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.

Assessment of DPOAE test-retest difference curves via hierarchical Gaussian processes.

PubMed

Bao, Junshu; Hanson, Timothy; McMillan, Garnett P; Knight, Kristin

2017-03-01

Distortion product otoacoustic emissions (DPOAE) testing is a promising alternative to behavioral hearing tests and auditory brainstem response testing of pediatric cancer patients. The central goal of this study is to assess whether significant changes in the DPOAE frequency/emissions curve (DP-gram) occur in pediatric patients in a test-retest scenario. This is accomplished through the construction of normal reference charts, or credible regions, that DP-gram differences lie in, as well as contour probabilities that measure how abnormal (or in a certain sense rare) a test-retest difference is. A challenge is that the data were collected over varying frequencies, at different time points from baseline, and on possibly one or both ears. A hierarchical structural equation Gaussian process model is proposed to handle the different sources of correlation in the emissions measurements, wherein both subject-specific random effects and variance components governing the smoothness and variability of each child's Gaussian process are coupled together. © 2016, The International Biometric Society.

Cosmology on ultralarge scales with intensity mapping of the neutral hydrogen 21 cm emission: limits on primordial non-Gaussianity.

PubMed

Camera, Stefano; Santos, Mário G; Ferreira, Pedro G; Ferramacho, Luís

2013-10-25

The large-scale structure of the Universe supplies crucial information about the physical processes at play at early times. Unresolved maps of the intensity of 21 cm emission from neutral hydrogen HI at redshifts z=/~1-5 are the best hope of accessing the ultralarge-scale information, directly related to the early Universe. A purpose-built HI intensity experiment may be used to detect the large scale effects of primordial non-Gaussianity, placing stringent bounds on different models of inflation. We argue that it may be possible to place tight constraints on the non-Gaussianity parameter f(NL), with an error close to σ(f(NL))~1.

A qualitative assessment of a random process proposed as an atmospheric turbulence model

NASA Technical Reports Server (NTRS)

Sidwell, K.

1977-01-01

A random process is formed by the product of two Gaussian processes and the sum of that product with a third Gaussian process. The resulting total random process is interpreted as the sum of an amplitude modulated process and a slowly varying, random mean value. The properties of the process are examined, including an interpretation of the process in terms of the physical structure of atmospheric motions. The inclusion of the mean value variation gives an improved representation of the properties of atmospheric motions, since the resulting process can account for the differences in the statistical properties of atmospheric velocity components and their gradients. The application of the process to atmospheric turbulence problems, including the response of aircraft dynamic systems, is examined. The effects of the mean value variation upon aircraft loads are small in most cases, but can be important in the measurement and interpretation of atmospheric turbulence data.

Individualized Gaussian process-based prediction and detection of local and global gray matter abnormalities in elderly subjects.

PubMed

Ziegler, G; Ridgway, G R; Dahnke, R; Gaser, C

2014-08-15

Structural imaging based on MRI is an integral component of the clinical assessment of patients with potential dementia. We here propose an individualized Gaussian process-based inference scheme for clinical decision support in healthy and pathological aging elderly subjects using MRI. The approach aims at quantitative and transparent support for clinicians who aim to detect structural abnormalities in patients at risk of Alzheimer's disease or other types of dementia. Firstly, we introduce a generative model incorporating our knowledge about normative decline of local and global gray matter volume across the brain in elderly. By supposing smooth structural trajectories the models account for the general course of age-related structural decline as well as late-life accelerated loss. Considering healthy subjects' demography and global brain parameters as informative about normal brain aging variability affords individualized predictions in single cases. Using Gaussian process models as a normative reference, we predict new subjects' brain scans and quantify the local gray matter abnormalities in terms of Normative Probability Maps (NPM) and global z-scores. By integrating the observed expectation error and the predictive uncertainty, the local maps and global scores exploit the advantages of Bayesian inference for clinical decisions and provide a valuable extension of diagnostic information about pathological aging. We validate the approach in simulated data and real MRI data. We train the GP framework using 1238 healthy subjects with ages 18-94 years, and predict in 415 independent test subjects diagnosed as healthy controls, Mild Cognitive Impairment and Alzheimer's disease. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Individualized Gaussian process-based prediction and detection of local and global gray matter abnormalities in elderly subjects

PubMed Central

Ziegler, G.; Ridgway, G.R.; Dahnke, R.; Gaser, C.

2014-01-01

Structural imaging based on MRI is an integral component of the clinical assessment of patients with potential dementia. We here propose an individualized Gaussian process-based inference scheme for clinical decision support in healthy and pathological aging elderly subjects using MRI. The approach aims at quantitative and transparent support for clinicians who aim to detect structural abnormalities in patients at risk of Alzheimer's disease or other types of dementia. Firstly, we introduce a generative model incorporating our knowledge about normative decline of local and global gray matter volume across the brain in elderly. By supposing smooth structural trajectories the models account for the general course of age-related structural decline as well as late-life accelerated loss. Considering healthy subjects' demography and global brain parameters as informative about normal brain aging variability affords individualized predictions in single cases. Using Gaussian process models as a normative reference, we predict new subjects' brain scans and quantify the local gray matter abnormalities in terms of Normative Probability Maps (NPM) and global z-scores. By integrating the observed expectation error and the predictive uncertainty, the local maps and global scores exploit the advantages of Bayesian inference for clinical decisions and provide a valuable extension of diagnostic information about pathological aging. We validate the approach in simulated data and real MRI data. We train the GP framework using 1238 healthy subjects with ages 18–94 years, and predict in 415 independent test subjects diagnosed as healthy controls, Mild Cognitive Impairment and Alzheimer's disease. PMID:24742919

Gaussian process regression for geometry optimization

NASA Astrophysics Data System (ADS)

Denzel, Alexander; Kästner, Johannes

2018-03-01

We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Matérn kernel and the squared exponential kernel. The Matérn kernel performs much better. We give a detailed description of the optimization procedures. These include overshooting the step resulting from GPR in order to obtain a higher degree of interpolation vs. extrapolation. In a benchmark against the Limited-memory Broyden-Fletcher-Goldfarb-Shanno optimizer of the DL-FIND library on 26 test systems, we found the new optimizer to generally reduce the number of required optimization steps.

Suborbital spaceplane optimization using non-stationary Gaussian processes

NASA Astrophysics Data System (ADS)

Dufour, Robin; de Muelenaere, Julien; Elham, Ali

2014-10-01

This paper presents multidisciplinary design optimization of a sub-orbital spaceplane. The optimization includes three disciplines: the aerodynamics, the structure and the trajectory. An Adjoint Euler code is used to calculate the aerodynamic lift and drag of the vehicle as well as their derivatives with respect to the design variables. A new surrogate model has been developed based on a non-stationary Gaussian process. That model was used to estimate the aerodynamic characteristics of the vehicle during the trajectory optimization. The trajectory of thevehicle has been optimized together with its geometry in order to maximize the amount of payload that can be carried by the spaceplane.

Some new results on the statistics of radio wave scintillation. I - Empirical evidence for Gaussian statistics

NASA Technical Reports Server (NTRS)

Rino, C. L.; Livingston, R. C.; Whitney, H. E.

1976-01-01

This paper presents an analysis of ionospheric scintillation data which shows that the underlying statistical structure of the signal can be accurately modeled by the additive complex Gaussian perturbation predicted by the Born approximation in conjunction with an application of the central limit theorem. By making use of this fact, it is possible to estimate the in-phase, phase quadrature, and cophased scattered power by curve fitting to measured intensity histograms. By using this procedure, it is found that typically more than 80% of the scattered power is in phase quadrature with the undeviated signal component. Thus, the signal is modeled by a Gaussian, but highly non-Rician process. From simultaneous UHF and VHF data, only a weak dependence of this statistical structure on changes in the Fresnel radius is deduced. The signal variance is found to have a nonquadratic wavelength dependence. It is hypothesized that this latter effect is a subtle manifestation of locally homogeneous irregularity structures, a mathematical model proposed by Kolmogorov (1941) in his early studies of incompressible fluid turbulence.

Breaking Gaussian incompatibility on continuous variable quantum systems

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

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

2015-08-15

We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.

Equivalent linearization for fatigue life estimates of a nonlinear structure

NASA Technical Reports Server (NTRS)

Miles, R. N.

1989-01-01

An analysis is presented of the suitability of the method of equivalent linearization for estimating the fatigue life of a nonlinear structure. Comparisons are made of the fatigue life of a nonlinear plate as predicted using conventional equivalent linearization and three other more accurate methods. The excitation of the plate is assumed to be Gaussian white noise and the plate response is modeled using a single resonant mode. The methods used for comparison consist of numerical simulation, a probabalistic formulation, and a modification of equivalent linearization which avoids the usual assumption that the response process is Gaussian. Remarkably close agreement is obtained between all four methods, even for cases where the response is significantly linear.

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.

Gaussian process based independent analysis for temporal source separation in fMRI.

PubMed

Hald, Ditte Høvenhoff; Henao, Ricardo; Winther, Ole

2017-05-15

Functional Magnetic Resonance Imaging (fMRI) gives us a unique insight into the processes of the brain, and opens up for analyzing the functional activation patterns of the underlying sources. Task-inferred supervised learning with restrictive assumptions in the regression set-up, restricts the exploratory nature of the analysis. Fully unsupervised independent component analysis (ICA) algorithms, on the other hand, can struggle to detect clear classifiable components on single-subject data. We attribute this shortcoming to inadequate modeling of the fMRI source signals by failing to incorporate its temporal nature. fMRI source signals, biological stimuli and non-stimuli-related artifacts are all smooth over a time-scale compatible with the sampling time (TR). We therefore propose Gaussian process ICA (GPICA), which facilitates temporal dependency by the use of Gaussian process source priors. On two fMRI data sets with different sampling frequency, we show that the GPICA-inferred temporal components and associated spatial maps allow for a more definite interpretation than standard temporal ICA methods. The temporal structures of the sources are controlled by the covariance of the Gaussian process, specified by a kernel function with an interpretable and controllable temporal length scale parameter. We propose a hierarchical model specification, considering both instantaneous and convolutive mixing, and we infer source spatial maps, temporal patterns and temporal length scale parameters by Markov Chain Monte Carlo. A companion implementation made as a plug-in for SPM can be downloaded from https://github.com/dittehald/GPICA. Copyright © 2017 Elsevier Inc. All rights reserved.

Galaxy formation

PubMed Central

Peebles, P. J. E.

1998-01-01

It is argued that within the standard Big Bang cosmological model the bulk of the mass of the luminous parts of the large galaxies likely had been assembled by redshift z ∼ 10. Galaxy assembly this early would be difficult to fit in the widely discussed adiabatic cold dark matter model for structure formation, but it could agree with an isocurvature version in which the cold dark matter is the remnant of a massive scalar field frozen (or squeezed) from quantum fluctuations during inflation. The squeezed field fluctuations would be Gaussian with zero mean, and the distribution of the field mass therefore would be the square of a random Gaussian process. This offers a possibly interesting new direction for the numerical exploration of models for cosmic structure formation. PMID:9419326

Adaptive smoothing based on Gaussian processes regression increases the sensitivity and specificity of fMRI data.

PubMed

Strappini, Francesca; Gilboa, Elad; Pitzalis, Sabrina; Kay, Kendrick; McAvoy, Mark; Nehorai, Arye; Snyder, Abraham Z

2017-03-01

Temporal and spatial filtering of fMRI data is often used to improve statistical power. However, conventional methods, such as smoothing with fixed-width Gaussian filters, remove fine-scale structure in the data, necessitating a tradeoff between sensitivity and specificity. Specifically, smoothing may increase sensitivity (reduce noise and increase statistical power) but at the cost loss of specificity in that fine-scale structure in neural activity patterns is lost. Here, we propose an alternative smoothing method based on Gaussian processes (GP) regression for single subjects fMRI experiments. This method adapts the level of smoothing on a voxel by voxel basis according to the characteristics of the local neural activity patterns. GP-based fMRI analysis has been heretofore impractical owing to computational demands. Here, we demonstrate a new implementation of GP that makes it possible to handle the massive data dimensionality of the typical fMRI experiment. We demonstrate how GP can be used as a drop-in replacement to conventional preprocessing steps for temporal and spatial smoothing in a standard fMRI pipeline. We present simulated and experimental results that show the increased sensitivity and specificity compared to conventional smoothing strategies. Hum Brain Mapp 38:1438-1459, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

A stochastic-geometric model of soil variation in Pleistocene patterned ground

NASA Astrophysics Data System (ADS)

Lark, Murray; Meerschman, Eef; Van Meirvenne, Marc

2013-04-01

In this paper we examine the spatial variability of soil in parent material with complex spatial structure which arises from complex non-linear geomorphic processes. We show that this variability can be better-modelled by a stochastic-geometric model than by a standard Gaussian random field. The benefits of the new model are seen in the reproduction of features of the target variable which influence processes like water movement and pollutant dispersal. Complex non-linear processes in the soil give rise to properties with non-Gaussian distributions. Even under a transformation to approximate marginal normality, such variables may have a more complex spatial structure than the Gaussian random field model of geostatistics can accommodate. In particular the extent to which extreme values of the variable are connected in spatially coherent regions may be misrepresented. As a result, for example, geostatistical simulation generally fails to reproduce the pathways for preferential flow in an environment where coarse infill of former fluvial channels or coarse alluvium of braided streams creates pathways for rapid movement of water. Multiple point geostatistics has been developed to deal with this problem. Multiple point methods proceed by sampling from a set of training images which can be assumed to reproduce the non-Gaussian behaviour of the target variable. The challenge is to identify appropriate sources of such images. In this paper we consider a mode of soil variation in which the soil varies continuously, exhibiting short-range lateral trends induced by local effects of the factors of soil formation which vary across the region of interest in an unpredictable way. The trends in soil variation are therefore only apparent locally, and the soil variation at regional scale appears random. We propose a stochastic-geometric model for this mode of soil variation called the Continuous Local Trend (CLT) model. We consider a case study of soil formed in relict patterned ground with pronounced lateral textural variations arising from the presence of infilled ice-wedges of Pleistocene origin. We show how knowledge of the pedogenetic processes in this environment, along with some simple descriptive statistics, can be used to select and fit a CLT model for the apparent electrical conductivity (ECa) of the soil. We use the model to simulate realizations of the CLT process, and compare these with realizations of a fitted Gaussian random field. We show how statistics that summarize the spatial coherence of regions with small values of ECa, which are expected to have coarse texture and so larger saturated hydraulic conductivity, are better reproduced by the CLT model than by the Gaussian random field. This suggests that the CLT model could be used to generate an unlimited supply of training images to allow multiple point geostatistical simulation or prediction of this or similar variables.

Non-Gaussian effects, space-time decoupling, and mobility bifurcation in glassy hard-sphere fluids and suspensions.

PubMed

Saltzman, Erica J; Schweizer, Kenneth S

2006-12-01

Brownian trajectory simulation methods are employed to fully establish the non-Gaussian fluctuation effects predicted by our nonlinear Langevin equation theory of single particle activated dynamics in glassy hard-sphere fluids. The consequences of stochastic mobility fluctuations associated with the space-time complexities of the transient localization and barrier hopping processes have been determined. The incoherent dynamic structure factor was computed for a range of wave vectors and becomes of an increasingly non-Gaussian form for volume fractions beyond the (naive) ideal mode coupling theory (MCT) transition. The non-Gaussian parameter (NGP) amplitude increases markedly with volume fraction and is well described by a power law in the maximum restoring force of the nonequilibrium free energy profile. The time scale associated with the NGP peak becomes much smaller than the alpha relaxation time for systems characterized by significant entropic barriers. An alternate non-Gaussian parameter that probes the long time alpha relaxation process displays a different shape, peak intensity, and time scale of its maximum. However, a strong correspondence between the classic and alternate NGP amplitudes is predicted which suggests a deep connection between the early and final stages of cage escape. Strong space-time decoupling emerges at high volume fractions as indicated by a nondiffusive wave vector dependence of the relaxation time and growth of the translation-relaxation decoupling parameter. Displacement distributions exhibit non-Gaussian behavior at intermediate times, evolving into a strongly bimodal form with slow and fast subpopulations at high volume fractions. Qualitative and semiquantitative comparisons of the theoretical results with colloid experiments, ideal MCT, and multiple simulation studies are presented.

Preservation of Gaussian state entanglement in a quantum beat laser by reservoir engineering

NASA Astrophysics Data System (ADS)

Qurban, Misbah; Islam, Rameez ul; Ge, Guo-Qin; Ikram, Manzoor

2018-04-01

Quantum beat lasers have been considered as sources of entangled radiation in continuous variables such as Gaussian states. In order to preserve entanglement and to minimize entanglement degradation due to the system’s interaction with the surrounding environment, we propose to engineer environment modes through insertion of another system in between the laser resonator and the environment. This makes the environment surrounding the two-mode laser a structured reservoir. It not only enhances the entanglement among two modes of the laser but also preserves the entanglement for sufficiently longer times, a stringent requirement for quantum information processing tasks.

Stable Lévy motion with inverse Gaussian subordinator

NASA Astrophysics Data System (ADS)

Kumar, A.; Wyłomańska, A.; Gajda, J.

2017-09-01

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

Progress in integrated-circuit horn antennas for receiver applications. Part 1: Antenna design

NASA Technical Reports Server (NTRS)

Eleftheriades, George V.; Ali-Ahmad, Walid Y.; Rebeiz, Gabriel M.

1992-01-01

The purpose of this work is to present a systematic method for the design of multimode quasi-integrated horn antennas. The design methodology is based on the Gaussian beam approach and the structures are optimized for achieving maximum fundamental Gaussian coupling efficiency. For this purpose, a hybrid technique is employed in which the integrated part of the antennas is treated using full-wave analysis, whereas the machined part is treated using an approximate method. This results in a simple and efficient design process. The developed design procedure has been applied for the design of a 20, a 23, and a 25 dB quasi-integrated horn antennas, all with a Gaussian coupling efficiency exceeding 97 percent. The designed antennas have been tested and characterized using both full-wave analysis and 90 GHz/370 GHz measurements.

Principles of diffusion kurtosis imaging and its role in early diagnosis of neurodegenerative disorders.

PubMed

Arab, Anas; Wojna-Pelczar, Anna; Khairnar, Amit; Szabó, Nikoletta; Ruda-Kucerova, Jana

2018-05-01

Pathology of neurodegenerative diseases can be correlated with intra-neuronal as well as extracellular changes which lead to neuronal degeneration. The central nervous system (CNS) is a complex structure comprising of many biological barriers. These microstructural barriers might be affected by a variety of pathological processes. Specifically, changes in the brain tissue's microstructure affect the diffusion of water which can be assessed non-invasively by diffusion weighted (DW) magnetic resonance imaging (MRI) techniques. Diffusion tensor imaging (DTI) is a diffusion MRI technique that considers diffusivity as a Gaussian process, i.e. does not account for any diffusion hindrance. However, environment of the brain tissues is characterized by a non-Gaussian diffusion. Therefore, diffusion kurtosis imaging (DKI) was developed as an extension of DTI method in order to quantify the non-Gaussian distribution of water diffusion. This technique represents a promising approach for early diagnosis of neurodegenerative diseases when the neurodegenerative process starts. Hence, the purpose of this article is to summarize the ongoing clinical and preclinical research on Parkinson's, Alzheimer's and Huntington diseases, using DKI and to discuss the role of this technique as an early stage biomarker of neurodegenerative conditions. Copyright © 2018 Elsevier Inc. All rights reserved.

An effective introduction to structural crystallography using 1D Gaussian atoms

NASA Astrophysics Data System (ADS)

Smith, Emily; Evans, Gwyndaf; Foadi, James

2017-11-01

The most important quantitative aspects of computational structural crystallography can be introduced in a satisfactory way using 1D truncated and periodic Gaussian functions to represent the atoms in a crystal lattice. This paper describes in detail and demonstrates 1D structural crystallography starting with the definition of such truncated Gaussians. The availability of the computer programme CRONE makes possible the repetition of the examples provided in the paper as well as the creation of new ones.

Gaussian process regression to accelerate geometry optimizations relying on numerical differentiation

NASA Astrophysics Data System (ADS)

Schmitz, Gunnar; Christiansen, Ove

2018-06-01

We study how with means of Gaussian Process Regression (GPR) geometry optimizations, which rely on numerical gradients, can be accelerated. The GPR interpolates a local potential energy surface on which the structure is optimized. It is found to be efficient to combine results on a low computational level (HF or MP2) with the GPR-calculated gradient of the difference between the low level method and the target method, which is a variant of explicitly correlated Coupled Cluster Singles and Doubles with perturbative Triples correction CCSD(F12*)(T) in this study. Overall convergence is achieved if both the potential and the geometry are converged. Compared to numerical gradient-based algorithms, the number of required single point calculations is reduced. Although introducing an error due to the interpolation, the optimized structures are sufficiently close to the minimum of the target level of theory meaning that the reference and predicted minimum only vary energetically in the μEh regime.

The Laplace method for probability measures in Banach spaces

NASA Astrophysics Data System (ADS)

Piterbarg, V. I.; Fatalov, V. R.

1995-12-01

Contents §1. Introduction Chapter I. Asymptotic analysis of continual integrals in Banach space, depending on a large parameter §2. The large deviation principle and logarithmic asymptotics of continual integrals §3. Exact asymptotics of Gaussian integrals in Banach spaces: the Laplace method 3.1. The Laplace method for Gaussian integrals taken over the whole Hilbert space: isolated minimum points ([167], I) 3.2. The Laplace method for Gaussian integrals in Hilbert space: the manifold of minimum points ([167], II) 3.3. The Laplace method for Gaussian integrals in Banach space ([90], [174], [176]) 3.4. Exact asymptotics of large deviations of Gaussian norms §4. The Laplace method for distributions of sums of independent random elements with values in Banach space 4.1. The case of a non-degenerate minimum point ([137], I) 4.2. A degenerate isolated minimum point and the manifold of minimum points ([137], II) §5. Further examples 5.1. The Laplace method for the local time functional of a Markov symmetric process ([217]) 5.2. The Laplace method for diffusion processes, a finite number of non-degenerate minimum points ([116]) 5.3. Asymptotics of large deviations for Brownian motion in the Hölder norm 5.4. Non-asymptotic expansion of a strong stable law in Hilbert space ([41]) Chapter II. The double sum method - a version of the Laplace method in the space of continuous functions §6. Pickands' method of double sums 6.1. General situations 6.2. Asymptotics of the distribution of the maximum of a Gaussian stationary process 6.3. Asymptotics of the probability of a large excursion of a Gaussian non-stationary process §7. Probabilities of large deviations of trajectories of Gaussian fields 7.1. Homogeneous fields and fields with constant dispersion 7.2. Finitely many maximum points of dispersion 7.3. Manifold of maximum points of dispersion 7.4. Asymptotics of distributions of maxima of Wiener fields §8. Exact asymptotics of large deviations of the norm of Gaussian vectors and processes with values in the spaces L_k^p and l^2. Gaussian fields with the set of parameters in Hilbert space 8.1 Exact asymptotics of the distribution of the l_k^p-norm of a Gaussian finite-dimensional vector with dependent coordinates, p > 1 8.2. Exact asymptotics of probabilities of high excursions of trajectories of processes of type \\chi^2 8.3. Asymptotics of the probabilities of large deviations of Gaussian processes with a set of parameters in Hilbert space [74] 8.4. Asymptotics of distributions of maxima of the norms of l^2-valued Gaussian processes 8.5. Exact asymptotics of large deviations for the l^2-valued Ornstein-Uhlenbeck process Bibliography

Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Siopsis, George; Weedbrook, Christian

2018-02-01

With the significant advancement in quantum computation during the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used technique in supervised classical machine learning. Here we introduce an algorithm for Gaussian process regression using continuous-variable quantum systems that can be realized with technology based on photonic quantum computers under certain assumptions regarding distribution of data and availability of efficient quantum access. Our algorithm shows that by using a continuous-variable quantum computer a dramatic speedup in computing Gaussian process regression can be achieved, i.e., the possibility of exponentially reducing the time to compute. Furthermore, our results also include a continuous-variable quantum-assisted singular value decomposition method of nonsparse low rank matrices and forms an important subroutine in our Gaussian process regression algorithm.

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.

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.

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.

2002-01-01

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

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

Park, Chanyoung; Kim, Nam H.

Structural elements, such as stiffened panels and lap joints, are basic components of aircraft structures. For aircraft structural design, designers select predesigned elements satisfying the design load requirement based on their load-carrying capabilities. Therefore, estimation of safety envelope of structural elements for load tolerances would be a good investment for design purpose. In this article, a method of estimating safety envelope is presented using probabilistic classification, which can estimate a specific level of failure probability under both aleatory and epistemic uncertainties. An important contribution of this article is that the calculation uncertainty is reflected in building a safety envelope usingmore » Gaussian process, and the effect of element test data on reducing the calculation uncertainty is incorporated by updating the Gaussian process model with the element test data. It is shown that even one element test can significantly reduce the calculation uncertainty due to lacking knowledge of actual physics, so that conservativeness in a safety envelope is significantly reduced. The proposed approach was demonstrated with a cantilever beam example, which represents a structural element. The example shows that calculation uncertainty provides about 93% conservativeness against the uncertainty due to a few element tests. As a result, it is shown that even a single element test can increase the load tolerance modeled with the safety envelope by 20%.« less

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

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.

Estimating Mixture of Gaussian Processes by Kernel Smoothing

PubMed Central

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

2014-01-01

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

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

Light beam shaping and homogenization (LSBH) by irregular microlens structure for medical applications

NASA Astrophysics Data System (ADS)

Semchishen, Vladimir A.; Mrochen, Michael; Seminogov, Vladimir N.; Panchenko, Vladislav Y.; Seiler, Theo

1998-04-01

Purpose: The increasing interest in a homogeneous Gaussian light beam profile for applications in ophthalmology e.g. photorefractive keratectomy (PRK) requests simple optical systems with low energy losses. Therefore, we developed the Light Shaping Beam Homogenizer (LSBH) working from UV up to mid-IR. Method: The irregular microlenses structure on a quartz surface was fabricated by using photolithography, chemical etching and chemical polishing processes. This created a three dimensional structure on the quartz substrate characterized in case of a Gaussian beam by random law distribution of individual irregularities tilts. The LSBH was realized for the 193 nm and the 2.94 micrometer wavelengths. Simulation results obtained by 3-D analysis for an arbitrary incident light beam were compared to experimental results. Results: The correlation to a numerical Gaussian fit is better than 94% with high uniformity for an incident beam with an intensity modulation of nearly 100%. In the far field the cross section of the beam shows always rotation symmetry. Transmittance and damage threshold of the LSBH are only dependent on the substrate characteristics. Conclusions: considering our experimental and simulation results it is possible to control the angular distribution of the beam intensity after LSBH with higher efficiency compared to diffraction or holographic optical elements.

An Improved Gaussian Mixture Model for Damage Propagation Monitoring of an Aircraft Wing Spar under Changing Structural Boundary Conditions.

PubMed

Qiu, Lei; Yuan, Shenfang; Mei, Hanfei; Fang, Fang

2016-02-26

Structural Health Monitoring (SHM) technology is considered to be a key technology to reduce the maintenance cost and meanwhile ensure the operational safety of aircraft structures. It has gradually developed from theoretic and fundamental research to real-world engineering applications in recent decades. The problem of reliable damage monitoring under time-varying conditions is a main issue for the aerospace engineering applications of SHM technology. Among the existing SHM methods, Guided Wave (GW) and piezoelectric sensor-based SHM technique is a promising method due to its high damage sensitivity and long monitoring range. Nevertheless the reliability problem should be addressed. Several methods including environmental parameter compensation, baseline signal dependency reduction and data normalization, have been well studied but limitations remain. This paper proposes a damage propagation monitoring method based on an improved Gaussian Mixture Model (GMM). It can be used on-line without any structural mechanical model and a priori knowledge of damage and time-varying conditions. With this method, a baseline GMM is constructed first based on the GW features obtained under time-varying conditions when the structure under monitoring is in the healthy state. When a new GW feature is obtained during the on-line damage monitoring process, the GMM can be updated by an adaptive migration mechanism including dynamic learning and Gaussian components split-merge. The mixture probability distribution structure of the GMM and the number of Gaussian components can be optimized adaptively. Then an on-line GMM can be obtained. Finally, a best match based Kullback-Leibler (KL) divergence is studied to measure the migration degree between the baseline GMM and the on-line GMM to reveal the weak cumulative changes of the damage propagation mixed in the time-varying influence. A wing spar of an aircraft is used to validate the proposed method. The results indicate that the crack propagation under changing structural boundary conditions can be monitored reliably. The method is not limited by the properties of the structure, and thus it is feasible to be applied to composite structure.

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

Towards better modelling of drug-loading in solid lipid nanoparticles: Molecular dynamics, docking experiments and Gaussian Processes machine learning.

PubMed

Hathout, Rania M; Metwally, Abdelkader A

2016-11-01

This study represents one of the series applying computer-oriented processes and tools in digging for information, analysing data and finally extracting correlations and meaningful outcomes. In this context, binding energies could be used to model and predict the mass of loaded drugs in solid lipid nanoparticles after molecular docking of literature-gathered drugs using MOE® software package on molecularly simulated tripalmitin matrices using GROMACS®. Consequently, Gaussian processes as a supervised machine learning artificial intelligence technique were used to correlate the drugs' descriptors (e.g. M.W., xLogP, TPSA and fragment complexity) with their molecular docking binding energies. Lower percentage bias was obtained compared to previous studies which allows the accurate estimation of the loaded mass of any drug in the investigated solid lipid nanoparticles by just projecting its chemical structure to its main features (descriptors). Copyright © 2016 Elsevier B.V. All rights reserved.

Dynamic design of ecological monitoring networks for non-Gaussian spatio-temporal data

USGS Publications Warehouse

Wikle, C.K.; Royle, J. Andrew

2005-01-01

Many ecological processes exhibit spatial structure that changes over time in a coherent, dynamical fashion. This dynamical component is often ignored in the design of spatial monitoring networks. Furthermore, ecological variables related to processes such as habitat are often non-Gaussian (e.g. Poisson or log-normal). We demonstrate that a simulation-based design approach can be used in settings where the data distribution is from a spatio-temporal exponential family. The key random component in the conditional mean function from this distribution is then a spatio-temporal dynamic process. Given the computational burden of estimating the expected utility of various designs in this setting, we utilize an extended Kalman filter approximation to facilitate implementation. The approach is motivated by, and demonstrated on, the problem of selecting sampling locations to estimate July brood counts in the prairie pothole region of the U.S.

Crystallographic Topology 2: Overview and Work in Progress

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

Johnson, C.K.

1999-08-01

This overview describes an application of contemporary geometric topology and stochastic process concepts to structural crystallography. In this application, crystallographic groups become orbifolds, crystal structures become Morse functions on orbifolds, and vibrating atoms in a crystal become vector valued Gaussian measures with the Radon-Nikodym property. Intended crystallographic benefits include new methods for visualization of space groups and crystal structures, analysis of the thermal motion patterns seen in ORTEP drawings, and a classification scheme for crystal structures based on their Heegaard splitting properties.

Angle-domain common-image gathers from anisotropic Gaussian beam migration and its application to anisotropy-induced imaging errors analysis

NASA Astrophysics Data System (ADS)

Han, Jianguang; Wang, Yun; Yu, Changqing; Chen, Peng

2017-02-01

An approach for extracting angle-domain common-image gathers (ADCIGs) from anisotropic Gaussian beam prestack depth migration (GB-PSDM) is presented in this paper. The propagation angle is calculated in the process of migration using the real-value traveltime information of Gaussian beam. Based on the above, we further investigate the effects of anisotropy on GB-PSDM, where the corresponding ADCIGs are extracted to assess the quality of migration images. The test results of the VTI syncline model and the TTI thrust sheet model show that anisotropic parameters ɛ, δ, and tilt angle 𝜃, have a great influence on the accuracy of the migrated image in anisotropic media, and ignoring any one of them will cause obvious imaging errors. The anisotropic GB-PSDM with the true anisotropic parameters can obtain more accurate seismic images of subsurface structures in anisotropic media.

A path integral approach to the Hodgkin-Huxley model

NASA Astrophysics Data System (ADS)

Baravalle, Roman; Rosso, Osvaldo A.; Montani, Fernando

2017-11-01

To understand how single neurons process sensory information, it is necessary to develop suitable stochastic models to describe the response variability of the recorded spike trains. Spikes in a given neuron are produced by the synergistic action of sodium and potassium of the voltage-dependent channels that open or close the gates. Hodgkin and Huxley (HH) equations describe the ionic mechanisms underlying the initiation and propagation of action potentials, through a set of nonlinear ordinary differential equations that approximate the electrical characteristics of the excitable cell. Path integral provides an adequate approach to compute quantities such as transition probabilities, and any stochastic system can be expressed in terms of this methodology. We use the technique of path integrals to determine the analytical solution driven by a non-Gaussian colored noise when considering the HH equations as a stochastic system. The different neuronal dynamics are investigated by estimating the path integral solutions driven by a non-Gaussian colored noise q. More specifically we take into account the correlational structures of the complex neuronal signals not just by estimating the transition probability associated to the Gaussian approach of the stochastic HH equations, but instead considering much more subtle processes accounting for the non-Gaussian noise that could be induced by the surrounding neural network and by feedforward correlations. This allows us to investigate the underlying dynamics of the neural system when different scenarios of noise correlations are considered.

A Stochastic Kinematic Model of Class Averaging in Single-Particle Electron Microscopy

PubMed Central

Park, Wooram; Midgett, Charles R.; Madden, Dean R.; Chirikjian, Gregory S.

2011-01-01

Single-particle electron microscopy is an experimental technique that is used to determine the 3D structure of biological macromolecules and the complexes that they form. In general, image processing techniques and reconstruction algorithms are applied to micrographs, which are two-dimensional (2D) images taken by electron microscopes. Each of these planar images can be thought of as a projection of the macromolecular structure of interest from an a priori unknown direction. A class is defined as a collection of projection images with a high degree of similarity, presumably resulting from taking projections along similar directions. In practice, micrographs are very noisy and those in each class are aligned and averaged in order to reduce the background noise. Errors in the alignment process are inevitable due to noise in the electron micrographs. This error results in blurry averaged images. In this paper, we investigate how blurring parameters are related to the properties of the background noise in the case when the alignment is achieved by matching the mass centers and the principal axes of the experimental images. We observe that the background noise in micrographs can be treated as Gaussian. Using the mean and variance of the background Gaussian noise, we derive equations for the mean and variance of translational and rotational misalignments in the class averaging process. This defines a Gaussian probability density on the Euclidean motion group of the plane. Our formulation is validated by convolving the derived blurring function representing the stochasticity of the image alignments with the underlying noiseless projection and comparing with the original blurry image. PMID:21660125

Determining the Structure of Oxalate Anion Using Infrared and Raman Spectroscopy Coupled with Gaussian Calculations

ERIC Educational Resources Information Center

Peterson, Karen I.; Pullman, David P.

2016-01-01

A laboratory project for the upper-division physical chemistry laboratory is described, and it combines IR and Raman spectroscopies with Gaussian electronic structure calculations to determine the structure of the oxalate anion in solid alkali oxalates and in aqueous solution. The oxalate anion has two limiting structures whose vibrational spectra…

Safety envelope for load tolerance of structural element design based on multi-stage testing

DOE PAGES

Park, Chanyoung; Kim, Nam H.

2016-09-06

Structural elements, such as stiffened panels and lap joints, are basic components of aircraft structures. For aircraft structural design, designers select predesigned elements satisfying the design load requirement based on their load-carrying capabilities. Therefore, estimation of safety envelope of structural elements for load tolerances would be a good investment for design purpose. In this article, a method of estimating safety envelope is presented using probabilistic classification, which can estimate a specific level of failure probability under both aleatory and epistemic uncertainties. An important contribution of this article is that the calculation uncertainty is reflected in building a safety envelope usingmore » Gaussian process, and the effect of element test data on reducing the calculation uncertainty is incorporated by updating the Gaussian process model with the element test data. It is shown that even one element test can significantly reduce the calculation uncertainty due to lacking knowledge of actual physics, so that conservativeness in a safety envelope is significantly reduced. The proposed approach was demonstrated with a cantilever beam example, which represents a structural element. The example shows that calculation uncertainty provides about 93% conservativeness against the uncertainty due to a few element tests. As a result, it is shown that even a single element test can increase the load tolerance modeled with the safety envelope by 20%.« less

Retinal vessel enhancement based on the Gaussian function and image fusion

NASA Astrophysics Data System (ADS)

Moraru, Luminita; Obreja, Cristian Dragoş

2017-01-01

The Gaussian function is essential in the construction of the Frangi and COSFIRE (combination of shifted filter responses) filters. The connection of the broken vessels and an accurate extraction of the vascular structure is the main goal of this study. Thus, the outcome of the Frangi and COSFIRE edge detection algorithms are fused using the Dempster-Shafer algorithm with the aim to improve detection and to enhance the retinal vascular structure. For objective results, the average diameters of the retinal vessels provided by Frangi, COSFIRE and Dempster-Shafer fusion algorithms are measured. These experimental values are compared to the ground truth values provided by manually segmented retinal images. We prove the superiority of the fusion algorithm in terms of image quality by using the figure of merit objective metric that correlates the effects of all post-processing techniques.

Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states

PubMed Central

Bonet-Luz, Esther

2016-01-01

The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest’s theorem is shown to be Lie–Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie–Poisson structure associated with another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models that have previously appeared in the chemical physics literature. PMID:27279764

Rate Constants for Fine-Structure Excitations in O - H Collisions with Error Bars Obtained by Machine Learning

NASA Astrophysics Data System (ADS)

Vieira, Daniel; Krems, Roman

2017-04-01

Fine-structure transitions in collisions of O(3Pj) with atomic hydrogen are an important cooling mechanism in the interstellar medium; knowledge of the rate coefficients for these transitions has a wide range of astrophysical applications. The accuracy of the theoretical calculation is limited by inaccuracy in the ab initio interaction potentials used in the coupled-channel quantum scattering calculations from which the rate coefficients can be obtained. In this work we use the latest ab initio results for the O(3Pj) + H interaction potentials to improve on previous calculations of the rate coefficients. We further present a machine-learning technique based on Gaussian Process regression to determine the sensitivity of the rate coefficients to variations of the underlying adiabatic interaction potentials. To account for the inaccuracy inherent in the ab initio calculations we compute error bars for the rate coefficients corresponding to 20% variation in each of the interaction potentials. We obtain these error bars by fitting a Gaussian Process model to a data set of potential curves and rate constants. We use the fitted model to do sensitivity analysis, determining the relative importance of individual adiabatic potential curves to a given fine-structure transition. NSERC.

Speckle lithography for fabricating Gaussian, quasi-random 2D structures and black silicon structures.

PubMed

Bingi, Jayachandra; Murukeshan, Vadakke Matham

2015-12-18

Laser speckle pattern is a granular structure formed due to random coherent wavelet interference and generally considered as noise in optical systems including photolithography. Contrary to this, in this paper, we use the speckle pattern to generate predictable and controlled Gaussian random structures and quasi-random structures photo-lithographically. The random structures made using this proposed speckle lithography technique are quantified based on speckle statistics, radial distribution function (RDF) and fast Fourier transform (FFT). The control over the speckle size, density and speckle clustering facilitates the successful fabrication of black silicon with different surface structures. The controllability and tunability of randomness makes this technique a robust method for fabricating predictable 2D Gaussian random structures and black silicon structures. These structures can enhance the light trapping significantly in solar cells and hence enable improved energy harvesting. Further, this technique can enable efficient fabrication of disordered photonic structures and random media based devices.

Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams

NASA Astrophysics Data System (ADS)

Dennis, M. R.; Alonso, M. A.

2017-02-01

The connection between Poincaré spheres for polarization and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic two-dimensional harmonic oscillator in Hamiltonian mechanics, its canonical quantization and semiclassical interpretation. This leads to the interpretation of structured Gaussian modes, the Hermite-Gaussian, Laguerre-Gaussian and generalized Hermite-Laguerre-Gaussian modes as eigenfunctions of operators corresponding to the classical constants of motion of the two-dimensional oscillator, which acquire an extra significance as families of classical ellipses upon semiclassical quantization. This article is part of the themed issue 'Optical orbital angular momentum'.

EMG prediction from Motor Cortical Recordings via a Non-Negative Point Process Filter

PubMed Central

Nazarpour, Kianoush; Ethier, Christian; Paninski, Liam; Rebesco, James M.; Miall, R. Chris; Miller, Lee E.

2012-01-01

A constrained point process filtering mechanism for prediction of electromyogram (EMG) signals from multi-channel neural spike recordings is proposed here. Filters from the Kalman family are inherently sub-optimal in dealing with non-Gaussian observations, or a state evolution that deviates from the Gaussianity assumption. To address these limitations, we modeled the non-Gaussian neural spike train observations by using a generalized linear model (GLM) that encapsulates covariates of neural activity, including the neurons’ own spiking history, concurrent ensemble activity, and extrinsic covariates (EMG signals). In order to predict the envelopes of EMGs, we reformulated the Kalman filter (KF) in an optimization framework and utilized a non-negativity constraint. This structure characterizes the non-linear correspondence between neural activity and EMG signals reasonably. The EMGs were recorded from twelve forearm and hand muscles of a behaving monkey during a grip-force task. For the case of limited training data, the constrained point process filter improved the prediction accuracy when compared to a conventional Wiener cascade filter (a linear causal filter followed by a static non-linearity) for different bin sizes and delays between input spikes and EMG output. For longer training data sets, results of the proposed filter and that of the Wiener cascade filter were comparable. PMID:21659018

Image interpolation and denoising for division of focal plane sensors using Gaussian processes.

PubMed

Gilboa, Elad; Cunningham, John P; Nehorai, Arye; Gruev, Viktor

2014-06-16

Image interpolation and denoising are important techniques in image processing. These methods are inherent to digital image acquisition as most digital cameras are composed of a 2D grid of heterogeneous imaging sensors. Current polarization imaging employ four different pixelated polarization filters, commonly referred to as division of focal plane polarization sensors. The sensors capture only partial information of the true scene, leading to a loss of spatial resolution as well as inaccuracy of the captured polarization information. Interpolation is a standard technique to recover the missing information and increase the accuracy of the captured polarization information. Here we focus specifically on Gaussian process regression as a way to perform a statistical image interpolation, where estimates of sensor noise are used to improve the accuracy of the estimated pixel information. We further exploit the inherent grid structure of this data to create a fast exact algorithm that operates in ����(N(3/2)) (vs. the naive ���� (N³)), thus making the Gaussian process method computationally tractable for image data. This modeling advance and the enabling computational advance combine to produce significant improvements over previously published interpolation methods for polarimeters, which is most pronounced in cases of low signal-to-noise ratio (SNR). We provide the comprehensive mathematical model as well as experimental results of the GP interpolation performance for division of focal plane polarimeter.

Quantum key distillation from Gaussian states by Gaussian operations.

PubMed

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

2005-01-14

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

Gaussian Process Interpolation for Uncertainty Estimation in Image Registration

PubMed Central

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

2014-01-01

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

Resource theory of non-Gaussian operations

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Probabilistic Estimates of Global Mean Sea Level and its Underlying Processes

NASA Astrophysics Data System (ADS)

Hay, C.; Morrow, E.; Kopp, R. E.; Mitrovica, J. X.

2015-12-01

Local sea level can vary significantly from the global mean value due to a suite of processes that includes ongoing sea-level changes due to the last ice age, land water storage, ocean circulation changes, and non-uniform sea-level changes that arise when modern-day land ice rapidly melts. Understanding these sources of spatial and temporal variability is critical to estimating past and present sea-level change and projecting future sea-level rise. Using two probabilistic techniques, a multi-model Kalman smoother and Gaussian process regression, we have reanalyzed 20th century tide gauge observations to produce a new estimate of global mean sea level (GMSL). Our methods allow us to extract global information from the sparse tide gauge field by taking advantage of the physics-based and model-derived geometry of the contributing processes. Both methods provide constraints on the sea-level contribution of glacial isostatic adjustment (GIA). The Kalman smoother tests multiple discrete models of glacial isostatic adjustment (GIA), probabilistically computing the most likely GIA model given the observations, while the Gaussian process regression characterizes the prior covariance structure of a suite of GIA models and then uses this structure to estimate the posterior distribution of local rates of GIA-induced sea-level change. We present the two methodologies, the model-derived geometries of the underlying processes, and our new probabilistic estimates of GMSL and GIA.

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.

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.

Some error bounds for K-iterated Gaussian recursive filters

NASA Astrophysics Data System (ADS)

Cuomo, Salvatore; Galletti, Ardelio; Giunta, Giulio; Marcellino, Livia

2016-10-01

Recursive filters (RFs) have achieved a central role in several research fields over the last few years. For example, they are used in image processing, in data assimilation and in electrocardiogram denoising. More in particular, among RFs, the Gaussian RFs are an efficient computational tool for approximating Gaussian-based convolutions and are suitable for digital image processing and applications of the scale-space theory. As is a common knowledge, the Gaussian RFs, applied to signals with support in a finite domain, generate distortions and artifacts, mostly localized at the boundaries. Heuristic and theoretical improvements have been proposed in literature to deal with this issue (namely boundary conditions). They include the case in which a Gaussian RF is applied more than once, i.e. the so called K-iterated Gaussian RFs. In this paper, starting from a summary of the comprehensive mathematical background, we consider the case of the K-iterated first-order Gaussian RF and provide the study of its numerical stability and some component-wise theoretical error bounds.

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.

[Method of correcting sensitivity nonuniformity using gaussian distribution on 3.0 Tesla abdominal MRI].

PubMed

Hayashi, Norio; Miyati, Tosiaki; Takanaga, Masako; Ohno, Naoki; Hamaguchi, Takashi; Kozaka, Kazuto; Sanada, Shigeru; Yamamoto, Tomoyuki; Matsui, Osamu

2011-01-01

In the direction where the phased array coil used in parallel magnetic resonance imaging (MRI) is perpendicular to the arrangement, sensitivity falls significantly. Moreover, in a 3.0 tesla (3T) abdominal MRI, the quality of the image is reduced by changes in the relaxation time, reinforcement of the magnetic susceptibility effect, etc. In a 3T MRI, which has a high resonant frequency, the signal of the depths (central part) is reduced in the trunk part. SCIC, which is sensitivity correction processing, has inadequate correction processing, such as that edges are emphasized and the central part is corrected. Therefore, we used 3T with a Gaussian distribution. The uneven compensation processing for sensitivity of an abdomen MR image was considered. The correction processing consisted of the following methods. 1) The center of gravity of the domain of the human body in an abdomen MR image was calculated. 2) The correction coefficient map was created from the center of gravity using the Gaussian distribution. 3) The sensitivity correction image was created from the correction coefficient map and the original picture image. Using the Gaussian correction to process the image, the uniformity calculated using the NEMA method was improved significantly compared to the original image of a phantom. In a visual evaluation by radiologists, the uniformity was improved significantly using the Gaussian correction processing. Because of the homogeneous improvement of the abdomen image taken using 3T MRI, the Gaussian correction processing is considered to be a very useful technique.

Monogamy inequality for distributed gaussian entanglement.

PubMed

Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio

2007-02-02

We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.

An empirical analysis of the distribution of overshoots in a stationary Gaussian stochastic process

NASA Technical Reports Server (NTRS)

Carter, M. C.; Madison, M. W.

1973-01-01

The frequency distribution of overshoots in a stationary Gaussian stochastic process is analyzed. The primary processes involved in this analysis are computer simulation and statistical estimation. Computer simulation is used to simulate stationary Gaussian stochastic processes that have selected autocorrelation functions. An analysis of the simulation results reveals a frequency distribution for overshoots with a functional dependence on the mean and variance of the process. Statistical estimation is then used to estimate the mean and variance of a process. It is shown that for an autocorrelation function, the mean and the variance for the number of overshoots, a frequency distribution for overshoots can be estimated.

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.

Separation of components from a scale mixture of Gaussian white noises

NASA Astrophysics Data System (ADS)

Vamoş, Călin; Crăciun, Maria

2010-05-01

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

Speckle lithography for fabricating Gaussian, quasi-random 2D structures and black silicon structures

PubMed Central

Bingi, Jayachandra; Murukeshan, Vadakke Matham

2015-01-01

Laser speckle pattern is a granular structure formed due to random coherent wavelet interference and generally considered as noise in optical systems including photolithography. Contrary to this, in this paper, we use the speckle pattern to generate predictable and controlled Gaussian random structures and quasi-random structures photo-lithographically. The random structures made using this proposed speckle lithography technique are quantified based on speckle statistics, radial distribution function (RDF) and fast Fourier transform (FFT). The control over the speckle size, density and speckle clustering facilitates the successful fabrication of black silicon with different surface structures. The controllability and tunability of randomness makes this technique a robust method for fabricating predictable 2D Gaussian random structures and black silicon structures. These structures can enhance the light trapping significantly in solar cells and hence enable improved energy harvesting. Further, this technique can enable efficient fabrication of disordered photonic structures and random media based devices. PMID:26679513

Poly-Gaussian model of randomly rough surface in rarefied gas flow

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

Aksenova, Olga A.; Khalidov, Iskander A.

2014-12-09

Surface roughness is simulated by the model of non-Gaussian random process. Our results for the scattering of rarefied gas atoms from a rough surface using modified approach to the DSMC calculation of rarefied gas flow near a rough surface are developed and generalized applying the poly-Gaussian model representing probability density as the mixture of Gaussian densities. The transformation of the scattering function due to the roughness is characterized by the roughness operator. Simulating rough surface of the walls by the poly-Gaussian random field expressed as integrated Wiener process, we derive a representation of the roughness operator that can be appliedmore » in numerical DSMC methods as well as in analytical investigations.« less

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.

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.

Recurrence plots of discrete-time Gaussian stochastic processes

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

A novel Gaussian-Sinc mixed basis set for electronic structure calculations

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

Jerke, Jonathan L.; Lee, Young; Tymczak, C. J.

2015-08-14

A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree–Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the “localized” and “delocalized” regions. A basis set for each region is combined to make a new basis methodology—a lattice of orthonormal sinc functions is used to represent the “delocalized” regions and the atom-centered Gaussian functions are used to represent the “localized” regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definablemore » and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree–Fock energies for atoms up to neon, the diatomic systems H{sub 2}, O{sub 2}, and N{sub 2}, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species.« less

The statistics of peaks of Gaussian random fields. [cosmological density fluctuations

NASA Technical Reports Server (NTRS)

Bardeen, J. M.; Bond, J. R.; Kaiser, N.; Szalay, A. S.

1986-01-01

A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.

Hermite-Gaussian beams with self-forming spiral phase distribution

NASA Astrophysics Data System (ADS)

Zinchik, Alexander A.; Muzychenko, Yana B.

2014-05-01

Spiral laser beams is a family of laser beams that preserve the structural stability up to scale and rotate with the propagation. Properties of spiral beams are of practical interest for laser technology, medicine and biotechnology. Researchers use a spiral beams for movement and manipulation of microparticles. Spiral beams have a complicated phase distribution in cross section. This paper describes the results of analytical and computer simulation of Hermite-Gaussian beams with self-forming spiral phase distribution. In the simulation used a laser beam consisting of the sum of the two modes HG TEMnm and TEMn1m1. The coefficients n1, n, m1, m were varied. Additional phase depending from the coefficients n, m, m1, n1 imposed on the resulting beam. As a result, formed the Hermite Gaussian beam phase distribution which takes the form of a spiral in the process of distribution. For modeling was used VirtualLab 5.0 (manufacturer LightTrans GmbH).

Propagation properties of cylindrical sinc Gaussian beam

NASA Astrophysics Data System (ADS)

Eyyuboğlu, Halil T.; Bayraktar, Mert

2016-09-01

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

Biasing and the search for primordial non-Gaussianity beyond the local type

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

Gleyzes, Jérôme; De Putter, Roland; Doré, Olivier

Primordial non-Gaussianity encodes valuable information about the physics of inflation, including the spectrum of particles and interactions. Significant improvements in our understanding of non-Gaussanity beyond Planck require information from large-scale structure. The most promising approach to utilize this information comes from the scale-dependent bias of halos. For local non-Gaussanity, the improvements available are well studied but the potential for non-Gaussianity beyond the local type, including equilateral and quasi-single field inflation, is much less well understood. In this paper, we forecast the capabilities of large-scale structure surveys to detect general non-Gaussianity through galaxy/halo power spectra. We study how non-Gaussanity can bemore » distinguished from a general biasing model and where the information is encoded. For quasi-single field inflation, significant improvements over Planck are possible in some regions of parameter space. We also show that the multi-tracer technique can significantly improve the sensitivity for all non-Gaussianity types, providing up to an order of magnitude improvement for equilateral non-Gaussianity over the single-tracer measurement.« less

Extracting Primordial Non-Gaussianity from Large Scale Structure in the Post-Planck Era

NASA Astrophysics Data System (ADS)

Dore, Olivier

Astronomical observations have become a unique tool to probe fundamental physics. Cosmology, in particular, emerged as a data-driven science whose phenomenological modeling has achieved great success: in the post-Planck era, key cosmological parameters are measured to percent precision. A single model reproduces a wealth of astronomical observations involving very distinct physical processes at different times. This success leads to fundamental physical questions. One of the most salient is the origin of the primordial perturbations that grew to form the large-scale structures we now observe. More and more cosmological observables point to inflationary physics as the origin of the structure observed in the universe. Inflationary physics predict the statistical properties of the primordial perturbations and it is thought to be slightly non-Gaussian. The detection of this small deviation from Gaussianity represents the next frontier in early Universe physics. To measure it would provide direct, unique and quantitative insights about the physics at play when the Universe was only a fraction of a second old, thus probing energies untouchable otherwise. En par with the well-known relic gravitational wave radiation -- the famous ``B-modes'' -- it is one the few probes of inflation. This departure from Gaussianity leads to very specific signature in the large scale clustering of galaxies. Observing large-scale structure, we can thus establish a direct connection with fundamental theories of the early universe. In the post-Planck era, large-scale structures are our most promising pathway to measuring this primordial signal. Current estimates suggests that the next generation of space or ground based large scale structure surveys (e.g. the ESA EUCLID or NASA WFIRST missions) might enable a detection of this signal. This potential huge payoff requires us to solidify the theoretical predictions supporting these measurements. Even if the exact signal we are looking for is of unknown amplitude, it is obvious that we must measure it as well as these ground breaking data set will permit. We propose to develop the supporting theoretical work to the point where the complete non-gaussianian signature can be extracted from these data sets. We will do so by developing three complementary directions: - We will develop the appropriate formalism to measure and model galaxy clustering on the largest scales. - We will study the impact of non-Gaussianity on higher-order statistics, the most promising statistics for our purpose.. - We will explicit the connection between these observables and the microphysics of a large class of inflation models, but also identify fundamental limitations to this interpretation.

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

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

In this work the question of stability of the vortex Bessel-Gaussian optical beams formed in turbulent atmosphere is theoretically considered. The detailed analysis of features of spatial structure of distribution of mean intensity of vortex Bessel-Gaussian optical beams in turbulent atmosphere are analyzed. The quantitative criterion of possibility of formation of vortex Bessel-Gaussian optical beams in turbulent atmosphere is derived. It is shown that stability of the form of a vortex Bessel-Gaussian optical beam during propagation in turbulent atmosphere increases with increase of value of a topological charge of this optical beam.

Structured Kernel Subspace Learning for Autonomous Robot Navigation.

PubMed

Kim, Eunwoo; Choi, Sungjoon; Oh, Songhwai

2018-02-14

This paper considers two important problems for autonomous robot navigation in a dynamic environment, where the goal is to predict pedestrian motion and control a robot with the prediction for safe navigation. While there are several methods for predicting the motion of a pedestrian and controlling a robot to avoid incoming pedestrians, it is still difficult to safely navigate in a dynamic environment due to challenges, such as the varying quality and complexity of training data with unwanted noises. This paper addresses these challenges simultaneously by proposing a robust kernel subspace learning algorithm based on the recent advances in nuclear-norm and l 1 -norm minimization. We model the motion of a pedestrian and the robot controller using Gaussian processes. The proposed method efficiently approximates a kernel matrix used in Gaussian process regression by learning low-rank structured matrix (with symmetric positive semi-definiteness) to find an orthogonal basis, which eliminates the effects of erroneous and inconsistent data. Based on structured kernel subspace learning, we propose a robust motion model and motion controller for safe navigation in dynamic environments. We evaluate the proposed robust kernel learning in various tasks, including regression, motion prediction, and motion control problems, and demonstrate that the proposed learning-based systems are robust against outliers and outperform existing regression and navigation methods.

Quantum entanglement beyond Gaussian criteria

PubMed Central

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

2009-01-01

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

Quantum entanglement beyond Gaussian criteria.

PubMed

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

2009-12-22

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

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.

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.

Self-assembled structures of Gaussian nematic particles.

PubMed

Nikoubashman, Arash; Likos, Christos N

2010-03-17

We investigate the stable crystalline configurations of a nematic liquid crystal made of soft parallel ellipsoidal particles interacting via a repulsive, anisotropic Gaussian potential. For this purpose, we use genetic algorithms (GA) in order to predict all relevant and possible solid phase candidates into which this fluid can freeze. Subsequently we present and discuss the emerging novel structures and the resulting zero-temperature phase diagram of this system. The latter features a variety of crystalline arrangements, in which the elongated Gaussian particles in general do not align with any one of the high-symmetry crystallographic directions, a compromise arising from the interplay and competition between anisotropic repulsions and crystal ordering. Only at very strong degrees of elongation does a tendency of the Gaussian nematics to align with the longest axis of the elementary unit cell emerge.

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.

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.

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

PubMed

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

2017-08-01

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

The application of feature selection to the development of Gaussian process models for percutaneous absorption.

PubMed

Lam, Lun Tak; Sun, Yi; Davey, Neil; Adams, Rod; Prapopoulou, Maria; Brown, Marc B; Moss, Gary P

2010-06-01

The aim was to employ Gaussian processes to assess mathematically the nature of a skin permeability dataset and to employ these methods, particularly feature selection, to determine the key physicochemical descriptors which exert the most significant influence on percutaneous absorption, and to compare such models with established existing models. Gaussian processes, including automatic relevance detection (GPRARD) methods, were employed to develop models of percutaneous absorption that identified key physicochemical descriptors of percutaneous absorption. Using MatLab software, the statistical performance of these models was compared with single linear networks (SLN) and quantitative structure-permeability relationships (QSPRs). Feature selection methods were used to examine in more detail the physicochemical parameters used in this study. A range of statistical measures to determine model quality were used. The inherently nonlinear nature of the skin data set was confirmed. The Gaussian process regression (GPR) methods yielded predictive models that offered statistically significant improvements over SLN and QSPR models with regard to predictivity (where the rank order was: GPR > SLN > QSPR). Feature selection analysis determined that the best GPR models were those that contained log P, melting point and the number of hydrogen bond donor groups as significant descriptors. Further statistical analysis also found that great synergy existed between certain parameters. It suggested that a number of the descriptors employed were effectively interchangeable, thus questioning the use of models where discrete variables are output, usually in the form of an equation. The use of a nonlinear GPR method produced models with significantly improved predictivity, compared with SLN or QSPR models. Feature selection methods were able to provide important mechanistic information. However, it was also shown that significant synergy existed between certain parameters, and as such it was possible to interchange certain descriptors (i.e. molecular weight and melting point) without incurring a loss of model quality. Such synergy suggested that a model constructed from discrete terms in an equation may not be the most appropriate way of representing mechanistic understandings of skin absorption.

Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables.

PubMed

Heck, Daniel W; Erdfelder, Edgar; Kieslich, Pascal J

2018-05-24

Multinomial processing tree models assume that discrete cognitive states determine observed response frequencies. Generalized processing tree (GPT) models extend this conceptual framework to continuous variables such as response times, process-tracing measures, or neurophysiological variables. GPT models assume finite-mixture distributions, with weights determined by a processing tree structure, and continuous components modeled by parameterized distributions such as Gaussians with separate or shared parameters across states. We discuss identifiability, parameter estimation, model testing, a modeling syntax, and the improved precision of GPT estimates. Finally, a GPT version of the feature comparison model of semantic categorization is applied to computer-mouse trajectories.

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

Entropy of level-cut random Gaussian structures at different volume fractions

NASA Astrophysics Data System (ADS)

Marčelja, Stjepan

2017-10-01

Cutting random Gaussian fields at a given level can create a variety of morphologically different two- or several-phase structures that have often been used to describe physical systems. The entropy of such structures depends on the covariance function of the generating Gaussian random field, which in turn depends on its spectral density. But the entropy of level-cut structures also depends on the volume fractions of different phases, which is determined by the selection of the cutting level. This dependence has been neglected in earlier work. We evaluate the entropy of several lattice models to show that, even in the cases of strongly coupled systems, the dependence of the entropy of level-cut structures on molar fractions of the constituents scales with the simple ideal noninteracting system formula. In the last section, we discuss the application of the results to binary or ternary fluids and microemulsions.

The modulation transfer function and signal-to-noise ratio of different digital filters: a technical approach.

PubMed

Brüllmann, D D; d'Hoedt, B

2011-05-01

The aim of this study was to illustrate the influence of digital filters on the signal-to-noise ratio (SNR) and modulation transfer function (MTF) of digital images. The article will address image pre-processing that may be beneficial for the production of clinically useful digital radiographs with lower radiation dose. Three filters, an arithmetic mean filter, a median filter and a Gaussian filter (standard deviation (SD) = 0.4), with kernel sizes of 3 × 3 pixels and 5 × 5 pixels were tested. Synthetic images with exactly increasing amounts of Gaussian noise were created to gather linear regression of SNR before and after application of digital filters. Artificial stripe patterns with defined amounts of line pairs per millimetre were used to calculate MTF before and after the application of the digital filters. The Gaussian filter with a 5 × 5 kernel size caused the highest noise suppression (SNR increased from 2.22, measured in the synthetic image, to 11.31 in the filtered image). The smallest noise reduction was found with the 3 × 3 median filter. The application of the median filters resulted in no changes in MTF at the different resolutions but did result in the deletion of smaller structures. The 5 × 5 Gaussian filter and the 5 × 5 arithmetic mean filter showed the strongest changes of MTF. The application of digital filters can improve the SNR of a digital sensor; however, MTF can be adversely affected. As such, imaging systems should not be judged solely on their quoted spatial resolutions because pre-processing may influence image quality.

Gaussian process regression of chirplet decomposed ultrasonic B-scans of a simulated design case

NASA Astrophysics Data System (ADS)

Wertz, John; Homa, Laura; Welter, John; Sparkman, Daniel; Aldrin, John

2018-04-01

The US Air Force seeks to implement damage tolerant lifecycle management of composite structures. Nondestructive characterization of damage is a key input to this framework. One approach to characterization is model-based inversion of the ultrasonic response from damage features; however, the computational expense of modeling the ultrasonic waves within composites is a major hurdle to implementation. A surrogate forward model with sufficient accuracy and greater computational efficiency is therefore critical to enabling model-based inversion and damage characterization. In this work, a surrogate model is developed on the simulated ultrasonic response from delamination-like structures placed at different locations within a representative composite layup. The resulting B-scans are decomposed via the chirplet transform, and a Gaussian process model is trained on the chirplet parameters. The quality of the surrogate is tested by comparing the B-scan for a delamination configuration not represented within the training data set. The estimated B-scan has a maximum error of ˜15% for an estimated reduction in computational runtime of ˜95% for 200 function calls. This considerable reduction in computational expense makes full 3D characterization of impact damage tractable.

Model fitting for small skin permeability data sets: hyperparameter optimisation in Gaussian Process Regression.

PubMed

Ashrafi, Parivash; Sun, Yi; Davey, Neil; Adams, Roderick G; Wilkinson, Simon C; Moss, Gary Patrick

2018-03-01

The aim of this study was to investigate how to improve predictions from Gaussian Process models by optimising the model hyperparameters. Optimisation methods, including Grid Search, Conjugate Gradient, Random Search, Evolutionary Algorithm and Hyper-prior, were evaluated and applied to previously published data. Data sets were also altered in a structured manner to reduce their size, which retained the range, or 'chemical space' of the key descriptors to assess the effect of the data range on model quality. The Hyper-prior Smoothbox kernel results in the best models for the majority of data sets, and they exhibited significantly better performance than benchmark quantitative structure-permeability relationship (QSPR) models. When the data sets were systematically reduced in size, the different optimisation methods generally retained their statistical quality, whereas benchmark QSPR models performed poorly. The design of the data set, and possibly also the approach to validation of the model, is critical in the development of improved models. The size of the data set, if carefully controlled, was not generally a significant factor for these models and that models of excellent statistical quality could be produced from substantially smaller data sets. © 2018 Royal Pharmaceutical Society.

Formation of propagation invariant laser beams with anamorphic optical systems

NASA Astrophysics Data System (ADS)

Soskind, Y. G.

2015-03-01

Propagation invariant structured laser beams play an important role in several photonics applications. A majority of propagation invariant beams are usually produced in the form of laser modes emanating from stable laser cavities. This work shows that anamorphic optical systems can be effectively employed to transform input propagation invariant laser beams and produce a variety of alternative propagation invariant structured laser beam distributions with different shapes and phase structures. This work also presents several types of anamorphic lens systems suitable for transforming the input laser modes into a variety of structured propagation invariant beams. The transformations are applied to different laser mode types, including Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian field distributions. The influence of the relative azimuthal orientation between the input laser modes and the anamorphic optical systems on the resulting transformed propagation invariant beams is presented as well.

Simulation of time series by distorted Gaussian processes

NASA Technical Reports Server (NTRS)

Greenhall, C. A.

1977-01-01

Distorted stationary Gaussian process can be used to provide computer-generated imitations of experimental time series. A method of analyzing a source time series and synthesizing an imitation is shown, and an example using X-band radiometer data is given.

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:

Multi-pose facial correction based on Gaussian process with combined kernel function

NASA Astrophysics Data System (ADS)

Shi, Shuyan; Ji, Ruirui; Zhang, Fan

2018-04-01

In order to improve the recognition rate of various postures, this paper proposes a method of facial correction based on Gaussian Process which build a nonlinear regression model between the front and the side face with combined kernel function. The face images with horizontal angle from -45° to +45° can be properly corrected to front faces. Finally, Support Vector Machine is employed for face recognition. Experiments on CAS PEAL R1 face database show that Gaussian process can weaken the influence of pose changes and improve the accuracy of face recognition to certain extent.

Occupancy mapping and surface reconstruction using local Gaussian processes with Kinect sensors.

PubMed

Kim, Soohwan; Kim, Jonghyuk

2013-10-01

Although RGB-D sensors have been successfully applied to visual SLAM and surface reconstruction, most of the applications aim at visualization. In this paper, we propose a noble method of building continuous occupancy maps and reconstructing surfaces in a single framework for both navigation and visualization. Particularly, we apply a Bayesian nonparametric approach, Gaussian process classification, to occupancy mapping. However, it suffers from high-computational complexity of O(n(3))+O(n(2)m), where n and m are the numbers of training and test data, respectively, limiting its use for large-scale mapping with huge training data, which is common with high-resolution RGB-D sensors. Therefore, we partition both training and test data with a coarse-to-fine clustering method and apply Gaussian processes to each local clusters. In addition, we consider Gaussian processes as implicit functions, and thus extract iso-surfaces from the scalar fields, continuous occupancy maps, using marching cubes. By doing that, we are able to build two types of map representations within a single framework of Gaussian processes. Experimental results with 2-D simulated data show that the accuracy of our approximated method is comparable to previous work, while the computational time is dramatically reduced. We also demonstrate our method with 3-D real data to show its feasibility in large-scale environments.

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.

Spatial intensity distribution of controlled-NOT gate carrying orbital angular momentum via photonic band gap structure

NASA Astrophysics Data System (ADS)

Zhang, Yan; Wang, Xiaorui; Zhe Zhang, Yun

2018-07-01

By employing the different topological charges of a Laguerre–Gaussian beam as a qubit, we experimentally demonstrate a controlled-NOT (CNOT) gate with light beams carrying orbital angular momentum via a photonic band gap structure in a hot atomic ensemble. Through a degenerate four-wave mixing process, the spatial distribution of the CNOT gate including splitting and spatial shift can be affected by the Kerr nonlinear effect in multilevel atomic systems. Moreover, the intensity variations of the CNOT gate can be controlled by the relative phase modulation. This research can be useful for applications in quantum information processing.

Gaussian maximally multipartite-entangled states

NASA Astrophysics Data System (ADS)

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

2009-12-01

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

Unconventional signal detection techniques with Gaussian probability mixtures adaptation in non-AWGN channels: full resolution receiver

NASA Astrophysics Data System (ADS)

Chabdarov, Shamil M.; Nadeev, Adel F.; Chickrin, Dmitry E.; Faizullin, Rashid R.

2011-04-01

In this paper we discuss unconventional detection technique also known as «full resolution receiver». This receiver uses Gaussian probability mixtures for interference structure adaptation. Full resolution receiver is alternative to conventional matched filter receivers in the case of non-Gaussian interferences. For the DS-CDMA forward channel with presence of complex interferences sufficient performance increasing was shown.

A nonlinear cointegration approach with applications to structural health monitoring

NASA Astrophysics Data System (ADS)

Shi, H.; Worden, K.; Cross, E. J.

2016-09-01

One major obstacle to the implementation of structural health monitoring (SHM) is the effect of operational and environmental variabilities, which may corrupt the signal of structural degradation. Recently, an approach inspired from the community of econometrics, called cointegration, has been employed to eliminate the adverse influence from operational and environmental changes and still maintain sensitivity to structural damage. However, the linear nature of cointegration may limit its application when confronting nonlinear relations between system responses. This paper proposes a nonlinear cointegration method based on Gaussian process regression (GPR); the method is constructed under the Engle-Granger framework, and tests for unit root processes are conducted both before and after the GPR is applied. The proposed approach is examined with real engineering data from the monitoring of the Z24 Bridge.

Stationary moments, diffusion limits, and extinction times for logistic growth with random catastrophes.

PubMed

Schlomann, Brandon H

2018-06-06

A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare, catastrophic events, which are increasingly observed at scales ranging from global fisheries to intestinal microbiota. Due to mathematical challenges, growth processes with random catastrophes are less well characterized and it remains unclear how their consequences differ from those of Gaussian processes. In the face of a changing climate and predicted increases in ecological catastrophes, as well as increased interest in harnessing microbes for therapeutics, these processes have never been more relevant. To better understand them, I revisit here a differential equation model of logistic growth coupled to density-independent catastrophes that arrive as a Poisson process, and derive new analytic results that reveal its statistical structure. First, I derive exact expressions for the model's stationary moments, revealing a single effective catastrophe parameter that largely controls low order statistics. Then, I use weak convergence theorems to construct its Gaussian analog in a limit of frequent, small catastrophes, keeping the stationary population mean constant for normalization. Numerically computing statistics along this limit shows how they transform as the dynamics shifts from catastrophes to diffusions, enabling quantitative comparisons. For example, the mean time to extinction increases monotonically by orders of magnitude, demonstrating significantly higher extinction risk under catastrophes than under diffusions. Together, these results provide insight into a wide range of stochastic dynamical systems important for ecology and conservation. Copyright © 2018 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Wu, Zhenkun; Gu, Yuzong

2016-12-01

The propagation of two-dimensional beams is analytically and numerically investigated in strongly nonlocal nonlinear media (SNNM) based on the ABCD matrix. The two-dimensional beams reported in this paper are described by the product of the superposition of generalized Laguerre-Gaussian (LG), Hermite-Gaussian (HG), Bessel-Gaussian (BG), and circular Airy (CA) beams, carrying an orbital angular momentum (OAM). Owing to OAM and the modulation of SNNM, we find that the propagation of these two-dimensional beams exhibits complete rotation and periodic inversion: the spatial intensity profile first extends and then diminishes, and during the propagation the process repeats to form a breath-like phenomenon.

Analysis of randomly time varying systems by gaussian closure technique

NASA Astrophysics Data System (ADS)

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

1982-07-01

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

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.

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.

Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.

PubMed

de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos

2011-01-01

In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.

Compact structure and non-Gaussian dynamics of ring polymer melts.

PubMed

Brás, Ana R; Goossen, Sebastian; Krutyeva, Margarita; Radulescu, Aurel; Farago, Bela; Allgaier, Jürgen; Pyckhout-Hintzen, Wim; Wischnewski, Andreas; Richter, Dieter

2014-05-28

We present a neutron scattering analysis of the structure and dynamics of PEO polymer rings with a molecular weight 2.5 times higher than the entanglement mass. The melt structure was found to be more compact than a Gaussian model would suggest. With increasing time the center of mass (c.o.m.) diffusion undergoes a transition from sub-diffusive to diffusive behavior. The transition time agrees well with the decorrelation time predicted by a mode coupling approach. As a novel feature well pronounced non-Gaussian behavior of the c.o.m. diffusion was found that shows surprising analogies to the cage effect known from glassy systems. Finally, the longest wavelength Rouse modes are suppressed possibly as a consequence of an onset of lattice animal features as hypothesized in theoretical approaches.

Structured Laguerre-Gaussian beams for mitigation of spherical aberration in tightly focused regimes

NASA Astrophysics Data System (ADS)

Haddadi, S.; Bouzid, O.; Fromager, M.; Hasnaoui, A.; Harfouche, A.; Cagniot, E.; Forbes, A.; Aït-Ameur, K.

2018-04-01

Many laser applications utilise a focused laser beam having a single-lobed intensity profile in the focal plane, ideally with the highest possible on-axis intensity. Conventionally, this is achieved with the lowest-order Laguerre-Gaussian mode (LG00), the Gaussian beam, in a tight focusing configuration. However, tight focusing often involves significant spherical aberration due to the high numerical aperture of the systems involved, thus degrading the focal quality. Here, we demonstrate that a high-order radial LG p0 mode can be tailored to meet and in some instances exceed the performance of the Gaussian. We achieve this by phase rectification of the mode using a simple binary diffractive optic. By way of example, we show that the focusing of a rectified LG50 beam is almost insensitive to a spherical aberration coefficient of over three wavelengths, in contrast with the usual Gaussian beam for which the intensity of the focal spot is reduced by a factor of two. This work paves the way towards enhanced focal spots using structured light.

A Bernoulli Gaussian Watermark for Detecting Integrity Attacks in Control Systems

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

Weerakkody, Sean; Ozel, Omur; Sinopoli, Bruno

We examine the merit of Bernoulli packet drops in actively detecting integrity attacks on control systems. The aim is to detect an adversary who delivers fake sensor measurements to a system operator in order to conceal their effect on the plant. Physical watermarks, or noisy additive Gaussian inputs, have been previously used to detect several classes of integrity attacks in control systems. In this paper, we consider the analysis and design of Gaussian physical watermarks in the presence of packet drops at the control input. On one hand, this enables analysis in a more general network setting. On the othermore » hand, we observe that in certain cases, Bernoulli packet drops can improve detection performance relative to a purely Gaussian watermark. This motivates the joint design of a Bernoulli-Gaussian watermark which incorporates both an additive Gaussian input and a Bernoulli drop process. We characterize the effect of such a watermark on system performance as well as attack detectability in two separate design scenarios. Here, we consider a correlation detector for attack recognition. We then propose efficiently solvable optimization problems to intelligently select parameters of the Gaussian input and the Bernoulli drop process while addressing security and performance trade-offs. Finally, we provide numerical results which illustrate that a watermark with packet drops can indeed outperform a Gaussian watermark.« less

Identification of damage in composite structures using Gaussian mixture model-processed Lamb waves

NASA Astrophysics Data System (ADS)

Wang, Qiang; Ma, Shuxian; Yue, Dong

2018-04-01

Composite materials have comprehensively better properties than traditional materials, and therefore have been more and more widely used, especially because of its higher strength-weight ratio. However, the damage of composite structures is usually varied and complicated. In order to ensure the security of these structures, it is necessary to monitor and distinguish the structural damage in a timely manner. Lamb wave-based structural health monitoring (SHM) has been proved to be effective in online structural damage detection and evaluation; furthermore, the characteristic parameters of the multi-mode Lamb wave varies in response to different types of damage in the composite material. This paper studies the damage identification approach for composite structures using the Lamb wave and the Gaussian mixture model (GMM). The algorithm and principle of the GMM, and the parameter estimation, is introduced. Multi-statistical characteristic parameters of the excited Lamb waves are extracted, and the parameter space with reduced dimensions is adopted by principal component analysis (PCA). The damage identification system using the GMM is then established through training. Experiments on a glass fiber-reinforced epoxy composite laminate plate are conducted to verify the feasibility of the proposed approach in terms of damage classification. The experimental results show that different types of damage can be identified according to the value of the likelihood function of the GMM.

Parallel and Distributed Systems for Probabilistic Reasoning

DTIC Science & Technology

2012-12-01

work at CMU I had the opportunity to work with Andreas Krause on Gaussian process models for signal quality estimation in wireless sensor networks ...we reviewed the natural parallelization of the belief propagation algorithm using the synchronous schedule and demonstrated both theoretically and...problem is that the power-law sparsity structure, commonly found in graphs derived from natural phenomena (e.g., social networks and the web

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

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Behnke, marlana N.; Przekop, Adam

2010-01-01

High-cycle fatigue of an elastic-plastic beam structure under the combined action of thermal and high-intensity non-Gaussian acoustic loadings is considered. Such loadings can be highly damaging when snap-through motion occurs between thermally post-buckled equilibria. The simulated non-Gaussian loadings investigated have a range of skewness and kurtosis typical of turbulent boundary layer pressure fluctuations in the vicinity of forward facing steps. Further, the duration and steadiness of high excursion peaks is comparable to that found in such turbulent boundary layer data. Response and fatigue life estimates are found to be insensitive to the loading distribution, with the minor exception of cases involving plastic deformation. In contrast, the fatigue life estimate was found to be highly affected by a different type of non-Gaussian loading having bursts of high excursion peaks.

On the application of Rice's exceedance statistics to atmospheric turbulence.

NASA Technical Reports Server (NTRS)

Chen, W. Y.

1972-01-01

Discrepancies produced by the application of Rice's exceedance statistics to atmospheric turbulence are examined. First- and second-order densities from several data sources have been measured for this purpose. Particular care was paid to each selection of turbulence that provides stationary mean and variance over the entire segment. Results show that even for a stationary segment of turbulence, the process is still highly non-Gaussian, in spite of a Gaussian appearance for its first-order distribution. Data also indicate strongly non-Gaussian second-order distributions. It is therefore concluded that even stationary atmospheric turbulence with a normal first-order distribution cannot be considered a Gaussian process, and consequently the application of Rice's exceedance statistics should be approached with caution.

Edge detection - Image-plane versus digital processing

NASA Technical Reports Server (NTRS)

Huck, Friedrich O.; Fales, Carl L.; Park, Stephen K.; Triplett, Judith A.

1987-01-01

To optimize edge detection with the familiar Laplacian-of-Gaussian operator, it has become common to implement this operator with a large digital convolution mask followed by some interpolation of the processed data to determine the zero crossings that locate edges. It is generally recognized that this large mask causes substantial blurring of fine detail. It is shown that the spatial detail can be improved by a factor of about four with either the Wiener-Laplacian-of-Gaussian filter or an image-plane processor. The Wiener-Laplacian-of-Gaussian filter minimizes the image-gathering degradations if the scene statistics are at least approximately known and also serves as an interpolator to determine the desired zero crossings directly. The image-plane processor forms the Laplacian-of-Gaussian response by properly combining the optical design of the image-gathering system with a minimal three-by-three lateral-inhibitory processing mask. This approach, which is suggested by Marr's model of early processing in human vision, also reduces data processing by about two orders of magnitude and data transmission by up to an order of magnitude.

Vibronic Boson Sampling: Generalized Gaussian Boson Sampling for Molecular Vibronic Spectra at Finite Temperature.

PubMed

Huh, Joonsuk; Yung, Man-Hong

2017-08-07

Molecular vibroic spectroscopy, where the transitions involve non-trivial Bosonic correlation due to the Duschinsky Rotation, is strongly believed to be in a similar complexity class as Boson Sampling. At finite temperature, the problem is represented as a Boson Sampling experiment with correlated Gaussian input states. This molecular problem with temperature effect is intimately related to the various versions of Boson Sampling sharing the similar computational complexity. Here we provide a full description to this relation in the context of Gaussian Boson Sampling. We find a hierarchical structure, which illustrates the relationship among various Boson Sampling schemes. Specifically, we show that every instance of Gaussian Boson Sampling with an initial correlation can be simulated by an instance of Gaussian Boson Sampling without initial correlation, with only a polynomial overhead. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes. We refer such a generalized Gaussian Boson Sampling motivated by the molecular sampling problem as Vibronic Boson Sampling.

Probabilistic solutions of nonlinear oscillators excited by combined colored and white noise excitations

NASA Astrophysics Data System (ADS)

Siu-Siu, Guo; Qingxuan, Shi

2017-03-01

In this paper, single-degree-of-freedom (SDOF) systems combined to Gaussian white noise and Gaussian/non-Gaussian colored noise excitations are investigated. By expressing colored noise excitation as a second-order filtered white noise process and introducing colored noise as an additional state variable, the equation of motion for SDOF system under colored noise is then transferred artificially to multi-degree-of-freedom (MDOF) system under white noise excitations with four-coupled first-order differential equations. As a consequence, corresponding Fokker-Planck-Kolmogorov (FPK) equation governing the joint probabilistic density function (PDF) of state variables increases to 4-dimension (4-D). Solution procedure and computer programme become much more sophisticated. The exponential-polynomial closure (EPC) method, widely applied for cases of SDOF systems under white noise excitations, is developed and improved for cases of systems under colored noise excitations and for solving the complex 4-D FPK equation. On the other hand, Monte Carlo simulation (MCS) method is performed to test the approximate EPC solutions. Two examples associated with Gaussian and non-Gaussian colored noise excitations are considered. Corresponding band-limited power spectral densities (PSDs) for colored noise excitations are separately given. Numerical studies show that the developed EPC method provides relatively accurate estimates of the stationary probabilistic solutions, especially the ones in the tail regions of the PDFs. Moreover, statistical parameter of mean-up crossing rate (MCR) is taken into account, which is important for reliability and failure analysis. Hopefully, our present work could provide insights into the investigation of structures under random loadings.

Multilevel geometry optimization

NASA Astrophysics Data System (ADS)

Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.

2000-02-01

Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.

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.

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.

Model-checking techniques based on cumulative residuals.

PubMed

Lin, D Y; Wei, L J; Ying, Z

2002-03-01

Residuals have long been used for graphical and numerical examinations of the adequacy of regression models. Conventional residual analysis based on the plots of raw residuals or their smoothed curves is highly subjective, whereas most numerical goodness-of-fit tests provide little information about the nature of model misspecification. In this paper, we develop objective and informative model-checking techniques by taking the cumulative sums of residuals over certain coordinates (e.g., covariates or fitted values) or by considering some related aggregates of residuals, such as moving sums and moving averages. For a variety of statistical models and data structures, including generalized linear models with independent or dependent observations, the distributions of these stochastic processes tinder the assumed model can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be easily generated by computer simulation. Each observed process can then be compared, both graphically and numerically, with a number of realizations from the Gaussian process. Such comparisons enable one to assess objectively whether a trend seen in a residual plot reflects model misspecification or natural variation. The proposed techniques are particularly useful in checking the functional form of a covariate and the link function. Illustrations with several medical studies are provided.

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.

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

Random Process Simulation for stochastic fatigue analysis. Ph.D. Thesis - Rice Univ., Houston, Tex.

NASA Technical Reports Server (NTRS)

Larsen, Curtis E.

1988-01-01

A simulation technique is described which directly synthesizes the extrema of a random process and is more efficient than the Gaussian simulation method. Such a technique is particularly useful in stochastic fatigue analysis because the required stress range moment E(R sup m), is a function only of the extrema of the random stress process. The family of autoregressive moving average (ARMA) models is reviewed and an autoregressive model is presented for modeling the extrema of any random process which has a unimodal power spectral density (psd). The proposed autoregressive technique is found to produce rainflow stress range moments which compare favorably with those computed by the Gaussian technique and to average 11.7 times faster than the Gaussian technique. The autoregressive technique is also adapted for processes having bimodal psd's. The adaptation involves using two autoregressive processes to simulate the extrema due to each mode and the superposition of these two extrema sequences. The proposed autoregressive superposition technique is 9 to 13 times faster than the Gaussian technique and produces comparable values for E(R sup m) for bimodal psd's having the frequency of one mode at least 2.5 times that of the other mode.

Using an artificial neural network to classify multicomponent emission lines with integral field spectroscopy from SAMI and S7

NASA Astrophysics Data System (ADS)

Hampton, E. J.; Medling, A. M.; Groves, B.; Kewley, L.; Dopita, M.; Davies, R.; Ho, I.-T.; Kaasinen, M.; Leslie, S.; Sharp, R.; Sweet, S. M.; Thomas, A. D.; Allen, J.; Bland-Hawthorn, J.; Brough, S.; Bryant, J. J.; Croom, S.; Goodwin, M.; Green, A.; Konstantantopoulos, I. S.; Lawrence, J.; López-Sánchez, Á. R.; Lorente, N. P. F.; McElroy, R.; Owers, M. S.; Richards, S. N.; Shastri, P.

2017-09-01

Integral field spectroscopy (IFS) surveys are changing how we study galaxies and are creating vastly more spectroscopic data available than before. The large number of resulting spectra makes visual inspection of emission line fits an infeasible option. Here, we present a demonstration of an artificial neural network (ANN) that determines the number of Gaussian components needed to describe the complex emission line velocity structures observed in galaxies after being fit with lzifu. We apply our ANN to IFS data for the S7 survey, conducted using the Wide Field Spectrograph on the ANU 2.3 m Telescope, and the SAMI Galaxy Survey, conducted using the SAMI instrument on the 4 m Anglo-Australian Telescope. We use the spectral fitting code lzifu (Ho et al. 2016a) to fit the emission line spectra of individual spaxels from S7 and SAMI data cubes with 1-, 2- and 3-Gaussian components. We demonstrate that using an ANN is comparable to astronomers performing the same visual inspection task of determining the best number of Gaussian components to describe the physical processes in galaxies. The advantage of our ANN is that it is capable of processing the spectra for thousands of galaxies in minutes, as compared to the years this task would take individual astronomers to complete by visual inspection.

Selective excitation for spectral editing and assignment in separated local field experiments of oriented membrane proteins

NASA Astrophysics Data System (ADS)

Koroloff, Sophie N.; Nevzorov, Alexander A.

2017-01-01

Spectroscopic assignment of NMR spectra for oriented uniformly labeled membrane proteins embedded in their native-like bilayer environment is essential for their structure determination. However, sequence-specific assignment in oriented-sample (OS) NMR is often complicated by insufficient resolution and spectral crowding. Therefore, the assignment process is usually done by a laborious and expensive "shotgun" method involving multiple selective labeling of amino acid residues. Presented here is a strategy to overcome poor spectral resolution in crowded regions of 2D spectra by selecting resolved "seed" residues via soft Gaussian pulses inserted into spin-exchange separated local-field experiments. The Gaussian pulse places the selected polarization along the z-axis while dephasing the other signals before the evolution of the 1H-15N dipolar couplings. The transfer of magnetization is accomplished via mismatched Hartmann-Hahn conditions to the nearest-neighbor peaks via the proton bath. By optimizing the length and amplitude of the Gaussian pulse, one can also achieve a phase inversion of the closest peaks, thus providing an additional phase contrast. From the superposition of the selective spin-exchanged SAMPI4 onto the fully excited SAMPI4 spectrum, the 15N sites that are directly adjacent to the selectively excited residues can be easily identified, thereby providing a straightforward method for initiating the assignment process in oriented membrane proteins.

Gaussian windows: A tool for exploring multivariate data

NASA Technical Reports Server (NTRS)

Jaeckel, Louis A.

1990-01-01

Presented here is a method for interactively exploring a large set of quantitative multivariate data, in order to estimate the shape of the underlying density function. It is assumed that the density function is more or less smooth, but no other specific assumptions are made concerning its structure. The local structure of the data in a given region may be examined by viewing the data through a Gaussian window, whose location and shape are chosen by the user. A Gaussian window is defined by giving each data point a weight based on a multivariate Gaussian function. The weighted sample mean and sample covariance matrix are then computed, using the weights attached to the data points. These quantities are used to compute an estimate of the shape of the density function in the window region. The local structure of the data is described by a method similar to the method of principal components. By taking many such local views of the data, we can form an idea of the structure of the data set. The method is applicable in any number of dimensions. The method can be used to find and describe simple structural features such as peaks, valleys, and saddle points in the density function, and also extended structures in higher dimensions. With some practice, we can apply our geometrical intuition to these structural features in any number of dimensions, so that we can think about and describe the structure of the data. Since the computations involved are relatively simple, the method can easily be implemented on a small computer.

Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme

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

Kitagawa, Akira; Takeoka, Masahiro; Sasaki, Masahide

2005-08-15

We study the measurement-induced non-Gaussian operation on the single- and two-mode Gaussian squeezed vacuum states with beam splitters and on-off type photon detectors, with which mixed non-Gaussian states are generally obtained in the conditional process. It is known that the entanglement can be enhanced via this non-Gaussian operation on the two-mode squeezed vacuum state. We show that, in the range of practical squeezing parameters, the conditional outputs are still close to Gaussian states, but their second order variances of quantum fluctuations and correlations are effectively suppressed and enhanced, respectively. To investigate an operational meaning of these states, especially entangled states,more » we also evaluate the quantum dense coding scheme from the viewpoint of the mutual information, and we show that non-Gaussian entangled state can be advantageous compared with the original two-mode squeezed state.« less

Detecting and modelling structures on the micro and the macro scales: Assessing their effects on solute transport behaviour

NASA Astrophysics Data System (ADS)

Haslauer, C. P.; Bárdossy, A.; Sudicky, E. A.

2017-09-01

This paper demonstrates quantitative reasoning to separate the dataset of spatially distributed variables into different entities and subsequently characterize their geostatistical properties, properly. The main contribution of the paper is a statistical based algorithm that matches the manual distinction results. This algorithm is based on measured data and is generally applicable. In this paper, it is successfully applied at two datasets of saturated hydraulic conductivity (K) measured at the Borden (Canada) and the Lauswiesen (Germany) aquifers. The boundary layer was successfully delineated at Borden despite its only mild heterogeneity and only small statistical differences between the divided units. The methods are verified with the more heterogeneous Lauswiesen aquifer K data-set, where a boundary layer has previously been delineated. The effects of the macro- and the microstructure on solute transport behaviour are evaluated using numerical solute tracer experiments. Within the microscale structure, both Gaussian and non-Gaussian models of spatial dependence of K are evaluated. The effects of heterogeneity both on the macro- and the microscale are analysed using numerical tracer experiments based on four scenarios: including or not including the macroscale structures and optimally fitting a Gaussian or a non-Gaussian model for the spatial dependence in the micro-structure. The paper shows that both micro- and macro-scale structures are important, as in each of the four possible geostatistical scenarios solute transport behaviour differs meaningfully.

Shaping propagation invariant laser beams

NASA Astrophysics Data System (ADS)

Soskind, Michael; Soskind, Rose; Soskind, Yakov

2015-11-01

Propagation-invariant structured laser beams possess several unique properties and play an important role in various photonics applications. The majority of propagation invariant beams are produced in the form of laser modes emanating from stable laser cavities. Therefore, their spatial structure is limited by the intracavity mode formation. We show that several types of anamorphic optical systems (AOSs) can be effectively employed to shape laser beams into a variety of propagation invariant structured fields with different shapes and phase distributions. We present a propagation matrix approach for designing AOSs and defining mode-matching conditions required for preserving propagation invariance of the output shaped fields. The propagation matrix approach was selected, as it provides a more straightforward approach in designing AOSs for shaping propagation-invariant laser beams than the alternative technique based on the Gouy phase evolution, especially in the case of multielement AOSs. Several practical configurations of optical systems that are suitable for shaping input laser beams into a diverse variety of structured propagation invariant laser beams are also presented. The laser beam shaping approach was applied by modeling propagation characteristics of several input laser beam types, including Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian structured field distributions. The influence of the Ince-Gaussian beam semifocal separation parameter and the azimuthal orientation between the input laser beams and the AOSs onto the resulting shape of the propagation invariant laser beams is presented as well.

Renyi entropy measures of heart rate Gaussianity.

PubMed

Lake, Douglas E

2006-01-01

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

MuLoG, or How to Apply Gaussian Denoisers to Multi-Channel SAR Speckle Reduction?

PubMed

Deledalle, Charles-Alban; Denis, Loic; Tabti, Sonia; Tupin, Florence

2017-09-01

Speckle reduction is a longstanding topic in synthetic aperture radar (SAR) imaging. Since most current and planned SAR imaging satellites operate in polarimetric, interferometric, or tomographic modes, SAR images are multi-channel and speckle reduction techniques must jointly process all channels to recover polarimetric and interferometric information. The distinctive nature of SAR signal (complex-valued, corrupted by multiplicative fluctuations) calls for the development of specialized methods for speckle reduction. Image denoising is a very active topic in image processing with a wide variety of approaches and many denoising algorithms available, almost always designed for additive Gaussian noise suppression. This paper proposes a general scheme, called MuLoG (MUlti-channel LOgarithm with Gaussian denoising), to include such Gaussian denoisers within a multi-channel SAR speckle reduction technique. A new family of speckle reduction algorithms can thus be obtained, benefiting from the ongoing progress in Gaussian denoising, and offering several speckle reduction results often displaying method-specific artifacts that can be dismissed by comparison between results.

Issues in the digital implementation of control compensators. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Moroney, P.

1979-01-01

Techniques developed for the finite-precision implementation of digital filters were used, adapted, and extended for digital feedback compensators, with particular emphasis on steady state, linear-quadratic-Gaussian compensators. Topics covered include: (1) the linear-quadratic-Gaussian problem; (2) compensator structures; (3) architectural issues: serialism, parallelism, and pipelining; (4) finite wordlength effects: quantization noise, quantizing the coefficients, and limit cycles; and (5) the optimization of structures.

Second order Pseudo-gaussian shaper

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

Beche, Jean-Francois

2002-11-22

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

Optical assembly of microparticles into highly ordered structures using Ince-Gaussian beams

NASA Astrophysics Data System (ADS)

Woerdemann, Mike; Alpmann, Christina; Denz, Cornelia

2011-03-01

Ince-Gaussian (IG) beams are a third complete family of solutions of the paraxial Helmholtz equation. While many applications of Hermite-Gaussian and Laguerre-Gaussian beams have been demonstrated for manipulation of microparticles, the potential of the more general class of IG beams has not yet been exploited at all. We describe the unique properties of IG beams with respect to optical trapping applications, demonstrate a flexible experimental realization of arbitrary IG beams and prove the concept by creating two- and three-dimensional, highly ordered assemblies of typical microparticles. The concept is universal and can easily be integrated into existing holographic optical tweezers setups.

Metasurface-assisted orbital angular momentum carrying Bessel-Gaussian Laser: proposal and simulation.

PubMed

Zhou, Nan; Wang, Jian

2018-05-23

Bessel-Gaussian beams have distinct properties of suppressed diffraction divergence and self-reconstruction. In this paper, we propose and simulate metasurface-assisted orbital angular momentum (OAM) carrying Bessel-Gaussian laser. The laser can be regarded as a Fabry-Perot cavity formed by one partially transparent output plane mirror and the other metasurface-based reflector mirror. The gain medium of Nd:YVO 4 enables the lasing wavelength at 1064 nm with a 808 nm laser serving as the pump. The sub-wavelength structure of metasurface facilitates flexible spatial light manipulation. The compact metasurface-based reflector provides combined phase functions of an axicon and a spherical mirror. By appropriately selecting the size of output mirror and inserting mode-selection element in the laser cavity, different orders of OAM-carrying Bessel-Gaussian lasing modes are achievable. The lasing Bessel-Gaussian 0 , Bessel-Gaussian 01 + , Bessel-Gaussian 02 + and Bessel-Gaussian 03 + modes have high fidelities of ~0.889, ~0.889, ~0.881 and ~0.879, respectively. The metasurface fabrication tolerance and the dependence of threshold power and output lasing power on the length of gain medium, beam radius of pump and transmittance of output mirror are also discussed. The obtained results show successful implementation of metasurface-assisted OAM-carrying Bessel-Gaussian laser with favorable performance. The metasurface-assisted OAM-carrying Bessel-Gaussian laser may find wide OAM-enabled communication and non-communication applications.

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.

On estimating the phase of periodic waveform in additive Gaussian noise, part 2

NASA Astrophysics Data System (ADS)

Rauch, L. L.

1984-11-01

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

Is the Non-Dipole Magnetic Field Random?

NASA Technical Reports Server (NTRS)

Walker, Andrew D.; Backus, George E.

1996-01-01

Statistical modelling of the Earth's magnetic field B has a long history. In particular, the spherical harmonic coefficients of scalar fields derived from B can be treated as Gaussian random variables. In this paper, we give examples of highly organized fields whose spherical harmonic coefficients pass tests for independent Gaussian random variables. The fact that coefficients at some depth may be usefully summarized as independent samples from a normal distribution need not imply that there really is some physical, random process at that depth. In fact, the field can be extremely structured and still be regarded for some purposes as random. In this paper, we examined the radial magnetic field B(sub r) produced by the core, but the results apply to any scalar field on the core-mantle boundary (CMB) which determines B outside the CMB.

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

NASA Technical Reports Server (NTRS)

Rauch, L. L.

1984-01-01

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

Detecting Compartmental non-Gaussian Diffusion with Symmetrized Double-PFG MRI

PubMed Central

Paulsen, Jeffrey L.; Özarslan, Evren; Komlosh, Michal E.; Basser, Peter J.; Song, Yi-Qiao

2015-01-01

Diffusion in tissue and porous media is known to be non-Gaussian and has been used for clinical indications of stroke and other tissue pathologies. However, when conventional NMR techniques are applied to biological tissues and other heterogeneous materials, the presence of multiple compartments (pores) with different Gaussian diffusivities will also contribute to the measurement of non-Gaussian behavior. Here we present Symmetrized Double PFG (sd-PFG), which can separate these two contributions to non-Gaussian signal decay as having distinct angular modulation frequencies. In contrast to prior angular d-PFG methods, sd-PFG can unambiguously extract kurtosis as an oscillation from samples with isotropic or uniformly oriented anisotropic pores, and can generally extract a combination of compartmental anisotropy and kurtosis. The method further fixes its sensitivity with respect to the time-dependence of the apparent diffusion coefficient. We experimentally demonstrate the measurement of the fourth moment (kurtosis) of diffusion and find it consistent with theoretical predictions. By enabling the unambiguous identification of contributions of compartmental kurtosis to the signal, sd-PFG has the potential to help identify the underlying micro-structural changes corresponding to current kurtosis based diagnostics and act as a novel source of contrast to better resolve tissue micro-structure. PMID:26434812

Improved Discrete Approximation of Laplacian of Gaussian

NASA Technical Reports Server (NTRS)

Shuler, Robert L., Jr.

2004-01-01

An improved method of computing a discrete approximation of the Laplacian of a Gaussian convolution of an image has been devised. The primary advantage of the method is that without substantially degrading the accuracy of the end result, it reduces the amount of information that must be processed and thus reduces the amount of circuitry needed to perform the Laplacian-of- Gaussian (LOG) operation. Some background information is necessary to place the method in context. The method is intended for application to the LOG part of a process of real-time digital filtering of digitized video data that represent brightnesses in pixels in a square array. The particular filtering process of interest is one that converts pixel brightnesses to binary form, thereby reducing the amount of information that must be performed in subsequent correlation processing (e.g., correlations between images in a stereoscopic pair for determining distances or correlations between successive frames of the same image for detecting motions). The Laplacian is often included in the filtering process because it emphasizes edges and textures, while the Gaussian is often included because it smooths out noise that might not be consistent between left and right images or between successive frames of the same image.

A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation.

PubMed

Huang, Yong; Tao, Gang

2014-09-01

The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.

A feedback control strategy for the airfoil system under non-Gaussian colored noise excitation

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

Huang, Yong, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn; Tao, Gang, E-mail: hy@njust.edu.cn, E-mail: taogang@njust.edu.cn

2014-09-01

The stability of a binary airfoil with feedback control under stochastic disturbances, a non-Gaussian colored noise, is studied in this paper. First, based on some approximated theories and methods the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process. Furthermore, via the stochastic averaging method and the logarithmic polar transformation, one dimensional diffusion process can be obtained. At last by applying the boundary conditions, the largest Lyapunov exponent which can determine the almost-sure stability of the system and the effective region of control parameters is calculated.

Neural pulse frequency modulation of an exponentially correlated Gaussian process

NASA Technical Reports Server (NTRS)

Hutchinson, C. E.; Chon, Y.-T.

1976-01-01

The effect of NPFM (Neural Pulse Frequency Modulation) on a stationary Gaussian input, namely an exponentially correlated Gaussian input, is investigated with special emphasis on the determination of the average number of pulses in unit time, known also as the average frequency of pulse occurrence. For some classes of stationary input processes where the formulation of the appropriate multidimensional Markov diffusion model of the input-plus-NPFM system is possible, the average impulse frequency may be obtained by a generalization of the approach adopted. The results are approximate and numerical, but are in close agreement with Monte Carlo computer simulation results.

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.

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.

Elegant Ince—Gaussian breathers in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

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

2012-06-01

A novel class of optical breathers, called elegant Ince—Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell's mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schrödinger equation.

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

PubMed

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

2017-10-01

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

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

PubMed Central

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

2017-01-01

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

Fresnel zone plate with apodized aperture for hard X-ray Gaussian beam optics.

PubMed

Takeuchi, Akihisa; Uesugi, Kentaro; Suzuki, Yoshio; Itabashi, Seiichi; Oda, Masatoshi

2017-05-01

Fresnel zone plates with apodized apertures [apodization FZPs (A-FZPs)] have been developed to realise Gaussian beam optics in the hard X-ray region. The designed zone depth of A-FZPs gradually decreases from the center to peripheral regions. Such a zone structure forms a Gaussian-like smooth-shouldered aperture function which optically behaves as an apodization filter and produces a Gaussian-like focusing spot profile. Optical properties of two types of A-FZP, i.e. a circular type and a one-dimensional type, have been evaluated by using a microbeam knife-edge scan test, and have been carefully compared with those of normal FZP optics. Advantages of using A-FZPs are introduced.

Disappearance of Anisotropic Intermittency in Large-amplitude MHD Turbulence and Its Comparison with Small-amplitude MHD Turbulence

NASA Astrophysics Data System (ADS)

Yang, Liping; Zhang, Lei; He, Jiansen; Tu, Chuanyi; Li, Shengtai; Wang, Xin; Wang, Linghua

2018-03-01

Multi-order structure functions in the solar wind are reported to display a monofractal scaling when sampled parallel to the local magnetic field and a multifractal scaling when measured perpendicularly. Whether and to what extent will the scaling anisotropy be weakened by the enhancement of turbulence amplitude relative to the background magnetic strength? In this study, based on two runs of the magnetohydrodynamic (MHD) turbulence simulation with different relative levels of turbulence amplitude, we investigate and compare the scaling of multi-order magnetic structure functions and magnetic probability distribution functions (PDFs) as well as their dependence on the direction of the local field. The numerical results show that for the case of large-amplitude MHD turbulence, the multi-order structure functions display a multifractal scaling at all angles to the local magnetic field, with PDFs deviating significantly from the Gaussian distribution and a flatness larger than 3 at all angles. In contrast, for the case of small-amplitude MHD turbulence, the multi-order structure functions and PDFs have different features in the quasi-parallel and quasi-perpendicular directions: a monofractal scaling and Gaussian-like distribution in the former, and a conversion of a monofractal scaling and Gaussian-like distribution into a multifractal scaling and non-Gaussian tail distribution in the latter. These results hint that when intermittencies are abundant and intense, the multifractal scaling in the structure functions can appear even if it is in the quasi-parallel direction; otherwise, the monofractal scaling in the structure functions remains even if it is in the quasi-perpendicular direction.

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States

NASA Astrophysics Data System (ADS)

Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas

2017-11-01

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States.

PubMed

Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas

2017-11-03

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

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

PubMed

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

2016-05-13

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

Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach.

PubMed

Rosso, O A; Zunino, L; Pérez, D G; Figliola, A; Larrondo, H A; Garavaglia, M; Martín, M T; Plastino, A

2007-12-01

By recourse to appropriate information theory quantifiers (normalized Shannon entropy and Martín-Plastino-Rosso intensive statistical complexity measure), we revisit the characterization of Gaussian self-similar stochastic processes from a Bandt-Pompe viewpoint. We show that the ensuing approach exhibits considerable advantages with respect to other treatments. In particular, clear quantifiers gaps are found in the transition between the continuous processes and their associated noises.

Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.

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

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

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

Rayleigh-Taylor instability of radiation pressure accelerated ultrathin foils by laser having Gaussian and super-Gaussian intensity distribution is investigated using a single fluid code. The foil is allowed to have ring shaped surface ripples. The radiation pressure force on such a foil is non-uniform with finite transverse component F{sub r}; F{sub r} varies periodically with r. Subsequently, the ripple grows as the foil moves ahead along z. With a Gaussian beam, the foil acquires an overall curvature due to non-uniformity in radiation pressure and gets thinner. In the process, the ripple perturbation is considerably washed off. With super-Gaussian beam, the ripplemore » is found to be more strongly washed out. In order to avoid transmission of the laser through the thinning foil, a criterion on the foil thickness is obtained.« less

Effect of central obscuration on the LDR point spread function

NASA Technical Reports Server (NTRS)

Vanzyl, Jakob J.

1988-01-01

It is well known that Gaussian apodization of an aperture reduces the sidelobe levels of its point spread function (PSF). In the limit where the standard deviation of the Gaussian function is much smaller than the diameter of the aperture, the sidelobes completely disappear. However, when Gaussian apodization is applied to the Large Deployable Reflector (LDR) array consisting of 84 hexagonal panels, it is found that the sidelobe level only decreases by about 2.5 dB. The reason for this is explained. The PSF is shown for an array consisting of 91 uniformly illuminated hexagonal apertures; this array is identical to the LDR array, except that the central hole in the LDR array is filled with seven additional panels. For comparison, the PSF of the uniformly illuminated LDR array is shown. Notice that it is already evident that the sidelobe structure of the LDR array is different from that of the full array of 91 panels. The PSF's of the same two arrays are shown, but with the illumination apodized with a Gaussian function to have 20 dB tapering at the edges of the arrays. While the sidelobes of the full array have decreased dramatically, those of the LDR array changed in structure, but stayed at almost the same level. This result is not completely surprising, since the Gaussian apodization tends to emphasize the contributions from the central portion of the array; exactly where the hole in the LDR array is located. The two most important conclusions are: the size of the central hole should be minimized, and a simple Gaussian apodization scheme to suppress the sidelobes in the PSF should not be used. A more suitable apodization scheme would be a Gaussian annular ring.

Is it worth changing pattern recognition methods for structural health monitoring?

NASA Astrophysics Data System (ADS)

Bull, L. A.; Worden, K.; Cross, E. J.; Dervilis, N.

2017-05-01

The key element of this work is to demonstrate alternative strategies for using pattern recognition algorithms whilst investigating structural health monitoring. This paper looks to determine if it makes any difference in choosing from a range of established classification techniques: from decision trees and support vector machines, to Gaussian processes. Classification algorithms are tested on adjustable synthetic data to establish performance metrics, then all techniques are applied to real SHM data. To aid the selection of training data, an informative chain of artificial intelligence tools is used to explore an active learning interaction between meaningful clusters of data.

Disentangling inhibition-based and retrieval-based aftereffects of distractors: Cognitive versus motor processes.

PubMed

Singh, Tarini; Laub, Ruth; Burgard, Jan Pablo; Frings, Christian

2018-05-01

Selective attention refers to the ability to selectively act upon relevant information at the expense of irrelevant information. Yet, in many experimental tasks, what happens to the representation of the irrelevant information is still debated. Typically, 2 approaches to distractor processing have been suggested, namely distractor inhibition and distractor-based retrieval. However, it is also typical that both processes are hard to disentangle. For instance, in the negative priming literature (for a review Frings, Schneider, & Fox, 2015) this has been a continuous debate since the early 1980s. In the present study, we attempted to prove that both processes exist, but that they reflect distractor processing at different levels of representation. Distractor inhibition impacts stimulus representation, whereas distractor-based retrieval impacts mainly motor processes. We investigated both processes in a distractor-priming task, which enables an independent measurement of both processes. For our argument that both processes impact different levels of distractor representation, we estimated the exponential parameter (τ) and Gaussian components (μ, σ) of the exponential Gaussian reaction-time (RT) distribution, which have previously been used to independently test the effects of cognitive and motor processes (e.g., Moutsopoulou & Waszak, 2012). The distractor-based retrieval effect was evident for the Gaussian component, which is typically discussed as reflecting motor processes, but not for the exponential parameter, whereas the inhibition component was evident for the exponential parameter, which is typically discussed as reflecting cognitive processes, but not for the Gaussian parameter. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

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

Characterizing structural association alterations within brain networks in normal aging using Gaussian Bayesian networks.

PubMed

Guo, Xiaojuan; Wang, Yan; Chen, Kewei; Wu, Xia; Zhang, Jiacai; Li, Ke; Jin, Zhen; Yao, Li

2014-01-01

Recent multivariate neuroimaging studies have revealed aging-related alterations in brain structural networks. However, the sensory/motor networks such as the auditory, visual and motor networks, have obtained much less attention in normal aging research. In this study, we used Gaussian Bayesian networks (BN), an approach investigating possible inter-regional directed relationship, to characterize aging effects on structural associations between core brain regions within each of these structural sensory/motor networks using volumetric MRI data. We then further examined the discriminability of BN models for the young (N = 109; mean age =22.73 years, range 20-28) and old (N = 82; mean age =74.37 years, range 60-90) groups. The results of the BN modeling demonstrated that structural associations exist between two homotopic brain regions from the left and right hemispheres in each of the three networks. In particular, compared with the young group, the old group had significant connection reductions in each of the three networks and lesser connection numbers in the visual network. Moreover, it was found that the aging-related BN models could distinguish the young and old individuals with 90.05, 73.82, and 88.48% accuracy for the auditory, visual, and motor networks, respectively. Our findings suggest that BN models can be used to investigate the normal aging process with reliable statistical power. Moreover, these differences in structural inter-regional interactions may help elucidate the neuronal mechanism of anatomical changes in normal aging.

Detecting compartmental non-Gaussian diffusion with symmetrized double-PFG MRI.

PubMed

Paulsen, Jeffrey L; Özarslan, Evren; Komlosh, Michal E; Basser, Peter J; Song, Yi-Qiao

2015-11-01

Diffusion in tissue and porous media is known to be non-Gaussian and has been used for clinical indications of stroke and other tissue pathologies. However, when conventional NMR techniques are applied to biological tissues and other heterogeneous materials, the presence of multiple compartments (pores) with different Gaussian diffusivities will also contribute to the measurement of non-Gaussian behavior. Here we present symmetrized double PFG (sd-PFG), which can separate these two contributions to non-Gaussian signal decay as having distinct angular modulation frequencies. In contrast to prior angular d-PFG methods, sd-PFG can unambiguously extract kurtosis as an oscillation from samples with isotropic or uniformly oriented anisotropic pores, and can generally extract a combination of compartmental anisotropy and kurtosis. The method further fixes its sensitivity with respect to the time dependence of the apparent diffusion coefficient. We experimentally demonstrate the measurement of the fourth cumulant (kurtosis) of diffusion and find it consistent with theoretical predictions. By enabling the unambiguous identification of contributions of compartmental kurtosis to the signal, sd-PFG has the potential to help identify the underlying micro-structural changes corresponding to current kurtosis based diagnostics, and act as a novel source of contrast to better resolve tissue micro-structure. Copyright © 2015 John Wiley & Sons, Ltd.

Interaction of doughnut-shaped laser pulses with glasses

DOE PAGES

Zhukov, Vladimir P.; Rubenchik, Alexander M.; Fedoruk, Mikhail P.; ...

2017-01-26

Non-Gaussian laser beams can open new opportunities for microfabrication, including ultrashort laser direct writing. By using a model based on Maxwell’s equations, we investigate the dynamics of doughnut-shaped laser beams focused inside fused silica glass, in comparison with Gaussian pulses of the same energy. The laser propagation dynamics reveals intriguing features of beam splitting and sudden collapse toward the beam axis, overcoming the intensity clamping effect. The resulting structure of light absorption represents a very hot, hollow nanocylinder, which can lead to an implosion process that brings matter to extreme thermodynamic states. Furthermore, by monitoring the simulations of the lasermore » beam scattering we see a considerable difference in both the blueshift and the angular distribution of scattered light for different laser energies, suggesting that investigations of the spectra of scattered radiation can be used as a diagnostic of laser-produced electron plasmas in transparent materials.« less

Front-surface fabrication of moderate aspect ratio micro-channels in fused silica by single picosecond Gaussian-Bessel laser pulse

NASA Astrophysics Data System (ADS)

Liu, Xin; Sanner, Nicolas; Sentis, Marc; Stoian, Razvan; Zhao, Wei; Cheng, Guanghua; Utéza, Olivier

2018-02-01

Single-shot Gaussian-Bessel laser beams of 1 ps pulse duration and of 0.9 μm core size and 60 μm depth of focus are used for drilling micro-channels on front side of fused silica in ambient condition. Channels ablated at different pulse energies are fully characterized by AFM and post-processing polishing procedures. We identify experimental energy conditions (typically 1.5 µJ) suitable to fabricate non-tapered channels with mean diameter of 1.2 µm and length of 40 μm while maintaining an utmost quality of the front opening of the channels. In addition, by further applying accurate post-polishing procedure, channels with high surface quality and moderate aspect ratio down to a few units are accessible, which would find interest in the surface micro-structuring of materials, with perspective of further scalability to meta-material specifications.

Propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere.

PubMed

Zhou, Guoquan; Cai, Yangjian; Chu, Xiuxiang

2012-04-23

The propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity and the degree of the polarization of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system are derived in turbulent atmosphere, respectively. The average intensity distribution and the degree of the polarization of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters, the topological charge, the transverse coherent lengths, and the structure constant of the atmospheric turbulence on the propagation of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are also examined in detail. This research is beneficial to the practical applications in free-space optical communications and the remote sensing of the dark hollow beams. © 2012 Optical Society of America

Demonstration of Monogamy Relations for Einstein-Podolsky-Rosen Steering in Gaussian Cluster States.

PubMed

Deng, Xiaowei; Xiang, Yu; Tian, Caixing; Adesso, Gerardo; He, Qiongyi; Gong, Qihuang; Su, Xiaolong; Xie, Changde; Peng, Kunchi

2017-06-09

Understanding how quantum resources can be quantified and distributed over many parties has profound applications in quantum communication. As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. By reconstructing the covariance matrix of a continuous variable four-mode square Gaussian cluster state subject to asymmetric loss, we quantify the amount of bipartite steering with a variable number of modes per party, and verify recently introduced monogamy relations for Gaussian steerability, which establish quantitative constraints on the security of information shared among different parties. We observe a very rich structure for the steering distribution, and demonstrate one-way EPR steering of the cluster state under Gaussian measurements, as well as one-to-multimode steering. Our experiment paves the way for exploiting EPR steering in Gaussian cluster states as a valuable resource for multiparty quantum information tasks.

Demonstration of Monogamy Relations for Einstein-Podolsky-Rosen Steering in Gaussian Cluster States

NASA Astrophysics Data System (ADS)

Deng, Xiaowei; Xiang, Yu; Tian, Caixing; Adesso, Gerardo; He, Qiongyi; Gong, Qihuang; Su, Xiaolong; Xie, Changde; Peng, Kunchi

2017-06-01

Understanding how quantum resources can be quantified and distributed over many parties has profound applications in quantum communication. As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. By reconstructing the covariance matrix of a continuous variable four-mode square Gaussian cluster state subject to asymmetric loss, we quantify the amount of bipartite steering with a variable number of modes per party, and verify recently introduced monogamy relations for Gaussian steerability, which establish quantitative constraints on the security of information shared among different parties. We observe a very rich structure for the steering distribution, and demonstrate one-way EPR steering of the cluster state under Gaussian measurements, as well as one-to-multimode steering. Our experiment paves the way for exploiting EPR steering in Gaussian cluster states as a valuable resource for multiparty quantum information tasks.

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

NASA Astrophysics Data System (ADS)

Sabapathy, Krishna Kumar; Winter, Andreas

2017-06-01

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

Linear Scaling Density Functional Calculations with Gaussian Orbitals

NASA Technical Reports Server (NTRS)

Scuseria, Gustavo E.

1999-01-01

Recent advances in linear scaling algorithms that circumvent the computational bottlenecks of large-scale electronic structure simulations make it possible to carry out density functional calculations with Gaussian orbitals on molecules containing more than 1000 atoms and 15000 basis functions using current workstations and personal computers. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.

q-Gaussian distributions and multiplicative stochastic processes for analysis of multiple financial time series

NASA Astrophysics Data System (ADS)

Sato, Aki-Hiro

2010-12-01

This study considers q-Gaussian distributions and stochastic differential equations with both multiplicative and additive noises. In the M-dimensional case a q-Gaussian distribution can be theoretically derived as a stationary probability distribution of the multiplicative stochastic differential equation with both mutually independent multiplicative and additive noises. By using the proposed stochastic differential equation a method to evaluate a default probability under a given risk buffer is proposed.

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.

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.

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.

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.

An Automated Energy Detection Algorithm Based on Morphological Filter Processing with a Semi-Disk Structure

DTIC Science & Technology

2018-01-01

statistical moments of order 2, 3, and 4. The probability density function (PDF) of the vibrational time series of a good bearing has a Gaussian...ARL-TR-8271 ● JAN 2018 US Army Research Laboratory An Automated Energy Detection Algorithm Based on Morphological Filter...when it is no longer needed. Do not return it to the originator. ARL-TR-8271 ● JAN 2018 US Army Research Laboratory An Automated

A Detailed Derivation of Gaussian Orbital-Based Matrix Elements in Electron Structure Calculations

ERIC Educational Resources Information Center

Petersson, T.; Hellsing, B.

2010-01-01

A detailed derivation of analytic solutions is presented for overlap, kinetic, nuclear attraction and electron repulsion integrals involving Cartesian Gaussian-type orbitals. It is demonstrated how s-type orbitals can be used to evaluate integrals with higher angular momentum via the properties of Hermite polynomials and differentiation with…

Log-amplitude variance and wave structure function: A new perspective for Gaussian beams

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

Miller, W.B.; Ricklin, J.C.; Andrews, L.C.

1993-04-01

Two naturally linked pairs of nondimensional parameters are identified such that either pair, together with wavelength and path length, completely specifies the diffractive propagation environment for a lowest-order paraxial Gaussian beam. Both parameter pairs are intuitive, and within the context of locally homogeneous and isotropic turbulence they reflect the long-recognized importance of the Fresnel zone size in the behavior of Rytov propagation statistics. These parameter pairs, called, respectively, the transmitter and receiver parameters, also provide a change in perspective in the analysis of optical turbulence effects on Gaussian beams by unifying a number of behavioral traits previously observed or predicted,more » and they create an environment in which the determination of limiting interrelationships between beam forms is especially simple. The fundamental nature of the parameter pairs becomes apparent in the derived analytical expressions for the log-amplitude variance and the wave structure function. These expressions verify general optical turbulence-related characteristics predicted for Gaussian beams, provide additional insights into beam-wave behavior, and are convenient tools for beam-wave analysis. 22 refs., 10 figs., 2 tabs.« less

Resolving the structure of the Galactic foreground using Herschel measurements and the Kriging technique

NASA Astrophysics Data System (ADS)

Pinter, S.; Bagoly, Z.; Balázs, L. G.; Horvath, I.; Racz, I. I.; Zahorecz, S.; Tóth, L. V.

2018-05-01

Investigating the distant extragalactic Universe requires a subtraction of the Galactic foreground. One of the major difficulties deriving the fine structure of the galactic foreground is the embedded foreground and background point sources appearing in the given fields. It is especially so in the infrared. We report our study subtracting point sources from Herschel images with Kriging, an interpolation method where the interpolated values are modelled by a Gaussian process governed by prior covariances. Using the Kriging method on Herschel multi-wavelength observations the structure of the Galactic foreground can be studied with much higher resolution than previously, leading to a better foreground subtraction at the end.

Research in Stochastic Processes and their Applications

DTIC Science & Technology

1993-01-01

goal is to learn how Gaussian and linear signal processing methodologies should be adapted to deal with non-Gaussian regimes. Part III continues the... smoothi fmictions in /I, ami we have a chain C ... C tir C ... C /I’) C 11_ C ... C 1t_, C_ ... C ¢’, 10 4o = fH,; H =H;, H, (Hilbert space). 4ý is a Fr

Gaussian entanglement generation from coherence using beam-splitters

PubMed Central

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

2016-01-01

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

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.

Effect of lensing non-Gaussianity on the CMB power spectra

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

Lewis, Antony; Pratten, Geraint, E-mail: antony@cosmologist.info, E-mail: geraint.pratten@gmail.com

2016-12-01

Observed CMB anisotropies are lensed, and the lensed power spectra can be calculated accurately assuming the lensing deflections are Gaussian. However, the lensing deflections are actually slightly non-Gaussian due to both non-linear large-scale structure growth and post-Born corrections. We calculate the leading correction to the lensed CMB power spectra from the non-Gaussianity, which is determined by the lensing bispectrum. Assuming no primordial non-Gaussianity, the lowest-order result gives ∼ 0.3% corrections to the BB and EE polarization spectra on small-scales. However we show that the effect on EE is reduced by about a factor of two by higher-order Gaussian lensing smoothing,more » rendering the total effect safely negligible for the foreseeable future. We give a simple analytic model for the signal expected from skewness of the large-scale lensing field; the effect is similar to a net demagnification and hence a small change in acoustic scale (and therefore out of phase with the dominant lensing smoothing that predominantly affects the peaks and troughs of the power spectrum).« less

Gaussian pre-filtering for uncertainty minimization in digital image correlation using numerically-designed speckle patterns

NASA Astrophysics Data System (ADS)

Mazzoleni, Paolo; Matta, Fabio; Zappa, Emanuele; Sutton, Michael A.; Cigada, Alfredo

2015-03-01

This paper discusses the effect of pre-processing image blurring on the uncertainty of two-dimensional digital image correlation (DIC) measurements for the specific case of numerically-designed speckle patterns having particles with well-defined and consistent shape, size and spacing. Such patterns are more suitable for large measurement surfaces on large-scale specimens than traditional spray-painted random patterns without well-defined particles. The methodology consists of numerical simulations where Gaussian digital filters with varying standard deviation are applied to a reference speckle pattern. To simplify the pattern application process for large areas and increase contrast to reduce measurement uncertainty, the speckle shape, mean size and on-center spacing were selected to be representative of numerically-designed patterns that can be applied on large surfaces through different techniques (e.g., spray-painting through stencils). Such 'designer patterns' are characterized by well-defined regions of non-zero frequency content and non-zero peaks, and are fundamentally different from typical spray-painted patterns whose frequency content exhibits near-zero peaks. The effect of blurring filters is examined for constant, linear, quadratic and cubic displacement fields. Maximum strains between ±250 and ±20,000 με are simulated, thus covering a relevant range for structural materials subjected to service and ultimate stresses. The robustness of the simulation procedure is verified experimentally using a physical speckle pattern subjected to constant displacements. The stability of the relation between standard deviation of the Gaussian filter and measurement uncertainty is assessed for linear displacement fields at varying image noise levels, subset size, and frequency content of the speckle pattern. It is shown that bias error as well as measurement uncertainty are minimized through Gaussian pre-filtering. This finding does not apply to typical spray-painted patterns without well-defined particles, for which image blurring is only beneficial in reducing bias errors.

An Effective Post-Filtering Framework for 3-D PET Image Denoising Based on Noise and Sensitivity Characteristics

NASA Astrophysics Data System (ADS)

Kim, Ji Hye; Ahn, Il Jun; Nam, Woo Hyun; Ra, Jong Beom

2015-02-01

Positron emission tomography (PET) images usually suffer from a noticeable amount of statistical noise. In order to reduce this noise, a post-filtering process is usually adopted. However, the performance of this approach is limited because the denoising process is mostly performed on the basis of the Gaussian random noise. It has been reported that in a PET image reconstructed by the expectation-maximization (EM), the noise variance of each voxel depends on its mean value, unlike in the case of Gaussian noise. In addition, we observe that the variance also varies with the spatial sensitivity distribution in a PET system, which reflects both the solid angle determined by a given scanner geometry and the attenuation information of a scanned object. Thus, if a post-filtering process based on the Gaussian random noise is applied to PET images without consideration of the noise characteristics along with the spatial sensitivity distribution, the spatially variant non-Gaussian noise cannot be reduced effectively. In the proposed framework, to effectively reduce the noise in PET images reconstructed by the 3-D ordinary Poisson ordered subset EM (3-D OP-OSEM), we first denormalize an image according to the sensitivity of each voxel so that the voxel mean value can represent its statistical properties reliably. Based on our observation that each noisy denormalized voxel has a linear relationship between the mean and variance, we try to convert this non-Gaussian noise image to a Gaussian noise image. We then apply a block matching 4-D algorithm that is optimized for noise reduction of the Gaussian noise image, and reconvert and renormalize the result to obtain a final denoised image. Using simulated phantom data and clinical patient data, we demonstrate that the proposed framework can effectively suppress the noise over the whole region of a PET image while minimizing degradation of the image resolution.

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.

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

PubMed Central

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

2016-01-01

In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student’s t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods. PMID:27187405

A multiscale filter for noise reduction of low-dose cone beam projections.

PubMed

Yao, Weiguang; Farr, Jonathan B

2015-08-21

The Poisson or compound Poisson process governs the randomness of photon fluence in cone beam computed tomography (CBCT) imaging systems. The probability density function depends on the mean (noiseless) of the fluence at a certain detector. This dependence indicates the natural requirement of multiscale filters to smooth noise while preserving structures of the imaged object on the low-dose cone beam projection. In this work, we used a Gaussian filter, exp(-x2/2σ(2)(f)) as the multiscale filter to de-noise the low-dose cone beam projections. We analytically obtained the expression of σ(f), which represents the scale of the filter, by minimizing local noise-to-signal ratio. We analytically derived the variance of residual noise from the Poisson or compound Poisson processes after Gaussian filtering. From the derived analytical form of the variance of residual noise, optimal σ(2)(f)) is proved to be proportional to the noiseless fluence and modulated by local structure strength expressed as the linear fitting error of the structure. A strategy was used to obtain the reliable linear fitting error: smoothing the projection along the longitudinal direction to calculate the linear fitting error along the lateral direction and vice versa. The performance of our multiscale filter was examined on low-dose cone beam projections of a Catphan phantom and a head-and-neck patient. After performing the filter on the Catphan phantom projections scanned with pulse time 4 ms, the number of visible line pairs was similar to that scanned with 16 ms, and the contrast-to-noise ratio of the inserts was higher than that scanned with 16 ms about 64% in average. For the simulated head-and-neck patient projections with pulse time 4 ms, the visibility of soft tissue structures in the patient was comparable to that scanned with 20 ms. The image processing took less than 0.5 s per projection with 1024   ×   768 pixels.

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.

Efficient 3D porous microstructure reconstruction via Gaussian random field and hybrid optimization.

PubMed

Jiang, Z; Chen, W; Burkhart, C

2013-11-01

Obtaining an accurate three-dimensional (3D) structure of a porous microstructure is important for assessing the material properties based on finite element analysis. Whereas directly obtaining 3D images of the microstructure is impractical under many circumstances, two sets of methods have been developed in literature to generate (reconstruct) 3D microstructure from its 2D images: one characterizes the microstructure based on certain statistical descriptors, typically two-point correlation function and cluster correlation function, and then performs an optimization process to build a 3D structure that matches those statistical descriptors; the other method models the microstructure using stochastic models like a Gaussian random field and generates a 3D structure directly from the function. The former obtains a relatively accurate 3D microstructure, but computationally the optimization process can be very intensive, especially for problems with large image size; the latter generates a 3D microstructure quickly but sacrifices the accuracy due to issues in numerical implementations. A hybrid optimization approach of modelling the 3D porous microstructure of random isotropic two-phase materials is proposed in this paper, which combines the two sets of methods and hence maintains the accuracy of the correlation-based method with improved efficiency. The proposed technique is verified for 3D reconstructions based on silica polymer composite images with different volume fractions. A comparison of the reconstructed microstructures and the optimization histories for both the original correlation-based method and our hybrid approach demonstrates the improved efficiency of the approach. © 2013 The Authors Journal of Microscopy © 2013 Royal Microscopical Society.

Activation rates for nonlinear stochastic flows driven by non-Gaussian noise

NASA Astrophysics Data System (ADS)

van den Broeck, C.; Hänggi, P.

1984-11-01

Activation rates are calculated for stochastic bistable flows driven by asymmetric dichotomic Markov noise (a two-state Markov process). This noise contains as limits both a particular type of non-Gaussian white shot noise and white Gaussian noise. Apart from investigating the role of colored noise on the escape rates, one can thus also study the influence of the non-Gaussian nature of the noise on these rates. The rate for white shot noise differs in leading order (Arrhenius factor) from the corresponding rate for white Gaussian noise of equal strength. In evaluating the rates we demonstrate the advantage of using transport theory over a mean first-passage time approach for cases with generally non-white and non-Gaussian noise sources. For white shot noise with exponentially distributed weights we succeed in evaluating the mean first-passage time of the corresponding integro-differential master-equation dynamics. The rate is shown to coincide in the weak noise limit with the inverse mean first-passage time.

Quantitative comparison of self-healing ability between Bessel–Gaussian beam and Airy beam

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

Wen, Wei; Chu, Xiuxiang, E-mail: xiuxiangchu@yahoo.com

The self-healing ability during propagation process is one of the most important properties of non-diffracting beams. This ability has crucial advantages to light sheet-based microscopy to reduce scattering artefacts, increase the quality of the image and enhance the resolution of microscopy. Based on similarity between two infinite-dimensional complex vectors in Hilbert space, the ability to a Bessel–Gaussian beam and an Airy beam have been studied and compared. Comparing the evolution of the similarity of Bessel–Gaussian beam with Airy beam under the same conditions, we find that Bessel–Gaussian beam has stronger self-healing ability and is more stable than that of Airymore » beam. To confirm this result, the intensity profiles of Bessel–Gaussian beam and Airy beam with different similarities are numerically calculated and compared.« less

Real-time model learning using Incremental Sparse Spectrum Gaussian Process Regression.

PubMed

Gijsberts, Arjan; Metta, Giorgio

2013-05-01

Novel applications in unstructured and non-stationary human environments require robots that learn from experience and adapt autonomously to changing conditions. Predictive models therefore not only need to be accurate, but should also be updated incrementally in real-time and require minimal human intervention. Incremental Sparse Spectrum Gaussian Process Regression is an algorithm that is targeted specifically for use in this context. Rather than developing a novel algorithm from the ground up, the method is based on the thoroughly studied Gaussian Process Regression algorithm, therefore ensuring a solid theoretical foundation. Non-linearity and a bounded update complexity are achieved simultaneously by means of a finite dimensional random feature mapping that approximates a kernel function. As a result, the computational cost for each update remains constant over time. Finally, algorithmic simplicity and support for automated hyperparameter optimization ensures convenience when employed in practice. Empirical validation on a number of synthetic and real-life learning problems confirms that the performance of Incremental Sparse Spectrum Gaussian Process Regression is superior with respect to the popular Locally Weighted Projection Regression, while computational requirements are found to be significantly lower. The method is therefore particularly suited for learning with real-time constraints or when computational resources are limited. Copyright © 2012 Elsevier Ltd. All rights reserved.

Structural studies on serum albumins under green light irradiation.

PubMed

Comorosan, Sorin; Polosan, Silviu; Popescu, Irinel; Ionescu, Elena; Mitrica, Radu; Cristache, Ligia; State, Alina Elena

2010-10-01

This paper presents two new experimental results: the protective effect of green light (GL) on ultraviolet (UV) denaturation of proteins, and the effect of GL on protein macromolecular structures. The protective effect of GL was revealed on two serum albumins, bovine (BSA) and human (HSA), and recorded by electrophoresis, absorption, and circular dichroism spectra. The effect of GL irradiation on protein structure was recorded by using fluorescence spectroscopy and electrophoresis. These new effects were modeled by quantum-chemistry computation using Gaussian 03 W, leading to good fit between theoretical and experimental absorption and circular dichroism spectra. A mechanism for these phenomena is suggested, based on a double-photon absorption process. This nonlinear effect may lead to generation of long-lived Rydberg macromolecular systems, capable of long-range interactions. These newly suggested systems, with macroscopic quantum coherence behaviors, may block the UV denaturation processes.

Conditional and unconditional Gaussian quantum dynamics

NASA Astrophysics Data System (ADS)

Genoni, Marco G.; Lami, Ludovico; Serafini, Alessio

2016-07-01

This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as 'general-dyne') quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.

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.

On the constrained classical capacity of infinite-dimensional covariant quantum channels

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

Holevo, A. S.

The additivity of the minimal output entropy and that of the χ-capacity are known to be equivalent for finite-dimensional irreducibly covariant quantum channels. In this paper, we formulate a list of conditions allowing to establish similar equivalence for infinite-dimensional covariant channels with constrained input. This is then applied to bosonic Gaussian channels with quadratic input constraint to extend the classical capacity results of the recent paper [Giovannetti et al., Commun. Math. Phys. 334(3), 1553-1571 (2015)] to the case where the complex structures associated with the channel and with the constraint operator need not commute. In particular, this implies a multimodemore » generalization of the “threshold condition,” obtained for single mode in Schäfer et al. [Phys. Rev. Lett. 111, 030503 (2013)], and the proof of the fact that under this condition the classical “Gaussian capacity” resulting from optimization over only Gaussian inputs is equal to the full classical capacity. Complex structures correspond to different squeezings, each with its own normal modes, vacuum and coherent states, and the gauge. Thus our results apply, e.g., to multimode channels with a squeezed Gaussian noise under the standard input energy constraint, provided the squeezing is not too large as to violate the generalized threshold condition. We also investigate the restrictiveness of the gauge-covariance condition for single- and multimode bosonic Gaussian channels.« less

Adaptive Quadrature Detection for Multicarrier Continuous-Variable Quantum Key Distribution

NASA Astrophysics Data System (ADS)

Gyongyosi, Laszlo; Imre, Sandor

2015-03-01

We propose the adaptive quadrature detection for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD scheme uses Gaussian subcarrier continuous variables for the information conveying and Gaussian sub-channels for the transmission. The proposed multicarrier detection scheme dynamically adapts to the sub-channel conditions using a corresponding statistics which is provided by our sophisticated sub-channel estimation procedure. The sub-channel estimation phase determines the transmittance coefficients of the sub-channels, which information are used further in the adaptive quadrature decoding process. We define the technique called subcarrier spreading to estimate the transmittance conditions of the sub-channels with a theoretical error-minimum in the presence of a Gaussian noise. We introduce the terms of single and collective adaptive quadrature detection. We also extend the results for a multiuser multicarrier CVQKD scenario. We prove the achievable error probabilities, the signal-to-noise ratios, and quantify the attributes of the framework. The adaptive detection scheme allows to utilize the extra resources of multicarrier CVQKD and to maximize the amount of transmittable information. This work was partially supported by the GOP-1.1.1-11-2012-0092 (Secure quantum key distribution between two units on optical fiber network) project sponsored by the EU and European Structural Fund, and by the COST Action MP1006.

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.

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

PubMed

Palacios, Julia A; Minin, Vladimir N

2013-03-01

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

The effect of optically active turbulence on Gaussian laser beams in the ocean

NASA Astrophysics Data System (ADS)

Nootz, G.; Matt, S.; Jarosz, E.; Hou, W.

2016-02-01

Motivated by the high resolution and data transfer potential, optical imaging and communication methods are intensely investigated for marine applications. The majority of research focuses on overcoming the strong scattering of light by particles present in the ocean. However when operating in very clear water the limiting factor for such applications can be the strongly forward biased scattering from optically active turbulent layers. For this presentation the effect of optically active turbulence on focused Gaussian beams has been studied in the field, in a controlled laboratory test tank, and by numerical simulations. For the field experiments a telescoping rigid underwater sensor structure (TRUSS) was deployed in the Bahamas equipped with a diffractive optics element projecting a matrix of beams towards a fast beam profiler. Image processing techniques are used to extract the beam wander and beam breathing. The results are compared to theoretical values for the optical turbulence strength derived from the measured temperature microstructure at the test side. Laboratory and simulated experiments are carried out in a physical and numerical Rayleigh-Benard convection turbulence tank of the same geometry. A focused Gaussian laser beam is propagated through the test tank and recorded with a camera from the back side of a diffuser. Similarly, a focused Gaussian beam is propagated numerically by means of split-step Fourier method through the simulated turbulence environment. Results will be presented for weak to moderate turbulence as they are most typical for oceanic conditions. Conclusions about the effect on optical imaging and communication applications will be discussed.

Random scalar fields and hyperuniformity

NASA Astrophysics Data System (ADS)

Ma, Zheng; Torquato, Salvatore

2017-06-01

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystals and liquids. Hyperuniform systems have attracted recent attention because they are endowed with novel transport and optical properties. Recently, the hyperuniformity concept has been generalized to characterize two-phase media, scalar fields, and random vector fields. In this paper, we devise methods to explicitly construct hyperuniform scalar fields. Specifically, we analyze spatial patterns generated from Gaussian random fields, which have been used to model the microwave background radiation and heterogeneous materials, the Cahn-Hilliard equation for spinodal decomposition, and Swift-Hohenberg equations that have been used to model emergent pattern formation, including Rayleigh-Bénard convection. We show that the Gaussian random scalar fields can be constructed to be hyperuniform. We also numerically study the time evolution of spinodal decomposition patterns and demonstrate that they are hyperuniform in the scaling regime. Moreover, we find that labyrinth-like patterns generated by the Swift-Hohenberg equation are effectively hyperuniform. We show that thresholding (level-cutting) a hyperuniform Gaussian random field to produce a two-phase random medium tends to destroy the hyperuniformity of the progenitor scalar field. We then propose guidelines to achieve effectively hyperuniform two-phase media derived from thresholded non-Gaussian fields. Our investigation paves the way for new research directions to characterize the large-structure spatial patterns that arise in physics, chemistry, biology, and ecology. Moreover, our theoretical results are expected to guide experimentalists to synthesize new classes of hyperuniform materials with novel physical properties via coarsening processes and using state-of-the-art techniques, such as stereolithography and 3D printing.

Accuracy improvement in laser stripe extraction for large-scale triangulation scanning measurement system

NASA Astrophysics Data System (ADS)

Zhang, Yang; Liu, Wei; Li, Xiaodong; Yang, Fan; Gao, Peng; Jia, Zhenyuan

2015-10-01

Large-scale triangulation scanning measurement systems are widely used to measure the three-dimensional profile of large-scale components and parts. The accuracy and speed of the laser stripe center extraction are essential for guaranteeing the accuracy and efficiency of the measuring system. However, in the process of large-scale measurement, multiple factors can cause deviation of the laser stripe center, including the spatial light intensity distribution, material reflectivity characteristics, and spatial transmission characteristics. A center extraction method is proposed for improving the accuracy of the laser stripe center extraction based on image evaluation of Gaussian fitting structural similarity and analysis of the multiple source factors. First, according to the features of the gray distribution of the laser stripe, evaluation of the Gaussian fitting structural similarity is estimated to provide a threshold value for center compensation. Then using the relationships between the gray distribution of the laser stripe and the multiple source factors, a compensation method of center extraction is presented. Finally, measurement experiments for a large-scale aviation composite component are carried out. The experimental results for this specific implementation verify the feasibility of the proposed center extraction method and the improved accuracy for large-scale triangulation scanning measurements.

Efficiency-enhanced photon sieve using Gaussian/overlapping distribution of pinholes

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

Sabatyan, A.; Mirzaie, S.

2011-04-10

A class of photon sieve is introduced whose structure is based on the overlapping pinholes in the innermost zones. This kind of distribution is produced by, for example, a particular form of Gaussian function. The focusing property of the proposed model was examined theoretically and experimentally. It is shown that under He-Ne laser and white light illumination, the focal spot size of this novel structure has considerably smaller FWHM than a photon sieve with randomly distributed pinholes and a Fresnel zone plate. In addition, secondary maxima have been suppressed effectively.

Graph Kernels for Molecular Similarity.

PubMed

Rupp, Matthias; Schneider, Gisbert

2010-04-12

Molecular similarity measures are important for many cheminformatics applications like ligand-based virtual screening and quantitative structure-property relationships. Graph kernels are formal similarity measures defined directly on graphs, such as the (annotated) molecular structure graph. Graph kernels are positive semi-definite functions, i.e., they correspond to inner products. This property makes them suitable for use with kernel-based machine learning algorithms such as support vector machines and Gaussian processes. We review the major types of kernels between graphs (based on random walks, subgraphs, and optimal assignments, respectively), and discuss their advantages, limitations, and successful applications in cheminformatics. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Advanced Electronic Structure Calculations For Nanoelectronics Using Finite Element Bases and Effective Mass Theory.

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

Gamble, John King; Nielsen, Erik; Baczewski, Andrew David

This paper describes our work over the past few years to use tools from quantum chemistry to describe electronic structure of nanoelectronic devices. These devices, dubbed "artificial atoms", comprise a few electrons, con ned by semiconductor heterostructures, impurities, and patterned electrodes, and are of intense interest due to potential applications in quantum information processing, quantum sensing, and extreme-scale classical logic. We detail two approaches we have employed: nite-element and Gaussian basis sets, exploring the interesting complications that arise when techniques that were intended to apply to atomic systems are instead used for artificial, solid-state devices.

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.

Ince Gaussian beams in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Deng, Dongmei; Guo, Qi

2008-07-01

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

celerite: Scalable 1D Gaussian Processes in C++, Python, and Julia

NASA Astrophysics Data System (ADS)

Foreman-Mackey, Daniel; Agol, Eric; Ambikasaran, Sivaram; Angus, Ruth

2017-09-01

celerite provides fast and scalable Gaussian Process (GP) Regression in one dimension and is implemented in C++, Python, and Julia. The celerite API is designed to be familiar to users of george and, like george, celerite is designed to efficiently evaluate the marginalized likelihood of a dataset under a GP model. This is then be used alongside a non-linear optimization or posterior inference library for the best results.

Performance Evaluation of Satellite Communication Systems Operating in the Q/V/W Bands

DTIC Science & Technology

2013-06-30

cloud liquid water content (blue line = original MODIS data, red line = underlying Gaussian process) and of rainfall ( NIMROD rain rate data) .. 3-22...correlation of rainfall as obtained from an extensive set of rain field collected by the NIMROD weather radar network [Luini and Capsoni, 2012] has been...underlying Gaussian process) Rain ( NIMROD data) Figure 3-21. Decorrelation with distance of the cloud liquid water content (blue line = original

Experimental results of active control on a large structure to suppress vibration

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1991-01-01

Three design methods, Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR), H-infinity, and mu-synthesis, are used to obtain compensators for suppressing the vibrations of a 10-bay vertical truss structure, a component typical of what may be used to build a large space structure. For the design process the plant dynamic characteristics of the structure were determined experimentally using an identification method. The resulting compensators were implemented on a digital computer and tested for their ability to suppress the first bending mode response of the 10-bay vertical truss. Time histories of the measured motion are presented, and modal damping obtained during the experiments are compared with analytical predictions. The advantages and disadvantages of using the various design methods are discussed.

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.

An empirical analysis of the distribution of the duration of overshoots in a stationary gaussian stochastic process

NASA Technical Reports Server (NTRS)

Parrish, R. S.; Carter, M. C.

1974-01-01

This analysis utilizes computer simulation and statistical estimation. Realizations of stationary gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrelation parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters was estimated. Thus, given the autocorrelation parameter, crossing level, mean, and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time was calculated.

Marcus canonical integral for non-Gaussian processes and its computation: pathwise simulation and tau-leaping algorithm.

PubMed

Li, Tiejun; Min, Bin; Wang, Zhiming

2013-03-14

The stochastic integral ensuring the Newton-Leibnitz chain rule is essential in stochastic energetics. Marcus canonical integral has this property and can be understood as the Wong-Zakai type smoothing limit when the driving process is non-Gaussian. However, this important concept seems not well-known for physicists. In this paper, we discuss Marcus integral for non-Gaussian processes and its computation in the context of stochastic energetics. We give a comprehensive introduction to Marcus integral and compare three equivalent definitions in the literature. We introduce the exact pathwise simulation algorithm and give the error analysis. We show how to compute the thermodynamic quantities based on the pathwise simulation algorithm. We highlight the information hidden in the Marcus mapping, which plays the key role in determining thermodynamic quantities. We further propose the tau-leaping algorithm, which advance the process with deterministic time steps when tau-leaping condition is satisfied. The numerical experiments and its efficiency analysis show that it is very promising.

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

Remaining Useful Life Prediction for Lithium-Ion Batteries Based on Gaussian Processes Mixture

PubMed Central

Li, Lingling; Wang, Pengchong; Chao, Kuei-Hsiang; Zhou, Yatong; Xie, Yang

2016-01-01

The remaining useful life (RUL) prediction of Lithium-ion batteries is closely related to the capacity degeneration trajectories. Due to the self-charging and the capacity regeneration, the trajectories have the property of multimodality. Traditional prediction models such as the support vector machines (SVM) or the Gaussian Process regression (GPR) cannot accurately characterize this multimodality. This paper proposes a novel RUL prediction method based on the Gaussian Process Mixture (GPM). It can process multimodality by fitting different segments of trajectories with different GPR models separately, such that the tiny differences among these segments can be revealed. The method is demonstrated to be effective for prediction by the excellent predictive result of the experiments on the two commercial and chargeable Type 1850 Lithium-ion batteries, provided by NASA. The performance comparison among the models illustrates that the GPM is more accurate than the SVM and the GPR. In addition, GPM can yield the predictive confidence interval, which makes the prediction more reliable than that of traditional models. PMID:27632176

The Augmented Lagrange Multipliers Method for Matrix Completion from Corrupted Samplings with Application to Mixed Gaussian-Impulse Noise Removal

PubMed Central

Meng, Fan; Yang, Xiaomei; Zhou, Chenghu

2014-01-01

This paper studies the problem of the restoration of images corrupted by mixed Gaussian-impulse noise. In recent years, low-rank matrix reconstruction has become a research hotspot in many scientific and engineering domains such as machine learning, image processing, computer vision and bioinformatics, which mainly involves the problem of matrix completion and robust principal component analysis, namely recovering a low-rank matrix from an incomplete but accurate sampling subset of its entries and from an observed data matrix with an unknown fraction of its entries being arbitrarily corrupted, respectively. Inspired by these ideas, we consider the problem of recovering a low-rank matrix from an incomplete sampling subset of its entries with an unknown fraction of the samplings contaminated by arbitrary errors, which is defined as the problem of matrix completion from corrupted samplings and modeled as a convex optimization problem that minimizes a combination of the nuclear norm and the -norm in this paper. Meanwhile, we put forward a novel and effective algorithm called augmented Lagrange multipliers to exactly solve the problem. For mixed Gaussian-impulse noise removal, we regard it as the problem of matrix completion from corrupted samplings, and restore the noisy image following an impulse-detecting procedure. Compared with some existing methods for mixed noise removal, the recovery quality performance of our method is dominant if images possess low-rank features such as geometrically regular textures and similar structured contents; especially when the density of impulse noise is relatively high and the variance of Gaussian noise is small, our method can outperform the traditional methods significantly not only in the simultaneous removal of Gaussian noise and impulse noise, and the restoration ability for a low-rank image matrix, but also in the preservation of textures and details in the image. PMID:25248103

Generation and propagation of a sine-azimuthal wavefront modulated Gaussian beam

PubMed Central

Lao, Guanming; Zhang, Zhaohui; Luo, Meilan; Zhao, Daomu

2016-01-01

We introduce a method for modulating the Gaussian beam by means of sine-azimuthal wavefront and carry out the experimental generation. The analytical propagation formula of such a beam passing through a paraxial ABCD optical system is derived, by which the intensity properties of the sine-azimuthal wavefront modulated Gaussian (SWMG) beam are examined both theoretically and experimentally. Both of the experimental and theoretical results show that the SWMG beam goes through the process from beam splitting to a Gaussian-like profile, which is closely determined by the phase factor and the propagation distance. Appropriate phase factor and short distance are helpful for the splitting of beam. However, in the cases of large phase factor and focal plane, the intensity distributions tend to take a Gaussian form. Such unique features may be of importance in particle trapping and medical applications. PMID:27443798

Gate engineered heterostructure junctionless TFET with Gaussian doping profile for ambipolar suppression and electrical performance improvement

NASA Astrophysics Data System (ADS)

Aghandeh, Hadi; Sedigh Ziabari, Seyed Ali

2017-11-01

This study investigates a junctionless tunnel field-effect transistor with a dual material gate and a heterostructure channel/source interface (DMG-H-JLTFET). We find that using the heterostructure interface improves device behavior by reducing the tunneling barrier width at the channel/source interface. Simultaneously, the dual material gate structure decreases ambipolar current by increasing the tunneling barrier width at the drain/channel interface. The performance of the device is analyzed based on the energy band diagram at on, off, and ambipolar states. Numerical simulations demonstrate improvements in ION, IOFF, ION/IOFF, subthreshold slope (SS), transconductance and cut-off frequency and suppressed ambipolar behavior. Next, the workfunction optimization of dual material gate is studied. It is found that if appropriate workfunctions are selected for tunnel and auxiliary gates, the JLTFET exhibits considerably improved performance. We then study the influence of Gaussian doping distribution at the drain and the channel on the ambipolar performance of the device and find that a Gaussian doping profile and a dual material gate structure remarkably reduce ambipolar current. Gaussian doped DMG-H-JLTFET, also exhibits enhanced IOFF, ION/IOFF, SS and a low threshold voltage without degrading IOFF.

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.

Guided filtering for solar image/video processing

NASA Astrophysics Data System (ADS)

Xu, Long; Yan, Yihua; Cheng, Jun

2017-06-01

A new image enhancement algorithm employing guided filtering is proposed in this work for the enhancement of solar images and videos so that users can easily figure out important fine structures embedded in the recorded images/movies for solar observation. The proposed algorithm can efficiently remove image noises, including Gaussian and impulse noises. Meanwhile, it can further highlight fibrous structures on/beyond the solar disk. These fibrous structures can clearly demonstrate the progress of solar flare, prominence coronal mass emission, magnetic field, and so on. The experimental results prove that the proposed algorithm gives significant enhancement of visual quality of solar images beyond original input and several classical image enhancement algorithms, thus facilitating easier determination of interesting solar burst activities from recorded images/movies.

A Novel Signal Modeling Approach for Classification of Seizure and Seizure-Free EEG Signals.

PubMed

Gupta, Anubha; Singh, Pushpendra; Karlekar, Mandar

2018-05-01

This paper presents a signal modeling-based new methodology of automatic seizure detection in EEG signals. The proposed method consists of three stages. First, a multirate filterbank structure is proposed that is constructed using the basis vectors of discrete cosine transform. The proposed filterbank decomposes EEG signals into its respective brain rhythms: delta, theta, alpha, beta, and gamma. Second, these brain rhythms are statistically modeled with the class of self-similar Gaussian random processes, namely, fractional Brownian motion and fractional Gaussian noises. The statistics of these processes are modeled using a single parameter called the Hurst exponent. In the last stage, the value of Hurst exponent and autoregressive moving average parameters are used as features to design a binary support vector machine classifier to classify pre-ictal, inter-ictal (epileptic with seizure free interval), and ictal (seizure) EEG segments. The performance of the classifier is assessed via extensive analysis on two widely used data set and is observed to provide good accuracy on both the data set. Thus, this paper proposes a novel signal model for EEG data that best captures the attributes of these signals and hence, allows to boost the classification accuracy of seizure and seizure-free epochs.

On fatigue crack growth under random loading

NASA Astrophysics Data System (ADS)

Zhu, W. Q.; Lin, Y. K.; Lei, Y.

1992-09-01

A probabilistic analysis of the fatigue crack growth, fatigue life and reliability of a structural or mechanical component is presented on the basis of fracture mechanics and theory of random processes. The material resistance to fatigue crack growth and the time-history of the stress are assumed to be random. Analytical expressions are obtained for the special case in which the random stress is a stationary narrow-band Gaussian random process, and a randomized Paris-Erdogan law is applicable. As an example, the analytical method is applied to a plate with a central crack, and the results are compared with those obtained from digital Monte Carlo simulations.

Pure Gaussian state generation via dissipation: a quantum stochastic differential equation approach.

PubMed

Yamamoto, Naoki

2012-11-28

Recently, the complete characterization of a general Gaussian dissipative system having a unique pure steady state was obtained. This result provides a clear guideline for engineering an environment such that the dissipative system has a desired pure steady state such as a cluster state. In this paper, we describe the system in terms of a quantum stochastic differential equation (QSDE) so that the environment channels can be explicitly dealt with. Then, a physical meaning of that characterization, which cannot be seen without the QSDE representation, is clarified; more specifically, the nullifier dynamics of any Gaussian system generating a unique pure steady state is passive. In addition, again based on the QSDE framework, we provide a general and practical method to implement a desired dissipative Gaussian system, which has a structure of quantum state transfer.

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.

A real-time multi-scale 2D Gaussian filter based on FPGA

NASA Astrophysics Data System (ADS)

Luo, Haibo; Gai, Xingqin; Chang, Zheng; Hui, Bin

2014-11-01

Multi-scale 2-D Gaussian filter has been widely used in feature extraction (e.g. SIFT, edge etc.), image segmentation, image enhancement, image noise removing, multi-scale shape description etc. However, their computational complexity remains an issue for real-time image processing systems. Aimed at this problem, we propose a framework of multi-scale 2-D Gaussian filter based on FPGA in this paper. Firstly, a full-hardware architecture based on parallel pipeline was designed to achieve high throughput rate. Secondly, in order to save some multiplier, the 2-D convolution is separated into two 1-D convolutions. Thirdly, a dedicate first in first out memory named as CAFIFO (Column Addressing FIFO) was designed to avoid the error propagating induced by spark on clock. Finally, a shared memory framework was designed to reduce memory costs. As a demonstration, we realized a 3 scales 2-D Gaussian filter on a single ALTERA Cyclone III FPGA chip. Experimental results show that, the proposed framework can computing a Multi-scales 2-D Gaussian filtering within one pixel clock period, is further suitable for real-time image processing. Moreover, the main principle can be popularized to the other operators based on convolution, such as Gabor filter, Sobel operator and so on.

Ship Detection in SAR Image Based on the Alpha-stable Distribution

PubMed Central

Wang, Changcheng; Liao, Mingsheng; Li, Xiaofeng

2008-01-01

This paper describes an improved Constant False Alarm Rate (CFAR) ship detection algorithm in spaceborne synthetic aperture radar (SAR) image based on Alpha-stable distribution model. Typically, the CFAR algorithm uses the Gaussian distribution model to describe statistical characteristics of a SAR image background clutter. However, the Gaussian distribution is only valid for multilook SAR images when several radar looks are averaged. As sea clutter in SAR images shows spiky or heavy-tailed characteristics, the Gaussian distribution often fails to describe background sea clutter. In this study, we replace the Gaussian distribution with the Alpha-stable distribution, which is widely used in impulsive or spiky signal processing, to describe the background sea clutter in SAR images. In our proposed algorithm, an initial step for detecting possible ship targets is employed. Then, similar to the typical two-parameter CFAR algorithm, a local process is applied to the pixel identified as possible target. A RADARSAT-1 image is used to validate this Alpha-stable distribution based algorithm. Meanwhile, known ship location data during the time of RADARSAT-1 SAR image acquisition is used to validate ship detection results. Validation results show improvements of the new CFAR algorithm based on the Alpha-stable distribution over the CFAR algorithm based on the Gaussian distribution. PMID:27873794

Backscattering from a Gaussian distributed, perfectly conducting, rough surface

NASA Technical Reports Server (NTRS)

Brown, G. S.

1977-01-01

The problem of scattering by random surfaces possessing many scales of roughness is analyzed. The approach is applicable to bistatic scattering from dielectric surfaces, however, this specific analysis is restricted to backscattering from a perfectly conducting surface in order to more clearly illustrate the method. The surface is assumed to be Gaussian distributed so that the surface height can be split into large and small scale components, relative to the electromagnetic wavelength. A first order perturbation approach is employed wherein the scattering solution for the large scale structure is perturbed by the small scale diffraction effects. The scattering from the large scale structure is treated via geometrical optics techniques. The effect of the large scale surface structure is shown to be equivalent to a convolution in k-space of the height spectrum with the following: the shadowing function, a polarization and surface slope dependent function, and a Gaussian factor resulting from the unperturbed geometrical optics solution. This solution provides a continuous transition between the near normal incidence geometrical optics and wide angle Bragg scattering results.

Reproducing the Ensemble Average Polar Solvation Energy of a Protein from a Single Structure: Gaussian-Based Smooth Dielectric Function for Macromolecular Modeling.

PubMed

Chakravorty, Arghya; Jia, Zhe; Li, Lin; Zhao, Shan; Alexov, Emil

2018-02-13

Typically, the ensemble average polar component of solvation energy (ΔG polar solv ) of a macromolecule is computed using molecular dynamics (MD) or Monte Carlo (MC) simulations to generate conformational ensemble and then single/rigid conformation solvation energy calculation is performed on each snapshot. The primary objective of this work is to demonstrate that Poisson-Boltzmann (PB)-based approach using a Gaussian-based smooth dielectric function for macromolecular modeling previously developed by us (Li et al. J. Chem. Theory Comput. 2013, 9 (4), 2126-2136) can reproduce that ensemble average (ΔG polar solv ) of a protein from a single structure. We show that the Gaussian-based dielectric model reproduces the ensemble average ΔG polar solv (⟨ΔG polar solv ⟩) from an energy-minimized structure of a protein regardless of the minimization environment (structure minimized in vacuo, implicit or explicit waters, or crystal structure); the best case, however, is when it is paired with an in vacuo-minimized structure. In other minimization environments (implicit or explicit waters or crystal structure), the traditional two-dielectric model can still be selected with which the model produces correct solvation energies. Our observations from this work reflect how the ability to appropriately mimic the motion of residues, especially the salt bridge residues, influences a dielectric model's ability to reproduce the ensemble average value of polar solvation free energy from a single in vacuo-minimized structure.

Optimization of nonlinear, non-Gaussian Bayesian filtering for diagnosis and prognosis of monotonic degradation processes

NASA Astrophysics Data System (ADS)

Corbetta, Matteo; Sbarufatti, Claudio; Giglio, Marco; Todd, Michael D.

2018-05-01

The present work critically analyzes the probabilistic definition of dynamic state-space models subject to Bayesian filters used for monitoring and predicting monotonic degradation processes. The study focuses on the selection of the random process, often called process noise, which is a key perturbation source in the evolution equation of particle filtering. Despite the large number of applications of particle filtering predicting structural degradation, the adequacy of the picked process noise has not been investigated. This paper reviews existing process noise models that are typically embedded in particle filters dedicated to monitoring and predicting structural damage caused by fatigue, which is monotonic in nature. The analysis emphasizes that existing formulations of the process noise can jeopardize the performance of the filter in terms of state estimation and remaining life prediction (i.e., damage prognosis). This paper subsequently proposes an optimal and unbiased process noise model and a list of requirements that the stochastic model must satisfy to guarantee high prognostic performance. These requirements are useful for future and further implementations of particle filtering for monotonic system dynamics. The validity of the new process noise formulation is assessed against experimental fatigue crack growth data from a full-scale aeronautical structure using dedicated performance metrics.

Efficient statistically accurate algorithms for the Fokker-Planck equation in large dimensions

NASA Astrophysics Data System (ADS)

Chen, Nan; Majda, Andrew J.

2018-02-01

Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing the fat tailed highly intermittent probability density functions (PDFs) of complex systems in turbulence, neuroscience and excitable media. In this article, efficient statistically accurate algorithms are developed for solving both the transient and the equilibrium solutions of Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures. The algorithms involve a hybrid strategy that requires only a small number of ensembles. Here, a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious non-parametric Gaussian kernel density estimation in the remaining low-dimensional subspace. Particularly, the parametric method provides closed analytical formulae for determining the conditional Gaussian distributions in the high-dimensional subspace and is therefore computationally efficient and accurate. The full non-Gaussian PDF of the system is then given by a Gaussian mixture. Different from traditional particle methods, each conditional Gaussian distribution here covers a significant portion of the high-dimensional PDF. Therefore a small number of ensembles is sufficient to recover the full PDF, which overcomes the curse of dimensionality. Notably, the mixture distribution has significant skill in capturing the transient behavior with fat tails of the high-dimensional non-Gaussian PDFs, and this facilitates the algorithms in accurately describing the intermittency and extreme events in complex turbulent systems. It is shown in a stringent set of test problems that the method only requires an order of O (100) ensembles to successfully recover the highly non-Gaussian transient PDFs in up to 6 dimensions with only small errors.

Permutation entropy of fractional Brownian motion and fractional Gaussian noise

NASA Astrophysics Data System (ADS)

Zunino, L.; Pérez, D. G.; Martín, M. T.; Garavaglia, M.; Plastino, A.; Rosso, O. A.

2008-06-01

We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays.

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.

Can we use the q-Gaussian of ambient noise fluctuations as a vulnerability index? A case study in Cultural Heritage buildings

NASA Astrophysics Data System (ADS)

Vallianatos, Filippos; Koutalonis, Ioannis; Moisidi, Margarita; Chatzopoulos, Georgios

2018-05-01

In this work we study in terms of Tsallis statistical mechanics the properties of microtremors' fluctuations in two church bell towers, which are monuments of cultural heritage, in the city of Chania (Crete, Greece). We have shown that fluctuations of ambient vibrations recordings in the Church tower bells follow a q-Gaussian distribution. The behavior of Tsallis q parameter with the level (high) of the measuring point within the tower and the amplification factors at that points as extracted from horizontal-to-vertical (HVSR) spectral ratios are presented and discussed. Since q decreases as the amplification factor increases, we could suggest q as a vulnerability index, where, as q decreases approaching unity, then the structural system is getting more vulnerable. The latter approach suggests that introducing ideas of Tsallis statistics could be useful in characterizing extremely complex processes as that governed the estimation of seismic vulnerability in which a multidisciplinary approach is required.

Extended wavelet transformation to digital holographic reconstruction: application to the elliptical, astigmatic Gaussian beams.

PubMed

Remacha, Clément; Coëtmellec, Sébastien; Brunel, Marc; Lebrun, Denis

2013-02-01

Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented.

Parameterization of cloud lidar backscattering profiles by means of asymmetrical Gaussians

NASA Astrophysics Data System (ADS)

del Guasta, Massimo; Morandi, Marco; Stefanutti, Leopoldo

1995-06-01

A fitting procedure for cloud lidar data processing is shown that is based on the computation of the first three moments of the vertical-backscattering (or -extinction) profile. Single-peak clouds or single cloud layers are approximated to asymmetrical Gaussians. The algorithm is particularly stable with respect to noise and processing errors, and it is much faster than the equivalent least-squares approach. Multilayer clouds can easily be treated as a sum of single asymmetrical Gaussian peaks. The method is suitable for cloud-shape parametrization in noisy lidar signatures (like those expected from satellite lidars). It also permits an improvement of cloud radiative-property computations that are based on huge lidar data sets for which storage and careful examination of single lidar profiles can't be carried out.

FROM FINANCE TO COSMOLOGY: THE COPULA OF LARGE-SCALE STRUCTURE

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

Scherrer, Robert J.; Berlind, Andreas A.; Mao, Qingqing

2010-01-01

Any multivariate distribution can be uniquely decomposed into marginal (one-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an important new methodology for analyzing the density field in large-scale structure. We derive the empirical two-point copula for the evolved dark matter density field. We find that this empirical copula is well approximated by a Gaussian copula. We consider the possibility that the full n-point copula is also Gaussian and describe some of the consequences of this hypothesis. Future directions for investigation are discussed.

Nanostructuring of sapphire using time-modulated nanosecond laser pulses

NASA Astrophysics Data System (ADS)

Lorenz, P.; Zagoranskiy, I.; Ehrhardt, M.; Bayer, L.; Zimmer, K.

2017-02-01

The nanostructuring of dielectric surfaces using laser radiation is still a challenge. The IPSM-LIFE (laser-induced front side etching using in-situ pre-structured metal layer) method allows the easy, large area and fast laser nanostructuring of dielectrics. At IPSM-LIFE a metal covered dielectric is irradiated where the structuring is assisted by a self-organized molten metal layer deformation process. The IPSM-LIFE can be divided into two steps: STEP 1: The irradiation of thin metal layers on dielectric surfaces results in a melting and nanostructuring process of the metal layer and partially of the dielectric surface. STEP 2: A subsequent high laser fluence treatment of the metal nanostructures result in a structuring of the dielectric surface. At this study a sapphire substrate Al2O3(1-102) was covered with a 10 nm thin molybdenum layer and irradiated by an infrared laser with an adjustable time-dependent pulse form with a time resolution of 1 ns (wavelength λ = 1064 nm, pulse duration Δtp = 1 - 600 ns, Gaussian beam profile). The laser treatment allows the fabrication of different surface structures into the sapphire surface due to a pattern transfer process. The resultant structures were investigated by scanning electron microscopy (SEM). The process was simulated and the simulation results were compared with experimental results.

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

A brain MRI bias field correction method created in the Gaussian multi-scale space

NASA Astrophysics Data System (ADS)

Chen, Mingsheng; Qin, Mingxin

2017-07-01

A pre-processing step is needed to correct for the bias field signal before submitting corrupted MR images to such image-processing algorithms. This study presents a new bias field correction method. The method creates a Gaussian multi-scale space by the convolution of the inhomogeneous MR image with a two-dimensional Gaussian function. In the multi-Gaussian space, the method retrieves the image details from the differentiation of the original image and convolution image. Then, it obtains an image whose inhomogeneity is eliminated by the weighted sum of image details in each layer in the space. Next, the bias field-corrected MR image is retrieved after the Υ correction, which enhances the contrast and brightness of the inhomogeneity-eliminated MR image. We have tested the approach on T1 MRI and T2 MRI with varying bias field levels and have achieved satisfactory results. Comparison experiments with popular software have demonstrated superior performance of the proposed method in terms of quantitative indices, especially an improvement in subsequent image segmentation.

Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence

NASA Astrophysics Data System (ADS)

Adesso, Gerardo; Serafini, Alessio; Illuminati, Fabrizio

2006-03-01

We present a complete analysis of the multipartite entanglement of three-mode Gaussian states of continuous-variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations can be quantified by a proper convex roof extension of the squared logarithmic negativity, the continuous-variable tangle, or contangle. We review and elucidate in detail the proof that in multimode Gaussian states the contangle satisfies a monogamy inequality constraint [G. Adesso and F. Illuminati, New J. Phys8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communications and defines a measure of genuine tripartite entanglements. We determine the analytical expression of the residual contangle for arbitrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such states. This analysis yields that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/W states of continuous-variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the W states of three qubits. We finally consider the effect of decoherence on three-mode Gaussian states, studying the decay of the residual contangle. The GHZ/W states are shown to be maximally robust against losses and thermal noise.

Fast and Accurate Multivariate Gaussian Modeling of Protein Families: Predicting Residue Contacts and Protein-Interaction Partners

PubMed Central

Feinauer, Christoph; Procaccini, Andrea; Zecchina, Riccardo; Weigt, Martin; Pagnani, Andrea

2014-01-01

In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our method aims at extracting such constraints from rapidly accumulating sequence data, and thereby at inferring protein structure and function from sequence information alone. Recently, global statistical inference methods (e.g. direct-coupling analysis, sparse inverse covariance estimation) have achieved a breakthrough towards this aim, and their predictions have been successfully implemented into tertiary and quaternary protein structure prediction methods. However, due to the discrete nature of the underlying variable (amino-acids), exact inference requires exponential time in the protein length, and efficient approximations are needed for practical applicability. Here we propose a very efficient multivariate Gaussian modeling approach as a variant of direct-coupling analysis: the discrete amino-acid variables are replaced by continuous Gaussian random variables. The resulting statistical inference problem is efficiently and exactly solvable. We show that the quality of inference is comparable or superior to the one achieved by mean-field approximations to inference with discrete variables, as done by direct-coupling analysis. This is true for (i) the prediction of residue-residue contacts in proteins, and (ii) the identification of protein-protein interaction partner in bacterial signal transduction. An implementation of our multivariate Gaussian approach is available at the website http://areeweb.polito.it/ricerca/cmp/code. PMID:24663061

PAREMD: A parallel program for the evaluation of momentum space properties of atoms and molecules

NASA Astrophysics Data System (ADS)

Meena, Deep Raj; Gadre, Shridhar R.; Balanarayan, P.

2018-03-01

The present work describes a code for evaluating the electron momentum density (EMD), its moments and the associated Shannon information entropy for a multi-electron molecular system. The code works specifically for electronic wave functions obtained from traditional electronic structure packages such as GAMESS and GAUSSIAN. For the momentum space orbitals, the general expression for Gaussian basis sets in position space is analytically Fourier transformed to momentum space Gaussian basis functions. The molecular orbital coefficients of the wave function are taken as an input from the output file of the electronic structure calculation. The analytic expressions of EMD are evaluated over a fine grid and the accuracy of the code is verified by a normalization check and a numerical kinetic energy evaluation which is compared with the analytic kinetic energy given by the electronic structure package. Apart from electron momentum density, electron density in position space has also been integrated into this package. The program is written in C++ and is executed through a Shell script. It is also tuned for multicore machines with shared memory through OpenMP. The program has been tested for a variety of molecules and correlated methods such as CISD, Møller-Plesset second order (MP2) theory and density functional methods. For correlated methods, the PAREMD program uses natural spin orbitals as an input. The program has been benchmarked for a variety of Gaussian basis sets for different molecules showing a linear speedup on a parallel architecture.

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

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.

Spin-Hall effect in the scattering of structured light from plasmonic nanowire

NASA Astrophysics Data System (ADS)

Sharma, Deepak K.; Kumar, Vijay; Vasista, Adarsh B.; Chaubey, Shailendra K.; Kumar, G. V. Pavan

2018-06-01

Spin-orbit interactions are subwavelength phenomena which can potentially lead to numerous device related applications in nanophotonics. Here, we report Spin-Hall effect in the forward scattering of Hermite-Gaussian and Gaussian beams from a plasmonic nanowire. Asymmetric scattered radiation distribution was observed for circularly polarized beams. Asymmetry in the scattered radiation distribution changes the sign when the polarization handedness inverts. We found a significant enhancement in the Spin-Hall effect for Hermite-Gaussian beam as compared to Gaussian beam for constant input power. The difference between scattered powers perpendicular to the long axis of the plasmonic nanowire was used to quantify the enhancement. In addition to it, nodal line of HG beam acts as the marker for the Spin-Hall shift. Numerical calculations corroborate experimental observations and suggest that the Spin flow component of Poynting vector associated with the circular polarization is responsible for the Spin-Hall effect and its enhancement.

A new method for the identification of non-Gaussian line profiles in elliptical galaxies

NASA Technical Reports Server (NTRS)

Van Der Marel, Roeland P.; Franx, Marijn

1993-01-01

A new parameterization for the line profiles of elliptical galaxies, the Gauss-Hermite series, is proposed. This approach expands the line profile as a sum of orthogonal functions which minimizes the correlations between the errors in the parameters of the fit. This method also make use of the fact that Gaussians provide good low-order fits to observed line profiles. The method yields measurements of the line strength, mean radial velocity, and the velocity dispersion as well as two extra parameters, h3 and h4, that measure asymmetric and symmetric deviations of the line profiles from a Gaussian, respectively. The new method was used to derive profiles for three elliptical galaxies which all have asymmetric line profiles on the major axis with symmetric deviations from a Gaussian. Results confirm that elliptical galaxies have complex structures due to their complex formation history.

Beyond Roughness: Maximum-Likelihood Estimation of Topographic "Structure" on Venus and Elsewhere in the Solar System

NASA Astrophysics Data System (ADS)

Simons, F. J.; Eggers, G. L.; Lewis, K. W.; Olhede, S. C.

2015-12-01

What numbers "capture" topography? If stationary, white, and Gaussian: mean and variance. But "whiteness" is strong; we are led to a "baseline" over which to compute means and variances. We then have subscribed to topography as a correlated process, and to the estimation (noisy, afftected by edge effects) of the parameters of a spatial or spectral covariance function. What if the covariance function or the point process itself aren't Gaussian? What if the region under study isn't regularly shaped or sampled? How can results from differently sized patches be compared robustly? We present a spectral-domain "Whittle" maximum-likelihood procedure that circumvents these difficulties and answers the above questions. The key is the Matern form, whose parameters (variance, range, differentiability) define the shape of the covariance function (Gaussian, exponential, ..., are all special cases). We treat edge effects in simulation and in estimation. Data tapering allows for the irregular regions. We determine the estimation variance of all parameters. And the "best" estimate may not be "good enough": we test whether the "model" itself warrants rejection. We illustrate our methodology on geologically mapped patches of Venus. Surprisingly few numbers capture planetary topography. We derive them, with uncertainty bounds, we simulate "new" realizations of patches that look to the geologists exactly as if they were derived from similar processes. Our approach holds in 1, 2, and 3 spatial dimensions, and generalizes to multiple variables, e.g. when topography and gravity are being considered jointly (perhaps linked by flexural rigidity, erosion, or other surface and sub-surface modifying processes). Our results have widespread implications for the study of planetary topography in the Solar System, and are interpreted in the light of trying to derive "process" from "parameters", the end goal to assign likely formation histories for the patches under consideration. Our results should also be relevant for whomever needed to perform spatial interpolation or out-of-sample extension (e.g. kriging), machine learning and feature detection, on geological data. We present procedural details but focus on high-level results that have real-world implications for the study of Venus, Earth, other planets, and moons.

SU-G-IeP3-08: Image Reconstruction for Scanning Imaging System Based On Shape-Modulated Point Spreading Function

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

Wang, Ruixing; Yang, LV; Xu, Kele

Purpose: Deconvolution is a widely used tool in the field of image reconstruction algorithm when the linear imaging system has been blurred by the imperfect system transfer function. However, due to the nature of Gaussian-liked distribution for point spread function (PSF), the components with coherent high frequency in the image are hard to restored in most of the previous scanning imaging system, even the relatively accurate PSF is acquired. We propose a novel method for deconvolution of images which are obtained by using shape-modulated PSF. Methods: We use two different types of PSF - Gaussian shape and donut shape -more » to convolute the original image in order to simulate the process of scanning imaging. By employing deconvolution of the two images with corresponding given priors, the image quality of the deblurred images are compared. Then we find the critical size of the donut shape compared with the Gaussian shape which has similar deconvolution results. Through calculation of tightened focusing process using radially polarized beam, such size of donut is achievable under same conditions. Results: The effects of different relative size of donut and Gaussian shapes are investigated. When the full width at half maximum (FWHM) ratio of donut and Gaussian shape is set about 1.83, similar resolution results are obtained through our deconvolution method. Decreasing the size of donut will favor the deconvolution method. A mask with both amplitude and phase modulation is used to create a donut-shaped PSF compared with the non-modulated Gaussian PSF. Donut with size smaller than our critical value is obtained. Conclusion: The utility of donutshaped PSF are proved useful and achievable in the imaging and deconvolution processing, which is expected to have potential practical applications in high resolution imaging for biological samples.« less

Large Footprint LiDAR Data Processing for Ground Detection and Biomass Estimation

NASA Astrophysics Data System (ADS)

Zhuang, Wei

Ground detection in large footprint waveform Light Detection And Ranging (LiDAR) data is important in calculating and estimating downstream products, especially in forestry applications. For example, tree heights are calculated as the difference between the ground peak and first returned signal in a waveform. Forest attributes, such as aboveground biomass, are estimated based on the tree heights. This dissertation investigated new metrics and algorithms for estimating aboveground biomass and extracting ground peak location in large footprint waveform LiDAR data. In the first manuscript, an accurate and computationally efficient algorithm, named Filtering and Clustering Algorithm (FICA), was developed based on a set of multiscale second derivative filters for automatically detecting the ground peak in an waveform from Land, Vegetation and Ice Sensor. Compared to existing ground peak identification algorithms, FICA was tested in different land cover type plots and showed improved accuracy in ground detections of the vegetation plots and similar accuracy in developed area plots. Also, FICA adopted a peak identification strategy rather than following a curve-fitting process, and therefore, exhibited improved efficiency. In the second manuscript, an algorithm was developed specifically for shrub waveforms. The algorithm only partially fitted the shrub canopy reflection and detected the ground peak by investigating the residual signal, which was generated by deducting a Gaussian fitting function from the raw waveform. After the deduction, the overlapping ground peak was identified as the local maximum of the residual signal. In addition, an applicability model was built for determining waveforms where the proposed PCF algorithm should be applied. In the third manuscript, a new set of metrics was developed to increase accuracy in biomass estimation models. The metrics were based on the results of Gaussian decomposition. They incorporated both waveform intensity represented by the area covered by a Gaussian function and its associated heights, which was the centroid of the Gaussian function. By considering signal reflection of different vegetation layers, the developed metrics obtained better estimation accuracy in aboveground biomass when compared to existing metrics. In addition, the new developed metrics showed strong correlation with other forest structural attributes, such as mean Diameter at Breast Height (DBH) and stem density. In sum, the dissertation investigated the various techniques for large footprint waveform LiDAR processing for detecting the ground peak and estimating biomass. The novel techniques developed in this dissertation showed better performance than existing methods or metrics.

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

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.

Dynamics of a Landau-Zener non-dissipative system with fluctuating energy levels

NASA Astrophysics Data System (ADS)

Fai, L. C.; Diffo, J. T.; Ateuafack, M. E.; Tchoffo, M.; Fouokeng, G. C.

2014-12-01

This paper considers a Landau-Zener (two-level) system influenced by a three-dimensional Gaussian and non-Gaussian coloured noise and finds a general form of the time dependent diabatic quantum bit (qubit) flip transition probabilities in the fast, intermediate and slow noise limits. The qubit flip probability is observed to mimic (for low-frequencies noise) that of the standard LZ problem. The qubit flip probability is also observed to be the measure of quantum coherence of states. The transition probability is observed to be tailored by non-Gaussian low-frequency noise and otherwise by Gaussian low-frequency coloured noise. Intermediate and fast noise limits are observed to alter the memory of the system in time and found to improve and control quantum information processing.

Local pulmonary structure classification for computer-aided nodule detection

NASA Astrophysics Data System (ADS)

Bahlmann, Claus; Li, Xianlin; Okada, Kazunori

2006-03-01

We propose a new method of classifying the local structure types, such as nodules, vessels, and junctions, in thoracic CT scans. This classification is important in the context of computer aided detection (CAD) of lung nodules. The proposed method can be used as a post-process component of any lung CAD system. In such a scenario, the classification results provide an effective means of removing false positives caused by vessels and junctions thus improving overall performance. As main advantage, the proposed solution transforms the complex problem of classifying various 3D topological structures into much simpler 2D data clustering problem, to which more generic and flexible solutions are available in literature, and which is better suited for visualization. Given a nodule candidate, first, our solution robustly fits an anisotropic Gaussian to the data. The resulting Gaussian center and spread parameters are used to affine-normalize the data domain so as to warp the fitted anisotropic ellipsoid into a fixed-size isotropic sphere. We propose an automatic method to extract a 3D spherical manifold, containing the appropriate bounding surface of the target structure. Scale selection is performed by a data driven entropy minimization approach. The manifold is analyzed for high intensity clusters, corresponding to protruding structures. Techniques involve EMclustering with automatic mode number estimation, directional statistics, and hierarchical clustering with a modified Bhattacharyya distance. The estimated number of high intensity clusters explicitly determines the type of pulmonary structures: nodule (0), attached nodule (1), vessel (2), junction (>3). We show accurate classification results for selected examples in thoracic CT scans. This local procedure is more flexible and efficient than current state of the art and will help to improve the accuracy of general lung CAD systems.

Soliton propagation in tapered silicon core fibers.

PubMed

Peacock, Anna C

2010-11-01

Numerical simulations are used to investigate soliton-like propagation in tapered silicon core optical fibers. The simulations are based on a realistic tapered structure with nanoscale core dimensions and a decreasing anomalous dispersion profile to compensate for the effects of linear and nonlinear loss. An intensity misfit parameter is used to establish the optimum taper dimensions that preserve the pulse shape while reducing temporal broadening. Soliton formation from Gaussian input pulses is also observed--further evidence of the potential for tapered silicon fibers to find use in a range of signal processing applications.

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.

'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.

A Gaussian Processes Technique for Short-term Load Forecasting with Considerations of Uncertainty

NASA Astrophysics Data System (ADS)

Ohmi, Masataro; Mori, Hiroyuki

In this paper, an efficient method is proposed to deal with short-term load forecasting with the Gaussian Processes. Short-term load forecasting plays a key role to smooth power system operation such as economic load dispatching, unit commitment, etc. Recently, the deregulated and competitive power market increases the degree of uncertainty. As a result, it is more important to obtain better prediction results to save the cost. One of the most important aspects is that power system operator needs the upper and lower bounds of the predicted load to deal with the uncertainty while they require more accurate predicted values. The proposed method is based on the Bayes model in which output is expressed in a distribution rather than a point. To realize the model efficiently, this paper proposes the Gaussian Processes that consists of the Bayes linear model and kernel machine to obtain the distribution of the predicted value. The proposed method is successively applied to real data of daily maximum load forecasting.

Gaussian process tomography for soft x-ray spectroscopy at WEST without equilibrium information

NASA Astrophysics Data System (ADS)

Wang, T.; Mazon, D.; Svensson, J.; Li, D.; Jardin, A.; Verdoolaege, G.

2018-06-01

Gaussian process tomography (GPT) is a recently developed tomography method based on the Bayesian probability theory [J. Svensson, JET Internal Report EFDA-JET-PR(11)24, 2011 and Li et al., Rev. Sci. Instrum. 84, 083506 (2013)]. By modeling the soft X-ray (SXR) emissivity field in a poloidal cross section as a Gaussian process, the Bayesian SXR tomography can be carried out in a robust and extremely fast way. Owing to the short execution time of the algorithm, GPT is an important candidate for providing real-time reconstructions with a view to impurity transport and fast magnetohydrodynamic control. In addition, the Bayesian formalism allows quantifying uncertainty on the inferred parameters. In this paper, the GPT technique is validated using a synthetic data set expected from the WEST tokamak, and the results are shown of its application to the reconstruction of SXR emissivity profiles measured on Tore Supra. The method is compared with the standard algorithm based on minimization of the Fisher information.

Log-normal distribution from a process that is not multiplicative but is additive.

PubMed

Mouri, Hideaki

2013-10-01

The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal distribution. Although the sum tends eventually to a Gaussian distribution, the distribution of the sum is always close to a log-normal distribution rather than to any Gaussian distribution if the summands are numerous enough. This is in contrast to the current consensus that any log-normal distribution is due to a product of random variables, i.e., a multiplicative process, or equivalently to nonlinearity of the system. In fact, the log-normal distribution is also observable for a sum, i.e., an additive process that is typical of linear systems. We show conditions for such a sum, an analytical example, and an application to random scalar fields such as those of turbulence.

Recovering Galaxy Properties Using Gaussian Process SED Fitting

NASA Astrophysics Data System (ADS)

Iyer, Kartheik; Awan, Humna

2018-01-01

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

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.

gWEGA: GPU-accelerated WEGA for molecular superposition and shape comparison.

PubMed

Yan, Xin; Li, Jiabo; Gu, Qiong; Xu, Jun

2014-06-05

Virtual screening of a large chemical library for drug lead identification requires searching/superimposing a large number of three-dimensional (3D) chemical structures. This article reports a graphic processing unit (GPU)-accelerated weighted Gaussian algorithm (gWEGA) that expedites shape or shape-feature similarity score-based virtual screening. With 86 GPU nodes (each node has one GPU card), gWEGA can screen 110 million conformations derived from an entire ZINC drug-like database with diverse antidiabetic agents as query structures within 2 s (i.e., screening more than 55 million conformations per second). The rapid screening speed was accomplished through the massive parallelization on multiple GPU nodes and rapid prescreening of 3D structures (based on their shape descriptors and pharmacophore feature compositions). Copyright © 2014 Wiley Periodicals, Inc.

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

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

Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu; Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089; Ghanem, Roger G., E-mail: ghanem@usc.edu

2017-07-15

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

NASA Astrophysics Data System (ADS)

Tsilifis, Panagiotis; Ghanem, Roger G.

2017-07-01

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

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

Crack propagation monitoring in a full-scale aircraft fatigue test based on guided wave-Gaussian mixture model

NASA Astrophysics Data System (ADS)

Qiu, Lei; Yuan, Shenfang; Bao, Qiao; Mei, Hanfei; Ren, Yuanqiang

2016-05-01

For aerospace application of structural health monitoring (SHM) technology, the problem of reliable damage monitoring under time-varying conditions must be addressed and the SHM technology has to be fully validated on real aircraft structures under realistic load conditions on ground before it can reach the status of flight test. In this paper, the guided wave (GW) based SHM method is applied to a full-scale aircraft fatigue test which is one of the most similar test status to the flight test. To deal with the time-varying problem, a GW-Gaussian mixture model (GW-GMM) is proposed. The probability characteristic of GW features, which is introduced by time-varying conditions is modeled by GW-GMM. The weak cumulative variation trend of the crack propagation, which is mixed in time-varying influence can be tracked by the GW-GMM migration during on-line damage monitoring process. A best match based Kullback-Leibler divergence is proposed to measure the GW-GMM migration degree to reveal the crack propagation. The method is validated in the full-scale aircraft fatigue test. The validation results indicate that the reliable crack propagation monitoring of the left landing gear spar and the right wing panel under realistic load conditions are achieved.

Improving particle filters in rainfall-runoff models: application of the resample-move step and development of the ensemble Gaussian particle filter

NASA Astrophysics Data System (ADS)

Plaza Guingla, D. A.; Pauwels, V. R.; De Lannoy, G. J.; Matgen, P.; Giustarini, L.; De Keyser, R.

2012-12-01

The objective of this work is to analyze the improvement in the performance of the particle filter by including a resample-move step or by using a modified Gaussian particle filter. Specifically, the standard particle filter structure is altered by the inclusion of the Markov chain Monte Carlo move step. The second choice adopted in this study uses the moments of an ensemble Kalman filter analysis to define the importance density function within the Gaussian particle filter structure. Both variants of the standard particle filter are used in the assimilation of densely sampled discharge records into a conceptual rainfall-runoff model. In order to quantify the obtained improvement, discharge root mean square errors are compared for different particle filters, as well as for the ensemble Kalman filter. First, a synthetic experiment is carried out. The results indicate that the performance of the standard particle filter can be improved by the inclusion of the resample-move step, but its effectiveness is limited to situations with limited particle impoverishment. The results also show that the modified Gaussian particle filter outperforms the rest of the filters. Second, a real experiment is carried out in order to validate the findings from the synthetic experiment. The addition of the resample-move step does not show a considerable improvement due to performance limitations in the standard particle filter with real data. On the other hand, when an optimal importance density function is used in the Gaussian particle filter, the results show a considerably improved performance of the particle filter.

Non-Gaussian structure of B-mode polarization after delensing

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

Namikawa, Toshiya; Nagata, Ryo, E-mail: namikawa@slac.stanford.edu, E-mail: rnagata@post.kek.jp

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less

Non-Gaussian structure of B-mode polarization after delensing

NASA Astrophysics Data System (ADS)

Namikawa, Toshiya; Nagata, Ryo

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. In this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. As a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.

Non-Gaussian structure of B-mode polarization after delensing

DOE PAGES

Namikawa, Toshiya; Nagata, Ryo

2015-10-01

The B-mode polarization of the cosmic microwave background on large scales has been considered as a probe of gravitational waves from the cosmic inflation. Ongoing and future experiments will, however, suffer from contamination due to the B-modes of non-primordial origins, one of which is the lensing induced B-mode polarization. Subtraction of the lensing B-modes, usually referred to as delensing, will be required for further improvement of detection sensitivity of the gravitational waves. In such experiments, knowledge of statistical properties of the B-modes after delensing is indispensable to likelihood analysis particularly because the lensing B-modes are known to be non-Gaussian. Inmore » this paper, we study non-Gaussian structure of the delensed B-modes on large scales, comparing it with that of the lensing B-modes. In particular, we investigate the power spectrum correlation matrix and the probability distribution function (PDF) of the power spectrum amplitude. Assuming an experiment in which the quadratic delensing is an almost optimal method, we find that delensing reduces correlations of the lensing B-mode power spectra between different multipoles, and that the PDF of the power spectrum amplitude is well described as a normal distribution function with a variance larger than that in the case of a Gaussian field. These features are well captured by an analytic model based on the 4th order Edgeworth expansion. Furthermore, as a consequence of the non-Gaussianity, the constraint on the tensor-to-scalar ratio after delensing is degraded within approximately a few percent, which depends on the multipole range included in the analysis.« less

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Entanglement sensitivity to signal attenuation and amplification

NASA Astrophysics Data System (ADS)

Filippov, Sergey N.; Ziman, Mário

2014-07-01

We analyze general laws of continuous-variable entanglement dynamics during the deterministic attenuation and amplification of the physical signal carrying the entanglement. These processes are inevitably accompanied by noises, so we find fundamental limitations on noise intensities that destroy entanglement of Gaussian and non-Gaussian input states. The phase-insensitive amplification Φ1⊗Φ2⊗⋯ΦN with the power gain κi≥2 (≈3 dB, i =1,...,N) is shown to destroy entanglement of any N-mode Gaussian state even in the case of quantum-limited performance. In contrast, we demonstrate non-Gaussian states with the energy of a few photons such that their entanglement survives within a wide range of noises beyond quantum-limited performance for any degree of attenuation or gain. We detect entanglement preservation properties of the channel Φ1⊗Φ2, where each mode is deterministically attenuated or amplified. Gaussian states of high energy are shown to be robust to very asymmetric attenuations, whereas non-Gaussian states are at an advantage in the case of symmetric attenuation and general amplification. If Φ1=Φ2, the total noise should not exceed 1/2√κ2+1 to guarantee entanglement preservation.

Genuine multipartite entanglement of symmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure

NASA Astrophysics Data System (ADS)

Adesso, Gerardo; Illuminati, Fabrizio

2008-10-01

We investigate the structural aspects of genuine multipartite entanglement in Gaussian states of continuous variable systems. Generalizing the results of Adesso and Illuminati [Phys. Rev. Lett. 99, 150501 (2007)], we analyze whether the entanglement shared by blocks of modes distributes according to a strong monogamy law. This property, once established, allows us to quantify the genuine N -partite entanglement not encoded into 2,…,K,…,(N-1) -partite quantum correlations. Strong monogamy is numerically verified, and the explicit expression of the measure of residual genuine multipartite entanglement is analytically derived, by a recursive formula, for a subclass of Gaussian states. These are fully symmetric (permutation-invariant) states that are multipartitioned into blocks, each consisting of an arbitrarily assigned number of modes. We compute the genuine multipartite entanglement shared by the blocks of modes and investigate its scaling properties with the number and size of the blocks, the total number of modes, the global mixedness of the state, and the squeezed resources needed for state engineering. To achieve the exact computation of the block entanglement, we introduce and prove a general result of symplectic analysis: Correlations among K blocks in N -mode multisymmetric and multipartite Gaussian states, which are locally invariant under permutation of modes within each block, can be transformed by a local (with respect to the partition) unitary operation into correlations shared by K single modes, one per block, in effective nonsymmetric states where N-K modes are completely uncorrelated. Due to this theorem, the above results, such as the derivation of the explicit expression for the residual multipartite entanglement, its nonnegativity, and its scaling properties, extend to the subclass of non-symmetric Gaussian states that are obtained by the unitary localization of the multipartite entanglement of symmetric states. These findings provide strong numerical evidence that the distributed Gaussian entanglement is strongly monogamous under and possibly beyond specific symmetry constraints, and that the residual continuous-variable tangle is a proper measure of genuine multipartite entanglement for permutation-invariant Gaussian states under any multipartition of the modes.

The statistics of primordial density fluctuations

NASA Astrophysics Data System (ADS)

Barrow, John D.; Coles, Peter

1990-05-01

The statistical properties of the density fluctuations produced by power-law inflation are investigated. It is found that, even the fluctuations present in the scalar field driving the inflation are Gaussian, the resulting density perturbations need not be, due to stochastic variations in the Hubble parameter. All the moments of the density fluctuations are calculated, and is is argued that, for realistic parameter choices, the departures from Gaussian statistics are small and would have a negligible effect on the large-scale structure produced in the model. On the other hand, the model predicts a power spectrum with n not equal to 1, and this could be good news for large-scale structure.

Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence

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

Adesso, Gerardo; Centre for Quantum Computation, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA; Serafini, Alessio

2006-03-15

We present a complete analysis of the multipartite entanglement of three-mode Gaussian states of continuous-variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations can be quantified by a proper convex roof extension of the squared logarithmic negativity, the continuous-variable tangle, or contangle. We review and elucidate in detail the proof that in multimode Gaussian states the contangle satisfies a monogamy inequalitymore » constraint [G. Adesso and F. Illuminati, New J. Phys8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communications and defines a measure of genuine tripartite entanglements. We determine the analytical expression of the residual contangle for arbitrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such states. This analysis yields that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/W states of continuous-variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the W states of three qubits. We finally consider the effect of decoherence on three-mode Gaussian states, studying the decay of the residual contangle. The GHZ/W states are shown to be maximally robust against losses and thermal noise.« less

Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes.

PubMed

Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D

2016-10-01

This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. © The Author 2016. Published by Oxford University Press.

On the nature of persistence in dendrochronologic records with implications for hydrology

USGS Publications Warehouse

Landwehr, J.M.; Matalas, N.C.

1986-01-01

Hydrologic processes are generally held to be persistent and not secularly independent. Impetus for this view was given by Hurst in his work which dealt with properties of the rescaled range of many types of long geophysical records, in particular dendrochronologic records, in addition to hydrologic records. Mandelbrot introduced an infinite memory stationary process, the fractional Gaussian noise process (F), as an explanation for Hurst's observations. This is in contrast to other explanations which have been predicated on the implicit non-stationarity of the process underlying the construction of the records. In this work, we introduce a stationary finite memory process which arises naturally from a physical concept and show that it can accommodate the persistence structures observed for dendrochronological records more successfully than an F or any other of a family of related processes examined herein. Further, some question arises as to the empirical plausibility of an F process. Dendrochronologic records are used because they are widely held to be surrogates for records of average hydrologic phenomena and the length of these records allows one to explore questions of stochastic process structure which cannot be explored with great validity in the case of generally much shorter hydrologic records. ?? 1986.

A multiscale filter for noise reduction of low-dose cone beam projections

NASA Astrophysics Data System (ADS)

Yao, Weiguang; Farr, Jonathan B.

2015-08-01

The Poisson or compound Poisson process governs the randomness of photon fluence in cone beam computed tomography (CBCT) imaging systems. The probability density function depends on the mean (noiseless) of the fluence at a certain detector. This dependence indicates the natural requirement of multiscale filters to smooth noise while preserving structures of the imaged object on the low-dose cone beam projection. In this work, we used a Gaussian filter, \\text{exp}≤ft(-{{x}2}/2σ f2\\right) as the multiscale filter to de-noise the low-dose cone beam projections. We analytically obtained the expression of {σf} , which represents the scale of the filter, by minimizing local noise-to-signal ratio. We analytically derived the variance of residual noise from the Poisson or compound Poisson processes after Gaussian filtering. From the derived analytical form of the variance of residual noise, optimal σ f2 is proved to be proportional to the noiseless fluence and modulated by local structure strength expressed as the linear fitting error of the structure. A strategy was used to obtain the reliable linear fitting error: smoothing the projection along the longitudinal direction to calculate the linear fitting error along the lateral direction and vice versa. The performance of our multiscale filter was examined on low-dose cone beam projections of a Catphan phantom and a head-and-neck patient. After performing the filter on the Catphan phantom projections scanned with pulse time 4 ms, the number of visible line pairs was similar to that scanned with 16 ms, and the contrast-to-noise ratio of the inserts was higher than that scanned with 16 ms about 64% in average. For the simulated head-and-neck patient projections with pulse time 4 ms, the visibility of soft tissue structures in the patient was comparable to that scanned with 20 ms. The image processing took less than 0.5 s per projection with 1024   ×   768 pixels.

Reflection of a TE-polarised Gaussian beam from a layered structure under conditions of resonance excitation of waveguide modes

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

Sokolov, V I; Marusin, N V; Molchanova, S I

2014-11-30

The problem of reflection of a TE-polarised Gaussian light beam from a layered structure under conditions of resonance excitation of waveguide modes using a total internal reflection prism is considered. Using the spectral approach we have derived the analytic expressions for the mode propagation lengths, widths and depths of m-lines (sharp and narrow dips in the angular dependence of the specular reflection coefficient), depending on the structure parameters. It is shown that in the case of weak coupling, when the propagation lengths l{sub m} of the waveguide modes are mainly determined by the extinction coefficient in the film, the depthmore » of m-lines grows with the mode number m. In the case of strong coupling, when l{sub m} is determined mainly by the radiation of modes into the prism, the depth of m-lines decreases with increasing m. The change in the TE-polarised Gaussian beam shape after its reflection from the layered structure is studied, which is determined by the energy transfer from the incident beam into waveguide modes that propagate along the structure by the distance l{sub m}, are radiated in the direction of specular reflection and interfere with a part of the beam reflected from the working face of the prism. It is shown that this interference can lead to the field intensity oscillations near m-lines. The analysis of different methods for determining the parameters of thin-film structures is presented, including the measurement of mode angles θ{sub m} and the reflected beam shape. The methods are based on simultaneous excitation of a few waveguide modes in the film with a strongly focused monochromatic Gaussian beam, the waist width of which is much smaller than the propagation length of the modes. As an example of using these methods, the refractive index and the thickness of silicon monoxide film on silica substrate at the wavelength 633 nm are determined. (fibre and integrated-optical structures)« less

A prediction model for cognitive performance in health ageing using diffusion tensor imaging with graph theory.

PubMed

Yun, Ruijuan; Lin, Chung-Chih; Wu, Shuicai; Huang, Chu-Chung; Lin, Ching-Po; Chao, Yi-Ping

2013-01-01

In this study, we employed diffusion tensor imaging (DTI) to construct brain structural network and then derive the connection matrices from 96 healthy elderly subjects. The correlation analysis between these topological properties of network based on graph theory and the Cognitive Abilities Screening Instrument (CASI) index were processed to extract the significant network characteristics. These characteristics were then integrated to estimate the models by various machine-learning algorithms to predict user's cognitive performance. From the results, linear regression model and Gaussian processes model showed presented better abilities with lower mean absolute errors of 5.8120 and 6.25 to predict the cognitive performance respectively. Moreover, these extracted topological properties of brain structural network derived from DTI also could be regarded as the bio-signatures for further evaluation of brain degeneration in healthy aged and early diagnosis of mild cognitive impairment (MCI).

Robustness analysis of superpixel algorithms to image blur, additive Gaussian noise, and impulse noise

NASA Astrophysics Data System (ADS)

Brekhna, Brekhna; Mahmood, Arif; Zhou, Yuanfeng; Zhang, Caiming

2017-11-01

Superpixels have gradually become popular in computer vision and image processing applications. However, no comprehensive study has been performed to evaluate the robustness of superpixel algorithms in regard to common forms of noise in natural images. We evaluated the robustness of 11 recently proposed algorithms to different types of noise. The images were corrupted with various degrees of Gaussian blur, additive white Gaussian noise, and impulse noise that either made the object boundaries weak or added extra information to it. We performed a robustness analysis of simple linear iterative clustering (SLIC), Voronoi Cells (VCells), flooding-based superpixel generation (FCCS), bilateral geodesic distance (Bilateral-G), superpixel via geodesic distance (SSS-G), manifold SLIC (M-SLIC), Turbopixels, superpixels extracted via energy-driven sampling (SEEDS), lazy random walk (LRW), real-time superpixel segmentation by DBSCAN clustering, and video supervoxels using partially absorbing random walks (PARW) algorithms. The evaluation process was carried out both qualitatively and quantitatively. For quantitative performance comparison, we used achievable segmentation accuracy (ASA), compactness, under-segmentation error (USE), and boundary recall (BR) on the Berkeley image database. The results demonstrated that all algorithms suffered performance degradation due to noise. For Gaussian blur, Bilateral-G exhibited optimal results for ASA and USE measures, SLIC yielded optimal compactness, whereas FCCS and DBSCAN remained optimal for BR. For the case of additive Gaussian and impulse noises, FCCS exhibited optimal results for ASA, USE, and BR, whereas Bilateral-G remained a close competitor in ASA and USE for Gaussian noise only. Additionally, Turbopixel demonstrated optimal performance for compactness for both types of noise. Thus, no single algorithm was able to yield optimal results for all three types of noise across all performance measures. Conclusively, to solve real-world problems effectively, more robust superpixel algorithms must be developed.

Parametrization and Optimization of Gaussian Non-Markovian Unravelings for Open Quantum Dynamics

NASA Astrophysics Data System (ADS)

Megier, Nina; Strunz, Walter T.; Viviescas, Carlos; Luoma, Kimmo

2018-04-01

We derive a family of Gaussian non-Markovian stochastic Schrödinger equations for the dynamics of open quantum systems. The different unravelings correspond to different choices of squeezed coherent states, reflecting different measurement schemes on the environment. Consequently, we are able to give a single shot measurement interpretation for the stochastic states and microscopic expressions for the noise correlations of the Gaussian process. By construction, the reduced dynamics of the open system does not depend on the squeezing parameters. They determine the non-Hermitian Gaussian correlation, a wide range of which are compatible with the Markov limit. We demonstrate the versatility of our results for quantum information tasks in the non-Markovian regime. In particular, by optimizing the squeezing parameters, we can tailor unravelings for improving entanglement bounds or for environment-assisted entanglement protection.

Restoration of Static JPEG Images and RGB Video Frames by Means of Nonlinear Filtering in Conditions of Gaussian and Non-Gaussian Noise

NASA Astrophysics Data System (ADS)

Sokolov, R. I.; Abdullin, R. R.

2017-11-01

The use of nonlinear Markov process filtering makes it possible to restore both video stream frames and static photos at the stage of preprocessing. The present paper reflects the results of research in comparison of these types image filtering quality by means of special algorithm when Gaussian or non-Gaussian noises acting. Examples of filter operation at different values of signal-to-noise ratio are presented. A comparative analysis has been performed, and the best filtered kind of noise has been defined. It has been shown the quality of developed algorithm is much better than quality of adaptive one for RGB signal filtering at the same a priori information about the signal. Also, an advantage over median filter takes a place when both fluctuation and pulse noise filtering.

Gaussian Processes for Prediction of Homing Pigeon Flight Trajectories

NASA Astrophysics Data System (ADS)

Mann, Richard; Freeman, Robin; Osborne, Michael; Garnett, Roman; Meade, Jessica; Armstrong, Chris; Biro, Dora; Guilford, Tim; Roberts, Stephen

2009-12-01

We construct and apply a stochastic Gaussian Process (GP) model of flight trajectory generation for pigeons trained to home from specific release sites. The model shows increasing predictive power as the birds become familiar with the sites, mirroring the animal's learning process. We show how the increasing similarity between successive flight trajectories can be used to infer, with increasing accuracy, an idealised route that captures the repeated spatial aspects of the bird's flight. We subsequently use techniques associated with reduced-rank GP approximations to objectively identify the key waypoints used by each bird to memorise its idiosyncratic habitual route between the release site and the home loft.

Cramer-Rao Bound for Gaussian Random Processes and Applications to Radar Processing of Atmospheric Signals

NASA Technical Reports Server (NTRS)

Frehlich, Rod

1993-01-01

Calculations of the exact Cramer-Rao Bound (CRB) for unbiased estimates of the mean frequency, signal power, and spectral width of Doppler radar/lidar signals (a Gaussian random process) are presented. Approximate CRB's are derived using the Discrete Fourier Transform (DFT). These approximate results are equal to the exact CRB when the DFT coefficients are mutually uncorrelated. Previous high SNR limits for CRB's are shown to be inaccurate because the discrete summations cannot be approximated with integration. The performance of an approximate maximum likelihood estimator for mean frequency approaches the exact CRB for moderate signal to noise ratio and moderate spectral width.

Efficient Statistically Accurate Algorithms for the Fokker-Planck Equation in Large Dimensions

NASA Astrophysics Data System (ADS)

Chen, N.; Majda, A.

2017-12-01

Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing the fat tailed highly intermittent probability density functions (PDFs) of complex systems in turbulence, neuroscience and excitable media. In this article, efficient statistically accurate algorithms are developed for solving both the transient and the equilibrium solutions of Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures. The algorithms involve a hybrid strategy that requires only a small number of ensembles. Here, a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious non-parametric Gaussian kernel density estimation in the remaining low-dimensional subspace. Particularly, the parametric method, which is based on an effective data assimilation framework, provides closed analytical formulae for determining the conditional Gaussian distributions in the high-dimensional subspace. Therefore, it is computationally efficient and accurate. The full non-Gaussian PDF of the system is then given by a Gaussian mixture. Different from the traditional particle methods, each conditional Gaussian distribution here covers a significant portion of the high-dimensional PDF. Therefore a small number of ensembles is sufficient to recover the full PDF, which overcomes the curse of dimensionality. Notably, the mixture distribution has a significant skill in capturing the transient behavior with fat tails of the high-dimensional non-Gaussian PDFs, and this facilitates the algorithms in accurately describing the intermittency and extreme events in complex turbulent systems. It is shown in a stringent set of test problems that the method only requires an order of O(100) ensembles to successfully recover the highly non-Gaussian transient PDFs in up to 6 dimensions with only small errors.

Energy pumping in electrical circuits under avalanche noise.

PubMed

Kanazawa, Kiyoshi; Sagawa, Takahiro; Hayakawa, Hisao

2014-07-01

We theoretically study energy pumping processes in an electrical circuit with avalanche diodes, where non-Gaussian athermal noise plays a crucial role. We show that a positive amount of energy (work) can be extracted by an external manipulation of the circuit in a cyclic way, even when the system is spatially symmetric. We discuss the properties of the energy pumping process for both quasistatic and finite-time cases, and analytically obtain formulas for the amounts of the work and the power. Our results demonstrate the significance of the non-Gaussianity in energetics of electrical circuits.

An Imager Gaussian Process Machine Learning Methodology for Cloud Thermodynamic Phase classification

NASA Astrophysics Data System (ADS)

Marchant, B.; Platnick, S. E.; Meyer, K.

2017-12-01

The determination of cloud thermodynamic phase from MODIS and VIIRS instruments is an important first step in cloud optical retrievals, since ice and liquid clouds have different optical properties. To continue improving the cloud thermodynamic phase classification algorithm, a machine-learning approach, based on Gaussian processes, has been developed. The new proposed methodology provides cloud phase uncertainty quantification and improves the algorithm portability between MODIS and VIIRS. We will present new results, through comparisons between MODIS and CALIOP v4, and for VIIRS as well.

Dimension from covariance matrices.

PubMed

Carroll, T L; Byers, J M

2017-02-01

We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.

A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors.

PubMed

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

2016-09-01

Our present work proposes a new survival model in a Bayesian context to analyze right-censored survival data for populations with a surviving fraction, assuming that the log failure time follows a generalized extreme value distribution. Many applications require a more flexible modeling of covariate information than a simple linear or parametric form for all covariate effects. It is also necessary to include the spatial variation in the model, since it is sometimes unexplained by the covariates considered in the analysis. Therefore, the nonlinear covariate effects and the spatial effects are incorporated into the systematic component of our model. Gaussian processes (GPs) provide a natural framework for modeling potentially nonlinear relationship and have recently become extremely powerful in nonlinear regression. Our proposed model adopts a semiparametric Bayesian approach by imposing a GP prior on the nonlinear structure of continuous covariate. With the consideration of data availability and computational complexity, the conditionally autoregressive distribution is placed on the region-specific frailties to handle spatial correlation. The flexibility and gains of our proposed model are illustrated through analyses of simulated data examples as well as a dataset involving a colon cancer clinical trial from the state of Iowa. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Inference for local autocorrelations in locally stationary models.

PubMed

Zhao, Zhibiao

2015-04-01

For non-stationary processes, the time-varying correlation structure provides useful insights into the underlying model dynamics. We study estimation and inferences for local autocorrelation process in locally stationary time series. Our constructed simultaneous confidence band can be used to address important hypothesis testing problems, such as whether the local autocorrelation process is indeed time-varying and whether the local autocorrelation is zero. In particular, our result provides an important generalization of the R function acf() to locally stationary Gaussian processes. Simulation studies and two empirical applications are developed. For the global temperature series, we find that the local autocorrelations are time-varying and have a "V" shape during 1910-1960. For the S&P 500 index, we conclude that the returns satisfy the efficient-market hypothesis whereas the magnitudes of returns show significant local autocorrelations.

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

NASA Astrophysics Data System (ADS)

Mashhadi, L.

2017-12-01

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

Numerical modeling of Gaussian beam propagation and diffraction in inhomogeneous media based on the complex eikonal equation

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Hui

2018-05-01

Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss-Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.

Practical limitation for continuous-variable quantum cryptography using coherent States.

PubMed

Namiki, Ryo; Hirano, Takuya

2004-03-19

In this Letter, first, we investigate the security of a continuous-variable quantum cryptographic scheme with a postselection process against individual beam splitting attack. It is shown that the scheme can be secure in the presence of the transmission loss owing to the postselection. Second, we provide a loss limit for continuous-variable quantum cryptography using coherent states taking into account excess Gaussian noise on quadrature distribution. Since the excess noise is reduced by the loss mechanism, a realistic intercept-resend attack which makes a Gaussian mixture of coherent states gives a loss limit in the presence of any excess Gaussian noise.

On Gaussian feedback capacity

NASA Technical Reports Server (NTRS)

Dembo, Amir

1989-01-01

Pinsker and Ebert (1970) proved that in channels with additive Gaussian noise, feedback at most doubles the capacity. Cover and Pombra (1989) proved that feedback at most adds half a bit per transmission. Following their approach, the author proves that in the limit as signal power approaches either zero (very low SNR) or infinity (very high SNR), feedback does not increase the finite block-length capacity (which for nonstationary Gaussian channels replaces the standard notion of capacity that may not exist). Tighter upper bounds on the capacity are obtained in the process. Specializing these results to stationary channels, the author recovers some of the bounds recently obtained by Ozarow.

Common inputs in subthreshold membrane potential: The role of quiescent states in neuronal activity

NASA Astrophysics Data System (ADS)

Montangie, Lisandro; Montani, Fernando

2018-06-01

Experiments in certain regions of the cerebral cortex suggest that the spiking activity of neuronal populations is regulated by common non-Gaussian inputs across neurons. We model these deviations from random-walk processes with q -Gaussian distributions into simple threshold neurons, and investigate the scaling properties in large neural populations. We show that deviations from the Gaussian statistics provide a natural framework to regulate population statistics such as sparsity, entropy, and specific heat. This type of description allows us to provide an adequate strategy to explain the information encoding in the case of low neuronal activity and its possible implications on information transmission.

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.

A relativistic signature in large-scale structure

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Bertacca, Daniele; Bruni, Marco; Koyama, Kazuya; Maartens, Roy; Matarrese, Sabino; Sasaki, Misao; Verde, Licia; Wands, David

2016-09-01

In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the dark matter density field on large scales-even if the primordial metric perturbation is Gaussian. Intrinsic non-Gaussianity in the large-scale dark matter overdensity in GR is real and physical. However, the variance smoothed on a local physical scale is not correlated with the large-scale curvature perturbation, so that there is no relativistic signature in the galaxy bias when using the simplest model of bias. It is an open question whether the observable mass proxies such as luminosity or weak lensing correspond directly to the physical mass in the simple halo bias model. If not, there may be observables that encode this relativistic signature.

Ionospheric scintillation studies

NASA Technical Reports Server (NTRS)

Rino, C. L.; Freemouw, E. J.

1973-01-01

The diffracted field of a monochromatic plane wave was characterized by two complex correlation functions. For a Gaussian complex field, these quantities suffice to completely define the statistics of the field. Thus, one can in principle calculate the statistics of any measurable quantity in terms of the model parameters. The best data fits were achieved for intensity statistics derived under the Gaussian statistics hypothesis. The signal structure that achieved the best fit was nearly invariant with scintillation level and irregularity source (ionosphere or solar wind). It was characterized by the fact that more than 80% of the scattered signal power is in phase quadrature with the undeviated or coherent signal component. Thus, the Gaussian-statistics hypothesis is both convenient and accurate for channel modeling work.

Four tails problems for dynamical collapse theories

NASA Astrophysics Data System (ADS)

McQueen, Kelvin J.

2015-02-01

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory.

The Undergraduate ALFALFA Groups Project: Properties of the Galaxy Group MKW 11

NASA Astrophysics Data System (ADS)

Manglitz, Scott; Russell, P.; Turner, J.; Crone, M.

2009-01-01

The Undergraduate ALFALFA team is an NSF-funded collaboration of 14 institutions that supports undergraduate research using data from the Arecibo Legacy Fast ALFA (ALFALFA) survey. As part of this project, we are examining MKW 11, a galaxy group with an unusual, irregular X-ray distribution centered on what appears to be an X-ray bright tidal filament. Its optical velocity distribution is large and non-Gaussian, suggesting that it is in the process of merging. Here we present the position and velocity structure of MKW 11 using the radio sources in the blind ALFALFA survey. Besides a complicated structure, our results suggest a deficiency of HI gas in galaxies that are near the center of the group.

A Concept for Measuring Electron Distribution Functions Using Collective Thomson Scattering

NASA Astrophysics Data System (ADS)

Milder, A. L.; Froula, D. H.

2017-10-01

A.B. Langdon proposed that stable non-Maxwellian distribution functions are realized in coronal inertial confinement fusion plasmas via inverse bremsstrahlung heating. For Zvosc2 Zvosc2 vth2 > 1 , vth2 > 1 , the inverse bremsstrahlung heating rate is sufficiently fast to compete with electron-electron collisions. This process preferentially heats the subthermal electrons leading to super-Gaussian distribution functions. A method to identify the super-Gaussian order of the distribution functions in these plasmas using collective Thomson scattering will be proposed. By measuring the collective Thomson spectra over a range of angles the density, temperature and super-Gaussian order can be determined. This is accomplished by fitting non-Maxwellian distribution data with a super-Gaussian model; in order to match the density and electron temperature to within 10%, the super-Gaussian order must be varied. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.

Synthesis and analysis of discriminators under influence of broadband non-Gaussian noise

NASA Astrophysics Data System (ADS)

Artyushenko, V. M.; Volovach, V. I.

2018-01-01

We considered the problems of the synthesis and analysis of discriminators, when the useful signal is exposed to non-Gaussian additive broadband noise. It is shown that in this case, the discriminator of the tracking meter should contain the nonlinear transformation unit, the characteristics of which are determined by the Fisher information relative to the probability density function of the mixture of non-Gaussian broadband noise and mismatch errors. The parameters of the discriminatory and phase characteristics of the discriminators working under the above conditions are obtained. It is shown that the efficiency of non-linear processing depends on the ratio of power of FM noise to the power of Gaussian noise. The analysis of the information loss of signal transformation caused by the linear section of discriminatory characteristics of the unit of nonlinear transformations of the discriminator is carried out. It is shown that the average slope of the nonlinear transformation characteristic is determined by the Fisher information relative to the probability density function of the mixture of non-Gaussian noise and mismatch errors.

Perturbative Gaussianizing transforms for cosmological fields

NASA Astrophysics Data System (ADS)

Hall, Alex; Mead, Alexander

2018-01-01

Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.

Optimization of morphological parameters for mitigation pits on rear KDP surface: experiments and numerical modeling.

PubMed

Yang, Hao; Cheng, Jian; Chen, Mingjun; Wang, Jian; Liu, Zhichao; An, Chenhui; Zheng, Yi; Hu, Kehui; Liu, Qi

2017-07-24

In high power laser systems, precision micro-machining is an effective method to mitigate the laser-induced surface damage growth on potassium dihydrogen phosphate (KDP) crystal. Repaired surfaces with smooth spherical and Gaussian contours can alleviate the light field modulation caused by damage site. To obtain the optimal repairing structure parameters, finite element method (FEM) models for simulating the light intensification caused by the mitigation pits on rear KDP surface were established. The light intensity modulation of these repairing profiles was compared by changing the structure parameters. The results indicate the modulation is mainly caused by the mutual interference between the reflected and incident lights on the rear surface. Owing to the total reflection, the light intensity enhancement factors (LIEFs) of the spherical and Gaussian mitigation pits sharply increase when the width-depth ratios are near 5.28 and 3.88, respectively. To achieve the optimal mitigation effect, the width-depth ratios greater than 5.3 and 4.3 should be applied to the spherical and Gaussian repaired contours. Particularly, for the cases of width-depth ratios greater than 5.3, the spherical repaired contour is preferred to achieve lower light intensification. The laser damage test shows that when the width-depth ratios are larger than 5.3, the spherical repaired contour presents higher laser damage resistance than that of Gaussian repaired contour, which agrees well with the simulation results.

Recent advances in PC-Linux systems for electronic structure computations by optimized compilers and numerical libraries.

PubMed

Yu, Jen-Shiang K; Yu, Chin-Hui

2002-01-01

One of the most frequently used packages for electronic structure research, GAUSSIAN 98, is compiled on Linux systems with various hardware configurations, including AMD Athlon (with the "Thunderbird" core), AthlonMP, and AthlonXP (with the "Palomino" core) systems as well as the Intel Pentium 4 (with the "Willamette" core) machines. The default PGI FORTRAN compiler (pgf77) and the Intel FORTRAN compiler (ifc) are respectively employed with different architectural optimization options to compile GAUSSIAN 98 and test the performance improvement. In addition to the BLAS library included in revision A.11 of this package, the Automatically Tuned Linear Algebra Software (ATLAS) library is linked against the binary executables to improve the performance. Various Hartree-Fock, density-functional theories, and the MP2 calculations are done for benchmarking purposes. It is found that the combination of ifc with ATLAS library gives the best performance for GAUSSIAN 98 on all of these PC-Linux computers, including AMD and Intel CPUs. Even on AMD systems, the Intel FORTRAN compiler invariably produces binaries with better performance than pgf77. The enhancement provided by the ATLAS library is more significant for post-Hartree-Fock calculations. The performance on one single CPU is potentially as good as that on an Alpha 21264A workstation or an SGI supercomputer. The floating-point marks by SpecFP2000 have similar trends to the results of GAUSSIAN 98 package.

Locally optimum nonlinearities for DCT watermark detection.

PubMed

Briassouli, Alexia; Strintzis, Michael G

2004-12-01

The issue of copyright protection of digital multimedia data has attracted a lot of attention during the last decade. An efficient copyright protection method that has been gaining popularity is watermarking, i.e., the embedding of a signature in a digital document that can be detected only by its rightful owner. Watermarks are usually blindly detected using correlating structures, which would be optimal in the case of Gaussian data. However, in the case of DCT-domain image watermarking, the data is more heavy-tailed and the correlator is clearly suboptimal. Nonlinear receivers have been shown to be particularly well suited for the detection of weak signals in heavy-tailed noise, as they are locally optimal. This motivates the use of the Gaussian-tailed zero-memory nonlinearity, as well as the locally optimal Cauchy nonlinearity for the detection of watermarks in DCT transformed images. We analyze the performance of these schemes theoretically and compare it to that of the traditionally used Gaussian correlator, but also to the recently proposed generalized Gaussian detector, which outperforms the correlator. The theoretical analysis and the actual performance of these systems is assessed through experiments, which verify the theoretical analysis and also justify the use of nonlinear structures for watermark detection. The performance of the correlator and the nonlinear detectors in the presence of quantization is also analyzed, using results from dither theory, and also verified experimentally.

Nested polynomial trends for the improvement of Gaussian process-based predictors

NASA Astrophysics Data System (ADS)

Perrin, G.; Soize, C.; Marque-Pucheu, S.; Garnier, J.

2017-10-01

The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.

Bayesian Treed Multivariate Gaussian Process with Adaptive Design: Application to a Carbon Capture Unit

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

Konomi, Bledar A.; Karagiannis, Georgios; Sarkar, Avik

2014-05-16

Computer experiments (numerical simulations) are widely used in scientific research to study and predict the behavior of complex systems, which usually have responses consisting of a set of distinct outputs. The computational cost of the simulations at high resolution are often expensive and become impractical for parametric studies at different input values. To overcome these difficulties we develop a Bayesian treed multivariate Gaussian process (BTMGP) as an extension of the Bayesian treed Gaussian process (BTGP) in order to model and evaluate a multivariate process. A suitable choice of covariance function and the prior distributions facilitates the different Markov chain Montemore » Carlo (MCMC) movements. We utilize this model to sequentially sample the input space for the most informative values, taking into account model uncertainty and expertise gained. A simulation study demonstrates the use of the proposed method and compares it with alternative approaches. We apply the sequential sampling technique and BTMGP to model the multiphase flow in a full scale regenerator of a carbon capture unit. The application presented in this paper is an important tool for research into carbon dioxide emissions from thermal power plants.« 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.

A median-Gaussian filtering framework for Moiré pattern noise removal from X-ray microscopy image.

PubMed

Wei, Zhouping; Wang, Jian; Nichol, Helen; Wiebe, Sheldon; Chapman, Dean

2012-02-01

Moiré pattern noise in Scanning Transmission X-ray Microscopy (STXM) imaging introduces significant errors in qualitative and quantitative image analysis. Due to the complex origin of the noise, it is difficult to avoid Moiré pattern noise during the image data acquisition stage. In this paper, we introduce a post-processing method for filtering Moiré pattern noise from STXM images. This method includes a semi-automatic detection of the spectral peaks in the Fourier amplitude spectrum by using a local median filter, and elimination of the spectral noise peaks using a Gaussian notch filter. The proposed median-Gaussian filtering framework shows good results for STXM images with the size of power of two, if such parameters as threshold, sizes of the median and Gaussian filters, and size of the low frequency window, have been properly selected. Copyright © 2011 Elsevier Ltd. All rights reserved.

Covariances and spectra of the kinematics and dynamics of nonlinear waves

NASA Technical Reports Server (NTRS)

Tung, C. C.; Huang, N. E.

1985-01-01

Using the Stokes waves as a model of nonlinear waves and considering the linear component as a narrow-band Gaussian process, the covariances and spectra of velocity and acceleration components and pressure for points in the vicinity of still water level were derived taking into consideration the effects of free surface fluctuations. The results are compared with those obtained earlier using linear Gaussian waves.

An adaptive confidence limit for periodic non-steady conditions fault detection

NASA Astrophysics Data System (ADS)

Wang, Tianzhen; Wu, Hao; Ni, Mengqi; Zhang, Milu; Dong, Jingjing; Benbouzid, Mohamed El Hachemi; Hu, Xiong

2016-05-01

System monitoring has become a major concern in batch process due to the fact that failure rate in non-steady conditions is much higher than in steady ones. A series of approaches based on PCA have already solved problems such as data dimensionality reduction, multivariable decorrelation, and processing non-changing signal. However, if the data follows non-Gaussian distribution or the variables contain some signal changes, the above approaches are not applicable. To deal with these concerns and to enhance performance in multiperiod data processing, this paper proposes a fault detection method using adaptive confidence limit (ACL) in periodic non-steady conditions. The proposed ACL method achieves four main enhancements: Longitudinal-Standardization could convert non-Gaussian sampling data to Gaussian ones; the multiperiod PCA algorithm could reduce dimensionality, remove correlation, and improve the monitoring accuracy; the adaptive confidence limit could detect faults under non-steady conditions; the fault sections determination procedure could select the appropriate parameter of the adaptive confidence limit. The achieved result analysis clearly shows that the proposed ACL method is superior to other fault detection approaches under periodic non-steady conditions.

Dirichlet Process Gaussian-mixture model: An application to localizing coalescing binary neutron stars with gravitational-wave observations

NASA Astrophysics Data System (ADS)

Del Pozzo, W.; Berry, C. P. L.; Ghosh, A.; Haines, T. S. F.; Singer, L. P.; Vecchio, A.

2018-06-01

We reconstruct posterior distributions for the position (sky area and distance) of a simulated set of binary neutron-star gravitational-waves signals observed with Advanced LIGO and Advanced Virgo. We use a Dirichlet Process Gaussian-mixture model, a fully Bayesian non-parametric method that can be used to estimate probability density functions with a flexible set of assumptions. The ability to reliably reconstruct the source position is important for multimessenger astronomy, as recently demonstrated with GW170817. We show that for detector networks comparable to the early operation of Advanced LIGO and Advanced Virgo, typical localization volumes are ˜104-105 Mpc3 corresponding to ˜102-103 potential host galaxies. The localization volume is a strong function of the network signal-to-noise ratio, scaling roughly ∝ϱnet-6. Fractional localizations improve with the addition of further detectors to the network. Our Dirichlet Process Gaussian-mixture model can be adopted for localizing events detected during future gravitational-wave observing runs, and used to facilitate prompt multimessenger follow-up.

A Prediction Model for Functional Outcomes in Spinal Cord Disorder Patients Using Gaussian Process Regression.

PubMed

Lee, Sunghoon Ivan; Mortazavi, Bobak; Hoffman, Haydn A; Lu, Derek S; Li, Charles; Paak, Brian H; Garst, Jordan H; Razaghy, Mehrdad; Espinal, Marie; Park, Eunjeong; Lu, Daniel C; Sarrafzadeh, Majid

2016-01-01

Predicting the functional outcomes of spinal cord disorder patients after medical treatments, such as a surgical operation, has always been of great interest. Accurate posttreatment prediction is especially beneficial for clinicians, patients, care givers, and therapists. This paper introduces a prediction method for postoperative functional outcomes by a novel use of Gaussian process regression. The proposed method specifically considers the restricted value range of the target variables by modeling the Gaussian process based on a truncated Normal distribution, which significantly improves the prediction results. The prediction has been made in assistance with target tracking examinations using a highly portable and inexpensive handgrip device, which greatly contributes to the prediction performance. The proposed method has been validated through a dataset collected from a clinical cohort pilot involving 15 patients with cervical spinal cord disorder. The results show that the proposed method can accurately predict postoperative functional outcomes, Oswestry disability index and target tracking scores, based on the patient's preoperative information with a mean absolute error of 0.079 and 0.014 (out of 1.0), respectively.

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.

Maximum likelihood clustering with dependent feature trees

NASA Technical Reports Server (NTRS)

Chittineni, C. B. (Principal Investigator)

1981-01-01

The decomposition of mixture density of the data into its normal component densities is considered. The densities are approximated with first order dependent feature trees using criteria of mutual information and distance measures. Expressions are presented for the criteria when the densities are Gaussian. By defining different typs of nodes in a general dependent feature tree, maximum likelihood equations are developed for the estimation of parameters using fixed point iterations. The field structure of the data is also taken into account in developing maximum likelihood equations. Experimental results from the processing of remotely sensed multispectral scanner imagery data are included.

Using Gaussian windows to explore a multivariate data set

NASA Technical Reports Server (NTRS)

Jaeckel, Louis A.

1991-01-01

In an earlier paper, I recounted an exploratory analysis, using Gaussian windows, of a data set derived from the Infrared Astronomical Satellite. Here, my goals are to develop strategies for finding structural features in a data set in a many-dimensional space, and to find ways to describe the shape of such a data set. After a brief review of Gaussian windows, I describe the current implementation of the method. I give some ways of describing features that we might find in the data, such as clusters and saddle points, and also extended structures such as a 'bar', which is an essentially one-dimensional concentration of data points. I then define a distance function, which I use to determine which data points are 'associated' with a feature. Data points not associated with any feature are called 'outliers'. I then explore the data set, giving the strategies that I used and quantitative descriptions of the features that I found, including clusters, bars, and a saddle point. I tried to use strategies and procedures that could, in principle, be used in any number of dimensions.

GIFTed Demons: deformable image registration with local structure-preserving regularization using supervoxels for liver applications

PubMed Central

Gleeson, Fergus V.; Brady, Michael; Schnabel, Julia A.

2018-01-01

Abstract. Deformable image registration, a key component of motion correction in medical imaging, needs to be efficient and provides plausible spatial transformations that reliably approximate biological aspects of complex human organ motion. Standard approaches, such as Demons registration, mostly use Gaussian regularization for organ motion, which, though computationally efficient, rule out their application to intrinsically more complex organ motions, such as sliding interfaces. We propose regularization of motion based on supervoxels, which provides an integrated discontinuity preserving prior for motions, such as sliding. More precisely, we replace Gaussian smoothing by fast, structure-preserving, guided filtering to provide efficient, locally adaptive regularization of the estimated displacement field. We illustrate the approach by applying it to estimate sliding motions at lung and liver interfaces on challenging four-dimensional computed tomography (CT) and dynamic contrast-enhanced magnetic resonance imaging datasets. The results show that guided filter-based regularization improves the accuracy of lung and liver motion correction as compared to Gaussian smoothing. Furthermore, our framework achieves state-of-the-art results on a publicly available CT liver dataset. PMID:29662918

GIFTed Demons: deformable image registration with local structure-preserving regularization using supervoxels for liver applications.

PubMed

Papież, Bartłomiej W; Franklin, James M; Heinrich, Mattias P; Gleeson, Fergus V; Brady, Michael; Schnabel, Julia A

2018-04-01

Deformable image registration, a key component of motion correction in medical imaging, needs to be efficient and provides plausible spatial transformations that reliably approximate biological aspects of complex human organ motion. Standard approaches, such as Demons registration, mostly use Gaussian regularization for organ motion, which, though computationally efficient, rule out their application to intrinsically more complex organ motions, such as sliding interfaces. We propose regularization of motion based on supervoxels, which provides an integrated discontinuity preserving prior for motions, such as sliding. More precisely, we replace Gaussian smoothing by fast, structure-preserving, guided filtering to provide efficient, locally adaptive regularization of the estimated displacement field. We illustrate the approach by applying it to estimate sliding motions at lung and liver interfaces on challenging four-dimensional computed tomography (CT) and dynamic contrast-enhanced magnetic resonance imaging datasets. The results show that guided filter-based regularization improves the accuracy of lung and liver motion correction as compared to Gaussian smoothing. Furthermore, our framework achieves state-of-the-art results on a publicly available CT liver dataset.

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.

Theoretical model of a polarization diffractive elements for the light beams conversion holographic formation in PDLCs

NASA Astrophysics Data System (ADS)

Sharangovich, Sergey N.; Semkin, Artem O.

2017-12-01

In this work a theoretical model of the holographic formation of the polarization diffractive optical elements for the transformation of Gaussian light beams into Bessel-like ones in polymer-dispersed liquid crystals (PDLC) is developed. The model is based on solving the equations of photo-induced Fredericks transition processes for polarization diffractive elements formation by orthogonally polarized light beams with inhomogeneous amplitude and phase profiles. The results of numerical simulation of the material's dielectric tensor changing due to the structure's formation process are presented for various recording beams' polarization states. Based on the results of numerical simulation, the ability to form the diffractive optical elements for light beams transformation by the polarization holography methods is shown.

Predicting Error Bars for QSAR Models

NASA Astrophysics Data System (ADS)

Schroeter, Timon; Schwaighofer, Anton; Mika, Sebastian; Ter Laak, Antonius; Suelzle, Detlev; Ganzer, Ursula; Heinrich, Nikolaus; Müller, Klaus-Robert

2007-09-01

Unfavorable physicochemical properties often cause drug failures. It is therefore important to take lipophilicity and water solubility into account early on in lead discovery. This study presents log D7 models built using Gaussian Process regression, Support Vector Machines, decision trees and ridge regression algorithms based on 14556 drug discovery compounds of Bayer Schering Pharma. A blind test was conducted using 7013 new measurements from the last months. We also present independent evaluations using public data. Apart from accuracy, we discuss the quality of error bars that can be computed by Gaussian Process models, and ensemble and distance based techniques for the other modelling approaches.

Gaussian Process Regression Model in Spatial Logistic Regression

NASA Astrophysics Data System (ADS)

Sofro, A.; Oktaviarina, A.

2018-01-01

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

Fast and Scalable Gaussian Process Modeling with Applications to Astronomical Time Series

NASA Astrophysics Data System (ADS)

Foreman-Mackey, Daniel; Agol, Eric; Ambikasaran, Sivaram; Angus, Ruth

2017-12-01

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large data sets. Gaussian processes (GPs) are a popular class of models used for this purpose, but since the computational cost scales, in general, as the cube of the number of data points, their application has been limited to small data sets. In this paper, we present a novel method for GPs modeling in one dimension where the computational requirements scale linearly with the size of the data set. We demonstrate the method by applying it to simulated and real astronomical time series data sets. These demonstrations are examples of probabilistic inference of stellar rotation periods, asteroseismic oscillation spectra, and transiting planet parameters. The method exploits structure in the problem when the covariance function is expressed as a mixture of complex exponentials, without requiring evenly spaced observations or uniform noise. This form of covariance arises naturally when the process is a mixture of stochastically driven damped harmonic oscillators—providing a physical motivation for and interpretation of this choice—but we also demonstrate that it can be a useful effective model in some other cases. We present a mathematical description of the method and compare it to existing scalable GP methods. The method is fast and interpretable, with a range of potential applications within astronomical data analysis and beyond. We provide well-tested and documented open-source implementations of this method in C++, Python, and Julia.

Characterizing CDOM Spectral Variability Across Diverse Regions and Spectral Ranges

NASA Astrophysics Data System (ADS)

Grunert, Brice K.; Mouw, Colleen B.; Ciochetto, Audrey B.

2018-01-01

Satellite remote sensing of colored dissolved organic matter (CDOM) has focused on CDOM absorption (aCDOM) at a reference wavelength, as its magnitude provides insight into the underwater light field and large-scale biogeochemical processes. CDOM spectral slope, SCDOM, has been treated as a constant or semiconstant parameter in satellite retrievals of aCDOM despite significant regional and temporal variabilities. SCDOM and other optical metrics provide insights into CDOM composition, processing, food web dynamics, and carbon cycling. To date, much of this work relies on fluorescence techniques or aCDOM in spectral ranges unavailable to current and planned satellite sensors (e.g., <300 nm). In preparation for anticipated future hyperspectral satellite missions, we take the first step here of exploring global variability in SCDOM and fit deviations in the aCDOM spectra using the recently proposed Gaussian decomposition method. From this, we investigate if global variability in retrieved SCDOM and Gaussian components is significant and regionally distinct. We iteratively decreased the spectral range considered and analyzed the number, location, and magnitude of fitted Gaussian components to understand if a reduced spectral range impacts information obtained within a common spectral window. We compared the fitted slope from the Gaussian decomposition method to absorption-based indices that indicate CDOM composition to determine the ability of satellite-derived slope to inform the analysis and modeling of large-scale biogeochemical processes. Finally, we present implications of the observed variability for remote sensing of CDOM characteristics via SCDOM.

Lensing of the CMB: non-Gaussian aspects.

PubMed

Zaldarriaga, M

2001-06-01

We compute the small angle limit of the three- and four-point function of the cosmic microwave background (CMB) temperature induced by the gravitational lensing effect by the large-scale structure of the universe. We relate the non-Gaussian aspects presented in this paper with those in our previous studies of the lensing effects. We interpret the statistics proposed in previous work in terms of different configurations of the four-point function and show how they relate to the statistic that maximizes the S/N.

R2C: improving ab initio residue contact map prediction using dynamic fusion strategy and Gaussian noise filter.

PubMed

Yang, Jing; Jin, Qi-Yu; Zhang, Biao; Shen, Hong-Bin

2016-08-15

Inter-residue contacts in proteins dictate the topology of protein structures. They are crucial for protein folding and structural stability. Accurate prediction of residue contacts especially for long-range contacts is important to the quality of ab inito structure modeling since they can enforce strong restraints to structure assembly. In this paper, we present a new Residue-Residue Contact predictor called R2C that combines machine learning-based and correlated mutation analysis-based methods, together with a two-dimensional Gaussian noise filter to enhance the long-range residue contact prediction. Our results show that the outputs from the machine learning-based method are concentrated with better performance on short-range contacts; while for correlated mutation analysis-based approach, the predictions are widespread with higher accuracy on long-range contacts. An effective query-driven dynamic fusion strategy proposed here takes full advantages of the two different methods, resulting in an impressive overall accuracy improvement. We also show that the contact map directly from the prediction model contains the interesting Gaussian noise, which has not been discovered before. Different from recent studies that tried to further enhance the quality of contact map by removing its transitive noise, we designed a new two-dimensional Gaussian noise filter, which was especially helpful for reinforcing the long-range residue contact prediction. Tested on recent CASP10/11 datasets, the overall top L/5 accuracy of our final R2C predictor is 17.6%/15.5% higher than the pure machine learning-based method and 7.8%/8.3% higher than the correlated mutation analysis-based approach for the long-range residue contact prediction. http://www.csbio.sjtu.edu.cn/bioinf/R2C/Contact:hbshen@sjtu.edu.cn Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Analysis of statistical properties of laser speckles, forming in skin and mucous of colon: potential application in laser surgery

NASA Astrophysics Data System (ADS)

Rubtsov, Vladimir; Kapralov, Sergey; Chalyk, Iuri; Ulianova, Onega; Ulyanov, Sergey

2013-02-01

Statistical properties of laser speckles, formed in skin and mucous of colon have been analyzed and compared. It has been demonstrated that first and second order statistics of "skin" speckles and "mucous" speckles are quite different. It is shown that speckles, formed in mucous, are not Gaussian one. Layered structure of colon mucous causes formation of speckled biospeckles. First- and second- order statistics of speckled speckles have been reviewed in this paper. Statistical properties of Fresnel and Fraunhofer doubly scattered and cascade speckles are described. Non-gaussian statistics of biospeckles may lead to high localization of intensity of coherent light in human tissue during the laser surgery. Way of suppression of highly localized non-gaussian speckles is suggested.

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.

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.

The effect of spherical aberration on the phase singularities of focused dark-hollow Gaussian beams

NASA Astrophysics Data System (ADS)

Luo, Yamei; Lü, Baida

2009-06-01

The phase singularities of focused dark-hollow Gaussian beams in the presence of spherical aberration are studied. It is shown that the evolution behavior of phase singularities of focused dark-hollow Gaussian beams in the focal region depends not only on the truncation parameter and beam order, but also on the spherical aberration. The spherical aberration leads to an asymmetric spatial distribution of singularities outside the focal plane and to a shift of singularities near the focal plane. The reorganization process of singularities and spatial distribution of singularities are additionally dependent on the sign of the spherical aberration. The results are illustrated by numerical examples.

Gaussian ancillary bombardment

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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.

Robust watermark technique using masking and Hermite transform.

PubMed

Coronel, Sandra L Gomez; Ramírez, Boris Escalante; Mosqueda, Marco A Acevedo

2016-01-01

The following paper evaluates a watermark algorithm designed for digital images by using a perceptive mask and a normalization process, thus preventing human eye detection, as well as ensuring its robustness against common processing and geometric attacks. The Hermite transform is employed because it allows a perfect reconstruction of the image, while incorporating human visual system properties; moreover, it is based on the Gaussian functions derivates. The applied watermark represents information of the digital image proprietor. The extraction process is blind, because it does not require the original image. The following techniques were utilized in the evaluation of the algorithm: peak signal-to-noise ratio, the structural similarity index average, the normalized crossed correlation, and bit error rate. Several watermark extraction tests were performed, with against geometric and common processing attacks. It allowed us to identify how many bits in the watermark can be modified for its adequate extraction.

Persistence Probabilities of Two-Sided (Integrated) Sums of Correlated Stationary Gaussian Sequences

NASA Astrophysics Data System (ADS)

Aurzada, Frank; Buck, Micha

2018-02-01

We study the persistence probability for some two-sided, discrete-time Gaussian sequences that are discrete-time analogues of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in continuous time in Molchan (Commun Math Phys 205(1):97-111, 1999) and Molchan (J Stat Phys 167(6):1546-1554, 2017) to a wide class of discrete-time processes.

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.

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.

Explicitly-correlated Gaussian geminals in electronic structure calculations

NASA Astrophysics Data System (ADS)

Szalewicz, Krzysztof; Jeziorski, Bogumił

2010-11-01

Explicitly correlated functions have been used since 1929, but initially only for two-electron systems. In 1960, Boys and Singer showed that if the correlating factor is of Gaussian form, many-electron integrals can be computed for general molecules. The capability of explicitly correlated Gaussian (ECG) functions to accurately describe many-electron atoms and molecules was demonstrated only in the early 1980s when Monkhorst, Zabolitzky and the present authors cast the many-body perturbation theory (MBPT) and coupled cluster (CC) equations as a system of integro-differential equations and developed techniques of solving these equations with two-electron ECG functions (Gaussian-type geminals, GTG). This work brought a new accuracy standard to MBPT/CC calculations. In 1985, Kutzelnigg suggested that the linear r 12 correlating factor can also be employed if n-electron integrals, n > 2, are factorised with the resolution of identity. Later, this factor was replaced by more general functions f (r 12), most often by ? , usually represented as linear combinations of Gaussian functions which makes the resulting approach (called F12) a special case of the original GTG expansion. The current state-of-art is that, for few-electron molecules, ECGs provide more accurate results than any other basis available, but for larger systems the F12 approach is the method of choice, giving significant improvements over orbital calculations.

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.

Laser micro-machining strategies for transparent brittle materials using ultrashort pulsed lasers

NASA Astrophysics Data System (ADS)

Bernard, Benjamin; Matylitsky, Victor

2017-02-01

Cutting and drilling of transparent materials using short pulsed laser systems are important industrial production processes. Applications ranging from sapphire cutting, hardened glass processing, and flat panel display cutting, to diamond processing are possible. The ablation process using a Gaussian laser beam incident on the topside of a sample with several parallel overlapping lines leads to a V-shaped structured groove. This limits the structuring depth for a given kerf width. The unique possibility for transparent materials to start the ablation process from the backside of the sample is a well-known strategy to improve the aspect ratio of the ablated features. This work compares the achievable groove depth depending on the kerf width for front-side and back-side ablation and presents the best relation between the kerf width and number of overscans. Additionally, the influence of the number of pulses in one burst train on the ablation efficiency is investigated. The experiments were carried out using Spirit HE laser from Spectra-Physics, with the features of adjustable pulse duration from <400 fs to 10 ps, three different repetition rates (100 kHz, 200 kHz and 400 kHz) and average output powers of >16 W ( at 1040 nm wavelength).

On switching response surface models, with applications to the structural health monitoring of bridges

NASA Astrophysics Data System (ADS)

Worden, K.; Cross, E. J.

2018-01-01

Structural Health Monitoring (SHM) is the engineering discipline of diagnosing damage and estimating safe remaining life for structures and systems. Often, SHM is accomplished by detecting changes in measured quantities from the structure of interest; if there are no competing explanations for the changes, one infers that they are the result of damage. If the structure of interest is subject to changes in its environmental or operational conditions, one must understand the effects of these changes in order that one does not falsely claim that damage has occurred when changes in measured quantities are observed. This problem - the problem of confounding influences - is particularly pressing for civil infrastructure where the given structure is usually openly exposed to the weather and may be subject to strongly varying operational conditions. One approach to understanding confounding influences is to construct a data-based response surface model that can represent measurement variations as a function of environmental and operational variables. The models can then be used to remove environmental and operational variations so that change detection algorithms signal the occurrence of damage alone. The current paper is concerned with such response surface models in the case of SHM of bridges. In particular, classes of response surface models that can switch discontinuously between regimes are discussed. Recently, it has been shown that Gaussian Process (GP) models are an effective means of developing response surface or surrogate models. However, the GP approach runs into difficulties if changes in the latent variables cause the structure of interest to abruptly switch between regimes. A good example here, which is well known in the SHM literature, is given by the Z24 Bridge in Switzerland which completely changed its dynamical behaviour when it cooled below zero degrees Celsius as the asphalt of the deck stiffened. The solution proposed here is to adopt the recently-proposed Treed Gaussian Process (TGP) model as an alternative. The approach is illustrated here on the Z24 bridge and also on data from the Tamar Bridge in the UK which shows marked switching behaviour in certain of its dynamical characteristics when its ambient wind conditions change. It is shown that treed GPs provide an effective approach to response surface modelling and that in the Tamar case, a linear model is in fact sufficient to solve the problem.

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.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2006-11-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2010-06-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Multi-fidelity Gaussian process regression for prediction of random fields

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

Parussini, L.; Venturi, D., E-mail: venturi@ucsc.edu; Perdikaris, P.

We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgersmore » equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.« less

Log-amplitude statistics for Beck-Cohen superstatistics

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Konno, Hidetoshi

2013-05-01

As a possible generalization of Beck-Cohen superstatistical processes, we study non-Gaussian processes with temporal heterogeneity of local variance. To characterize the variance heterogeneity, we define log-amplitude cumulants and log-amplitude autocovariance and derive closed-form expressions of the log-amplitude cumulants for χ2, inverse χ2, and log-normal superstatistical distributions. Furthermore, we show that χ2 and inverse χ2 superstatistics with degree 2 are closely related to an extreme value distribution, called the Gumbel distribution. In these cases, the corresponding superstatistical distributions result in the q-Gaussian distribution with q=5/3 and the bilateral exponential distribution, respectively. Thus, our finding provides a hypothesis that the asymptotic appearance of these two special distributions may be explained by a link with the asymptotic limit distributions involving extreme values. In addition, as an application of our approach, we demonstrated that non-Gaussian fluctuations observed in a stock index futures market can be well approximated by the χ2 superstatistical distribution with degree 2.

Equivalent peak resolution: characterization of the extent of separation for two components based on their relative peak overlap.

PubMed

Dvořák, Martin; Svobodová, Jana; Dubský, Pavel; Riesová, Martina; Vigh, Gyula; Gaš, Bohuslav

2015-03-01

Although the classical formula of peak resolution was derived to characterize the extent of separation only for Gaussian peaks of equal areas, it is often used even when the peaks follow non-Gaussian distributions and/or have unequal areas. This practice can result in misleading information about the extent of separation in terms of the severity of peak overlap. We propose here the use of the equivalent peak resolution value, a term based on relative peak overlap, to characterize the extent of separation that had been achieved. The definition of equivalent peak resolution is not constrained either by the form(s) of the concentration distribution function(s) of the peaks (Gaussian or non-Gaussian) or the relative area of the peaks. The equivalent peak resolution value and the classically defined peak resolution value are numerically identical when the separated peaks are Gaussian and have identical areas and SDs. Using our new freeware program, Resolution Analyzer, one can calculate both the classically defined and the equivalent peak resolution values. With the help of this tool, we demonstrate here that the classical peak resolution values mischaracterize the extent of peak overlap even when the peaks are Gaussian but have different areas. We show that under ideal conditions of the separation process, the relative peak overlap value is easily accessible by fitting the overall peak profile as the sum of two Gaussian functions. The applicability of the new approach is demonstrated on real separations. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Effect of chain stiffness on the structure of single-chain polymer nanoparticles

NASA Astrophysics Data System (ADS)

Moreno, Angel J.; Bacova, Petra; Lo Verso, Federica; Arbe, Arantxa; Colmenero, Juan; Pomposo, José A.

2018-01-01

Polymeric single-chain nanoparticles (SCNPs) are soft nano-objects synthesized by purely intramolecular cross-linking of single polymer chains. By means of computer simulations, we investigate the conformational properties of SCNPs as a function of the bending stiffness of their linear polymer precursors. We investigate a broad range of characteristic ratios from the fully flexible case to those typical of bulky synthetic polymers. Increasing stiffness hinders bonding of groups separated by short contour distances and increases looping over longer distances, leading to more compact nanoparticles with a structure of highly interconnected loops. This feature is reflected in a crossover in the scaling behaviour of several structural observables. The scaling exponents change from those characteristic for Gaussian chains or rings in θ-solvents in the fully flexible limit, to values resembling fractal or ‘crumpled’ globular behaviour for very stiff SCNPs. We characterize domains in the SCNPs. These are weakly deformable regions that can be seen as disordered analogues of domains in disordered proteins. Increasing stiffness leads to bigger and less deformable domains. Surprisingly, the scaling behaviour of the domains is in all cases similar to that of Gaussian chains or rings, irrespective of the stiffness and degree of cross-linking. It is the spatial arrangement of the domains which determines the global structure of the SCNP (sparse Gaussian-like object or crumpled globule). Since intramolecular stiffness can be varied through the specific chemistry of the precursor or by introducing bulky side groups in its backbone, our results propose a new strategy to tune the global structure of SCNPs.

Improved deconvolution of very weak confocal signals.

PubMed

Day, Kasey J; La Rivière, Patrick J; Chandler, Talon; Bindokas, Vytas P; Ferrier, Nicola J; Glick, Benjamin S

2017-01-01

Deconvolution is typically used to sharpen fluorescence images, but when the signal-to-noise ratio is low, the primary benefit is reduced noise and a smoother appearance of the fluorescent structures. 3D time-lapse (4D) confocal image sets can be improved by deconvolution. However, when the confocal signals are very weak, the popular Huygens deconvolution software erases fluorescent structures that are clearly visible in the raw data. We find that this problem can be avoided by prefiltering the optical sections with a Gaussian blur. Analysis of real and simulated data indicates that the Gaussian blur prefilter preserves meaningful signals while enabling removal of background noise. This approach is very simple, and it allows Huygens to be used with 4D imaging conditions that minimize photodamage.

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.

Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes

PubMed Central

Gibaud, Thomas; Kaplan, C. Nadir; Sharma, Prerna; Zakhary, Mark J.; Ward, Andrew; Oldenbourg, Rudolf; Meyer, Robert B.; Kamien, Randall D.; Powers, Thomas R.; Dogic, Zvonimir

2017-01-01

In the presence of a nonadsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one-rod-length–thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study elasticity of fluid sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes composed of a mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit, disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime, the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration, and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes. PMID:28411214

A multivariate multilevel Gaussian model with a mixed effects structure in the mean and covariance part.

PubMed

Li, Baoyue; Bruyneel, Luk; Lesaffre, Emmanuel

2014-05-20

A traditional Gaussian hierarchical model assumes a nested multilevel structure for the mean and a constant variance at each level. We propose a Bayesian multivariate multilevel factor model that assumes a multilevel structure for both the mean and the covariance matrix. That is, in addition to a multilevel structure for the mean we also assume that the covariance matrix depends on covariates and random effects. This allows to explore whether the covariance structure depends on the values of the higher levels and as such models heterogeneity in the variances and correlation structure of the multivariate outcome across the higher level values. The approach is applied to the three-dimensional vector of burnout measurements collected on nurses in a large European study to answer the research question whether the covariance matrix of the outcomes depends on recorded system-level features in the organization of nursing care, but also on not-recorded factors that vary with countries, hospitals, and nursing units. Simulations illustrate the performance of our modeling approach. Copyright © 2013 John Wiley & Sons, Ltd.

Upscaling anomalous reactive kinetics (A+B-->C) from pore scale Lagrangian velocity analysis

NASA Astrophysics Data System (ADS)

De Anna, P.; Tartakovsky, A. M.; Le Borgne, T.; Dentz, M.

2011-12-01

Natural flow fields in porous media display a complex spatio-temporal organization due to heterogeneous geological structures at different scales. This multiscale disorder implies anomalous dispersion, mixing and reaction kinetics (Berkowitz et al. RG 2006, Tartakovsky PRE 2010). Here, we focus on the upscaling of anomalous kinetics arising from pore scale, non Gaussian and correlated, velocity distributions. We consider reactive front simulations, where a component A displaces a component B that saturates initially the porous domain. The reactive component C is produced at the dispersive front located at interface between the A and B domains. The simulations are performed with the SPH method. As the mixing zone grows, the total mass of C produced increases with time. The scaling of this evolution with time is different from that which would be obtained from the homogeneous advection dispersion reaction equation. This anomalous kinetics property is related to spatial structure of the reactive mixture, and its evolution with time under the combined action of advective and diffusive processes. We discuss the different scaling regimes arising depending on the dominant process that governs mixing. In order to upscale these processes, we analyze the Lagrangian velocity properties, which are characterized by the non Gaussian distributions and long range temporal correlation. The main origin of these properties is the existence of very low velocity regions where solute particles can remain trapped for a long time. Another source of strong correlation is the channeling of flow in localized high velocity regions, which created finger-like structures in the concentration field. We show the spatial Markovian, and temporal non Markovian, nature of the Lagrangian velocity field. Therefore, an upscaled model can be defined as a correlated Continuous Time Random Walk (Le Borgne et al. PRL 2008). A key feature of this model is the definition of a transition probability density for Lagrangian velocities across a characteristic correlation distance. We quantify this transition probability density from pore scale simulations and use it in the effective stochastic model. In this framework, we investigate the ability of this effective model to represent correctly dispersion and mixing.

Parametric geometric model and hydrodynamic shape optimization of a flying-wing structure underwater glider

NASA Astrophysics Data System (ADS)

Wang, Zhen-yu; Yu, Jian-cheng; Zhang, Ai-qun; Wang, Ya-xing; Zhao, Wen-tao

2017-12-01

Combining high precision numerical analysis methods with optimization algorithms to make a systematic exploration of a design space has become an important topic in the modern design methods. During the design process of an underwater glider's flying-wing structure, a surrogate model is introduced to decrease the computation time for a high precision analysis. By these means, the contradiction between precision and efficiency is solved effectively. Based on the parametric geometry modeling, mesh generation and computational fluid dynamics analysis, a surrogate model is constructed by adopting the design of experiment (DOE) theory to solve the multi-objects design optimization problem of the underwater glider. The procedure of a surrogate model construction is presented, and the Gaussian kernel function is specifically discussed. The Particle Swarm Optimization (PSO) algorithm is applied to hydrodynamic design optimization. The hydrodynamic performance of the optimized flying-wing structure underwater glider increases by 9.1%.

Deformation analysis of MEMS structures by modified digital moiré methods

NASA Astrophysics Data System (ADS)

Liu, Zhanwei; Lou, Xinhao; Gao, Jianxin

2010-11-01

Quantitative deformation analysis of micro-fabricated electromechanical systems is of importance for the design and functional control of microsystems. In this paper, two modified digital moiré processing methods, Gaussian blurring algorithm combined with digital phase shifting and geometrical phase analysis (GPA) technique based on digital moiré method, are developed to quantitatively analyse the deformation behaviour of micro-electro-mechanical system (MEMS) structures. Measuring principles and experimental procedures of the two methods are described in detail. A digital moiré fringe pattern is generated by superimposing a specimen grating etched directly on a microstructure surface with a digital reference grating (DRG). Most of the grating noise is removed from the digital moiré fringes, which enables the phase distribution of the moiré fringes to be obtained directly. Strain measurement result of a MEMS structure demonstrates the feasibility of the two methods.

Stress influenced trapping processes in Si based multi-quantum well structures and heavy ions implanted Si

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

Ciurea, Magdalena Lidia, E-mail: ciurea@infim.ro; Lazanu, Sorina, E-mail: ciurea@infim.ro

2014-10-06

Multi-quantum well structures and Si wafers implanted with heavy iodine and bismuth ions are studied in order to evaluate the influence of stress on the parameters of trapping centers. The experimental method of thermostimullatedcurrents without applied bias is used, and the trapping centers are filled by illumination. By modeling the discharge curves, we found in multilayered structures the parameters of both 'normal' traps and 'stress-induced' ones, the last having a Gaussian-shaped temperature dependence of the cross section. The stress field due to the presence of stopped heavy ions implanted into Si was modeled by a permanent electric field. The increasemore » of the strain from the neighborhood of I ions to the neighborhood of Bi ions produces the broadening of some energy levels and also a temperature dependence of the cross sections for all levels.« less

Stress influenced trapping processes in Si based multi-quantum well structures and heavy ions implanted Si

NASA Astrophysics Data System (ADS)

Ciurea, Magdalena Lidia; Lazanu, Sorina

2014-10-01

Multi-quantum well structures and Si wafers implanted with heavy iodine and bismuth ions are studied in order to evaluate the influence of stress on the parameters of trapping centers. The experimental method of thermostimullatedcurrents without applied bias is used, and the trapping centers are filled by illumination. By modeling the discharge curves, we found in multilayered structures the parameters of both 'normal' traps and 'stress-induced' ones, the last having a Gaussian-shaped temperature dependence of the cross section. The stress field due to the presence of stopped heavy ions implanted into Si was modeled by a permanent electric field. The increase of the strain from the neighborhood of I ions to the neighborhood of Bi ions produces the broadening of some energy levels and also a temperature dependence of the cross sections for all levels.

Machine Learning Estimates of Natural Product Conformational Energies

PubMed Central

Rupp, Matthias; Bauer, Matthias R.; Wilcken, Rainer; Lange, Andreas; Reutlinger, Michael; Boeckler, Frank M.; Schneider, Gisbert

2014-01-01

Machine learning has been used for estimation of potential energy surfaces to speed up molecular dynamics simulations of small systems. We demonstrate that this approach is feasible for significantly larger, structurally complex molecules, taking the natural product Archazolid A, a potent inhibitor of vacuolar-type ATPase, from the myxobacterium Archangium gephyra as an example. Our model estimates energies of new conformations by exploiting information from previous calculations via Gaussian process regression. Predictive variance is used to assess whether a conformation is in the interpolation region, allowing a controlled trade-off between prediction accuracy and computational speed-up. For energies of relaxed conformations at the density functional level of theory (implicit solvent, DFT/BLYP-disp3/def2-TZVP), mean absolute errors of less than 1 kcal/mol were achieved. The study demonstrates that predictive machine learning models can be developed for structurally complex, pharmaceutically relevant compounds, potentially enabling considerable speed-ups in simulations of larger molecular structures. PMID:24453952

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).

Persistent homology and non-Gaussianity

NASA Astrophysics Data System (ADS)

Cole, Alex; Shiu, Gary

2018-03-01

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

Designing Multi-target Compound Libraries with Gaussian Process Models.

PubMed

Bieler, Michael; Reutlinger, Michael; Rodrigues, Tiago; Schneider, Petra; Kriegl, Jan M; Schneider, Gisbert

2016-05-01

We present the application of machine learning models to selecting G protein-coupled receptor (GPCR)-focused compound libraries. The library design process was realized by ant colony optimization. A proprietary Boehringer-Ingelheim reference set consisting of 3519 compounds tested in dose-response assays at 11 GPCR targets served as training data for machine learning and activity prediction. We compared the usability of the proprietary data with a public data set from ChEMBL. Gaussian process models were trained to prioritize compounds from a virtual combinatorial library. We obtained meaningful models for three of the targets (5-HT2c , MCH, A1), which were experimentally confirmed for 12 of 15 selected and synthesized or purchased compounds. Overall, the models trained on the public data predicted the observed assay results more accurately. The results of this study motivate the use of Gaussian process regression on public data for virtual screening and target-focused compound library design. © 2016 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution Non-Commercial NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

Efficient gaussian density formulation of volume and surface areas of macromolecules on graphical processing units.

PubMed

Zhang, Baofeng; Kilburg, Denise; Eastman, Peter; Pande, Vijay S; Gallicchio, Emilio

2017-04-15

We present an algorithm to efficiently compute accurate volumes and surface areas of macromolecules on graphical processing unit (GPU) devices using an analytic model which represents atomic volumes by continuous Gaussian densities. The volume of the molecule is expressed by means of the inclusion-exclusion formula, which is based on the summation of overlap integrals among multiple atomic densities. The surface area of the molecule is obtained by differentiation of the molecular volume with respect to atomic radii. The many-body nature of the model makes a port to GPU devices challenging. To our knowledge, this is the first reported full implementation of this model on GPU hardware. To accomplish this, we have used recursive strategies to construct the tree of overlaps and to accumulate volumes and their gradients on the tree data structures so as to minimize memory contention. The algorithm is used in the formulation of a surface area-based non-polar implicit solvent model implemented as an open source plug-in (named GaussVol) for the popular OpenMM library for molecular mechanics modeling. GaussVol is 50 to 100 times faster than our best optimized implementation for the CPUs, achieving speeds in excess of 100 ns/day with 1 fs time-step for protein-sized systems on commodity GPUs. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Approximate bandpass and frequency response models of the difference of Gaussian filter

NASA Astrophysics Data System (ADS)

Birch, Philip; Mitra, Bhargav; Bangalore, Nagachetan M.; Rehman, Saad; Young, Rupert; Chatwin, Chris

2010-12-01

The Difference of Gaussian (DOG) filter is widely used in optics and image processing as, among other things, an edge detection and correlation filter. It has important biological applications and appears to be part of the mammalian vision system. In this paper we analyse the filter and provide details of the full width half maximum, bandwidth and frequency response in order to aid the full characterisation of its performance.

Linear Space-Variant Image Restoration of Photon-Limited Images

DTIC Science & Technology

1978-03-01

levels of performance of the wavefront seisor. The parameter ^ represents the residual rms wavefront error ^measurement noise plus ♦ttting error...known to be optimum only when the signal and noise are uncorrelated stationary random processes «nd when the noise statistics are gaussian. In the...regime of photon-Iimited imaging, the noise is non-gaussian and signaI-dependent, and it is therefore reasonable to assume that tome form of linear

Reduced electrical bandwidth receivers for direct detection 4-ary PPM optical communication intersatellite links

NASA Technical Reports Server (NTRS)

Davidson, Frederic M.; Sun, Xiaoli

1993-01-01

One of the major sources of noise in a direct detection optical communication receiver is the shot noise due to the quantum nature of the photodetector. The shot noise is signal dependent and is neither Gaussian nor wide sense stationary. When a photomultiplier tube (PMT) or an avalanche photodiode (APD) is used, there is also a multiplicative excess noise due to the randomness of the internal photodetector gain. Generally speaking, the radio frequency (RF) communication theory cannot be applied to direct detection optical communication systems because noise in RF communication systems is usually additive and Gaussian. A receiver structure which is mathematically optimal for signal dependent shot noise is derived. Several suboptimal receiver structures are discussed and compared with the optimal receiver. The objective is to find a receiver structure which is easy to implement and gives close to optimal performance.

Large-scale structure non-Gaussianities with modal methods

NASA Astrophysics Data System (ADS)

Schmittfull, Marcel

2016-10-01

Relying on a separable modal expansion of the bispectrum, the implementation of a fast estimator for the full bispectrum of a 3d particle distribution is presented. The computational cost of accurate bispectrum estimation is negligible relative to simulation evolution, so the bispectrum can be used as a standard diagnostic whenever the power spectrum is evaluated. As an application, the time evolution of gravitational and primordial dark matter bispectra was measured in a large suite of N-body simulations. The bispectrum shape changes characteristically when the cosmic web becomes dominated by filaments and halos, therefore providing a quantitative probe of 3d structure formation. Our measured bispectra are determined by ~ 50 coefficients, which can be used as fitting formulae in the nonlinear regime and for non-Gaussian initial conditions. We also compare the measured bispectra with predictions from the Effective Field Theory of Large Scale Structures (EFTofLSS).

Frequency conversion of structured light.

PubMed

Steinlechner, Fabian; Hermosa, Nathaniel; Pruneri, Valerio; Torres, Juan P

2016-02-15

Coherent frequency conversion of structured light, i.e. the ability to manipulate the carrier frequency of a wave front without distorting its spatial phase and intensity profile, provides the opportunity for numerous novel applications in photonic technology and fundamental science. In particular, frequency conversion of spatial modes carrying orbital angular momentum can be exploited in sub-wavelength resolution nano-optics and coherent imaging at a wavelength different from that used to illuminate an object. Moreover, coherent frequency conversion will be crucial for interfacing information stored in the high-dimensional spatial structure of single and entangled photons with various constituents of quantum networks. In this work, we demonstrate frequency conversion of structured light from the near infrared (803 nm) to the visible (527 nm). The conversion scheme is based on sum-frequency generation in a periodically poled lithium niobate crystal pumped with a 1540-nm Gaussian beam. We observe frequency-converted fields that exhibit a high degree of similarity with the input field and verify the coherence of the frequency-conversion process via mode projection measurements with a phase mask and a single-mode fiber. Our results demonstrate the suitability of exploiting the technique for applications in quantum information processing and coherent imaging.

Evolution of CMB spectral distortion anisotropies and tests of primordial non-Gaussianity

NASA Astrophysics Data System (ADS)

Chluba, Jens; Dimastrogiovanni, Emanuela; Amin, Mustafa A.; Kamionkowski, Marc

2017-04-01

Anisotropies in distortions to the frequency spectrum of the cosmic microwave background (CMB) can be created through spatially varying heating processes in the early Universe. For instance, the dissipation of small-scale acoustic modes does create distortion anisotropies, in particular for non-Gaussian primordial perturbations. In this work, we derive approximations that allow describing the associated distortion field. We provide a systematic formulation of the problem using Fourier-space window functions, clarifying and generalizing previous approximations. Our expressions highlight the fact that the amplitudes of the spectral-distortion fluctuations induced by non-Gaussianity depend also on the homogeneous value of those distortions. Absolute measurements are thus required to obtain model-independent distortion constraints on primordial non-Gaussianity. We also include a simple description for the evolution of distortions through photon diffusion, showing that these corrections can usually be neglected. Our formulation provides a systematic framework for computing higher order correlation functions of distortions with CMB temperature anisotropies and can be extended to describe correlations with polarization anisotropies.

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

Probabilistic PCA of censored data: accounting for uncertainties in the visualization of high-throughput single-cell qPCR data.

PubMed

Buettner, Florian; Moignard, Victoria; Göttgens, Berthold; Theis, Fabian J

2014-07-01

High-throughput single-cell quantitative real-time polymerase chain reaction (qPCR) is a promising technique allowing for new insights in complex cellular processes. However, the PCR reaction can be detected only up to a certain detection limit, whereas failed reactions could be due to low or absent expression, and the true expression level is unknown. Because this censoring can occur for high proportions of the data, it is one of the main challenges when dealing with single-cell qPCR data. Principal component analysis (PCA) is an important tool for visualizing the structure of high-dimensional data as well as for identifying subpopulations of cells. However, to date it is not clear how to perform a PCA of censored data. We present a probabilistic approach that accounts for the censoring and evaluate it for two typical datasets containing single-cell qPCR data. We use the Gaussian process latent variable model framework to account for censoring by introducing an appropriate noise model and allowing a different kernel for each dimension. We evaluate this new approach for two typical qPCR datasets (of mouse embryonic stem cells and blood stem/progenitor cells, respectively) by performing linear and non-linear probabilistic PCA. Taking the censoring into account results in a 2D representation of the data, which better reflects its known structure: in both datasets, our new approach results in a better separation of known cell types and is able to reveal subpopulations in one dataset that could not be resolved using standard PCA. The implementation was based on the existing Gaussian process latent variable model toolbox (https://github.com/SheffieldML/GPmat); extensions for noise models and kernels accounting for censoring are available at http://icb.helmholtz-muenchen.de/censgplvm. © The Author 2014. Published by Oxford University Press. All rights reserved.

Probabilistic PCA of censored data: accounting for uncertainties in the visualization of high-throughput single-cell qPCR data

PubMed Central

Buettner, Florian; Moignard, Victoria; Göttgens, Berthold; Theis, Fabian J.

2014-01-01

Motivation: High-throughput single-cell quantitative real-time polymerase chain reaction (qPCR) is a promising technique allowing for new insights in complex cellular processes. However, the PCR reaction can be detected only up to a certain detection limit, whereas failed reactions could be due to low or absent expression, and the true expression level is unknown. Because this censoring can occur for high proportions of the data, it is one of the main challenges when dealing with single-cell qPCR data. Principal component analysis (PCA) is an important tool for visualizing the structure of high-dimensional data as well as for identifying subpopulations of cells. However, to date it is not clear how to perform a PCA of censored data. We present a probabilistic approach that accounts for the censoring and evaluate it for two typical datasets containing single-cell qPCR data. Results: We use the Gaussian process latent variable model framework to account for censoring by introducing an appropriate noise model and allowing a different kernel for each dimension. We evaluate this new approach for two typical qPCR datasets (of mouse embryonic stem cells and blood stem/progenitor cells, respectively) by performing linear and non-linear probabilistic PCA. Taking the censoring into account results in a 2D representation of the data, which better reflects its known structure: in both datasets, our new approach results in a better separation of known cell types and is able to reveal subpopulations in one dataset that could not be resolved using standard PCA. Availability and implementation: The implementation was based on the existing Gaussian process latent variable model toolbox (https://github.com/SheffieldML/GPmat); extensions for noise models and kernels accounting for censoring are available at http://icb.helmholtz-muenchen.de/censgplvm. Contact: fbuettner.phys@gmail.com Supplementary information: Supplementary data are available at Bioinformatics online. PMID:24618470

Software Applications on the Peregrine System | High-Performance Computing

Science.gov Websites

programming and optimization. Gaussian Chemistry Program for calculating molecular electronic structure and Materials Science Open-source classical molecular dynamics program designed for massively parallel systems framework Q-Chem Chemistry ab initio quantum chemistry package for predictin molecular structures

Improved Linear Algebra Methods for Redshift Computation from Limited Spectrum Data - II

NASA Technical Reports Server (NTRS)

Foster, Leslie; Waagen, Alex; Aijaz, Nabella; Hurley, Michael; Luis, Apolo; Rinsky, Joel; Satyavolu, Chandrika; Gazis, Paul; Srivastava, Ashok; Way, Michael

2008-01-01

Given photometric broadband measurements of a galaxy, Gaussian processes may be used with a training set to solve the regression problem of approximating the redshift of this galaxy. However, in practice solving the traditional Gaussian processes equation is too slow and requires too much memory. We employed several methods to avoid this difficulty using algebraic manipulation and low-rank approximation, and were able to quickly approximate the redshifts in our testing data within 17 percent of the known true values using limited computational resources. The accuracy of one method, the V Formulation, is comparable to the accuracy of the best methods currently used for this problem.

Predicting Error Bars for QSAR Models

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

Schroeter, Timon; Technische Universitaet Berlin, Department of Computer Science, Franklinstrasse 28/29, 10587 Berlin; Schwaighofer, Anton

2007-09-18

Unfavorable physicochemical properties often cause drug failures. It is therefore important to take lipophilicity and water solubility into account early on in lead discovery. This study presents log D{sub 7} models built using Gaussian Process regression, Support Vector Machines, decision trees and ridge regression algorithms based on 14556 drug discovery compounds of Bayer Schering Pharma. A blind test was conducted using 7013 new measurements from the last months. We also present independent evaluations using public data. Apart from accuracy, we discuss the quality of error bars that can be computed by Gaussian Process models, and ensemble and distance based techniquesmore » for the other modelling approaches.« less

Time reversibility of intracranial human EEG recordings in mesial temporal lobe epilepsy

NASA Astrophysics Data System (ADS)

van der Heyden, M. J.; Diks, C.; Pijn, J. P. M.; Velis, D. N.

1996-02-01

Intracranial electroencephalograms from patients suffering from mesial temporal lobe epilepsy were tested for time reversibility. If the recorded time series is irreversible, the input of the recording system cannot be a realisation of a linear Gaussian random process. We confirmed experimentally that the measurement equipment did not introduce irreversibility in the recorded output when the input was a realisation of a linear Gaussian random process. In general, the non-seizure recordings are reversible, whereas the seizure recordings are irreversible. These results suggest that time reversibility is a useful property for the characterisation of human intracranial EEG recordings in mesial temporal lobe epilepsy.

On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization

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

Konomi, Bledar A.; Karagiannis, Georgios; Lin, Guang

2015-02-01

The Bayesian treed Gaussian process (BTGP) has gained popularity in recent years because it provides a straightforward mechanism for modeling non-stationary data and can alleviate computational demands by fitting models to less data. The extension of BTGP to the multivariate setting requires us to model the cross-covariance and to propose efficient algorithms that can deal with trans-dimensional MCMC moves. In this paper we extend the cross-covariance of the Bayesian treed multivariate Gaussian process (BTMGP) to that of linear model of Coregionalization (LMC) cross-covariances. Different strategies have been developed to improve the MCMC mixing and invert smaller matrices in the Bayesianmore » inference. Moreover, we compare the proposed BTMGP with existing multiple BTGP and BTMGP in test cases and multiphase flow computer experiment in a full scale regenerator of a carbon capture unit. The use of the BTMGP with LMC cross-covariance helped to predict the computer experiments relatively better than existing competitors. The proposed model has a wide variety of applications, such as computer experiments and environmental data. In the case of computer experiments we also develop an adaptive sampling strategy for the BTMGP with LMC cross-covariance function.« less

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

The series product for gaussian quantum input processes

NASA Astrophysics Data System (ADS)

Gough, John E.; James, Matthew R.

2017-02-01

We present a theory for connecting quantum Markov components into a network with quantum input processes in a Gaussian state (including thermal and squeezed). One would expect on physical grounds that the connection rules should be independent of the state of the input to the network. To compute statistical properties, we use a version of Wicks' theorem involving fictitious vacuum fields (Fock space based representation of the fields) and while this aids computation, and gives a rigorous formulation, the various representations need not be unitarily equivalent. In particular, a naive application of the connection rules would lead to the wrong answer. We establish the correct interconnection rules, and show that while the quantum stochastic differential equations of motion display explicitly the covariances (thermal and squeezing parameters) of the Gaussian input fields we introduce the Wick-Stratonovich form which leads to a way of writing these equations that does not depend on these covariances and so corresponds to the universal equations written in terms of formal quantum input processes. We show that a wholly consistent theory of quantum open systems in series can be developed in this way, and as required physically, is universal and in particular representation-free.

Acceleration of on-axis and ring-shaped electron beams in wakefields driven by Laguerre-Gaussian pulses

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

Zhang, Guo-Bo; Key Laboratory for Laser Plasmas; Chen, Min, E-mail: minchen@sjtu.edu.cn, E-mail: yanyunma@126.com

2016-03-14

The acceleration of electron beams with multiple transverse structures in wakefields driven by Laguerre-Gaussian pulses has been studied through three-dimensional (3D) particle-in-cell simulations. Under different laser-plasma conditions, the wakefield shows different transverse structures. In general cases, the wakefield shows a donut-like structure and it accelerates the ring-shaped hollow electron beam. When a lower plasma density or a smaller laser spot size is used, besides the donut-like wakefield, a central bell-like wakefield can also be excited. The wake sets in the center of the donut-like wake. In this case, both a central on-axis electron beam and a ring-shaped electron beam aremore » simultaneously accelerated. Further, reducing the plasma density or laser spot size leads to an on-axis electron beam acceleration only. The research is beneficial for some potential applications requiring special pulse beam structures, such as positron acceleration and collimation.« less

Reversible wavefront shaping between Gaussian and Airy beams by mimicking gravitational field

NASA Astrophysics Data System (ADS)

Wang, Xiangyang; Liu, Hui; Sheng, Chong; Zhu, Shining

2018-02-01

In this paper, we experimentally demonstrate reversible wavefront shaping through mimicking gravitational field. A gradient-index micro-structured optical waveguide with special refractive index profile was constructed whose effective index satisfying a gravitational field profile. Inside the waveguide, an incident broad Gaussian beam is firstly transformed into an accelerating beam, and the generated accelerating beam is gradually changed back to a Gaussian beam afterwards. To validate our experiment, we performed full-wave continuum simulations that agree with the experimental results. Furthermore, a theoretical model was established to describe the evolution of the laser beam based on Landau’s method, showing that the accelerating beam behaves like the Airy beam in the small range in which the linear potential approaches zero. To our knowledge, such a reversible wavefront shaping technique has not been reported before.

Implementing of lognormal humidity and cloud-related control variables for the NCEP GSI hybrid EnVAR Assimilation scheme.

NASA Astrophysics Data System (ADS)

Fletcher, S. J.; Kleist, D.; Ide, K.

2017-12-01

As the resolution of operational global numerical weather prediction system approach the meso-scale, then the assumption of Gaussianity for the errors at these scales may not valid. However, it is also true that synoptic variables that are positive definite in behavior, for example humidity, cannot be optimally analyzed with a Gaussian error structure, where the increment could force the full field to go negative. In this presentation we present the initial work of implementing a mixed Gaussian-lognormal approximation for the temperature and moisture variable in both the ensemble and variational component of the NCEP GSI hybrid EnVAR. We shall also lay the foundation for the implementation of the lognormal approximation to cloud related control variables to allow for a possible more consistent assimilation of cloudy radiances.

Gaussian Accelerated Molecular Dynamics: Theory, Implementation, and Applications

PubMed Central

Miao, Yinglong; McCammon, J. Andrew

2018-01-01

A novel Gaussian Accelerated Molecular Dynamics (GaMD) method has been developed for simultaneous unconstrained enhanced sampling and free energy calculation of biomolecules. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of the biomolecules. Furthermore, by constructing a boost potential that follows a Gaussian distribution, accurate reweighting of GaMD simulations is achieved via cumulant expansion to the second order. The free energy profiles obtained from GaMD simulations allow us to identify distinct low energy states of the biomolecules and characterize biomolecular structural dynamics quantitatively. In this chapter, we present the theory of GaMD, its implementation in the widely used molecular dynamics software packages (AMBER and NAMD), and applications to the alanine dipeptide biomolecular model system, protein folding, biomolecular large-scale conformational transitions and biomolecular recognition. PMID:29720925

Generation of 2 µm Laguerre-Gaussian mode in a Tm:LuYAG solid-state laser

NASA Astrophysics Data System (ADS)

Liu, Qiyao; Ding, Manman; Zhao, Yongguang; Zhou, Wei; Shen, Deyuan

2018-04-01

In this article, we discuss the first vortex laser in the 2 µm spectral range directly generated from a Tm:LuYAG oscillator, in which a pump beam with annular intensity distribution is employed in line with Laguerre-Gaussian modes. Laser thresholds of different-order Laguerre-Gaussian modes are theoretically analyzed and discussed. Vortex lasers with orbital angular momentum of ħ and  -ħ were experimentally produced with corresponding output powers of 1.75 W and 1.64 W, respectively. This directly emitted vortex laser generated in the ~2 µm region from a compact and robust Tm:LuYAG oscillator has potential applications in the areas of molecular spectroscopy and organic material processing amongst others.

Numerical investigations of non-collinear optical parametric chirped pulse amplification for Laguerre-Gaussian vortex beam

NASA Astrophysics Data System (ADS)

Xu, Lu; Yu, Lianghong; Liang, Xiaoyan

2016-04-01

We present for the first time a scheme to amplify a Laguerre-Gaussian vortex beam based on non-collinear optical parametric chirped pulse amplification (OPCPA). In addition, a three-dimensional numerical model of non-collinear optical parametric amplification was deduced in the frequency domain, in which the effects of non-collinear configuration, temporal and spatial walk-off, group-velocity dispersion and diffraction were also taken into account, to trace the dynamics of the Laguerre-Gaussian vortex beam and investigate its critical parameters in the non-collinear OPCPA process. Based on the numerical simulation results, the scheme shows promise for implementation in a relativistic twisted laser pulse system, which will diversify the light-matter interaction field.

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.

Design and fabrication of optical homogenizer with micro structure by injection molding process

NASA Astrophysics Data System (ADS)

Chen, C.-C. A.; Chang, S.-W.; Weng, C.-J.

2008-08-01

This paper is to design and fabricate an optical homogenizer with hybrid design of collimator, toroidal lens array, and projection lens for beam shaping of Gaussian beam into uniform cylindrical beam. TracePro software was used to design the geometry of homogenizer and simulation of injection molding was preceded by Moldflow MPI to evaluate the mold design for injection molding process. The optical homogenizer is a cylindrical part with thickness 8.03 mm and diameter 5 mm. The micro structure of toroidal array has groove height designed from 12 μm to 99 μm. An electrical injection molding machine and PMMA (n= 1.4747) were selected to perform the experiment. Experimental results show that the optics homogenizer has achieved the transfer ratio of grooves (TRG) as 88.98% and also the optical uniformity as 68% with optical efficiency as 91.88%. Future study focuses on development of an optical homogenizer for LED light source.

The Fluctuation-Dissipation Theorem of Colloidal Particle's energy on 2D Periodic Substrates: A Monte Carlo Study of thermal noise-like fluctuation and diffusion like Brownian motion

NASA Astrophysics Data System (ADS)

Najafi, Amin

2014-05-01

Using the Monte Carlo simulations, we have calculated mean-square fluctuations in statistical mechanics, such as those for colloids energy configuration are set on square 2D periodic substrates interacting via a long range screened Coulomb potential on any specific and fixed substrate. Random fluctuations with small deviations from the state of thermodynamic equilibrium arise from the granular structure of them and appear as thermal diffusion with Gaussian distribution structure as well. The variations are showing linear form of the Fluctuation-Dissipation Theorem on the energy of particles constitutive a canonical ensemble with continuous diffusion process of colloidal particle systems. The noise-like variation of the energy per particle and the order parameter versus the Brownian displacement of sum of large number of random steps of particles at low temperatures phase are presenting a markovian process on colloidal particles configuration, too.

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

NASA Astrophysics Data System (ADS)

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

2013-09-01

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

Gaussian random bridges and a geometric model for information equilibrium

NASA Astrophysics Data System (ADS)

Mengütürk, Levent Ali

2018-03-01

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

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.

Multifractal Properties of Process Control Variables

NASA Astrophysics Data System (ADS)

Domański, Paweł D.

2017-06-01

Control system is an inevitable element of any industrial installation. Its quality affects overall process performance significantly. The assessment, whether control system needs any improvement or not, requires relevant and constructive measures. There are various methods, like time domain based, Minimum Variance, Gaussian and non-Gaussian statistical factors, fractal and entropy indexes. Majority of approaches use time series of control variables. They are able to cover many phenomena. But process complexities and human interventions cause effects that are hardly visible for standard measures. It is shown that the signals originating from industrial installations have multifractal properties and such an analysis may extend standard approach to further observations. The work is based on industrial and simulation data. The analysis delivers additional insight into the properties of control system and the process. It helps to discover internal dependencies and human factors, which are hardly detectable.

Is There a Critical Distance for Fickian Transport? - a Statistical Approach to Sub-Fickian Transport Modelling in Porous Media

NASA Astrophysics Data System (ADS)

Most, S.; Nowak, W.; Bijeljic, B.

2014-12-01

Transport processes in porous media are frequently simulated as particle movement. This process can be formulated as a stochastic process of particle position increments. At the pore scale, the geometry and micro-heterogeneities prohibit the commonly made assumption of independent and normally distributed increments to represent dispersion. Many recent particle methods seek to loosen this assumption. Recent experimental data suggest that we have not yet reached the end of the need to generalize, because particle increments show statistical dependency beyond linear correlation and over many time steps. The goal of this work is to better understand the validity regions of commonly made assumptions. We are investigating after what transport distances can we observe: A statistical dependence between increments, that can be modelled as an order-k Markov process, boils down to order 1. This would be the Markovian distance for the process, where the validity of yet-unexplored non-Gaussian-but-Markovian random walks would start. A bivariate statistical dependence that simplifies to a multi-Gaussian dependence based on simple linear correlation (validity of correlated PTRW). Complete absence of statistical dependence (validity of classical PTRW/CTRW). The approach is to derive a statistical model for pore-scale transport from a powerful experimental data set via copula analysis. The model is formulated as a non-Gaussian, mutually dependent Markov process of higher order, which allows us to investigate the validity ranges of simpler models.

Non-Gaussianity and cross-scale coupling in interplanetary magnetic field turbulence during a rope-rope magnetic reconnection event

NASA Astrophysics Data System (ADS)

Miranda, Rodrigo A.; Schelin, Adriane B.; Chian, Abraham C.-L.; Ferreira, José L.

2018-03-01

In a recent paper (Chian et al., 2016) it was shown that magnetic reconnection at the interface region between two magnetic flux ropes is responsible for the genesis of interplanetary intermittent turbulence. The normalized third-order moment (skewness) and the normalized fourth-order moment (kurtosis) display a quadratic relation with a parabolic shape that is commonly observed in observational data from turbulence in fluids and plasmas, and is linked to non-Gaussian fluctuations due to coherent structures. In this paper we perform a detailed study of the relation between the skewness and the kurtosis of the modulus of the magnetic field |B| during a triple interplanetary magnetic flux rope event. In addition, we investigate the skewness-kurtosis relation of two-point differences of |B| for the same event. The parabolic relation displays scale dependence and is found to be enhanced during magnetic reconnection, rendering support for the generation of non-Gaussian coherent structures via rope-rope magnetic reconnection. Our results also indicate that a direct coupling between the scales of magnetic flux ropes and the scales within the inertial subrange occurs in the solar wind.

The value of a kurtosis metric in estimating the hazard to hearing of complex industrial noise exposures.

PubMed

Qiu, Wei; Hamernik, Roger P; Davis, Robert I

2013-05-01

A series of Gaussian and non-Gaussian equal energy noise exposures were designed with the objective of establishing the extent to which the kurtosis statistic could be used to grade the severity of noise trauma produced by the exposures. Here, 225 chinchillas distributed in 29 groups, with 6 to 8 animals per group, were exposed at 97 dB SPL. The equal energy exposures were presented either continuously for 5 d or on an interrupted schedule for 19 d. The non-Gaussian noises all differed in the level of the kurtosis statistic or in the temporal structure of the noise, where the latter was defined by different peak, interval, and duration histograms of the impact noise transients embedded in the noise signal. Noise-induced trauma was estimated from auditory evoked potential hearing thresholds and surface preparation histology that quantified sensory cell loss. Results indicated that the equal energy hypothesis is a valid unifying principle for estimating the consequences of an exposure if and only if the equivalent energy exposures had the same kurtosis. Furthermore, for the same level of kurtosis the detailed temporal structure of an exposure does not have a strong effect on trauma.

Transient Calibration of a Variably-Saturated Groundwater Flow Model By Iterative Ensemble Smoothering: Synthetic Case and Application to the Flow Induced During Shaft Excavation and Operation of the Bure Underground Research Laboratory

NASA Astrophysics Data System (ADS)

Lam, D. T.; Kerrou, J.; Benabderrahmane, H.; Perrochet, P.

2017-12-01

The calibration of groundwater flow models in transient state can be motivated by the expected improved characterization of the aquifer hydraulic properties, especially when supported by a rich transient dataset. In the prospect of setting up a calibration strategy for a variably-saturated transient groundwater flow model of the area around the ANDRA's Bure Underground Research Laboratory, we wish to take advantage of the long hydraulic head and flowrate time series collected near and at the access shafts in order to help inform the model hydraulic parameters. A promising inverse approach for such high-dimensional nonlinear model, and which applicability has been illustrated more extensively in other scientific fields, could be an iterative ensemble smoother algorithm initially developed for a reservoir engineering problem. Furthermore, the ensemble-based stochastic framework will allow to address to some extent the uncertainty of the calibration for a subsequent analysis of a flow process dependent prediction. By assimilating the available data in one single step, this method iteratively updates each member of an initial ensemble of stochastic realizations of parameters until the minimization of an objective function. However, as it is well known for ensemble-based Kalman methods, this correction computed from approximations of covariance matrices is most efficient when the ensemble realizations are multi-Gaussian. As shown by the comparison of the updated ensemble mean obtained for our simplified synthetic model of 2D vertical flow by using either multi-Gaussian or multipoint simulations of parameters, the ensemble smoother fails to preserve the initial connectivity of the facies and the parameter bimodal distribution. Given the geological structures depicted by the multi-layered geological model built for the real case, our goal is to find how to still best leverage the performance of the ensemble smoother while using an initial ensemble of conditional multi-Gaussian simulations or multipoint simulations as conceptually consistent as possible. Performance of the algorithm including additional steps to help mitigate the effects of non-Gaussian patterns, such as Gaussian anamorphosis, or resampling of facies from the training image using updated local probability constraints will be assessed.

Structural features that predict real-value fluctuations of globular proteins

PubMed Central

Jamroz, Michal; Kolinski, Andrzej; Kihara, Daisuke

2012-01-01

It is crucial to consider dynamics for understanding the biological function of proteins. We used a large number of molecular dynamics trajectories of non-homologous proteins as references and examined static structural features of proteins that are most relevant to fluctuations. We examined correlation of individual structural features with fluctuations and further investigated effective combinations of features for predicting the real-value of residue fluctuations using the support vector regression. It was found that some structural features have higher correlation than crystallographic B-factors with fluctuations observed in molecular dynamics trajectories. Moreover, support vector regression that uses combinations of static structural features showed accurate prediction of fluctuations with an average Pearson’s correlation coefficient of 0.669 and a root mean square error of 1.04 Å. This correlation coefficient is higher than the one observed for the prediction by the Gaussian network model. An advantage of the developed method over the Gaussian network models is that the former predicts the real-value of fluctuation. The results help improve our understanding of relationships between protein structure and fluctuation. Furthermore, the developed method provides a convienient practial way to predict fluctuations of proteins using easily computed static structural features of proteins. PMID:22328193

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.

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.

Understanding nanocellulose chirality and structure–properties relationship at the single fibril level

PubMed Central

Usov, Ivan; Nyström, Gustav; Adamcik, Jozef; Handschin, Stephan; Schütz, Christina; Fall, Andreas; Bergström, Lennart; Mezzenga, Raffaele

2015-01-01

Nanocellulose fibrils are ubiquitous in nature and nanotechnologies but their mesoscopic structural assembly is not yet fully understood. Here we study the structural features of rod-like cellulose nanoparticles on a single particle level, by applying statistical polymer physics concepts on electron and atomic force microscopy images, and we assess their physical properties via quantitative nanomechanical mapping. We show evidence of right-handed chirality, observed on both bundles and on single fibrils. Statistical analysis of contours from microscopy images shows a non-Gaussian kink angle distribution. This is inconsistent with a structure consisting of alternating amorphous and crystalline domains along the contour and supports process-induced kink formation. The intrinsic mechanical properties of nanocellulose are extracted from nanoindentation and persistence length method for transversal and longitudinal directions, respectively. The structural analysis is pushed to the level of single cellulose polymer chains, and their smallest associated unit with a proposed 2 × 2 chain-packing arrangement. PMID:26108282

Structure and atomic correlations in molecular systems probed by XAS reverse Monte Carlo refinement

NASA Astrophysics Data System (ADS)

Di Cicco, Andrea; Iesari, Fabio; Trapananti, Angela; D'Angelo, Paola; Filipponi, Adriano

2018-03-01

The Reverse Monte Carlo (RMC) algorithm for structure refinement has been applied to x-ray absorption spectroscopy (XAS) multiple-edge data sets for six gas phase molecular systems (SnI2, CdI2, BBr3, GaI3, GeBr4, GeI4). Sets of thousands of molecular replicas were involved in the refinement process, driven by the XAS data and constrained by available electron diffraction results. The equilibrated configurations were analysed to determine the average tridimensional structure and obtain reliable bond and bond-angle distributions. Detectable deviations from Gaussian models were found in some cases. This work shows that a RMC refinement of XAS data is able to provide geometrical models for molecular structures compatible with present experimental evidence. The validation of this approach on simple molecular systems is particularly important in view of its possible simple extension to more complex and extended systems including metal-organic complexes, biomolecules, or nanocrystalline systems.

Void statistics, scaling, and the origins of large-scale structure

NASA Technical Reports Server (NTRS)

Fry, J. N.; Giovanelli, Riccardo; Haynes, Martha P.; Melott, Adrian L.; Scherrer, Robert J.

1989-01-01

The probability that a volume of the universe of given size and shape spaced at random will be void of galaxies is used here to study various models of the origin of cosmological structures. Numerical simulations are conducted on hot-particle and cold-particle-modulated inflationary models with and without biasing, on isothermal or initially Poisson models, and on models where structure is seeded by loops of cosmic string. For the Pisces-Perseus redshift compilation of Giovanelli and Haynes (1985), it is found that hierarchical scaling is obeyed for subsamples constructed with different limiting magnitudes and subsamples taken at random. This result confirms that the hierarchical ansatz holds valid to high order and supports the idea that structure in the observed universe evolves by a regular process from an almost Gaussian primordial state. Neutrino models without biasing show the effect of a strong feature in the initial power spectrum. Cosmic string models do not agree well with the galaxy data.

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

Monte Carlo based toy model for fission process

NASA Astrophysics Data System (ADS)

Kurniadi, R.; Waris, A.; Viridi, S.

2014-09-01

There are many models and calculation techniques to obtain visible image of fission yield process. In particular, fission yield can be calculated by using two calculations approach, namely macroscopic approach and microscopic approach. This work proposes another calculation approach in which the nucleus is treated as a toy model. Hence, the fission process does not represent real fission process in nature completely. The toy model is formed by Gaussian distribution of random number that randomizes distance likesthe distance between particle and central point. The scission process is started by smashing compound nucleus central point into two parts that are left central and right central points. These three points have different Gaussian distribution parameters such as mean (μCN, μL, μR), and standard deviation (σCN, σL, σR). By overlaying of three distributions, the number of particles (NL, NR) that are trapped by central points can be obtained. This process is iterated until (NL, NR) become constant numbers. Smashing process is repeated by changing σL and σR, randomly.

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

NASA Technical Reports Server (NTRS)

Mashiku, Alinda; Garrison, James L.; Carpenter, J. Russell

2012-01-01

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite-Gaussian beams

NASA Astrophysics Data System (ADS)

Chen, Y. F.; Chang, C. C.; Lee, C. Y.; Tung, J. C.; Liang, H. C.; Huang, K. F.

2018-01-01

Theoretical wave functions are analytically derived to characterize the propagation evolution of the Hermite-Gaussian (HG) beams transformed by a single-lens astigmatic mode converter with arbitrary angle. The derived wave functions are related to the combination of the rotation transform and the antisymmetric fractional Fourier transform. The derived formula is systematically validated by using an off-axis diode-pumped solid-state laser to generate various high-order HG beams for mode conversions. In addition to validation, the creation and evolution of vortex structures in the transformed HG beams are numerically manifested. The present theoretical analyses can be used not only to characterize the evolution of the transformed beams but to design the optical vortex beams with various forms.

Clustering fossils in solid inflation

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

Akhshik, Mohammad, E-mail: m.akhshik@ipm.ir

In solid inflation the single field non-Gaussianity consistency condition is violated. As a result, the long tenor perturbation induces observable clustering fossils in the form of quadrupole anisotropy in large scale structure power spectrum. In this work we revisit the bispectrum analysis for the scalar-scalar-scalar and tensor-scalar-scalar bispectrum for the general parameter space of solid. We consider the parameter space of the model in which the level of non-Gaussianity generated is consistent with the Planck constraints. Specializing to this allowed range of model parameter we calculate the quadrupole anisotropy induced from the long tensor perturbations on the power spectrum ofmore » the scalar perturbations. We argue that the imprints of clustering fossil from primordial gravitational waves on large scale structures can be detected from the future galaxy surveys.« less

Filtering of higher-order laser modes using plasma structures

NASA Astrophysics Data System (ADS)

Djordjevic, Blagoje; Benedetti, Carlo; Schroeder, Carl; Esarey, Eric; Leemans, Wim

2017-10-01

Plasma structures based on leaky channels are proposed to filter higher-order laser mode content. The evolution and propagation of non-Gaussian laser pulses in leaky channels is studied, and it is shown that, for appropriate laser-plasma parameters, the higher-order laser mode content may be removed while the fundamental mode remains well-guided. The behavior of the multi-mode laser pulse is described analytically, including the derivation of the leakage coefficients, and compared to numerical calculations. Gaussian laser pulse propagation, without higher-order mode content, improves guiding in parabolic plasma channels, enabling extended interaction lengths for laser-plasma accelerator applications. This work was supported by the Director, Office of Science, Office of High Energy Physics, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Improved deconvolution of very weak confocal signals

PubMed Central

Day, Kasey J.; La Rivière, Patrick J.; Chandler, Talon; Bindokas, Vytas P.; Ferrier, Nicola J.; Glick, Benjamin S.

2017-01-01

Deconvolution is typically used to sharpen fluorescence images, but when the signal-to-noise ratio is low, the primary benefit is reduced noise and a smoother appearance of the fluorescent structures. 3D time-lapse (4D) confocal image sets can be improved by deconvolution. However, when the confocal signals are very weak, the popular Huygens deconvolution software erases fluorescent structures that are clearly visible in the raw data. We find that this problem can be avoided by prefiltering the optical sections with a Gaussian blur. Analysis of real and simulated data indicates that the Gaussian blur prefilter preserves meaningful signals while enabling removal of background noise. This approach is very simple, and it allows Huygens to be used with 4D imaging conditions that minimize photodamage. PMID:28868135

Improved deconvolution of very weak confocal signals

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

Day, Kasey J.; La Riviere, Patrick J.; Chandler, Talon

Deconvolution is typically used to sharpen fluorescence images, but when the signal-to-noise ratio is low, the primary benefit is reduced noise and a smoother appearance of the fluorescent structures. 3D time-lapse (4D) confocal image sets can be improved by deconvolution. However, when the confocal signals are very weak, the popular Huygens deconvolution software erases fluorescent structures that are clearly visible in the raw data. We find that this problem can be avoided by prefiltering the optical sections with a Gaussian blur. Analysis of real and simulated data indicates that the Gaussian blur prefilter preserves meaningful signals while enabling removal ofmore » background noise. Here, this approach is very simple, and it allows Huygens to be used with 4D imaging conditions that minimize photodamage.« less

Improved deconvolution of very weak confocal signals

DOE PAGES

Day, Kasey J.; La Riviere, Patrick J.; Chandler, Talon; ...

2017-06-06

Deconvolution is typically used to sharpen fluorescence images, but when the signal-to-noise ratio is low, the primary benefit is reduced noise and a smoother appearance of the fluorescent structures. 3D time-lapse (4D) confocal image sets can be improved by deconvolution. However, when the confocal signals are very weak, the popular Huygens deconvolution software erases fluorescent structures that are clearly visible in the raw data. We find that this problem can be avoided by prefiltering the optical sections with a Gaussian blur. Analysis of real and simulated data indicates that the Gaussian blur prefilter preserves meaningful signals while enabling removal ofmore » background noise. Here, this approach is very simple, and it allows Huygens to be used with 4D imaging conditions that minimize photodamage.« less

Optical polarimetry and molecular line studies of L1157 dark molecular cloud

NASA Astrophysics Data System (ADS)

Sharma, Ekta; Soam, Archana; Gopinathan, Maheswar

2018-04-01

Filaments are omnipresent in molecular clouds which are believed to fragment into cores. The detailed process of the evolution from filaments to cores depends critically on the physical conditions in the star forming region. This study aims at characterising gas motions using velocity structure and finding the dynamical importance of magnetic fields in the filament morphology. The plane-of-the-sky component of the magnetic field has been measured using optical polarization of the background stars. The orientation is found to be almost perpendicular to the filament implying its dynamical importance in the evolution of the cloud. Optical polarimetric results match very well with the sub millimetre polarization angles obtained in the inner core regions. The magnetic fields are found to have an orientation of 130° east with respect to north. The angular offset between the outflow axis and the magnetic field direction is found to be 25°. Values for parameters like the excitation temperature, optical depth and column densities have been derived using molecular lines. Optically thick lines show non-gaussian features. The non-thermal widths tell about the presence of turbulent motions whereas the C180 lines follow Gaussian features almost at all the locations observed in the filament.

Fuzzy C-means classification for corrosion evolution of steel images

NASA Astrophysics Data System (ADS)

Trujillo, Maite; Sadki, Mustapha

2004-05-01

An unavoidable problem of metal structures is their exposure to rust degradation during their operational life. Thus, the surfaces need to be assessed in order to avoid potential catastrophes. There is considerable interest in the use of patch repair strategies which minimize the project costs. However, to operate such strategies with confidence in the long useful life of the repair, it is essential that the condition of the existing coatings and the steel substrate can be accurately quantified and classified. This paper describes the application of fuzzy set theory for steel surfaces classification according to the steel rust time. We propose a semi-automatic technique to obtain image clustering using the Fuzzy C-means (FCM) algorithm and we analyze two kinds of data to study the classification performance. Firstly, we investigate the use of raw images" pixels without any pre-processing methods and neighborhood pixels. Secondly, we apply Gaussian noise to the images with different standard deviation to study the FCM method tolerance to Gaussian noise. The noisy images simulate the possible perturbations of the images due to the weather or rust deposits in the steel surfaces during typical on-site acquisition procedures

Tearing of thin spherical shells adhered to equally curved rigid substrates

NASA Astrophysics Data System (ADS)

McMahan, Connor; Lee, Anna; Marthelot, Joel; Reis, Pedro

Lasik (Laser-Assisted in Situ Keratomileusis) eye surgery involves the tearing of the corneal epithelium to remodel the corneal stroma for corrections such as myopia, hyperopia and astigmatism. One issue with this procedure is that during the tearing of the corneal epithelium, if the two propagating cracks coalesce, a flap detaches which could cause significant complications in the recovery of the patient. We seek to gain a predictive physical understanding of this process by performing precision desktop experiments on an analogue model system. First, thin spherical shells of nearly uniform thickness are fabricated by the coating of hemispherical molds with a polymer solution, which upon curing yields an elastic and brittle structure. We then create two notches near the equator of the shell and tear a flap by pulling tangentially to the spherical substrate, towards its pole. The resulting fracture paths are characterized by high-resolution 3D digital scanning. Our primary focus is on establishing how the positive Gaussian curvature of the system affects the path of the crack tip. Our results are directly contrasted against previous studies on systems with zero Gaussian curvature, where films were torn from planar and cylindrical substrates.

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

NASA Astrophysics Data System (ADS)

Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M.; Derocher, Andrew E.; Lewis, Mark A.; Jonsen, Ian D.; Mills Flemming, Joanna

2016-05-01

State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.

A Separable Insertion Method to Calculate Atomic and Molecular Resonances on a FE-DVR Grid using Exterior Complex Scaling

NASA Astrophysics Data System (ADS)

Abeln, Brant Anthony

The study of metastable electronic resonances, anion or neutral states of finite lifetime, in molecules is an important area of research where currently no theoretical technique is generally applicable. The role of theory is to calculate both the position and width, which is proportional to the inverse of the lifetime, of these resonances and how they vary with respect to nuclear geometry in order to generate potential energy surfaces. These surfaces are the basis of time-dependent models of the molecular dynamics where the system moves towards vibrational excitation or fragmentation. Three fundamental electronic processes that can be modeled this way are dissociative electronic attachment, vibrational excitation through electronic impact and autoionization. Currently, experimental investigation into these processes is being preformed on polyatomic molecules while theoreticians continue their fifty-year-old search for robust methods to calculate them. The separable insertion method, investigated in this thesis, seeks to tackle the problem of calculating metastable resonances by using existing quantum chemistry tools along with a grid-based method employing exterior complex scaling (ECS). Modern quantum chemistry methods are extremely efficient at calculating ground and (bound) excited electronic states of atoms and molecules by utilizing Gaussian basis functions. These functions provide both a numerically fast and analytic solution to the necessary two-electron, six-dimensional integrals required in structure calculations. However, these computer programs, based on analytic Gaussian basis sets, cannot construct solutions that are not square-integrable, such as resonance wavefunctions. ECS, on the other hand, can formally calculate resonance solutions by rotating the asymptotic electronic coordinates into the complex plane. The complex Siegert energies for resonances, Eres = ER - iGamma/2 where ER is the real-valued position of the resonance and Gamma is the width of the resonance, can be found directly as an isolated pole in the complex energy plane. Unlike the straight complex scaling, ECS on the electronic coordinates overcomes the non-analytic behavior of the nuclear attraction potential, as a function of complex [special characters omitted] where the sum is over each nucleus in a molecular system. Discouragingly, the Gaussian basis functions, which are computationally well-suited for bound electronic structure, fail at forming an effective basis set for ECS due to the derivative discontinuity generated by the complex coordinate rotation and the piecewise defined contour. This thesis seeks to explore methods for implementing ECS indirectly without losing the numerical simplicity and power of Gaussian basis sets. The separable insertion method takes advantage of existing software by constructing a N2-term separable potential of the target system using Gaussian functions to be inserted into a finite-element discrete variable representation (FE-DVR) grid that implements ECS. This work reports an exhaustive investigation into this approach for calculating resonances. This thesis shows that this technique is successful at describing an anion shape resonance of a closed-shell atom or molecule in the static-exchange approximation. This method is applied to the 2P Be-, 2pig N2- and 2pi u CO2- shape resonances to calculate their complex Seigert energies. Additionally, many details on the exact construction of the separable potential and of the expansion basis are explored. The future work considers methods for faster convergence of the resonance energy, moving beyond the static-exchange approximation and applying this technique to polyatomic systems of interest.

Using surface curvature to map geomorphic process regimes in a bedrock landscape, Henry Mountains, Utah

NASA Astrophysics Data System (ADS)

Corbett, S.; Sklar, L. S.; Davis, J.

2009-12-01

Linkages between form and process are much better understood in soil-mantled landscapes than in bedrock landscapes, despite the wide occurrence of bedrock landscapes in arid and mountainous terrain. Soil-mantled hillslope topography can be characterized by hillslope gradient and its spatial derivative, which is commonly referred to as curvature and defined as the Laplacian of elevation. Surface curvature can also be quantified using techniques that are invariant to the orientation of the surface. These approaches are useful in many geoscience applications, including structural analysis of folded surfaces within deforming crustal blocks. Here we explore the use of surface curvature of bedrock topography as a metric to identify and map distinct geomorphic process regimes in a landscape devoid of soil cover. Our study site is Simpson Creek, a 2.5 km2 watershed on the east flank of Mt. Hillers in the Henry Mountains, Utah, which drains to the Colorado River in Glen Canyon. The land surface is entirely exposed Navajo Sandstone bedrock, with isolated patches of wind-blown sand deposits. The channel network is discontinuous, with alternating reaches of steep, deeply-incised, frequently-potholed slots, and lower-gradient, sand-bedded channels. Hillslope topography is characterized by dome-shaped and sub-linear ridges, and is influenced by prominent structural joints. We calculate two measures of the surface-normal curvature using an ALSM-derived digital elevation model. The mean and Gaussian surface curvatures are the average and product respectively of the magnitudes of the maximum and minimum curvature vectors, obtained by differentiating a polynomial fit at each point in a grid with 1 m spacing. Plots of mean versus Gaussian curvature reveal distinct clusters of landscape elements, which we associate with specific process regimes. In this parameter space, there are four quadrants, classified as dome, basin, synformal saddle and antiformal saddle. The channel and valley network corresponds to negative mean curvature, where concave and convex profile segments plot as basins and synformal saddles (positive and negative Gaussian curvature) respectively. We are able to use surface curvature to map what can be interpreted as bedrock channel width, as well as knickpoints, sand-bedrock bed transitions, and even individual large potholes. The tips of the channel network also have a distinct surface-curvature signature, and are associated with prominent polygonal bedrock fracturing at the sub-meter scale. In the hillslope portion of the landscape (positive mean curvature), the distribution of landscape elements has several modes, including a characteristic dome curvature that may be associated with sheet jointing and weathering-influenced exfoliation erosion, and an antiformal saddle curvature where solution pits occur, particularly on higher ridges most distant from the main-stem slot canyon channels. One key goal of this work is to quantify the effect of variable erosion rate on the distribution of process regime as expressed by these characteristic modes of bedrock surface curvature.

Contributions to the simulation of turbulence

NASA Technical Reports Server (NTRS)

Dutton, J. A.; Kerman, B. R.; Petersen, E. L.

1976-01-01

The simulation modeling of turbulence in the boundary layer in consolidated in terms of boundary layer similarity principles and empirical results. The modeling is extended for some aspects of the nonlinear and non-Gaussian structure of the turbulence. Properties of the discrete gust form structure of the modeled turbulence are identified.

Fast Gaussian kernel learning for classification tasks based on specially structured global optimization.

PubMed

Zhong, Shangping; Chen, Tianshun; He, Fengying; Niu, Yuzhen

2014-09-01

For a practical pattern classification task solved by kernel methods, the computing time is mainly spent on kernel learning (or training). However, the current kernel learning approaches are based on local optimization techniques, and hard to have good time performances, especially for large datasets. Thus the existing algorithms cannot be easily extended to large-scale tasks. In this paper, we present a fast Gaussian kernel learning method by solving a specially structured global optimization (SSGO) problem. We optimize the Gaussian kernel function by using the formulated kernel target alignment criterion, which is a difference of increasing (d.i.) functions. Through using a power-transformation based convexification method, the objective criterion can be represented as a difference of convex (d.c.) functions with a fixed power-transformation parameter. And the objective programming problem can then be converted to a SSGO problem: globally minimizing a concave function over a convex set. The SSGO problem is classical and has good solvability. Thus, to find the global optimal solution efficiently, we can adopt the improved Hoffman's outer approximation method, which need not repeat the searching procedure with different starting points to locate the best local minimum. Also, the proposed method can be proven to converge to the global solution for any classification task. We evaluate the proposed method on twenty benchmark datasets, and compare it with four other Gaussian kernel learning methods. Experimental results show that the proposed method stably achieves both good time-efficiency performance and good classification performance. Copyright © 2014 Elsevier Ltd. All rights reserved.

Spin-Hall effect in the scattering of structured light from plasmonic nanowire.

PubMed

Sharma, Deepak K; Kumar, Vijay; Vasista, Adarsh B; Chaubey, Shailendra K; Kumar, G V Pavan

2018-06-01

Spin-orbit interactions are subwavelength phenomena that can potentially lead to numerous device-related applications in nanophotonics. Here, we report the spin-Hall effect in the forward scattering of Hermite-Gaussian (HG) and Gaussian beams from a plasmonic nanowire. Asymmetric scattered radiation distribution was observed for circularly polarized beams. Asymmetry in the scattered radiation distribution changes the sign when the polarization handedness inverts. We found a significant enhancement in the spin-Hall effect for a HG beam compared to a Gaussian beam for constant input power. The difference between scattered powers perpendicular to the long axis of the plasmonic nanowire was used to quantify the enhancement. In addition, the nodal line of the HG beam acts as the marker for the spin-Hall shift. Numerical calculations corroborate experimental observations and suggest that the spin flow component of the Poynting vector associated with the circular polarization is responsible for the spin-Hall effect and its enhancement.

Rapidity window dependences of higher order cumulants and diffusion master equation

NASA Astrophysics Data System (ADS)

Kitazawa, Masakiyo

2015-10-01

We study the rapidity window dependences of higher order cumulants of conserved charges observed in relativistic heavy ion collisions. The time evolution and the rapidity window dependence of the non-Gaussian fluctuations are described by the diffusion master equation. Analytic formulas for the time evolution of cumulants in a rapidity window are obtained for arbitrary initial conditions. We discuss that the rapidity window dependences of the non-Gaussian cumulants have characteristic structures reflecting the non-equilibrium property of fluctuations, which can be observed in relativistic heavy ion collisions with the present detectors. It is argued that various information on the thermal and transport properties of the hot medium can be revealed experimentally by the study of the rapidity window dependences, especially by the combined use, of the higher order cumulants. Formulas of higher order cumulants for a probability distribution composed of sub-probabilities, which are useful for various studies of non-Gaussian cumulants, are also presented.

Accelerated Gaussian mixture model and its application on image segmentation

NASA Astrophysics Data System (ADS)

Zhao, Jianhui; Zhang, Yuanyuan; Ding, Yihua; Long, Chengjiang; Yuan, Zhiyong; Zhang, Dengyi

2013-03-01

Gaussian mixture model (GMM) has been widely used for image segmentation in recent years due to its superior adaptability and simplicity of implementation. However, traditional GMM has the disadvantage of high computational complexity. In this paper an accelerated GMM is designed, for which the following approaches are adopted: establish the lookup table for Gaussian probability matrix to avoid the repetitive probability calculations on all pixels, employ the blocking detection method on each block of pixels to further decrease the complexity, change the structure of lookup table from 3D to 1D with more simple data type to reduce the space requirement. The accelerated GMM is applied on image segmentation with the help of OTSU method to decide the threshold value automatically. Our algorithm has been tested through image segmenting of flames and faces from a set of real pictures, and the experimental results prove its efficiency in segmentation precision and computational cost.

Novel palmprint representations for palmprint recognition

NASA Astrophysics Data System (ADS)

Li, Hengjian; Dong, Jiwen; Li, Jinping; Wang, Lei

2015-02-01

In this paper, we propose a novel palmprint recognition algorithm. Firstly, the palmprint images are represented by the anisotropic filter. The filters are built on Gaussian functions along one direction, and on second derivative of Gaussian functions in the orthogonal direction. Also, this choice is motivated by the optimal joint spatial and frequency localization of the Gaussian kernel. Therefore,they can better approximate the edge or line of palmprint images. A palmprint image is processed with a bank of anisotropic filters at different scales and rotations for robust palmprint features extraction. Once these features are extracted, subspace analysis is then applied to the feature vectors for dimension reduction as well as class separability. Experimental results on a public palmprint database show that the accuracy could be improved by the proposed novel representations, compared with Gabor.

Determination of Cross-Sectional Area of Focused Picosecond Gaussian Laser Beam

NASA Technical Reports Server (NTRS)

Ledesma, Rodolfo; Fitz-Gerald, James; Palmieri, Frank; Connell, John

2018-01-01

Measurement of the waist diameter of a focused Gaussian-beam at the 1/e(sup 2) intensity, also referred to as spot size, is key to determining the fluence in laser processing experiments. Spot size measurements are also helpful to calculate the threshold energy and threshold fluence of a given material. This work reports an application of a conventional method, by analyzing single laser ablated spots for different laser pulse energies, to determine the cross-sectional area of a focused Gaussian-beam, which has a nominal pulse width of approx. 10 ps. Polished tungsten was used as the target material, due to its low surface roughness and low ablation threshold, to measure the beam waist diameter. From the ablative spot measurements, the ablation threshold fluence of the tungsten substrate was also calculated.

Detection methods for non-Gaussian gravitational wave stochastic backgrounds

NASA Astrophysics Data System (ADS)

Drasco, Steve; Flanagan, Éanna É.

2003-04-01

A gravitational wave stochastic background can be produced by a collection of independent gravitational wave events. There are two classes of such backgrounds, one for which the ratio of the average time between events to the average duration of an event is small (i.e., many events are on at once), and one for which the ratio is large. In the first case the signal is continuous, sounds something like a constant hiss, and has a Gaussian probability distribution. In the second case, the discontinuous or intermittent signal sounds something like popcorn popping, and is described by a non-Gaussian probability distribution. In this paper we address the issue of finding an optimal detection method for such a non-Gaussian background. As a first step, we examine the idealized situation in which the event durations are short compared to the detector sampling time, so that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. For this situation we derive an appropriate version of the maximum likelihood detection statistic. We compare the performance of this statistic to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. In general the maximum likelihood statistic performs better than the cross-correlation statistic when the stochastic background is sufficiently non-Gaussian, resulting in a gain factor in the minimum gravitational-wave energy density necessary for detection. This gain factor ranges roughly between 1 and 3, depending on the duty cycle of the background, for realistic observing times and signal strengths for both ground and space based detectors. The computational cost of the statistic, although significantly greater than that of the cross-correlation statistic, is not unreasonable. Before the statistic can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned detectors with realistic, colored, non-Gaussian noise.

Solute concentration at a well in non-Gaussian aquifers under constant and time-varying pumping schedule

NASA Astrophysics Data System (ADS)

Libera, Arianna; de Barros, Felipe P. J.; Riva, Monica; Guadagnini, Alberto

2017-10-01

Our study is keyed to the analysis of the interplay between engineering factors (i.e., transient pumping rates versus less realistic but commonly analyzed uniform extraction rates) and the heterogeneous structure of the aquifer (as expressed by the probability distribution characterizing transmissivity) on contaminant transport. We explore the joint influence of diverse (a) groundwater pumping schedules (constant and variable in time) and (b) representations of the stochastic heterogeneous transmissivity (T) field on temporal histories of solute concentrations observed at an extraction well. The stochastic nature of T is rendered by modeling its natural logarithm, Y = ln T, through a typical Gaussian representation and the recently introduced Generalized sub-Gaussian (GSG) model. The latter has the unique property to embed scale-dependent non-Gaussian features of the main statistics of Y and its (spatial) increments, which have been documented in a variety of studies. We rely on numerical Monte Carlo simulations and compute the temporal evolution at the well of low order moments of the solute concentration (C), as well as statistics of the peak concentration (Cp), identified as the environmental performance metric of interest in this study. We show that the pumping schedule strongly affects the pattern of the temporal evolution of the first two statistical moments of C, regardless the nature (Gaussian or non-Gaussian) of the underlying Y field, whereas the latter quantitatively influences their magnitude. Our results show that uncertainty associated with C and Cp estimates is larger when operating under a transient extraction scheme than under the action of a uniform withdrawal schedule. The probability density function (PDF) of Cp displays a long positive tail in the presence of time-varying pumping schedule. All these aspects are magnified in the presence of non-Gaussian Y fields. Additionally, the PDF of Cp displays a bimodal shape for all types of pumping schemes analyzed, independent of the type of heterogeneity considered.

Spatio-thermal depth correction of RGB-D sensors based on Gaussian processes in real-time

NASA Astrophysics Data System (ADS)

Heindl, Christoph; Pönitz, Thomas; Stübl, Gernot; Pichler, Andreas; Scharinger, Josef

2018-04-01

Commodity RGB-D sensors capture color images along with dense pixel-wise depth information in real-time. Typical RGB-D sensors are provided with a factory calibration and exhibit erratic depth readings due to coarse calibration values, ageing and thermal influence effects. This limits their applicability in computer vision and robotics. We propose a novel method to accurately calibrate depth considering spatial and thermal influences jointly. Our work is based on Gaussian Process Regression in a four dimensional Cartesian and thermal domain. We propose to leverage modern GPUs for dense depth map correction in real-time. For reproducibility we make our dataset and source code publicly available.

Static and transient performance prediction for CFB boilers using a Bayesian-Gaussian Neural Network

NASA Astrophysics Data System (ADS)

Ye, Haiwen; Ni, Weidou

1997-06-01

A Bayesian-Gaussian Neural Network (BGNN) is put forward in this paper to predict the static and transient performance of Circulating Fluidized Bed (CFB) boilers. The advantages of this network over Back-Propagation Neural Networks (BPNNs), easier determination of topology, simpler and time saving in training process as well as self-organizing ability, make this network more practical in on-line performance prediction for complicated processes. Simulation shows that this network is comparable to the BPNNs in predicting the performance of CFB boilers. Good and practical on-line performance predictions are essential for operation guide and model predictive control of CFB boilers, which are under research by the authors.

Incorporating Skew into RMS Surface Roughness Probability Distribution

NASA Technical Reports Server (NTRS)

Stahl, Mark T.; Stahl, H. Philip.

2013-01-01

The standard treatment of RMS surface roughness data is the application of a Gaussian probability distribution. This handling of surface roughness ignores the skew present in the surface and overestimates the most probable RMS of the surface, the mode. Using experimental data we confirm the Gaussian distribution overestimates the mode and application of an asymmetric distribution provides a better fit. Implementing the proposed asymmetric distribution into the optical manufacturing process would reduce the polishing time required to meet surface roughness specifications.

On estimating the phase of a periodic waveform in additive Gaussian noise, part 3

NASA Technical Reports Server (NTRS)

Rauch, L. L.

1991-01-01

Motivated by advances in signal processing technology that support more complex algorithms, researchers have taken a new look at the problem of estimating the phase and other parameters of a nearly periodic waveform in additive Gaussian noise, based on observation during a given time interval. Parts 1 and 2 are very briefly reviewed. In part 3, the actual performances of some of the highly nonlinear estimation algorithms of parts 1 and 2 are evaluated by numerical simulation using Monte Carlo techniques.

Invariant polarimetric contrast parameters of light with Gaussian fluctuations in three dimensions.

PubMed

Réfrégier, Philippe; Roche, Muriel; Goudail, François

2006-01-01

We propose a rigorous definition of the minimal set of parameters that characterize the difference between two partially polarized states of light whose electric fields vary in three dimensions with Gaussian fluctuations. Although two such states are a priori defined by eighteen parameters, we demonstrate that the performance of processing tasks such as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by three scalar functions of these parameters. These functions define a "polarimetric contrast" that simplifies the analysis and the specification of processing techniques on polarimetric signals and images. This result can also be used to analyze the definition of the degree of polarization of a three-dimensional state of light with Gaussian fluctuations in comparison, with respect to its polarimetric contrast parameters, with a totally depolarized light. We show that these contrast parameters are a simple function of the degrees of polarization previously proposed by Barakat [Opt. Acta 30, 1171 (1983)] and Setälä et al. [Phys. Rev. Lett. 88, 123902 (2002)]. Finally, we analyze the dimension of the set of contrast parameters in different particular situations.

Statistics of a neuron model driven by asymmetric colored noise.

PubMed

Müller-Hansen, Finn; Droste, Felix; Lindner, Benjamin

2015-02-01

Irregular firing of neurons can be modeled as a stochastic process. Here we study the perfect integrate-and-fire neuron driven by dichotomous noise, a Markovian process that jumps between two states (i.e., possesses a non-Gaussian statistics) and exhibits nonvanishing temporal correlations (i.e., represents a colored noise). Specifically, we consider asymmetric dichotomous noise with two different transition rates. Using a first-passage-time formulation, we derive exact expressions for the probability density and the serial correlation coefficient of the interspike interval (time interval between two subsequent neural action potentials) and the power spectrum of the spike train. Furthermore, we extend the model by including additional Gaussian white noise, and we give approximations for the interspike interval (ISI) statistics in this case. Numerical simulations are used to validate the exact analytical results for pure dichotomous noise, and to test the approximations of the ISI statistics when Gaussian white noise is included. The results may help to understand how correlations and asymmetry of noise and signals in nerve cells shape neuronal firing statistics.

A dynamic feedforward neural network based on gaussian particle swarm optimization and its application for predictive control.

PubMed

Han, Min; Fan, Jianchao; Wang, Jun

2011-09-01

A dynamic feedforward neural network (DFNN) is proposed for predictive control, whose adaptive parameters are adjusted by using Gaussian particle swarm optimization (GPSO) in the training process. Adaptive time-delay operators are added in the DFNN to improve its generalization for poorly known nonlinear dynamic systems with long time delays. Furthermore, GPSO adopts a chaotic map with Gaussian function to balance the exploration and exploitation capabilities of particles, which improves the computational efficiency without compromising the performance of the DFNN. The stability of the particle dynamics is analyzed, based on the robust stability theory, without any restrictive assumption. A stability condition for the GPSO+DFNN model is derived, which ensures a satisfactory global search and quick convergence, without the need for gradients. The particle velocity ranges could change adaptively during the optimization process. The results of a comparative study show that the performance of the proposed algorithm can compete with selected algorithms on benchmark problems. Additional simulation results demonstrate the effectiveness and accuracy of the proposed combination algorithm in identifying and controlling nonlinear systems with long time delays.

Parametric adaptive filtering and data validation in the bar GW detector AURIGA

NASA Astrophysics Data System (ADS)

Ortolan, A.; Baggio, L.; Cerdonio, M.; Prodi, G. A.; Vedovato, G.; Vitale, S.

2002-04-01

We report on our experience gained in the signal processing of the resonant GW detector AURIGA. Signal amplitude and arrival time are estimated by means of a matched-adaptive Wiener filter. The detector noise, entering in the filter set-up, is modelled as a parametric ARMA process; to account for slow non-stationarity of the noise, the ARMA parameters are estimated on an hourly basis. A requirement of the set-up of an unbiased Wiener filter is the separation of time spans with 'almost Gaussian' noise from non-Gaussian and/or strongly non-stationary time spans. The separation algorithm consists basically of a variance estimate with the Chauvenet convergence method and a threshold on the Curtosis index. The subsequent validation of data is strictly connected with the separation procedure: in fact, by injecting a large number of artificial GW signals into the 'almost Gaussian' part of the AURIGA data stream, we have demonstrated that the effective probability distributions of the signal-to-noise ratio χ2 and the time of arrival are those that are expected.

Implication of observed cloud variability for parameterizations of microphysical and radiative transfer processes in climate models

NASA Astrophysics Data System (ADS)

Huang, D.; Liu, Y.

2014-12-01

The effects of subgrid cloud variability on grid-average microphysical rates and radiative fluxes are examined by use of long-term retrieval products at the Tropical West Pacific (TWP), Southern Great Plains (SGP), and North Slope of Alaska (NSA) sites of the Department of Energy's Atmospheric Radiation Measurement (ARM) Program. Four commonly used distribution functions, the truncated Gaussian, Gamma, lognormal, and Weibull distributions, are constrained to have the same mean and standard deviation as observed cloud liquid water content. The PDFs are then used to upscale relevant physical processes to obtain grid-average process rates. It is found that the truncated Gaussian representation results in up to 30% mean bias in autoconversion rate whereas the mean bias for the lognormal representation is about 10%. The Gamma and Weibull distribution function performs the best for the grid-average autoconversion rate with the mean relative bias less than 5%. For radiative fluxes, the lognormal and truncated Gaussian representations perform better than the Gamma and Weibull representations. The results show that the optimal choice of subgrid cloud distribution function depends on the nonlinearity of the process of interest and thus there is no single distribution function that works best for all parameterizations. Examination of the scale (window size) dependence of the mean bias indicates that the bias in grid-average process rates monotonically increases with increasing window sizes, suggesting the increasing importance of subgrid variability with increasing grid sizes.

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

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

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

2017-03-01

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

The meta-Gaussian Bayesian Processor of forecasts and associated preliminary experiments

NASA Astrophysics Data System (ADS)

Chen, Fajing; Jiao, Meiyan; Chen, Jing

2013-04-01

Public weather services are trending toward providing users with probabilistic weather forecasts, in place of traditional deterministic forecasts. Probabilistic forecasting techniques are continually being improved to optimize available forecasting information. The Bayesian Processor of Forecast (BPF), a new statistical method for probabilistic forecast, can transform a deterministic forecast into a probabilistic forecast according to the historical statistical relationship between observations and forecasts generated by that forecasting system. This technique accounts for the typical forecasting performance of a deterministic forecasting system in quantifying the forecast uncertainty. The meta-Gaussian likelihood model is suitable for a variety of stochastic dependence structures with monotone likelihood ratios. The meta-Gaussian BPF adopting this kind of likelihood model can therefore be applied across many fields, including meteorology and hydrology. The Bayes theorem with two continuous random variables and the normal-linear BPF are briefly introduced. The meta-Gaussian BPF for a continuous predictand using a single predictor is then presented and discussed. The performance of the meta-Gaussian BPF is tested in a preliminary experiment. Control forecasts of daily surface temperature at 0000 UTC at Changsha and Wuhan stations are used as the deterministic forecast data. These control forecasts are taken from ensemble predictions with a 96-h lead time generated by the National Meteorological Center of the China Meteorological Administration, the European Centre for Medium-Range Weather Forecasts, and the US National Centers for Environmental Prediction during January 2008. The results of the experiment show that the meta-Gaussian BPF can transform a deterministic control forecast of surface temperature from any one of the three ensemble predictions into a useful probabilistic forecast of surface temperature. These probabilistic forecasts quantify the uncertainty of the control forecast; accordingly, the performance of the probabilistic forecasts differs based on the source of the underlying deterministic control forecasts.

Singularity-sensitive gauge-based radar rainfall adjustment methods for urban hydrological applications

NASA Astrophysics Data System (ADS)

Wang, L.-P.; Ochoa-Rodríguez, S.; Onof, C.; Willems, P.

2015-09-01

Gauge-based radar rainfall adjustment techniques have been widely used to improve the applicability of radar rainfall estimates to large-scale hydrological modelling. However, their use for urban hydrological applications is limited as they were mostly developed based upon Gaussian approximations and therefore tend to smooth off so-called "singularities" (features of a non-Gaussian field) that can be observed in the fine-scale rainfall structure. Overlooking the singularities could be critical, given that their distribution is highly consistent with that of local extreme magnitudes. This deficiency may cause large errors in the subsequent urban hydrological modelling. To address this limitation and improve the applicability of adjustment techniques at urban scales, a method is proposed herein which incorporates a local singularity analysis into existing adjustment techniques and allows the preservation of the singularity structures throughout the adjustment process. In this paper the proposed singularity analysis is incorporated into the Bayesian merging technique and the performance of the resulting singularity-sensitive method is compared with that of the original Bayesian (non singularity-sensitive) technique and the commonly used mean field bias adjustment. This test is conducted using as case study four storm events observed in the Portobello catchment (53 km2) (Edinburgh, UK) during 2011 and for which radar estimates, dense rain gauge and sewer flow records, as well as a recently calibrated urban drainage model were available. The results suggest that, in general, the proposed singularity-sensitive method can effectively preserve the non-normality in local rainfall structure, while retaining the ability of the original adjustment techniques to generate nearly unbiased estimates. Moreover, the ability of the singularity-sensitive technique to preserve the non-normality in rainfall estimates often leads to better reproduction of the urban drainage system's dynamics, particularly of peak runoff flows.

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

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

Zhang, Jiangjiang; Li, Weixuan; Zeng, Lingzao

Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU-demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimations of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two-stage manner. Since the two-stage MCMC requires extra original model evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate approximation of the original model can be adaptively constructed with low computational cost. Based on this idea, we propose amore » Gaussian process (GP) surrogate-based Bayesian experimental design and parameter estimation approach for groundwater contaminant source identification problems. A major advantage of the GP surrogate is that it provides a convenient estimation of the approximation error, which can be incorporated in the Bayesian formula to avoid over-confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed-up compared to our previous work using two-stage MCMC.« less

Thermal time constant: optimising the skin temperature predictive modelling in lower limb prostheses using Gaussian processes

PubMed Central

Buis, Arjan

2016-01-01

Elevated skin temperature at the body/device interface of lower-limb prostheses is one of the major factors that affect tissue health. The heat dissipation in prosthetic sockets is greatly influenced by the thermal conductive properties of the hard socket and liner material employed. However, monitoring of the interface temperature at skin level in lower-limb prosthesis is notoriously complicated. This is due to the flexible nature of the interface liners used which requires consistent positioning of sensors during donning and doffing. Predicting the residual limb temperature by monitoring the temperature between socket and liner rather than skin and liner could be an important step in alleviating complaints on increased temperature and perspiration in prosthetic sockets. To predict the residual limb temperature, a machine learning algorithm – Gaussian processes is employed, which utilizes the thermal time constant values of commonly used socket and liner materials. This Letter highlights the relevance of thermal time constant of prosthetic materials in Gaussian processes technique which would be useful in addressing the challenge of non-invasively monitoring the residual limb skin temperature. With the introduction of thermal time constant, the model can be optimised and generalised for a given prosthetic setup, thereby making the predictions more reliable. PMID:27695626

Thermal time constant: optimising the skin temperature predictive modelling in lower limb prostheses using Gaussian processes.

PubMed

Mathur, Neha; Glesk, Ivan; Buis, Arjan

2016-06-01

Elevated skin temperature at the body/device interface of lower-limb prostheses is one of the major factors that affect tissue health. The heat dissipation in prosthetic sockets is greatly influenced by the thermal conductive properties of the hard socket and liner material employed. However, monitoring of the interface temperature at skin level in lower-limb prosthesis is notoriously complicated. This is due to the flexible nature of the interface liners used which requires consistent positioning of sensors during donning and doffing. Predicting the residual limb temperature by monitoring the temperature between socket and liner rather than skin and liner could be an important step in alleviating complaints on increased temperature and perspiration in prosthetic sockets. To predict the residual limb temperature, a machine learning algorithm - Gaussian processes is employed, which utilizes the thermal time constant values of commonly used socket and liner materials. This Letter highlights the relevance of thermal time constant of prosthetic materials in Gaussian processes technique which would be useful in addressing the challenge of non-invasively monitoring the residual limb skin temperature. With the introduction of thermal time constant, the model can be optimised and generalised for a given prosthetic setup, thereby making the predictions more reliable.

Probabilistic analysis and fatigue damage assessment of offshore mooring system due to non-Gaussian bimodal tension processes

NASA Astrophysics Data System (ADS)

Chang, Anteng; Li, Huajun; Wang, Shuqing; Du, Junfeng

2017-08-01

Both wave-frequency (WF) and low-frequency (LF) components of mooring tension are in principle non-Gaussian due to nonlinearities in the dynamic system. This paper conducts a comprehensive investigation of applicable probability density functions (PDFs) of mooring tension amplitudes used to assess mooring-line fatigue damage via the spectral method. Short-term statistical characteristics of mooring-line tension responses are firstly investigated, in which the discrepancy arising from Gaussian approximation is revealed by comparing kurtosis and skewness coefficients. Several distribution functions based on present analytical spectral methods are selected to express the statistical distribution of the mooring-line tension amplitudes. Results indicate that the Gamma-type distribution and a linear combination of Dirlik and Tovo-Benasciutti formulas are suitable for separate WF and LF mooring tension components. A novel parametric method based on nonlinear transformations and stochastic optimization is then proposed to increase the effectiveness of mooring-line fatigue assessment due to non-Gaussian bimodal tension responses. Using time domain simulation as a benchmark, its accuracy is further validated using a numerical case study of a moored semi-submersible platform.

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.

Studies on system and measuring method of far-field beam divergency in near field by Ronchi ruling

NASA Astrophysics Data System (ADS)

Zhou, Chenbo; Yang, Li; Ma, Wenli; Yan, Peiying; Fan, Tianquan; He, Shangfeng

1996-10-01

Up to now, as large as seven times of Rayleigh-range or more is needed in measuring the far-field Gaussian beam divergency. This method is very inconvenient for the determination of the output beam divergency of the industrial product such as He-Ne lasers and the measuring unit will occupy a large space. The measurement and the measuring accuracy will be greatly influenced by the environment. Application of the Ronchi ruling to the measurement of far-field divergency of Gaussian beam in near-field is analyzed in the paper. The theoretical research and the experiments show that this measuring method is convenient in industrial application. The measuring system consists of a precision mechanical unit which scans Gaussian beam with a microdisplaced Ronchi ruling, a signal sampling system, a single-chip microcomputer data processing system and an electronic unit with microprinter output. The characteristics of the system is stable and the repeatability errors of the system are low. The spot size and far-field divergency of visible Gaussian laser beam can be measured with the system.

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.

Constructing petal modes from the coherent superposition of Laguerre-Gaussian modes

NASA Astrophysics Data System (ADS)

Naidoo, Darryl; Forbes, Andrew; Ait-Ameur, Kamel; Brunel, Marc

2011-03-01

An experimental approach in generating Petal-like transverse modes, which are similar to what is seen in porro-prism resonators, has been successfully demonstrated. We hypothesize that the petal-like structures are generated from a coherent superposition of Laguerre-Gaussian modes of zero radial order and opposite azimuthal order. To verify this hypothesis, visually based comparisons such as petal peak to peak diameter and the angle between adjacent petals are drawn between experimental data and simulated data. The beam quality factor of the Petal-like transverse modes and an inner product interaction is also experimentally compared to numerical results.

Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium

NASA Astrophysics Data System (ADS)

Zou, Defeng; Li, Xiaohui; Chai, Tong; Zheng, Hairong

2018-05-01

In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ω0 are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.

Yes, the GIGP Really Does Work--And Is Workable!

ERIC Educational Resources Information Center

Burrell, Quentin L.; Fenton, Michael R.

1993-01-01

Discusses the generalized inverse Gaussian-Poisson (GIGP) process for informetric modeling. Negative binomial distribution is discussed, construction of the GIGP process is explained, zero-truncated GIGP is considered, and applications of the process with journals, library circulation statistics, and database index terms are described. (50…

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing.

PubMed

Ramme, Austin J; Shivanna, Kiran H; Magnotta, Vincent A; Grosland, Nicole M

2011-10-01

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.

Correlators in tensor models from character calculus

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2017-11-01

We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz) character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.

Discretisation Schemes for Level Sets of Planar Gaussian Fields

NASA Astrophysics Data System (ADS)

Beliaev, D.; Muirhead, S.

2018-01-01

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

Motion streaks do not influence the perceived position of stationary flashed objects.

PubMed

Pavan, Andrea; Bellacosa Marotti, Rosilari

2012-01-01

In the present study, we investigated whether motion streaks, produced by fast moving dots Geisler 1999, distort the positional map of stationary flashed objects producing the well-known motion-induced position shift illusion (MIPS). The illusion relies on motion-processing mechanisms that induce local distortions in the positional map of the stimulus which is derived by shape-processing mechanisms. To measure the MIPS, two horizontally offset Gaussian blobs, placed above and below a central fixation point, were flashed over two fields of dots moving in opposite directions. Subjects judged the position of the top Gaussian blob relative to the bottom one. The results showed that neither fast (motion streaks) nor slow moving dots influenced the perceived spatial position of the stationary flashed objects, suggesting that background motion does not interact with the shape-processing mechanisms involved in MIPS.

Dynamic decomposition of spatiotemporal neural signals

PubMed Central

2017-01-01

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals. PMID:28558039

Reducing computation in an i-vector speaker recognition system using a tree-structured universal background model

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

McClanahan, Richard; De Leon, Phillip L.

The majority of state-of-the-art speaker recognition systems (SR) utilize speaker models that are derived from an adapted universal background model (UBM) in the form of a Gaussian mixture model (GMM). This is true for GMM supervector systems, joint factor analysis systems, and most recently i-vector systems. In all of the identified systems, the posterior probabilities and sufficient statistics calculations represent a computational bottleneck in both enrollment and testing. We propose a multi-layered hash system, employing a tree-structured GMM–UBM which uses Runnalls’ Gaussian mixture reduction technique, in order to reduce the number of these calculations. Moreover, with this tree-structured hash, wemore » can trade-off reduction in computation with a corresponding degradation of equal error rate (EER). As an example, we also reduce this computation by a factor of 15× while incurring less than 10% relative degradation of EER (or 0.3% absolute EER) when evaluated with NIST 2010 speaker recognition evaluation (SRE) telephone data.« less

Reducing computation in an i-vector speaker recognition system using a tree-structured universal background model

DOE PAGES

McClanahan, Richard; De Leon, Phillip L.

2014-08-20

The majority of state-of-the-art speaker recognition systems (SR) utilize speaker models that are derived from an adapted universal background model (UBM) in the form of a Gaussian mixture model (GMM). This is true for GMM supervector systems, joint factor analysis systems, and most recently i-vector systems. In all of the identified systems, the posterior probabilities and sufficient statistics calculations represent a computational bottleneck in both enrollment and testing. We propose a multi-layered hash system, employing a tree-structured GMM–UBM which uses Runnalls’ Gaussian mixture reduction technique, in order to reduce the number of these calculations. Moreover, with this tree-structured hash, wemore » can trade-off reduction in computation with a corresponding degradation of equal error rate (EER). As an example, we also reduce this computation by a factor of 15× while incurring less than 10% relative degradation of EER (or 0.3% absolute EER) when evaluated with NIST 2010 speaker recognition evaluation (SRE) telephone data.« less

Evaluation of higher order statistics parameters for multi channel sEMG using different force levels.

PubMed

Naik, Ganesh R; Kumar, Dinesh K

2011-01-01

The electromyograpy (EMG) signal provides information about the performance of muscles and nerves. The shape of the muscle signal and motor unit action potential (MUAP) varies due to the movement of the position of the electrode or due to changes in contraction level. This research deals with evaluating the non-Gaussianity in Surface Electromyogram signal (sEMG) using higher order statistics (HOS) parameters. To achieve this, experiments were conducted for four different finger and wrist actions at different levels of Maximum Voluntary Contractions (MVCs). Our experimental analysis shows that at constant force and for non-fatiguing contractions, probability density functions (PDF) of sEMG signals were non-Gaussian. For lesser MVCs (below 30% of MVC) PDF measures tends to be Gaussian process. The above measures were verified by computing the Kurtosis values for different MVCs.

Nonlinear and non-Gaussian Bayesian based handwriting beautification

NASA Astrophysics Data System (ADS)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

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.

Photocurrent spectroscopy of pentacene thin film transistors

NASA Astrophysics Data System (ADS)

Breban, Mihaela

We demonstrate the application of photocurrent modulation spectroscopy in characterizing the performance of organic thin-film transistors. A parallel analysis of the direct current and photocurrent voltage characteristics provides a model free determination of the field-effect mobility and the density of free carriers in the transistor channel as a function of the applied gate voltage. Applying this technique to pentacene thin-film transistors demonstrates that the mobility increases as V1/3g . The free-carrier density is approximately 1/10 of the expected capacitive charge, and the mobility increases monotonically with the free carrier density, consistent with the trap and release model of transport. Also, the modulated photocurrent spectroscopy can be used as a probe of defect states in pentacene thin film transistors, measuring simultaneously the magnitude and the phase of the photocurrent as a function of the modulation frequency. This is accomplished by modeling the photo-carrier generation process as exciton dissociation via interaction with localized traps. Experimental data reveal a Gaussian distribution of localized states centered around 0.3 eV above the highest occupied molecular orbital. We also investigated the effect of the gate dielectric material with our probe and found that the position of the extracted Gaussian slightly shifts, consistent with the expected image charge effect for Pn through the dielectric substrate. Also shifts in the Gaussian position for samples fabricated with variable deposition conditions are correlated with changes in Pn morphology. The morphological differences between Pn films were also detected in current-voltage characteristics and photocurrent spectra. However, the origin of the ubiquitous 0.3 eV defect in Pn seems to be unrelated to structural differences in Pn films.

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

PubMed

Westgate, Philip M; Burchett, Woodrow W

2017-03-15

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

State Estimation for Linear Systems Driven Simultaneously by Wiener and Poisson Processes.

DTIC Science & Technology

1978-12-01

The state estimation problem of linear stochastic systems driven simultaneously by Wiener and Poisson processes is considered, especially the case...where the incident intensities of the Poisson processes are low and the system is observed in an additive white Gaussian noise. The minimum mean squared

Structure of gamma-ray burst jets: intrinsic versus apparent properties

NASA Astrophysics Data System (ADS)

Salafia, O. S.; Ghisellini, G.; Pescalli, A.; Ghirlanda, G.; Nappo, F.

2015-07-01

With this paper we introduce the concept of apparent structure of a gamma-ray burst (GRB) jet, as opposed to its intrinsic structure. The latter is customarily defined specifying the functions ɛ(θ) (the energy emitted per jet unit solid angle) and Γ(θ) (the Lorentz factor of the emitting material); the apparent structure is instead defined by us as the isotropic equivalent energy Eiso(θv) as a function of the viewing angle θv. We show how to predict the apparent structure of a jet given its intrinsic structure. We find that a Gaussian intrinsic structure yields a power-law apparent structure: this opens a new viewpoint on the Gaussian (which can be understood as a proxy for a realistic narrow, well-collimated jet structure) as a possible candidate for a quasi-universal GRB jet structure. We show that such a model (a) is consistent with recent constraints on the observed luminosity function of GRBs; (b) implies fewer orphan afterglows with respect to the standard uniform model; (c) can break out the progenitor star (in the collapsar scenario) without wasting an unreasonable amount of energy; (d) is compatible with the explanation of the Amati correlation as a viewing angle effect; (e) can be very standard in energy content, and still yield a very wide range of observed isotropic equivalent energies.

Statistical Analysis of Crystallization Database Links Protein Physico-Chemical Features with Crystallization Mechanisms

PubMed Central

Fusco, Diana; Barnum, Timothy J.; Bruno, Andrew E.; Luft, Joseph R.; Snell, Edward H.; Mukherjee, Sayan; Charbonneau, Patrick

2014-01-01

X-ray crystallography is the predominant method for obtaining atomic-scale information about biological macromolecules. Despite the success of the technique, obtaining well diffracting crystals still critically limits going from protein to structure. In practice, the crystallization process proceeds through knowledge-informed empiricism. Better physico-chemical understanding remains elusive because of the large number of variables involved, hence little guidance is available to systematically identify solution conditions that promote crystallization. To help determine relationships between macromolecular properties and their crystallization propensity, we have trained statistical models on samples for 182 proteins supplied by the Northeast Structural Genomics consortium. Gaussian processes, which capture trends beyond the reach of linear statistical models, distinguish between two main physico-chemical mechanisms driving crystallization. One is characterized by low levels of side chain entropy and has been extensively reported in the literature. The other identifies specific electrostatic interactions not previously described in the crystallization context. Because evidence for two distinct mechanisms can be gleaned both from crystal contacts and from solution conditions leading to successful crystallization, the model offers future avenues for optimizing crystallization screens based on partial structural information. The availability of crystallization data coupled with structural outcomes analyzed through state-of-the-art statistical models may thus guide macromolecular crystallization toward a more rational basis. PMID:24988076

Statistical analysis of crystallization database links protein physico-chemical features with crystallization mechanisms.

PubMed

Fusco, Diana; Barnum, Timothy J; Bruno, Andrew E; Luft, Joseph R; Snell, Edward H; Mukherjee, Sayan; Charbonneau, Patrick

2014-01-01

X-ray crystallography is the predominant method for obtaining atomic-scale information about biological macromolecules. Despite the success of the technique, obtaining well diffracting crystals still critically limits going from protein to structure. In practice, the crystallization process proceeds through knowledge-informed empiricism. Better physico-chemical understanding remains elusive because of the large number of variables involved, hence little guidance is available to systematically identify solution conditions that promote crystallization. To help determine relationships between macromolecular properties and their crystallization propensity, we have trained statistical models on samples for 182 proteins supplied by the Northeast Structural Genomics consortium. Gaussian processes, which capture trends beyond the reach of linear statistical models, distinguish between two main physico-chemical mechanisms driving crystallization. One is characterized by low levels of side chain entropy and has been extensively reported in the literature. The other identifies specific electrostatic interactions not previously described in the crystallization context. Because evidence for two distinct mechanisms can be gleaned both from crystal contacts and from solution conditions leading to successful crystallization, the model offers future avenues for optimizing crystallization screens based on partial structural information. The availability of crystallization data coupled with structural outcomes analyzed through state-of-the-art statistical models may thus guide macromolecular crystallization toward a more rational basis.

DESCRIPTION OF ATMOSPHERIC TRANSPORT PROCESSES IN EULERIAN AIR QUALITY MODELS

EPA Science Inventory

Key differences among many types of air quality models are the way atmospheric advection and turbulent diffusion processes are treated. Gaussian models use analytical solutions of the advection-diffusion equations. Lagrangian models use a hypothetical air parcel concept effecti...

Nonlocal means-based speckle filtering for ultrasound images

PubMed Central

Coupé, Pierrick; Hellier, Pierre; Kervrann, Charles; Barillot, Christian

2009-01-01

In image processing, restoration is expected to improve the qualitative inspection of the image and the performance of quantitative image analysis techniques. In this paper, an adaptation of the Non Local (NL-) means filter is proposed for speckle reduction in ultrasound (US) images. Originally developed for additive white Gaussian noise, we propose to use a Bayesian framework to derive a NL-means filter adapted to a relevant ultrasound noise model. Quantitative results on synthetic data show the performances of the proposed method compared to well-established and state-of-the-art methods. Results on real images demonstrate that the proposed method is able to preserve accurately edges and structural details of the image. PMID:19482578

An optimal control approach to the design of moving flight simulators

NASA Technical Reports Server (NTRS)

Sivan, R.; Ish-Shalom, J.; Huang, J.-K.

1982-01-01

An abstract flight simulator design problem is formulated in the form of an optimal control problem, which is solved for the linear-quadratic-Gaussian special case using a mathematical model of the vestibular organs. The optimization criterion used is the mean-square difference between the physiological outputs of the vestibular organs of the pilot in the aircraft and the pilot in the simulator. The dynamical equations are linearized, and the output signal is modeled as a random process with rational power spectral density. The method described yields the optimal structure of the simulator's motion generator, or 'washout filter'. A two-degree-of-freedom flight simulator design, including single output simulations, is presented.

Linear programming phase unwrapping for dual-wavelength digital holography.

PubMed

Wang, Zhaomin; Jiao, Jiannan; Qu, Weijuan; Yang, Fang; Li, Hongru; Tian, Ailing; Asundi, Anand

2017-01-20

A linear programming phase unwrapping method in dual-wavelength digital holography is proposed and verified experimentally. The proposed method uses the square of height difference as a convergence standard and theoretically gives the boundary condition in a searching process. A simulation was performed by unwrapping step structures at different levels of Gaussian noise. As a result, our method is capable of recovering the discontinuities accurately. It is robust and straightforward. In the experiment, a microelectromechanical systems sample and a cylindrical lens were measured separately. The testing results were in good agreement with true values. Moreover, the proposed method is applicable not only in digital holography but also in other dual-wavelength interferometric techniques.

Linear-quadratic-Gaussian synthesis with reduced parameter sensitivity

NASA Technical Reports Server (NTRS)

Lin, J. Y.; Mingori, D. L.

1992-01-01

We present a method for improving the tolerance of a conventional LQG controller to parameter errors in the plant model. The improvement is achieved by introducing additional terms reflecting the structure of the parameter errors into the LQR cost function, and also the process and measurement noise models. Adjusting the sizes of these additional terms permits a trade-off between robustness and nominal performance. Manipulation of some of the additional terms leads to high gain controllers while other terms lead to low gain controllers. Conditions are developed under which the high-gain approach asymptotically recovers the robustness of the corresponding full-state feedback design, and the low-gain approach makes the closed-loop poles asymptotically insensitive to parameter errors.

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

NASA Astrophysics Data System (ADS)

Tripathy, Rohit; Bilionis, Ilias; Gonzalez, Marcial

2016-09-01

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

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

Tripathy, Rohit, E-mail: rtripath@purdue.edu; Bilionis, Ilias, E-mail: ibilion@purdue.edu; Gonzalez, Marcial, E-mail: marcial-gonzalez@purdue.edu

2016-09-15

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range ofmore » physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.« less