L.; Bair, Clayton H.; Barnes, Norman

1989-01-01

Gaussian Beam Laser Resonator Program models laser resonators by use of Gaussian-beam-propagation techniques. Used to determine radii of beams as functions of position in laser resonators. Algorithm used in program has three major components. First, ray-transfer matrix for laser resonator must be calculated. Next, initial parameters of beam calculated. Finally, propagation of beam through optical elements computed. Written in Microsoft FORTRAN (Version 4.01).

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

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

Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao

2017-10-18

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less

Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian

NASA Astrophysics Data System (ADS)

Teneng, Dean

2013-09-01

We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.

Model-independent test for scale-dependent non-Gaussianities in the cosmic microwave background.

PubMed

Räth, C; Morfill, G E; Rossmanith, G; Banday, A J; Górski, K M

2009-04-03

We present a model-independent method to test for scale-dependent non-Gaussianities in combination with scaling indices as test statistics. Therefore, surrogate data sets are generated, in which the power spectrum of the original data is preserved, while the higher order correlations are partly randomized by applying a scale-dependent shuffling procedure to the Fourier phases. We apply this method to the Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background and find signatures for non-Gaussianities on large scales. Further tests are required to elucidate the origin of the detected anomalies.

Probing the cosmological initial conditions using the CMB

NASA Astrophysics Data System (ADS)

Yadav, Amit P. S.

In the last few decades, advances in observational cosmology have given us a standard model of cosmology. The basic cosmological parameters have been laid out to high precision. Cosmologists have started asking questions about the nature of the cosmological initial conditions. Many ambitious experiments such as Planck satellite, EBEX, ACT, CAPMAP, QUaD, BICEP, SPIDER, QUIET, and GEM are underway. Experiments like these will provide us with a wealth of information about CMB polarization, CMB lensing, and polarization foregrounds. These experiments will be complemented with great observational campaigns to map the 3D structure in the Universe and new particle physics constraints from the Large Hadron Collider. In my graduate work I have made explicit how observations of the CMB temperature and E-polarization anisotropies can be combined to provide optimal constraints on models of the early universe at the highest energies. I have developed new ways of constraining models of the early universe using CMB temperature and polarization data. Inflation is one of the most promising theories of the early universe. Different inflationary models predict different amounts of non-Gaussian perturbations. Although any non-Gaussianity predicted by the canonical inflation model is very small, there exist models which can generate significant amounts of non-Gaussianities. Hence any characterization of non-Gaussianity of the primordial perturbations constrains the models of inflation. The information in the bispectrum (or higher order moments) is completely independent of the power spectrum constraints on the amplitude of primordial power spectrum (A), the scalar spectral index of the primordial power spectrum ns, and the running of the primordial power spectrum. My work has made it possible to extract the bispectrum information from large, high resolution CMB temperature and polarization data. We have demonstrated that the primordial adiabatic perturbations can be reconstructed using CMB temperature and E-polarization information (Yadav and Wandelt 2005). One of the main motivations of reconstructing the primordial perturbations is to study the primordial non-Gaussianities. Since the amplitude of primordial non-Gaussianity is very small, any enhancement in sensitivity to the primordial features is useful because it improves the characterization of the primordial non-Gaussianity. Our reconstruction allows us to be more sensitive to the primordial features, whereas most of the current probes of non-Gaussianity do not specifically select for them. We have also developed a fast cubic (bispectrum) estimator of non-Gaussianity f NL of local type, using combined temperature and E-polarization data (Yadavet al. 2007). The estimator is computationally efficient, scaling as O( N 3/2 ) compared to the O( N 5/2 ) scaling of the brute force bispectrum calculation for sky maps with N pixels. For the Planck satellite, this translates into a speed-up by factors of millions, reducing the required computing time from thousands of years to just hours and thus making f NL estimation feasible. The speed of our estimator allows us to study its statistical properties using Monte Carlo simulations. Our estimator in its original form was optimal for homogeneous noise. In order to apply our estimator to realistic data, the estimator needed to be able to deal with inhomogeneous noise. We have generalized the fast polarized estimator to deal with inhomogeneous noise. The generalized estimator is also computationally efficient, scaling as O( N 3/2 ). Furthermore, we have studied and characterized our estimators in the presence of realistic noise, finite resolution, incomplete sky-coverage, and using non-Gaussian CMB maps (Yadavet al. 2008a). We have also developed a numerical code to generate CMB temperature and polarization non-Gaussian maps starting from a given primordial non-Gaussianity (f NL ) (Liguori et al. 2007). In the process of non-Gaussian CMB map making, the code also generates corresponding non-Gaussian primordial curvature perturbations. We use these curvature perturbations to quantify the quality of the tomographic reconstruction method described in (Yadav and Wandelt 2005). We check whether the tomographic reconstruction method preserves the non-Gaussian features, especially the phase information, in the reconstructed curvature perturbations (Yadav et al. in preparation). Finally, using our estimator we found (Yadav and Wandelt 2008) evidence for primordial non-Gaussianity of the local type (f NL ) in the temperature anisotropy of the Cosmic Microwave Background. Analyzing the bispectrum of the WMAP 3-year data up to l max =750 we find 27< f NL <147 (95% CL). This amounts to a rejection of f NL =0 at 2.8s, disfavoring canonical single field slow-roll inflation. The signal is robust to variations in l max , frequency, and masks. No known foreground, instrument systematic, or secondary anisotropy explains it. We explore the impact of several analysis choices on the quoted significance and find 2.5s to be conservative.

Football fever: goal distributions and non-Gaussian statistics

NASA Astrophysics Data System (ADS)

Bittner, E.; Nußbaumer, A.; Janke, W.; Weigel, M.

2009-02-01

Analyzing football score data with statistical techniques, we investigate how the not purely random, but highly co-operative nature of the game is reflected in averaged properties such as the probability distributions of scored goals for the home and away teams. As it turns out, especially the tails of the distributions are not well described by the Poissonian or binomial model resulting from the assumption of uncorrelated random events. Instead, a good effective description of the data is provided by less basic distributions such as the negative binomial one or the probability densities of extreme value statistics. To understand this behavior from a microscopical point of view, however, no waiting time problem or extremal process need be invoked. Instead, modifying the Bernoulli random process underlying the Poissonian model to include a simple component of self-affirmation seems to describe the data surprisingly well and allows to understand the observed deviation from Gaussian statistics. The phenomenological distributions used before can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments, including data from all past tournaments of the “FIFA World Cup” series, and found the proposed models to be applicable rather universally. In particular, here we analyze the results of the German women’s premier football league and consider the two separate German men’s premier leagues in the East and West during the cold war times as well as the unified league after 1990 to see how scoring in football and the component of self-affirmation depend on cultural and political circumstances.

Investigating the relation between the geometric properties of river basins and the filtering parameters for regional land hydrology applications using GRACE models

NASA Astrophysics Data System (ADS)

Piretzidis, Dimitrios; Sideris, Michael G.

2016-04-01

This study investigates the possibilities of local hydrology signal extraction using GRACE data and conventional filtering techniques. The impact of the basin shape has also been studied in order to derive empirical rules for tuning the GRACE filter parameters. GRACE CSR Release 05 monthly solutions were used from April 2002 to August 2015 (161 monthly solutions in total). SLR data were also used to replace the GRACE C2,0 coefficient, and a de-correlation filter with optimal parameters for CSR Release 05 data was applied to attenuate the correlation errors of monthly mass differences. For basins located at higher latitudes, the effect of Glacial Isostatic Adjustment (GIA) was taken into account using the ICE-6G model. The study focuses on three geometric properties, i.e., the area, the convexity and the width in the longitudinal direction, of 100 basins with global distribution. Two experiments have been performed. The first one deals with the determination of the Gaussian smoothing radius that minimizes the gaussianity of GRACE equivalent water height (EWH) over the selected basins. The EWH kurtosis was selected as a metric of gaussianity. The second experiment focuses on the derivation of the Gaussian smoothing radius that minimizes the RMS difference between GRACE data and a hydrology model. The GLDAS 1.0 Noah hydrology model was chosen, which shows good agreement with GRACE data according to previous studies. Early results show that there is an apparent relation between the geometric attributes of the basins examined and the Gaussian radius derived from the two experiments. The kurtosis analysis experiment tends to underestimate the optimal Gaussian radius, which is close to 200-300 km in many cases. Empirical rules for the selection of the Gaussian radius have been also developed for sub-regional scale basins.

Gaussian solitary waves and compactons in Fermi–Pasta–Ulam lattices with Hertzian potentials

PubMed Central

James, Guillaume; Pelinovsky, Dmitry

2014-01-01

We consider a class of fully nonlinear Fermi–Pasta–Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order α>1. This class of systems incorporates a classical Hertzian model describing acoustic wave propagation in chains of touching beads in the absence of precompression. We analyse the propagation of localized waves when α is close to unity. Solutions varying slowly in space and time are searched with an appropriate scaling, and two asymptotic models of the chain of particles are derived consistently. The first one is a logarithmic Korteweg–de Vries (KdV) equation and possesses linearly orbitally stable Gaussian solitary wave solutions. The second model consists of a generalized KdV equation with Hölder-continuous fractional power nonlinearity and admits compacton solutions, i.e. solitary waves with compact support. When , we numerically establish the asymptotically Gaussian shape of exact FPU solitary waves with near-sonic speed and analytically check the pointwise convergence of compactons towards the limiting Gaussian profile. PMID:24808748

Ewald Summation Approach to Potential Models of Aqueous Electrolytes Involving Gaussian Charges and Induced Dipoles: Formal and Simulation Results

DOE PAGES

Chialvo, Ariel A.; Vlcek, Lukas

2014-11-01

We present a detailed derivation of the complete set of expressions required for the implementation of an Ewald summation approach to handle the long-range electrostatic interactions of polar and ionic model systems involving Gaussian charges and induced dipole moments with a particular application to the isobaricisothermal molecular dynamics simulation of our Gaussian Charge Polarizable (GCP) water model and its extension to aqueous electrolytes solutions. The set comprises the individual components of the potential energy, electrostatic potential, electrostatic field and gradient, the electrostatic force and the corresponding virial. Moreover, we show how the derived expressions converge to known point-based electrostatic counterpartsmore » when the parameters, defining the Gaussian charge and induced-dipole distributions, are extrapolated to their limiting point values. Finally, we illustrate the Ewald implementation against the current reaction field approach by isothermal-isobaric molecular dynamics of ambient GCP water for which we compared the outcomes of the thermodynamic, microstructural, and polarization behavior.« less

Noise effects in nonlinear biochemical signaling

NASA Astrophysics Data System (ADS)

Bostani, Neda; Kessler, David A.; Shnerb, Nadav M.; Rappel, Wouter-Jan; Levine, Herbert

2012-01-01

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it is a priori obvious that this approximation can violate physical constraints, such as the positivity of chemical concentrations. Here, we show that even when such nonphysical fluctuations are rare, an exact solution of the Gaussian model shows that the model can yield unphysical results. This is done in the context of a simple incoherent-feedforward model which exhibits perfect adaptation in the deterministic limit. We show how one can use the natural separation of time scales in this model to yield an approximate model, that is analytically solvable, including its dynamical response to an environmental change. Alternatively, one can employ a cutoff procedure to regularize the Gaussian result.

Bayesian seismic inversion based on rock-physics prior modeling for the joint estimation of acoustic impedance, porosity and lithofacies

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

Passos de Figueiredo, Leandro, E-mail: leandrop.fgr@gmail.com; Grana, Dario; Santos, Marcio

We propose a Bayesian approach for seismic inversion to estimate acoustic impedance, porosity and lithofacies within the reservoir conditioned to post-stack seismic and well data. The link between elastic and petrophysical properties is given by a joint prior distribution for the logarithm of impedance and porosity, based on a rock-physics model. The well conditioning is performed through a background model obtained by well log interpolation. Two different approaches are presented: in the first approach, the prior is defined by a single Gaussian distribution, whereas in the second approach it is defined by a Gaussian mixture to represent the well datamore » multimodal distribution and link the Gaussian components to different geological lithofacies. The forward model is based on a linearized convolutional model. For the single Gaussian case, we obtain an analytical expression for the posterior distribution, resulting in a fast algorithm to compute the solution of the inverse problem, i.e. the posterior distribution of acoustic impedance and porosity as well as the facies probability given the observed data. For the Gaussian mixture prior, it is not possible to obtain the distributions analytically, hence we propose a Gibbs algorithm to perform the posterior sampling and obtain several reservoir model realizations, allowing an uncertainty analysis of the estimated properties and lithofacies. Both methodologies are applied to a real seismic dataset with three wells to obtain 3D models of acoustic impedance, porosity and lithofacies. The methodologies are validated through a blind well test and compared to a standard Bayesian inversion approach. Using the probability of the reservoir lithofacies, we also compute a 3D isosurface probability model of the main oil reservoir in the studied field.« less

The Gaussian Laser Angular Distribution in HYDRA's 3D Laser Ray Trace Package

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

Sepke, Scott M.

In this note, the angular distribution of rays launched by the 3D LZR ray trace package is derived for Gaussian beams (npower==2) with bm model=3±. Beams with bm model=+3 have a nearly at distribution, and beams with bm model=-3 have a nearly linear distribution when the spot size is large compared to the wavelength.

Robust Gaussian Graphical Modeling via l1 Penalization

PubMed Central

Sun, Hokeun; Li, Hongzhe

2012-01-01

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

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

PubMed

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

2012-01-01

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

Tests for Gaussianity of the MAXIMA-1 cosmic microwave background map.

PubMed

Wu, J H; Balbi, A; Borrill, J; Ferreira, P G; Hanany, S; Jaffe, A H; Lee, A T; Rabii, B; Richards, P L; Smoot, G F; Stompor, R; Winant, C D

2001-12-17

Gaussianity of the cosmological perturbations is one of the key predictions of standard inflation, but it is violated by other models of structure formation such as cosmic defects. We present the first test of the Gaussianity of the cosmic microwave background (CMB) on subdegree angular scales, where deviations from Gaussianity are most likely to occur. We apply the methods of moments, cumulants, the Kolmogorov test, the chi(2) test, and Minkowski functionals in eigen, real, Wiener-filtered, and signal-whitened spaces, to the MAXIMA-1 CMB anisotropy data. We find that the data, which probe angular scales between 10 arcmin and 5 deg, are consistent with Gaussianity. These results show consistency with the standard inflation and place constraints on the existence of cosmic defects.

Genomic Prediction of Genotype × Environment Interaction Kernel Regression Models.

PubMed

Cuevas, Jaime; Crossa, José; Soberanis, Víctor; Pérez-Elizalde, Sergio; Pérez-Rodríguez, Paulino; Campos, Gustavo de Los; Montesinos-López, O A; Burgueño, Juan

2016-11-01

In genomic selection (GS), genotype × environment interaction (G × E) can be modeled by a marker × environment interaction (M × E). The G × E may be modeled through a linear kernel or a nonlinear (Gaussian) kernel. In this study, we propose using two nonlinear Gaussian kernels: the reproducing kernel Hilbert space with kernel averaging (RKHS KA) and the Gaussian kernel with the bandwidth estimated through an empirical Bayesian method (RKHS EB). We performed single-environment analyses and extended to account for G × E interaction (GBLUP-G × E, RKHS KA-G × E and RKHS EB-G × E) in wheat ( L.) and maize ( L.) data sets. For single-environment analyses of wheat and maize data sets, RKHS EB and RKHS KA had higher prediction accuracy than GBLUP for all environments. For the wheat data, the RKHS KA-G × E and RKHS EB-G × E models did show up to 60 to 68% superiority over the corresponding single environment for pairs of environments with positive correlations. For the wheat data set, the models with Gaussian kernels had accuracies up to 17% higher than that of GBLUP-G × E. For the maize data set, the prediction accuracy of RKHS EB-G × E and RKHS KA-G × E was, on average, 5 to 6% higher than that of GBLUP-G × E. The superiority of the Gaussian kernel models over the linear kernel is due to more flexible kernels that accounts for small, more complex marker main effects and marker-specific interaction effects. Copyright © 2016 Crop Science Society of America.

On the Limitations of Taylor’s Hypothesis in Parker Solar Probe’s Measurements near the Alfvén Critical Point

NASA Astrophysics Data System (ADS)

Bourouaine, Sofiane; Perez, Jean C.

2018-05-01

In this Letter, we present an analysis of two-point, two-time correlation functions from high-resolution numerical simulations of Reflection-driven Alfvén Turbulence near the Alfvén critical point r c. The simulations model the turbulence in a prescribed background solar wind model chosen to match observational constraints. This analysis allows us to investigate the temporal decorrelation of solar wind turbulence and the validity of Taylor’s approximation near the heliocentric distance r c, which Parker Solar Probe (PSP) is expected to explore in the coming years. The simulations show that the temporal decay of the Fourier-transformed turbulence decorrelation function is better described by a Gaussian model rather than a pure exponential time decay, and that the decorrelation frequency is almost linear with perpendicular wave number k ⊥ (perpendicular with respect to the background magnetic field {{\\boldsymbol{B}}}0). Based on the simulations, we conclude that Taylor’s approximation cannot be used in this instance to provide a connection between the frequency ω of the time signal (measured in the probe frame) and the wavevector k ⊥ of the fluctuations because the frequency k ⊥ V sc (V sc is the spacecraft speed) near r c is comparable to the estimated decorrelation frequency. However, the use of Taylor’s approximation still leads to the correct spectral indices of the power spectra measured at the spacecraft frame. In this Letter, based on a Gaussian model, we suggest a modified relationship between ω and k ⊥, which might be useful in the interpretation of future PSP measurements.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

PubMed

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

2017-04-21

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

User's manual for the Gaussian windows program

NASA Technical Reports Server (NTRS)

Jaeckel, Louis A.

1992-01-01

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

Distributed phased array architecture study

NASA Technical Reports Server (NTRS)

Bourgeois, Brian

1987-01-01

Variations in amplifiers and phase shifters can cause degraded antenna performance, depending also on the environmental conditions and antenna array architecture. The implementation of distributed phased array hardware was studied with the aid of the DISTAR computer program as a simulation tool. This simulation provides guidance in hardware simulation. Both hard and soft failures of the amplifiers in the T/R modules are modeled. Hard failures are catastrophic: no power is transmitted to the antenna elements. Noncatastrophic or soft failures are modeled as a modified Gaussian distribution. The resulting amplitude characteristics then determine the array excitation coefficients. The phase characteristics take on a uniform distribution. Pattern characteristics such as antenna gain, half power beamwidth, mainbeam phase errors, sidelobe levels, and beam pointing errors were studied as functions of amplifier and phase shifter variations. General specifications for amplifier and phase shifter tolerances in various architecture configurations for C band and S band were determined.

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

PubMed

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

2016-09-01

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

Flexible Link Functions in Nonparametric Binary Regression with Gaussian Process Priors

PubMed Central

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

2015-01-01

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

Loop corrections to primordial non-Gaussianity

NASA Astrophysics Data System (ADS)

Boran, Sibel; Kahya, E. O.

2018-02-01

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

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.

1994-01-01

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

Transformation (normalization) of slope gradient and surface curvatures, automated for statistical analyses from DEMs

NASA Astrophysics Data System (ADS)

Csillik, O.; Evans, I. S.; Drăguţ, L.

2015-03-01

Automated procedures are developed to alleviate long tails in frequency distributions of morphometric variables. They minimize the skewness of slope gradient frequency distributions, and modify the kurtosis of profile and plan curvature distributions toward that of the Gaussian (normal) model. Box-Cox (for slope) and arctangent (for curvature) transformations are tested on nine digital elevation models (DEMs) of varying origin and resolution, and different landscapes, and shown to be effective. Resulting histograms are illustrated and show considerable improvements over those for previously recommended slope transformations (sine, square root of sine, and logarithm of tangent). Unlike previous approaches, the proposed method evaluates the frequency distribution of slope gradient values in a given area and applies the most appropriate transform if required. Sensitivity of the arctangent transformation is tested, showing that Gaussian-kurtosis transformations are acceptable also in terms of histogram shape. Cube root transformations of curvatures produced bimodal histograms. The transforms are applicable to morphometric variables and many others with skewed or long-tailed distributions. By avoiding long tails and outliers, they permit parametric statistics such as correlation, regression and principal component analyses to be applied, with greater confidence that requirements for linearity, additivity and even scatter of residuals (constancy of error variance) are likely to be met. It is suggested that such transformations should be routinely applied in all parametric analyses of long-tailed variables. Our Box-Cox and curvature automated transformations are based on a Python script, implemented as an easy-to-use script tool in ArcGIS.

Accounting for Non-Gaussian Sources of Spatial Correlation in Parametric Functional Magnetic Resonance Imaging Paradigms I: Revisiting Cluster-Based Inferences.

PubMed

Gopinath, Kaundinya; Krishnamurthy, Venkatagiri; Sathian, K

2018-02-01

In a recent study, Eklund et al. employed resting-state functional magnetic resonance imaging data as a surrogate for null functional magnetic resonance imaging (fMRI) datasets and posited that cluster-wise family-wise error (FWE) rate-corrected inferences made by using parametric statistical methods in fMRI studies over the past two decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; this was principally because the spatial autocorrelation functions (sACF) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggested otherwise. Here, we show that accounting for non-Gaussian signal components such as those arising from resting-state neural activity as well as physiological responses and motion artifacts in the null fMRI datasets yields first- and second-level general linear model analysis residuals with nearly uniform and Gaussian sACF. Further comparison with nonparametric permutation tests indicates that cluster-based FWE corrected inferences made with Gaussian spatial noise approximations are valid.

Blended particle filters for large-dimensional chaotic dynamical systems

PubMed Central

Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.

2014-01-01

A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886

A 2D Gaussian-Beam-Based Method for Modeling the Dichroic Surfaces of Quasi-Optical Systems

NASA Astrophysics Data System (ADS)

Elis, Kevin; Chabory, Alexandre; Sokoloff, Jérôme; Bolioli, Sylvain

2016-08-01

In this article, we propose an approach in the spectral domain to treat the interaction of a field with a dichroic surface in two dimensions. For a Gaussian beam illumination of the surface, the reflected and transmitted fields are approximated by one reflected and one transmitted Gaussian beams. Their characteristics are determined by means of a matching in the spectral domain, which requires a second-order approximation of the dichroic surface response when excited by plane waves. This approximation is of the same order as the one used in Gaussian beam shooting algorithm to model curved interfaces associated with lenses, reflector, etc. The method uses general analytical formulations for the GBs that depend either on a paraxial or far-field approximation. Numerical experiments are led to test the efficiency of the method in terms of accuracy and computation time. They include a parametric study and a case for which the illumination is provided by a horn antenna. For the latter, the incident field is firstly expressed as a sum of Gaussian beams by means of Gabor frames.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-04-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-07-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modelling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modelling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a pre-conditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Direct Importance Estimation with Gaussian Mixture Models

NASA Astrophysics Data System (ADS)

Yamada, Makoto; Sugiyama, Masashi

The ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extention of the Kullback-Leibler importance estimation procedure (KLIEP), an importance estimation method using linear or kernel models. An advantage of GMMs is that covariance matrices can also be learned through an expectation-maximization procedure, so the proposed method — which we call the Gaussian mixture KLIEP (GM-KLIEP) — is expected to work well when the true importance function has high correlation. Through experiments, we show the validity of the proposed approach.

Bayesian calibration of the Community Land Model using surrogates

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

Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi

2014-02-01

We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditional on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural errormore » in CLM under two error models. We find that surrogate models can be created for CLM in most cases. The posterior distributions are more predictive than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters' distributions significantly. The structural error model reveals a correlation time-scale which can be used to identify the physical process that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.« less

Selecting salient frames for spatiotemporal video modeling and segmentation.

PubMed

Song, Xiaomu; Fan, Guoliang

2007-12-01

We propose a new statistical generative model for spatiotemporal video segmentation. The objective is to partition a video sequence into homogeneous segments that can be used as "building blocks" for semantic video segmentation. The baseline framework is a Gaussian mixture model (GMM)-based video modeling approach that involves a six-dimensional spatiotemporal feature space. Specifically, we introduce the concept of frame saliency to quantify the relevancy of a video frame to the GMM-based spatiotemporal video modeling. This helps us use a small set of salient frames to facilitate the model training by reducing data redundancy and irrelevance. A modified expectation maximization algorithm is developed for simultaneous GMM training and frame saliency estimation, and the frames with the highest saliency values are extracted to refine the GMM estimation for video segmentation. Moreover, it is interesting to find that frame saliency can imply some object behaviors. This makes the proposed method also applicable to other frame-related video analysis tasks, such as key-frame extraction, video skimming, etc. Experiments on real videos demonstrate the effectiveness and efficiency of the proposed method.

A simple mathematical model of gradual Darwinian evolution: emergence of a Gaussian trait distribution in adaptation along a fitness gradient.

PubMed

Biktashev, Vadim N

2014-04-01

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.

Development of a GPU-Accelerated 3-D Full-Wave Code for Electromagnetic Wave Propagation in a Cold Plasma

NASA Astrophysics Data System (ADS)

Woodbury, D.; Kubota, S.; Johnson, I.

2014-10-01

Computer simulations of electromagnetic wave propagation in magnetized plasmas are an important tool for both plasma heating and diagnostics. For active millimeter-wave and microwave diagnostics, accurately modeling the evolution of the beam parameters for launched, reflected or scattered waves in a toroidal plasma requires that calculations be done using the full 3-D geometry. Previously, we reported on the application of GPGPU (General-Purpose computing on Graphics Processing Units) to a 3-D vacuum Maxwell code using the FDTD (Finite-Difference Time-Domain) method. Tests were done for Gaussian beam propagation with a hard source antenna, utilizing the parallel processing capabilities of the NVIDIA K20M. In the current study, we have modified the 3-D code to include a soft source antenna and an induced current density based on the cold plasma approximation. Results from Gaussian beam propagation in an inhomogeneous anisotropic plasma, along with comparisons to ray- and beam-tracing calculations will be presented. Additional enhancements, such as advanced coding techniques for improved speedup, will also be investigated. Supported by U.S. DoE Grant DE-FG02-99-ER54527 and in part by the U.S. DoE, Office of Science, WDTS under the Science Undergraduate Laboratory Internship program.

Detection of dual-band infrared small target based on joint dynamic sparse representation

NASA Astrophysics Data System (ADS)

Zhou, Jinwei; Li, Jicheng; Shi, Zhiguang; Lu, Xiaowei; Ren, Dongwei

2015-10-01

Infrared small target detection is a crucial and yet still is a difficult issue in aeronautic and astronautic applications. Sparse representation is an important mathematic tool and has been used extensively in image processing in recent years. Joint sparse representation is applied in dual-band infrared dim target detection in this paper. Firstly, according to the characters of dim targets in dual-band infrared images, 2-dimension Gaussian intensity model was used to construct target dictionary, then the dictionary was classified into different sub-classes according to different positions of Gaussian function's center point in image block; The fact that dual-band small targets detection can use the same dictionary and the sparsity doesn't lie in atom-level but in sub-class level was utilized, hence the detection of targets in dual-band infrared images was converted to be a joint dynamic sparse representation problem. And the dynamic active sets were used to describe the sparse constraint of coefficients. Two modified sparsity concentration index (SCI) criteria was proposed to evaluate whether targets exist in the images. In experiments, it shows that the proposed algorithm can achieve better detecting performance and dual-band detection is much more robust to noise compared with single-band detection. Moreover, the proposed method can be expanded to multi-spectrum small target detection.

Spatio-temporal modelling of wind speed variations and extremes in the Caribbean and the Gulf of Mexico

NASA Astrophysics Data System (ADS)

Rychlik, Igor; Mao, Wengang

2018-02-01

The wind speed variability in the North Atlantic has been successfully modelled using a spatio-temporal transformed Gaussian field. However, this type of model does not correctly describe the extreme wind speeds attributed to tropical storms and hurricanes. In this study, the transformed Gaussian model is further developed to include the occurrence of severe storms. In this new model, random components are added to the transformed Gaussian field to model rare events with extreme wind speeds. The resulting random field is locally stationary and homogeneous. The localized dependence structure is described by time- and space-dependent parameters. The parameters have a natural physical interpretation. To exemplify its application, the model is fitted to the ECMWF ERA-Interim reanalysis data set. The model is applied to compute long-term wind speed distributions and return values, e.g., 100- or 1000-year extreme wind speeds, and to simulate random wind speed time series at a fixed location or spatio-temporal wind fields around that location.

Separation of the low-frequency atmospheric variability into non-Gaussian multidimensional sources by Independent Subspace Analysis

NASA Astrophysics Data System (ADS)

Pires, Carlos; Ribeiro, Andreia

2016-04-01

An efficient nonlinear method of statistical source separation of space-distributed non-Gaussian distributed data is proposed. The method relies in the so called Independent Subspace Analysis (ISA), being tested on a long time-series of the stream-function field of an atmospheric quasi-geostrophic 3-level model (QG3) simulating the winter's monthly variability of the Northern Hemisphere. ISA generalizes the Independent Component Analysis (ICA) by looking for multidimensional and minimally dependent, uncorrelated and non-Gaussian distributed statistical sources among the rotated projections or subspaces of the multivariate probability distribution of the leading principal components of the working field whereas ICA restrict to scalar sources. The rationale of that technique relies upon the projection pursuit technique, looking for data projections of enhanced interest. In order to accomplish the decomposition, we maximize measures of the sources' non-Gaussianity by contrast functions which are given by squares of nonlinear, cross-cumulant-based correlations involving the variables spanning the sources. Therefore sources are sought matching certain nonlinear data structures. The maximized contrast function is built in such a way that it provides the minimization of the mean square of the residuals of certain nonlinear regressions. The issuing residuals, followed by spherization, provide a new set of nonlinear variable changes that are at once uncorrelated, quasi-independent and quasi-Gaussian, representing an advantage with respect to the Independent Components (scalar sources) obtained by ICA where the non-Gaussianity is concentrated into the non-Gaussian scalar sources. The new scalar sources obtained by the above process encompass the attractor's curvature thus providing improved nonlinear model indices of the low-frequency atmospheric variability which is useful since large circulation indices are nonlinearly correlated. The non-Gaussian tested sources (dyads and triads, respectively of two and three dimensions) lead to a dense data concentration along certain curves or surfaces, nearby which the clusters' centroids of the joint probability density function tend to be located. That favors a better splitting of the QG3 atmospheric model's weather regimes: the positive and negative phases of the Arctic Oscillation and positive and negative phases of the North Atlantic Oscillation. The leading model's non-Gaussian dyad is associated to a positive correlation between: 1) the squared anomaly of the extratropical jet-stream and 2) the meridional jet-stream meandering. Triadic sources coming from maximized third-order cross cumulants between pairwise uncorrelated components reveal situations of triadic wave resonance and nonlinear triadic teleconnections, only possible thanks to joint non-Gaussianity. That kind of triadic synergies are accounted for an Information-Theoretic measure: the Interaction Information. The dominant model's triad occurs between anomalies of: 1) the North Pole anomaly pressure 2) the jet-stream intensity at the Eastern North-American boundary and 3) the jet-stream intensity at the Eastern Asian boundary. Publication supported by project FCT UID/GEO/50019/2013 - Instituto Dom Luiz.

FIBER AND INTEGRATED OPTICS: Use of the offset method in an analysis of a non-Gaussian field distribution in single-mode fiber waveguides

NASA Astrophysics Data System (ADS)

Belov, A. V.; Kurkov, Andrei S.; Chikolini, A. V.

1990-08-01

An offset method is modified to allow an analysis of the distribution of fields in a single-mode fiber waveguide without recourse to the Gaussian approximation. A new approximation for the field is obtained for fiber waveguides with a step refractive index profile and a special analysis employing the Hankel transformation is applied to waveguides with a distributed refractive index. The field distributions determined by this method are compared with the corresponding distributions calculated from the refractive index of a preform from which the fibers are drawn. It is shown that these new approaches can be used to determine the dimensions of a mode spot defined in different ways and to forecast the dispersion characteristics of single-mode fiber waveguides.

Automatic arrival time detection for earthquakes based on Modified Laplacian of Gaussian filter

NASA Astrophysics Data System (ADS)

Saad, Omar M.; Shalaby, Ahmed; Samy, Lotfy; Sayed, Mohammed S.

2018-04-01

Precise identification of onset time for an earthquake is imperative in the right figuring of earthquake's location and different parameters that are utilized for building seismic catalogues. P-wave arrival detection of weak events or micro-earthquakes cannot be precisely determined due to background noise. In this paper, we propose a novel approach based on Modified Laplacian of Gaussian (MLoG) filter to detect the onset time even in the presence of very weak signal-to-noise ratios (SNRs). The proposed algorithm utilizes a denoising-filter algorithm to smooth the background noise. In the proposed algorithm, we employ the MLoG mask to filter the seismic data. Afterward, we apply a Dual-threshold comparator to detect the onset time of the event. The results show that the proposed algorithm can detect the onset time for micro-earthquakes accurately, with SNR of -12 dB. The proposed algorithm achieves an onset time picking accuracy of 93% with a standard deviation error of 0.10 s for 407 field seismic waveforms. Also, we compare the results with short and long time average algorithm (STA/LTA) and the Akaike Information Criterion (AIC), and the proposed algorithm outperforms them.

On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis.

PubMed

Li, Bing; Chun, Hyonho; Zhao, Hongyu

2014-09-01

We introduce a nonparametric method for estimating non-gaussian graphical models based on a new statistical relation called additive conditional independence, which is a three-way relation among random vectors that resembles the logical structure of conditional independence. Additive conditional independence allows us to use one-dimensional kernel regardless of the dimension of the graph, which not only avoids the curse of dimensionality but also simplifies computation. It also gives rise to a parallel structure to the gaussian graphical model that replaces the precision matrix by an additive precision operator. The estimators derived from additive conditional independence cover the recently introduced nonparanormal graphical model as a special case, but outperform it when the gaussian copula assumption is violated. We compare the new method with existing ones by simulations and in genetic pathway analysis.

Vapor–Liquid Equilibrium and Polarization Behavior of the GCP Water Model: Gaussian Charge-on-Spring versus Dipole Self-Consistent Field Approaches to Induced Polarization

DOE PAGES

Chialvo, Ariel A.; Moucka, Filip; Vlcek, Lukas; ...

2015-03-24

Here we implemented the Gaussian charge-on-spring (GCOS) version of the original self-consistent field implementation of the Gaussian Charge Polarizable water model and test its accuracy to represent the polarization behavior of the original model involving smeared charges and induced dipole moments. Moreover, for that purpose we adapted the recently developed multiple-particle-move (MPM) within the Gibbs and isochoric-isothermal ensembles Monte Carlo methods for the efficient simulation of polarizable fluids. We also assessed the accuracy of the GCOS representation by a direct comparison of the resulting vapor-liquid phase envelope, microstructure, and relevant microscopic descriptors of water polarization along the orthobaric curve againstmore » the corresponding quantities from the actual GCP water model.« less

A study on thermal damage during hyperthermia treatment based on DPL model for multilayer tissues using finite element Legendre wavelet Galerkin approach.

PubMed

Kumar, Dinesh; Rai, K N

2016-12-01

Hyperthermia is a process that uses heat from the spatial heat source to kill cancerous cells without damaging the surrounding healthy tissues. Efficacy of hyperthermia technique is related to achieve temperature at the infected cells during the treatment process. A mathematical model on heat transfer in multilayer tissues in finite domain is proposed to predict the control temperature profile at hyperthermia position. The treatment technique uses dual-phase-lag model of heat transfer in multilayer tissues with modified Gaussian distribution heat source subjected to the most generalized boundary condition and interface at the adjacent layers. The complete dual-phase-lag model of bioheat transfer is solved using finite element Legendre wavelet Galerkin approach. The present solution has been verified with exact solution in a specific case and provides a good accuracy. The effect of the variability of different parameters such as lagging times, external heat source, metabolic heat source and the most generalized boundary condition on temperature profile in multilayer tissues is analyzed and also discussed the effective approach of hyperthermia treatment. Furthermore, we studied the modified thermal damage model with regeneration of healthy tissues as well. For viewpoint of thermal damage, the least thermal damage has been observed in boundary condition of second kind. The article concludes with a discussion of better opportunities for future clinical application of hyperthermia treatment. Copyright © 2016 Elsevier Ltd. All rights reserved.

Self-affirmation model for football goal distributions

NASA Astrophysics Data System (ADS)

Bittner, E.; Nußbaumer, A.; Janke, W.; Weigel, M.

2007-06-01

Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out that in particular the tails of the distributions are not well described by independent Bernoulli trials, but rather well modeled by negative binomial or generalized extreme value distributions. To understand this behavior from first principles, we suggest to modify the Bernoulli random process to include a simple component of self-affirmation which seems to describe the data surprisingly well and allows to interpret the observed deviation from Gaussian statistics. The phenomenological distributions used before can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments and found the proposed models to be applicable rather universally. In particular, here we compare men's and women's leagues and the separate German leagues during the cold war times and find some remarkable differences.

Nuclear DNA contents of Echinchloa crus-galli and its Gaussian relationships with environments

NASA Astrophysics Data System (ADS)

Li, Dan-Dan; Lu, Yong-Liang; Guo, Shui-Liang; Yin, Li-Ping; Zhou, Ping; Lou, Yu-Xia

2017-02-01

Previous studies on plant nuclear DNA content variation and its relationships with environmental gradients produced conflicting results. We speculated that the relationships between nuclear DNA content of a widely-distributed species and its environmental gradients might be non-linear if it was sampled in a large geographical gradient. Echinochloa crus-galli (L.) P. Beauv. is a worldwide species, but without documents on its intraspecific variation of nuclear DNA content. Our objectives are: 1) to detect intraspecific variation scope of E. crus-galli in its nuclear DNA content, and 2) to testify whether nuclear DNA content of the species changes with environmental gradients following Gaussian models if its populations were sampled in a large geographical gradient. We collected seeds of 36 Chinese populations of E. crus-galli across a wide geographical gradient, and sowed them in a homogeneous field to get their offspring to determine their nuclear DNA content. We analyzed the relationships of nuclear DNA content of these populations with latitude, longitude, and nineteen bioclimatic variables by using Gaussian and linear models. (1) Nuclear DNA content varied from 2.113 to 2.410 pg among 36 Chinese populations of E. crus-galli, with a mean value of 2.256 pg. (2) Gaussian correlations of nuclear DNA content (y) with geographical gradients were detected, with latitude (x) following y = 2.2923*e -(x - 24.9360)2/2*63.79452 (r = 0.546, P < 0.001), and with longitude (x) following y = 2.2933*e -(x - 116.1801)2/2*44.74502 (r = 0.672, P < 0.001). (3) Among the nineteen bioclimatic variables, except temperature isothermality, precipitations of the wettest month, the wettest quarter and the warmest quarter, the others could be better fit with nuclear DNA content by using Gaussian models than by linear models. There exists intra-specific variation among 36 Chinese populations of E. crus-galli, Gaussian models could be applied to fit the correlations of its Nuclear DNA content with geographical and most bioclimatic gradients.

Infrared video based gas leak detection method using modified FAST features

NASA Astrophysics Data System (ADS)

Wang, Min; Hong, Hanyu; Huang, Likun

2018-03-01

In order to detect the invisible leaking gas that is usually dangerous and easily leads to fire or explosion in time, many new technologies have arisen in the recent years, among which the infrared video based gas leak detection is widely recognized as a viable tool. However, all the moving regions of a video frame can be detected as leaking gas regions by the existing infrared video based gas leak detection methods, without discriminating the property of each detected region, e.g., a walking person in a video frame may be also detected as gas by the current gas leak detection methods.To solve this problem, we propose a novel infrared video based gas leak detection method in this paper, which is able to effectively suppress strong motion disturbances.Firstly, the Gaussian mixture model(GMM) is used to establish the background model.Then due to the observation that the shapes of gas regions are different from most rigid moving objects, we modify the Features From Accelerated Segment Test (FAST) algorithm and use the modified FAST (mFAST) features to describe each connected component. In view of the fact that the statistical property of the mFAST features extracted from gas regions is different from that of other motion regions, we propose the Pixel-Per-Points (PPP) condition to further select candidate connected components.Experimental results show that the algorithm is able to effectively suppress most strong motion disturbances and achieve real-time leaking gas detection.

Mixed-effects Gaussian process functional regression models with application to dose-response curve prediction.

PubMed

Shi, J Q; Wang, B; Will, E J; West, R M

2012-11-20

We propose a new semiparametric model for functional regression analysis, combining a parametric mixed-effects model with a nonparametric Gaussian process regression model, namely a mixed-effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose-response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose-response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient-specific treatment regime. Copyright © 2012 John Wiley & Sons, Ltd.

Bayesian Analysis of Non-Gaussian Long-Range Dependent Processes

NASA Astrophysics Data System (ADS)

Graves, T.; Franzke, C.; Gramacy, R. B.; Watkins, N. W.

2012-12-01

Recent studies have strongly suggested that surface temperatures exhibit long-range dependence (LRD). The presence of LRD would hamper the identification of deterministic trends and the quantification of their significance. It is well established that LRD processes exhibit stochastic trends over rather long periods of time. Thus, accurate methods for discriminating between physical processes that possess long memory and those that do not are an important adjunct to climate modeling. We have used Markov Chain Monte Carlo algorithms to perform a Bayesian analysis of Auto-Regressive Fractionally-Integrated Moving-Average (ARFIMA) processes, which are capable of modeling LRD. Our principal aim is to obtain inference about the long memory parameter, d,with secondary interest in the scale and location parameters. We have developed a reversible-jump method enabling us to integrate over different model forms for the short memory component. We initially assume Gaussianity, and have tested the method on both synthetic and physical time series such as the Central England Temperature. Many physical processes, for example the Faraday time series from Antarctica, are highly non-Gaussian. We have therefore extended this work by weakening the Gaussianity assumption. Specifically, we assume a symmetric α -stable distribution for the innovations. Such processes provide good, flexible, initial models for non-Gaussian processes with long memory. We will present a study of the dependence of the posterior variance σ d of the memory parameter d on the length of the time series considered. This will be compared with equivalent error diagnostics for other measures of d.

PERIOD ESTIMATION FOR SPARSELY SAMPLED QUASI-PERIODIC LIGHT CURVES APPLIED TO MIRAS

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

He, Shiyuan; Huang, Jianhua Z.; Long, James

2016-12-01

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

Accretion rates of protoplanets. II - Gaussian distributions of planetesimal velocities

NASA Technical Reports Server (NTRS)

Greenzweig, Yuval; Lissauer, Jack J.

1992-01-01

In the present growth-rate calculations for a protoplanet that is embedded in a disk of planetesimals with triaxial Gaussian velocity dispersion and uniform surface density, the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is found to be enhanced by a factor of about 3 relative to the case where all planetesimals' eccentricities and inclinations are equal to the rms values of those disk variables having locally Gaussian velocity dispersion. This accretion-rate enhancement should be incorporated by all models that assume a single random velocity for all planetesimals in lieu of a Gaussian distribution.

Solar cycle variation of interstellar neutral He, Ne, O density and pick-up ions along the Earth's orbit

NASA Astrophysics Data System (ADS)

Sokół, Justyna M.; Bzowski, Maciej; Kubiak, Marzena A.; Möbius, Eberhard

2016-06-01

We simulated the modulation of the interstellar neutral (ISN) He, Ne, and O density and pick-up ion (PUI) production rate and count rate along the Earth's orbit over the solar cycle (SC) from 2002 to 2013 to verify if SC-related effects may modify the inferred ecliptic longitude of the ISN inflow direction. We adopted the classical PUI model with isotropic distribution function and adiabatic cooling, modified by time- and heliolatitude-dependent ionization rates and non-zero injection speed of PUIs. We found that the ionization losses have a noticeable effect on the derivation of the ISN inflow longitude based on the Gaussian fit to the crescent and cone peak locations. We conclude that the non-zero radial velocity of the ISN flow and the energy range of the PUI distribution function that is accumulated are of importance for a precise reproduction of the PUI count rate along the Earth orbit. However, the temporal and latitudinal variations of the ionization in the heliosphere, and particularly their variation on the SC time-scale, may significantly modify the shape of PUI cone and crescent and also their peak positions from year to year and thus bias by a few degrees the derived longitude of the ISN gas inflow direction.

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

PubMed

Xu, Qingyang; Zhang, Chengjin; Zhang, Li

2014-01-01

Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA.

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

PubMed Central

Xu, Qingyang; Zhang, Chengjin; Zhang, Li

2014-01-01

Estimation of distribution algorithm (EDA) is an intelligent optimization algorithm based on the probability statistics theory. A fast elitism Gaussian estimation of distribution algorithm (FEGEDA) is proposed in this paper. The Gaussian probability model is used to model the solution distribution. The parameters of Gaussian come from the statistical information of the best individuals by fast learning rule. A fast learning rule is used to enhance the efficiency of the algorithm, and an elitism strategy is used to maintain the convergent performance. The performances of the algorithm are examined based upon several benchmarks. In the simulations, a one-dimensional benchmark is used to visualize the optimization process and probability model learning process during the evolution, and several two-dimensional and higher dimensional benchmarks are used to testify the performance of FEGEDA. The experimental results indicate the capability of FEGEDA, especially in the higher dimensional problems, and the FEGEDA exhibits a better performance than some other algorithms and EDAs. Finally, FEGEDA is used in PID controller optimization of PMSM and compared with the classical-PID and GA. PMID:24892059

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

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.; Serror, Jeremy

2014-01-01

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

A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Stochastic Modeling of CO2 Migrations and Chemical Reactions in Deep Saline Formations

NASA Astrophysics Data System (ADS)

Ni, C.; Lee, I.; Lin, C.

2013-12-01

Carbon capture and storage (CCS) has been recognized the feasible technology that can significant reduce the anthropogenic CO2 emissions from large point sources. The CO2 injection in geological formations is one of the options to permanently store the captured CO2. Based on this concept a large number of target formations have been identified and intensively investigated with different types of techniques such as the hydrogeophysical experiments or numerical simulations. The numerical simulations of CO2 migrations in saline formations recently gather much attention because a number of models are available for this purpose and there are potential sites existing in many countries. The lower part of Cholan Formation (CF) near Changhua Coastal Industrial Park (CCIP) in west central Taiwan was identified the largest potential site for CO2 sequestration. The top elevations of the KF in this area varies from 1300 to 1700m below the sea level. Laboratory experiment showed that the permeability of CF is 10-14 to 10-12 m2. Over the years the offshore seismic survey and limited onshore borehole logs have provided information for the simulation of CO2 migration in the CF although the original investigations might not focus on the purpose of CO2 sequestration. In this study we modify the TOUGHREACT model to consider the small-scale heterogeneity in target formation and the cap rock of upper CF. A Monte Carlo Simulation (MCS) approach based on the TOUGHREACT model is employed to quantify the effect of small-scale heterogeneity on the CO2 migrations and hydrochemical reactions in the CF. We assume that the small-scale variability of permeability in KF can be described with a known Gaussian distribution. Therefore, the Gaussian type random field generator such as Sequential Gaussian Simulation (SGSIM) in Geostatistical Software Library (GSLIB) can be used to provide the random permeability realizations for the MCS. A variety of statistical parameters such as the variances and correlation lengths in a Gaussian covariance model are varied in the MCS and the uncertainty of the CO2 and other chemical concentrations are evaluated based on 144 random realizations. In this study a constant injection rate of100Mt/year supercritical CO2 is applied in the bottom of CF. The continuous injection time is 20 years and the uncertainty results are evaluated at 100 years. By comparing with the case without small-scale variability simulation results show that the CO2 plume sizes in the horizontal direction increase from tens of meters to hundreds of meters when the variances of small-scale variability are varied from 1.0 to 4.0. The changes of correlation lengths (i.e., from 100m, 200m, to 400m) show small contribution on the size increases of CO2 plumes. Other uncertainties of chemical concentrations show behaviors similar to the CO2 plume patterns.

Generalized seasonal autoregressive integrated moving average models for count data with application to malaria time series with low case numbers.

PubMed

Briët, Olivier J T; Amerasinghe, Priyanie H; Vounatsou, Penelope

2013-01-01

With the renewed drive towards malaria elimination, there is a need for improved surveillance tools. While time series analysis is an important tool for surveillance, prediction and for measuring interventions' impact, approximations by commonly used Gaussian methods are prone to inaccuracies when case counts are low. Therefore, statistical methods appropriate for count data are required, especially during "consolidation" and "pre-elimination" phases. Generalized autoregressive moving average (GARMA) models were extended to generalized seasonal autoregressive integrated moving average (GSARIMA) models for parsimonious observation-driven modelling of non Gaussian, non stationary and/or seasonal time series of count data. The models were applied to monthly malaria case time series in a district in Sri Lanka, where malaria has decreased dramatically in recent years. The malaria series showed long-term changes in the mean, unstable variance and seasonality. After fitting negative-binomial Bayesian models, both a GSARIMA and a GARIMA deterministic seasonality model were selected based on different criteria. Posterior predictive distributions indicated that negative-binomial models provided better predictions than Gaussian models, especially when counts were low. The G(S)ARIMA models were able to capture the autocorrelation in the series. G(S)ARIMA models may be particularly useful in the drive towards malaria elimination, since episode count series are often seasonal and non-stationary, especially when control is increased. Although building and fitting GSARIMA models is laborious, they may provide more realistic prediction distributions than do Gaussian methods and may be more suitable when counts are low.

Generalized Seasonal Autoregressive Integrated Moving Average Models for Count Data with Application to Malaria Time Series with Low Case Numbers

PubMed Central

Briët, Olivier J. T.; Amerasinghe, Priyanie H.; Vounatsou, Penelope

2013-01-01

Introduction With the renewed drive towards malaria elimination, there is a need for improved surveillance tools. While time series analysis is an important tool for surveillance, prediction and for measuring interventions’ impact, approximations by commonly used Gaussian methods are prone to inaccuracies when case counts are low. Therefore, statistical methods appropriate for count data are required, especially during “consolidation” and “pre-elimination” phases. Methods Generalized autoregressive moving average (GARMA) models were extended to generalized seasonal autoregressive integrated moving average (GSARIMA) models for parsimonious observation-driven modelling of non Gaussian, non stationary and/or seasonal time series of count data. The models were applied to monthly malaria case time series in a district in Sri Lanka, where malaria has decreased dramatically in recent years. Results The malaria series showed long-term changes in the mean, unstable variance and seasonality. After fitting negative-binomial Bayesian models, both a GSARIMA and a GARIMA deterministic seasonality model were selected based on different criteria. Posterior predictive distributions indicated that negative-binomial models provided better predictions than Gaussian models, especially when counts were low. The G(S)ARIMA models were able to capture the autocorrelation in the series. Conclusions G(S)ARIMA models may be particularly useful in the drive towards malaria elimination, since episode count series are often seasonal and non-stationary, especially when control is increased. Although building and fitting GSARIMA models is laborious, they may provide more realistic prediction distributions than do Gaussian methods and may be more suitable when counts are low. PMID:23785448

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

An empirical description of the dispersion of 5th and 95th percentiles in worldwide anthropometric data applied to estimating accommodation with unknown correlation values.

PubMed

Albin, Thomas J; Vink, Peter

2015-01-01

Anthropometric data are assumed to have a Gaussian (Normal) distribution, but if non-Gaussian, accommodation estimates are affected. When data are limited, users may choose to combine anthropometric elements by Combining Percentiles (CP) (adding or subtracting), despite known adverse effects. This study examined whether global anthropometric data are Gaussian distributed. It compared the Median Correlation Method (MCM) of combining anthropometric elements with unknown correlations to CP to determine if MCM provides better estimates of percentile values and accommodation. Percentile values of 604 male and female anthropometric data drawn from seven countries worldwide were expressed as standard scores. The standard scores were tested to determine if they were consistent with a Gaussian distribution. Empirical multipliers for determining percentile values were developed.In a test case, five anthropometric elements descriptive of seating were combined in addition and subtraction models. Percentile values were estimated for each model by CP, MCM with Gaussian distributed data, or MCM with empirically distributed data. The 5th and 95th percentile values of a dataset of global anthropometric data are shown to be asymmetrically distributed. MCM with empirical multipliers gave more accurate estimates of 5th and 95th percentiles values. Anthropometric data are not Gaussian distributed. The MCM method is more accurate than adding or subtracting percentiles.

Gaussianization for fast and accurate inference from cosmological data

NASA Astrophysics Data System (ADS)

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

2016-06-01

We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box-Cox transformations and generalizations thereof. This permits an analytical reconstruction of the posterior from a point sample, like a Markov chain, and simplifies the subsequent joint analysis with other experiments. This way, a multivariate posterior density can be reported efficiently, by compressing the information contained in Markov Chain Monte Carlo samples. Further, the model evidence integral (I.e. the marginal likelihood) can be computed analytically. This method is analogous to the search for normal parameters in the cosmic microwave background, but is more general. The search for the optimally Gaussianizing transformation is performed computationally through a maximum-likelihood formalism; its quality can be judged by how well the credible regions of the posterior are reproduced. We demonstrate that our method outperforms kernel density estimates in this objective. Further, we select marginal posterior samples from Planck data with several distinct strongly non-Gaussian features, and verify the reproduction of the marginal contours. To demonstrate evidence computation, we Gaussianize the joint distribution of data from weak lensing and baryon acoustic oscillations, for different cosmological models, and find a preference for flat Λcold dark matter. Comparing to values computed with the Savage-Dickey density ratio, and Population Monte Carlo, we find good agreement of our method within the spread of the other two.

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

PubMed

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

2016-01-01

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

On the robustness of the q-Gaussian family

NASA Astrophysics Data System (ADS)

Sicuro, Gabriele; Tempesta, Piergiulio; Rodríguez, Antonio; Tsallis, Constantino

2015-12-01

We introduce three deformations, called α-, β- and γ-deformation respectively, of a N-body probabilistic model, first proposed by Rodríguez et al. (2008), having q-Gaussians as N → ∞ limiting probability distributions. The proposed α- and β-deformations are asymptotically scale-invariant, whereas the γ-deformation is not. We prove that, for both α- and β-deformations, the resulting deformed triangles still have q-Gaussians as limiting distributions, with a value of q independent (dependent) on the deformation parameter in the α-case (β-case). In contrast, the γ-case, where we have used the celebrated Q-numbers and the Gauss binomial coefficients, yields other limiting probability distribution functions, outside the q-Gaussian family. These results suggest that scale-invariance might play an important role regarding the robustness of the q-Gaussian family.

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

PubMed

Liu, Zhiguang; Zhou, Liuyang; Leung, Howard; Shum, Hubert P H

2016-11-01

Depth sensor based 3D human motion estimation hardware such as Kinect has made interactive applications more popular recently. However, it is still challenging to accurately recognize postures from a single depth camera due to the inherently noisy data derived from depth images and self-occluding action performed by the user. In this paper, we propose a new real-time probabilistic framework to enhance the accuracy of live captured postures that belong to one of the action classes in the database. We adopt the Gaussian Process model as a prior to leverage the position data obtained from Kinect and marker-based motion capture system. We also incorporate a temporal consistency term into the optimization framework to constrain the velocity variations between successive frames. To ensure that the reconstructed posture resembles the accurate parts of the observed posture, we embed a set of joint reliability measurements into the optimization framework. A major drawback of Gaussian Process is its cubic learning complexity when dealing with a large database due to the inverse of a covariance matrix. To solve the problem, we propose a new method based on a local mixture of Gaussian Processes, in which Gaussian Processes are defined in local regions of the state space. Due to the significantly decreased sample size in each local Gaussian Process, the learning time is greatly reduced. At the same time, the prediction speed is enhanced as the weighted mean prediction for a given sample is determined by the nearby local models only. Our system also allows incrementally updating a specific local Gaussian Process in real time, which enhances the likelihood of adapting to run-time postures that are different from those in the database. Experimental results demonstrate that our system can generate high quality postures even under severe self-occlusion situations, which is beneficial for real-time applications such as motion-based gaming and sport training.

Accounting for Non-Gaussian Sources of Spatial Correlation in Parametric Functional Magnetic Resonance Imaging Paradigms II: A Method to Obtain First-Level Analysis Residuals with Uniform and Gaussian Spatial Autocorrelation Function and Independent and Identically Distributed Time-Series.

PubMed

Gopinath, Kaundinya; Krishnamurthy, Venkatagiri; Lacey, Simon; Sathian, K

2018-02-01

In a recent study Eklund et al. have shown that cluster-wise family-wise error (FWE) rate-corrected inferences made in parametric statistical method-based functional magnetic resonance imaging (fMRI) studies over the past couple of decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; principally because the spatial autocorrelation functions (sACFs) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggest otherwise. Hence, the residuals from general linear model (GLM)-based fMRI activation estimates in these studies may not have possessed a homogenously Gaussian sACF. Here we propose a method based on the assumption that heterogeneity and non-Gaussianity of the sACF of the first-level GLM analysis residuals, as well as temporal autocorrelations in the first-level voxel residual time-series, are caused by unmodeled MRI signal from neuronal and physiological processes as well as motion and other artifacts, which can be approximated by appropriate decompositions of the first-level residuals with principal component analysis (PCA), and removed. We show that application of this method yields GLM residuals with significantly reduced spatial correlation, nearly Gaussian sACF and uniform spatial smoothness across the brain, thereby allowing valid cluster-based FWE-corrected inferences based on assumption of Gaussian spatial noise. We further show that application of this method renders the voxel time-series of first-level GLM residuals independent, and identically distributed across time (which is a necessary condition for appropriate voxel-level GLM inference), without having to fit ad hoc stochastic colored noise models. Furthermore, the detection power of individual subject brain activation analysis is enhanced. This method will be especially useful for case studies, which rely on first-level GLM analysis inferences.

Semisupervised Gaussian Process for Automated Enzyme Search.

PubMed

Mellor, Joseph; Grigoras, Ioana; Carbonell, Pablo; Faulon, Jean-Loup

2016-06-17

Synthetic biology is today harnessing the design of novel and greener biosynthesis routes for the production of added-value chemicals and natural products. The design of novel pathways often requires a detailed selection of enzyme sequences to import into the chassis at each of the reaction steps. To address such design requirements in an automated way, we present here a tool for exploring the space of enzymatic reactions. Given a reaction and an enzyme the tool provides a probability estimate that the enzyme catalyzes the reaction. Our tool first considers the similarity of a reaction to known biochemical reactions with respect to signatures around their reaction centers. Signatures are defined based on chemical transformation rules by using extended connectivity fingerprint descriptors. A semisupervised Gaussian process model associated with the similar known reactions then provides the probability estimate. The Gaussian process model uses information about both the reaction and the enzyme in providing the estimate. These estimates were validated experimentally by the application of the Gaussian process model to a newly identified metabolite in Escherichia coli in order to search for the enzymes catalyzing its associated reactions. Furthermore, we show with several pathway design examples how such ability to assign probability estimates to enzymatic reactions provides the potential to assist in bioengineering applications, providing experimental validation to our proposed approach. To the best of our knowledge, the proposed approach is the first application of Gaussian processes dealing with biological sequences and chemicals, the use of a semisupervised Gaussian process framework is also novel in the context of machine learning applied to bioinformatics. However, the ability of an enzyme to catalyze a reaction depends on the affinity between the substrates of the reaction and the enzyme. This affinity is generally quantified by the Michaelis constant KM. Therefore, we also demonstrate using Gaussian process regression to predict KM given a substrate-enzyme pair.

Gaussian noise and time-reversal symmetry in nonequilibrium Langevin models.

PubMed

Vainstein, M H; Rubí, J M

2007-03-01

We show that in driven systems the Gaussian nature of the fluctuating force and time reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the probability distribution function, which can be shown to satisfy time-independent relations. We have corroborated this feature by explicitly analyzing a model for the stretching of a polymer and a model for a suspension of noninteracting Brownian particles in steady flow.

Development and application of a non-Gaussian atmospheric turbulence model for use in flight simulators

NASA Technical Reports Server (NTRS)

Reeves, P. M.; Campbell, G. S.; Ganzer, V. M.; Joppa, R. G.

1974-01-01

A method is described for generating time histories which model the frequency content and certain non-Gaussian probability characteristics of atmospheric turbulence including the large gusts and patchy nature of turbulence. Methods for time histories using either analog or digital computation are described. A STOL airplane was programmed into a 6-degree-of-freedom flight simulator, and turbulence time histories from several atmospheric turbulence models were introduced. The pilots' reactions are described.

Fitted Hanbury-Brown Twiss radii versus space-time variances in flow-dominated models

NASA Astrophysics Data System (ADS)

Frodermann, Evan; Heinz, Ulrich; Lisa, Michael Annan

2006-04-01

The inability of otherwise successful dynamical models to reproduce the Hanbury-Brown Twiss (HBT) radii extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the RHIC HBT Puzzle. Most comparisons between models and experiment exploit the fact that for Gaussian sources the HBT radii agree with certain combinations of the space-time widths of the source that can be directly computed from the emission function without having to evaluate, at significant expense, the two-particle correlation function. We here study the validity of this approach for realistic emission function models, some of which exhibit significant deviations from simple Gaussian behavior. By Fourier transforming the emission function, we compute the two-particle correlation function, and fit it with a Gaussian to partially mimic the procedure used for measured correlation functions. We describe a novel algorithm to perform this Gaussian fit analytically. We find that for realistic hydrodynamic models the HBT radii extracted from this procedure agree better with the data than the values previously extracted from the space-time widths of the emission function. Although serious discrepancies between the calculated and the measured HBT radii remain, we show that a more apples-to-apples comparison of models with data can play an important role in any eventually successful theoretical description of RHIC HBT data.

Fitted Hanbury-Brown-Twiss radii versus space-time variances in flow-dominated models

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

Frodermann, Evan; Heinz, Ulrich; Lisa, Michael Annan

2006-04-15

The inability of otherwise successful dynamical models to reproduce the Hanbury-Brown-Twiss (HBT) radii extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the RHIC HBT Puzzle. Most comparisons between models and experiment exploit the fact that for Gaussian sources the HBT radii agree with certain combinations of the space-time widths of the source that can be directly computed from the emission function without having to evaluate, at significant expense, the two-particle correlation function. We here study the validity of this approach for realistic emission function models, some of which exhibit significant deviations from simplemore » Gaussian behavior. By Fourier transforming the emission function, we compute the two-particle correlation function, and fit it with a Gaussian to partially mimic the procedure used for measured correlation functions. We describe a novel algorithm to perform this Gaussian fit analytically. We find that for realistic hydrodynamic models the HBT radii extracted from this procedure agree better with the data than the values previously extracted from the space-time widths of the emission function. Although serious discrepancies between the calculated and the measured HBT radii remain, we show that a more apples-to-apples comparison of models with data can play an important role in any eventually successful theoretical description of RHIC HBT data.« less

A Gaussian beam method for ultrasonic non-destructive evaluation modeling

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

The integrated bispectrum in modified gravity theories

NASA Astrophysics Data System (ADS)

Munshi, Dipak

2017-01-01

Gravity-induced non-Gaussianity can provide important clues to Modified Gravity (MG) Theories. Several recent studies have suggested using the Integrated Bispectrum (IB) as a probe for squeezed configuration of bispectrum. Extending previous studies on the IB, we include redshift-space distortions to study a class of (parametrised) MG theories that include the string-inspired Dvali, Gabadadze & Porrati (DGP) model. Various contributions from redshift-space distortions are derived in a transparent manner, and squeezed contributions from these terms are derived separately. Results are obtained using the Zel'dovich Approximation (ZA). Results are also presented for projected surveys (2D). We use the Press-Schechter (PS) and Sheth-Tormen (ST) mass functions to compute the IB for collapsed objects that can readily be extended to peak-theory based approaches. The cumulant correlators (CCs) generalise the ordinary cumulants and are known to probe collapsed configurations of higher order correlation functions. We generalise the concept of CCs to halos of different masses. We also introduce a generating function based approach to analyse more general non-local biasing models. The Fourier representations of the CCs, the skew-spectrum, or the kurt-spctra are discussed in this context. The results are relevant for the study of the Minkowski Functionals (MF) of collapsed tracers in redshift-space.

The integrated bispectrum in modified gravity theories

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

Munshi, Dipak, E-mail: D.Munshi@sussex.ac.uk

2017-01-01

Gravity-induced non-Gaussianity can provide important clues to Modified Gravity (MG) Theories. Several recent studies have suggested using the Integrated Bispectrum (IB) as a probe for squeezed configuration of bispectrum. Extending previous studies on the IB, we include redshift-space distortions to study a class of (parametrised) MG theories that include the string-inspired Dvali, Gabadadze and Porrati (DGP) model. Various contributions from redshift-space distortions are derived in a transparent manner, and squeezed contributions from these terms are derived separately. Results are obtained using the Zel'dovich Approximation (ZA). Results are also presented for projected surveys (2D). We use the Press-Schechter (PS) and Sheth-Tormenmore » (ST) mass functions to compute the IB for collapsed objects that can readily be extended to peak-theory based approaches. The cumulant correlators (CCs) generalise the ordinary cumulants and are known to probe collapsed configurations of higher order correlation functions. We generalise the concept of CCs to halos of different masses. We also introduce a generating function based approach to analyse more general non-local biasing models. The Fourier representations of the CCs, the skew-spectrum, or the kurt-spctra are discussed in this context. The results are relevant for the study of the Minkowski Functionals (MF) of collapsed tracers in redshift-space.« less

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

Wang, Yi; Xue, Wei, E-mail: yw366@cam.ac.uk, E-mail: wei.xue@sissa.it

We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experimentsmore » do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.« less

Sloppy-slotted ALOHA

NASA Technical Reports Server (NTRS)

Crozier, Stewart N.

1990-01-01

Random access signaling, which allows slotted packets to spill over into adjacent slots, is investigated. It is shown that sloppy-slotted ALOHA can always provide higher throughput than conventional slotted ALOHA. The degree of improvement depends on the timing error distribution. Throughput performance is presented for Gaussian timing error distributions, modified to include timing error corrections. A general channel capacity lower bound, independent of the specific timing error distribution, is also presented.

New approach for T-wave peak detection and T-wave end location in 12-lead paced ECG signals based on a mathematical model.

PubMed

Madeiro, João P V; Nicolson, William B; Cortez, Paulo C; Marques, João A L; Vázquez-Seisdedos, Carlos R; Elangovan, Narmadha; Ng, G Andre; Schlindwein, Fernando S

2013-08-01

This paper presents an innovative approach for T-wave peak detection and subsequent T-wave end location in 12-lead paced ECG signals based on a mathematical model of a skewed Gaussian function. Following the stage of QRS segmentation, we establish search windows using a number of the earliest intervals between each QRS offset and subsequent QRS onset. Then, we compute a template based on a Gaussian-function, modified by a mathematical procedure to insert asymmetry, which models the T-wave. Cross-correlation and an approach based on the computation of Trapezium's area are used to locate, respectively, the peak and end point of each T-wave throughout the whole raw ECG signal. For evaluating purposes, we used a database of high resolution 12-lead paced ECG signals, recorded from patients with ischaemic cardiomyopathy (ICM) in the University Hospitals of Leicester NHS Trust, UK, and the well-known QT database. The average T-wave detection rates, sensitivity and positive predictivity, were both equal to 99.12%, for the first database, and, respectively, equal to 99.32% and 99.47%, for QT database. The average time errors computed for T-wave peak and T-wave end locations were, respectively, -0.38±7.12 ms and -3.70±15.46 ms, for the first database, and 1.40±8.99 ms and 2.83±15.27 ms, for QT database. The results demonstrate the accuracy, consistency and robustness of the proposed method for a wide variety of T-wave morphologies studied. Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

A class of exact solutions for biomacromolecule diffusion-reaction in live cells.

PubMed

Sadegh Zadeh, Kouroush; Montas, Hubert J

2010-06-07

A class of novel explicit analytic solutions for a system of n+1 coupled partial differential equations governing biomolecular mass transfer and reaction in living organisms are proposed, evaluated, and analyzed. The solution process uses Laplace and Hankel transforms and results in a recursive convolution of an exponentially scaled Gaussian with modified Bessel functions. The solution is developed for wide range of biomolecular binding kinetics from pure diffusion to multiple binding reactions. The proposed approach provides solutions for both Dirac and Gaussian laser beam (or fluorescence-labeled biomacromolecule) profiles during the course of a Fluorescence Recovery After Photobleaching (FRAP) experiment. We demonstrate that previous models are simplified forms of our theory for special cases. Model analysis indicates that at the early stages of the transport process, biomolecular dynamics is governed by pure diffusion. At large times, the dominant mass transfer process is effective diffusion. Analysis of the sensitivity equations, derived analytically and verified by finite difference differentiation, indicates that experimental biologists should use full space-time profile (instead of the averaged time series) obtained at the early stages of the fluorescence microscopy experiments to extract meaningful physiological information from the protocol. Such a small time frame requires improved bioinstrumentation relative to that in use today. Our mathematical analysis highlights several limitations of the FRAP protocol and provides strategies to improve it. The proposed model can be used to study biomolecular dynamics in molecular biology, targeted drug delivery in normal and cancerous tissues, motor-driven axonal transport in normal and abnormal nervous systems, kinetics of diffusion-controlled reactions between enzyme and substrate, and to validate numerical simulators of biological mass transport processes in vivo. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Lower white matter microstructure in the superior longitudinal fasciculus is associated with increased response time variability in adults with attention-deficit/ hyperactivity disorder.

PubMed

Wolfers, Thomas; Onnink, A Marten H; Zwiers, Marcel P; Arias-Vasquez, Alejandro; Hoogman, Martine; Mostert, Jeanette C; Kan, Cornelis C; Slaats-Willemse, Dorine; Buitelaar, Jan K; Franke, Barbara

2015-09-01

Response time variability (RTV) is consistently increased in patients with attention-deficit/hyperactivity disorder (ADHD). A right-hemispheric frontoparietal attention network model has been implicated in these patients. The 3 main connecting fibre tracts in this network, the superior longitudinal fasciculus (SLF), inferior longitudinal fasciculus (ILF) and the cingulum bundle (CB), show microstructural abnormalities in patients with ADHD. We hypothesized that the microstructural integrity of the 3 white matter tracts of this network are associated with ADHD and RTV. We examined RTV in adults with ADHD by modelling the reaction time distribution as an exponentially modified Gaussian (ex-Gaussian) function with the parameters μ, σ and τ, the latter of which has been attributed to lapses of attention. We assessed adults with ADHD and healthy controls using a sustained attention task. Diffusion tensor imaging-derived fractional anisotropy (FA) values were determined to quantify bilateral microstructural integrity of the tracts of interest. We included 100 adults with ADHD and 96 controls in our study. Increased τ was associated with ADHD diagnosis and was linked to symptoms of inattention. An inverse correlation of τ with mean FA was seen in the right SLF of patients with ADHD, but no direct association between the mean FA of the 6 regions of interest with ADHD could be observed. Regions of interest were defined a priori based on the attentional network model for ADHD and thus we might have missed effects in other networks. This study suggests that reduced microstructural integrity of the right SLF is associated with elevated τ in patients with ADHD.

Lower white matter microstructure in the superior longitudinal fasciculus is associated with increased response time variability in adults with attention-deficit/hyperactivity disorder

PubMed Central

Wolfers, Thomas; Onnink, A. Marten H.; Zwiers, Marcel P.; Arias-Vasquez, Alejandro; Hoogman, Martine; Mostert, Jeanette C.; Kan, Cornelis C.; Slaats-Willemse, Dorine; Buitelaar, Jan K.; Franke, Barbara

2015-01-01

Background Response time variability (RTV) is consistently increased in patients with attention-deficit/hyperactivity disorder (ADHD). A right-hemispheric frontoparietal attention network model has been implicated in these patients. The 3 main connecting fibre tracts in this network, the superior longitudinal fasciculus (SLF), inferior longitudinal fasciculus (ILF) and the cingulum bundle (CB), show microstructural abnormalities in patients with ADHD. We hypothesized that the microstructural integrity of the 3 white matter tracts of this network are associated with ADHD and RTV. Methods We examined RTV in adults with ADHD by modelling the reaction time distribution as an exponentially modified Gaussian (ex-Gaussian) function with the parameters μ, σ and τ, the latter of which has been attributed to lapses of attention. We assessed adults with ADHD and healthy controls using a sustained attention task. Diffusion tensor imaging–derived fractional anisotropy (FA) values were determined to quantify bilateral microstructural integrity of the tracts of interest. Results We included 100 adults with ADHD and 96 controls in our study. Increased τ was associated with ADHD diagnosis and was linked to symptoms of inattention. An inverse correlation of τ with mean FA was seen in the right SLF of patients with ADHD, but no direct association between the mean FA of the 6 regions of interest with ADHD could be observed. Limitations Regions of interest were defined a priori based on the attentional network model for ADHD and thus we might have missed effects in other networks. Conclusion This study suggests that reduced microstructural integrity of the right SLF is associated with elevated τ in patients with ADHD. PMID:26079698

S/G-1: an ab initio force-field blending frozen Hermite Gaussian densities and distributed multipoles. Proof of concept and first applications to metal cations.

PubMed

Chaudret, Robin; Gresh, Nohad; Narth, Christophe; Lagardère, Louis; Darden, Thomas A; Cisneros, G Andrés; Piquemal, Jean-Philip

2014-09-04

We demonstrate as a proof of principle the capabilities of a novel hybrid MM'/MM polarizable force field to integrate short-range quantum effects in molecular mechanics (MM) through the use of Gaussian electrostatics. This lead to a further gain in accuracy in the representation of the first coordination shell of metal ions. It uses advanced electrostatics and couples two point dipole polarizable force fields, namely, the Gaussian electrostatic model (GEM), a model based on density fitting, which uses fitted electronic densities to evaluate nonbonded interactions, and SIBFA (sum of interactions between fragments ab initio computed), which resorts to distributed multipoles. To understand the benefits of the use of Gaussian electrostatics, we evaluate first the accuracy of GEM, which is a pure density-based Gaussian electrostatics model on a test Ca(II)-H2O complex. GEM is shown to further improve the agreement of MM polarization with ab initio reference results. Indeed, GEM introduces nonclassical effects by modeling the short-range quantum behavior of electric fields and therefore enables a straightforward (and selective) inclusion of the sole overlap-dependent exchange-polarization repulsive contribution by means of a Gaussian damping function acting on the GEM fields. The S/G-1 scheme is then introduced. Upon limiting the use of Gaussian electrostatics to metal centers only, it is shown to be able to capture the dominant quantum effects at play on the metal coordination sphere. S/G-1 is able to accurately reproduce ab initio total interaction energies within closed-shell metal complexes regarding each individual contribution including the separate contributions of induction, polarization, and charge-transfer. Applications of the method are provided for various systems including the HIV-1 NCp7-Zn(II) metalloprotein. S/G-1 is then extended to heavy metal complexes. Tested on Hg(II) water complexes, S/G-1 is shown to accurately model polarization up to quadrupolar response level. This opens up the possibility of embodying explicit scalar relativistic effects in molecular mechanics thanks to the direct transferability of ab initio pseudopotentials. Therefore, incorporating GEM-like electron density for a metal cation enable the introduction of nonambiguous short-range quantum effects within any point-dipole based polarizable force field without the need of an extensive parametrization.

Errors associated with fitting Gaussian profiles to noisy emission-line spectra

NASA Technical Reports Server (NTRS)

Lenz, Dawn D.; Ayres, Thomas R.

1992-01-01

Landman et al. (1982) developed prescriptions to predict profile fitting errors for Gaussian emission lines perturbed by white noise. We show that their scaling laws can be generalized to more complicated signal-dependent 'noise models' of common astronomical detector systems.

Apodization of two-dimensional pupils with aberrations

NASA Astrophysics Data System (ADS)

Reddy, Andra Naresh Kumar; Hashemi, Mahdieh; Khonina, Svetlana Nikolaevna

2018-06-01

The technique proposed to enhance the resolution of the point spread function (PSF) of an optical system underneath defocussing and spherical aberrations. The method of approach is based on the amplitude and phase masking in a ring aperture for modifying the light intensity distribution in the Gaussian focal plane (YD = 0) and in the defocussed planes (YD= π and YD= 2π ). The width of the annulus modifies the distribution of the light intensity in the side lobes of the resultant PSF. In the presence of an asymmetry in the phase of the annulus, the Hanning amplitude apodizer [cos(π β ρ )] employed in the pupil function can modify the spatial distribution of light in the maximum defocussed plane ({Y}D = 2π ), results in PSF with improved resolution.

Evaluation of regional and local atmospheric dispersion models for the analysis of traffic-related air pollution in urban areas

NASA Astrophysics Data System (ADS)

Fallah-Shorshani, Masoud; Shekarrizfard, Maryam; Hatzopoulou, Marianne

2017-10-01

Dispersion of road transport emissions in urban metropolitan areas is typically simulated using Gaussian models that ignore the turbulence and drag induced by buildings, which are especially relevant for areas with dense downtown cores. To consider the effect of buildings, street canyon models are used but often at the level of single urban corridors and small road networks. In this paper, we compare and validate two dispersion models with widely varying algorithms, across a modelling domain consisting of the City of Montreal, Canada accounting for emissions of more 40,000 roads. The first dispersion model is based on flow decomposition into the urban canopy sub-flow as well as overlying airflow. It takes into account the specific height and geometry of buildings along each road. The second model is a Gaussian puff dispersion model, which handles complex terrain and incorporates three-dimensional meteorology, but accounts for buildings only through variations in the initial vertical mixing coefficient. Validation against surface observations indicated that both models under-predicted measured concentrations. Average weekly exposure surfaces derived from both models were found to be reasonably correlated (r = 0.8) although the Gaussian dispersion model tended to underestimate concentrations around the roadways compared to the street canyon model. In addition, both models were used to estimate exposures of a representative sample of the Montreal population composed of 1319 individuals. Large differences were noted whereby exposures derived from the Gaussian puff model were significantly lower than exposures derived from the street canyon model, an expected result considering the concentration of population around roadways. These differences have large implications for the analyses of health effects associated with NO2 exposure.

CFHTLenS: a Gaussian likelihood is a sufficient approximation for a cosmological analysis of third-order cosmic shear statistics

NASA Astrophysics Data System (ADS)

Simon, P.; Semboloni, E.; van Waerbeke, L.; Hoekstra, H.; Erben, T.; Fu, L.; Harnois-Déraps, J.; Heymans, C.; Hildebrandt, H.; Kilbinger, M.; Kitching, T. D.; Miller, L.; Schrabback, T.

2015-05-01

We study the correlations of the shear signal between triplets of sources in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) to probe cosmological parameters via the matter bispectrum. In contrast to previous studies, we adopt a non-Gaussian model of the data likelihood which is supported by our simulations of the survey. We find that for state-of-the-art surveys, similar to CFHTLenS, a Gaussian likelihood analysis is a reasonable approximation, albeit small differences in the parameter constraints are already visible. For future surveys we expect that a Gaussian model becomes inaccurate. Our algorithm for a refined non-Gaussian analysis and data compression is then of great utility especially because it is not much more elaborate if simulated data are available. Applying this algorithm to the third-order correlations of shear alone in a blind analysis, we find a good agreement with the standard cosmological model: Σ _8=σ _8(Ω _m/0.27)^{0.64}=0.79^{+0.08}_{-0.11} for a flat Λ cold dark matter cosmology with h = 0.7 ± 0.04 (68 per cent credible interval). Nevertheless our models provide only moderately good fits as indicated by χ2/dof = 2.9, including a 20 per cent rms uncertainty in the predicted signal amplitude. The models cannot explain a signal drop on scales around 15 arcmin, which may be caused by systematics. It is unclear whether the discrepancy can be fully explained by residual point spread function systematics of which we find evidence at least on scales of a few arcmin. Therefore we need a better understanding of higher order correlations of cosmic shear and their systematics to confidently apply them as cosmological probes.

Predicting complex traits using a diffusion kernel on genetic markers with an application to dairy cattle and wheat data

PubMed Central

2013-01-01

Background Arguably, genotypes and phenotypes may be linked in functional forms that are not well addressed by the linear additive models that are standard in quantitative genetics. Therefore, developing statistical learning models for predicting phenotypic values from all available molecular information that are capable of capturing complex genetic network architectures is of great importance. Bayesian kernel ridge regression is a non-parametric prediction model proposed for this purpose. Its essence is to create a spatial distance-based relationship matrix called a kernel. Although the set of all single nucleotide polymorphism genotype configurations on which a model is built is finite, past research has mainly used a Gaussian kernel. Results We sought to investigate the performance of a diffusion kernel, which was specifically developed to model discrete marker inputs, using Holstein cattle and wheat data. This kernel can be viewed as a discretization of the Gaussian kernel. The predictive ability of the diffusion kernel was similar to that of non-spatial distance-based additive genomic relationship kernels in the Holstein data, but outperformed the latter in the wheat data. However, the difference in performance between the diffusion and Gaussian kernels was negligible. Conclusions It is concluded that the ability of a diffusion kernel to capture the total genetic variance is not better than that of a Gaussian kernel, at least for these data. Although the diffusion kernel as a choice of basis function may have potential for use in whole-genome prediction, our results imply that embedding genetic markers into a non-Euclidean metric space has very small impact on prediction. Our results suggest that use of the black box Gaussian kernel is justified, given its connection to the diffusion kernel and its similar predictive performance. PMID:23763755

ENSO's non-stationary and non-Gaussian character: the role of climate shifts

NASA Astrophysics Data System (ADS)

Boucharel, J.; Dewitte, B.; Garel, B.; Du Penhoat, Y.

2009-07-01

El Niño Southern Oscillation (ENSO) is the dominant mode of climate variability in the Pacific, having socio-economic impacts on surrounding regions. ENSO exhibits significant modulation on decadal to inter-decadal time scales which is related to changes in its characteristics (onset, amplitude, frequency, propagation, and predictability). Some of these characteristics tend to be overlooked in ENSO studies, such as its asymmetry (the number and amplitude of warm and cold events are not equal) and the deviation of its statistics from those of the Gaussian distribution. These properties could be related to the ability of the current generation of coupled models to predict ENSO and its modulation. Here, ENSO's non-Gaussian nature and asymmetry are diagnosed from in situ data and a variety of models (from intermediate complexity models to full-physics coupled general circulation models (CGCMs)) using robust statistical tools initially designed for financial mathematics studies. In particular α-stable laws are used as theoretical background material to measure (and quantify) the non-Gaussian character of ENSO time series and to estimate the skill of ``naïve'' statistical models in producing deviation from Gaussian laws and asymmetry. The former are based on non-stationary processes dominated by abrupt changes in mean state and empirical variance. It is shown that the α-stable character of ENSO may result from the presence of climate shifts in the time series. Also, cool (warm) periods are associated with ENSO statistics having a stronger (weaker) tendency towards Gaussianity and lower (greater) asymmetry. This supports the hypothesis of ENSO being rectified by changes in mean state through nonlinear processes. The relationship between changes in mean state and nonlinearity (skewness) is further investigated both in the Zebiak and Cane (1987)'s model and the models of the Intergovernmental Panel for Climate Change (IPCC). Whereas there is a clear relationship in all models between ENSO asymmetry (as measured by skewness or nonlinear advection) and changes in mean state, they exhibit a variety of behaviour with regard to α-stability. This suggests that the dynamics associated with climate shifts and the occurrence of extreme events involve higher-order statistical moments that cannot be accounted for solely by nonlinear advection.

Uncertainty relations for angular momentum eigenstates in two and three spatial dimensions

NASA Astrophysics Data System (ADS)

Bracher, Christian

2011-03-01

I reexamine Heisenberg's uncertainty relation for two- and three-dimensional wave packets with fixed angular momentum quantum numbers m or ℓ. A simple proof shows that the product of the average extent Δr and Δp of a two-dimensional wave packet in position and momentum space is bounded from below by ΔrΔp ≥ℏ(|m|+1). The minimum uncertainty is attained by modified Gaussian wave packets that are special eigenstates of the two-dimensional isotropic harmonic oscillator, which include the ground states of electrons in a uniform magnetic field. Similarly, the inequality ΔrΔp ≥ℏ(ℓ +3/2) holds for three-dimensional wave packets with fixed total angular momentum ℓ and the equality holds for a Gaussian radial profile. I also discuss some applications of these uncertainty relations.

Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski functionals

NASA Astrophysics Data System (ADS)

Buchert, Thomas; France, Martin J.; Steiner, Frank

2017-05-01

Despite the wealth of Planck results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of NG the lack of complete data introduces model-dependences. Aiming at detecting the NGs of the CMB temperature anisotropy δ T , while paying particular attention to a model-independent quantification of NGs, our analysis is based upon statistical and morphological univariate descriptors, respectively: the probability density function P(δ T) , related to v0, the first Minkowski Functional (MF), and the two other MFs, v1 and v2. From their analytical Gaussian predictions we build the discrepancy functions {{ Δ }k} (k  =  P, 0, 1, 2) which are applied to an ensemble of 105 CMB realization maps of the Λ CDM model and to the Planck CMB maps. In our analysis we use general Hermite expansions of the {{ Δ }k} up to the 12th order, where the coefficients are explicitly given in terms of cumulants. Assuming hierarchical ordering of the cumulants, we obtain the perturbative expansions generalizing the second order expansions of Matsubara to arbitrary order in the standard deviation {σ0} for P(δ T) and v0, where the perturbative expansion coefficients are explicitly given in terms of complete Bell polynomials. The comparison of the Hermite expansions and the perturbative expansions is performed for the Λ CDM map sample and the Planck data. We confirm the weak level of non-Gaussianity (1-2)σ of the foreground corrected masked Planck 2015 maps.

Real-Time Noise Reduction for Mossbauer Spectroscopy through Online Implementation of a Modified Kalman Filter

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

Abrecht, David G.; Schwantes, Jon M.; Kukkadapu, Ravi K.

2015-02-01

Spectrum-processing software that incorporates a gaussian smoothing kernel within the statistics of first-order Kalman filtration has been developed to provide cross-channel spectral noise reduction for increased real-time signal-to-noise ratios for Mossbauer spectroscopy. The filter was optimized for the breadth of the gaussian using the Mossbauer spectrum of natural iron foil, and comparisons between the peak broadening, signal-to-noise ratios, and shifts in the calculated hyperfine parameters are presented. The results of optimization give a maximum improvement in the signal-to-noise ratio of 51.1% over the unfiltered spectrum at a gaussian breadth of 27 channels, or 2.5% of the total spectrum width. Themore » full-width half-maximum of the spectrum peaks showed an increase of 19.6% at this optimum point, indicating a relatively weak increase in the peak broadening relative to the signal enhancement, leading to an overall increase in the observable signal. Calculations of the hyperfine parameters showed no statistically significant deviations were introduced from the application of the filter, confirming the utility of this filter for spectroscopy applications.« less

Analysis of the PEDOT:PSS/Si nanowire hybrid solar cell with a tail state model

NASA Astrophysics Data System (ADS)

Ho, Kuan-Ying; Li, Chi-Kang; Syu, Hong-Jhang; Lai, Yi; Lin, Ching-Fuh; Wu, Yuh-Renn

2016-12-01

In this paper, the electrical properties of the poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate) (PEDOT:PSS)/silicon nanowire hybrid solar cell have been analyzed and an optimized structure is proposed. In addition, the planar PEDOT:PSS/c-Si hybrid solar cell is also modeled for comparison. We first developed a simulation software which is capable of modeling organic/inorganic hybrid solar cells by including Gaussian shape density of states into Poisson and drift-diffusion solver to present the tail states and trap states in the organic material. Therefore, the model can handle carrier transport, generation, and recombination in both organic and inorganic materials. Our results show that at the applied voltage near open-circuit voltage (Voc), the recombination rate becomes much higher at the PEDOT:PSS/Si interface region, which limits the fill factor and Voc. Hence, a modified structure with a p-type amorphous silicon (a-Si) layer attached on the interface of Si layer and an n+-type Si layer inserted near the bottom contact are proposed. The highest conversion efficiency of 16.10% can be achieved if both structures are applied.

Optimizing BAO measurements with non-linear transformations of the Lyman-α forest

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

Wang, Xinkang; Font-Ribera, Andreu; Seljak, Uroš, E-mail: xinkang.wang@berkeley.edu, E-mail: afont@lbl.gov, E-mail: useljak@berkeley.edu

2015-04-01

We explore the effect of applying a non-linear transformation to the Lyman-α forest transmitted flux F=e{sup −τ} and the ability of analytic models to predict the resulting clustering amplitude. Both the large-scale bias of the transformed field (signal) and the amplitude of small scale fluctuations (noise) can be arbitrarily modified, but we were unable to find a transformation that increases significantly the signal-to-noise ratio on large scales using Taylor expansion up to the third order. In particular, however, we achieve a 33% improvement in signal to noise for Gaussianized field in transverse direction. On the other hand, we explore anmore » analytic model for the large-scale biasing of the Lyα forest, and present an extension of this model to describe the biasing of the transformed fields. Using hydrodynamic simulations we show that the model works best to describe the biasing with respect to velocity gradients, but is less successful in predicting the biasing with respect to large-scale density fluctuations, especially for very nonlinear transformations.« less

The Topology of Large-Scale Structure in the 1.2 Jy IRAS Redshift Survey

NASA Astrophysics Data System (ADS)

Protogeros, Zacharias A. M.; Weinberg, David H.

1997-11-01

We measure the topology (genus) of isodensity contour surfaces in volume-limited subsets of the 1.2 Jy IRAS redshift survey, for smoothing scales λ = 4, 7, and 12 h-1 Mpc. At 12 h-1 Mpc, the observed genus curve has a symmetric form similar to that predicted for a Gaussian random field. At the shorter smoothing lengths, the observed genus curve shows a modest shift in the direction of an isolated cluster or ``meatball'' topology. We use mock catalogs drawn from cosmological N-body simulations to investigate the systematic biases that affect topology measurements in samples of this size and to determine the full covariance matrix of the expected random errors. We incorporate the error correlations into our evaluations of theoretical models, obtaining both frequentist assessments of absolute goodness of fit and Bayesian assessments of models' relative likelihoods. We compare the observed topology of the 1.2 Jy survey to the predictions of dynamically evolved, unbiased, gravitational instability models that have Gaussian initial conditions. The model with an n = -1 power-law initial power spectrum achieves the best overall agreement with the data, though models with a low-density cold dark matter power spectrum and an n = 0 power-law spectrum are also consistent. The observed topology is inconsistent with an initially Gaussian model that has n = -2, and it is strongly inconsistent with a Voronoi foam model, which has a non-Gaussian, bubble topology.

Action detection by double hierarchical multi-structure space-time statistical matching model

NASA Astrophysics Data System (ADS)

Han, Jing; Zhu, Junwei; Cui, Yiyin; Bai, Lianfa; Yue, Jiang

2018-03-01

Aimed at the complex information in videos and low detection efficiency, an actions detection model based on neighboring Gaussian structure and 3D LARK features is put forward. We exploit a double hierarchical multi-structure space-time statistical matching model (DMSM) in temporal action localization. First, a neighboring Gaussian structure is presented to describe the multi-scale structural relationship. Then, a space-time statistical matching method is proposed to achieve two similarity matrices on both large and small scales, which combines double hierarchical structural constraints in model by both the neighboring Gaussian structure and the 3D LARK local structure. Finally, the double hierarchical similarity is fused and analyzed to detect actions. Besides, the multi-scale composite template extends the model application into multi-view. Experimental results of DMSM on the complex visual tracker benchmark data sets and THUMOS 2014 data sets show the promising performance. Compared with other state-of-the-art algorithm, DMSM achieves superior performances.

Estimating Risk of Natural Gas Portfolios by Using GARCH-EVT-Copula Model.

PubMed

Tang, Jiechen; Zhou, Chao; Yuan, Xinyu; Sriboonchitta, Songsak

2015-01-01

This paper concentrates on estimating the risk of Title Transfer Facility (TTF) Hub natural gas portfolios by using the GARCH-EVT-copula model. We first use the univariate ARMA-GARCH model to model each natural gas return series. Second, the extreme value distribution (EVT) is fitted to the tails of the residuals to model marginal residual distributions. Third, multivariate Gaussian copula and Student t-copula are employed to describe the natural gas portfolio risk dependence structure. Finally, we simulate N portfolios and estimate value at risk (VaR) and conditional value at risk (CVaR). Our empirical results show that, for an equally weighted portfolio of five natural gases, the VaR and CVaR values obtained from the Student t-copula are larger than those obtained from the Gaussian copula. Moreover, when minimizing the portfolio risk, the optimal natural gas portfolio weights are found to be similar across the multivariate Gaussian copula and Student t-copula and different confidence levels.

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets.

PubMed

Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O; Gelfand, Alan E

2016-01-01

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online.

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

PubMed Central

Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O.; Gelfand, Alan E.

2018-01-01

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online. PMID:29720777

Estimating Risk of Natural Gas Portfolios by Using GARCH-EVT-Copula Model

PubMed Central

Tang, Jiechen; Zhou, Chao; Yuan, Xinyu; Sriboonchitta, Songsak

2015-01-01

This paper concentrates on estimating the risk of Title Transfer Facility (TTF) Hub natural gas portfolios by using the GARCH-EVT-copula model. We first use the univariate ARMA-GARCH model to model each natural gas return series. Second, the extreme value distribution (EVT) is fitted to the tails of the residuals to model marginal residual distributions. Third, multivariate Gaussian copula and Student t-copula are employed to describe the natural gas portfolio risk dependence structure. Finally, we simulate N portfolios and estimate value at risk (VaR) and conditional value at risk (CVaR). Our empirical results show that, for an equally weighted portfolio of five natural gases, the VaR and CVaR values obtained from the Student t-copula are larger than those obtained from the Gaussian copula. Moreover, when minimizing the portfolio risk, the optimal natural gas portfolio weights are found to be similar across the multivariate Gaussian copula and Student t-copula and different confidence levels. PMID:26351652

Action detection by double hierarchical multi-structure space–time statistical matching model

NASA Astrophysics Data System (ADS)

Han, Jing; Zhu, Junwei; Cui, Yiyin; Bai, Lianfa; Yue, Jiang

2018-06-01

Aimed at the complex information in videos and low detection efficiency, an actions detection model based on neighboring Gaussian structure and 3D LARK features is put forward. We exploit a double hierarchical multi-structure space-time statistical matching model (DMSM) in temporal action localization. First, a neighboring Gaussian structure is presented to describe the multi-scale structural relationship. Then, a space-time statistical matching method is proposed to achieve two similarity matrices on both large and small scales, which combines double hierarchical structural constraints in model by both the neighboring Gaussian structure and the 3D LARK local structure. Finally, the double hierarchical similarity is fused and analyzed to detect actions. Besides, the multi-scale composite template extends the model application into multi-view. Experimental results of DMSM on the complex visual tracker benchmark data sets and THUMOS 2014 data sets show the promising performance. Compared with other state-of-the-art algorithm, DMSM achieves superior performances.

Integrating a street-canyon model with a regional Gaussian dispersion model for improved characterisation of near-road air pollution

NASA Astrophysics Data System (ADS)

Fallah-Shorshani, Masoud; Shekarrizfard, Maryam; Hatzopoulou, Marianne

2017-03-01

The development and use of dispersion models that simulate traffic-related air pollution in urban areas has risen significantly in support of air pollution exposure research. In order to accurately estimate population exposure, it is important to generate concentration surfaces that take into account near-road concentrations as well as the transport of pollutants throughout an urban region. In this paper, an integrated modelling chain was developed to simulate ambient Nitrogen Dioxide (NO2) in a dense urban neighbourhood while taking into account traffic emissions, the regional background, and the transport of pollutants within the urban canopy. For this purpose, we developed a hybrid configuration including 1) a street canyon model, which simulates pollutant transfer along streets and intersections, taking into account the geometry of buildings and other obstacles, and 2) a Gaussian puff model, which resolves the transport of contaminants at the top of the urban canopy and accounts for regional meteorology. Each dispersion model was validated against measured concentrations and compared against the hybrid configuration. Our results demonstrate that the hybrid approach significantly improves the output of each model on its own. An underestimation appears clearly for the Gaussian model and street-canyon model compared to observed data. This is due to ignoring the building effect by the Gaussian model and undermining the contribution of other roads by the canyon model. The hybrid approach reduced the RMSE (of observed vs. predicted concentrations) by 16%-25% compared to each model on its own, and increased FAC2 (fraction of predictions within a factor of two of the observations) by 10%-34%.

Relativistic corrections and non-Gaussianity in radio continuum surveys

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

Maartens, Roy; Zhao, Gong-Bo; Bacon, David

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 andmore » 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.« less

Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations

DOE PAGES

Del-Castillo-Negrete, Diego B.; Moradi, Sara; Anderson, Johan

2016-09-01

Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of -stable Levy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Levy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Levy fluctuations. The absolute value ofmore » the power law decay exponents are linearly proportional to the Levy index. Furthermore, the observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Levy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.« less

Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations

NASA Astrophysics Data System (ADS)

Moradi, Sara; del-Castillo-Negrete, Diego; Anderson, Johan

2016-09-01

Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of α-stable Lévy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Lévy fluctuations. The absolute value of the power law decay exponents is linearly proportional to the Lévy index α. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Lévy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

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

Ruban, V. P., E-mail: ruban@itp.ac.ru

2015-05-15

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less

Optimal modeling of 1D azimuth correlations in the context of Bayesian inference

NASA Astrophysics Data System (ADS)

De Kock, Michiel B.; Eggers, Hans C.; Trainor, Thomas A.

2015-09-01

Analysis and interpretation of spectrum and correlation data from high-energy nuclear collisions is currently controversial because two opposing physics narratives derive contradictory implications from the same data, one narrative claiming collision dynamics is dominated by dijet production and projectile-nucleon fragmentation, the other claiming collision dynamics is dominated by a dense, flowing QCD medium. Opposing interpretations seem to be supported by alternative data models, and current model-comparison schemes are unable to distinguish between them. There is clearly need for a convincing new methodology to break the deadlock. In this study we introduce Bayesian inference (BI) methods applied to angular correlation data as a basis to evaluate competing data models. For simplicity the data considered are projections of two-dimensional (2D) angular correlations onto a 1D azimuth from three centrality classes of 200-GeV Au-Au collisions. We consider several data models typical of current model choices, including Fourier series (FS) and a Gaussian plus various combinations of individual cosine components. We evaluate model performance with BI methods and with power-spectrum analysis. We find that FS-only models are rejected in all cases by Bayesian analysis, which always prefers a Gaussian. A cylindrical quadrupole cos(2 ϕ ) is required in some cases but rejected for 0%-5%-central Au-Au collisions. Given a Gaussian centered at the azimuth origin, "higher harmonics" cos(m ϕ ) for m >2 are rejected. A model consisting of Gaussian +dipole cos(ϕ )+quadrupole cos(2 ϕ ) provides good 1D data descriptions in all cases.

The Mass-dependent Star Formation Histories of Disk Galaxies: Infall Model Versus Observations

NASA Astrophysics Data System (ADS)

Chang, R. X.; Hou, J. L.; Shen, S. Y.; Shu, C. G.

2010-10-01

We introduce a simple model to explore the star formation histories of disk galaxies. We assume that the disk originate and grows by continuous gas infall. The gas infall rate is parameterized by the Gaussian formula with one free parameter: the infall-peak time tp . The Kennicutt star formation law is adopted to describe how much cold gas turns into stars. The gas outflow process is also considered in our model. We find that, at a given galactic stellar mass M *, the model adopting a late infall-peak time tp results in blue colors, low-metallicity, high specific star formation rate (SFR), and high gas fraction, while the gas outflow rate mainly influences the gas-phase metallicity and star formation efficiency mainly influences the gas fraction. Motivated by the local observed scaling relations, we "construct" a mass-dependent model by assuming that the low-mass galaxy has a later infall-peak time tp and a larger gas outflow rate than massive systems. It is shown that this model can be in agreement with not only the local observations, but also with the observed correlations between specific SFR and galactic stellar mass SFR/M * ~ M * at intermediate redshifts z < 1. Comparison between the Gaussian-infall model and the exponential-infall model is also presented. It shows that the exponential-infall model predicts a higher SFR at early stage and a lower SFR later than that of Gaussian infall. Our results suggest that the Gaussian infall rate may be more reasonable in describing the gas cooling process than the exponential infall rate, especially for low-mass systems.

XDGMM: eXtreme Deconvolution Gaussian Mixture Modeling

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

A non-Gaussian option pricing model based on Kaniadakis exponential deformation

NASA Astrophysics Data System (ADS)

Moretto, Enrico; Pasquali, Sara; Trivellato, Barbara

2017-09-01

A way to make financial models effective is by letting them to represent the so called "fat tails", i.e., extreme changes in stock prices that are regarded as almost impossible by the standard Gaussian distribution. In this article, the Kaniadakis deformation of the usual exponential function is used to define a random noise source in the dynamics of price processes capable of capturing such real market phenomena.

Particle rejuvenation of Rao-Blackwellized sequential Monte Carlo smoothers for conditionally linear and Gaussian models

NASA Astrophysics Data System (ADS)

Nguyen, Ngoc Minh; Corff, Sylvain Le; Moulines, Éric

2017-12-01

This paper focuses on sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use Rao-Blackwellization: particle approximation is used to sample sequences of hidden regimes while the Gaussian states are explicitly integrated conditional on the sequence of regimes and observations, using variants of the Kalman filter/smoother. The first successful attempt to use Rao-Blackwellization for smoothing extends the Bryson-Frazier smoother for Gaussian linear state space models using the generalized two-filter formula together with Kalman filters/smoothers. More recently, a forward-backward decomposition of smoothing distributions mimicking the Rauch-Tung-Striebel smoother for the regimes combined with backward Kalman updates has been introduced. This paper investigates the benefit of introducing additional rejuvenation steps in all these algorithms to sample at each time instant new regimes conditional on the forward and backward particles. This defines particle-based approximations of the smoothing distributions whose support is not restricted to the set of particles sampled in the forward or backward filter. These procedures are applied to commodity markets which are described using a two-factor model based on the spot price and a convenience yield for crude oil data.

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

PubMed

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

2013-01-01

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

Inverse Gaussian gamma distribution model for turbulence-induced fading in free-space optical communication.

PubMed

Cheng, Mingjian; Guo, Ya; Li, Jiangting; Zheng, Xiaotong; Guo, Lixin

2018-04-20

We introduce an alternative distribution to the gamma-gamma (GG) distribution, called inverse Gaussian gamma (IGG) distribution, which can efficiently describe moderate-to-strong irradiance fluctuations. The proposed stochastic model is based on a modulation process between small- and large-scale irradiance fluctuations, which are modeled by gamma and inverse Gaussian distributions, respectively. The model parameters of the IGG distribution are directly related to atmospheric parameters. The accuracy of the fit among the IGG, log-normal, and GG distributions with the experimental probability density functions in moderate-to-strong turbulence are compared, and results indicate that the newly proposed IGG model provides an excellent fit to the experimental data. As the receiving diameter is comparable with the atmospheric coherence radius, the proposed IGG model can reproduce the shape of the experimental data, whereas the GG and LN models fail to match the experimental data. The fundamental channel statistics of a free-space optical communication system are also investigated in an IGG-distributed turbulent atmosphere, and a closed-form expression for the outage probability of the system is derived with Meijer's G-function.

Revisiting Gaussian Process Regression Modeling for Localization in Wireless Sensor Networks

PubMed Central

Richter, Philipp; Toledano-Ayala, Manuel

2015-01-01

Signal strength-based positioning in wireless sensor networks is a key technology for seamless, ubiquitous localization, especially in areas where Global Navigation Satellite System (GNSS) signals propagate poorly. To enable wireless local area network (WLAN) location fingerprinting in larger areas while maintaining accuracy, methods to reduce the effort of radio map creation must be consolidated and automatized. Gaussian process regression has been applied to overcome this issue, also with auspicious results, but the fit of the model was never thoroughly assessed. Instead, most studies trained a readily available model, relying on the zero mean and squared exponential covariance function, without further scrutinization. This paper studies the Gaussian process regression model selection for WLAN fingerprinting in indoor and outdoor environments. We train several models for indoor/outdoor- and combined areas; we evaluate them quantitatively and compare them by means of adequate model measures, hence assessing the fit of these models directly. To illuminate the quality of the model fit, the residuals of the proposed model are investigated, as well. Comparative experiments on the positioning performance verify and conclude the model selection. In this way, we show that the standard model is not the most appropriate, discuss alternatives and present our best candidate. PMID:26370996

Beating the curse of dimension with accurate statistics for the Fokker-Planck equation in complex turbulent systems.

PubMed

Chen, Nan; Majda, Andrew J

2017-12-05

Solving the Fokker-Planck equation for high-dimensional complex dynamical systems is an important issue. Recently, the authors developed efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures, which contain many strong non-Gaussian features such as intermittency and fat-tailed probability density functions (PDFs). The algorithms involve a hybrid strategy with a small number of samples [Formula: see text], where a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious Gaussian kernel density estimation in the remaining low-dimensional subspace. In this article, two effective strategies are developed and incorporated into these algorithms. The first strategy involves a judicious block decomposition of the conditional covariance matrix such that the evolutions of different blocks have no interactions, which allows an extremely efficient parallel computation due to the small size of each individual block. The second strategy exploits statistical symmetry for a further reduction of [Formula: see text] The resulting algorithms can efficiently solve the Fokker-Planck equation with strongly non-Gaussian PDFs in much higher dimensions even with orders in the millions and thus beat the curse of dimension. The algorithms are applied to a [Formula: see text]-dimensional stochastic coupled FitzHugh-Nagumo model for excitable media. An accurate recovery of both the transient and equilibrium non-Gaussian PDFs requires only [Formula: see text] samples! In addition, the block decomposition facilitates the algorithms to efficiently capture the distinct non-Gaussian features at different locations in a [Formula: see text]-dimensional two-layer inhomogeneous Lorenz 96 model, using only [Formula: see text] samples. Copyright © 2017 the Author(s). Published by PNAS.

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

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

Harlim, John, E-mail: jharlim@psu.edu; Mahdi, Adam, E-mail: amahdi@ncsu.edu; Majda, Andrew J., E-mail: jonjon@cims.nyu.edu

2014-01-15

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partialmore » noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.« less

A continuous mixing model for pdf simulations and its applications to combusting shear flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Chen, J.-Y.

1991-01-01

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in this work. A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models.

Non-Gaussian bias: insights from discrete density peaks

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

Desjacques, Vincent; Riotto, Antonio; Gong, Jinn-Ouk, E-mail: Vincent.Desjacques@unige.ch, E-mail: jinn-ouk.gong@apctp.org, E-mail: Antonio.Riotto@unige.ch

2013-09-01

Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastlymore » simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out that statistics of thresholded regions can be computed using the same formalism. Our results suggest that halo clustering statistics can be modelled consistently (in the sense that the Gaussian and non-Gaussian bias factors agree with peak-background split expectations) from a Lagrangian bias relation only if the latter is specified as a set of constraints imposed on the linear density field. This is clearly not the case of standard Lagrangian local bias. Therefore, one is led to consider additional variables beyond the local mass overdensity.« less

Multi-resolution analysis for region of interest extraction in thermographic nondestructive evaluation

NASA Astrophysics Data System (ADS)

Ortiz-Jaramillo, B.; Fandiño Toro, H. A.; Benitez-Restrepo, H. D.; Orjuela-Vargas, S. A.; Castellanos-Domínguez, G.; Philips, W.

2012-03-01

Infrared Non-Destructive Testing (INDT) is known as an effective and rapid method for nondestructive inspection. It can detect a broad range of near-surface structuring flaws in metallic and composite components. Those flaws are modeled as a smooth contour centered at peaks of stored thermal energy, termed Regions of Interest (ROI). Dedicated methodologies must detect the presence of those ROIs. In this paper, we present a methodology for ROI extraction in INDT tasks. The methodology deals with the difficulties due to the non-uniform heating. The non-uniform heating affects low spatial/frequencies and hinders the detection of relevant points in the image. In this paper, a methodology for ROI extraction in INDT using multi-resolution analysis is proposed, which is robust to ROI low contrast and non-uniform heating. The former methodology includes local correlation, Gaussian scale analysis and local edge detection. In this methodology local correlation between image and Gaussian window provides interest points related to ROIs. We use a Gaussian window because thermal behavior is well modeled by Gaussian smooth contours. Also, the Gaussian scale is used to analyze details in the image using multi-resolution analysis avoiding low contrast, non-uniform heating and selection of the Gaussian window size. Finally, local edge detection is used to provide a good estimation of the boundaries in the ROI. Thus, we provide a methodology for ROI extraction based on multi-resolution analysis that is better or equal compared with the other dedicate algorithms proposed in the state of art.

On the cause of the non-Gaussian distribution of residuals in geomagnetism

NASA Astrophysics Data System (ADS)

Hulot, G.; Khokhlov, A.

2017-12-01

To describe errors in the data, Gaussian distributions naturally come to mind. In many practical instances, indeed, Gaussian distributions are appropriate. In the broad field of geomagnetism, however, it has repeatedly been noted that residuals between data and models often display much sharper distributions, sometimes better described by a Laplace distribution. In the present study, we make the case that such non-Gaussian behaviors are very likely the result of what is known as mixture of distributions in the statistical literature. Mixtures arise as soon as the data do not follow a common distribution or are not properly normalized, the resulting global distribution being a mix of the various distributions followed by subsets of the data, or even individual datum. We provide examples of the way such mixtures can lead to distributions that are much sharper than Gaussian distributions and discuss the reasons why such mixtures are likely the cause of the non-Gaussian distributions observed in geomagnetism. We also show that when properly selecting sub-datasets based on geophysical criteria, statistical mixture can sometimes be avoided and much more Gaussian behaviors recovered. We conclude with some general recommendations and point out that although statistical mixture always tends to sharpen the resulting distribution, it does not necessarily lead to a Laplacian distribution. This needs to be taken into account when dealing with such non-Gaussian distributions.

Theoretical analysis of non-Gaussian heterogeneity effects on subsurface flow and transport

NASA Astrophysics Data System (ADS)

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

2017-04-01

Much of the stochastic groundwater literature is devoted to the analysis of flow and transport in Gaussian or multi-Gaussian log hydraulic conductivity (or transmissivity) fields, Y(x)=ln\\func K(x) (x being a position vector), characterized by one or (less frequently) a multiplicity of spatial correlation scales. Yet Y and many other variables and their (spatial or temporal) increments, ΔY, are known to be generally non-Gaussian. One common manifestation of non-Gaussianity is that whereas frequency distributions of Y often exhibit mild peaks and light tails, those of increments ΔY are generally symmetric with peaks that grow sharper, and tails that become heavier, as separation scale or lag between pairs of Y values decreases. A statistical model that captures these disparate, scale-dependent distributions of Y and ΔY in a unified and consistent manner has been recently proposed by us. This new "generalized sub-Gaussian (GSG)" model has the form Y(x)=U(x)G(x) where G(x) is (generally, but not necessarily) a multiscale Gaussian random field and U(x) is a nonnegative subordinator independent of G. The purpose of this paper is to explore analytically, in an elementary manner, lead-order effects that non-Gaussian heterogeneity described by the GSG model have on the stochastic description of flow and transport. Recognizing that perturbation expansion of hydraulic conductivity K=eY diverges when Y is sub-Gaussian, we render the expansion convergent by truncating Y's domain of definition. We then demonstrate theoretically and illustrate by way of numerical examples that, as the domain of truncation expands, (a) the variance of truncated Y (denoted by Yt) approaches that of Y and (b) the pdf (and thereby moments) of Yt increments approach those of Y increments and, as a consequence, the variogram of Yt approaches that of Y. This in turn guarantees that perturbing Kt=etY to second order in σYt (the standard deviation of Yt) yields results which approach those we obtain upon perturbing K=eY to second order in σY even as the corresponding series diverges. Our analysis is rendered mathematically tractable by considering mean-uniform steady state flow in an unbounded, two-dimensional domain of mildly heterogeneous Y with a single-scale function G having an isotropic exponential covariance. Results consist of expressions for (a) lead-order autocovariance and cross-covariance functions of hydraulic head, velocity, and advective particle displacement and (b) analogues of preasymptotic as well as asymptotic Fickian dispersion coefficients. We compare these theoretically and graphically with corresponding expressions developed in the literature for Gaussian Y. We find the former to differ from the latter by a factor k = /2 ( <> denoting ensemble expectation) and the GSG covariance of longitudinal velocity to contain an additional nugget term depending on this same factor. In the limit as Y becomes Gaussian, k reduces to one and the nugget term drops out.