Uniform dimension results for Gaussian random fields
Institute of Scientific and Technical Information of China (English)
2009-01-01
Let X = {X(t),t ∈ RN} be a Gaussian random field with values in Rd defined by X(t) =(X1(t),...,Xd(t)), t ∈ RN.(1) The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed.It is shown that in general the uniform Hausdorff dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.When X is an(N,d)-Gaussian random field as in(1),where X1,...,Xd are independent copies of a real valued,centered Gaussian random field X0 which is anisotropic in the time variable.We establish uniform Hausdorff dimension results for the image sets of X.These results extend the corresponding results on one-dimensional Brownian motion,fractional Brownian motion and the Brownian sheet.
Ergodicity and Gaussianity for Spherical Random Fields
Marinucci, Domenico
2009-01-01
We investigate the relationship between ergodicity and asymptotic Gaussianity of isotropic spherical random fields, in the high-resolution (or high-frequency) limit. In particular, our results suggest that under a wide variety of circumstances the two conditions are equivalent, i.e. the sample angular power spectrum may converge to the population value if and only if the underlying field is asymptotically Gaussian, in the high frequency sense. These findings may shed some light on the role of Cosmic Variance in Cosmic Microwave Background (CMB) radiation data analysis.
Gaussian Markov random fields theory and applications
Rue, Havard
2005-01-01
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.
A note on moving average models for Gaussian random fields
DEFF Research Database (Denmark)
Hansen, Linda Vadgård; Thorarinsdottir, Thordis L.
The class of moving average models offers a flexible modeling framework for Gaussian random fields with many well known models such as the Matérn covariance family and the Gaussian covariance falling under this framework. Moving average models may also be viewed as a kernel smoothing of a Lévy...
Sampling Strategies for Fast Updating of Gaussian Markov Random Fields
Brown, D. Andrew; McMahan, Christopher S.
2017-01-01
Gaussian Markov random fields (GMRFs) are popular for modeling temporal or spatial dependence in large areal datasets due to their ease of interpretation and computational convenience afforded by conditional independence and their sparse precision matrices needed for random variable generation. Using such models inside a Markov chain Monte Carlo algorithm requires repeatedly simulating random fields. This is a nontrivial issue, especially when the full conditional precision matrix depends on ...
Tail Approximations of Integrals of Gaussian Random Fields
Liu, Jingchen
2010-01-01
This paper develops asymptotic approximations of $P(\\int_T e^{f(t)}dt > b)$ as $b\\rightarrow \\infty$ for homogeneous smooth Gaussian random field, $f$, living on a compact $d$-dimensional Jordan measurable set $T$. The integral of exponent of Gaussian random field is an important random variable for many generic models in spatial point processes, portfolio risk analysis, asset pricing and so forth. The analysis technique consists of two steps: 1. evaluate the tail probability $P(\\int_\\Delta e^{f(t)}dt > b)$ over a small domain $\\Delta$ depending on $b$, where $mes(\\Delta) \\rightarrow 0$ as $b\\rightarrow \\infty$ and $mes(\\cdot)$ is the Lebesgue measure; 2. with $\\Delta$ appropriately chosen, we show that $P(\\int_T e^{f(t)}dt > b) =(1+o(1)) mes(T) mes^{-1}(\\Delta) P(\\int_\\Delta e^{f(t)}dt > b)$.
Three-dimensional extinction mapping using Gaussian random fields
Sale, S E
2014-01-01
We present a scheme for using stellar catalogues to map the three-dimensional distributions of extinction and dust within our Galaxy. Extinction is modelled as a Gaussian random field, whose covariance function is set by a simple physical model of the ISM that assumes a Kolmogorov-like power spectrum of turbulent fluctuations. As extinction is modelled as a random field, the spatial resolution of the resulting maps is set naturally by the data available; there is no need to impose any spatial binning. We verify the validity of our scheme by testing it on simulated extinction fields and show that its precision is significantly improved over previous dust-mapping efforts. The approach we describe here can make use of any photometric, spectroscopic or astrometric data; it is not limited to any particular survey. Consequently, it can be applied to a wide range of data from both existing and future surveys.
Gaussian Random Field: Physical Origin of Sersic Profiles
Cen, Renyue
2014-01-01
While the Sersic profile family provide adequate fits for the surface brightness profiles of observed galaxies, the physical origin is unknown. We show that, if the cosmological density field are seeded by random gaussian fluctuations, as in the standard cold dark matter model, galaxies with steep central profiles have simultaneously extended envelopes of shallow profiles in the outskirts, whereas galaxies with shallow central profiles are accompanied by steep density profiles in the outskirts. These properties are in accord with those of the Sersic profile family. Moreover, galaxies with steep central profiles form their central regions in smaller denser subunits that possibly merge subsequently, which naturally leads to formation of bulges. In contrast, galaxies with shallow central profiles form their central regions in a coherent fashion without significant substructure, a necessary condition for disk galaxy formation. Thus, the scenario is self-consistent with respect to the correlation between observed ...
Path properties of lp-valued Gaussian random fields
Institute of Scientific and Technical Information of China (English)
Yong-Kab; CHOI
2007-01-01
)[16]Book S A,Shore T R.On large intervals in the Cs(o)rg(o)-Révész theorem on increments of a Wiener process.Z Wahrsch Verw Gebiete,46:1-11 (1978)[17]Choi Y K,K(o)no N.How big are the increments of a two-parameter Gaussian process? J Theoret Probab,12(1):105-129 (1999)[18]Lin Z Y,Choi Y K.Some limit theorems for fractional Levy Brownian fields.Stoch Proc & Their Appl,82:229-244 (1999)[19]Lin Z Y,Lee S H,Hwang K S et al.Some limit theorems on the increments of lp-valued multi-parameter Gaussian processes.Acta Math Sinica,English Ser,20(6):1019-1028 (2004)[20]Slepian D.The one-sided barrier problem for Gaussian noise.Bell System Tech J,41:463-501 (1962)[21]Choi Y K,Lin Z Y,Sung H S et al.Limit behaviors for the increments of a d-dimensional multi-parameter Gaussian process.J Korean Math Soc,42(6):1265-1278 (2005)[22]Leadbetter M R,Lindgren G,Rootzen H.Extremes and Related Properties of Random Sequences and Processes.New York:Springer-Verlag,1983[23]Li W V,Shao Q M.A normal comparison inequality and its applications.Probab Theory & Rel Fields,122:494-508 (2002)
Yan, Yuan
2017-07-13
Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.
Gaussian conditional random fields for regression in remote sensing
Radosavljevic, Vladan
that uses multiple unstructured predictors to form its features and at the same time exploits structure among outputs. By constraining the feature functions to quadratic functions of outputs, we show that the CRF model can be conveniently represented in a Gaussian canonical form. The appeal of proposed Gaussian Conditional Random Fields (GCRF) model is in its conceptual simplicity and computational efficiency of learning and inference through use of sparse matrix computations. Experimental results provide strong evidence that the GCRF achieves better accuracy than non-structured models. We improve the representational power of the GCRF model by (1) introducing the adaptive feature function that can learn nonlinear relationships between inputs and outputs and (2) allowing the weights of feature functions to be dependent on inputs. The GCRF is also readily applicable to other regression applications where there is a need for knowledge integration, data fusion, and exploitation of correlation among output variables.
Versatility and robustness of Gaussian random fields for modelling random media
Quintanilla, John A.; Chen, Jordan T.; Reidy, Richard F.; Allen, Andrew J.
2007-06-01
One of the authors (JAQ) has recently introduced a method of modelling random materials using excursion sets of Gaussian random fields. This method uses convex quadratic programming to find the optimal admissible field autocorrelation function, providing both theoretical and computational advantages over other techniques such as simulated annealing. In this paper, we discuss the application of this algorithm to model various aerogel systems given small-angle neutron scattering data. We also present new results concerning the robustness of this method.
Gaussian Random Field: Physical Origin of Sersic Profiles
Cen, Renyue
2014-08-01
While the Sersic profile family provides adequate fits for the surface brightness profiles of observed galaxies, its physical origin is unknown. We show that if the cosmological density field is seeded by random Gaussian fluctuations, as in the standard cold dark matter model, galaxies with steep central profiles have simultaneously extended envelopes of shallow profiles in the outskirts, whereas galaxies with shallow central profiles are accompanied by steep density profiles in the outskirts. These properties are in accord with those of the Sersic profile family. Moreover, galaxies with steep central profiles form their central regions in smaller denser subunits that possibly merge subsequently, which naturally leads to the formation of bulges. In contrast, galaxies with shallow central profiles form their central regions in a coherent fashion without significant substructure, a necessary condition for disk galaxy formation. Thus, the scenario is self-consistent with respect to the correlation between observed galaxy morphology and the Sersic index. We further predict that clusters of galaxies should display a similar trend, which should be verifiable observationally.
Prediction of Geological Subsurfaces Based on Gaussian Random Field Models
Energy Technology Data Exchange (ETDEWEB)
Abrahamsen, Petter
1997-12-31
During the sixties, random functions became practical tools for predicting ore reserves with associated precision measures in the mining industry. This was the start of the geostatistical methods called kriging. These methods are used, for example, in petroleum exploration. This thesis reviews the possibilities for using Gaussian random functions in modelling of geological subsurfaces. It develops methods for including many sources of information and observations for precise prediction of the depth of geological subsurfaces. The simple properties of Gaussian distributions make it possible to calculate optimal predictors in the mean square sense. This is done in a discussion of kriging predictors. These predictors are then extended to deal with several subsurfaces simultaneously. It is shown how additional velocity observations can be used to improve predictions. The use of gradient data and even higher order derivatives are also considered and gradient data are used in an example. 130 refs., 44 figs., 12 tabs.
On Gaussian random supergravity
Energy Technology Data Exchange (ETDEWEB)
Bachlechner, Thomas C. [Department of Physics, Cornell University,Physical Sciences Building 428, Ithaca, NY 14853 (United States)
2014-04-08
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kähler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with |F|≪M{sub susy} or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log (P)∝−N. We argue that random supergravities lead to potentially interesting inflationary dynamics.
On Gaussian random supergravity
Bachlechner, Thomas C.
2014-04-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kähler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with | F| ≪ M susy or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log( P ) ∝ - N. We argue that random supergravities lead to potentially interesting inflationary dynamics.
On Gaussian Random Supergravity
Bachlechner, Thomas C
2014-01-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kahler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with |F|<< M_{susy} or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log(P)\\propto -N. We argue that random supergravities lead to potentially interesting inflationary dynamics...
Using convex quadratic programming to model random media with Gaussian random fields
Quintanilla, John A.; Jones, W. Max
2007-04-01
Excursion sets of Gaussian random fields (GRFs) have been frequently used in the literature to model two-phase random media with measurable phase autocorrelation functions. The goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function. In this paper, we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all admissible field autocorrelation functions, instead of optimizing only over a predetermined parametrized family. The results from using this technique indicate that the GRF model is significantly more versatile than observed in previous studies. An application to modeling a base-catalyzed tetraethoxysilane aerogel system given small-angle neutron scattering data is also presented
Luan, Nana
2011-01-01
Let $X= \\{X(t), t \\in \\R^N\\}$ be a Gaussian random field with values in $\\R^d$ defined by \\[ X(t) = \\big(X_1(t),..., X_d(t)\\big),\\qquad t \\in \\R^N, \\] where $X_1, ..., X_d$ are independent copies of a real-valued, centered, anisotropic Gaussian random field $X_0$ which has stationary increments and the property of strong local nondeterminism. In this paper we determine the exact Hausdorff measure function for the range $X([0, 1]^N)$. We also provide a sufficient condition for a Gaussian random field with stationary increments to be strongly locally nondeterministic. This condition is given in terms of the spectral measures of the Gaussian random fields which may contain either an absolutely continuous or discrete part. This result strengthens and extends significantly the related theorems of Berman (1973, 1988), Pitt (1978) and Xiao (2007, 2009), and will have wider applicability beyond the scope of the present paper.
DEFF Research Database (Denmark)
Franchin, P.; Ditlevsen, Ove Dalager; Kiureghian, Armen Der
2002-01-01
The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals...... are considered to be Gaussian. Conventional FORM analysis yields the linearization point of the idealized limit-state surface. A model correction factor is then introduced to push the idealized limit-state surface onto the actual limit-state surface. A few iterations yield a good approximation of the reliability...... reliability method; Model correction factor method; Nataf field integration; Non-Gaussion random field; Random field integration; Structural reliability; Pile foundation reliability...
On Gaussian random supergravity
Bachlechner, Thomas C.
2014-01-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial K\\"ahler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a nume...
Return probability and recurrence for the random walk driven by two-dimensional Gaussian free field
Biskup, Marek; Ding, Jian; Goswami, Subhajit
2016-01-01
Given any $\\gamma>0$ and for $\\eta=\\{\\eta_v\\}_{v\\in \\mathbb Z^2}$ denoting a sample of the two-dimensional discrete Gaussian free field on $\\mathbb Z^2$ pinned at the origin, we consider the random walk on $\\mathbb Z^2$ among random conductances where the conductance of edge $(u, v)$ is given by $\\mathrm{e}^{\\gamma(\\eta_u + \\eta_v)}$. We show that, for almost every $\\eta$, this random walk is recurrent and that, with probability tending to 1 as $T\\to \\infty$, the return probability at time $2...
Modeling and statistical analysis of non-Gaussian random fields with heavy-tailed distributions
Nezhadhaghighi, Mohsen Ghasemi; Nakhlband, Abbas
2017-04-01
In this paper, we investigate and develop an alternative approach to the numerical analysis and characterization of random fluctuations with the heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare fluctuations. We identify the heavy-tailed random fluctuations based on the scaling properties of the tail exponent of the PDF, power-law growth of q th order correlation function, and the self-similar properties of the contour lines in two-dimensional random fields. Moreover, this work leads to a substitution for the fractional Edwards-Wilkinson (EW) equation that works in the presence of μ -stable Lévy noise. Our proposed model explains the configuration dynamics of the systems with heavy-tailed correlated random fluctuations. We also present an alternative solution to the fractional EW equation in the presence of μ -stable Lévy noise in the steady state, which is implemented numerically, using the μ -stable fractional Lévy motion. Based on the analysis of the self-similar properties of contour loops, we numerically show that the scaling properties of contour loop ensembles can qualitatively and quantitatively distinguish non-Gaussian random fields from Gaussian random fluctuations.
FINITE VARIANCE OF THE NUMBER OF STATIONARY POINTS OF A GAUSSIAN RANDOM FIELD
Estrade, Anne; Fournier, Julie
2015-01-01
Let X be a real-valued stationary Gaussian random field defined on $R^d$ (d ≥ 1), with almost every realization of class $C^2$. This paper is concerned with the random variable giving the number of points in $T$ (a compact set of $R^d$) where the gradient $X'$ takes a fixed value $v\\in R^d$, $N_{X'}(T, v) = \\{t \\in T : X'(t) = v\\}$. More precisely, it deals with the finiteness of the variance of $N_{X'} (T, v)$, under some non-degeneracy hypothesis on $X$. For d = 1, the so-called " Geman con...
ITAC volume assessment through a Gaussian hidden Markov random field model-based algorithm.
Passera, Katia M; Potepan, Paolo; Brambilla, Luca; Mainardi, Luca T
2008-01-01
In this paper, a semi-automatic segmentation method for volume assessment of Intestinal-type adenocarcinoma (ITAC) is presented and validated. The method is based on a Gaussian hidden Markov random field (GHMRF) model that represents an advanced version of a finite Gaussian mixture (FGM) model as it encodes spatial information through the mutual influences of neighboring sites. To fit the GHMRF model an expectation maximization (EM) algorithm is used. We applied the method to a magnetic resonance data sets (each of them composed by T1-weighted, Contrast Enhanced T1-weighted and T2-weighted images) for a total of 49 tumor-contained slices. We tested GHMRF performances with respect to FGM by both a numerical and a clinical evaluation. Results show that the proposed method has a higher accuracy in quantifying lesion area than FGM and it can be applied in the evaluation of tumor response to therapy.
Rotation and Scale Space Random Fields and the Gaussian Kinematic Formula
Adler, Robert J; Taylor, Jonathan E
2011-01-01
We provide a new approach, along with extensions, to results in two important papers of Worsley, Siegmund and coworkers closely tied to the statistical analysis of fMRI (functional magnetic resonance imaging) brain data. These papers studied approximations for the exceedence probabilities of scale and rotation space random fields, the latter playing an important role in the statistical analysis of fMRI data. The techniques used there came either from the Euler characteristic heuristic or via tube formulae, and to a large extent were carefully attuned to the specific examples of the paper. This paper treats the same problem, but via calculations arising from the so-called Gaussian kinematic formula. This allows for extensions of the Worsley-Siegmund results to a wide class of non-Gaussian cases. In addition, it allows one to obtain results for rotation space random fields in any dimension via reasonably straightforward Riemannian geometric calculations, whereas previously only the two-dimensional case could be...
Stochastic generation of explicit pore structures by thresholding Gaussian random fields
Energy Technology Data Exchange (ETDEWEB)
Hyman, Jeffrey D., E-mail: jhyman@lanl.gov [Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721-0089 (United States); Computational Earth Science, Earth and Environmental Sciences (EES-16), and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87544 (United States); Winter, C. Larrabee, E-mail: winter@email.arizona.edu [Program in Applied Mathematics, University of Arizona, Tucson, AZ 85721-0089 (United States); Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721-0011 (United States)
2014-11-15
We provide a description and computational investigation of an efficient method to stochastically generate realistic pore structures. Smolarkiewicz and Winter introduced this specific method in pores resolving simulation of Darcy flows (Smolarkiewicz and Winter, 2010 [1]) without giving a complete formal description or analysis of the method, or indicating how to control the parameterization of the ensemble. We address both issues in this paper. The method consists of two steps. First, a realization of a correlated Gaussian field, or topography, is produced by convolving a prescribed kernel with an initial field of independent, identically distributed random variables. The intrinsic length scales of the kernel determine the correlation structure of the topography. Next, a sample pore space is generated by applying a level threshold to the Gaussian field realization: points are assigned to the void phase or the solid phase depending on whether the topography over them is above or below the threshold. Hence, the topology and geometry of the pore space depend on the form of the kernel and the level threshold. Manipulating these two user prescribed quantities allows good control of pore space observables, in particular the Minkowski functionals. Extensions of the method to generate media with multiple pore structures and preferential flow directions are also discussed. To demonstrate its usefulness, the method is used to generate a pore space with physical and hydrological properties similar to a sample of Berea sandstone. -- Graphical abstract: -- Highlights: •An efficient method to stochastically generate realistic pore structures is provided. •Samples are generated by applying a level threshold to a Gaussian field realization. •Two user prescribed quantities determine the topology and geometry of the pore space. •Multiple pore structures and preferential flow directions can be produced. •A pore space based on Berea sandstone is generated.
Stochastic generation of explicit pore structures by thresholding Gaussian random fields
Hyman, Jeffrey D.; Winter, C. Larrabee
2014-11-01
We provide a description and computational investigation of an efficient method to stochastically generate realistic pore structures. Smolarkiewicz and Winter introduced this specific method in pores resolving simulation of Darcy flows (Smolarkiewicz and Winter, 2010 [1]) without giving a complete formal description or analysis of the method, or indicating how to control the parameterization of the ensemble. We address both issues in this paper. The method consists of two steps. First, a realization of a correlated Gaussian field, or topography, is produced by convolving a prescribed kernel with an initial field of independent, identically distributed random variables. The intrinsic length scales of the kernel determine the correlation structure of the topography. Next, a sample pore space is generated by applying a level threshold to the Gaussian field realization: points are assigned to the void phase or the solid phase depending on whether the topography over them is above or below the threshold. Hence, the topology and geometry of the pore space depend on the form of the kernel and the level threshold. Manipulating these two user prescribed quantities allows good control of pore space observables, in particular the Minkowski functionals. Extensions of the method to generate media with multiple pore structures and preferential flow directions are also discussed. To demonstrate its usefulness, the method is used to generate a pore space with physical and hydrological properties similar to a sample of Berea sandstone.
Multi-fidelity Gaussian process regression for prediction of random fields
Energy Technology Data Exchange (ETDEWEB)
Parussini, L. [Department of Engineering and Architecture, University of Trieste (Italy); Venturi, D., E-mail: venturi@ucsc.edu [Department of Applied Mathematics and Statistics, University of California Santa Cruz (United States); Perdikaris, P. [Department of Mechanical Engineering, Massachusetts Institute of Technology (United States); Karniadakis, G.E. [Division of Applied Mathematics, Brown University (United States)
2017-05-01
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 Burgers 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.
Hausdorff-type Measures of the Sample Path of Gaussian Random Fields
Institute of Scientific and Technical Information of China (English)
Zhen-long Chen; San-yang Liu
2005-01-01
Let φ be a Hausdorff measure function and ∧ be an infinite increasing sequence of positive integers.The Hausdorff-type measure φ - m∧ associated to φ and ∧ is studied. Let X(t)(t ∈ RN) be certain Gaussian random fields in Rd. We give the exact Hausdorff measure of the graph set GrX([0, 1]N), and evaluate the exact φ - m∧ measure of the image and graph set of X(t). A necessary and sufficient condition on the sequence ∧ is given so that the usual Hausdorff measure function for X([0, 1]N) and GrX([0,1]N) are still the correct measure functions. If the sequence ∧ increases faster, then some smaller measure functions will give positive and finite (φ, ∧)-Hausdorff measure for X([0, 1]N) and GTX([0, 1]N).
Energy Technology Data Exchange (ETDEWEB)
Zentner, I. [IMSIA, UMR EDF-ENSTA-CNRS-CEA 9219, Université Paris-Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau Cedex (France); Ferré, G., E-mail: gregoire.ferre@ponts.org [CERMICS – Ecole des Ponts ParisTech, 6 et 8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne la Vallée Cedex 2 (France); Poirion, F. [Department of Structural Dynamics and Aeroelasticity, ONERA, BP 72, 29 avenue de la Division Leclerc, 92322 Chatillon Cedex (France); Benoit, M. [Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE), UMR 7342 (CNRS, Aix-Marseille Université, Ecole Centrale Marseille), 49 rue Frédéric Joliot-Curie, BP 146, 13384 Marseille Cedex 13 (France)
2016-06-01
In this paper, a new method for the identification and simulation of non-Gaussian and non-stationary stochastic fields given a database is proposed. It is based on two successive biorthogonal decompositions aiming at representing spatio–temporal stochastic fields. The proposed double expansion allows to build the model even in the case of large-size problems by separating the time, space and random parts of the field. A Gaussian kernel estimator is used to simulate the high dimensional set of random variables appearing in the decomposition. The capability of the method to reproduce the non-stationary and non-Gaussian features of random phenomena is illustrated by applications to earthquakes (seismic ground motion) and sea states (wave heights).
Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel
2016-07-01
A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of field and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.
The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields
Vladimirov, Igor G
2012-01-01
We consider an "elastic" version of the statistical mechanical monomer-dimer problem on the n-dimensional integer lattice. Our setting includes the classical "rigid" formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan" EDM systems where the dimer potential is a weighted l1-distance and the auxiliary GRF is a Markov random fie...
Hadjiagapiou, Ioannis A.
2014-03-01
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The Sherrington-Kirkpatrick Ising spin glass with random couplings in the presence of a random magnetic field is investigated in detail within the framework of the replica method. The two random variables (exchange integral interaction and random magnetic field) are drawn from a joint Gaussian probability density function characterized by a correlation coefficient ρ. The thermodynamic properties and phase diagrams are studied with respect to the natural parameters of both random components of the system contained in the probability density. The de Almeida-Thouless line is explored as a function of temperature, ρ and other system parameters. The entropy for zero temperature as well as for non zero temperatures is partly negative or positive, acquiring positive branches as h0 increases.
Real-time Gaussian Markov random-field-based ground tracking for ground penetrating radar data
Bradbury, Kyle; Torrione, Peter A.; Collins, Leslie
2009-05-01
Current ground penetrating radar algorithms for landmine detection require accurate estimates of the location of the air/ground interface to maintain high levels of performance. However, the presence of surface clutter, natural soil roughness, and antenna motion lead to uncertainty in these estimates. Previous work on improving estimates of the location of the air/ground interface have focused on one-dimensional filtering techniques to localize the air/ground interface. In this work, we propose an algorithm for interface localization using a 2- D Gaussian Markov random field (GMRF). The GMRF provides a statistical model of the surface structure, which enables the application of statistical optimization techniques. In this work, the ground location is inferred using iterated conditional modes (ICM) optimization which maximizes the conditional pseudo-likelihood of the GMRF at a point, conditioned on its neighbors. To illustrate the efficacy of the proposed interface localization approach, pre-screener performance with and without the proposed ground localization algorithm is compared. We show that accurate localization of the air/ground interface provides the potential for future performance improvements.
Gaussian random field power spectrum and the S\\'ersic law
Nipoti, Carlo
2015-01-01
The surface-brightness profiles of galaxies are well described by the S\\'ersic law: systems with high S\\'ersic index m have steep central profiles and shallow outer profiles, while systems with low m have shallow central profiles and steep outer profiles. R. Cen (2014, ApJL, 790, L24) has conjectured that these profiles arise naturally in the standard cosmological model with initial density fluctuations represented by a Gaussian random field (GRF). We explore and confirm this hypothesis with N-body simulations of dissipationless collapses in which the initial conditions are generated from GRFs with different power spectra. The numerical results show that GRFs with more power on small scales lead to systems with higher m. In our purely dissipationless simulations the S\\'ersic index is in the range 2
Betti Numbers of Gaussian Fields
Park, Changbom; Pranav, Pratyush; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A.
2013-01-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be
Directory of Open Access Journals (Sweden)
Phil Diamond
2003-01-01
Full Text Available Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.
Gaussian free fields for mathematicians
Sheffield, Scott
2003-01-01
The d-dimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a d-dimensional-time analog of Brownian motion. Just as Brownian motion is the limit of the simple random walk (when time and space are appropriately scaled), the GFF is the limit of many incrementally varying random functions on d-dimensional grids. We present an overview of the GFF and some of the properties that are useful in light of recent connections between the GFF and the Schramm-L...
Krebsbach, K.; Friederichs, P.
2014-12-01
The generation of reliable precipitation products that explicitly account for spatial and temporal structures of precipitation events requires a combination of data with a variety of error structures and temporal resolutions. In-situ measurements are relatively accurate, but available only at sparse and irregularly distributed locations, whereas remote measurements cover areas but suffer from spatially and temporally inhomogeneous systematic errors. Besides gauge measurements are available on coarser spatial and temporal resolution in contrast to remote sensing measurements which are given on a fine spatial and temporal resolution. In our study we use precipitation rates from the composit of two X-band radars in Bonn and Jülich in Germany. Our aim is to formulate a statistical space-time model that aggregates and disaggregates precipitation rates from radar and gauge observations. We model a Gaussian random field as underlying process, where we face the task of dealing with a large non-Gaussian data set. To start the analysis of the unadjusted radar rainfall rates, we follow the work of D. Allcroft and C. Glasbey (2003) and transform the data to a truncated Gaussian distribution. The advantage of the latent variable approach is that it takes account of the occurence of rainfall and the intensity using a single process. We proceed by estimating the empirical correlation from these transformed values with maximum likelihood methods and fit a parametric correlation function that gives rise to a Gaussian random field. Since the transformation gives censored values to dry locations, we simulate values for this area that lie below some threshold and extend the Gaussian field to the whole domain. In order to merge gauge and radar data for precipitation, we first aggregate the data to a scale on which the comparison is reasonable and then disaggregate again back to smaller desirable scales. The disaggregation step consists of calculating the difference between radar
Spectral turning bands for efficient Gaussian random fields generation on GPUs and accelerators
Hunger, L.; Cosenza, B.; Kimeswenger, S.; Fahringer, T.
2015-11-01
A random field (RF) is a set of correlated random variables associated with different spatial locations. RF generation algorithms are of crucial importance for many scientific areas, such as astrophysics, geostatistics, computer graphics, and many others. Current approaches commonly make use of 3D fast Fourier transform (FFT), which does not scale well for RF bigger than the available memory; they are also limited to regular rectilinear meshes. We introduce random field generation with the turning band method (RAFT), an RF generation algorithm based on the turning band method that is optimized for massively parallel hardware such as GPUs and accelerators. Our algorithm replaces the 3D FFT with a lower-order, one-dimensional FFT followed by a projection step and is further optimized with loop unrolling and blocking. RAFT can easily generate RF on non-regular (non-uniform) meshes and efficiently produce fields with mesh sizes bigger than the available device memory by using a streaming, out-of-core approach. Our algorithm generates RF with the correct statistical behavior and is tested on a variety of modern hardware, such as NVIDIA Tesla, AMD FirePro and Intel Phi. RAFT is faster than the traditional methods on regular meshes and has been successfully applied to two real case scenarios: planetary nebulae and cosmological simulations.
Le Maitre, Olivier
2015-01-07
We address model dimensionality reduction in the Bayesian inference of Gaussian fields, considering prior covariance function with unknown hyper-parameters. The Karhunen-Loeve (KL) expansion of a prior Gaussian process is traditionally derived assuming fixed covariance function with pre-assigned hyperparameter values. Thus, the modes strengths of the Karhunen-Loeve expansion inferred using available observations, as well as the resulting inferred process, dependent on the pre-assigned values for the covariance hyper-parameters. Here, we seek to infer the process and its the covariance hyper-parameters in a single Bayesian inference. To this end, the uncertainty in the hyper-parameters is treated by means of a coordinate transformation, leading to a KL-type expansion on a fixed reference basis of spatial modes, but with random coordinates conditioned on the hyper-parameters. A Polynomial Chaos (PC) expansion of the model prediction is also introduced to accelerate the Bayesian inference and the sampling of the posterior distribution with MCMC method. The PC expansion of the model prediction also rely on a coordinates transformation, enabling us to avoid expanding the dependence of the prediction with respect to the covariance hyper-parameters. We demonstrate the efficiency of the proposed method on a transient diffusion equation by inferring spatially-varying log-diffusivity fields from noisy data.
Jin, Ick Hoon; Yuan, Ying; Bandyopadhyay, Dipankar
2016-01-01
Research in dental caries generates data with two levels of hierarchy: that of a tooth overall and that of the different surfaces of the tooth. The outcomes often exhibit spatial referencing among neighboring teeth and surfaces, i.e., the disease status of a tooth or surface might be influenced by the status of a set of proximal teeth/surfaces. Assessments of dental caries (tooth decay) at the tooth level yield binary outcomes indicating the presence/absence of teeth, and trinary outcomes at the surface level indicating healthy, decayed, or filled surfaces. The presence of these mixed discrete responses complicates the data analysis under a unified framework. To mitigate complications, we develop a Bayesian two-level hierarchical model under suitable (spatial) Markov random field assumptions that accommodates the natural hierarchy within the mixed responses. At the first level, we utilize an autologistic model to accommodate the spatial dependence for the tooth-level binary outcomes. For the second level and conditioned on a tooth being non-missing, we utilize a Potts model to accommodate the spatial referencing for the surface-level trinary outcomes. The regression models at both levels were controlled for plausible covariates (risk factors) of caries, and remain connected through shared parameters. To tackle the computational challenges in our Bayesian estimation scheme caused due to the doubly-intractable normalizing constant, we employ a double Metropolis-Hastings sampler. We compare and contrast our model performances to the standard non-spatial (naive) model using a small simulation study, and illustrate via an application to a clinical dataset on dental caries. PMID:27807470
DEFF Research Database (Denmark)
Yura, Harold; Hanson, Steen Grüner
2012-01-01
Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the......Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set...... with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative...
Gaussian Random Fields Methods for Fork-Join Network with Synchronization Constraints
2014-12-22
research papers, under review in Mathematics of Operations Research (minor revision) and Annals of Applied Probability. One paper was on the finalist...2.00 1.00 Hongyuan Lu, Guodong Pang. Heavy Traffic Limits for A Fork-Join Network In the Halfin-Whitt Regime, Annals of Applied Probability (11 2014...fellowships for further studies in science , mathematics, engineering or technology fields: Student Metrics This section only applies to graduating
Betti numbers of Gaussian fields
Park, Changbom; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A
2013-01-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be used to distinguish topological spaces. In the case of the excursion sets of a three-dimensional field there are three possibly non-zero Betti numbers; $\\beta_0$ is the number of connected regions, $\\beta_1$ is the number of circular holes, and $\\beta_2$ is the number of three-dimensional voids. Their sum with alternating signs is the genus of the surface of excursion regions. It is found that each Betti number has a dominant contribution to the genus in a specific threshold range. $\\beta_0$ dominates the high-threshold part of the genus curve measuring the abundance of high density regions (clusters). $\\beta_1$ dominates the genus near the median thresholds which measures the topology of negatively curved iso-den...
Integration of non-Gaussian fields
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Mohr, Gunnar; Hoffmeyer, Pernille
1996-01-01
enough to justify that it is sufficiently accurate for the applications to shortcut the problem and just assume that the distribution of the relevant stochastic integral is Gaussian. An earlier published example exhibiting this problem concerns silo pressure fields. [Ditlevsen, O., Christensen, C......The limitations of the validity of the central limit theorem argument as applied to definite integrals of non-Gaussian random fields are empirically explored by way of examples. The purpose is to investigate in specific cases whether the asymptotic convergence to the Gaussian distribution is fast....... and Randrup-Thomsen, S. Reliability of silo ring under lognormal stochastic pressure using stochastic interpolation. Proc. IUTAM Symp., Probabilistic Structural Mechanics: Advances in Structural Reliability Methods, San Antonio, TX, USA, June 1993 (eds.: P. D. Spanos & Y.-T. Wu) pp. 134-162. Springer, Berlin...
Segovia, Fermín.; Salas-Gonzalez, Diego; Górriz, Juan M.; Ramírez, Javier; Martínez-Murcia, Francisco J.
2017-03-01
18F-DMFP-PET is a neuroimaging modality that allows us to analyze the striatal dopamine. Thus, it is recently emerging as an effective tool to assist the diagnosis of Parkinsonism and differentiate among parkinsonian syndromes. However the analysis of these data, which require specific preprocessing methods, is still poorly covered. In this work we demonstrate a novel methodology based on Hidden Markov Random Fields (HMRF) and the Gaussian distribution to preprocess 18F-DMFP-PET data. First, we performed a selection of voxels based on the analysis of the histogram in order to remove low-signal regions and regions outside the brain. Specifically, we modeled the histogram of intensities of a neuroimage with a mixture of two Gaussians and then, using a HMRF algorithm the voxels corresponding to the low-intensity Gaussian were discarded. This procedure is similar to the tissue segmentation usually applied to Magnetic Resonance Imaging data. Secondly, the intensity of the selected voxels was scaled so that the Gaussian that models the histogram for each neuroimage has same mean and standard deviation. This step made comparable the data from different patients, without removing the characteristic patterns of each patient's disorder. The proposed approach was evaluated using a computer system based on statistical classification that separated the neuroimages according to the parkinsonian variant they represented. The proposed approach achieved higher accuracy rates than standard approaches for voxel selection (based on atlases) and intensity normalization (based on the global mean).
Stochastic Geometry and Topology of Non-Gaussian Fields
Beuman, T.H.; Turner, A.M.; Vitelli, V.
2012-01-01
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter and cosmology to biomedical imaging. The stan
Gaussian Networks Generated by Random Walks
Javarone, Marco Alberto
2014-01-01
We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been adopted to perform community detection, exploration tasks and to study temporal networks. Moreover, they have been used also to generate scale-free networks. In this work, we define a random walker that plays the role of "edges-generator". In particular, the random walker generates new connections and uses these ones to visit each node of a network. As result, the proposed model allows to achieve networks provided with a Gaussian degree distribution, and moreover, some features as the clustering coefficient and the assortativity show a critical behavior. Finally, we performed numerical simulations to study the behavior and the properties of the cited model.
Gaussian and non-Gaussian inverse modeling of groundwater flow using copulas and random mixing
Bárdossy, András.; Hörning, Sebastian
2016-06-01
This paper presents a new copula-based methodology for Gaussian and non-Gaussian inverse modeling of groundwater flow. The presented approach is embedded in a Monte Carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function. The target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields. The corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability, and honors all the observations of hydraulic transmissivities. The constraints related to hydraulic head observations are nonlinear. In order to fulfill these constraints, a connected domain in the weight space, inside which all linear constraints are fulfilled, is identified. This domain is defined analytically and includes an infinite number of conditional fields (i.e., conditioned on the observed hydraulic transmissivities), and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads. This procedure enables the simulation of a great number of solutions for the inverse problem, allowing a reasonable quantification of the associated uncertainties. The methodology can be used for fields with Gaussian copula dependence, and fields with specific non-Gaussian copula dependence. Further, arbitrary marginal distributions can be considered.
Characterisation of random Gaussian and non-Gaussian stress processes in terms of extreme responses
Directory of Open Access Journals (Sweden)
Colin Bruno
2015-01-01
Full Text Available In the field of military land vehicles, random vibration processes generated by all-terrain wheeled vehicles in motion are not classical stochastic processes with a stationary and Gaussian nature. Non-stationarity of processes induced by the variability of the vehicle speed does not form a major difficulty because the designer can have good control over the vehicle speed by characterising the histogram of instantaneous speed of the vehicle during an operational situation. Beyond this non-stationarity problem, the hard point clearly lies in the fact that the random processes are not Gaussian and are generated mainly by the non-linear behaviour of the undercarriage and the strong occurrence of shocks generated by roughness of the terrain. This non-Gaussian nature is expressed particularly by very high flattening levels that can affect the design of structures under extreme stresses conventionally acquired by spectral approaches, inherent to Gaussian processes and based essentially on spectral moments of stress processes. Due to these technical considerations, techniques for characterisation of random excitation processes generated by this type of carrier need to be changed, by proposing innovative characterisation methods based on time domain approaches as described in the body of the text rather than spectral domain approaches.
Phase Correlations in Non-Gaussian Fields
Matsubara, T
2003-01-01
A breakthrough in understanding the phase information of Fourier modes in non-Gaussian fields is presented, discovering the general relation between phase correlations and the hierarchy of polyspectra. Although the exact relations involve the expansions of infinite series, one can truncate these expansions in weakly non-Gaussian fields. The phase sum, $\\theta_{\\sbfm{k}_1} + >... + \\theta_{\\sbfm{k}_N}$, satisfying $\\bfm{k}_1 + ... + \\bfm{k}_N = 0$, is found to be non-uniformly distributed in non-Gaussian fields, and the non-uniformness is represented by the polyspectra. A numerical demonstration proves that the distribution of the phase sum is the robust estimator of the non-Gaussianity.
Institute of Scientific and Technical Information of China (English)
杨涛
2014-01-01
For the low resolution and the large fuzziness of the organizational structure of human brain at the edge of MR image scanned, a better threshold MR image segmentation method based on fuzzy Markov random field clustering and Gaussian curves is proposed. In the algorithm, fuzzy theory is introduced into the statistics of the pixel neighborhood attributes, and fuzzy Markov ran-dom field is set up. Then the optimum one-dimensional projection histogram of two-dimensional histogram is fit with Gaussian curves and found segmentation points in each class region. Finally, image segmentation is realized in the two-dimensional histo-gram. Experiments show that the proposed algorithm can improve the effective resolution of the various brain tissues, and it is better than the one-dimensional Otsu method and two-dimensional Otsu method in the noise robustness and partition connectivity of the re-sult.%针对扫描的人脑组织MR图像边缘分辨率低、模糊性大的特点，本文提出了一种基于模糊Markov随机场和Gaussian曲线相结合的MR图像最佳阈值分割方法。该方法通过对图像的像素邻域属性的统计将模糊论引入其中，建立模糊Markov随机场，并利用Gaussian曲线对二维直方图最佳一维投影进行拟合，确定出图像中各脑组织的二维阈值点，在二维直方图上实现对脑组织的分割。通过实验表明，本算法能够有效提高脑组织的分辨率，对噪声的鲁棒性、结果区域的连通性相对于一维Otsu和二维Otsu算法都有了很大的提高。
Higher moments of weighted integrals of non-Gaussian fields
DEFF Research Database (Denmark)
Mohr, Gunnar
1999-01-01
In general, the exact probability distribution of a definite integral of a given non-Gaussian random field is not known. Some information about this unknown distribution can be obtained from the 3rd and 4th moment of the integral. Approximations to these moments can be calculated by discretizing...... the integral and replacing the integrand by third-degree polynomials of correlated Gaussian Variables which reproduce the first four moments and the correlation function of the field correctly. The method described (see Ditlevsen O, Mohr G, Hoffmeyer P. Integration of non-Gaussian fields. Probabilistic...... engineering mechanics, 1996) based on these ideas is discussed and further developed and used in a computer program which produces fairly accurate approximations to the mentioned moments with no restrictions put on the weight function applied to the field and the correlation function of the field...
DEFF Research Database (Denmark)
Frier, Christian; Sørensen, John Dalsgaard
2005-01-01
around the reinforcement exceeds a critical threshold value. In the present paper FERM (the Finite Element Reliability Method) is employed for obtaining the probability of exceeding a critical chloride concentration level at the reinforcement bars using MCS (Monte Carlo Simulation). The chloride ingress...... is modeled by a 2-dimensional diffusion process by FEM (Finite Element Method) and the diffusion coefficient, surface chloride concentration and reinforcement cover depth are modeled by multidimensional stochastic fields, which are discretized using the EOLE (Expansion Optimum Linear Estimation) approach......For many reinforced concrete structures corrosion of the reinforcement is an important problem since it can result in expensive maintenance and repair actions. Further, a significant reduction of the load-bearing capacity can occur. One mode of corrosion initiation occurs when the chloride content...
Generation of correlated finite alphabet waveforms using gaussian random variables
Jardak, Seifallah
2014-09-01
Correlated waveforms have a number of applications in different fields, such as radar and communication. It is very easy to generate correlated waveforms using infinite alphabets, but for some of the applications, it is very challenging to use them in practice. Moreover, to generate infinite alphabet constant envelope correlated waveforms, the available research uses iterative algorithms, which are computationally very expensive. In this work, we propose simple novel methods to generate correlated waveforms using finite alphabet constant and non-constant-envelope symbols. To generate finite alphabet waveforms, the proposed method map the Gaussian random variables onto the phase-shift-keying, pulse-amplitude, and quadrature-amplitude modulation schemes. For such mapping, the probability-density-function of Gaussian random variables is divided into M regions, where M is the number of alphabets in the corresponding modulation scheme. By exploiting the mapping function, the relationship between the cross-correlation of Gaussian and finite alphabet symbols is derived. To generate equiprobable symbols, the area of each region is kept same. If the requirement is to have each symbol with its own unique probability, the proposed scheme allows us that as well. Although, the proposed scheme is general, the main focus of this paper is to generate finite alphabet waveforms for multiple-input multiple-output radar, where correlated waveforms are used to achieve desired beampatterns. © 2014 IEEE.
Eddy diffusivities of inertial particles in random Gaussian flows
Boi, Simone; Muratore-Ginanneschi, Paolo
2016-01-01
We investigate the large-scale transport of inertial particles. We derive explicit analytic expressions for the eddy diffusivities for generic Stokes times. These latter expressions are exact for any shear flow while they correspond to the leading contribution either in the deviation from the shear flow geometry or in the P\\'eclet number of general random Gaussian velocity fields. Our explicit expressions allow us to investigate the role of inertia for such a class of flows and to make exact links with the analogous transport problem for tracer particles.
Higher Moments of Weighted Integrals of Non-Gaussian Fields
DEFF Research Database (Denmark)
Mohr, Gunnar
1996-01-01
In general , the exact probability distribution of a definite non-Gaussian random field is not known. Some information about this unknown distribution can be obtained from the 3rd and 4th moment of the integral. Approximations to these moments are calculated by a numerical technique based...... on recursive application of Winterstein approximations) moment fitted linear combinations of Hermite Polynomials of standard Gaussian variables). By use of computerized symbol manipulations it is practicable to obtain exact moments (up to order 4) of partial weighted sums of mutually dependent variables...
On the Shaker Simulation of Wind-Induced Non-Gaussian Random Vibration
Directory of Open Access Journals (Sweden)
Fei Xu
2016-01-01
Full Text Available Gaussian signal is produced by ordinary random vibration controllers to test the products in the laboratory, while the field data is usually non-Gaussian. Two methodologies are presented in this paper for shaker simulation of wind-induced non-Gaussian vibration. The first methodology synthesizes the non-Gaussian signal offline and replicates it on the shaker in the Time Waveform Replication (TWR mode. A new synthesis method is used to model the non-Gaussian signal as a Gaussian signal multiplied by an amplitude modulation function (AMF. A case study is presented to show that the synthesized non-Gaussian signal has the same power spectral density (PSD, probability density function (PDF, and loading cycle distribution (LCD as the field data. The second methodology derives a damage equivalent Gaussian signal from the non-Gaussian signal based on the fatigue damage spectrum (FDS and the extreme response spectrum (ERS and reproduces it on the shaker in the closed-loop frequency domain control mode. The PSD level and the duration time of the derived Gaussian signal can be manipulated for accelerated testing purpose. A case study is presented to show that the derived PSD matches the damage potential of the non-Gaussian environment for both fatigue and peak response.
Correlations between zeros of non-Gaussian random polynomials
Bleher, Pavel M.; Di, Xiaojun
2003-01-01
The existence of the scaling limit and its universality, for correlations between zeros of {\\it Gaussian} random polynomials, or more generally, {\\it Gaussian} random sections of powers of a line bundle over a compact manifold has been proved in a great generality in the works [BBL2], [Ha], [BD], [BSZ1]-[BSZ4], and others. In the present work we prove the existence of the scaling limit for a class of {\\it non-Gaussian} random polynomials. Our main result is that away from the origin the scali...
Anomalous scaling in a non-Gaussian random shell model for passive scalars
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, we have introduced a shell-model of Kraichnan's passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and δ correlated in time, and its introduction is inspired by She and Lév(e)que (Phys. Rev. Lett. 72,336 (1994)). For comparison, we also give the passive scalar advected by the Gaussian random velocity field. The anomalous scaling exponents H(p) of passive scalar advected by these two kinds of random velocities above are determined for structure function with values of p up to 15 by Monte Carlo simulations of the random shell model, with Gear methods used to solve the stochastic differential equations. We find that the H(p) advected by the non-Gaussian random velocity is not more anomalous than that advected by the Gaussian random velocity. Whether the advecting velocity is non-Gaussian or Gaussian, similar scaling exponents of passive scalar are obtained with the same molecular diffusivity.
Internal DLA and the Gaussian free field
Jerison, David; Sheffield, Scott
2011-01-01
In previous works, we showed that the internal DLA cluster on \\Z^d with t particles is a.s. spherical up to a maximal error of O(\\log t) if d=2 and O(\\sqrt{\\log t}) if d > 2. This paper addresses "average error": in a certain sense, the average deviation of internal DLA from its mean shape is of constant order when d=2 and of order r^{1-d/2} (for a radius r cluster) in general. Appropriately normalized, the fluctuations (taken over time and space) scale to a variant of the Gaussian free field.
Energy Technology Data Exchange (ETDEWEB)
Zimbardo, G.; Veltri, P. (Dipartimento di Fisica, Universita della Calabria, I-87030 Arcavacata di Rende (Italy))
1995-02-01
The transport of magnetic field lines is studied numerically in the case where strong three-dimensional magnetic fluctuations are superimposed to a uniform average magnetic field. The magnetic percolation of field lines between magnetic islands is found, as well as a non-Gaussian regime where the field lines exhibit Levy random walks, changing from Levy flights to trapped motion. Anomalous diffusion laws [l angle][Delta][ital x][sub [ital i
Partial summations of stationary sequences of non-Gaussian random variables
DEFF Research Database (Denmark)
Mohr, Gunnar; Ditlevsen, Ove Dalager
1996-01-01
-Gaussian variables up to the moments of the fourth order [Winterstein, S. R. Nonlinear vibration models for extremes and fatigue. J. Engng Mech. ASCE 114 (1988) 1772-1790](1). A method to obtain the Winterstein approximation to a partial sum of a sequence of Winterstein approximations is explained and results...... of convergence of the distribution of a sum (or an integral) of mutually dependent random variables to the Gaussian distribution. The paper is closely related to the work in Ditlevsen el al. [Ditlevsen, O., Mohr, G. & Hoffmeyer, P. Integration of non-Gaussian fields. Prob. Engng Mech 11 (1996) 15-23](2)....
Random scalar fields and hyperuniformity
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.
Analytical structure of Hermite Gaussian beam in far field
Institute of Scientific and Technical Information of China (English)
Zhou Guo-Quan; Chen Liang; Chu Xiu-Xiang
2007-01-01
Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical structure of Hermite Gaussian beam in far field is presented. The structural energy flux distributions are also investigated in the far field. The structural pictures of some Hermite Gaussian beams are depicted in the far field. As the structure of Hermite Gaussian beam is dominated by the transverse mode numbers and the initial transverse Gaussian half width, it is more complex than that of Gaussian beam. The ratios of the structural energy fluxes to the whole energy flux are independent of the transverse mode numbers and the initial transverse Gaussian half width. The present research reveals the internal vectorial structure of Hermite Gaussian beam from other viewpoint.
Generation of correlated finite alphabet waveforms using gaussian random variables
Ahmed, Sajid
2016-01-13
Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.
Pseudo-Hermitian ensemble of random Gaussian matrices.
Marinello, G; Pato, M P
2016-07-01
It is shown how pseudo-Hermiticity, a necessary condition satisfied by operators of PT symmetric systems can be introduced in the three Gaussian classes of random matrix theory. The model describes transitions from real eigenvalues to a situation in which, apart from a residual number, the eigenvalues are complex conjugate.
Pseudo-Hermitian ensemble of random Gaussian matrices
Marinello, G.; Pato, M. P.
2016-07-01
It is shown how pseudo-Hermiticity, a necessary condition satisfied by operators of PT symmetric systems can be introduced in the three Gaussian classes of random matrix theory. The model describes transitions from real eigenvalues to a situation in which, apart from a residual number, the eigenvalues are complex conjugate.
Random walks, random fields, and disordered systems
Černý, Jiří; Kotecký, Roman
2015-01-01
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a mod...
Wave propagation in non-Gaussian random media
Franco, Mariano; Calzetta, Esteban
2015-01-01
We develop a compact perturbative series for acoustic wave propagation in a medium with a non-Gaussian stochastic speed of sound. We use Martin-Siggia and Rose auxiliary field techniques to render the classical wave propagation problem into a ‘quantum’ field theory one, and then frame this problem within the so-called Schwinger-Keldysh of closed time-path (CTP) formalism. Variation of the so-called two-particle irreducible (2PI) effective action (EA), whose arguments are both the mean fields and the irreducible two point correlations, yields the Schwinger-Dyson and the Bethe-Salpeter equations. We work out the loop expansion of the 2PI CTP EA and show that, in the paradigmatic problem of overlapping spherical intrusions in an otherwise homogeneous medium, non-Gaussian corrections might be much larger than Gaussian ones at the same order of loops.
Fractional Gaussian noise: a random-matrix-theory inspired perspective
Jamali, Tayeb; Jafari, G R
2013-01-01
We introduce a particular construction of an autocorrelation matrix of a time series and its analysis based on the random-matrix theory (RMT) that is capable of unveiling the type of information about the statistical correlations which is inaccessible to the straight analysis of the autocorrelation function. Exploiting the well-studied hierarchy of the fractional Gaussian noise (fGn), an in situ criterion for the sake of a quantitative comparison with the autocorrelation data is offered. We demonstrate the applicability of our method by two paradigmatic examples from the orthodox context of the turbulence and the stock markets. Quite strikingly, a significant deviation from an fGn is observed despite a Gaussian distribution of the velocity profile of turbulence. In the latter context, on the contrary, a remarkable agreement with the fGn is achieved notwithstanding the non-Gaussianity in returns of the stock market.
Xu, Ganggang
2016-07-15
We propose a new class of trans-Gaussian random fields named Tukey g-and-h (TGH) random fields to model non-Gaussian spatial data. The proposed TGH random fields have extremely flexible marginal distributions, possibly skewed and/or heavy-tailed, and, therefore, have a wide range of applications. The special formulation of the TGH random field enables an automatic search for the most suitable transformation for the dataset of interest while estimating model parameters. Asymptotic properties of the maximum likelihood estimator and the probabilistic properties of the TGH random fields are investigated. An efficient estimation procedure, based on maximum approximated likelihood, is proposed and an extreme spatial outlier detection algorithm is formulated. Kriging and probabilistic prediction with TGH random fields are developed along with prediction confidence intervals. The predictive performance of TGH random fields is demonstrated through extensive simulation studies and an application to a dataset of total precipitation in the south east of the United States.
Note on non-Gaussianities in two-field inflation
Wang, Tower
2010-12-01
Two-field slow-roll inflation is the most conservative modification of a single-field model. The main motivations to study it are its entropic mode and non-Gaussianity. Several years ago, for a two-field model with additive separable potentials, Vernizzi and Wands invented an analytic method to estimate its non-Gaussianities. Later on, Choi et al. applied this method to the model with multiplicative separable potentials. In this note, we design a larger class of models whose non-Gaussianity can be estimated by the same method. Under some simplistic assumptions, roughly these models are unlikely able to generate a large non-Gaussianity. We look over some specific models of this class by scanning the full parameter space, but still no large non-Gaussianity appears in the slow-roll region. These models and scanning techniques would be useful for a future model hunt if observational evidence shows up for two-field inflation.
On Fatigue Life Under Stationary Gaussian Random Loads (A)
DEFF Research Database (Denmark)
Talreja, R.
1973-01-01
Power spectra are taken to represent stationary Gaussian random loads. Location, scale, and shape parameters are defined for power spectra and proposed as a convenient set of load parameters for random loads. The center frequency of a power spectrum, defined as its weighted average frequency......, is proposed as a measure of fatigue life. A servohydraulic closed loop testing machine is used to load specimens of carbon steel under six different power spectral shapes. Test results are utilized to evaluate a fatigue life function formulated in terms of the load parameters. The concept of a shape operator...
Gaussian vector fields on triangulated surfaces
DEFF Research Database (Denmark)
Ipsen, John H
2016-01-01
proven to be very useful to resolve the complex interplay between in-plane ordering of membranes and membrane conformations. In the present work we have developed a procedure for realistic representations of Gaussian models with in-plane vector degrees of freedoms on a triangulated surface. The method...
Energy Technology Data Exchange (ETDEWEB)
Wang, Yuan-Mei; Li, Jun-Gang, E-mail: jungl@bit.edu.cn; Zou, Jian
2017-06-15
Highlights: • Adaptive measurement strategy is used to detect the presence of a magnetic field. • Gaussian Ornstein–Uhlenbeck noise and non-Gaussian noise have been considered. • Weaker magnetic fields may be more easily detected than some stronger ones. - Abstract: By using the adaptive measurement method we study how to detect whether a weak magnetic field is actually present or not under Gaussian noise and non-Gaussian noise. We find that the adaptive measurement method can effectively improve the detection accuracy. For the case of Gaussian noise, we find the stronger the magnetic field strength, the easier for us to detect the magnetic field. Counterintuitively, for non-Gaussian noise, some weaker magnetic fields are more likely to be detected rather than some stronger ones. Finally, we give a reasonable physical interpretation.
Generating Correlated QPSK Waveforms By Exploiting Real Gaussian Random Variables
Jardak, Seifallah
2012-11-01
The design of waveforms with specified auto- and cross-correlation properties has a number of applications in multiple-input multiple-output (MIMO) radar, one of them is the desired transmit beampattern design. In this work, an algorithm is proposed to generate quadrature phase shift- keying (QPSK) waveforms with required cross-correlation properties using real Gaussian random-variables (RV’s). This work can be considered as the extension of what was presented in [1] to generate BPSK waveforms. This work will be extended for the generation of correlated higher-order phase shift-keying (PSK) and quadrature amplitude modulation (QAM) schemes that can better approximate the desired beampattern.
Tsuchida, Takahiro; Kimura, Koji
2016-09-01
Equivalent non-Gaussian excitation method is proposed to obtain the response moments up to the 4th order of dynamic systems under non-Gaussian random excitation. The non-Gaussian excitation is prescribed by the probability density and the power spectrum, and is described by an Ito stochastic differential equation. Generally, moment equations for the response, which are derived from the governing equations for the excitation and the system, are not closed due to the nonlinearity of the diffusion coefficient in the equation for the excitation even though the system is linear. In the equivalent non-Gaussian excitation method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by a quadratic polynomial. In numerical examples, a linear system subjected to nonGaussian excitations with bimodal and Rayleigh distributions is analyzed by using the present method. The results show that the method yields the variance, skewness and kurtosis of the response with high accuracy for non-Gaussian excitation with the widely different probability densities and bandwidth. The statistical moments of the equivalent non-Gaussian excitation are also investigated to describe the feature of the method.
Non-Gaussian gravitational clustering field statistics
Kitaura, F S
2010-01-01
In this work we investigate the multivariate statistical description of the matter distribution in the nonlinear regime. We introduce the multivariate Edgeworth expansion of the lognormal distribution to model the cosmological matter field. Such a technique could be useful to generate and reconstruct three-dimensional nonlinear cosmological density fields with the information of higher order correlation functions. We explicitly calculate the expansion up to third order in perturbation theory making use of the multivariate Hermite polynomials up to sixth order. The probability distribution function for the matter field includes at this level the two-point, the three-point and the four-point correlation functions. We use the hierarchical model to formulate the higher order correlation functions based on combinations of the two-point correlation function. This permits us to find compact expressions for the skewness and kurtosis terms of the expanded lognormal field which can be efficiently computed. The method i...
Finding a Large Submatrix of a Gaussian Random Matrix
Gamarnik, David
2016-01-01
We consider the problem of finding a $k\\times k$ submatrix of an $n\\times n$ matrix with i.i.d. standard Gaussian entries, which has a large average entry. It was shown earlier by Bhamidi et al. that the largest average value of such a matrix is $2\\sqrt{\\log n/k}$ with high probability. In the same paper an evidence was provided that a natural greedy algorithm called Largest Average Submatrix ($\\LAS$) should produce a matrix with average entry approximately $\\sqrt{2}$ smaller. In this paper we show that the matrix produced by the $\\LAS$ algorithm is indeed $\\sqrt{2\\log n/k}$ w.h.p. Then by drawing an analogy with the problem of finding cliques in random graphs, we propose a simple greedy algorithm which produces a $k\\times k$ matrix with asymptotically the same average value. Since the greedy algorithm is the best known algorithm for finding cliques in random graphs, it is tempting to believe that beating the factor $\\sqrt{2}$ performance gap suffered by both algorithms might be very challenging. Surprisingly...
Non-gaussianity from the trispectrum and vector field perturbations
Valenzuela-Toledo, Cesar A
2009-01-01
We use the \\delta N formalism to study the trispectrum T_\\zeta of the primordial curvature perturbation \\zeta when the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The level of non-gaussianity in the trispectrum, \\tau_{NL}, is calculated in this scenario and related to the level of non-gaussianity in the bispectrum, f_{NL}, and the level of statistical anisotropy in the power spectrum, g_\\zeta. Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on \\tau_{NL} from WMAP, for generic inflationary models, is done.
LARGE DEVIATION FOR THE EMPIRICAL CORRELATION COEFFICIENT OF TWO GAUSSIAN RANDOM VARIABLES
Institute of Scientific and Technical Information of China (English)
Shen Si
2007-01-01
In this article, the author obtains the large deviation principles for the empirical correlation coefficient of two Gaussian random variables X and Y. Especially, when considering two independent Gaussian random variables X, Y with the means EX, EY(both known), wherein the author gives two kinds of different proofs and gets the same results.
Topological recursion for Gaussian means and cohomological field theories
Andersen, Jørgen Ellegaard; Norbury, Paul; Penner, Robert C
2016-01-01
We use the explicit relation between genus filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces $M_{g,s}^{disc}$ (discrete volumes), to express Gaussian means in all genera as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate topological recursion of the Gaussian model into recurrent relations for coefficients of this expansion proving their integrality and positivity. As an application, we find the coefficients in the first subleading order for ${\\mathcal M}_{g,1}$ for all $g$ in three ways: by using the refined Harer--Zagier recursion, by exploiting the Givental-type decomposition of KPMM, and by an explicit diagram counting.
Dynamics of generalized Gaussian polymeric structures in random layered flows
Katyal, Divya; Kant, Rama
2015-04-01
We develop a formalism for the dynamics of a flexible branched polymer with arbitrary topology in the presence of random flows. This is achieved by employing the generalized Gaussian structure (GGS) approach and the Matheron-de Marsily model for the random layered flow. The expression for the average square displacement (ASD) of the center of mass of the GGS is obtained in such flow. The averaging is done over both the thermal noise and the external random flow. Although the formalism is valid for branched polymers with various complex topologies, we mainly focus here on the dynamics of the flexible star and dendrimer. We analyze the effect of the topology (the number and length of branches for stars and the number of generations for dendrimers) on the dynamics under the influence of external flow, which is characterized by their root-mean-square velocity, persistence flow length, and flow exponent α . Our analysis shows two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The influence of the topology of the GGS is unraveled in the intermediate-time regime, while the long-time regime is only weakly dependent on the topology of the polymer. With the decrease in the value of α , the magnitude of the ASD decreases, while the temporal exponent of the ASD increases in both the time regimes. Also there is an increase in both the magnitude of the ASD and the crossover time (from the subdiffusive to the superdiffusive regime) with an increase in the total mass of the polymeric structure.
Positive random fields for modeling material stiffness and compliance
DEFF Research Database (Denmark)
Hasofer, Abraham Michael; Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1998-01-01
with material properties modeled in terms of the considered random fields.The paper addsthe gamma field, the Fisher field, the beta field, and their reciprocal fields to the catalogue. These fields are all defined on the basis of sums of squares of independent standard Gaussian random variables.All the existing...... marginal moments and the correlation functions are obtained explicitly. Also an inverse Gaussian fieldis added to the catalogue. It is defined in terms of first passage times in correlated joint Brownian motions. Finally an n-dimensional random vector of positive components is defined such that it can...
Relativistic diffusive motion in random electromagnetic fields
Energy Technology Data Exchange (ETDEWEB)
Haba, Z, E-mail: zhab@ift.uni.wroc.pl [Institute of Theoretical Physics, University of Wroclaw, 50-204 Wroclaw, Plac Maxa Borna 9 (Poland)
2011-08-19
We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature {beta}{sup -1} = mc{sup 2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).
On generalized Gaussian free fields and stochastic homogenization
Gu, Yu; Mourrat, Jean-Christophe
2016-01-01
We study a generalization of the notion of Gaussian free field (GFF). Although the extension seems minor, we first show that a generalized GFF does not satisfy the spatial Markov property, unless it is a classical GFF. In stochastic homogenization, the scaling limit of the corrector is a possibly generalized GFF described in terms of an "effective fluctuation tensor" that we denote by $\\mathsf{Q}$. We prove an expansion of $\\mathsf{Q}$ in the regime of small ellipticity ratio. This expansion ...
Gaussian free fields at the integer quantum Hall plateau transition
Energy Technology Data Exchange (ETDEWEB)
Bondesan, R., E-mail: roberto.bondesan@phys.ox.ac.uk [Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP (United Kingdom); Wieczorek, D.; Zirnbauer, M.R. [Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln (Germany)
2017-05-15
In this work we put forward an effective Gaussian free field description of critical wavefunctions at the transition between plateaus of the integer quantum Hall effect. To this end, we expound our earlier proposal that powers of critical wave intensities prepared via point contacts behave as pure scaling fields obeying an Abelian operator product expansion. Our arguments employ the framework of conformal field theory and, in particular, lead to a multifractality spectrum which is parabolic. We also derive a number of old and new identities that hold exactly at the lattice level and hinge on the correspondence between the Chalker–Coddington network model and a supersymmetric vertex model.
Extreme value statistics of 2D Gaussian free field: effect of finite domains
Cao, X.; Rosso, A.; Santachiara, R.
2016-01-01
We study minima statistics of the 2D Gaussian free field (GFF) on circles in the unit disk with Dirichlet boundary condition. Free energy distributions of the associated random energy models are exactly calculated in the high temperature phase, and shown to satisfy the duality property, which enables us to predict the minima distribution by assuming the freezing scenario. Numerical tests are provided. Related questions concerning the GFF on a sphere are also considered.
Evolution of the Magnetic Field Line Diffusion Coefficient and Non-Gaussian Statistics
Snodin, A. P.; Ruffolo, D.; Matthaeus, W. H.
2016-08-01
The magnetic field line random walk (FLRW) plays an important role in the transport of energy and particles in turbulent plasmas. For magnetic fluctuations that are transverse or almost transverse to a large-scale mean magnetic field, theories describing the FLRW usually predict asymptotic diffusion of magnetic field lines perpendicular to the mean field. Such theories often depend on the assumption that one can relate the Lagrangian and Eulerian statistics of the magnetic field via Corrsin’s hypothesis, and additionally take the distribution of magnetic field line displacements to be Gaussian. Here we take an ordinary differential equation (ODE) model with these underlying assumptions and test how well it describes the evolution of the magnetic field line diffusion coefficient in 2D+slab magnetic turbulence, by comparisons to computer simulations that do not involve such assumptions. In addition, we directly test the accuracy of the Corrsin approximation to the Lagrangian correlation. Over much of the studied parameter space we find that the ODE model is in fairly good agreement with computer simulations, in terms of both the evolution and asymptotic values of the diffusion coefficient. When there is poor agreement, we show that this can be largely attributed to the failure of Corrsin’s hypothesis rather than the assumption of Gaussian statistics of field line displacements. The degree of non-Gaussianity, which we measure in terms of the kurtosis, appears to be an indicator of how well Corrsin’s approximation works.
Hertog, Maarten L. A. T. M.; Scheerlinck, Nico; Nicolaï, Bart M.
2009-01-01
When modelling the behaviour of horticultural products, demonstrating large sources of biological variation, we often run into the issue of non-Gaussian distributed model parameters. This work presents an algorithm to reproduce such correlated non-Gaussian model parameters for use with Monte Carlo simulations. The algorithm works around the problem of non-Gaussian distributions by transforming the observed non-Gaussian probability distributions using a proposed SKN-distribution function before applying the covariance decomposition algorithm to generate Gaussian random co-varying parameter sets. The proposed SKN-distribution function is based on the standard Gaussian distribution function and can exhibit different degrees of both skewness and kurtosis. This technique is demonstrated using a case study on modelling the ripening of tomato fruit evaluating the propagation of biological variation with time.
Gaussian point processes and two-by-two random matrix theory.
Nieminen, John M
2007-10-01
The statistics of the multidimensional Gaussian point process are discussed in connection with the spacing statistics of eigenvalues of 2x2 random matrices. We consider the three-dimensional Gaussian point process when two of the coordinates of a point are randomly chosen from a Gaussian distribution having a mean of zero and a variance of sigma;{2}=1 but the third coordinate is chosen from a Gaussian distribution having a variance in the range of 0random point being at a distance r from the origin is shown to be closely related to the nearest-neighbor spacing distribution of eigenvalues coming from an ensemble of 2x2 matrices defined by the French-Kota-Pandey-Mehta two-matrix model of random matrix theory. An elementary explanation of this result is given.
Freno, Antonino
2011-01-01
This book presents an exciting new synthesis of directed and undirected, discrete and continuous graphical models. Combining elements of Bayesian networks and Markov random fields, the newly introduced hybrid random fields are an interesting approach to get the best of both these worlds, with an added promise of modularity and scalability. The authors have written an enjoyable book---rigorous in the treatment of the mathematical background, but also enlivened by interesting and original historical and philosophical perspectives. -- Manfred Jaeger, Aalborg Universitet The book not only marks an
Non-Gaussianity in multiple three-form field inflation
Kumar, K Sravan; Nunes, Nelson J; Marto, João; Moniz, Paulo Vargas
2016-01-01
In this work, we present a method for implementing the $\\delta N$ formalism to study the primordial non-Gaussianity produced in multiple three-form field inflation. Using a dual description relating three-form fields to non-canonical scalar fields, and employing existing results, we produce expressions for the bispectrum of the curvature perturbation in terms of three-form quantities. We study the bispectrum generated in a two three-form field inflationary scenario for a particular potential which for suitable values of the parameters was found in earlier work to give values of the spectral index and ratio of tensor to scalar perturbations compatible with current bounds. We calculate the reduced bispectrum for this model, finding an amplitude in equilateral and orthogonal configurations of ${\\cal O}(1)$ and in the squeezed limit of ${\\cal O}(10^{-3})$. We confirm, therefore, that this three-form inflationary scenario is compatible with present observational constraints.
Non-Gaussian distribution of galaxies gravitational fields
Stephanovich, V A
2016-01-01
We perform a theoretical analysis of the observational relation between angular momentum and mass (richness) of the galaxy clusters. For that we calculate the distribution function of astronomical objects (like galaxies and/or smooth halos of different kinds) gravitational fields due to their tidal interaction. Within the statistical method of Chandrasekhar we are able to show that the distribution function is determined by the form of interaction between objects and for multipole (tidal) interaction it is never Gaussian. Our calculation permits to demonstrate that alignment of galaxies angular momenta increases with the cluster richness. The specific form of the corresponding dependence is due to assumptions made about cluster morphology.
A gaussian model for simulated geomagnetic field reversals
Wicht, Johannes; Meduri, Domenico G.
2016-10-01
Field reversals are the most spectacular events in the geomagnetic history but remain little understood. Here we explore the dipole behaviour in particularly long numerical dynamo simulations to reveal statistically significant conditions required for reversals and excursions to happen. We find that changes in the axial dipole moment behaviour are crucial while the equatorial dipole moment plays a negligible role. For small Rayleigh numbers, the axial dipole always remains strong and stable and obeys a clearly Gaussian probability distribution. Only when the Rayleigh number is increased sufficiently the axial dipole can reverse and its distribution becomes decisively non-Gaussian. Increased likelihoods around zero indicate a pronounced lingering in a new low dipole moment state. Reversals and excursions can only happen when axial dipole fluctuations are large enough to drive the system from the high dipole moment state assumed during stable polarity epochs into the low dipole moment state. Since it is just a matter of chance which polarity is amplified during dipole recovery, reversals and grand excursions, i.e. excursions during which the dipole assumes reverse polarity, are equally likely. While the overall reversal behaviour seems Earth-like, a closer comparison to palaeomagnetic findings suggests that the simulated events last too long and that grand excursions are too rare. For a particularly large Ekman number we find a second but less Earth-like type of reversals where the total field decays and recovers after a certain time.
Holographic non-Gaussianities in general single-field inflation
Isono, Hiroshi; Shiu, Gary; Wong, Sam S C; Zhou, Siyi
2016-01-01
We use holographic techniques to compute inflationary non-Gaussianities for general single-field inflation, including models with a non-trivial sound speed. In this holographic approach, the inflationary dynamics is captured by a relevant deformation of the dual conformal field theory (CFT) in the UV, while the inflationary correlators are computed by conformal perturbation theory. In this paper, we discuss the effects of higher derivative operators, such as $(\\partial_\\mu\\phi\\partial^\\mu\\phi)^{m}$, which are known to induce a non-trivial sound speed and source potentially large non-Gaussianities. We compute the full inflationary bispectra from the deformed CFT correlators. We also discuss the squeezed limit of the bispectra from the viewpoint of operator product expansions. As is generic in the holographic description of inflation, our power spectrum is blue tilted in the UV region. We extend our bispectrum computation to the IR region by resumming the conformal perturbations to all orders. We provide a self...
Off-Axis Gaussian Beams with Random Displacement in Atmospheric Turbulence
Directory of Open Access Journals (Sweden)
Yahya Baykal
2006-10-01
Full Text Available Our recent work in which we study the propagation of the general Hermite-sinusoidal-Gaussian laser beams in wireless broadband access telecommunication systems is elaborated in this paper to cover the special case of an off-axis Gaussian beam. We mainly investigate the propagation characteristics in atmospheric turbulence of an off-axis Gaussian beam possessing Gaussian distributed random displacement parameters. Our interest is to search for different types of laser beams that will improve the performance of a wireless broadband access system when atmospheric turbulence is considered. Our formulation is based on the basic solution of the second order mutual coherence function evaluated at the receiver plane. For fixed turbulence strength, the coherence length calculated at the receiver plane is found to decrease as the variance of the random displacement is increased. It is shown that as the turbulence becomes stronger, coherence lengths due to off-axis Gaussian beams tend to approach the same value, irrespective of the variance of the random displacement. As expected, the beam spreading is found to be pronounced for larger variance of displacement parameter. Average intensity profiles when atmospheric turbulence is present are plotted for different values of the variance of the random displacement parameter of the off-axis Gaussian beam.
Asymptotics of sums of lognormal random variables with Gaussian copula
DEFF Research Database (Denmark)
Asmussen, Søren; Rojas-Nandayapa, Leonardo
2008-01-01
Let (Y1, ..., Yn) have a joint n-dimensional Gaussian distribution with a general mean vector and a general covariance matrix, and let Xi = eYi, Sn = X1 + ⋯ + Xn. The asymptotics of P (Sn > x) as n → ∞ are shown to be the same as for the independent case with the same lognormal marginals. In part....... In particular, for identical marginals it holds that P (Sn > x) ∼ n P (X1 > x) no matter what the correlation structure is. © 2008 Elsevier B.V. All rights reserved....
The Gaussian streaming model and Lagrangian effective field theory
Vlah, Zvonimir; White, Martin
2016-01-01
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of int...
The Gaussian streaming model and convolution Lagrangian effective field theory
Vlah, Zvonimir; Castorina, Emanuele; White, Martin
2016-12-01
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.
Spatial Behaviour of Singularities in Fractal- and Gaussian Speckle Fields
DEFF Research Database (Denmark)
Angelsky, Oleg V.; Maksimyak, Alexander P.; Maksimyak, Peter P.
2009-01-01
Peculiarities of the spatial behaviour of the dislocation lines resulting from scattering of coherent radiation from random and fractal rough surfaces are studied. The technique of optical correlation is proposed for diagnostics of phase singularities in a complex speckle field by comparing...... the correlation lengths of amplitude and intensity of the local fields. It is shown that the dislocation lines in the field scattered by a fractal surface have fractal properties, while the dislocation lines scattered off a random surface have no fractal properties....
Detection of random signals in dependent Gaussian noise
Gualtierotti, Antonio F
2015-01-01
The book presents the necessary mathematical basis to obtain and rigorously use likelihoods for detection problems with Gaussian noise. To facilitate comprehension the text is divided into three broad areas – reproducing kernel Hilbert spaces, Cramér-Hida representations and stochastic calculus – for which a somewhat different approach was used than in their usual stand-alone context. One main applicable result of the book involves arriving at a general solution to the canonical detection problem for active sonar in a reverberation-limited environment. Nonetheless, the general problems dealt with in the text also provide a useful framework for discussing other current research areas, such as wavelet decompositions, neural networks, and higher order spectral analysis. The structure of the book, with the exposition presenting as many details as necessary, was chosen to serve both those readers who are chiefly interested in the results and those who want to learn the material from scratch. Hence, the text...
Level sets and extrema of random processes and fields
Azais, Jean-Marc
2009-01-01
A timely and comprehensive treatment of random field theory with applications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses how to understand the properties of the level sets of paths as well as how to compute the probability distribution of its extremal values, which are two general classes of problems that arise in the study of random processes and fields and in related applications. This book provides a unified and accessible approach to these two topics and their relationship to classical theory and Gaussian processes and fields, and the most modern research findings are also discussed. The authors begin with an introduction to the basic concepts of stochastic processes, including a modern review of Gaussian fields and their classical inequalities. Subsequent chapters are devoted to Rice formulas, regularity properties, and recent results on the tails of the distribution of the maximum. Finally, applications of random fields to various areas of mathematics a...
Coupling the Gaussian free fields with free and with zero boundary conditions via common level lines
Qian, Wei; Werner, Wendelin
2017-01-01
We describe level-line decompositions of the two-dimensional Gaussian Free Field (GFF) with free boundary conditions. In particular, we point out a simple way to couple the GFF with free boundary conditions in a domain with the GFF with zero boundary conditions in the same domain: Starting from the latter, one just has to sample at random all the signs of the height gaps on its boundary touching 0-level lines (these signs are alternating for the zero-boundary GFF) in order to obtain a free bo...
Associative Hierarchical Random Fields.
Ladický, L'ubor; Russell, Chris; Kohli, Pushmeet; Torr, Philip H S
2014-06-01
This paper makes two contributions: the first is the proposal of a new model-The associative hierarchical random field (AHRF), and a novel algorithm for its optimization; the second is the application of this model to the problem of semantic segmentation. Most methods for semantic segmentation are formulated as a labeling problem for variables that might correspond to either pixels or segments such as super-pixels. It is well known that the generation of super pixel segmentations is not unique. This has motivated many researchers to use multiple super pixel segmentations for problems such as semantic segmentation or single view reconstruction. These super-pixels have not yet been combined in a principled manner, this is a difficult problem, as they may overlap, or be nested in such a way that the segmentations form a segmentation tree. Our new hierarchical random field model allows information from all of the multiple segmentations to contribute to a global energy. MAP inference in this model can be performed efficiently using powerful graph cut based move making algorithms. Our framework generalizes much of the previous work based on pixels or segments, and the resulting labelings can be viewed both as a detailed segmentation at the pixel level, or at the other extreme, as a segment selector that pieces together a solution like a jigsaw, selecting the best segments from different segmentations as pieces. We evaluate its performance on some of the most challenging data sets for object class segmentation, and show that this ability to perform inference using multiple overlapping segmentations leads to state-of-the-art results.
Light scattering by small feldspar particles simulated using the Gaussian random sphere geometry
Veihelmann, B.; Nousiainen, T.; Kahnert, M.; Zande, W.J. van der
2006-01-01
The single-scattering properties of Gaussian random spheres are calculated using the discrete dipole approximation. The ensemble of model particles is assumed to be representative for a feldspar dust sample that is characteristic for weakly absorbing irregularly shaped mineral aerosol. The morpholog
Extreme Local Extrema of Two-Dimensional Discrete Gaussian Free Field
Biskup, Marek; Louidor, Oren
2016-07-01
We consider the discrete Gaussian Free Field in a square box in {mathbb{Z}^2} of side length N with zero boundary conditions and study the joint law of its properly-centered extreme values ( h) and their scaled spatial positions ( x) in the limit as {N to infty}. Restricting attention to extreme local maxima, i.e., the extreme points that are maximal in an r N -neighborhood thereof, we prove that the associated process tends, whenever {r_N to infty} and {r_N/N to 0}, to a Poisson point process with intensity measure {Z{(dx)}e^{-α h} dh}, where {α:= 2/√{g}} with g: = 2/π and where Z(dx) is a random Borel measure on [0, 1]2. In particular, this yields an integral representation of the law of the absolute maximum, similar to that found in the context of Branching Brownian Motion. We give evidence that the random measure Z is a version of the derivative martingale associated with the continuum Gaussian Free Field.
Simulation of heterogeneous two-phase media using random fields and level sets
Institute of Scientific and Technical Information of China (English)
George STEFANOU[1,2
2015-01-01
The accurate and efficient simulation of random heterogeneous media is important in the framework of modeling and design of complex materials across multiple length scales. It is usually assumed that the morphology of a random microstructure can be described as a non-Gaussian random field that is completely defined by its multivariate distribution. A particular kind of non-Gaussian random fields with great practical importance is that of translation fields resulting from a simple memory-less transformation of an underlying Gaussian field with known second-order statistics. This paper provides a critical examination of existing random field models of heterogeneous two-phase media with emphasis on level-cut random fields which are a special case of translation fields. The case of random level sets, often used to represent the geometry of physical systems, is also examined. Two numerical examples are provided to illustrate the basic features of the different approaches.
Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory
Pato, Mauricio P.; Oshanin, Gleb
2013-03-01
We study the probability distribution function P(β)n(w) of the Schmidt-like random variable w = x21/(∑j = 1nx2j/n), where xj, (j = 1, 2, …, n), are unordered eigenvalues of a given n × n β-Gaussian random matrix, β being the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual (randomly chosen) eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n → ∞ and for arbitrary β the distribution P(β)n(w) converges to the Marčenko-Pastur form, i.e. is defined as P_{n}^{( \\beta )}(w) \\sim \\sqrt{(4 - w)/w} for w ∈ [0, 4] and equals zero outside of the support, despite the fact that formally w is defined on the interval [0, n]. Furthermore, for Gaussian unitary ensembles (β = 2) we present exact explicit expressions for P(β = 2)n(w) which are valid for arbitrary n and analyse their behaviour.
A study on the Gaussianity and stationarity of the random noise in the seismic exploration
Wang, Dongmei; Li, Yue; Nie, Pengfei
2014-10-01
Seismic exploration is an important means of the resource exploration. With the increasing of the demand for oil, gas and mineral resources, the resources which are easy to explore are reducing. At the same time, the high signal to noise ratio and the high quality seismic data is required with the continuous improvement of the accuracy of seismic exploration. The characteristics of complex noise in the seismic record are needed to be analyzed in detail in order to suppress the random noise and achieve the preserved amplitude processing as much as possible. The paper researches the Gaussianity and stationarity of the random noise in the seismic exploration of land area in China. The research areas are plain with sandstone structure. First, a theoretical model verifies the effectiveness that the Shapiro-Wilk test method is used in Gaussian statistical research, and the combination of surrogate data and time-frequency analysis tests stationarity. Then, there are 98.54% of the record channels which refuse the assumption of the Gaussian noise, and 25.6% of the record channels which don't meet the stationarity noise analysis by the above method in the research area through the statistical analysis of the seismic noise. Finally, we discuss the causes of non-Gaussianity and quasi-stationarity, and analyze the application of judging the stationarity in the denoising processing.
Tightness of the recentered maximum of the two-dimensional discrete Gaussian Free Field
Bramson, Maury
2010-01-01
We consider the maximum of the discrete two dimensional Gaussian free field (GFF) in a box, and prove that its maximum, centered at its mean, is tight, settling a long-standing conjecture. The proof combines a recent observation of Bolthausen, Deuschel and Zeitouni with elements from (Bramson 1978) and comparison theorems for Gaussian fields. An essential part of the argument is the precise evaluation, up to an error of order 1, of the expected value of the maximum of the GFF in a box. Related Gaussian fields, such as the GFF on a two-dimensional torus, are also discussed.
Supplementary Material for: Tukey g-and-h Random Fields
Xu, Ganggang
2016-01-01
We propose a new class of transGaussian random fields named Tukey g-and-h (TGH) random fields to model non-Gaussian spatial data. The proposed TGH random fields have extremely flexible marginal distributions, possibly skewed and/or heavy-tailed, and, therefore, have a wide range of applications. The special formulation of the TGH random field enables an automatic search for the most suitable transformation for the dataset of interest while estimating model parameters. Asymptotic properties of the maximum likelihood estimator and the probabilistic properties of the TGH random fields are investigated. An efficient estimation procedure, based on maximum approximated likelihood, is proposed and an extreme spatial outlier detection algorithm is formulated. Kriging and probabilistic prediction with TGH random fields are developed along with prediction confidence intervals. The predictive performance of TGH random fields is demonstrated through extensive simulation studies and an application to a dataset of total precipitation in the south east of the United States. Supplementary materials for this article are available online.
Institute of Scientific and Technical Information of China (English)
ZHAO Xinyu; GANG Tie; ZHANG Bixing
2009-01-01
A nonparaxial multi-Gaussian beam model based on the rectangular aperture is proposed in order to overcome the hmitation of paraxial Gaussian beam model which losing accuracy in off-axis beam fields. With the method, acoustical field generated by an ultra-sonic linear phased array transducer is calculated and compared with the corresponding field obtained by Rayleigh-Sommerfeld integral, paraxial multi-Gaussian beam model, and Fraunhof-fer approximation method. Simulation examples show that nonparaxial multi-Gaussian beam model is not limited by the paraxial approximation condition and can predict efficiently and accurately the acoustical field radiated by a linear phased array transducer over a wide range of steering angles.
Reconstruction of Gaussian and log-normal fields with spectral smoothness
Oppermann, Niels; Bell, Michael R; Enßlin, Torsten A
2012-01-01
We develop a method to infer log-normal random fields from measurement data affected by Gaussian noise. The log-normal model is well suited to describe strictly positive signals with fluctuations whose amplitude varies over several orders of magnitude. We use the formalism of minimum Gibbs free energy to derive an algorithm that uses the signal's correlation structure to regularize the reconstruction. The correlation structure, described by the signal's power spectrum, is thereby reconstructed from the same data set. We further introduce a prior for the power spectrum that enforces spectral smoothness. The appropriateness of this prior in different scenarios is discussed and its effects on the reconstruction's results are demonstrated. We validate the performance of our reconstruction algorithm in a series of one- and two-dimensional test cases with varying degrees of non-linearity and different noise levels.
The Limit Theorems for Maxima of Stationary Gaussian Processes with Random Index
Institute of Scientific and Technical Information of China (English)
Zhong Quan TAN
2014-01-01
Let {X(t), t ≥ 0} be a standard (zero-mean, unit-variance) stationary Gaussian process with correlation function r(·) and continuous sample paths. In this paper, we consider the maxima M (T ) = max{X (t),∀t ∈ [0, T ]} with random index TT , where TT/T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M (TT ) exists under some additional conditions related to the correlation function r(·).
Extended q-Gaussian and q-exponential distributions from gamma random variables.
Budini, Adrián A
2015-05-01
The family of q-Gaussian and q-exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q-Gaussian and q-exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q-Gaussian and modified q-exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.
New Results On the Sum of Two Generalized Gaussian Random Variables
Soury, Hamza
2015-01-01
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based on this results, the probability density function (PDF) and the cumulative distribution function (CDF) of the sum distribution are obtained. These functions are expressed in terms of the bivariate Fox H function. Next, the statistics of the distribution of the sum, such as the moments, the cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of bivariate Fox H function, a solution to reduce such complexity is to approximate the sum of two independent GG random variables by one GG random variable with suitable shape factor. The approximation method depends on the utility of the system so three methods of estimate the shape factor are studied and presented.
New Results on the Sum of Two Generalized Gaussian Random Variables
Soury, Hamza
2016-01-06
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based on this results, the probability density function (PDF) and the cumulative distribution function (CDF) of the sum distribution are obtained. These functions are expressed in terms of the bivariate Fox H function. Next, the statistics of the distribution of the sum, such as the moments, the cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of bivariate Fox H function, a solution to reduce such complexity is to approximate the sum of two independent GG random variables by one GG random variable with suitable shape factor. The approximation method depends on the utility of the system so three methods of estimate the shape factor are studied and presented [1].
Markov Random Field Surface Reconstruction
DEFF Research Database (Denmark)
Paulsen, Rasmus Reinhold; Bærentzen, Jakob Andreas; Larsen, Rasmus
2010-01-01
) and knowledge about data (the observation model) in an orthogonal fashion. Local models that account for both scene-specific knowledge and physical properties of the scanning device are described. Furthermore, how the optimal distance field can be computed is demonstrated using conjugate gradients, sparse......A method for implicit surface reconstruction is proposed. The novelty in this paper is the adaption of Markov Random Field regularization of a distance field. The Markov Random Field formulation allows us to integrate both knowledge about the type of surface we wish to reconstruct (the prior...
Subquantum nonlocal correlations induced by the background random field
Khrennikov, Andrei
2011-10-01
We developed a purely field model of microphenomena—prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of quantum mechanics (QM) including correlations for entangled systems, but also gives a possibility to go beyond QM, i.e. to make predictions of phenomena that could be observed at the subquantum level. In this paper, we discuss one such prediction—the existence of nonlocal correlations between prequantum random fields corresponding to all quantum systems. (And by PCSFT, quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are 'entangled', but in the sense of classical signal theory. On the one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology—for Gaussian random fields with covariance operators corresponding to factorizable quantum states).
Institute of Scientific and Technical Information of China (English)
ZHANG Dong; GONG Xiu-Fen; LU Rong-Rong
2000-01-01
The superposition method of Gaussian beams is extended to describe the acoustical parametric field from a focusing source. The axial sound pressure of the difference frequency wave 1MHz generated due to the interaction of two primary wave 3.5 and 4.5MHz is theoretically calculated by using 10 items of Gaussian functions. Experimental results coincide well with the calculated results except for the case at the vicinity of the focusing source.
Representation of nonlinear random transformations by non-gaussian stochastic neural networks.
Turchetti, Claudio; Crippa, Paolo; Pirani, Massimiliano; Biagetti, Giorgio
2008-06-01
The learning capability of neural networks is equivalent to modeling physical events that occur in the real environment. Several early works have demonstrated that neural networks belonging to some classes are universal approximators of input-output deterministic functions. Recent works extend the ability of neural networks in approximating random functions using a class of networks named stochastic neural networks (SNN). In the language of system theory, the approximation of both deterministic and stochastic functions falls within the identification of nonlinear no-memory systems. However, all the results presented so far are restricted to the case of Gaussian stochastic processes (SPs) only, or to linear transformations that guarantee this property. This paper aims at investigating the ability of stochastic neural networks to approximate nonlinear input-output random transformations, thus widening the range of applicability of these networks to nonlinear systems with memory. In particular, this study shows that networks belonging to a class named non-Gaussian stochastic approximate identity neural networks (SAINNs) are capable of approximating the solutions of large classes of nonlinear random ordinary differential transformations. The effectiveness of this approach is demonstrated and discussed by some application examples.
Primordial non-Gaussianity in the Bispectrum of the Halo Density Field
Baldauf, Tobias; Senatore, Leonardo
2010-01-01
The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and their dependence on scale, shape and the non-Gaussianity parameter fNL. We compute the terms based on a multivariate bias expansion and the peak-background split method and show that non-Gaussian modifications to the bias parameters lead to amplifications of the tree level bispectrum that were ignored in previous studies. Our results are in a good agreement with published simulation measurements of the halo bispectrum. ...
Random Fields and Spin Glasses
De Dominicis, Cirano; Giardina, Irene
2010-06-01
1. A brief introduction; 2. The Random Field Ising model; 3. The dynamical approach; 4. The p=2 spherical model; 5. Mean field spin glasses: one-step RSB; 6. The Sherrington-Kirkpatrick model; 7. Mean field via TAP equations; 8. Spin glass above D=6; 9. Propagators, mostly replicon; 10. Ward-Takahashi identities and Goldstone modes; 11. Alternative approaches and conclusions; Appendices; Index.
Contribution of longitudinal electric field of a gaussian beam to second harmonic generation
Mishra, S. R.; Rustagi, K. C.
1990-01-01
A laser beam with a nonuniform transverse intensity profile necessarily has a longitudinal component of the electric field. We show that a detectable second harmonic can be generated due to coupling of this longitudinal component with the transverse field of a gaussian beam in a configuration in which second harmonic generation is forbidden for plane wave interaction.
Propagation of multi-Gaussian Schell-model vortex beams in isotropic random media.
Tang, Miaomiao; Zhao, Daomu
2015-12-14
The effect of isotropic and homogeneous random media on propagation characteristics of recently introduced multi-Gaussian Schell-model (MGSM) vortex beams is investigated. The analytical formula for the cross-spectral density function of such a beam propagating in random turbulent media is derived and used to explore the evolution of the spectral density, the degree of coherence and the turbulence-induced spreading. An example illustrates the fact that, at sufficiently large distance from the source, the source correlations modulation of the spectral distribution in free space is shown to be suppressed by the uniformly correlated turbulence. The impacts, arising from the index M, the correlation width of the source and the properties of the medium on such characteristics are analyzed in depth.
Critical behavior of the Gaussian model on fractal lattices in external magnetic field
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution constant and the external magnetic field of site i in this model depend on the coordination number qi of site i, and that the relation bqi/bqj=qi/qj holds among bqi's, where bqi is the Gaussian type distribution constant of site i. Using the decimation real-space renormalization group following the spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves and a family of the diamond-type hierarchical (or DH) lattices. At the critical points, it is found that the nearest-neighbor interaction and the magnetic field of site i can be expressed in the form K*=bqi/qi and h*qi=0, respectively. It is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices, and if the fractal dimensionality df=4, the Gaussian model and the mean field theories give the same results.
Ostrovsky, Dmitry
2016-09-01
A new family of Barnes beta distributions on (0, ∞) is introduced and its infinite divisibility, moment determinacy, scaling, and factorization properties are established. The Morris integral probability distribution is constructed from Barnes beta distributions of types (1, 0) and (2, 2), and its moment determinacy and involution invariance properties are established. For application, the maximum distributions of the 2D gaussian free field on the unit interval and circle with a non-random logarithmic potential are conjecturally related to the critical Selberg and Morris integral probability distributions, respectively, and expressed in terms of sums of Barnes beta distributions of types (1, 0) and (2, 2).
A Gaussian Model for Simulated Geomagnetic Field Reversals
Wicht, Johannes
2015-01-01
Field reversals are the most spectacular changes in the geomagnetic field but remain little understood. Paleomagnetic data primarily constrain the reversal rate and provide few additional clues. Reversals and excursions are characterized by a low in dipole moment that can last for some 10kyr. Some paleomagnetic records also suggest that the field decreases much slower before an reversals than it recovers afterwards and that the recovery phase may show an overshoot in field intensity. Here we study the dipole moment variations in several extremely long dynamo simulation to statistically explored the reversal and excursion properties. The numerical reversals are characterized by a switch from a high axial dipole moment state to a low axial dipole moment state. When analysing the respective transitions we find that decay and growth have very similar time scales and that there is no overshoot. Other properties are generally similar to paleomagnetic findings. The dipole moment has to decrease to about 30% of its m...
Independent constraints on local non-Gaussianity from the peculiar velocity and density fields
Ma, Yin-Zhe; Scott, Douglas
2013-01-01
Primordial, non-Gaussian perturbations can generate scale-dependent bias in the galaxy distribution. This in turn will modify correlations between galaxy positions and peculiar velocities at late times, since peculiar velocities reflect the underlying matter distribution, whereas galaxies are a biased tracer of the same. We study this effect, and show that non-Gaussianity can be constrained by comparing the observed peculiar velocity field to a model velocity field reconstructed from the galaxy density field assuming linear bias. The amplitude of the spatial correlations in the residual map obtained after subtracting one velocity field from the other is directly proportional to the strength of the primordial non-Gaussianity. We construct the corresponding likelihood function use it to constrain the amplitude of the linear flow $\\beta$ and the amplitude of local non-Gaussianity $f^{NL}_{local}$. Applying our method to two observational data sets, the Type-Ia supernovae (A1SN) and Spiral Field \\textit{I}-band (...
Think continuous: Markovian Gaussian models in spatial statistics
Simpson, Daniel; Rue, Håvard
2011-01-01
Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRFs with the more traditional Gaussian random field models as the Markov property is difficult to deploy in continuous space. Following the pioneering work of Lindgren et al. (2011), we expound on the link between Markovian Gaussian random fields and GMRFs. In particular, we discuss the theoretical and practical aspects of fast computation with continuously specified Markovian Gaussian random fields, as well as the clear advantages they offer in terms of clear, parsimonious and interpretable models of anisotropy and non-stationarity.
A Gaussian-product stochastic Gent-McWilliams parameterization
Grooms, Ian
2016-10-01
The locally-averaged horizontal buoyancy flux by mesoscale eddies is computed from eddy-resolving quasigeostrophic simulations of ocean-mesoscale eddy dynamics. This flux has a very non-Gaussian distribution peaked at zero, not at the mean value. This non-Gaussian flux distribution arises because the flux is a product of zero-mean random variables: the eddy velocity and buoyancy. A framework for stochastic Gent-McWilliams (GM) parameterization is presented. Gaussian random field models for subgrid-scale velocity and buoyancy are developed. The product of these Gaussian random fields is used to construct a non-Gaussian stochastic parameterization of the horizontal subgrid-scale density flux, which leads to a non-Gaussian stochastic GM parameterization. This new non-Gaussian stochastic GM parameterization is tested in an idealized box ocean model, and compared to a Gaussian approach that simply multiplies the deterministic GM parameterization by a Gaussian random field. The non-Gaussian approach has a significant impact on both the mean and variability of the simulations, more so than the Gaussian approach; for example, the non-Gaussian simulation has a much larger net kinetic energy and a stronger overturning circulation than a comparable Gaussian simulation. Future directions for development of the stochastic GM parameterization and extensions of the Gaussian-product approach are discussed.
Anomalous spectral behaviour of diffracted chirped Gaussian pulses in the near field
Institute of Scientific and Technical Information of China (English)
Pan Liu-Zhan; L(u) Bai-Da
2004-01-01
By using the Fourier transform method, analytical expressions for the axial power spectrum and near-field intensity in the spacetime domain of chirped Gaussian pulses diffracted at an aperture are derived, which permit us to study changes in spectral and temporal profiles of the chirped Gaussian pulses both analytically and numerically. Detailed numerical results and physical analysis show that spectral anomalies take place in the neighbourhood of certain critical distances, and the shifting of maximum and splitting of temporal intensity profiles appear. In particular, for ultrashort chirped pulses, there exists also spectral switch. Besides the truncation parameter, the chirp parameter and pulse duration affect the behaviour of spectral switches.
On the non-Gaussian correlation of the primordial curvature perturbation with vector fields
DEFF Research Database (Denmark)
Kumar Jain, Rajeev; Sloth, Martin Snoager
2013-01-01
We compute the three-point cross-correlation function of the primordial curvature perturbation generated during inflation with two powers of a vector field in a model where conformal invariance is broken by a direct coupling of the vector field with the inflaton. If the vector field is identified...... with the electromagnetic field, this correlation would be a non-Gaussian signature of primordial magnetic fields generated during inflation. We find that the signal is maximized for the flattened configuration where the wave number of the curvature perturbation is twice that of the vector field and in this limit...
Anisotropic Non-Gaussianity from a Two-Form Field
Ohashi, Junko; Tsujikawa, Shinji
2013-01-01
We study an inflationary scenario with a two-form field to which an inflaton couples non-trivially. First, we show that anisotropic inflation can be realized as an attractor solution and that the two-form hair remains during inflation. A statistical anisotropy can be developed because of a cumulative anisotropic interaction induced by the background two-form field. The power spectrum of curvature perturbations has a prolate-type anisotropy, in contrast to the vector models having an oblate-type anisotropy. We also evaluate the bispectrum and trispectrum of curvature perturbations by employing the in-in formalism based on the interacting Hamiltonians. We find that the non-linear estimators $f_{NL}$ and $\\tau_{NL}$ are correlated with the amplitude $g_*$ of the statistical anisotropy in the power spectrum. Unlike the vector models, both $f_{NL}$ and $\\tau_{NL}$ vanish in the squeezed limit. However, the estimator $f_{NL}$ can reach the order of 10 in the equilateral and enfolded limits. These results are consis...
High-dimensional Gaussian fields with isotropic increments seen through spin glasses
Klimovsky, Anton
2011-01-01
We study the free energy of a particle in (arbitrary) high-dimensional Gaussian random potentials with isotropic increments. We prove a computable saddle-point variational representation in terms of a Parisi-type functional for the free energy in the infinite-dimensional limit. The proofs are based on the techniques developed in the course of the rigorous analysis of the Sherrington-Kirkpatrick model with vector spins.
Mie scattering of Laguerre-Gaussian beams: photonic nanojets and near-field optical vortices
Kiselev, Alexei D
2014-01-01
We study Mie scattering of Laguerre-Gaussian (LG) light beams remodelled using the method of far-field matching. The theoretical results are used to analyze the optical field in the near-field region for purely azimuthal LG beams characterized by a nonzero azimuthal mode number $m_{LG}$. The mode number $m_{LG}$ is found to have a profound effect on the morphology of photonic nanojets and the near-field structure of optical vortices associated with the components of the electric field.
Liouville field theory and log-correlated Random Energy Models
Cao, Xiangyu; Rosso, Alberto; Santachiara, Raoul
2016-01-01
An exact mapping is established between the $c\\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry breaking methods. Operator product expansions in LFT allow to unveil novel universal behaviours of the log-correlated Random Energy class. High precision numerical tests are given.
Institute of Scientific and Technical Information of China (English)
LIN ZhenQuan; KONG XiangMu; JIN JinShuang; YANG ZhanRu
2001-01-01
The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences. The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction bonds. The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method. The critical points and all the critical exponents are obtained. The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices. When all the Gaussian distribution constants are the same, the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.
Critical behavior of the Gaussian model on fractal lattices in external magnetic field
Institute of Scientific and Technical Information of China (English)
孔祥木; 林振权; 朱建阳
2000-01-01
For inhomogeneous lattices we generalize the classical Gaussian model, i. e. it is pro-posed that the Gaussian type distribution constant and the external magnetic field of site / in this model depend on the coordination number q, of site i, and that the relation bq1/bq1 = q1/q1 holds among bq1s, where bq1 is the Gaussian type distribution constant of site /. Using the decimation real-spacerenormalization group following the spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves and a family of the diamond-type hierar-chical (or DH) lattices. At the critical points, it is found that the nearest-neighbor interaction and the magnetic field of site i can be expressed in the form K’ = bq1/q1 and hq =0, respectively. it is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices,
Institute of Scientific and Technical Information of China (English)
Li Lian-Huang; Guo Fu-Yuan
2009-01-01
This paper analyzes the characteristic of matching efficiency between the fundamental mode of two kinds of optical waveguides and its Gaussian approximate field.Then, it presents a new method where the mode-field half-width of Gaussian approximation for the fundamental mode should be defined according to the maximal matching efficiency method. The relationship between the mode-field half-width of the Gaussian approximate field obtained from the maximal matching efficiency and normalized frequency is studied; furthermore, two formulas of mode-field half-widths as a function of normalized frequency are proposed.
On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables
Al-Naffouri, Tareq Y.
2015-10-30
© 2015 IEEE. In this work, we propose a unified approach to evaluating the CDF and PDF of indefinite quadratic forms in Gaussian random variables. Such a quantity appears in many applications in communications, signal processing, information theory, and adaptive filtering. For example, this quantity appears in the mean-square-error (MSE) analysis of the normalized least-meansquare (NLMS) adaptive algorithm, and SINR associated with each beam in beam forming applications. The trick of the proposed approach is to replace inequalities that appear in the CDF calculation with unit step functions and to use complex integral representation of the the unit step function. Complex integration allows us then to evaluate the CDF in closed form for the zero mean case and as a single dimensional integral for the non-zero mean case. Utilizing the saddle point technique allows us to closely approximate such integrals in non zero mean case. We demonstrate how our approach can be extended to other scenarios such as the joint distribution of quadratic forms and ratios of such forms, and to characterize quadratic forms in isotropic distributed random variables.We also evaluate the outage probability in multiuser beamforming using our approach to provide an application of indefinite forms in communications.
Non-Gaussianity in single field models without slow-roll
Noller, Johannes
2011-01-01
We investigate non-Gaussianity in general single field models without assuming slow-roll conditions or the exact scale-invariance of the scalar power spectrum. The models considered include general single field inflation (e.g. DBI and canonical inflation) as well as bimetric models. We compute the full non-Gaussian amplitude, its size fnl, its shape, and the running with scale n_{NG}. In doing so we show that observational constraints allow significant violations of slow roll conditions and we derive explicit bounds on slow-roll parameters for fast-roll single field scenarios. A variety of new observational signatures is found for models respecting these bounds. We also explicitly construct concrete model implementations giving rise to this new phenomenology.
Destruction of first-order phase transition in a random-field Ising model
Energy Technology Data Exchange (ETDEWEB)
Crokidakis, Nuno; Nobre, Fernando D [Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro-RJ (Brazil)], E-mail: nuno@if.uff.br, E-mail: fdnobre@cbpf.br
2008-04-09
The phase transitions that occur in an infinite-range-interaction Ising ferromagnet in the presence of a double Gaussian random magnetic field are analyzed. Such random fields are defined as a superposition of two Gaussian distributions, presenting the same width {sigma}. It is argued that this distribution is more appropriate for a theoretical description of real systems than other simpler cases, i.e. the bimodal ({sigma} = 0) and single Gaussian distributions. It is shown that a low-temperature first-order phase transition may be destroyed for increasing values of {sigma}, similarly to what happens in the compound Fe{sub x}Mg{sub 1-x}Cl{sub 2}, whose finite-temperature first-order phase transition is presumably destroyed by an increase in the field randomness.
Reduced Wiener Chaos representation of random fields via basis adaptation and projection
Energy Technology Data Exchange (ETDEWEB)
Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu [Department of Mathematics, University of Southern California, Los Angeles, CA 90089 (United States); Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089 (United States); Ghanem, Roger G., E-mail: ghanem@usc.edu [Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089 (United States)
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.
Non-gaussianity at tree- and one-loop levels from vector field perturbations
Valenzuela-Toledo, Cesar A; Lyth, David H
2009-01-01
We study the spectrum P_\\zeta and bispectrum B_\\zeta of the primordial curvature perturbation \\zeta when the latter is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree level terms (both (either) in P_\\zeta and (or) in B_\\zeta) and viceversa. The level of non-gaussianity in the bispectrum, f_{NL}, is calculated and related to the level of statistical anisotropy in the power spectrum, g_\\zeta. For very small amounts of statistical anisotropy in the power spectrum, the level of non-gaussianity may be very high, in some cases exceeding the current observational limit.
Variational Infinite Hidden Conditional Random Fields
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja; Ghahramani, Zoubin
2015-01-01
Hidden conditional random fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An Infinite hidden conditional random field is a hidden conditional random field with a countably infinite number of
Zhai, Wangjian
2014-12-01
Electric-field-induced second-harmonic generation in asymmetrical Gaussian potential quantum wells is investigated using the effective mass approximation employing the compact density matrix method and the iterative approach. Our results show that the absolute value, the real part and the imaginary part of second-harmonic generation are greatly affected by the height of the Gaussian potential quantum wells, the range of the Gaussian confinement potential and the applied electric field. The relationship between the absolute value and the imaginary part of second-harmonic generation together with the relationship between the absolute value and the real part of second-harmonic generation is studied. It is found that no matter how the height of the Gaussian potential quantum wells, the range of the Gaussian confinement potential and the applied electric field vary, the resonant peaks of the absolute value of second-harmonic generation do not originate from the imaginary part but from the real part.
Perturbative Expansion around the Gaussian Effective Potential of the Fermion Field Theory
Lee, G H; Yee, J H; Lee, Geon Hyoung; Lee, Tack Hwi; Yee, Jae Hyung
1998-01-01
We have extended the perturbative expansion method around the Gaussian effective action to the fermionic field theory, by taking the 2-dimensional Gross-Neveu model as an example. We have computed both the zero temperature and the finite temperature effective potentials of the Gross-Neveu model up to the first perturbative correction terms, and have found that the critical temperature, at which dynamically broken symmetry is restored, is significantly improved for small value of the flavour number.
Full extremal process, cluster law and freezing for two-dimensional discrete Gaussian Free Field
Biskup, Marek; Louidor, Oren
2016-01-01
We study the extremal process associated with the Discrete Gaussian Free Field (DGFF) in scaled-up (square-)lattice versions of bounded open planar domains subject to mild regularity conditions on the boundary. We prove that, in the scaling limit, this process tends to a Cox process decorated by independent, correlated clusters whose distribution is completely characterized. As an application, we control the scaling limit of the discrete supercritical Liouville measure, extract a Poisson-Diri...
Temperature and field dependence of the mobility in 1D for a Gaussian density of states
Pasveer, W. F.; Bobbert, P. A.; Michels, M. A. J.
2004-01-01
The temperature and field-dependent mobility of a charge carrier in a gaussian density of states has been analyzed, based on a numerically exact solution of the Master equation. In this way we get a microscopic insight into the origin of the mobility and find some new features pointing to relevance of the Fermi level and of variable-range hopping to sites further away than nearest ones.
Extremes of random fields over arbitrary domains with application to concrete rupture stresses
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2004-01-01
To find the exact probability distribution of the global maximum or minimum of a random field within a bounded domain is a pending problem even for Gaussian fields. Except for very special examples of fields, recourse must be taken to approximate reasoning or asymptotic considerations to be judged....... In this paper, the distribution function is obtained in general for Gaussian fields over arbitrary bounded domains with piecewise continuous and differentiable boundaries, and as in earlier works the distribution function is tested against empirical distribution functions obtained by simulation of sample...
Llopis-Albert, Carlos; Capilla, José E.
2009-06-01
SummaryIn the first paper of this series a methodology for the generation of non-Gaussian transmissivity fields conditional to flow, mass transport and secondary data was presented. This methodology, referred to as the gradual conditioning (GC) method, constitutes a new and advanced powerful approach in the field of stochastic inverse modelling. It is based on gradually changing an initial transmissivity ( T) field, conditioned only to T and secondary data, to honour flow and transport measured data. The process is based on combining the initial T field with other seed T fields in successive iterations maintaining the stochastic structure of T, previously inferred from data. The iterative procedure involves the minimization of a penalty function which depends on one parameter, and is made up by the weighted summation of the square deviations among flow and/or transport variables, and the corresponding known measurements. The GC method leads gradually to a final simulated field, uniformly converging to a better reproduction of conditioning data as more iterations are performed. The methodology is now demonstrated on a synthetic aquifer in a non-multi-Gaussian stochastic framework. First, an initial T field is simulated, and retained as reference T field. With prescribed head boundary conditions, transient flow created by an abstraction well and a mass solute plume migrating through the formation, a long-term and large scale hypothetical tracer experiment is run in this reference synthetic aquifer. Then T, piezometric head ( h), solute concentration ( c) and travel time ( τ) are sampled at a limited number of points, and for different time steps where applicable. Using this limited amount of information the GC method is applied, conditioning to different sets of these sampled data and model results are compared to those from the reference synthetic aquifer. Results demonstrate the ability and robustness of the GC method to include different types of data without
Mean-field dynamic criticality and geometric transition in the Gaussian core model
Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa
2016-04-01
We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.
On the non-Gaussian correlation of the primordial curvature perturbation with vector fields
Jain, Rajeev Kumar
2012-01-01
We compute the three-point cross-correlation function of the primordial curvature perturbation generated during inflation with two powers of a vector field in a model where conformal invariance is broken by a direct coupling of the vector field with the inflaton. If the vector field is identified with the electromagnetic field, this correlation would be a non-Gaussian signature of primordial magnetic fields generated during inflation. We find that the signal is maximized for the flattened configuration where the wave number of the curvature perturbation is twice that of the vector field and in this limit, the magnetic non-linear parameter becomes as large as |b_{NL}| ~ 10^3. In the squeezed limit where the wave number of the curvature perturbation vanishes, our results agree with the magnetic consistency relation derived in arXiv:1207.4187.
On the non-Gaussian correlation of the primordial curvature perturbation with vector fields
Energy Technology Data Exchange (ETDEWEB)
Jain, Rajeev Kumar [Département de Physique Théorique and Center for Astroparticle Physics, Université de Genève, 24, Quai E. Ansermet, CH-1211 Genève 4 (Switzerland); Sloth, Martin S., E-mail: rajeev.jain@unige.ch, E-mail: sloth@cp3.dias.sdu.dk [CP3-Origins, Centre for Cosmology and Particle Physics Phenomenology, University of Southern Denmark, Campusvej 55, 5230 Odense M (Denmark)
2013-02-01
We compute the three-point cross-correlation function of the primordial curvature perturbation generated during inflation with two powers of a vector field in a model where conformal invariance is broken by a direct coupling of the vector field with the inflaton. If the vector field is identified with the electromagnetic field, this correlation would be a non-Gaussian signature of primordial magnetic fields generated during inflation. We find that the signal is maximized for the flattened configuration where the wave number of the curvature perturbation is twice that of the vector field and in this limit, the magnetic non-linear parameter becomes as large as |b{sub NL}| ∼ O(10{sup 3}). In the squeezed limit where the wave number of the curvature perturbation vanishes, our results agree with the magnetic consistency relation derived in arXiv:1207.4187.
Application of Gaussian moment method to a gene autoregulation model of rational vector field
Kang, Yan-Mei; Chen, Xi
2016-07-01
We take a lambda expression autoregulation model driven by multiplicative and additive noises as example to extend the Gaussian moment method from nonlinear stochastic systems of polynomial vector field to noisy biochemical systems of rational polynomial vector field. As a direct application of the extended method, we also disclose the phenomenon of stochastic resonance. It is found that the transcription rate can inhibit the stochastic resonant effect, but the degradation rate may enhance the phenomenon. These observations should be helpful in understanding the functional role of noise in gene autoregulation.
Yuan, Jian-Hui; Chen, Ni; Mo, Hua; Zhang, Yan; Zhang, Zhi-Hai
2015-12-01
A detailed investigation of the second harmonic generation in symmetrical and asymmetrical Gaussian potential quantum wells under the influence of applied electric field by using the compact-density-matrix approach and the finite difference method. The results show that the second-harmonic generation susceptibility obtained in two cases can reach the magnitude of 10-4 m/V, which depend dramatically on the applied electric field and the structural parameters. Finally, the resonant peak and its corresponding to the resonant energy are also taken into account.
Numeric Solutions of Dirac-Gursey Spinor Field Equation Under External Gaussian White Noise
Aydogmus, Fatma
2016-06-01
In this paper, we consider the Dirac-Gursey spinor field equation that has particle-like solutions derived classical field equations so-called instantons, formed by using Heisenberg ansatz, under the effect of an additional Gaussian white noise term. Our purpose is to understand how the behavior of spinor-type excited instantons in four dimensions can be affected by noise. Thus, we simulate the phase portraits and Poincaré sections of the obtained system numerically both with and without noise. Recurrence plots are also given for more detailed information regarding the system.
A Single Field Inflation Model with Large Local Non-Gaussianity
Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao
2013-01-01
A detection of large local form non-Gaussianity is considered to be able to rule out all single field inflation models. This statement is based on a single field consistency condition. Despite the awareness of some implicit assumptions in the derivation of this condition and the demonstration of corresponding examples that illustrate these caveats, to date there is still no explicit and self-consistent model which can serve as a counterexample to this statement. We present such a model in this Letter.
Glück, Ferenc
2016-01-01
It is a widely held view that analytical integration is more accurate than the numerical one. In some special cases, however, numerical integration can be more advantageous than analytical integration. In our paper we show this benefit for the case of electric potential and field computation of charged triangles and rectangles applied in the boundary element method (BEM). Analytical potential and field formulas are rather complicated (even in the simplest case of constant charge densities), they have usually large computation times, and at field points far from the elements they suffer from large rounding errors. On the other hand, Gaussian cubature, which is an efficient numerical integration method, yields simple and fast potential and field formulas that are very accurate far from the elements. The simplicity of the method is demonstrated by the physical picture: the triangles and rectangles with their continuous charge distributions are replaced by discrete point charges, whose simple potential and field ...
Efficient robust conditional random fields.
Song, Dongjin; Liu, Wei; Zhou, Tianyi; Tao, Dacheng; Meyer, David A
2015-10-01
Conditional random fields (CRFs) are a flexible yet powerful probabilistic approach and have shown advantages for popular applications in various areas, including text analysis, bioinformatics, and computer vision. Traditional CRF models, however, are incapable of selecting relevant features as well as suppressing noise from noisy original features. Moreover, conventional optimization methods often converge slowly in solving the training procedure of CRFs, and will degrade significantly for tasks with a large number of samples and features. In this paper, we propose robust CRFs (RCRFs) to simultaneously select relevant features. An optimal gradient method (OGM) is further designed to train RCRFs efficiently. Specifically, the proposed RCRFs employ the l1 norm of the model parameters to regularize the objective used by traditional CRFs, therefore enabling discovery of the relevant unary features and pairwise features of CRFs. In each iteration of OGM, the gradient direction is determined jointly by the current gradient together with the historical gradients, and the Lipschitz constant is leveraged to specify the proper step size. We show that an OGM can tackle the RCRF model training very efficiently, achieving the optimal convergence rate [Formula: see text] (where k is the number of iterations). This convergence rate is theoretically superior to the convergence rate O(1/k) of previous first-order optimization methods. Extensive experiments performed on three practical image segmentation tasks demonstrate the efficacy of OGM in training our proposed RCRFs.
Non-Gaussianity in two-field inflation beyond the slow-roll approximation
Jung, Gabriel
2016-01-01
We use the long-wavelength formalism to investigate the level of bispectral non-Gaussianity produced in two-field inflation models with standard kinetic terms. Even though the Planck satellite has so far not detected any primordial non-Gaussianity, it has tightened the constraints significantly, and it is important to better understand what regions of inflation model space have been ruled out, as well as prepare for the next generation of experiments that might reach the important milestone of Delta f_NL(local) = 1. We derive an alternative formulation of the previously derived integral expression for f_NL, which makes it easier to physically interpret the result and see which types of potentials can produce large non-Gaussianity. We apply this to the case of a sum potential and show that it is very difficult to satisfy simultaneously the conditions for a large f_NL and the observational constraints on the spectral index n_s. In the case of the sum of two monomial potentials and a constant we explicitly show ...
Shiraishi, Maresuke
2013-01-01
Primordial magnetic fields (PMFs) create a large squeezed-type non-Gaussianity in tensor perturbation, which generates non-Gaussian temperature fluctuations in the cosmic microwave background (CMB). We for the first time derive an observational constraint on such tensor non-Gaussianity from observed CMB maps. Analyzing temperature maps of the WMAP 7-year data, we find such tensor non-Gaussianity is consistent with zero. This gives an upper bound on PMF strength smoothed on $1 ~ {\\rm Mpc}$ as $B_{1 ~ \\rm Mpc} < 3.2 {\\rm nG}$ at 95% CL. We discuss some difficulties in constraining tensor non-Gaussianity due to spin and angle dependence of resultant CMB bispectrum.
Structural polarization properties of vector Gaussian beam in the far field
Institute of Scientific and Technical Information of China (English)
Zhou Guo-Quan; Ni Yong-Zhou; Chu Xiu-Xiang
2007-01-01
Based on the vector angular spectrum representation of optical beam and the method of stationary phase, the analytical TE and TM terms of vector Gaussian beam have been presented in the far field. By using the local polarization matrix, the polarization properties of the TE and TM terms in the far field are investigated, and it is found that the degree of their polarization is only determined by the spatial location. When the source is completely polarized, the TE and TM terms are both completely polarized in the far field. When the source is completely unpolarized, the TE and TM terms in the far field are partially polarized. The whole beam is also partially polarized except on the propagating axis. Moreover, the degrees of polarization of TE and TM terms are both larger than that of the whole beam.
The bispectrum covariance beyond Gaussianity: A log-normal approach
Martin, Sandra; Simon, Patrick
2011-01-01
To investigate and specify the statistical properties of cosmological fields with particular attention to possible non-Gaussian features, accurate formulae for the bispectrum and the bispectrum covariance are required. The bispectrum is the lowest-order statistic providing an estimate for non-Gaussianities of a distribution, and the bispectrum covariance depicts the errors of the bispectrum measurement and their correlation on different scales. Currently, there do exist fitting formulae for the bispectrum and an analytical expression for the bispectrum covariance, but the former is not very accurate and the latter contains several intricate terms and only one of them can be readily evaluated from the power spectrum of the studied field. Neglecting all higher-order terms results in the Gaussian approximation of the bispectrum covariance. We study the range of validity of this Gaussian approximation for two-dimensional non-Gaussian random fields. For this purpose, we simulate Gaussian and non-Gaussian random fi...
On intermediate level sets of two-dimensional discrete Gaussian Free Field
Biskup, Marek; Louidor, Oren
2016-01-01
We consider the discrete Gaussian Free Field (DGFF) in scaled-up (square-lattice) versions of suitably regular continuum domains $D\\subset\\mathbb C$ and describe the scaling limit, including local structure, of the level sets at heights growing as a $\\lambda$-multiple of the height of the absolute maximum, for any $\\lambda\\in(0,1)$. We prove that, in the scaling limit, the scaled spatial position of a typical point $x$ sampled from this level set is distributed according to a Liouville Quantu...
Critical Behavior of Gaussian Model on X Fractal Lattices in External Magnetic Fields
Institute of Scientific and Technical Information of China (English)
LI Ying; KONG Xiang-Mu; HUANG Jia-Yin
2003-01-01
Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and d-dimensional (d ＞ 2) Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality d (or the fractal dimensionality dr). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.
Institute of Scientific and Technical Information of China (English)
KANG Xiao-Ping; L(U) Bai-Da
2006-01-01
@@ The analytical expression characterizing the propagation of nonparaxial truncated cosine-Gaussian (CoG) beams in free space is derived, and some special cases are discussed. The extended power in the bucket (PIB) is proposed to characterize the beam quality of nonparaxial truncated beams in the far field. It is shown that the extended PIB is applicable to nonparaxial truncated beams, and the PIB of nonparaxial truncated CoG beams depends on the decentred parameter, waist-width-to-wavelength ratio, truncation parameter, and bucket size chosen.
Adaptive integral method with fast Gaussian gridding for solving combined field integral equations
Bakır, O.; Baǧ; Cı, H.; Michielssen, E.
Fast Gaussian gridding (FGG), a recently proposed nonuniform fast Fourier transform algorithm, is used to reduce the memory requirements of the adaptive integral method (AIM) for accelerating the method of moments-based solution of combined field integral equations pertinent to the analysis of scattering from three-dimensional perfect electrically conducting surfaces. Numerical results that demonstrate the efficiency and accuracy of the AIM-FGG hybrid in comparison to an AIM-accelerated solver, which uses moment matching to project surface sources onto an auxiliary grid, are presented.
Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free field
Ding, Jian
2011-01-01
We study the tail behavior for the maximum of discrete Gaussian free field on a 2D box with Dirichlet boundary condition after centering by its expectation. We show that it exhibits an exponential decay for the right tail and a double exponential decay for the left tail. In particular, our result implies that the variance of the maximum is of order 1, improving an $o(\\log n)$ bound by Chatterjee (2008) and confirming a folklore conjecture. An important ingredient for our proof is a result of Bramson and Zeitouni (2010), who proved the tightness of the centered maximum together with an evaluation of the expectation up to an additive constant.
Fyodorov, Yan V.; Le Doussal, Pierre; Rosso, Alberto
2009-10-01
We compute the distribution of the partition functions for a class of one-dimensional random energy models with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences represent various versions of the 1/f noise generated by sampling the two-dimensional Gaussian free field (2D GFF) along various planar curves. Our method extends the recent analysis of Fyodorov and Bouchaud (2008 J. Phys. A: Math. Theor. 41 372001) from the circular case to an interval and is based on an analytical continuation of the Selberg integral. In particular, we unveil a duality relation satisfied by the suitable generating function of free energy cumulants in the high temperature phase. It reinforces the freezing scenario hypothesis for that generating function, from which we derive the distribution of extrema for the 2D GFF on the [0,1] interval. We provide numerical checks of the circular case and the interval case and discuss universality and various extensions. The relevance to the distribution of the length of a segment in Liouville quantum gravity is noted.
Primordial non-Gaussianities of gravitational waves in the most general single-field inflation model
Gao, Xian; Yamaguchi, Masahide; Yokoyama, Jun'ichi
2011-01-01
We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in generalized G-inflation, i.e., the most general single-field inflation model with second order field equations. It is shown that the most general cubic action for the tensor perturbation (gravitational wave) $h_{ij}$ is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each $h_{ij}$. The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct gravitational wave detection experiments.
Energy Technology Data Exchange (ETDEWEB)
Očenášek, Jan, E-mail: ocenasek@ntc.zcu.cz; Voldřich, Josef [New Technologies Research Centre, University of West Bohemia in Pilsen, Plzeň 30614 (Czech Republic)
2015-12-21
Raman spectroscopy is a widely applied analytical technique with numerous applications that is based on inelastic scattering of monochromatic light, which is typically provided by a laser. Irradiation of a sample by a laser beam is always accompanied by an increase in the sample temperature, which may be unwanted or may be beneficial for studying temperature-related effects and determining thermal parameters. This work reports analyses of the temperature field induced by a Gaussian laser to calculate the Raman scattered intensity related to each temperature value of the nonuniform field present on the sample. The effective temperature of the probed field, calculated as an average weighted by the laser intensity, is demonstrated to be about 70% of the maximum temperature irrespective of the absorption coefficient or the laser focus. Finally, using crystalline silicon as a model material, it is shown that this effective value closely approximates the temperature value identified from the thermally related peak shift.
Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field
Institute of Scientific and Technical Information of China (English)
Khalid Bannora; Galal Ismail; Wafaa Hassan
2011-01-01
The thermodynamics and the phase diagram of random field Ising model (RFIM) on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field (B). A Gaussian distribution of random field (hi) with zero mean and variance = H2RF is considered. The free-energy (F), the magnetization (M) and the order parameter (q) are investigated for several values of coordination number (z). The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature TC = J/k and when HRF = 0 for finite z. The free-energy (F) values increase as T increases for different intensities of random field (HRF) and finite z. The internal energy (U) has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases. The ferromagnetic (FM)-paramagnetic (PM) phase boundary is clearly observed only when z →∞. While FM-PM-spin glass (SG) phase boundaries are present for finite z. The magnetic susceptibility (X) shows a sharp cusp at TC in a small random field for finite z and rounded different peaks on increasing HRF.
Two Dimensional Honeycomb Materials: Random Fields, Dissipation and Fluctuations
Frederico, T.; Oliveira, O.; de Paula, W.; Hussein, M. S.; Cardoso, T. R.
2017-02-01
In this paper, we propose a method to describe the many-body problem of electrons in honeycomb materials via the introduction of random fields which are coupled to the electrons and have a Gaussian distribution. From a one-body approach to the problem, after integrating exactly the contribution of the random fields, one builds a non-hermitian and dissipative effective Hamiltonian with two-body interactions. Our approach introduces besides the usual average over the electron field a second average over the random fields. The interplay of two averages enables the definition of various types of Green's functions which allow the investigation of fluctuation-dissipation characteristics of the interactions that are a manifestation of the many-body problem. In the current work, we study only the dissipative term, through the perturbative analysis of the dynamics associated the effective Hamiltonian generated by two different kinds of couplings. For the cases analyzed, the eigenstates of the effective Hamiltonian are complex and, therefore, some of the states have a finite life time. Moreover, we also investigate, in the mean field approximation, the most general parity conserving coupling to the random fields and compute the width of charge carriers Γ as a function of the Fermi energy E F . The theoretical prediction for Γ( E F ) is compared to the available experimental data for graphene. The good agreement between Γ t h e o and Γ e x p suggests that description of the many-body problem associated to the electrons in honeycomb materials can indeed be done via the introduction of random fields.
Sensing Random Electromagnetic Fields and Applications
2015-06-23
AFRL-OSR-VA-TR-2015-0172 SENSING RANDOM ELECTROMAGNETIC FIELDS AND APPLICATIONS Aristide Dogariu UNIVERSITY OF CENTRAL FLORIDA Final Report 06/23... Electromagnetic Fields and Applications 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK...14. ABSTRACT Random electromagnetic fields (REF) exist in all forms and one common origin is a result of the interaction of coherent fields with
Persistent Homology for Random Fields and Complexes
Adler, Robert J; Borman, Matthew S; Subag, Eliran; Weinberger, Shmuel
2010-01-01
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices, and, in most detail, the algebraic topology of the excursion sets of random fields.
Invariant domain watermarking using heaviside function of order alpha and fractional Gaussian field.
Abbasi, Almas; Woo, Chaw Seng; Ibrahim, Rabha Waell; Islam, Saeed
2015-01-01
Digital image watermarking is an important technique for the authentication of multimedia content and copyright protection. Conventional digital image watermarking techniques are often vulnerable to geometric distortions such as Rotation, Scaling, and Translation (RST). These distortions desynchronize the watermark information embedded in an image and thus disable watermark detection. To solve this problem, we propose an RST invariant domain watermarking technique based on fractional calculus. We have constructed a domain using Heaviside function of order alpha (HFOA). The HFOA models the signal as a polynomial for watermark embedding. The watermark is embedded in all the coefficients of the image. We have also constructed a fractional variance formula using fractional Gaussian field. A cross correlation method based on the fractional Gaussian field is used for watermark detection. Furthermore the proposed method enables blind watermark detection where the original image is not required during the watermark detection thereby making it more practical than non-blind watermarking techniques. Experimental results confirmed that the proposed technique has a high level of robustness.
Approximating a harmonizable isotropic random field
Directory of Open Access Journals (Sweden)
Randall J. Swift
2001-01-01
Full Text Available The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers a stochastic series approximation of a harmonizable isotropic random field. This approximation is useful for numerical simulation of such a field.
Multivariate stationary non-Gaussian process simulation for wind pressure fields
Sun, Ying; Su, Ning; Wu, Yue
2016-12-01
Stochastic simulation is an important means of acquiring fluctuating wind pressures for wind induced response analyses in structural engineering. The wind pressure acting on a large-span space structure can be characterized as a stationary non-Gaussian field. This paper reviews several simulation algorithms related to the Spectral Representation Method (SRM) and the Static Transformation Method (STM). Polynomial and Exponential transformation functions (PSTM and ESTM) are discussed. Deficiencies in current algorithms, with respect to accuracy, stability and efficiency, are analyzed, and the algorithms are improved for better practical application. In order to verify the improved algorithm, wind pressure fields on a large-span roof are simulated and compared with wind tunnel data. The simulation results fit well with the wind tunnel data, and the algorithm accuracy, stability and efficiency are shown to be better than those of current algorithms.
Ghotra, Harjit Singh; Kant, Niti
2017-01-01
Electron acceleration due to a circularly polarized (CP) Gaussian laser field has been investigated theoretically in magnetized plasma. A Gaussian laser beam possesses trapping forces on electrons during its propagation through plasma. A single particle simulation indicates a resonant enhancement of electron acceleration with a Gaussian laser beam. The plasma is magnetized with an axial magnetic field in same direction as that of laser beam propagation. The dependence of laser beam width parameter on electron energy gain with propagation distance has been presented graphically for different values of laser intensity. Electron energy gain is relatively high where the laser beam parameter is at its minimum value. Enhanced energy gain of the order of GeV is reported with magnetic field under 20 MG in plasma. It is also seen that the axial magnetic field maintains the electron acceleration for large propagation distance even with an increasing beam width parameter.
Institute of Scientific and Technical Information of China (English)
Lü Su-Ye; Lü Bai-Da
2009-01-01
Taking partially coherent cosh-Gaussian (ChG) beams as an example of more general partially coherent beams,we have studied the spectral degree of coherence of partially coherent ChG beams in the far field. It is shown that,unlike Gaussian Schell-model (GSM) beams,in the strict sense there do not exist two partially coherent ChG beams which can generate far fields with the same spectral degree of coherence. However,under certain conditions it is possible to find two partially coherent ChG beams with the same spectral degree of coherence in the far field.
Spectral Running and Non-Gaussianity from Slow-Roll Inflation in Generalised Two--Field Models
Choi, Ki-Young; van de Bruck, Carsten
2008-01-01
Theories beyond the standard model such as string theory motivate low energy effective field theories with several scalar fields which are not only coupled through a potential but also through their kinetic terms. For such theories we derive the general formulae for the running of the spectral indices for the adiabatic, isocurvature and correlation spectra in the case of two field inflation. We also compute the expected non-Gaussianity in such models for specific forms of the potentials. We find that the coupling has little impact on the level of non-Gaussianity during inflation.
Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.
de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos
2011-01-01
In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results.
Models of discretized moduli spaces, cohomological field theories, and Gaussian means
Andersen, Jørgen Ellegaard; Norbury, Paul; Penner, Robert C
2015-01-01
We prove combinatorially the explicit relation between genus filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM). The latter is the generating function for volumes of discretized (open) moduli spaces $M_{g,s}^{\\mathrm{disc}}$ given by $N_{g,s}(P_1,\\dots,P_s)$ for $(P_1,\\dots,P_s)\\in{\\mathbb Z}_+^s$. This generating function therefore enjoys the topological recursion, and we prove that it is simultaneously the generating function for ancestor invariants of a cohomological field theory thus enjoying the Givental decomposition. We use another Givental-type decomposition obtained for this model by the second authors in 1995 in terms of special times related to the discretisation of moduli spaces thus representing its asymptotic expansion terms (and therefore those of the Gaussian means) as finite sums over graphs weighted by lower-order monomials in times thus giving another proof of (quasi)polynomiality of the discrete volumes. As a...
DEFF Research Database (Denmark)
Dimitrov, Nikolay Krasimirov; Lazarov, Boyan Stefanov
2015-01-01
We demonstrate a method for incorporating wind measurements from multiple-point scanning lidars into the turbulence fields serving as input to wind turbine load simulations. The measurement values are included in the analysis by applying constraints to randomly generated turbulence fields...
Distributed estimation of a parametric field with random sensor placements
Alkhweldi, Marwan; Cao, Zhicheng; Schmid, Natalia A.
2015-05-01
This paper considers a problem of distributed function estimation in the case when sensor locations are modeled as Gaussian random variables. We consider a scenario where sensors are deployed in clusters with cluster centers known a priori (or estimated by a high performance GPS) and the average quadratic spread of sensors around the cluster center also known. Distributed sensors make noisy observations about an unknown parametric field generated by a physical object of interest (for example, magnetic field generated by a ferrous object and sensed by a network of magnetometers). Each sensor then performs local signal processing of its noisy observation and sends it to a central processor (called fusion center) in the wireless sensor network over parallel channels corrupted by fading and additive noise. The central processor combines the set of received signals to form an estimate of the unknown parametric field. In our numerical analysis, we involve a field shaped as a Gaussian bell. We experiment with the size of sensor clusters and with their number. A mean square error between the estimated parameters of the field and the true parameters used in simulations is involved as a performance measure. It can be shown that a relatively good estimate of the field can be obtained with only a small number of clusters. As the number of clusters increases, the estimation performance steadily improves. The results also indicate that, on the average, the number of clusters has more impact on the performance than the number of sensors per cluster, given the same size of the total network.
Effective field theory and non-Gaussianity from general inflationary states
Agarwal, Nishant; Tolley, Andrew J; Lin, Jennifer
2013-01-01
We study the effects of non-trivial initial quantum states for inflationary fluctuations within the context of the effective field theory for inflation constructed by Cheung et al. which allows us to discriminate between different initial states in a model-independent way. We develop a Green's function/path integral based formulation that incorporates initial state effects and use it to address questions such as how state-dependent is the consistency relation for the bispectrum, how many e-folds beyond the minimum required to solve the cosmological fine tunings of the big bang are we allowed so that some information from the initial state survives until late times, among others. We find that the so-called consistency condition relating the local limit of the bispectrum and the slow-roll parameter is a state-dependent statement that can be avoided for physically consistent initial states either with or without initial non-Gaussianities.
A spatiotemporal precipitation generator based on a censored latent Gaussian field
Baxevani, Anastassia; Lennartsson, Jan
2015-06-01
A daily stochastic spatiotemporal precipitation generator that yields precipitation realizations that are quantitatively consistent is described. The methodology relies on a latent Gaussian field that drives both the occurrence and intensity of the precipitation process. For the precipitation intensity, the marginal distributions, which are space and time dependent, are described by a composite model of a gamma distribution for observations below some threshold with a generalized Pareto distribution modeling the excesses above the threshold. Model parameters are estimated from data and extrapolated to locations and times with no direct observations using linear regression of position covariates. One advantage of such a model is that stochastic generator parameters are readily available at any location and time of the year inside the stationarity regions. The methodology is illustrated for a network of 12 locations in Sweden. Performance of the model is judged through its ability to accurately reproduce a series of spatial dependence measures and weather indices.
Integrals of random fields treated by the model correction factor method
DEFF Research Database (Denmark)
Franchin, P.; Ditlevsen, Ove Dalager; Kiureghian, Armen Der
2002-01-01
The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals...... are considered to be Gaussian. Conventional FORM analysis yields the linearization point of the idealized limit-state surface. A model correction factor is then introduced to push the idealized limit-state surface onto the actual limit-state surface. A few iterations yield a good approximation of the reliability...
Concentration inequalities for random fields via coupling
Chazottes, J. R.; Collet, P.; Kuelske, C.; Redig, F.
We present a new and simple approach to concentration inequalities in the context of dependent random processes and random fields. Our method is based on coupling and does not use information inequalities. In case one has a uniform control on the coupling, one obtains exponential concentration
APLIKASI MARKOV RANDOM FIELD PADA MASALAH INDUSTRI
Directory of Open Access Journals (Sweden)
Siana Halim
2002-01-01
Full Text Available Markov chain in the stochastic process is widely used in the industrial problems particularly in the problem of determining the market share of products. In this paper we are going to extend the one in the random field so called the Markov Random Field and applied also in the market share problem with restriction the market is considered as a discrete lattice and Pott's models are going to be used as the potential function. Metropolis sampler is going to be used to determine the stability condition. Abstract in Bahasa Indonesia : Rantai Markov dalam proses stokastik seringkali digunakan dalam penyelesaian masalah industri khususnya dalam masalah penentuan market share. Dalam artikel ini akan dibahas perluasan Rantai Markov tesebut ke dalam sebuah random field yang disebut sebagai Markov Random Field (MRF yang juga akan diaplikasikan pada masalah market share dengan batasan daerah pemasarannya dianggap sebagai sebuah lattice diskrit dan fungsi potensial yang akan digunakan adalah Potts models. Akan digunakan Metropolis sampler untuk menentukan kondisi stabil. Kata kunci: proses stokastik, Markov Random Field, Gibbs Random Field, Potts model, Metropolis sampling.
Johnson, Perry L
2016-01-01
The statistics of the velocity gradient tensor in turbulent flows are of both theoretical and practical importance. The Lagrangian view provides a privileged perspective for studying the dynamics of turbulence in general, and of the velocity gradient tensor in particular. Stochastic models for the Lagrangian evolution of velocity gradients in isotropic turbulence, with closure models for the pressure Hesssian and viscous Laplacian, have been shown to reproduce important features such as non-Gaussian probability distributions, skewness and vorticity strain-rate alignments. The Recent Fluid Deformation (RFD) closure introduced the idea of mapping an isotropic Lagrangian pressure Hessian as upstream initial condition using the fluid deformation tensor. Recent work on a Gaussian fields closure, however, has shown that even Gaussian isotropic velocity fields contain significant anisotropy for the conditional pressure Hessian tensor due to the inherent velocity-pressure couplings, and that assuming an isotropic pre...
Non-Gaussian approach for parametric random vibration of non-linear structures
Ibrahim, R. A.; Soundararajan, A.
1984-01-01
The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.
Second-order cosmological perturbations in two-field inflation and predictions for non-Gaussianity
Tzavara, Eleftheria
2013-01-01
Inflationary predictions for the power spectrum of the curvature perturbation have been verified to an excellent degree, leaving many models compatible with observations. In this thesis we studied third-order correlations, that might allow one to further distinguish between inflationary models. From all the possible extensions of the standard inflationary model, we chose to study two-field models with canonical kinetic terms and flat field space. The new feature is the presence of the so-called isocurvature perturbation. Its interplay with the adiabatic perturbation outside the horizon gives birth to non-linearities characteristic of multiple-field models. In this context, we established the second-order gauge-invariant form of the adiabatic and isocurvature perturbation and found the third-order action that describes their interactions. Furthermore, we built on and elaborated the long-wavelength formalism in order to acquire an expression for the parameter of non-Gaussianity fNL as a function of the potentia...
Hanel, R.; Thurner, S.; Tsallis, C.
2009-11-01
Extremization of the Boltzmann-Gibbs (BG) entropy S_{BG}=-kint dx p(x) ln p(x) under appropriate norm and width constraints yields the Gaussian distribution pG(x) ∝e-βx. Also, the basic solutions of the standard Fokker-Planck (FP) equation (related to the Langevin equation with additive noise), as well as the Central Limit Theorem attractors, are Gaussians. The simplest stochastic model with such features is N ↦∞ independent binary random variables, as first proved by de Moivre and Laplace. What happens for strongly correlated random variables? Such correlations are often present in physical situations as e.g. systems with long range interactions or memory. Frequently q-Gaussians, pq(x) ∝[1-(1-q)βx2]1/(1-q) [p1(x)=pG(x)] become observed. This is typically so if the Langevin equation includes multiplicative noise, or the FP equation to be nonlinear. Scale-invariance, e.g. exchangeable binary stochastic processes, allow a systematical analysis of the relation between correlations and non-Gaussian distributions. In particular, a generalized stochastic model yielding q-Gaussians for all (q ≠ 1) was missing. This is achieved here by using the Laplace-de Finetti representation theorem, which embodies strict scale-invariance of interchangeable random variables. We demonstrate that strict scale invariance together with q-Gaussianity mandates the associated extensive entropy to be BG.
Bamba, Kazuharu
2014-01-01
The generation of large-scale magnetic fields in inflationary cosmology is explored, in particular, in a kind of moduli inflation motivated by racetrack inflation in the context of the Type IIB string theory. In this model, the conformal invariance of the hypercharge electromagnetic fields is broken thanks to the coupling of both the scalar and pseudoscalar fields to the hypercharge electromagnetic fields. The following three cosmological observable quantities are first evaluated: The current magnetic field strength on the Hubble horizon scale, which is much smaller than the upper limit from the back reaction problem, the local non-Gaussianity of the curvature perturbations due to the existence of the massive gauge fields, and the tensor-to-scalar ratio. It is explicitly demonstrated that the resultant values of the local non-Gaussianity and the tensor-to-scalar ratio are consistent with the Planck data.
Dimitrov, Nikolay Krasimirov; Lazarov, Boyan Stefanov
2015-01-01
We demonstrate a method for incorporating wind measurements from multiple-point scanning lidars into the turbulence fields serving as input to wind turbine load simulations. The measurement values are included in the analysis by applying constraints to randomly generated turbulence fields. A numerical study shows the application of the constrained turbulence method to load simulations on a 10MW wind turbine model, using two example lidar patterns – a 5-point pattern forming a square with a ce...
Energy Technology Data Exchange (ETDEWEB)
McCoy, M.G.
1975-11-01
The problem of the numerical simulation of turbulent diffusion is studied. The two-dimensional velocity fields are assumed to be incompressible, homogeneous and stationary, and they are represented as stochastic processes. A technique is offered which creates velocity fields accurately representing the input statistics once a two point correlation function or an energy spectrum is given. Various complicated energy spectra may be represented utilizing this model. The program is then used to extract information concerning Gaussian diffusion processes. Various theories of other workers are tested including Taylor's classical representation of dispersion for times long compared with the Lagrangian correlation time. Also, a study is made of the relation between the Lagrangian and the Eulerian correlation function and a hypothesis is advanced and successfully tested. Questions concerning the relation between small eddies and the energy spectrum are considered. A criterion is advanced and successfully tested to decide whether small scale flow can be detected within the large eddies for any given spectrum. A method is developed to determine whether this small scale motion is in any sense periodic. Finally, the relation between two particle dispersion and the energy spectrum is studied anew and various theories are tested. (auth)
Discriminative learning of receptive fields from responses to non-Gaussian stimulus ensembles.
Directory of Open Access Journals (Sweden)
Arne F Meyer
Full Text Available Analysis of sensory neurons' processing characteristics requires simultaneous measurement of presented stimuli and concurrent spike responses. The functional transformation from high-dimensional stimulus space to the binary space of spike and non-spike responses is commonly described with linear-nonlinear models, whose linear filter component describes the neuron's receptive field. From a machine learning perspective, this corresponds to the binary classification problem of discriminating spike-eliciting from non-spike-eliciting stimulus examples. The classification-based receptive field (CbRF estimation method proposed here adapts a linear large-margin classifier to optimally predict experimental stimulus-response data and subsequently interprets learned classifier weights as the neuron's receptive field filter. Computational learning theory provides a theoretical framework for learning from data and guarantees optimality in the sense that the risk of erroneously assigning a spike-eliciting stimulus example to the non-spike class (and vice versa is minimized. Efficacy of the CbRF method is validated with simulations and for auditory spectro-temporal receptive field (STRF estimation from experimental recordings in the auditory midbrain of Mongolian gerbils. Acoustic stimulation is performed with frequency-modulated tone complexes that mimic properties of natural stimuli, specifically non-Gaussian amplitude distribution and higher-order correlations. Results demonstrate that the proposed approach successfully identifies correct underlying STRFs, even in cases where second-order methods based on the spike-triggered average (STA do not. Applied to small data samples, the method is shown to converge on smaller amounts of experimental recordings and with lower estimation variance than the generalized linear model and recent information theoretic methods. Thus, CbRF estimation may prove useful for investigation of neuronal processes in response to
Discriminative Learning of Receptive Fields from Responses to Non-Gaussian Stimulus Ensembles
Meyer, Arne F.; Diepenbrock, Jan-Philipp; Happel, Max F. K.; Ohl, Frank W.; Anemüller, Jörn
2014-01-01
Analysis of sensory neurons' processing characteristics requires simultaneous measurement of presented stimuli and concurrent spike responses. The functional transformation from high-dimensional stimulus space to the binary space of spike and non-spike responses is commonly described with linear-nonlinear models, whose linear filter component describes the neuron's receptive field. From a machine learning perspective, this corresponds to the binary classification problem of discriminating spike-eliciting from non-spike-eliciting stimulus examples. The classification-based receptive field (CbRF) estimation method proposed here adapts a linear large-margin classifier to optimally predict experimental stimulus-response data and subsequently interprets learned classifier weights as the neuron's receptive field filter. Computational learning theory provides a theoretical framework for learning from data and guarantees optimality in the sense that the risk of erroneously assigning a spike-eliciting stimulus example to the non-spike class (and vice versa) is minimized. Efficacy of the CbRF method is validated with simulations and for auditory spectro-temporal receptive field (STRF) estimation from experimental recordings in the auditory midbrain of Mongolian gerbils. Acoustic stimulation is performed with frequency-modulated tone complexes that mimic properties of natural stimuli, specifically non-Gaussian amplitude distribution and higher-order correlations. Results demonstrate that the proposed approach successfully identifies correct underlying STRFs, even in cases where second-order methods based on the spike-triggered average (STA) do not. Applied to small data samples, the method is shown to converge on smaller amounts of experimental recordings and with lower estimation variance than the generalized linear model and recent information theoretic methods. Thus, CbRF estimation may prove useful for investigation of neuronal processes in response to natural stimuli and
Generalized Whittle-Matern random field as a model of correlated fluctuations
Energy Technology Data Exchange (ETDEWEB)
Lim, S C [Faculty of Engineering, Multimedia University, Jalan Multimedia, Cyberjaya, 63100, Selangor Darul Ehsan (Malaysia); Teo, L P [Faculty of Information Technology, Multimedia University, Jalan Multimedia, Cyberjaya, 63100, Selangor Darul Ehsan (Malaysia)], E-mail: sclim@mmu.edu.my, E-mail: lpteo@mmu.edu.my
2009-03-13
This paper considers a generalization of the Gaussian random field with covariance function of the Whittle-Matern family. Such a random field can be obtained as the solution to the fractional stochastic differential equation with two fractional orders. Asymptotic properties of the covariance functions belonging to this generalized Whittle-Matern family are studied, which are used to deduce the sample path properties of the random field. The Whittle-Matern field has been widely used in modeling geostatistical data such as sea beam data, wind speed, field temperature and soil data. In this paper we show that the generalized Whittle-Matern field provides a more flexible model for wind speed data.
Random Gaussian process effect upon selective system of spectra heterodyne analyzer
Directory of Open Access Journals (Sweden)
N. F. Vollerner
1967-12-01
Full Text Available The formula is obtained that describe mean power changing the selective system output by changing speed tuning of the spectra heterodyne analyzer when searching random stationary processes.
Institute of Scientific and Technical Information of China (English)
Jun Ma; Lixin Guo; Xiangzhe Cheng
2009-01-01
The optical wave scattering from one-dimensional (1D) lossy dielectric Gaussian random rough surface is studied. The tapered incident wave is introduced into the classical Kirchhoff approximation (KA), and the shadowing effect is also taken into account to make the KA results have a high accuracy. The definition of the bistatic scattering coefficient of the modified KA and the method of moment (MOM) are unified. The characteristics of the optical wave scattering from the lossy dielectric Gaussian random rough surface of different parameters are analyzed by implementing MOM.
Modular design and implementation of field-programmable-gate-array-based Gaussian noise generator
Li, Yuan-Ping; Lee, Ta-Sung; Hwang, Jeng-Kuang
2016-05-01
The modular design of a Gaussian noise generator (GNG) based on field-programmable gate array (FPGA) technology was studied. A new range reduction architecture was included in a series of elementary function evaluation modules and was integrated into the GNG system. The approximation and quantisation errors for the square root module with a first polynomial approximation were high; therefore, we used the central limit theorem (CLT) to improve the noise quality. This resulted in an output rate of one sample per clock cycle. We subsequently applied Newton's method for the square root module, thus eliminating the need for the use of the CLT because applying the CLT resulted in an output rate of two samples per clock cycle (>200 million samples per second). Two statistical tests confirmed that our GNG is of high quality. Furthermore, the range reduction, which is used to solve a limited interval of the function approximation algorithms of the System Generator platform using Xilinx FPGAs, appeared to have a higher numerical accuracy, was operated at >350 MHz, and can be suitably applied for any function evaluation.
Vectorial Structure of Non-Paraxial Linearly Polarized Gaussian Beam in Far Field
Institute of Scientific and Technical Information of China (English)
ZHOU Guo-Quan; CHEN Liang; NI Yong-Zhou
2006-01-01
@@ According to the vectorial structure of non-paraxial electromagnetic beams and the method of stationary phase,the analytical TE and TM terms of non-paraxial linearly polarized Gaussian beam are presented in the far field.The influence of linearly polarized angle on the relative energy flux distributions of the whole beam and its TE and TM terms is studied. The beam spot of the TE term is perpendicular to the direction of linearly polarized angle, while that of the TM term coincides with the direction of linearly polarized angle. The whole beam spot is elliptical, and the long axis is located at the direction of linearly polarized angle. The relative energy flux distribution of the TE term is relatively centralized in the direction perpendicular to the linearly polarized angle.While that of the TM term is relatively centralized in the direction of linearly polarized angle. To obtain the isolated TM and TE terms, a polarizer should be put at the long and the short axis of the whole beam. spot,respectively.
Anomalous diffusion and Levy random walk of magnetic field lines in three dimensional turbulence
Energy Technology Data Exchange (ETDEWEB)
Zimbardo, G.; Veltri, P.; Basile, G.; Principato, S. [Dipartimento di Fisica, Universita della Calabria, I-87030 Arcavacata di Rende (Italy)
1995-07-01
The transport of magnetic field lines is studied numerically where three dimensional (3-D) magnetic fluctuations, with a power law spectrum, and periodic over the simulation box are superimposed on an average uniform magnetic field. The weak and the strong turbulence regime, {delta}{ital B}{similar_to}{ital B}{sub 0}, are investigated. In the weak turbulence case, magnetic flux tubes are separated from each other by percolating layers in which field lines undergo a chaotic motion. In this regime the field lines may exhibit Levy, rather than Gaussian, random walk, changing from Levy flights to trapped motion. The anomalous diffusion laws {l_angle}{Delta}{ital x}{sup 2}{sub {ital i}}{r_angle}{proportional_to}{ital s}{sup {alpha}} with {alpha}{gt}1 and {alpha}{lt}1, are obtained for a number of cases, and the non-Gaussian character of the field line random walk is pointed out by computing the kurtosis. Increasing the fluctuation level, and, therefore stochasticity, normal diffusion ({alpha}{congruent}1) is recovered and the kurtoses reach their Gaussian value. However, the numerical results show that neither the quasi-linear theory nor the two dimensional percolation theory can be safely extrapolated to the considered 3-D strong turbulence regime. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Randomization for Security in Half-Duplex Two-Way Gaussian Channels
Gamal, Aly El; Gamal, Hesham El
2009-01-01
This paper develops a new physical layer framework for secure two-way wireless communication in the presence of a passive eavesdropper, i.e., Eve. Our approach achieves perfect information theoretic secrecy via a novel randomized scheduling and power allocation scheme. The key idea is to allow Alice and Bob to send symbols at random time instants. While Alice will be able to determine the symbols transmitted by Bob, Eve will suffer from ambiguity regarding the source of any particular symbol. This desirable ambiguity is enhanced, in our approach, by randomizing the transmit power level. Our theoretical analysis, in a 2-D geometry, reveals the ability of the proposed approach to achieve relatively high secure data rates under mild conditions on the spatial location of Eve. These theoretical claims are then validated by experimental results using IEEE 802.15.4-enabled sensor boards in different configurations, motivated by the spatial characteristics of Wireless Body Area Networks (WBAN).
Entropy estimates for simple random fields
DEFF Research Database (Denmark)
Forchhammer, Søren; Justesen, Jørn
1995-01-01
We consider the problem of determining the maximum entropy of a discrete random field on a lattice subject to certain local constraints on symbol configurations. The results are expected to be of interest in the analysis of digitized images and two dimensional codes. We shall present some examples...... of binary and ternary fields with simple constraints. Exact results on the entropies are known only in a few cases, but we shall present close bounds and estimates that are computationally efficient...
Synchronization in the random-field Kuramoto model on complex networks
Lopes, M. A.; Lopes, E. M.; Yoon, S.; Mendes, J. F. F.; Goltsev, A. V.
2016-07-01
We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fields with uniformly distributed directions and homogeneous and heterogeneous (Gaussian) field magnitude distribution. In our analysis, we apply the Ott-Antonsen method and the annealed-network approximation to find the critical behavior of the order parameter. In the case of homogeneous fields, we find a tricritical point above which a second-order phase transition gives place to a first-order phase transition when the network is either fully connected or scale-free with the degree exponent γ >5 . Interestingly, for scale-free networks with 2 networks, although the fields increase the critical coupling for γ >3 . Our simulations support these analytical results.
Random field estimation approach to robot dynamics
Rodriguez, Guillermo
1990-01-01
The difference equations of Kalman filtering and smoothing recursively factor and invert the covariance of the output of a linear state-space system driven by a white-noise process. Here it is shown that similar recursive techniques factor and invert the inertia matrix of a multibody robot system. The random field models are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. They are easier to describe than the models based on classical mechanics, which typically require extensive derivation and manipulation of equations of motion for complex mechanical systems. With the spatially random models, more primitive locally specified computations result in a global collective system behavior equivalent to that obtained with deterministic models. The primary goal of applying random field estimation is to provide a concise analytical foundation for solving robot control and motion planning problems.
Energy Technology Data Exchange (ETDEWEB)
Smirnov, V.N.; Strokovskii, G.A. [St. Petersburg State Univ. (Russian Federation)
1994-10-01
An analytical form of expansion coefficients of a diffracted field for an arbitrary Hermite-Gaussian beam in an alien Hermite-Gaussian basis is obtained. A possible physical interpretation of the well-known Young phenomenological diffraction principle and experiments on diffraction of Hermite-Gaussian beams of the lowest types (n = 0 - 5) from half-plane are discussed. The case of nearly homogenous expansion corresponding to misalignment and mismatch of optical systems is also analyzed. 7 refs., 2 figs.
Interfaces in Random Field Ising Systems
Seppälä, Eira
2001-03-01
Domain walls are studied in random field Ising magnets at T=0 in two and three dimensions using exact ground state calculations. In 2D below the random field strength dependent length scale Lb the walls exhibit a super-rough behavior with a roughness exponent greater than unity ζ ~= 1.20 ± 0.05. The nearest-neighbor height difference probability distribution depends on the system size below L_b. Above Lb domains become fractal, ζ ~= 1.(E. T. Seppälä, V. Petäjä, and M. J. Alava, Phys. Rev. E 58), R5217 (1998). The energy fluctuation exponent has a value θ=1, contradicting the exponent relation θ = 2ζ -1 due to the broken scale-invariance, below Lb and vanishes for system sizes above L_b. The broken scale-invariance should be manifest also in Kardar-Parisi-Zhang problem with random-field noise.(E. Frey, U. C. Täuber, and H. K. Janssen, Europhys. Lett. 47), 14 (1999). In 3D there exists a transition between ferromagnetic and paramagnetic phases at the critical random field strength (Δ/J)_c. Below (Δ/J)c the roughness exponent is also greater ζ ~= 0.73 ± 0.03 than the functional-renormalization-group calculation result ζ = (5-d)/3.(D. Fisher, Phys. Rev. Lett. 56), 1964 (1986).(P. Chauve, P. Le Doussal, and K. Wiese, cond-mat/0006056.) The height differences are system size dependent in 3D, as well. The behavior of the domain walls in 2D below Lb with a constant external field, i.e., the random-bulk wetting, is demonstrated.(E. T. Seppälä, I. Sillanpää, and M. J. Alava, unpublished.)
Conditional Random Fields for Image Labeling
Directory of Open Access Journals (Sweden)
Tong Liu
2016-01-01
Full Text Available With the rapid development and application of CRFs (Conditional Random Fields in computer vision, many researchers have made some outstanding progress in this domain because CRFs solve the classical version of the label bias problem with respect to MEMMs (maximum entropy Markov models and HMMs (hidden Markov models. This paper reviews the research development and status of object recognition with CRFs and especially introduces two main discrete optimization methods for image labeling with CRFs: graph cut and mean field approximation. This paper describes graph cut briefly while it introduces mean field approximation more detailedly which has a substantial speed of inference and is researched popularly in recent years.
Short communication: Alteration of priors for random effects in Gaussian linear mixed model
DEFF Research Database (Denmark)
Vandenplas, Jérémie; Christensen, Ole Fredslund; Gengler, Nicholas
2014-01-01
, multiple-trait predictions of lactation yields, and Bayesian approaches integrating external information into genetic evaluations) need to alter both the mean and (co)variance of the prior distributions and, to our knowledge, most software packages available in the animal breeding community do not permit......Linear mixed models, for which the prior multivariate normal distributions of random effects are assumed to have a mean equal to 0, are commonly used in animal breeding. However, some statistical analyses (e.g., the consideration of a population under selection into a genomic scheme breeding...... such alterations. Therefore, the aim of this study was to propose a method to alter both the mean and (co)variance of the prior multivariate normal distributions of random effects of linear mixed models while using currently available software packages. The proposed method was tested on simulated examples with 3...
Highly directive and Gaussian far-field emission from “giant” photonic trumpets
DEFF Research Database (Denmark)
Stepanov, Petr; Delga, Adrien; Gregersen, Niels;
2015-01-01
Photonic trumpets are broadband dielectric antennas that efficiently funnel the emission of a pointlike quantum emitter—such as a semiconductor quantum dot—into a Gaussian free-space beam. After describing guidelines for the taper design, we present a “giant” photonic trumpet. The device features...
Das, Indrajit
2016-01-01
Collisions of gas particles with a drifting grain give rise to a mechanical torque on the grain. Recent work by Lazarian & Hoang showed that mechanical torques might play a significant role in aligning helical grains along the interstellar magnetic field direction, even in the case of subsonic drift. We compute the mechanical torques on 13 different irregular grains and examine their resulting rotational dynamics, assuming steady rotation about the principal axis of greatest moment of inertia. We find that the alignment efficiency in the subsonic drift regime depends sensitively on the grain shape, with more efficient alignment for shapes with a substantial mechanical torque even in the case of no drift. The alignment is typically more efficient for supersonic drift. A more rigorous analysis of the dynamics is required to definitively appraise the role of mechanical torques in grain alignment.
Field and intensity correlation in random media
Sebbah; Pnini; Genack
2000-11-01
We have obtained the spectral and spatial field correlation functions, C(E)(Deltaomega) and C(E)(Deltax), respectively, from measurement of the microwave field spectrum at a series of points along a line on the output of a random dielectric medium. C(E)(Deltaomega) and C(E)(Deltax) are shown to be the Fourier transforms, respectively, of the time of flight distribution, obtained from pulsed measurements, and of the specific intensity. Unlike C(E)(Deltaomega), the imaginary part of C(E)(Deltax) is shown to vanish as a result of the isotropy of the correlation function in the output plane. The complex square of the field correlation function gives the short-range or C1 contribution to the intensity correlation function C. Longer-range contributions to the intensity correlation function are obtained directly by subtracting C1 from C and are in good agreement with theory.
Non-Gaussian statistical models of surface wave fields for remote sensing applications
Huang, N. E.
1984-01-01
Based on the complete Stokes wave model with the bias term and using a simple mapping approach and an iteration solution method, we established a formula for the joint probability density function of the surface slope elevation of a nonlinear random wave field. The formula requires three parameters to define the whole density function: the rms surface elevation and slope values and the significant slope. This model represents the dynamics of the wave in a more direct way than the Gram-Charlier approximation. Based on this new statistical model and laboratory experiments, formula and numerical values of EM bias and dynamics bias are derived. The results indicate that various biases should be considered seriously if accuracy of the altimeter measurement is required in centimeter range.
Scattering from Alpha-Stable Non-Gaussian Distributed Surfaces
Institute of Scientific and Technical Information of China (English)
REN Yu-Chao; GUO Li-Xin; WU Zhen-Sen
2007-01-01
@@ The scattering problem of alpha-stable non-Gaussian distributed rough surfaces is studied. The alpha-stable non-Gaussian distribution is used to describe the surfaces that exhibit sharp and sparse peaks, not usually seen in Gaussian distributed surfaces. Then a magnetic field integral equation is formulated to calculate the scattered field and the scattering coefficient. Numerical simulations show that the magnitude distribution of the scattered field is affected significantly by the probability distribution of the surface when the height of the surface changes in a random way. In addition, simulation results are presented as bistatic scattering coefficient for alpha-stable distributed surfaces.
Fifth-order corrected field descriptions of the Hermite-Gaussian (0,0) and (0,1) mode laser beam.
Wang, J X; Scheid, W; Hoelss, M; Ho, Y K
2001-12-01
In this paper, we extend the work of Barton and Alexander [J. App. Phys. 66, 2800 (1989)] on the fifth-order corrected field expressions for a Hermite-Gaussian (0,0) mode laser beam to more general cases with adjustable parameters. The parametric dependence of the electron dynamics is investigated by numerical methods. Finally, the fifth-order corrected field equations for the Hermite-Gaussian (0,1) mode are also presented.
Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields
Directory of Open Access Journals (Sweden)
Martin Schlather
2015-02-01
Full Text Available Modeling of and inference on multivariate data that have been measured in space, such as temperature and pressure, are challenging tasks in environmental sciences, physics and materials science. We give an overview over and some background on modeling with cross- covariance models. The R package RandomFields supports the simulation, the parameter estimation and the prediction in particular for the linear model of coregionalization, the multivariate Matrn models, the delay model, and a spectrum of physically motivated vector valued models. An example on weather data is considered, illustrating the use of RandomFields for parameter estimation and prediction.
Post-Gaussian Effective Potential of Double sine-Gordon Field
Institute of Scientific and Technical Information of China (English)
CAI Wei-Ran; LOU Sen-Yue
2005-01-01
In the framework of the functional integral formalism, we calculate the effective potential of the double sine-Gordon (DsG) model up to the second order with an optimized expansion and the Coleman's normal-ordering prescription. Within the range of convergence, we make a comparison among the classicaland the effective potential of the first and second order. The numerical analysis shows that the DsG post-Gaussian EP possesses some fine global properties and makes a substantial and a concordant quantum correction to the features of the classical potential.
Institute of Scientific and Technical Information of China (English)
ZHU Guo-Zhen; SUN Yao; FU De-Yong
2004-01-01
@@ On the Schlieren photograph, a continuous ultrasonic Gaussian beam and its nonspecularly reflected beams [Chin.Phys. Lett. 16 (1999) 819] always have limited visual-width, although the theoretical spatial distribution of the sound field is a continuous function. To study this problem, the first step is to investigate the visual-width of the beam on the photograph related to the sound pressure at the centre of the beam by the threshold of the optical system caused by the refraction of light; the second step is to explain the visual-width of nonspecularly reflected field. By applying a relevant threshold, checked by the visual width of the incident beam, to cut the theoretical curves of the reflected sound field, one can find the visual-width of the two reflected beams and the gap between them correspond to that on the Schlieren photograph.
Onorato, M; Osborne, A R; Serio, M; Cavaleri, L; Brandini, C; Stansberg, C T
2004-12-01
We study random surface gravity wave fields and address the formation of large-amplitude waves in a laboratory environment. Experiments are performed in one of the largest wave tank facilities in the world. We present experimental evidence that the tail of the probability density function for wave height strongly depends on the Benjamin-Feir index (BFI)-i.e., the ratio between wave steepness and spectral bandwidth. While for a small BFI the probability density functions obtained experimentally are consistent with the Rayleigh distribution, for a large BFI the Rayleigh distribution clearly underestimates the probability of large events. These results confirm experimentally the fact that large-amplitude waves in random spectra may result from the modulational instability.
Arkhipov, Ievgen I.; Peřina, Jan; Peřina, Jan; Miranowicz, Adam
2016-07-01
The behavior of general nonclassical two-mode Gaussian states at a beam splitter is investigated. Single-mode nonclassicality as well as two-mode entanglement of both input and output states are analyzed suggesting their suitable quantifiers. These quantifiers are derived from local and global invariants of linear unitary two-mode transformations such that the sum of input (or output) local nonclassicality measures and entanglement measure gives a global invariant. This invariant quantifies the global nonclassicality resource. Mutual transformations of local nonclassicalities and entanglement induced by the beam splitter are analyzed considering incident noisy twin beams, single-mode noisy squeezed vacuum states, and states encompassing both squeezed states and twin beams. A rich tapestry of interesting nonclassical output states is predicted.
Generalized Gaussian Error Calculus
Grabe, Michael
2010-01-01
For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...
The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach
Lu, W F
1999-01-01
The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum in the field system is asymmetrical, which verifies an earlier conjecture. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for some portion of the aforementioned region. Besides, the masses of one particle and tow-particle bound state upon the symmetric vacuum are also calculated, and the resultant masses agree with the recent second-order results of fermion-mass perturbation for the massive Schwinger model.
Kang, Xiaoping; He, Zhong; Lü, Baida
2007-07-01
The far-field properties and beam quality of vectorial nonparaxial Hermite-Laguerre-Gaussian (HLG) beams are studied in detail, where, instead of the second-order-moments-based M2 factor, the extended power in the bucket (PIB) and βparameter are used to characterize the beam quality in the far field and the intensity in the formulae is replaced by the z component of the time-averaged Poynting vector . It is found that the PIB and βparameter of vectorial nonparaxial HLG beams depend on the mode indices n, m, αparameter and waist-width-to-wavelength ratio w0/ λ and the PIB and βparameter are additionally dependent on the bucket's size taken.
Bertolini, Daniele; Solon, Mikhail P; Walsh, Jonathan R; Zurek, Kathryn M
2015-01-01
We compute the non-Gaussian contribution to the covariance of the matter power spectrum at one-loop order in Standard Perturbation Theory (SPT), and using the framework of the effective field theory (EFT) of large scale structure (LSS). The complete one-loop contributions are evaluated for the first time, including the leading EFT corrections that involve seven independent operators, of which four appear in the power spectrum and bispectrum. In the basis where the three new operators are maximally uncorrelated, we find that two of them are suppressed at the few percent level relative to other contributions, and may thus be neglected. We extract the single remaining coefficient from N-body simulations, and obtain robust predictions for the non-Gaussian part of the covariance $C(k_i, k_j)$ up to $k_i + k_j \\sim$ 0.3 h/Mpc. The one-parameter prediction from EFT improves over SPT, with the analytic reach in wavenumber more than doubled.
Fedeli, Cosimo; Moscardini, Lauro; Cimatti, Andrea
2010-01-01
We investigate the constraints on primordial non-Gaussianity with varied bispectrum shapes that can be derived from the power spectrum of galaxies and clusters of galaxies detected in future wide field optical/near-infrared surveys. Having in mind the proposed ESA space mission \\emph{Euclid} as a specific example, we combine the spatial distribution of spectroscopically selected galaxies with that of weak lensing selected clusters. We use the physically motivated halo model in order to represent the correlation function of arbitrary tracers of the Large Scale Structure in the Universe. As naively expected, we find that galaxies are much more effective in jointly constrain the level of primordial non-Gaussianity $f_\\mathrm{NL}$ and the amplitude of the matter power spectrum $\\sigma_8$ than clusters of galaxies, due to the much lower abundance of the latter that is not adequately compensated by the larger effect on the power spectrum. Nevertheless, combination of the galaxy power spectrum with the cluster-galax...
Recursive Estimation of Gauss-Markov Random Fields Indexed over 1-D Space
Vats, Divyanshu
2009-01-01
This paper presents optimal recursive estimators for vector valued Gauss-Markov random \\emph{fields} taking values in $\\R^M$ and indexed by (intervals of) $\\R$ or $\\Z$. These 1-D fields are often called reciprocal processes. They correspond to two point boundary value fields, i.e., they have boundary conditions given at the end points of the indexing interval. To obtain the recursive estimators, we derive two classes of recursive representations for reciprocal processes. The first class transforms the Gaussian reciprocal process into a Gauss-Markov \\emph{process}, from which we derive forward and backwards recursive representations. The second representation folds the index set and transforms the original \\emph{field} taking values in $\\R^M$ into a Markov \\emph{process} taking values in $\\R^{2M}$. The folding corresponds to recursing the reciprocal process from the boundary points and telescoping inwards. From these recursive representations, Kalman filters and recursive smoothers are promptly derived.
About a solvable mean field model of a Gaussian spin glass
Barra, Adriano; Genovese, Giuseppe; Guerra, Francesco; Tantari, Daniele
2014-04-01
In a series of papers, we have studied a modified Hopfield model of a neural network, with learned words characterized by a Gaussian distribution. The model can be represented as a bipartite spin glass, with one party described by dichotomic Ising spins, and the other party by continuous spin variables, with an a priori Gaussian distribution. By application of standard interpolation methods, we have found it useful to compare the neural network model (bipartite) from one side, with two spin glass models, each monopartite, from the other side. Of these, the first is the usual Sherrington-Kirkpatrick model, the second is a spin glass model, with continuous spins and inbuilt highly nonlinear smooth cut-off interactions. This model is an invaluable laboratory for testing all techniques which have been useful in the study of spin glasses. The purpose of this paper is to give a synthetic description of the most peculiar aspects, by stressing the necessary novelties in the treatment. In particular, it will be shown that the control of the infinite volume limit, according to the well-known Guerra-Toninelli strategy, requires in addition one to consider the involvement of the cut-off interaction in the interpolation procedure. Moreover, the control of the ergodic region, the annealed case, cannot be directly achieved through the standard application of the Borel-Cantelli lemma, but requires previous modification of the interaction. This remark could find useful application in other cases. The replica symmetric expression for the free energy can be easily reached through a suitable version of the doubly stochastic interpolation technique. However, this model shares the unique property that the fully broken replica symmetry ansatz can be explicitly calculated. A very simple sum rule connects the general expression of the fully broken free energy trial function with the replica symmetric one. The definite sign of the error term shows that the replica solution is optimal. Then
Analytic model of the effect of poly-Gaussian roughness on rarefied gas flow near the surface
Aksenova, Olga A.; Khalidov, Iskander A.
2016-11-01
The dependence of the macro-parameters of the flow on surface roughness of the walls and on geometrical shape of the surface is investigated asymptotically and numerically in a rarefied gas molecular flow at high Knudsen numbers. Surface roughness is approximated in statistical simulation by the model of poly-Gaussian (with probability density as the mixture of Gaussian densities [1]) random process. Substantial difference is detected for considered models of the roughness (Gaussian, poly-Gaussian and simple models applied by other researchers), as well in asymptotical expressions [3], as in numerical results. For instance, the influence of surface roughness on momentum and energy exchange coefficients increases noticeably for poly-Gaussian model compared to Gaussian one (although the main properties of poly-Gaussian random processes and fields are similar to corresponding properties of Gaussian processes and fields). Main advantage of the model is based on relative simple relations between the parameters of the model and the basic statistical characteristics of random field. Considered statistical approach permits to apply not only diffuse-specular model of the local scattering function V0 of reflected gas atoms, but also Cercignani-Lampis scattering kernel or phenomenological models of scattering function. Thus, the comparison between poly-Gaussian and Gaussian models shows more significant effect of roughness in aerodynamic values for poly-Gaussian model.
Space-time correlations of a Gaussian interface
Dunlop, Francois M
2010-01-01
The serial harness introduced by Hammersley is equivalent, in the Gaussian case, to the Gaussian Solid-On-Solid interface model with parallel heat bath dynamics. Here we consider sub-lattice parallel dynamics, and give exact results about relaxation dynamics, based on the equivalence to the infinite time limit of a time periodic random field. We also give a numerical comparison to the harness process in continuous time studied by Hsiao and by Ferrari, Niederhauser and Pechersky.
Method for generating two coupled Gaussian stochastic processes
Jamali, Tayeb
2016-01-01
Most processes in nature are coupled; however, extensive null models for generating such processes still lacks. We present a new method to generate two coupled Gaussian stochastic processes with arbitrary correlation functions. This method is developed by modifying the Fourier filtering method. The robustness of this method is proved by generating two coupled fractional Brownian motions and extending its range of application to Gaussian random fields.
Itoh, Yuta; Amano, Toshiyuki; Iwai, Daisuke; Klinker, Gudrun
2016-11-01
We propose a method to calibrate viewpoint-dependent, channel-wise image blur of near-eye displays, especially of Optical See-Through Head-Mounted Displays (OST-HMDs). Imperfections in HMD optics cause channel-wise image shift and blur that degrade the image quality of the display at a user's viewpoint. If we can estimate such characteristics perfectly, we could mitigate the effect by applying correction techniques from the computational photography in computer vision as analogous to cameras. Unfortunately, directly applying existing calibration techniques of cameras to OST-HMDs is not a straightforward task. Unlike ordinary imaging systems, image blur in OST-HMDs is viewpoint-dependent, i.e., the optical characteristic of a display dynamically changes depending on the current viewpoint of the user. This constraint makes the problem challenging since we must measure image blur of an HMD, ideally, over the entire 3D eyebox in which a user can see an image. To overcome this problem, we model the viewpoint-dependent blur as a Gaussian Light Field (GLF) that stores spatial information of the display screen as a (4D) light field with depth information and the blur as point-spread functions in the form of Gaussian kernels, respectively. We first describe both our GLF model and a calibration procedure to learn a GLF for a given OST-HMD. We then apply our calibration method to two HMDs that use different optics: a cubic prism or holographic gratings. The results show that our method achieves significantly better accuracy in Point-Spread Function (PSF) estimations with an accuracy about 2 to 7 dB in Peak SNR.
Random Dieudonne modules, random p-divisible groups, and random curves over finite fields
Cais, Bryden; Zureick-Brown, David
2012-01-01
We describe a probability distribution on isomorphism classes of principally quasi-polarized p-divisible groups over a finite field k of characteristic p which can reasonably be thought of as "uniform distribution," and we compute the distribution of various statistics (p-corank, a-number, etc.) of p-divisible groups drawn from this distribution. It is then natural to ask to what extent the p-divisible groups attached to a randomly chosen hyperelliptic curve (resp. curve, resp. abelian variety) over k are uniformly distributed in this sense. For instance, one can ask whether the proportion of genus-g curves over F_p whose Jacobian is ordinary approaches the limit that such a heuristic would predict. This heuristic is analogous to conjectures of Cohen-Lenstra type for fields k of characteristic other than p, in which case the random p-divisible group is defined by a random matrix recording the action of Frobenius. Extensive numerical investigation reveals some cases of agreement with the heuristic and some int...
Extended power-law scaling of heavy-tailed random fields or processes
Directory of Open Access Journals (Sweden)
A. Guadagnini
2012-06-01
Full Text Available We analyze the scaling behaviors of two log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively. One set consists of 1-m scale pneumatic packer test data from six vertical and inclined boreholes spanning a decameters scale block of unsaturated fractured tuffs near Superior, Arizona, the other of pneumatic minipermeameter data measured at a spacing of 15 cm along two horizontal transects on a 21 m long outcrop of lower-shoreface bioturbated sandstone near Escalante, Utah. Order q sample structure functions of each data set scale as a power ξ (q of separation scale or lag, s, over limited ranges of s. A procedure known as Extended Self-Similarity (ESS extends this range to all lags and yields a nonlinear (concave functional relationship between ξ (q and q. Whereas the literature tends to associate extended and nonlinear power-law scaling with multifractals or fractional Laplace motions, we have shown elsewhere that (a ESS of data having a normal frequency distribution is theoretically consistent with (Gaussian truncated (additive, self-affine, monofractal fractional Brownian motion (tfBm, the latter being unique in predicting a breakdown in power-law scaling at small and large lags, and (b nonlinear power-law scaling of data having either normal or heavy-tailed frequency distributions is consistent with samples from sub-Gaussian random fields or processes subordinated to tfBm, stemming from lack of ergodicity which causes sample moments to scale differently than do their ensemble counterparts. Here we (i demonstrate that the above two data sets are consistent with sub-Gaussian random fields subordinated to tfBm and (ii provide maximum likelihood estimates of parameters characterizing the corresponding Lévy stable subordinators and tfBm functions.
Random Field Satisfying a Linear Partial Differential Equation with Random Forcing Term.
1984-01-01
physical approximation 12 may be taken equal to 1. For k = 0, the experimental spectral density function of the random fluctuations of the pressure in deep...fa e , tlpt 2 in R , and the power spectral density function is 1 0 y(v) - 27 2 2’ y I a +v Proof: In that case da = X 0dT and r(tl,t2) =- e , the...power spectral density function of the solution X is V R___ 1 __ 2 I The second order properties are the same for every Poisson, Gaussian, Levy centered
Efficient Incorporation of Markov Random Fields in Change Detection
DEFF Research Database (Denmark)
Aanæs, Henrik; Nielsen, Allan Aasbjerg; Carstensen, Jens Michael
2009-01-01
of noise, implying that the pixel-wise classifier is also noisy. There is thus a need for incorporating local homogeneity constraints into such a change detection framework. For this modelling task Markov Random Fields are suitable. Markov Random Fields have, however, previously been plagued by lack...
Random-field Ising model: Insight from zero-temperature simulations
Directory of Open Access Journals (Sweden)
P.E. Theodorakis
2014-12-01
Full Text Available We enlighten some critical aspects of the three-dimensional (d=3 random-field Ising model (RFIM from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian RFIM and an equal-weight trimodal RFIM. By implementing a computational approach that maps the ground-state of the system to the maximum-flow optimization problem of a network, we employ the most up-to-date version of the push-relabel algorithm and simulate large ensembles of disorder realizations of both models for a broad range of random-field values and systems sizes V=LxLxL, where L denotes linear lattice size and Lmax=156. Using as finite-size measures the sample-to-sample fluctuations of various quantities of physical and technical origin, and the primitive operations of the push-relabel algorithm, we propose, for both types of distributions, estimates of the critical field hmax and the critical exponent ν of the correlation length, the latter clearly suggesting that both models share the same universality class. Additional simulations of the Gaussian RFIM at the best-known value of the critical field provide the magnetic exponent ratio β/ν with high accuracy and clear out the controversial issue of the critical exponent α of the specific heat. Finally, we discuss the infinite-limit size extrapolation of energy- and order-parameter-based noise to signal ratios related to the self-averaging properties of the model, as well as the critical slowing down aspects of the algorithm.
Spectral representation of Gaussian semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2009-01-01
The aim of the present paper is to characterize the spectral representation of Gaussian semimartingales. That is, we provide necessary and sufficient conditions on the kernel K for X t =∫ K t (s) dN s to be a semimartingale. Here, N denotes an independently scattered Gaussian random measure...
Simulation of Random Fields with Non Multi-Gaussian Dependence Using Copulas
Directory of Open Access Journals (Sweden)
Vázquez-Guillén Felipe
2014-10-01
Full Text Available An approach to evaluate the confidence factor for structures at the end of an interval of time is proposed. The confidence factor indicates the adequacy of the performance level of a structure subjected to external loads. The factor considers the uncertainties implicit in the structural capacity and in the structural demand. The formulation is made in accordance with the Demand and Capacity Factor Design Format. Four scenarios are compared: a structural capacity deteriorates over a time interval, while structural demand remains constant, b only structural demand (for a given intensity varies in time, c both structural capacity and structural demand vary simultaneously in time, and d the effect of structural deterioration is neglected. The approach is applied to an offshore jacket platform. Deterioration is taken into account by analyzing the growth of fatigue cracks in both ends of several critical structural elements. It is concluded that for the evaluation of the confidence factor over an interval of interest, for the case analyzed, it is more significant to consider the variation in time of the structural capacity rather than that of the structural demand; however, it is recommended to consider both (structural capacity and structural demand in the analysis.
Hunziker, Jürg; Laloy, Eric; Linde, Niklas
2016-04-01
Deterministic inversion procedures can often explain field data, but they only deliver one final subsurface model that depends on the initial model and regularization constraints. This leads to poor insights about the uncertainties associated with the inferred model properties. In contrast, probabilistic inversions can provide an ensemble of model realizations that accurately span the range of possible models that honor the available calibration data and prior information allowing a quantitative description of model uncertainties. We reconsider the problem of inferring the dielectric permittivity (directly related to radar velocity) structure of the subsurface by inversion of first-arrival travel times from crosshole ground penetrating radar (GPR) measurements. We rely on the DREAM_(ZS) algorithm that is a state-of-the-art Markov chain Monte Carlo (MCMC) algorithm. Such algorithms need several orders of magnitude more forward simulations than deterministic algorithms and often become infeasible in high parameter dimensions. To enable high-resolution imaging with MCMC, we use a recently proposed dimensionality reduction approach that allows reproducing 2D multi-Gaussian fields with far fewer parameters than a classical grid discretization. We consider herein a dimensionality reduction from 5000 to 257 unknowns. The first 250 parameters correspond to a spectral representation of random and uncorrelated spatial fluctuations while the remaining seven geostatistical parameters are (1) the standard deviation of the data error, (2) the mean and (3) the variance of the relative electric permittivity, (4) the integral scale along the major axis of anisotropy, (5) the anisotropy angle, (6) the ratio of the integral scale along the minor axis of anisotropy to the integral scale along the major axis of anisotropy and (7) the shape parameter of the Matérn function. The latter essentially defines the type of covariance function (e.g., exponential, Whittle, Gaussian). We present
Random field distributed Heisenberg model on a thin film geometry
Energy Technology Data Exchange (ETDEWEB)
Akıncı, Ümit, E-mail: umit.akinci@deu.edu.tr
2014-11-15
The effects of the bimodal random field distribution on the thermal and magnetic properties of the Heisenberg thin film have been investigated by making use of a two spin cluster with the decoupling approximation. Particular attention has been devoted to the obtaining of phase diagrams and magnetization behaviors. The physical behaviors of special as well as tricritical points are discussed for a wide range of selected Hamiltonian parameters. For example, it is found that when the strength of a magnetic field increases, the locations of the special point (which is the ratio of the surface exchange interaction and the exchange interaction of the inner layers that makes the critical temperature of the film independent of the thickness) in the related plane decrease. Moreover, tricritical behavior has been obtained for higher values of the magnetic field, and influences of the varying Hamiltonian parameters on its behavior have been elucidated in detail in order to have a better understanding of the mechanism underlying the considered system. - Highlights: • Effect of bimodal random field distribution within the Heisenberg model is investigated. • Phase diagrams of the random field Heisenberg model in a thin film geometry are obtained. • Effect of the random field on the magnetic properties is obtained. • Variation of the special point with random field is determined. • Variation of the tricritical point with random field is determined.
Positive random fields for modeling material stiffness and compliance
DEFF Research Database (Denmark)
Hasofer, Abraham Michael; Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1998-01-01
Positive random fields with known marginal properties and known correlation function are not numerous in the literature. The most prominent example is the log\\-normal field for which the complete distribution is known and for which the reciprocal field is also lognormal. It is of interest to supp...
Energy Technology Data Exchange (ETDEWEB)
Behbahani, Siavosh R.; /SLAC /Stanford U., Phys. Dept. /Boston U.; Dymarsky, Anatoly; /Princeton, Inst. Advanced Study; Mirbabayi, Mehrdad; /New York U., CCPP /New York U.; Senatore, Leonardo; /Stanford U., Phys. Dept. /KIPAC, Menlo Park
2012-06-06
We apply the Effective Field Theory of Inflation to study the case where the continuous shift symmetry of the Goldstone boson {pi} is softly broken to a discrete subgroup. This case includes and generalizes recently proposed String Theory inspired models of Inflation based on Axion Monodromy. The models we study have the property that the 2-point function oscillates as a function of the wavenumber, leading to oscillations in the CMB power spectrum. The non-linear realization of time diffeomorphisms induces some self-interactions for the Goldstone boson that lead to a peculiar non-Gaussianity whose shape oscillates as a function of the wavenumber. We find that in the regime of validity of the effective theory, the oscillatory signal contained in the n-point correlation functions, with n > 2, is smaller than the one contained in the 2-point function, implying that the signature of oscillations, if ever detected, will be easier to find first in the 2-point function, and only then in the higher order correlation functions. Still the signal contained in higher-order correlation functions, that we study here in generality, could be detected at a subleading level, providing a very compelling consistency check for an approximate discrete shift symmetry being realized during inflation.
Ferreira, P G; Ferreira, Pedro G.; Magueijo, Joao
1997-01-01
Gaussian cosmic microwave background skies are fully specified by the power spectrum. The conventional method of characterizing non-Gaussian skies is to evaluate higher order moments, the n-point functions and their Fourier transforms. We argue that this method is inefficient, due to the redundancy of information existing in the complete set of moments. In this paper we propose a set of new statistics or non-Gaussian spectra to be extracted out of the angular distribution of the Fourier transform of the temperature anisotropies in the small field limit. These statistics complement the power spectrum and act as localization, shape, and connectedness statistics. They quantify generic non-Gaussian structure, and may be used in more general image processing tasks. We concentrate on a subset of these statistics and argue that while they carry no information in Gaussian theories they may be the best arena for making predictions in some non-Gaussian theories. As examples of applications we consider superposed Gaussi...
Hidden Conditional Random Fields for Action Recognition
Chen, L.; van der Aa, N.P.; Tan, R.T.; Veltkamp, R.C.
2014-01-01
In the field of action recognition, the design of features has been explored extensively, but the choice of action classification methods is limited. Commonly used classification methods like k-Nearest Neighbors and Support Vector Machines assume conditional independency between features. In contras
Institute of Scientific and Technical Information of China (English)
Zheng Ping; Gao Wei-Jian; Yin Jian-Ping
2006-01-01
We investigate the diffraction characteristics of an incident Gaussian beam cut by a straight edge bounding a semi-infinite opaque plane using Kirchhoff scalar wave theory in the Fresnel limit, and propose a new and simple mirror scheme to reflect atoms by using the intensity gradient induced by a blue-detuned semi-Gaussian laser beam. The optical potential of the diffracted light of the knife-cut semi-Gaussian beam for 85Rb atom and its spontaneous emission probability are calculated and compared with the performance of the evanescent-wave mirror. Our study shows that the optical potential of the diffracted light of the semi-Gaussian beam is far higher than that of the evanescent light wave, and the maximum normal velocity of the incident atoms can be far greater than that of the evanescent light wave under the same parameters, so the blue-detuned semi-Gaussian beam, as a novel atomic mirror, can be used to efficiently reflect cold atoms with a normal velocity of greater than 1 m/s. However, the intensity gradient (force) of the diffracted light of the semi-Gaussian-beam is much smaller than that of the evanescent light wave, so its spontaneous emission probability is greater than that from the evanescent-wave when the normal velocity of incident atoms is greater.
A hybrid random field model for scalable statistical learning.
Freno, A; Trentin, E; Gori, M
2009-01-01
This paper introduces hybrid random fields, which are a class of probabilistic graphical models aimed at allowing for efficient structure learning in high-dimensional domains. Hybrid random fields, along with the learning algorithm we develop for them, are especially useful as a pseudo-likelihood estimation technique (rather than a technique for estimating strict joint probability distributions). In order to assess the generality of the proposed model, we prove that the class of pseudo-likelihood distributions representable by hybrid random fields strictly includes the class of joint probability distributions representable by Bayesian networks. Once we establish this result, we develop a scalable algorithm for learning the structure of hybrid random fields, which we call 'Markov Blanket Merging'. On the one hand, we characterize some complexity properties of Markov Blanket Merging both from a theoretical and from the experimental point of view, using a series of synthetic benchmarks. On the other hand, we evaluate the accuracy of hybrid random fields (as learned via Markov Blanket Merging) by comparing them to various alternative statistical models in a number of pattern classification and link-prediction applications. As the results show, learning hybrid random fields by the Markov Blanket Merging algorithm not only reduces significantly the computational cost of structure learning with respect to several considered alternatives, but it also leads to models that are highly accurate as compared to the alternative ones.
Avendaño-Valencia, Luis David; Fassois, Spilios D.
2017-07-01
The study focuses on vibration response based health monitoring for an operating wind turbine, which features time-dependent dynamics under environmental and operational uncertainty. A Gaussian Mixture Model Random Coefficient (GMM-RC) model based Structural Health Monitoring framework postulated in a companion paper is adopted and assessed. The assessment is based on vibration response signals obtained from a simulated offshore 5 MW wind turbine. The non-stationarity in the vibration signals originates from the continually evolving, due to blade rotation, inertial properties, as well as the wind characteristics, while uncertainty is introduced by random variations of the wind speed within the range of 10-20 m/s. Monte Carlo simulations are performed using six distinct structural states, including the healthy state and five types of damage/fault in the tower, the blades, and the transmission, with each one of them characterized by four distinct levels. Random vibration response modeling and damage diagnosis are illustrated, along with pertinent comparisons with state-of-the-art diagnosis methods. The results demonstrate consistently good performance of the GMM-RC model based framework, offering significant performance improvements over state-of-the-art methods. Most damage types and levels are shown to be properly diagnosed using a single vibration sensor.
Ismail, G.; Bannora, K.; Hassan, S.
2004-12-01
A one-dimensional system of six coupled random field Ising spins is studied by Glauber dynamics. The nearest-neighbour and next-nearest-neighbour interactions are taken into consideration. Two distributions of random fields (RF) - binary and Gaussian distribution - are investigated. We consider four cases of exchange couplings: ferro-ferromagnetic (F-F), ferro-antiferromagnetic (F-AF), antiferro-ferromagnetic (AF-F) and antiferro-antiferromagnetic (AF-AF). The system is fully frustrated, undergoes a zero-temperature phase transition and has multiple local energy minima in both distributions. The dynamics of the four systems are solved exactly in both distributions of RF. The effects of random fields are discussed. The number of diverging relaxation times is equal to the number of energy minima minus one. The longest relaxation times verify the Arrhenius law with energy barrier determined by the energy needed to invert the ground-state spin configuration. At low temperatures, according to the Arrhenius law, the spectrum of relaxation times shows a double-peak distribution on a logarithmic scale. In the Gaussian distribution of RF the energy-barrier distribution is continuous while it is quasi-discrete in the binary distribution.
Chaudret, Robin; Gresh, Nohad; Narth, Christophe; Lagardère, Louis; Darden, Thomas A; Cisneros, G Andrés; Piquemal, Jean-Philip
2014-09-04
We demonstrate as a proof of principle the capabilities of a novel hybrid MM'/MM polarizable force field to integrate short-range quantum effects in molecular mechanics (MM) through the use of Gaussian electrostatics. This lead to a further gain in accuracy in the representation of the first coordination shell of metal ions. It uses advanced electrostatics and couples two point dipole polarizable force fields, namely, the Gaussian electrostatic model (GEM), a model based on density fitting, which uses fitted electronic densities to evaluate nonbonded interactions, and SIBFA (sum of interactions between fragments ab initio computed), which resorts to distributed multipoles. To understand the benefits of the use of Gaussian electrostatics, we evaluate first the accuracy of GEM, which is a pure density-based Gaussian electrostatics model on a test Ca(II)-H2O complex. GEM is shown to further improve the agreement of MM polarization with ab initio reference results. Indeed, GEM introduces nonclassical effects by modeling the short-range quantum behavior of electric fields and therefore enables a straightforward (and selective) inclusion of the sole overlap-dependent exchange-polarization repulsive contribution by means of a Gaussian damping function acting on the GEM fields. The S/G-1 scheme is then introduced. Upon limiting the use of Gaussian electrostatics to metal centers only, it is shown to be able to capture the dominant quantum effects at play on the metal coordination sphere. S/G-1 is able to accurately reproduce ab initio total interaction energies within closed-shell metal complexes regarding each individual contribution including the separate contributions of induction, polarization, and charge-transfer. Applications of the method are provided for various systems including the HIV-1 NCp7-Zn(II) metalloprotein. S/G-1 is then extended to heavy metal complexes. Tested on Hg(II) water complexes, S/G-1 is shown to accurately model polarization up to quadrupolar
Properties and simulation of α-permanental random fields
DEFF Research Database (Denmark)
Møller, Jesper; Rubak, Ege Holger
An α-permanental random field is briefly speaking a model for a collection of random variables with positive associations, where α is a positive number and the probability generating function is given in terms of a covariance or more general function so that density and moment expressions are given...... by certain α-permanents. Though such models possess many appealing probabilistic properties, many statisticians seem unaware of α-permanental random fields and their potential applications. The purpose of this paper is first to summarize useful probabilistic results using the simplest possible setting...
Anomalous transport in fluid field with random waiting time depending on the preceding jump length
Zhang, Hong; Li, Guo-Hua
2016-11-01
Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. Project supported by the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414) and the Opening Foundation of Geomathematics Key Laboratory of Sichuan Province, China (Grant No. scsxdz2013009).
Laguerre Gaussian beam multiplexing through turbulence
CSIR Research Space (South Africa)
Trichili, A
2014-08-17
Full Text Available We analyze the effect of atmospheric turbulence on the propagation of multiplexed Laguerre Gaussian modes. We present a method to multiplex Laguerre Gaussian modes using digital holograms and decompose the resulting field after encountering a...
Shape Modelling Using Markov Random Field Restoration of Point Correspondences
DEFF Research Database (Denmark)
Paulsen, Rasmus Reinhold; Hilger, Klaus Baggesen
2003-01-01
A method for building statistical point distribution models is proposed. The novelty in this paper is the adaption of Markov random field regularization of the correspondence field over the set of shapes. The new approach leads to a generative model that produces highly homogeneous polygonized sh...
Parameter estimation of hidden periodic model in random fields
Institute of Scientific and Technical Information of China (English)
何书元
1999-01-01
Two-dimensional hidden periodic model is an important model in random fields. The model is used in the field of two-dimensional signal processing, prediction and spectral analysis. A method of estimating the parameters for the model is designed. The strong consistency of the estimators is proved.
Aging in the two-dimensional random-field systems
Cheng, Xiang; Ma, Tianyu; Urazhdin, Sergei; Boettcher, Stefan
Random fields introduced into the classical Ising and Heisenberg spin models can roughen the energy landscape, leading to complex nonequilibrium dynamics. The effects of random fields on magnetism have been previously studied in the context of dilute antiferromagnets (AF), impure substrates, and magnetic alloys [ 1 ] . We utilized random-field spin models to simulate the observed magnetic aging in thin-film ferromagnet/antiferromagnet (F/AF) bilayers. Our experiments show extremely slow cooperative relaxation over a wide range of temperatures and magnetic fields [ 2 ] . In our simulations, the experimental system is coarse-grained into a random field Ising model on a 2D square lattice. Monte Carlo simulations indicate that aging processes may be associated with the glassy evolution of the magnetic domain walls, due to the pinning by the random fields. The scaling of the simulated aging agrees well with experiments. Both are consistent with either a small power-law or logarithmic dependence on time. We further discuss the topological effects on aging due to the dimensional crossover from the Ising to the Heisenberg regime. Supported through NSF grant DMR-1207431.
Institute of Scientific and Technical Information of China (English)
Zhu Kai-Cheng; Li Shao-Xin; Tang Ying; Zheng Xiao-Juan; Tang Hui-Qin
2012-01-01
A new kind of quantum non-Gaussian state with a vortex structure,termed a Bessel-Gaussian vortex state,is constructed,which is an eigenstate of the sum of squared annihilation operators a2 + b2.The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality.It is also found that a quantized vortex state is always in entanglement.And a scheme for generating such quantized vortex states is proposed.
Field-theoretic simulations of random copolymers with structural rigidity.
Mao, Shifan; MacPherson, Quinn; Qin, Jian; Spakowitz, Andrew J
2017-04-12
Copolymers play an important role in a range of soft-materials applications and biological phenomena. Prevalent works on block copolymer phase behavior use flexible chain models and incorporate interactions using a mean-field approximation. However, when phase separation takes place on length scales comparable to a few monomers, the structural rigidity of the monomers becomes important. In addition, concentration fluctuations become significant at short length scales, rendering the mean-field approximation invalid. In this work, we use simulation to address the role of finite monomer rigidity and concentration fluctuations in microphase segregation of random copolymers. Using a field-theoretic Monte-Carlo simulation of semiflexible polymers with random chemical sequences, we generate phase diagrams for random copolymers. We find that the melt morphology of random copolymers strongly depends on chain flexibility and chemical sequence correlation. Chemically anti-correlated copolymers undergo first-order phase transitions to local lamellar structures. With increasing degree of chemical correlation, this first-order phase transition is softened, and melts form microphases with irregular shaped domains. Our simulations in the homogeneous phase exhibit agreement with the density-density correlation from mean-field theory. However, conditions near a phase transition result in deviations between simulation and mean-field theory for the density-density correlation and the critical wavemode. Chain rigidity and sequence randomness lead to frustration in the segregated phase, introducing heterogeneity in the resulting morphologies.
Shandarin, S F; Xu, Y; Tegmark, M; Shandarin, Sergei F.; Feldman, Hume A.; Xu, Yongzhong; Tegmark, Max
2001-01-01
We test degree-scale cosmic microwave background (CMB) anisotropy for Gaussianity by studying the \\qmask map that was obtained from combining the QMAP and Saskatoon data. We compute seven morphological functions $M_i(\\dt)$, $i=1,...,7$: six \\mf and the number of regions $N_c$ at a hundred $\\dt$ levels. We also introduce a new parameterization of the morphological functions $M_i(A)$ in terms of the total area $A$ of the excursion set. We show that the latter considerably decorrelates the morphological statistics. We compare these results with those from 1000 Gaussian Monte Carlo maps with the same power spectrum, and conclude that the \\qmask map is neither a very typical nor a very exceptional realization of a Gaussian field. Roughly 20% of the 1000 Gaussian Monte Carlo maps differ more than the \\qmask map from the mean morphological parameters of the Gaussian fields.
Institute of Scientific and Technical Information of China (English)
罗俊杰; 苏成; 韩大建
2012-01-01
Simulation of stochastic fluctuating wind pressure field acting on roofs should meet the requirements of identity in statistical and spectral characteristics. The zero memory nonlinearity (ZMNL) transformation method was presented to generate the time histories of stochastic wind pressure. A detailed simulation procedure was provided, and two crucial problems were addressed. First, the standard covariance function for transforming multivariate non-Gaussian stochastic process vector into the corresponding Gaussian one was derived for simulating the stochastic wind pressure process following the lognormal distribution and the Weibull distribution. Second, a new method was proposed to cope with the problem of negative definite matrices of spectral density function appearing at certain frequencies while generating the Gaussian stochastic process vector. An illustrating example was given. It is shown that the proposed method can generate stochastic wind pressure field samples with the same specified statistical and spectral natures of the data obtained by wind tunnel experiment.%针对作用于屋盖结构随机风压场样本的统计特性要求,基于零记忆非线性转化法的理论,给出随机风压场的具体模拟过程.其中,解决了两个关键问题:①推导了服从对数正态分布和韦布尔分布的多点非高斯随机过程向量的标准化协方差,与相应高斯随机过程向量的标准化协方差的函数转化关系；②提出了分解谱密度函数修正法,解决利用谐波合成法模拟多点高斯随机过程向量时,功率谱密度函数矩阵在某些频率点出现负定的问题.经过具体算例表明,所提出的方法能生成合乎风洞实验数据统计特性要求的随机风压场样本.
Chialvo, Ariel A; Moucka, Filip; Vlcek, Lukas; Nezbeda, Ivo
2015-04-16
We developed the Gaussian charge-on-spring (GCOS) version of the original self-consistent field implementation of the Gaussian Charge Polarizable water model and test its accuracy to represent the polarization behavior of the original model involving smeared charges and induced dipole moments. For that purpose we adapted the recently proposed multiple-particle-move (MPM) within the Gibbs and isochoric-isothermal ensembles Monte Carlo methods for the efficient simulation of polarizable fluids. We assessed the accuracy of the GCOS representation by a direct comparison of the resulting vapor-liquid phase envelope, microstructure, and relevant microscopic descriptors of water polarization along the orthobaric curve against the corresponding quantities from the actual GCP water model.
Stochastic geometry, spatial statistics and random fields models and algorithms
2015-01-01
Providing a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, this volume places a special emphasis on fundamental classes of models and algorithms as well as on their applications, for example in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R, which are widely used in the mathematical community. It can be regarded as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered, with a focus on asymptotic methods.
Creep motion in a random-field Ising model.
Roters, L; Lübeck, S; Usadel, K D
2001-02-01
We analyze numerically a moving interface in the random-field Ising model which is driven by a magnetic field. Without thermal fluctuations the system displays a depinning phase transition, i.e., the interface is pinned below a certain critical value of the driving field. For finite temperatures the interface moves even for driving fields below the critical value. In this so-called creep regime the dependence of the interface velocity on the temperature is expected to obey an Arrhenius law. We investigate the details of this Arrhenius behavior in two and three dimensions and compare our results with predictions obtained from renormalization group approaches.
Horner, Jonathan S
2013-01-01
The Hamilton-Jacobi (HJ) approach for exploring inflationary trajectories is employed in the generation of generalised inflationary non-Gaussian signals arising from single field inflation. Scale dependent solutions for $f_{NL}$ are determined via the numerical integration of the three--point function in the curvature perturbation. This allows the full exploration of single field inflationary dynamics in the out-of-slow-roll regime and opens up the possibility of using future observations of non-Gaussianity to constraint the inflationary potential using model-independent methods. The distribution of `equilateral' $f_{NL}$ arising from single field inflation with both canonical and non-canonical kinetic terms are show as an example of the application of this procedure.
Generating Functionals for Quantum Field Theories with Random Potentials
Jain, Mudit
2015-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in context of the string theory landscape (e.g. cosmic inflation). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out ...
Energy Technology Data Exchange (ETDEWEB)
Zimbardo, G.
2005-07-01
Plasma transport in the presence of turbulence depends on a variety of parameters like the fluctuation level ? B/B0, the ratio between the particle Larmor radius and the turbulence correlation lengths, and the turbulence anisotropy. In this presentation, we review the results of numerical simulations of plasma and magnetic field line transport in the case of anisotropic magnetic turbulence, for parameter values close to those of the solar wind. We assume a uniform background magnetic field B0 = B0ez and a Fourier representation for magnetic fluctuations, with wavectors forming any angle with respect to B0. The energy density spectrum is a power law, and in k space the constant amplitude surfaces are ellipsoids, described by the correlation lengths lx, ly, lz, which quantify the anisotropy of turbulence. For magnetic field lines, we find that transport perpendicular to the background field depends on the Kubo number R = ? B B0 lz lx . For small Kubo numbers, R ? 1, we find anomalous, non Gaussian transport regimes (both sub and superdiffusive) which can be described as a Levy random walk. Increasing the Kubo number, i.e., the fluctuation level ? B/B0 and/or the ratio lz/lx, we find first a quasilinear and then a percolative regime, both corresponding to Gaussian diffusion. For particles, we find that transport parallel and perpendicular to the background magnetic field heavily depends on the turbulence anisotropy and on the particle Larmor radius. For turbulence levels typical of the solar wind, ? B/B0 ? 0.5 ?1, when the ratio between the particle Larmor radius and the turbulence correlation lengths is small, anomalous regimes are found in the case lz/lx ? 1, with Levy random walk (superdiffusion) along the magnetic field and subdiffusion in the perpendicular directions. Conversely, for lz/lx > 1 normal, Gaussian diffusion is found. Increasing the ratio between the particle Larmor radius and the turbulence correlation lengths, the parallel superdiffusion is
Magnetic properties of mixed Ising system with random field
Institute of Scientific and Technical Information of China (English)
Liang Ya-Qiu; Wei Guo-Zhu; Zhang Qi; Qiu Wei; Zang Shu-Liang
2004-01-01
A spin-1/2 and spin-3/2 mixed Ising system in a random field is studied by the use of effective-field theory with correlations. The phase diagrams and thermal behaviours of magnetizations are investigated numerically for the honeycomb lattice (z=3) and square lattice (z=4) respectively. The tricritical behaviours for both honeycomb and square lattices, as well as the reentrant behaviour for the square lattice are found.
Closed form maximum likelihood estimator of conditional random fields
Zhu, Zhemin; Hiemstra, Djoerd; Apers, Peter M.G.; Wombacher, Andreas
2013-01-01
Training Conditional Random Fields (CRFs) can be very slow for big data. In this paper, we present a new training method for CRFs called {\\em Empirical Training} which is motivated by the concept of co-occurrence rate. We show that the standard training (unregularized) can have many maximum likeliho
Infinite conditional random fields for human behavior analysis
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja
2013-01-01
Hidden conditional random fields (HCRFs) are discriminative latent variable models that have been shown to successfully learn the hidden structure of a given classification problem (provided an appropriate validation of the number of hidden states). In this brief, we present the infinite HCRF (iHCRF
Variational Hidden Conditional Random Fields with Coupled Dirichlet Process Mixtures
Bousmalis, K.; Zafeiriou, S.; Morency, L.P.; Pantic, Maja; Ghahramani, Z.
2013-01-01
Hidden Conditional Random Fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An infinite HCRF is an HCRF with a countably infinite number of hidden states, which rids us not only of the necessit
Anisotropic Fractional Brownian Random Fields as White Noise Functionals
Institute of Scientific and Technical Information of China (English)
Zhi-yuan Huang; Chu-jin Li
2005-01-01
This investigation aims at a new construction of anisotropic fractional Brownisn random fields by the white noise approach. Moreover, we investigate its distribution and sample properties (stationariness of increments, self-similarity, sample continuity) which will furnish some useful views to future applications.
Nonstationary random acoustic and electromagnetic fields as wave diffusion processes
Arnaut, L R
2007-01-01
We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as an ideal incoherent and statistically homogeneous isotropic random scalar or vector field, respectively. A physical model is constructed showing that the field dynamics can be characterized as a generalized diffusion process. The Langevin--It\\^{o} and Fokker--Planck equations are derived and their associated statistics and distributions for the complex analytic field, its magnitude and energy density are computed. The energy diffusion parameter is found to be proportional to the square of the ratio of the standard deviation of the source field to the characteristic time constant of the dynamic process, but is independent of the initial energy density, to first order. The energy drift vanishes in the asymptotic limit. The time-energy probability distribution is in general n...
Driving a Superconductor to Insulator Transition with Random Gauge Fields
Nguyen, H. Q.; Hollen, S. M.; Shainline, J.; Xu, J. M.; Valles, J. M.
2016-11-01
Typically the disorder that alters the interference of particle waves to produce Anderson localization is potential scattering from randomly placed impurities. Here we show that disorder in the form of random gauge fields that act directly on particle phases can also drive localization. We present evidence of a superfluid bose glass to insulator transition at a critical level of this gauge field disorder in a nano-patterned array of amorphous Bi islands. This transition shows signs of metallic transport near the critical point characterized by a resistance , indicative of a quantum phase transition. The critical disorder depends on interisland coupling in agreement with recent Quantum Monte Carlo simulations. We discuss how this disorder tuned SIT differs from the common frustration tuned SIT that also occurs in magnetic fields. Its discovery enables new high fidelity comparisons between theoretical and experimental studies of disorder effects on quantum critical systems.
Cosmological fluctuations of a random field and radiation fluid
Energy Technology Data Exchange (ETDEWEB)
Bastero-Gil, Mar [Departamento de Física Teórica y del Cosmos, Campus de Fuentenueva, Universidad de Granada, Granada, 18071 (Spain); Berera, Arjun [SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3JZ (United Kingdom); Moss, Ian G. [School of Mathematics and Statistics, Newcastlle University, Newcastle upon Tyne, NE1 7RU (United Kingdom); Ramos, Rudnei O., E-mail: mbg@ugr.es, E-mail: ab@ph.ed.ac.uk, E-mail: ian.moss@ncl.ac.uk, E-mail: rudnei@uerj.br [Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ, 20550-013 Brazil (Brazil)
2014-05-01
A generalization of the random fluid hydrodynamic fluctuation theory due to Landau and Lifshitz is applied to describe cosmological fluctuations in systems with radiation and scalar fields. The viscous pressures, parametrized in terms of the bulk and shear viscosity coefficients, and the respective random fluctuations in the radiation fluid are combined with the stochastic and dissipative scalar evolution equation. This results in a complete set of equations describing the perturbations in both scalar and radiation fluids. These derived equations are then studied, as an example, in the context of warm inflation. Similar treatments can be done for other cosmological early universe scenarios involving thermal or statistical fluctuations.
Segmentation of RGB-D indoor scenes by stacking random forests and conditional random fields
DEFF Research Database (Denmark)
Thøgersen, Mikkel; Guerrero, Sergio Escalera; Gonzàlez, Jordi
2016-01-01
on stacked classifiers; the benefits are two fold: on one hand, the system scales well to consider different types of complex features and, on the other hand, the use of stacked classifiers makes the performance of the proposed technique more accurate. The proposed method consists of a random forest using...... a stacked random forest which gives the final predictions. The model is tested on the renown NYU-v2 dataset and the recently available SUNRGBD dataset. The approach shows that simple multimodal features with the power of using multi-class multi-scale stacked sequential learners (MMSSL) can achieve slight...... random offset features in combination with a conditional random field (CRF) acting on a simple linear iterative clustering (SLIC) superpixel segmentation. The predictions of the CRF are filtered spatially by a multi-scale decomposition before merging it with the original feature set and applying...
Quintin, Jerome; Sherkatghanad, Zeinab; Cai, Yi-Fu; Brandenberger, Robert H.
2015-09-01
Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the nontrivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter fNL (which is of order unity before the bounce phase) is enhanced during the bounce phase if the curvature fluctuations grow. Hence, in such nonsingular bounce models with matter given by a single scalar field, there appears to be a tension between obtaining a small enough tensor-to-scalar ratio and not obtaining a value of fNL in excess of the current upper bounds. This conclusion may be considered as a "no-go" theorem that rules out any single field matter bounce cosmology starting with vacuum initial conditions for the fluctuations.
基于谱修正方法的非高斯风场模拟%Non-Gaussian Wind Field Simulation Based on Spectral Correction Method
Institute of Scientific and Technical Information of China (English)
孙芳锦; 张爱社
2012-01-01
To overcome disadvantages of Hermite-based spectral correction method, and to eliminate large consumption of the simulation due to computing coefficients of Hermite polynomial, a new method for simulating non-Gaussian wind field is proposed. Non-Gaussian cumulative distribution function (CDF) is employed to replace Hermit-based probability density function correction. Selecting arbitrary marginal PDF model as probability target model, and targeting power spectral density as sample function, the sample function is converged to the target probability density function and power spectral density through iteration correction. The method is applied to simulate non-Gaussian wind field of a real-life structure. The results compare well with the target spectrum. The method proposed here has fairly high accuracy and efficiency.%为克服基于Hermite谱修正方法的缺点,减少该方法中计算Hermite多项式系数所需耗费的大量机时,提出了一种模拟非高斯风压场的新方法,采用非高斯7积分布函数(CDF)映射技术来代替基于Hermite的概率密度函数(PDF)修正.选择任意边缘PDF模型作为概率目标模型,采用目标功率谱密度(PSD)作为样本函数,通过迭代修正该样本函数,使其收敛于目标概率密度函数和目标功率谱密度.将该方法应用于实际结构的非高斯风场模拟,模拟结果与目标谱符合良好,表明本文方法模拟非高斯风场具有较高的精确度和计算效率.
Liu, Xin; Zou, LiLi; Liu, Chenglin; Zhang, Zhi-Hai; Yuan, Jian-Hui
2016-03-01
In the present work, the effects of hydrostatic pressure, temperature, and magnetic field on the nonlinear optical rectification (OR) and second-harmonic generation (SHG) in asymmetrical Gaussian potential quantum well (QW) have been investigated theoretically. Here, the expressions for the optical properties are calculated by the compact-density-matrix approach and iterative method. Simultaneously, the energy eigenvalues and their corresponding eigenfunctions have been obtained by using the finite difference method. The energy eigenvalues and the shape of the confined potential are modulated by the hydrostatic pressure, temperature, and magnetic field. So the results of a number of numerical experiments indicate that the nonlinear OR and SHG strongly depends on the hydrostatic pressure, temperature, and magnetic field. This gives a new degree of freedom in various device applications based on the intersubband transitions of electrons.
Conditional random field-based gesture recognition with depth information
Chung, Hyunsook; Yang, Hee-Deok
2013-01-01
Gesture recognition is useful for human-computer interaction. The difficulty of gesture recognition is that instances of gestures vary both in motion and shape in three-dimensional (3-D) space. We use depth information generated using Microsoft's Kinect in order to detect 3-D human body components and apply a threshold model with a conditional random field in order to recognize meaningful gestures using continuous motion information. Body gesture recognition is achieved through a framework consisting of two steps. First, a human subject is described by a set of features, encoding the angular relationship between body components in 3-D space. Second, a feature vector is recognized using a threshold model with a conditional random field. In order to show the performance of the proposed method, we use a public data set, the Microsoft Research Cambridge-12 Kinect gesture database. The experimental results demonstrate that the proposed method can efficiently and effectively recognize body gestures automatically.
Efficient approximation of random fields for numerical applications
Harbrecht, Helmut
2015-01-07
We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.
A Novel Microaneurysms Detection Method Based on Local Applying of Markov Random Field.
Ganjee, Razieh; Azmi, Reza; Moghadam, Mohsen Ebrahimi
2016-03-01
Diabetic Retinopathy (DR) is one of the most common complications of long-term diabetes. It is a progressive disease and by damaging retina, it finally results in blindness of patients. Since Microaneurysms (MAs) appear as a first sign of DR in retina, early detection of this lesion is an essential step in automatic detection of DR. In this paper, a new MAs detection method is presented. The proposed approach consists of two main steps. In the first step, the MA candidates are detected based on local applying of Markov random field model (MRF). In the second step, these candidate regions are categorized to identify the correct MAs using 23 features based on shape, intensity and Gaussian distribution of MAs intensity. The proposed method is evaluated on DIARETDB1 which is a standard and publicly available database in this field. Evaluation of the proposed method on this database resulted in the average sensitivity of 0.82 for a confidence level of 75 as a ground truth. The results show that our method is able to detect the low contrast MAs with the background while its performance is still comparable to other state of the art approaches.
Directory of Open Access Journals (Sweden)
A. Guadagnini
2012-09-01
Full Text Available We analyze the scaling behaviors of two field-scale log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively. One set consists of 1-m scale pneumatic packer test data from six vertical and inclined boreholes spanning a decameters scale block of unsaturated fractured tuffs near Superior, Arizona, the other of pneumatic minipermeameter data measured at a spacing of 15 cm along three horizontal transects on a 21 m long and 6 m high outcrop of the Upper Cretaceous Straight Cliffs Formation, including lower-shoreface bioturbated and cross-bedded sandstone near Escalante, Utah. Order q sample structure functions of each data set scale as a power ξ(q of separation scale or lag, s, over limited ranges of s. A procedure known as extended self-similarity (ESS extends this range to all lags and yields a nonlinear (concave functional relationship between ξ(q and q. Whereas the literature tends to associate extended and nonlinear power-law scaling with multifractals or fractional Laplace motions, we have shown elsewhere that (a ESS of data having a normal frequency distribution is theoretically consistent with (Gaussian truncated (additive, self-affine, monofractal fractional Brownian motion (tfBm, the latter being unique in predicting a breakdown in power-law scaling at small and large lags, and (b nonlinear power-law scaling of data having either normal or heavy-tailed frequency distributions is consistent with samples from sub-Gaussian random fields or processes subordinated to tfBm or truncated fractional Gaussian noise (tfGn, stemming from lack of ergodicity which causes sample moments to scale differently than do their ensemble counterparts. Here we (i demonstrate that the above two data sets are consistent with sub-Gaussian random fields subordinated to tfBm or tfGn and (ii provide maximum likelihood estimates of parameters characterizing the
Joint Conditional Random Field Filter for Multi-Object Tracking
Directory of Open Access Journals (Sweden)
Luo Ronghua
2011-03-01
Full Text Available Object tracking can improve the performance of mobile robot especially in populated dynamic environments. A novel joint conditional random field Filter (JCRFF based on conditional random field with hierarchical structure is proposed for multi-object tracking by abstracting the data associations between objects and measurements to be a sequence of labels. Since the conditional random field makes no assumptions about the dependency structure between the observations and it allows non-local dependencies between the state and the observations, the proposed method can not only fuse multiple cues including shape information and motion information to improve the stability of tracking, but also integrate moving object detection and object tracking quite well. At the same time, implementation of multi-object tracking based on JCRFF with measurements from the laser range finder on a mobile robot is studied. Experimental results with the mobile robot developed in our lab show that the proposed method has higher precision and better stability than joint probabilities data association filter (JPDAF.
Visibility graphs of random scalar fields and spatial data
Lacasa, Lucas; Iacovacci, Jacopo
2017-07-01
We extend the family of visibility algorithms to map scalar fields of arbitrary dimension into graphs, enabling the analysis of spatially extended data structures as networks. We introduce several possible extensions and provide analytical results on the topological properties of the graphs associated to different types of real-valued matrices, which can be understood as the high and low disorder limits of real-valued scalar fields. In particular, we find a closed expression for the degree distribution of these graphs associated to uncorrelated random fields of generic dimension. This result holds independently of the field's marginal distribution and it directly yields a statistical randomness test, applicable in any dimension. We showcase its usefulness by discriminating spatial snapshots of two-dimensional white noise from snapshots of a two-dimensional lattice of diffusively coupled chaotic maps, a system that generates high dimensional spatiotemporal chaos. The range of potential applications of this combinatorial framework includes image processing in engineering, the description of surface growth in material science, soft matter or medicine, and the characterization of potential energy surfaces in chemistry, disordered systems, and high energy physics. An illustration on the applicability of this method for the classification of the different stages involved in carcinogenesis is briefly discussed.
Energy Technology Data Exchange (ETDEWEB)
Zimbardo, Gaetano [Dipartimento di Fisica, Universita della Calabria, Ponte P. Bucci, Cubo 31C, I-87036 Arcavacata di Rende (Italy)
2005-12-15
Plasma transport in the presence of turbulence depends on a variety of parameters such as the fluctuation level, {delta}B/B{sub 0}, the ratio between the particle Larmor radius and the turbulence correlation length, and the turbulence anisotropy. In this paper, we present the results of numerical simulations of plasma and magnetic field line transport in the case of anisotropic magnetic turbulence, for parameter values close to those of the solar wind. We assume a uniform background magnetic field B{sub 0} = B{sub 0} e{sub z} and a Fourier representation for magnetic fluctuations, which includes wavectors oblique with respect to B{sub 0}. The energy density spectrum is a power law, and in k space it is described by the correlation lengths l{sub x}, l{sub y}, l{sub z}, which quantify the anisotropy of turbulence. For magnetic field lines, transport perpendicular to the background field depends on the Kubo number R ({delta}B/B{sub 0}) (l{sub z}/l{sub x}). For small Kubo numbers, R << 1, anomalous, non-Gaussian transport regimes (both sub- and superdiffusive) are found, which can be described as a Levy random walk. Increasing the Kubo number, i.e. the fluctuation level, {delta}B/B{sub 0}, or the ratio l{sub z}/l{sub x}, we find first a quasilinear regime and then a percolative regime, both corresponding to Gaussian diffusion. For particles, we find that transport parallel and perpendicular to the background magnetic field depends heavily on the turbulence anisotropy and on the particle Larmor radius. For turbulence levels typical of the solar wind, {delta}B/B{sub 0}{approx_equal} 0.5-1, when the ratio between the particle Larmor radius and the turbulence correlation lengths is small, anomalous regimes are found in the case l{sub z}/l{sub x} {<=} 1, with a Levy random walk (superdiffusion) along the magnetic field and subdiffusion in the perpendicular directions. Conversely, for l{sub z}/l{sub x} > 1 normal Gaussian diffusion is found. A possible expression for
Auñón, Juan Miguel; Nieto-Vesperinas, Manuel
2014-01-01
We present a theory and computation method of radiation pressure from partially coherent light by establishing a coherent mode representation of the radiation forces. This is illustrated with the near field emitted from a Gaussian Schell model source, mechanically acting on a single cylinder with magnetodielectric behavior, or on a photonic molecule constituted by a pair of such cylinders. Thus after studying the force produced by a single particle, we address the effects of the spatial coherence on the bonding and anti-bonding states of two particles. The coherence length manifests the critical limitation of the contribution of evanescent modes to the scattered fields, and hence to the nature and strength of the electromagnetic fores, even when electric and/or magnetic partial wave resonances are excited.
Al-Saidi, W A; Krakauer, Henry; Zhang, Shiwei
2007-05-21
The authors present phaseless auxiliary-field (AF) quantum Monte Carlo (QMC) calculations of the ground states of some hydrogen-bonded systems. These systems were selected to test and benchmark different aspects of the new phaseless AF QMC method. They include the transition state of H+H(2) near the equilibrium geometry and in the van der Walls limit, as well as the H(2)O, OH, and H(2)O(2) molecules. Most of these systems present significant challenges for traditional independent-particle electronic structure approaches, and many also have exact results available. The phaseless AF QMC method is used either with a plane wave basis with pseudopotentials or with all-electron Gaussian basis sets. For some systems, calculations are done with both to compare and characterize the performance of AF QMC under different basis sets and different Hubbard-Stratonovich decompositions. Excellent results are obtained using as input single Slater determinant wave functions taken from independent-particle calculations. Comparisons of the Gaussian based AF QMC results with exact full configuration interaction show that the errors from controlling the phase problem with the phaseless approximation are small. At the large basis-size limit, the AF QMC results using both types of basis sets are in good agreement with each other and with experimental values.
Automatic lung tumor segmentation on PET/CT images using fuzzy Markov random field model.
Guo, Yu; Feng, Yuanming; Sun, Jian; Zhang, Ning; Lin, Wang; Sa, Yu; Wang, Ping
2014-01-01
The combination of positron emission tomography (PET) and CT images provides complementary functional and anatomical information of human tissues and it has been used for better tumor volume definition of lung cancer. This paper proposed a robust method for automatic lung tumor segmentation on PET/CT images. The new method is based on fuzzy Markov random field (MRF) model. The combination of PET and CT image information is achieved by using a proper joint posterior probability distribution of observed features in the fuzzy MRF model which performs better than the commonly used Gaussian joint distribution. In this study, the PET and CT simulation images of 7 non-small cell lung cancer (NSCLC) patients were used to evaluate the proposed method. Tumor segmentations with the proposed method and manual method by an experienced radiation oncologist on the fused images were performed, respectively. Segmentation results obtained with the two methods were similar and Dice's similarity coefficient (DSC) was 0.85 ± 0.013. It has been shown that effective and automatic segmentations can be achieved with this method for lung tumors which locate near other organs with similar intensities in PET and CT images, such as when the tumors extend into chest wall or mediastinum.
Automatic Lung Tumor Segmentation on PET/CT Images Using Fuzzy Markov Random Field Model
Directory of Open Access Journals (Sweden)
Yu Guo
2014-01-01
Full Text Available The combination of positron emission tomography (PET and CT images provides complementary functional and anatomical information of human tissues and it has been used for better tumor volume definition of lung cancer. This paper proposed a robust method for automatic lung tumor segmentation on PET/CT images. The new method is based on fuzzy Markov random field (MRF model. The combination of PET and CT image information is achieved by using a proper joint posterior probability distribution of observed features in the fuzzy MRF model which performs better than the commonly used Gaussian joint distribution. In this study, the PET and CT simulation images of 7 non-small cell lung cancer (NSCLC patients were used to evaluate the proposed method. Tumor segmentations with the proposed method and manual method by an experienced radiation oncologist on the fused images were performed, respectively. Segmentation results obtained with the two methods were similar and Dice’s similarity coefficient (DSC was 0.85 ± 0.013. It has been shown that effective and automatic segmentations can be achieved with this method for lung tumors which locate near other organs with similar intensities in PET and CT images, such as when the tumors extend into chest wall or mediastinum.
Heterogeneous Memorized Continuous Time Random Walks in an External Force Fields
Wang, Jun; Zhou, Ji; Lv, Long-Jin; Qiu, Wei-Yuan; Ren, Fu-Yao
2014-09-01
In this paper, we study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated memorized waiting times, which involves Reimann-Liouville fractional derivative or Reimann-Liouville fractional integral. We show that the mean squared displacement of the test particle which is dependent on its location of the form (El-Wakil and Zahran, Chaos Solitons Fractals, 12, 1929-1935, 2001) where is the anomalous exponent, the diffusion exponent is dependent on the model parameters. We obtain the Fokker-Planck-type dynamic equations, and their stationary solutions are of the Boltzmann-Gibbs form. These processes obey a generalized Einstein-Stokes-Smoluchowski relation and the second Einstein relation. We observe that the asymptotic behavior of waiting times and subordinations are of stretched Gaussian distributions. We also discuss the time averaged in the case of an harmonic potential, and show that the process exhibits aging and ergodicity breaking.
Singular-potential random-matrix model arising in mean-field glassy systems.
Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo
2014-06-01
We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.
Language Recognition Using Latent Dynamic Conditional Random Field Model with Phonological Features
Directory of Open Access Journals (Sweden)
Sirinoot Boonsuk
2014-01-01
Full Text Available Spoken language recognition (SLR has been of increasing interest in multilingual speech recognition for identifying the languages of speech utterances. Most existing SLR approaches apply statistical modeling techniques with acoustic and phonotactic features. Among the popular approaches, the acoustic approach has become of greater interest than others because it does not require any prior language-specific knowledge. Previous research on the acoustic approach has shown less interest in applying linguistic knowledge; it was only used as supplementary features, while the current state-of-the-art system assumes independency among features. This paper proposes an SLR system based on the latent-dynamic conditional random field (LDCRF model using phonological features (PFs. We use PFs to represent acoustic characteristics and linguistic knowledge. The LDCRF model was employed to capture the dynamics of the PFs sequences for language classification. Baseline systems were conducted to evaluate the features and methods including Gaussian mixture model (GMM based systems using PFs, GMM using cepstral features, and the CRF model using PFs. Evaluated on the NIST LRE 2007 corpus, the proposed method showed an improvement over the baseline systems. Additionally, it showed comparable result with the acoustic system based on i-vector. This research demonstrates that utilizing PFs can enhance the performance.
Singular-potential random-matrix model arising in mean-field glassy systems
Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo
2014-06-01
We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.
Applications of random field theory to functional connectivity.
Worsley, K J; Cao, J; Paus, T; Petrides, M; Evans, A C
1998-01-01
Functional connectivity between two voxels or regions of voxels can be measured by the correlation between voxel measurements from either PET CBF or BOLD fMRI images in 3D. We propose to look at the entire 6D matrix of correlations between all voxels and search for 6D local maxima. The main result is a new theoretical formula based on random field theory for the p-value of these local maxima, which distinguishes true correlations from background noise. This can be applied to crosscorrelations between two different sets of images--such as activations under two different tasks, as well as autocorrelations within the same set of images.
Extremes in random fields a theory and its applications
Yakir, Benjamin
2013-01-01
Presents a useful new technique for analyzing the extreme-value behaviour of random fields Modern science typically involves the analysis of increasingly complex data. The extreme values that emerge in the statistical analysis of complex data are often of particular interest. This book focuses on the analytical approximations of the statistical significance of extreme values. Several relatively complex applications of the technique to problems that emerge in practical situations are presented. All the examples are difficult to analyze using classical methods, and as a result, the author pr
Markov random fields for static foreground classification in surveillance systems
Fitzsimons, Jack K.; Lu, Thomas T.
2014-09-01
We present a novel technique for classifying static foreground in automated airport surveillance systems between abandoned and removed objects by representing the image as a Markov Random Field. The proposed algorithm computes and compares the net probability of the region of interest before and after the event occurs, hence finding which fits more naturally with their respective backgrounds. Having tested on a dataset from the PETS 2006, PETS 2007, AVSS20074, CVSG, VISOR, CANDELA and WCAM datasets, the algorithm has shown capable of matching the results of the state-of-the-art, is highly parallel and has a degree of robustness to noise and illumination changes.
Ensemble renormalization group for the random-field hierarchical model.
Decelle, Aurélien; Parisi, Giorgio; Rocchi, Jacopo
2014-03-01
The renormalization group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple models. In this work we study a real-space RG transformation on the Dyson hierarchical lattice with a random field, which leads to a reconstruction of the RG flow and to an evaluation of the critical exponents of the model at T=0. We show that this method gives very accurate estimations of the critical exponents by comparing our results with those obtained by some of us using an independent method.
Weger, R. C.; Lee, J.; Zhu, Tianri; Welch, R. M.
1992-01-01
The current controversy existing in reference to the regularity vs. clustering in cloud fields is examined by means of analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics. It is shown that the Poisson representation of random point processes is superior to pseudorandom-number-generated models and that pseudorandom-number-generated models bias the observed nearest-neighbor statistics towards regularity. Interpretation of this nearest-neighbor statistics is discussed for many cases of superpositions of clustering, randomness, and regularity. A detailed analysis is carried out of cumulus cloud field spatial distributions based upon Landsat, AVHRR, and Skylab data, showing that, when both large and small clouds are included in the cloud field distributions, the cloud field always has a strong clustering signal.
Random field Ising model and community structure in complex networks
Son, S.-W.; Jeong, H.; Noh, J. D.
2006-04-01
We propose a method to determine the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field Bs = +∞, Bt = -∞, and Bi≠s,t=0 for a node pair s and t. The ground state problem is equivalent to the so-called maximum flow problem, which can be solved exactly numerically with the help of a combinatorial optimization algorithm. The community structure is then identified from the ground state Ising spin domains for all pairs of s and t. Our method provides a criterion for the existence of the community structure, and is applicable equally well to unweighted and weighted networks. We demonstrate the performance of the method by applying it to the Barabási-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network. (Ising, Potts, etc.)
A Markov Random Field Model for Image Segmentation of Rice Planthopper in Rice Fields
Hongwei Yue; Ken Cai; Hanhui Lin; Hong Man; Zhaofeng Zeng
2016-01-01
It is meaningful to develop the automation segmentation of rice planthopper pests based on imaging technology in precision agriculture. However, rice planthopper images affected by light and complicated backgrounds in open rice fields make the segmentation difficult. This study proposed a segmentation approach of rice planthopper images based on the Markov random field to conduct effective segmentation. First, fractional order differential was introduced into the extraction proces...
Wang, Shouyu; Xue, Liang; Yan, Keding
2017-07-01
Light scattering from randomly rough surfaces is of great significance in various fields such as remote sensing and target identification. As numerical methods can obtain scattering distributions without complex setups and complicated operations, they become important tools in light scattering study. However, most of them suffer from huge computing load and low operating efficiency, limiting their applications in dynamic measurements and high-speed detections. Here, to overcome these disadvantages, microfacet slope probability density function based method is presented, providing scattering information without computing ensemble average from numerous scattered fields, thus it can obtain light scattering distributions with extremely fast speed. Additionally, it can reach high-computing accuracy quantitatively certificated by mature light scattering computing algorithms. It is believed the provided approach is useful in light scattering study and offers potentiality for real-time detections.
DEFF Research Database (Denmark)
Weir, D J; Monaco, R; Koshelets, V P;
2013-01-01
In this paper we use spontaneous flux production in annular superconductors to shed light on the Kibble–Zurek (KZ) scenario. In particular, we examine the effects of finite size and external fields, neither of which is directly amenable to the KZ analysis. Supported by 1D and 3D simulations, the ...
Measuring marine oil spill extent by Markov Random Fields
Moctezuma, Miguel; Parmiggiani, Flavio; Lopez Lopez, Ludwin
2014-10-01
The Deepwater Horizon oil spill of the Gulf of Mexico in the spring of 2010 was the largest accidental marine oil spill in the history of the petroleum industry. An immediate request, after the accident, was to detect the oil slick and to measure its extent: SAR images were the obvious tool to be employed for the task. This paper presents a processing scheme based on Markov Random Fields (MRF) theory. MRF theory describes the global information by probability terms involving local neighborhood representations of the SAR backscatter data. The random degradation introduced by speckle noise is dealt with a pre-processing stage which applies a nonlinear diffusion filter. Spatial context attributes are structured by the Bayes equation derived from a Maximum-A-Posteriori (MAP) estimation. The probability terms define an objective function of a MRF model whose goal is to detect contours and fine structures. The markovian segmentation problem is solved with a numerical optimization method. The scheme was applied to an Envisat/ASAR image over the Gulf of Mexico of May 9, 2010, when the oil spill was already fully developed. The final result was obtained with 51 recursion cycles, where, at each step, the segmentation consists of a 3-class label field (open sea and two oil slick thicknesses). Both the MRF model and the parameters of the stochastic optimization procedure will be provided, together with the area measurement of the two kinds of oil slick.
Grammatical-Restrained Hidden Conditional Random Fields for Bioinformatics applications
Directory of Open Access Journals (Sweden)
Martelli Pier
2009-10-01
Full Text Available Abstract Background Discriminative models are designed to naturally address classification tasks. However, some applications require the inclusion of grammar rules, and in these cases generative models, such as Hidden Markov Models (HMMs and Stochastic Grammars, are routinely applied. Results We introduce Grammatical-Restrained Hidden Conditional Random Fields (GRHCRFs as an extension of Hidden Conditional Random Fields (HCRFs. GRHCRFs while preserving the discriminative character of HCRFs, can assign labels in agreement with the production rules of a defined grammar. The main GRHCRF novelty is the possibility of including in HCRFs prior knowledge of the problem by means of a defined grammar. Our current implementation allows regular grammar rules. We test our GRHCRF on a typical biosequence labeling problem: the prediction of the topology of Prokaryotic outer-membrane proteins. Conclusion We show that in a typical biosequence labeling problem the GRHCRF performs better than CRF models of the same complexity, indicating that GRHCRFs can be useful tools for biosequence analysis applications. Availability GRHCRF software is available under GPLv3 licence at the website http://www.biocomp.unibo.it/~savojard/biocrf-0.9.tar.gz.
Shcherbakov, V. P.; Khokhlov, A. V.; Sycheva, N. K.
2015-09-01
The quadrature formula is obtained for the distribution function (DF) of the intensity of the geomagnetic field B and the corresponding virtual axial dipole moment VADM in the model of the Giant Gaussian Process (GGP). The predictions of this model are compared, up to a high degree of detail, with the empirical data for the Brunhes Epoch, which are contained in the global databases (GDB) for paleointensity. With a fixed latitude φ, the DFs f B ( B, φ) and f VADM(VADM, φ) are close to Gaussian within the first approximation. At the same time, the global DF f B ( B) has a high coefficient of asymmetry a = 0.35 since the mean of this function is latitude-dependent. In contrast, the global DF f VADM(VADM) has far lower asymmetry a = 0.16, since its mean barely varies with latitude. The comparison between the distribution histograms of VADM according to the PINT GDB data for the Brunhes Epoch and the results calculated by the BGP model shows that the empirical data and the calculations by the GGP model noticeably differ in the interval of the small VADM. Specifically, the histogram based on PINT GDB data shows a significant predominance of these data compared to the model predictions. At the same time, the same data fairly well agree with the GGP model in directions. This contradiction is probably accounted for by the underestimation of the paleointensity values in the experiments by the Thellier method if the rock carries chemical magnetization instead of thermal remanent magnetization. An alternative explanation suggests a short drop in the geomagnetic dynamo power associated with a simultaneous decrease in both the mean value of the axial dipole and in the variances of all the other terms of the spherical expansion of the geomagnetic field (i.e., quadrupole, octupole, and other components).
D'Amico, Guido
2014-01-01
We analyze primordial non-Gaussianity in single field inflationary models when the tensor/scalar ratio is large, $r \\sim 0.2$. Our results show that detectable levels of non-Gaussianity $f_{NL} \\sim 50$ are still possible in the simplest class of models described by the effective theory of inflation. However, the \\emph{shape} is very tightly constrained, making a sharp prediction that could be confirmed or falsified by a future detection of non-Gaussianity.
Level density for deformations of the Gaussian orthogonal ensemble
Bertuola, A C; Hussein, M S; Pato, M P; Sargeant, A J
2004-01-01
Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles we derive formulas for the average level density for (i) the transition from the Gaussian orthogonal ensemble (GOE) to the Poisson ensemble and (ii) the transition from the GOE to $m$ GOEs.
Energy Technology Data Exchange (ETDEWEB)
Hoejstrup, J. [NEG Micon Project Development A/S, Randers (Denmark); Hansen, K.S. [Denmarks Technical Univ., Dept. of Energy Engineering, Lyngby (Denmark); Pedersen, B.J. [VESTAS Wind Systems A/S, Lem (Denmark); Nielsen, M. [Risoe National Lab., Wind Energy and Atmospheric Physics, Roskilde (Denmark)
1999-03-01
The pdf`s of atmospheric turbulence have somewhat wider tails than a Gaussian, especially regarding accelerations, whereas velocities are close to Gaussian. This behaviour is being investigated using data from a large WEB-database in order to quantify the amount of non-Gaussianity. Models for non-Gaussian turbulence have been developed, by which artificial turbulence can be generated with specified distributions, spectra and cross-correlations. The artificial time series will then be used in load models and the resulting loads in the Gaussian and the non-Gaussian cases will be compared. (au)
Quantum Coherence and Random Fields at Mesoscopic Scales
Energy Technology Data Exchange (ETDEWEB)
Rosenbaum, Thomas F. [Univ. of Chicago, IL (United States)
2016-03-01
We seek to explore and exploit model, disordered and geometrically frustrated magnets where coherent spin clusters stably detach themselves from their surroundings, leading to extreme sensitivity to finite frequency excitations and the ability to encode information. Global changes in either the spin concentration or the quantum tunneling probability via the application of an external magnetic field can tune the relative weights of quantum entanglement and random field effects on the mesoscopic scale. These same parameters can be harnessed to manipulate domain wall dynamics in the ferromagnetic state, with technological possibilities for magnetic information storage. Finally, extensions from quantum ferromagnets to antiferromagnets promise new insights into the physics of quantum fluctuations and effective dimensional reduction. A combination of ac susceptometry, dc magnetometry, noise measurements, hole burning, non-linear Fano experiments, and neutron diffraction as functions of temperature, magnetic field, frequency, excitation amplitude, dipole concentration, and disorder address issues of stability, overlap, coherence, and control. We have been especially interested in probing the evolution of the local order in the progression from spin liquid to spin glass to long-range-ordered magnet.
Fuzzy Markov random fields versus chains for multispectral image segmentation.
Salzenstein, Fabien; Collet, Christophe
2006-11-01
This paper deals with a comparison of recent statistical models based on fuzzy Markov random fields and chains for multispectral image segmentation. The fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data. In this framework, we assume the dependence between bands and we express the general model for the covariance matrix. A fuzzy Markov chain model is developed in an unsupervised way. This method is compared with the fuzzy Markovian field model previously proposed by one of the authors. The segmentation task is processed with Bayesian tools, such as the well-known MPM (Mode of Posterior Marginals) criterion. Our goal is to compare the robustness and rapidity for both methods (fuzzy Markov fields versus fuzzy Markov chains). Indeed, such fuzzy-based procedures seem to be a good answer, e.g., for astronomical observations when the patterns present diffuse structures. Moreover, these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy. To validate both models, we perform and compare the segmentation on synthetic images and raw multispectral astronomical data.
A CONDITIONAL RANDOM FIELDS APPROACH TO BIOMEDICAL NAMED ENTITY RECOGNITION
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Named entity recognition is a fundamental task in biomedical data mining. In this letter, a named entity recognition system based on CRFs (Conditional Random Fields) for biomedical texts is presented. The system makes extensive use of a diverse set of features, including local features, full text features and external resource features. All features incorporated in this system are described in detail,and the impacts of different feature sets on the performance of the system are evaluated. In order to improve the performance of system, post-processing modules are exploited to deal with the abbreviation phenomena, cascaded named entity and boundary errors identification. Evaluation on this system proved that the feature selection has important impact on the system performance, and the post-processing explored has an important contribution on system performance to achieve better results.
Speckle Optical Tweezers: Micromanipulation with Random Light Fields
Volpe, Giorgio; Callegari, Agnese; Volpe, Giovanni; Gigan, Sylvain
2014-01-01
Current optical manipulation techniques rely on carefully engineered setups and samples. Although similar conditions are routinely met in research laboratories, it is still a challenge to manipulate microparticles when the environment is not well controlled and known a priori, since optical imperfections and scattering limit the applicability of this technique to real-life situations, such as in biomedical or microfluidic applications. Nonetheless, scattering of coherent light by disordered structures gives rise to speckles, random diffraction patterns with well-defined statistical properties. Here, we experimentally demonstrate how speckle fields can become a versatile tool to efficiently perform fundamental optical manipulation tasks such as trapping, guiding and sorting. We anticipate that the simplicity of these "speckle optical tweezers" will greatly broaden the perspectives of optical manipulation for real-life applications.
Strong mixing properties of max-infinitely divisible random fields
Dombry, Clément
2012-01-01
Let $\\eta=(\\eta(t))_{t\\in T}$ be a sample continuous max-infinitely random field on a locally compact metric space $T$. For a closed subset $S\\in T$, we note $\\eta_{S}$ the restriction of $\\eta$ to $S$. We consider $\\beta(S_1,S_2)$ the absolute regularity coefficient between $\\eta_{S_1}$ and $\\eta_{S_2}$, where $S_1,S_2$ are two disjoint closed subsets of $T$. Our main result is a simple upper bound for $\\beta(S_1,S_2)$ involving the exponent measure $\\mu$ of $\\eta$: we prove that $\\beta(S_1,S_2)\\leq 2\\int \\bbP[\\eta\
CLOUD IMAGE DETECTION BASED ON MARKOV RANDOM FIELD
Institute of Scientific and Technical Information of China (English)
Xu Xuemei; Guo Yuanwei; Wang Zhenfei
2012-01-01
In order to overcome the disadvantages of low accuracy rate,high complexity and poor robustness to image noise in many traditional algorithms of cloud image detection,this paper proposed a novel algorithm on the basis of Markov Random Field (MRF) modeling.This paper first defined algorithm model and derived the core factors affecting the performance of the algorithm,and then,the solving of this algorithm was obtained by the use of Belief Propagation (BP) algorithm and Iterated Conditional Modes (ICM) algorithm.Finally,experiments indicate that this algorithm for the cloud image detection has higher average accuracy rate which is about 98.76％ and the average result can also reach 96.92％ for different type of image noise.
5th Seminar on Stochastic Processes, Random Fields and Applications
Russo, Francesco; Dozzi, Marco
2008-01-01
This volume contains twenty-eight refereed research or review papers presented at the 5th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from May 30 to June 3, 2005. The seminar focused mainly on stochastic partial differential equations, random dynamical systems, infinite-dimensional analysis, approximation problems, and financial engineering. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance. Contributors: Y. Asai, J.-P. Aubin, C. Becker, M. Benaïm, H. Bessaih, S. Biagini, S. Bonaccorsi, N. Bouleau, N. Champagnat, G. Da Prato, R. Ferrière, F. Flandoli, P. Guasoni, V.B. Hallulli, D. Khoshnevisan, T. Komorowski, R. Léandre, P. Lescot, H. Lisei, J.A. López-Mimbela, V. Mandrekar, S. Méléard, A. Millet, H. Nagai, A.D. Neate, V. Orlovius, M. Pratelli, N. Privault, O. Raimond, M. Röckner, B. Rüdiger, W.J. Runggaldi...
Random field model reveals structure of the protein recombinational landscape.
Directory of Open Access Journals (Sweden)
Philip A Romero
Full Text Available We are interested in how intragenic recombination contributes to the evolution of proteins and how this mechanism complements and enhances the diversity generated by random mutation. Experiments have revealed that proteins are highly tolerant to recombination with homologous sequences (mutation by recombination is conservative; more surprisingly, they have also shown that homologous sequence fragments make largely additive contributions to biophysical properties such as stability. Here, we develop a random field model to describe the statistical features of the subset of protein space accessible by recombination, which we refer to as the recombinational landscape. This model shows quantitative agreement with experimental results compiled from eight libraries of proteins that were generated by recombining gene fragments from homologous proteins. The model reveals a recombinational landscape that is highly enriched in functional sequences, with properties dominated by a large-scale additive structure. It also quantifies the relative contributions of parent sequence identity, crossover locations, and protein fold to the tolerance of proteins to recombination. Intragenic recombination explores a unique subset of sequence space that promotes rapid molecular diversification and functional adaptation.
Institute of Scientific and Technical Information of China (English)
王志同
2016-01-01
Big data clustering process is a gaussian random process, thus in large-scale data classification, build sound data classification model, is very important to improve the ability of mathematical statistics. Binomial, poisson model with global solution of the convex optimization random clustering performance, using binomial, poisson model, the superiority of gaussian random data processing in finite dimensional space, for data clustering analysis. Build the KKT conditions of binomial, poisson model, obtains the binomial, poisson model polynomial kernel, the boundary value of periodic solution of a gaussian clustering feature decomposition, draw Schur complement functional criterion, binomial, poisson model of large-scale data classification system of mathematical statistics, eventually improve the accuracy of the large data clustering. Results show that the derived using binomial, poisson model in the process of gaussian random big data classification is of stable convergence, effectively improves the big data statistics and analysis ability.%大数据的聚类过程是高斯随机过程，因此在大数据分类中，构建稳健的数据分类模型，提高数理统计能力至关重要。二项-泊松模型具有全局解的凸优化随机聚类性能，利用二项-泊松模型对高斯随机性数据处理的优势，在有限维空间中，进行数据聚类分析。构建二项-泊松模型的KKT条件，取得二项-泊松模型的边值周期解多项式核，进行高斯聚类特征分解，得出Schur complement泛函准则，建立二项-泊松模型的数理统计大数据分类系统，最终验证了稳定性。推导结果表明，利用二项-泊松模型在高斯随机大数据分类过程中是稳定收敛的，有效提高了大数据的数理统计和分析能力。
Kleeorin, N; Sokoloff, D D
2002-01-01
Magnetic fluctuations with a zero mean field in a random flow with a finite correlation time and a small yet finite magnetic diffusion are studied. Equation for the second-order correlation function of a magnetic field is derived. This equation comprises spatial derivatives of high orders due to a non-local nature of magnetic field transport in a random velocity field with a finite correlation time. For a random Gaussian velocity field with a small correlation time the equation for the second-order correlation function of the magnetic field is a third-order partial differential equation. For this velocity field and a small magnetic diffusion with large magnetic Prandtl numbers the growth rate of the second moment of magnetic field is estimated. The finite correlation time of a turbulent velocity field causes an increase of the growth rate of magnetic fluctuations. It is demonstrated that the results obtained for the cases of a small yet finite magnetic diffusion and a zero magnetic diffusion are different. As...
Numerical analysis for random temperature fields of embankment in cold regions
Institute of Scientific and Technical Information of China (English)
LIU ZhiQiang; LAI YuanMing; ZHANG MingYi; ZHANG XueFu
2007-01-01
The stochastic finite element equations for random temperature are obtained using the first-order perturbation technique taking into account the random thermal properties and boundary condition,based on heat transfer variational principle.The local average method for 2-D is used to discretize random fields.Then,the random temperature fields of embankment in cold regions are investigated on condition that the thermal properties and boundary condition are taken as random fields,respectively,by using the program,which is written by the methods.The expected value of temperature field and the standard deviation of the temperature field of embankment in cold regions are obtained and analyzed.
Numerical analysis for random temperature fields of embankment in cold regions
Institute of Scientific and Technical Information of China (English)
2007-01-01
The stochastic finite element equations for random temperature are obtained using the first-order per-turbation technique taking into account the random thermal properties and boundary condition, based on heat transfer variational principle. The local average method for 2-D is used to discretize random fields. Then, the random temperature fields of embankment in cold regions are investigated on condi-tion that the thermal properties and boundary condition are taken as random fields, respectively, by using the program, which is written by the methods. The expected value of temperature field and the standard deviation of the temperature field of embankment in cold regions are obtained and analyzed.
Convergence of posteriors for discretized log Gaussian Cox processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus Plenge
2004-01-01
In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations...
Glaucoma progression detection using nonlocal Markov random field prior.
Belghith, Akram; Bowd, Christopher; Medeiros, Felipe A; Balasubramanian, Madhusudhanan; Weinreb, Robert N; Zangwill, Linda M
2014-10-01
Glaucoma is neurodegenerative disease characterized by distinctive changes in the optic nerve head and visual field. Without treatment, glaucoma can lead to permanent blindness. Therefore, monitoring glaucoma progression is important to detect uncontrolled disease and the possible need for therapy advancement. In this context, three-dimensional (3-D) spectral domain optical coherence tomography (SD-OCT) has been commonly used in the diagnosis and management of glaucoma patients. We present a new framework for detection of glaucoma progression using 3-D SD-OCT images. In contrast to previous works that use the retinal nerve fiber layer thickness measurement provided by commercially available instruments, we consider the whole 3-D volume for change detection. To account for the spatial voxel dependency, we propose the use of the Markov random field (MRF) model as a prior for the change detection map. In order to improve the robustness of the proposed approach, a nonlocal strategy was adopted to define the MRF energy function. To accommodate the presence of false-positive detection, we used a fuzzy logic approach to classify a 3-D SD-OCT image into a "non-progressing" or "progressing" glaucoma class. We compared the diagnostic performance of the proposed framework to the existing methods of progression detection.
A dissipative random velocity field for fully developed fluid turbulence
Chevillard, Laurent; Pereira, Rodrigo; Garban, Christophe
2016-11-01
We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectory. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model depending on a single free parameter that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments, including the intermittent corrections, and the existence of energy transfers across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter and derive analytically the spectrum of exponents of the structure functions in a simplified non dissipative case. A perturbative expansion shows that energy transfers indeed take place, justifying the dissipative nature of this random field.
DEFF Research Database (Denmark)
Højstrup, Jørgen; Hansen, Kurt S.; Pedersen, Bo Juul;
1999-01-01
The pdf's of atmosperic turbulence have somewhat wider tails than a Gaussian, especially regarding accelerations, whereas velocities are close to Gaussian. This behaviour has been investigated using data from a large WEB-database in order to quantify the amount of non-gaussianity. Models for non-...
Khaneja, Mamta; Ghosh, Santanu; Gautam, Seema; Kumar, Prashant; Rawat, J S; Chaudhury, P K; Vankar, V D; Kumar, Vikram
2015-05-01
High field emission (FE) current density from carbon nanotube (CNT) arrays grown on lithographically patterned silicon substrates is reported. A typical patterned field emitter array consists of bundles of nanotubes separated by a fixed gap and spread over the entire emission area. Emission performance from such an array having randomly oriented nanotube growth within each bundle is reported for different bundle sizes and separations. One typical sample with aligned CNTs within the bundle is also examined for comparison. It is seen that the current density from an array having random nanotube growth within the bundles is appreciably higher as compared to its aligned counterpart. The influence of structure on FE current densities as revealed by Raman spectroscopy is also seen. It is also observed that current density depends on edge length and increases with the same for all samples under study. Highest current density of -100 mA cm(-2) at an applied field of 5 V/μm is achieved from the random growth patterned sample with a bundle size of 2 μm and spacing of 4 μm between the bundles.
Gaussian vs non-Gaussian turbulence: impact on wind turbine loads
DEFF Research Database (Denmark)
Berg, Jacob; Natarajan, Anand; Mann, Jakob;
2016-01-01
From large-eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non-Gaussian counterpart. Time series from the two...... types of turbulence are then used as input to wind turbine load simulations under normal operations with the HAWC2 software package. A slight increase in the extreme loads of the tower base fore-aft moment is observed for high wind speeds when using non-Gaussian turbulence but is insignificant when...
A strong law of large numbers for harmonizable isotropic random fields
Directory of Open Access Journals (Sweden)
Randall J. Swift
1997-01-01
Full Text Available The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers a strong law of large numbers for the spherical average of a harmonizable isotropic random field.
Clustering, randomness, and regularity in cloud fields. 4: Stratocumulus cloud fields
Lee, J.; Chou, J.; Weger, R. C.; Welch, R. M.
1994-01-01
To complete the analysis of the spatial distribution of boundary layer cloudiness, the present study focuses on nine stratocumulus Landsat scenes. The results indicate many similarities between stratocumulus and cumulus spatial distributions. Most notably, at full spatial resolution all scenes exhibit a decidedly clustered distribution. The strength of the clustering signal decreases with increasing cloud size; the clusters themselves consist of a few clouds (less than 10), occupy a small percentage of the cloud field area (less than 5%), contain between 20% and 60% of the cloud field population, and are randomly located within the scene. In contrast, stratocumulus in almost every respect are more strongly clustered than are cumulus cloud fields. For instance, stratocumulus clusters contain more clouds per cluster, occupy a larger percentage of the total area, and have a larger percentage of clouds participating in clusters than the corresponding cumulus examples. To investigate clustering at intermediate spatial scales, the local dimensionality statistic is introduced. Results obtained from this statistic provide the first direct evidence for regularity among large (more than 900 m in diameter) clouds in stratocumulus and cumulus cloud fields, in support of the inhibition hypothesis of Ramirez and Bras (1990). Also, the size compensated point-to-cloud cumulative distribution function statistic is found to be necessary to obtain a consistent description of stratocumulus cloud distributions. A hypothesis regarding the underlying physical mechanisms responsible for cloud clustering is presented. It is suggested that cloud clusters often arise from 4 to 10 triggering events localized within regions less than 2 km in diameter and randomly distributed within the cloud field. As the size of the cloud surpasses the scale of the triggering region, the clustering signal weakens and the larger cloud locations become more random.
1992-11-01
be used with these h and h from now on. We assume that / and A are Lipschitz, of bounded variation , and bounded away from i-.ero. Consider dn equal...functions £ € lh f°’’ which £,£(0, ■),£(■,()) have bounded variation , and let C2 denote the space of continuous functions on [0, l]2. Equip D2 and C2...continuous as a map from C2 into D2([0,1] x [0,/J]). LI particular, we use the property that f>(-.-.z) has bounded variation uniformly in s, 0 < z
Markov random field modelling for fluid distributions from the seismic velocity structures
Kuwatani, T.; Nagata, K.; Okada, M.; Toriumi, M.
2011-12-01
Recent development of geophysical observations, such as seismic tomography, seismic reflection method and geomagnetic method, provide us detailed images of the earth's interior. However, it has still been difficult to interpret these data geologically, including predicting lithology and fluid distributions, mainly because (1) available data usually have large noise and uncertainty, and (2) the number of observable parameters is usually smaller than the number of target parameters. Therefore, the statistical analyses of geophysical data sets are essential for the objective and quantitative geological interpretation. We propose the use of Markov random field (MRF) model to geophysical image data as an alternative to classical deterministic approaches. The MRF model is a Bayesian stochastic model using a generalized form of Markov Chains, and is often applied to the analysis of images, particularly in the detection of visual patterns or textures. The MRF model assumes that the spatial gradients of physical properties are relatively small compared to the observational noises. By hyperparameter estimation, the variances of noises can be appropriately estimated only from available data sets without prior information about observational noises. In this study, we try to image the fluid distributions based on the seismic velocity structure by using the Markov random field model. According to Nakajima et al. (2005), seismic velocities (Vp and Vs) are expressed as functions of porosity and pore geometry using the unified formulation proposed by Takei (2002). Additionally, the spatial continuity of porosity and pore geometry is incorporated by Gaussian Markov Chains as prior probabilities. The most probable estimation can be obtained by maximizing the posterior probability of the fluid distribution given the observed velocity structures. In the present study, the steepest descent method was implemented in order to minimize the free energy (i.e. maximize the posterior
Optimality of Gaussian discord.
Pirandola, Stefano; Spedalieri, Gaetana; Braunstein, Samuel L; Cerf, Nicolas J; Lloyd, Seth
2014-10-03
In this Letter we exploit the recently solved conjecture on the bosonic minimum output entropy to show the optimality of Gaussian discord, so that the computation of quantum discord for bipartite Gaussian states can be restricted to local Gaussian measurements. We prove such optimality for a large family of Gaussian states, including all two-mode squeezed thermal states, which are the most typical Gaussian states realized in experiments. Our family also includes other types of Gaussian states and spans their entire set in a suitable limit where they become Choi matrices of Gaussian channels. As a result, we completely characterize the quantum correlations possessed by some of the most important bosonic states in quantum optics and quantum information.
Kouritzin, Michael A; Newton, Fraser; Wu, Biao
2013-04-01
Herein, we propose generating CAPTCHAs through random field simulation and give a novel, effective and efficient algorithm to do so. Indeed, we demonstrate that sufficient information about word tests for easy human recognition is contained in the site marginal probabilities and the site-to-nearby-site covariances and that these quantities can be embedded directly into certain conditional probabilities, designed for effective simulation. The CAPTCHAs are then partial random realizations of the random CAPTCHA word. We start with an initial random field (e.g., randomly scattered letter pieces) and use Gibbs resampling to re-simulate portions of the field repeatedly using these conditional probabilities until the word becomes human-readable. The residual randomness from the initial random field together with the random implementation of the CAPTCHA word provide significant resistance to attack. This results in a CAPTCHA, which is unrecognizable to modern optical character recognition but is recognized about 95% of the time in a human readability study.
Biomedical image analysis using Markov random fields & efficient linear programing.
Komodakis, Nikos; Besbes, Ahmed; Glocker, Ben; Paragios, Nikos
2009-01-01
Computer-aided diagnosis through biomedical image analysis is increasingly considered in health sciences. This is due to the progress made on the acquisition side, as well as on the processing one. In vivo visualization of human tissues where one can determine both anatomical and functional information is now possible. The use of these images with efficient intelligent mathematical and processing tools allows the interpretation of the tissues state and facilitates the task of the physicians. Segmentation and registration are the two most fundamental tools in bioimaging. The first aims to provide automatic tools for organ delineation from images, while the second focuses on establishing correspondences between observations inter and intra subject and modalities. In this paper, we present some recent results towards a common formulation addressing these problems, called the Markov Random Fields. Such an approach is modular with respect to the application context, can be easily extended to deal with various modalities, provides guarantees on the optimality properties of the obtained solution and is computationally efficient.
Conditional Random Fields for Pattern Recognition Applied to Structured Data
Directory of Open Access Journals (Sweden)
Tom Burr
2015-07-01
Full Text Available Pattern recognition uses measurements from an input domain, X, to predict their labels from an output domain, Y. Image analysis is one setting where one might want to infer whether a pixel patch contains an object that is “manmade” (such as a building or “natural” (such as a tree. Suppose the label for a pixel patch is “manmade”; if the label for a nearby pixel patch is then more likely to be “manmade” there is structure in the output domain that can be exploited to improve pattern recognition performance. Modeling P(X is difficult because features between parts of the model are often correlated. Therefore, conditional random fields (CRFs model structured data using the conditional distribution P(Y|X = x, without specifying a model for P(X, and are well suited for applications with dependent features. This paper has two parts. First, we overview CRFs and their application to pattern recognition in structured problems. Our primary examples are image analysis applications in which there is dependence among samples (pixel patches in the output domain. Second, we identify research topics and present numerical examples.
IMAGE SEGMENTATION BASED ON MARKOV RANDOM FIELD AND WATERSHED TECHNIQUES
Institute of Scientific and Technical Information of China (English)
纳瑟; 刘重庆
2002-01-01
This paper presented a method that incorporates Markov Random Field(MRF), watershed segmentation and merging techniques for performing image segmentation and edge detection tasks. MRF is used to obtain an initial estimate of x regions in the image under process where in MRF model, gray level x, at pixel location i, in an image X, depends on the gray levels of neighboring pixels. The process needs an initial segmented result. An initial segmentation is got based on K-means clustering technique and the minimum distance, then the region process in modeled by MRF to obtain an image contains different intensity regions. Starting from this we calculate the gradient values of that image and then employ a watershed technique. When using MRF method it obtains an image that has different intensity regions and has all the edge and region information, then it improves the segmentation result by superimpose closed and an accurate boundary of each region using watershed algorithm. After all pixels of the segmented regions have been processed, a map of primitive region with edges is generated. Finally, a merge process based on averaged mean values is employed. The final segmentation and edge detection result is one closed boundary per actual region in the image.
Rigorously testing multialternative decision field theory against random utility models.
Berkowitsch, Nicolas A J; Scheibehenne, Benjamin; Rieskamp, Jörg
2014-06-01
Cognitive models of decision making aim to explain the process underlying observed choices. Here, we test a sequential sampling model of decision making, multialternative decision field theory (MDFT; Roe, Busemeyer, & Townsend, 2001), on empirical grounds and compare it against 2 established random utility models of choice: the probit and the logit model. Using a within-subject experimental design, participants in 2 studies repeatedly choose among sets of options (consumer products) described on several attributes. The results of Study 1 showed that all models predicted participants' choices equally well. In Study 2, in which the choice sets were explicitly designed to distinguish the models, MDFT had an advantage in predicting the observed choices. Study 2 further revealed the occurrence of multiple context effects within single participants, indicating an interdependent evaluation of choice options and correlations between different context effects. In sum, the results indicate that sequential sampling models can provide relevant insights into the cognitive process underlying preferential choices and thus can lead to better choice predictions.
Magnetic Field Line Random Walk in Isotropic Turbulence with Zero Mean Field
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B 0)(l∥/l) for rms magnetic fluctuation b, large-scale mean field B 0, and parallel and perpendicular coherence scales l∥ and l, respectively. Here we examine the FLRW when R → ∞ by taking B 0 → 0 for finite bz (fluctuation component along B 0), which differs from the well-studied route with bz = 0 or bz Lt B 0 as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B 0 = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k -1 or k -2 moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B 0 → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD
Energy Technology Data Exchange (ETDEWEB)
Sonsrettee, W.; Ruffolo, D.; Snodin, A. P.; Wongpan, P. [Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400 (Thailand); Subedi, P.; Matthaeus, W. H. [Bartol Research Institute, University of Delaware, Newark, DE 19716 (United States); Chuychai, P., E-mail: bturbulence@gmail.com, E-mail: david.ruf@mahidol.ac.th, E-mail: andrew.snodin@gmail.com, E-mail: pat.wongpan@postgrad.otago.ac.nz, E-mail: piyanate@gmail.com, E-mail: prasub@udel.edu, E-mail: whm@udel.edu [Thailand Center of Excellence in Physics, CHE, Ministry of Education, Bangkok 10400 (Thailand)
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B {sub 0})(ℓ{sub ∥}/ℓ ) for rms magnetic fluctuation b, large-scale mean field B {sub 0}, and parallel and perpendicular coherence scales ℓ{sub ∥} and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B {sub 0} → 0 for finite b{sub z} (fluctuation component along B {sub 0}), which differs from the well-studied route with b{sub z} = 0 or b{sub z} << B {sub 0} as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B {sub 0} = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k {sup –1} or k {sup –2} moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B {sub 0} → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
CONVERGENCE RATES IN THE STRONG LAWS OF ASYMPTOTICALLY NEGATIVELY ASSOCIATED RANDOM FIELDS
Institute of Scientific and Technical Information of China (English)
ZhangLixin; WangXiuyun
1999-01-01
In this paper, a notion of negative side p-mixing (p -mixing) which can be regardedas asymptotic negative association is defined, and some Rosenthal type inequalities for p -mix-ing random fields are established. The complete convergence and almost sure summability onthe convergence rates with respect to the strong law of large numbers are also discussed for p--mixing random fields. The results obtained extend those for negatively associated sequences andp" -mixing random fields.
Heterogeneous Web Data Extraction Algorithm Based On Modified Hidden Conditional Random Fields
Cui Cheng
2014-01-01
As it is of great importance to extract useful information from heterogeneous Web data, in this paper, we propose a novel heterogeneous Web data extraction algorithm using a modified hidden conditional random fields model. Considering the traditional linear chain based conditional random fields can not effectively solve the problem of complex and heterogeneous Web data extraction, we modify the standard hidden conditional random fields in three aspects, which are 1) Using the hidden Markov mo...
Phase Diagram and Tricritical Behavior of a Spin-2 Transverse Ising Model in a Random Field
Institute of Scientific and Technical Information of China (English)
LIANG Ya-Qiu; WEI Guo-Zhu; SONG Li-Li; SONG Guo-Li; ZANG Shu-Liang
2004-01-01
The phase diagrams of a spin-2 transverse Ising model with a random field on honeycomb, square, and simple-cubic lattices, respectively, are investigated within the framework of an effective-field theory with correlations.We find the behavior of the tricritical point and the reentrant phenomenon for the system with any coordination number z, when the applied random field is bimodal. The behavior of the tricritical point is also examined as a function of applied transverse field. The reentrant phenomenon comes from the competition between the transverse field and the random field.
Representation and prediction for locally harmonizable isotropic random fields
Directory of Open Access Journals (Sweden)
Randall J. Swift
1995-01-01
Full Text Available The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers fields whose increments are harmonizable and isotropic. Spectral representations are obtained for locally harmonizable isotropic fields. A linear least squares prediction for locally harmonizable isotropic fields is considered.
Bearing Fault Classification Based on Conditional Random Field
Directory of Open Access Journals (Sweden)
Guofeng Wang
2013-01-01
Full Text Available Condition monitoring of rolling element bearing is paramount for predicting the lifetime and performing effective maintenance of the mechanical equipment. To overcome the drawbacks of the hidden Markov model (HMM and improve the diagnosis accuracy, conditional random field (CRF model based classifier is proposed. In this model, the feature vectors sequences and the fault categories are linked by an undirected graphical model in which their relationship is represented by a global conditional probability distribution. In comparison with the HMM, the main advantage of the CRF model is that it can depict the temporal dynamic information between the observation sequences and state sequences without assuming the independence of the input feature vectors. Therefore, the interrelationship between the adjacent observation vectors can also be depicted and integrated into the model, which makes the classifier more robust and accurate than the HMM. To evaluate the effectiveness of the proposed method, four kinds of bearing vibration signals which correspond to normal, inner race pit, outer race pit and roller pit respectively are collected from the test rig. And the CRF and HMM models are built respectively to perform fault classification by taking the sub band energy features of wavelet packet decomposition (WPD as the observation sequences. Moreover, K-fold cross validation method is adopted to improve the evaluation accuracy of the classifier. The analysis and comparison under different fold times show that the accuracy rate of classification using the CRF model is higher than the HMM. This method brings some new lights on the accurate classification of the bearing faults.
MRFalign: protein homology detection through alignment of Markov random fields.
Ma, Jianzhu; Wang, Sheng; Wang, Zhiyong; Xu, Jinbo
2014-03-01
Sequence-based protein homology detection has been extensively studied and so far the most sensitive method is based upon comparison of protein sequence profiles, which are derived from multiple sequence alignment (MSA) of sequence homologs in a protein family. A sequence profile is usually represented as a position-specific scoring matrix (PSSM) or an HMM (Hidden Markov Model) and accordingly PSSM-PSSM or HMM-HMM comparison is used for homolog detection. This paper presents a new homology detection method MRFalign, consisting of three key components: 1) a Markov Random Fields (MRF) representation of a protein family; 2) a scoring function measuring similarity of two MRFs; and 3) an efficient ADMM (Alternating Direction Method of Multipliers) algorithm aligning two MRFs. Compared to HMM that can only model very short-range residue correlation, MRFs can model long-range residue interaction pattern and thus, encode information for the global 3D structure of a protein family. Consequently, MRF-MRF comparison for remote homology detection shall be much more sensitive than HMM-HMM or PSSM-PSSM comparison. Experiments confirm that MRFalign outperforms several popular HMM or PSSM-based methods in terms of both alignment accuracy and remote homology detection and that MRFalign works particularly well for mainly beta proteins. For example, tested on the benchmark SCOP40 (8353 proteins) for homology detection, PSSM-PSSM and HMM-HMM succeed on 48% and 52% of proteins, respectively, at superfamily level, and on 15% and 27% of proteins, respectively, at fold level. In contrast, MRFalign succeeds on 57.3% and 42.5% of proteins at superfamily and fold level, respectively. This study implies that long-range residue interaction patterns are very helpful for sequence-based homology detection. The software is available for download at http://raptorx.uchicago.edu/download/. A summary of this paper appears in the proceedings of the RECOMB 2014 conference, April 2-5.
Ben Mahrsia, R.; Choubani, M.; Bouzaiene, L.; Maaref, H.
2015-08-01
Simulation of quantum dots (QD) is usually performed on the basis of abrupt changes between neighboring materials. In practice, it is not possible to construct such QD because in a real structure the interface between two adjacent materials is not a step. In the work discussed in this paper, vertically coupled InAs/GaAs quantum dots (VCQD) with a non-abrupt change between two neighboring materials are considered. A potential function in the form of a Gaussian distribution was used to show this effect. We also focused on studying the effect of structure, applied electric ( F) and magnetic ( B) fields, pressure ( P), and temperature ( T) on second-harmonic generation (SHG). The analytical expression for SHG was investigated theoretically by use of the density matrix approach, the effective mass, and the finite-difference method (FDM). It was found that the major resonant peak value of SHG is a non-monotonic function of the barrier width ( L B). Moreover, the major resonant peak of SHG is blue-shifted (red-shifted) and its magnitude increases (decreases) monotonically with increasing temperature (pressure). The results obtained also show that the magnitude and position of the resonant peaks of SHG are affected by changes in external conditions, for example applied electric and magnetic fields, structural dimensions of the coupled QD system, and relaxation time ( T 0). Calculations also show that SHG in a VCQD structure with a non-abrupt potential change can be controlled and optimized by appropriate choice of structural dimensions and the external conditions mentioned above.
Institute of Scientific and Technical Information of China (English)
于浛; 张秀杰; 陈建伟; 宋申民; 李鹏
2016-01-01
经典高斯滤波算法存在量测信息实时获取，以及过程噪声和量测噪声相互独立的假设条件。然而，在工程实际应用中该假设条件有时难以满足。本文针对一类具有随机量测时滞和同步相关噪声的高斯系统的状态估计问题，设计了一种高斯滤波框架形式的最优估计算法，并给出了所设计算法的三阶球径容积法则的次优实现形式-考虑随机量测时滞和同步相关噪声的容积卡尔曼滤波器(CKF–RDSCN)。其借助Bernoulli随机序列，来描述系统中可能存在的量测时滞现象，并利用高斯条件分布性质来解决噪声相关问题，在此基础上构建所提出的最优估计算法。仿真结果表明，相比于扩展卡尔曼滤波(EKF)，无迹卡尔曼滤波(UKF)以及容积卡尔曼滤波(CKF)，在含有随机量测时滞和噪声同步相关的状态估计问题中， CKF–RDSCN具有更高的精度和更好的数值稳定性。%The classical Gaussian filters are based on the assumption that measurements are acquired in time and nois-es of process and measurement are independent of each other. However, this assumption is sometimes hard to satisfy in practical applications. In this paper, an optimal estimation algorithm in the form of Gaussian filter framework is designed to solve the problem of states estimation of a Gaussian system with randomly delayed measurements and synchronously correlated noises, and the rule of third-degree spherical-radial cubature is employed to deduced the suboptimal estimation implementation of the proposed algorithms which is named cubature Kalman filter with randomly delayed measurements and synchronously correlated noises(CKF–RDSCN). It takes random sequence of Bernoulli to describe the possible situ-ation with respect to random delay in observation measurement and the property of Gaussian conditional distribution is utilized to solve the problem of noises correlation. Simulation results
Semikoz, V B
1994-01-01
We consider active-sterile neutrino conversions in the early universe hot plasma in the presence of a random magnetic field generated at the electroweak phase transition. Within a random field domain the magnetization asymmetry of the lepton antilepton plasma produced by a uniform constant magnetic field is huge in contrast to their small density asymmetry, leading to a drastic change in the active-sterile conversion rates. Assuming that the random field provides the seed for the galactic field one can estimate the restrictions from primordial nucleosynthesis. Requiring that the extra sterile \
Thermodynamical Properties of Spin-3／2 Ising Model in a Longitudinal Random Field with Crystal Field
Institute of Scientific and Technical Information of China (English)
LIANGYa-Qiu; WEIGuo-Zhu; ZHANGHong; SONGGuo-Li
2004-01-01
A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studied by using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point are investigated numerically for the honeycomb lattice when the random field is bimodal. In particular, the specific heat and the internal energy are examined in detail for the system with a crystal-field constant in the critical region where the ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interesting phenomena in the system.
Ye, J.; le Roux, J. A.; Arthur, A. D.
2015-12-01
Voyager spacecraft observations indicate that interstellar pickup ions are accelerated to ~1 MeV locally at the solar wind termination shock. We present modeling results of the diffusive shock acceleration (DSA) of locally born interstellar pickup ions at the solar wind termination shock by solving the standard focused transport equation numerically. Local time variations in the Parker spiral magnetic field angle are modeled using a q-Gaussian statistical description. The main results are: (1) The injection and DSA of pickup ions depends on the shape and width of the q-Gaussian distribution of the Parker spiral magnetic field angle. (2) Likewise, the accelerated pickup ion pitch-angle distribution also depends on the q-Gaussian distribution of the magnetic field angle. (3) The simulated accelerated pickup ion spectrum is much quieter far downstream than just behind the termination shock as observations show. (4) Magnetic reflection of accelerated pickup ions by the cross-shock magnetic field gradient results in the sporadic formation of highly anisotropic, energy-dependent intensity spikes in the accelerated pickup proton distribution at the termination shock.
Exact simulation of Brown-Resnick random fields at a finite number of locations
DEFF Research Database (Denmark)
Dieker, Ton; Mikosch, Thomas Valentin
2015-01-01
We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure.......We propose an exact simulation method for Brown-Resnick random fields, building on new representations for these stationary max-stable fields. The main idea is to apply suitable changes of measure....
Fractional generalized Lévy random fields as white noise functionals
Institute of Scientific and Technical Information of China (English)
HUANG Zhiyuan; LI Peiyan
2007-01-01
In this paper, we construct the fractional generalized Lévy random fields (FGLRF) as tempered white noise functionals. We find that this white noise approach is very effective in investigating the properties of these fields. Under some conditions, the fractional Lévy fields in the usual sense are obtained. In addition, we also present a method to construct the anisotropic fractional generalized Lévy random fields (AFGLRF).
Magnetic Field Line Random Walk in Isotropic Turbulence with Varying Mean Field
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.; Rowlands, G.; Vyas, S.
2016-08-01
In astrophysical plasmas, the magnetic field line random walk (FLRW) plays an important role in guiding particle transport. The FLRW behavior is scaled by the Kubo number R=(b/{B}0)({{\\ell }}\\parallel /{{\\ell }}\\perp ) for rms magnetic fluctuation b, large-scale mean field {{\\boldsymbol{B}}}0, and coherence scales parallel ({{\\ell }}\\parallel ) and perpendicular ({{\\ell }}\\perp ) to {{\\boldsymbol{B}}}0. Here we use a nonperturbative analytic framework based on Corrsin’s hypothesis, together with direct computer simulations, to examine the R-scaling of the FLRW for varying B 0 with finite b and isotropic fluctuations with {{\\ell }}\\parallel /{{\\ell }}\\perp =1, instead of the well-studied route of varying {{\\ell }}\\parallel /{{\\ell }}\\perp for b \\ll {B}0. The FLRW for isotropic magnetic fluctuations is also of astrophysical interest regarding transport processes in the interstellar medium. With a mean field, fluctuations may have variance anisotropy, so we consider limiting cases of isotropic variance and transverse variance (with b z = 0). We obtain analytic theories, and closed-form solutions for extreme cases. Padé approximants are provided to interpolate all versions of theory and simulations to any B 0. We demonstrate that, for isotropic turbulence, Corrsin-based theories generally work well, and with increasing R there is a transition from quasilinear to Bohm diffusion. This holds even with b z = 0, when different routes to R\\to ∞ are mathematically equivalent; in contrast with previous studies, we find that a Corrsin-based theory with random ballistic decorrelation works well even up to R = 400, where the effects of trapping are barely perceptible in simulation results.
Reduction of the Random Variables of the Turbulent Wind Field
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.
2012-01-01
of the integral domain; this becomes increasingly difficult as the dimensions of the integral domain increase. On the other hand efficiency of the AMC methods is closely dependent on the design points of the problem. Presence of many random variables may increase the number of the design points, hence affects......Applicability of the Probability Density Evolution Method (PDEM) for realizing evolution of the probability density for the wind turbines has rather strict bounds on the basic number of the random variables involved in the model. The efficiency of most of the Advanced Monte Carlo (AMC) methods, i.......e. Importance Sampling (IS) or Subset Simulation (SS), will be deteriorated on problems with many random variables. The problem with PDEM is that a multidimensional integral has to be carried out over the space defined by the random variables of the system. The numerical procedure requires discretization...
Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.
Lukin, Igor P
2016-04-20
The orbital angular momentum of vortex Bessel-Gaussian beams propagating in turbulent atmosphere is studied theoretically. The field of an optical beam is determined through the solution of the paraxial wave equation for a randomly inhomogeneous medium with fluctuations of the refraction index of the turbulent atmosphere. Peculiarities in the behavior of the total power of the vortex Bessel-Gaussian beam at the receiver (or transmitter) are examined. The dependence of the total power of the vortex Bessel-Gaussian beam on optical beam parameters, namely, the transverse wave number of optical radiation, amplitude factor radius, and, especially, topological charge of the optical beam, is analyzed in detail. It turns out that the mean value of the orbital angular momentum of the vortex Bessel-Gaussian beam remains constant during propagation in the turbulent atmosphere. It is shown that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam propagating in turbulent atmosphere calculated with the "mean-intensity" approximation is equal to zero identically. Thus, it is possible to declare confidently that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam in turbulent atmosphere is not very large.
Non-Gaussian Stochastic Gravity
Bates, Jason D.
2013-01-01
This paper presents a new, non-Gaussian formulation of stochastic gravity by incorporating the higher moments of the fluctuations of the quantum stress energy tensor for a free quantum scalar field in a consistent way. A scheme is developed for obtaining realizations of these fluctuations in terms of the Wightman function, and the behavior of the fluctuations is investigated. The resulting probability distribution for fluctuations of the energy density in Minkowski spacetime is found to be si...
Institute of Scientific and Technical Information of China (English)
李阔湖; 田明丽
2012-01-01
运用边界元素法把圆形高斯镜平凹腔的自再现模的衍射积分方程转化为有限阶矩阵方程.计算了圆形高斯镜取不同反射率膜斑半径和中心振幅反射率情况下基模的场强分布、相位分布和本征值.研究表明:腔内光场分布半径随反射率膜斑半径的减小而增大,中心振幅反射率不影响光场分布半径；反射率膜斑半径影响远场分布,当其数值较小时,在光束的远场分布主峰周围产生弱衍射环；当高斯镜中心全反射时,远场分布随反射率膜斑半径的变化无明显变化；模式本征值随反射率膜斑半径的增大而增大.%By means of boundary finite-element method, the field distribution and eigenvalue of the fundamental mode of the plano-concave resonator with a Gaussian-reflectivity plane mirror are calculated and discussed. The results show that the radius of the mode increase following the decreasing of the characteristic radius of the Gaussian-reflectivity. The radius of the mode is not affected by the changes of the amplitude-reflectivity of mirror center. The characteristic radius of the Gaussian-reflectivity affect the far field distribution of the laser mode. While its value is small, the far field distribution has the diffraction ring around the main peak. In addition, if light is reflected completely at the center of the Gaussian-reflectivity plane mirror, the changes of the far field distribution is not obvious with the characteristic radius of the Gaussian-reflectivity changing. The mode eigenvalue increases with the characteristic radius of the Gaussian-reflectivity increasing.
Realization of random-field Ising ferromagnetism in a molecular magnet
Wen, Bo; Subedi, P.; Bo, Lin; Yeshurun, Y.; Sarachik, M. P.; Kent, A. D.; Millis, A. J.; Lampropoulos, C.; Christou, G.
2010-07-01
The longitudinal magnetic susceptibility of single crystals of the molecular magnet Mn12 -acetate obeys a Curie-Weiss law, indicating a transition to a ferromagnetic phase at ˜0.9K . With increasing magnetic field applied transverse to the easy axis, a marked change is observed in the temperature dependence of the susceptibility, and the suppression of ferromagnetism is considerably more rapid than predicted by mean-field theory for an ordered single crystal. Our results can instead be fit by a Hamiltonian for a random-field Ising ferromagnet in a transverse magnetic field, where the randomness derives from the intrinsic distribution of locally tilted magnetic easy axes known to exist in Mn12 -acetate crystals, suggesting that Mn12 -acetate is a realization of the random-field Ising model in which the random field may be tuned by a field applied transverse to the easy axis.
Gaussian Intrinsic Entanglement
Mišta, Ladislav; Tatham, Richard
2016-12-01
We introduce a cryptographically motivated quantifier of entanglement in bipartite Gaussian systems called Gaussian intrinsic entanglement (GIE). The GIE is defined as the optimized mutual information of a Gaussian distribution of outcomes of measurements on parts of a system, conditioned on the outcomes of a measurement on a purifying subsystem. We show that GIE vanishes only on separable states and exhibits monotonicity under Gaussian local trace-preserving operations and classical communication. In the two-mode case, we compute GIE for all pure states as well as for several important classes of symmetric and asymmetric mixed states. Surprisingly, in all of these cases, GIE is equal to Gaussian Rényi-2 entanglement. As GIE is operationally associated with the secret-key agreement protocol and can be computed for several important classes of states, it offers a compromise between computable and physically meaningful entanglement quantifiers.
CSIR Research Space (South Africa)
Roux, FS
2009-01-01
Full Text Available . Gaussian beams with vortex dipoles CSIR National Laser Centre – p.2/30 Gaussian beam notation Gaussian beam in normalised coordinates: g(u, v, t) = exp ( −u 2 + v2 1− it ) u = xω0 v = yω0 t = zρ ρ = piω20 λ ω0 — 1/e2 beam waist radius; ρ— Rayleigh range ω ω...(z) 0 x z Rayleigh range Beam waist ρ ρ Rayleigh range CSIR National Laser Centre – p.3/30 Gaussian beam Gaussian beam in terms of amplitude and phase g(u, v, t) = exp ( −u 2 + v2 1 + t2 ) exp ( − it(u 2 + v2) 1 + t2 ) Normalised beam radius: √ 1 + t2...
Statistical calibration via Gaussianization in hot-wire anemometry
Gluzman, Igal; Cohen, Jacob; Oshman, Yaakov
2017-03-01
A statistical method is introduced, that is based on Gaussianization to estimate the nonlinear calibration curve of a hot-wire probe, relating the input flow velocity to the output (measured) voltage. The method uses as input a measured sequence of voltage samples, corresponding to different unknown flow velocities in the desired operational range, and only two measured voltages along with their known (calibrated) flow velocities. The method relies on the conditions that (1) the velocity signal is Gaussian distributed (or has another known distribution), and (2) the measured signal covers the desired velocity range over which the sensor is to be calibrated. The novel calibration method is validated against standard calibration methods using data acquired by hot-wire probes in wind-tunnel experiments. In these experiments, a hot-wire probe is placed at a certain region downstream of a cube-shaped body in a freestream of air flow, properly selected, so that the central limit theorem, when applied to the random velocity increments composing the instantaneous velocity in the wake, roughly holds, and renders the measured signal nearly Gaussian distributed. The statistical distribution of the velocity field in the wake is validated by mapping the first four statistical moments of the measured signals in different regions of the wake and comparing them with corresponding moments of the Gaussian distribution. The experimental data are used to evaluate the sensitivity of the method to the distribution of the measured signal, and the method is demonstrated to possess some robustness with respect to deviations from the Gaussian distribution.
Mean field theory of directed polymers with random complex weights
Derrida, B.; Evans, M. R.; Speer, E. R.
1993-09-01
We show that for the problem of directed polymers on a tree with i.i.d. random complex weights on each bond, three possible phases can exist; the phase of a particular system is determined by the distribution ρ of the random weights. For each of these three phases, we give the expression of the free energy per unit length in the limit of infinitely long polymers. Our proofs require several hypotheses on the distribution ρ, most importantly, that the amplitude and the phase of each complex weight be statistically independent. The main steps of our proofs use bounds on noninteger moments of the partition function and self averaging properties of the free energy. We illustrate our results by some examples and discuss possible generalizations to a larger class of distributions, to Random Energy Models, and to the finite dimensional case. We note that our results are not in agreement with the predictions of a recent replica approach to a similar problem.
Analytical reconstruction of isotropic turbulence spectra based on the Gaussian transform
Wohlbrandt, Attila; Hu, Nan; Guerin, Sebastien; Ewert, Roland
2015-01-01
The Random Particle Mesh (RPM) method used to simulate turbulence-induced broadband noise in several aeroacoustic applications is extended to realise isotropic turbulence spectra. With this method turbulent fluctuations are synthesised by filtering white noise with a Gaussian filter kernel that in turn gives a Gaussian spectrum. The Gaussian function is smooth and its derivatives and integrals are again Gaussian functions. The Gaussian filter is efficient and finds wide-spread applications in...
A Markov random field-based approach to speckle reduction
Lankoande, Ousseini
One of the major factors plaguing the performance of any coherent imaging system in general, and synthetic-aperture-radar (SAR) and ultrasound-medical-imaging systems in particular, is the presence of signal-dependent speckle noise. Grainy in appearance, speckle noise is primarily due to the phase fluctuations of the electromagnetic returned signals. Existing multiplicative models for speckle noise do not possess the level of generality required to capture and exploit the inherent spatial-correlation characteristics of speckle noise. The capability of Markov random fields (MRFs) to model spatially correlated and signal-dependent phenomena makes them an excellent choice for modeling speckled images without the need to adopt a multiplicative-noise model. In addition, a MRF framework can lend itself to many image-processing strategies that are not predicated on any multiplicative- or additive-noise assumptions. We propose a new mathematical framework for modeling and mitigating speckle noise that combines the flexibility and generality of a MRF with the physical properties of speckle noise drawn from the statistical optics principles. In particular, Goodman's conditional probability density function (cpdf) of the intensity of any two points in the speckled image and the associated correlation function are used to derive the cpdf of any center pixel intensity given its four neighbors. An important parameter of the cpdf, the coherence factor, characterizes the spatial correlation between two given pixels. For the first-order MRF model used in this dissertation, the coherence factor is restricted to only one value, which is estimated from the data using a pseudo-likelihood method. Equipped with the cpdf, the Hammersley-Clifford theorem is utilized to derive a convex Gibbs energy function that characterizes the MRF. Based on the proposed model, we introduce two speckle-reduction algorithms. The first algorithm, termed the simulated-annealing-MRF (SAMRF), is based on
Parity Violation in Graviton Non-gaussianity
Soda, Jiro; Nozawa, Masato
2011-01-01
We study parity violation in graviton non-gaussianity generated during inflation. We develop a useful formalism to calculate graviton non-gaussianity. Using this formalism, we explicitly calculate the parity violating part of the bispectrum for primordial gravitational waves in the exact de Sitter spacetime and prove that no parity violation appears in the non-gaussianity. We also extend the analysis to slow-roll inflation and find that the parity violation of the bispectrum is proportional to the slow-roll parameter. We argue that parity violating non-gaussianity can be tested by the CMB. Our results are also useful for calculating three-point function of the stress tensor in the non-conformal field theory through the gravity/field theory correspondence.
Lecture notes on non-Gaussianity
Byrnes, Christian T
2014-01-01
We discuss how primordial non-Gaussianity of the curvature perturbation helps to constrain models of the early universe. Observations are consistent with Gaussian initial conditions, compatible with the predictions of the simplest models of inflation. Deviations are constrained to be at the sub percent level, constraining alternative models such as those with multiple fields, non-canonical kinetic terms or breaking the slow-roll conditions. We introduce some of the most important models of inflation which generate non-Gaussian perturbations and provide practical tools on how to calculate the three-point correlation function for a popular class of non-Gaussian models. The current state of the field is summarised and an outlook is given.
Fast vectorized algorithm for the Monte Carlo Simulation of the Random Field Ising Model
Rieger, H
1992-01-01
An algoritm for the simulation of the 3--dimensional random field Ising model with a binary distribution of the random fields is presented. It uses multi-spin coding and simulates 64 physically different systems simultaneously. On one processor of a Cray YMP it reaches a speed of 184 Million spin updates per second. For smaller field strength we present a version of the algorithm that can perform 242 Million spin updates per second on the same machine.
A Markov Random Field Model for Image Segmentation of Rice Planthopper in Rice Fields
Directory of Open Access Journals (Sweden)
Hongwei Yue
2016-04-01
Full Text Available It is meaningful to develop the automation segmentation of rice planthopper pests based on imaging technology in precision agriculture. However, rice planthopper images affected by light and complicated backgrounds in open rice fields make the segmentation difficult. This study proposed a segmentation approach of rice planthopper images based on the Markov random field to conduct effective segmentation. First, fractional order differential was introduced into the extraction process of image texture features to gain complete texture information of rice planthopper images. Observation data modeling was established by a combination of image color features and texture features to overcome the disadvantages of insufficient image texture information. Finally, the improved potential function models, the neighborhood relationship between the pixel labels, and the attributes of pixels were defined. The segmentation results were assessed by quantitative evaluation. The experiments showed that the proposed improved approach in the study was more robust, especially with the changes in the illumination condition. This approach can effectively improve segmentation accuracy and promote vision segmentation results of rice planthopper images.
Comparison of the Sachs-Wolfe Effect for Gaussian and Non-Gaussian Fluctuations
Kung, J H
1993-01-01
A consequence of non-Gaussian perturbations on the Sachs-Wolfe effect is studied. For a particular power spectrum, predicted Sachs-Wolfe effects are calculated for two cases: Gaussian (random phase) configuration, and a specific kind of non-Gaussian configuration. We obtain a result that the Sachs-Wolfe effect for the latter case is smaller when each temperature fluctuation is properly normalized with respect to the corresponding mass fluctuation ${\\delta M\\over M}(R)$. The physical explanation and the generality of the result are discussed.
Gaussian and Non-Gaussian operations on non-Gaussian state: engineering non-Gaussianity
Directory of Open Access Journals (Sweden)
Olivares Stefano
2014-03-01
Full Text Available Multiple photon subtraction applied to a displaced phase-averaged coherent state, which is a non-Gaussian classical state, produces conditional states with a non trivial (positive Glauber-Sudarshan Prepresentation. We theoretically and experimentally demonstrate that, despite its simplicity, this class of conditional states cannot be fully characterized by direct detection of photon numbers. In particular, the non-Gaussianity of the state is a characteristics that must be assessed by phase-sensitive measurements. We also show that the non-Gaussianity of conditional states can be manipulated by choosing suitable conditioning values and composition of phase-averaged states.
A voxelation-corrected non-stationary 3D cluster-size test based on random field theory.
Li, Huanjie; Nickerson, Lisa D; Zhao, Xuna; Nichols, Thomas E; Gao, Jia-Hong
2015-09-01
Cluster-size tests (CSTs) based on random field theory (RFT) are commonly adopted to identify significant differences in brain images. However, the use of RFT in CSTs rests on the assumption of uniform smoothness (stationarity). When images are non-stationary, CSTs based on RFT will likely lead to increased false positives in smooth regions and reduced power in rough regions. An adjustment to the cluster size according to the local smoothness at each voxel has been proposed for the standard test based on RFT to address non-stationarity, however, this technique requires images with a large degree of spatial smoothing, large degrees of freedom and high intensity thresholding. Recently, we proposed a voxelation-corrected 3D CST based on Gaussian random field theory that does not place constraints on the degree of spatial smoothness. However, this approach is only applicable to stationary images, requiring further modification to enable use for non-stationary images. In this study, we present modifications of this method to develop a voxelation-corrected non-stationary 3D CST based on RFT. Both simulated and real data were used to compare the voxelation-corrected non-stationary CST to the standard cluster-size adjusted non-stationary CST based on RFT and the voxelation-corrected stationary CST. We found that voxelation-corrected stationary CST is liberal for non-stationary images and the voxelation-corrected non-stationary CST performs better than cluster-size adjusted non-stationary CST based on RFT under low smoothness, low intensity threshold and low degrees of freedom. Published by Elsevier Inc.
Remediating Computational Deficits at Third Grade: A Randomized Field Trial
Fuchs, Lynn S.; Powell, Sarah R.; Hamlett, Carol L.; Fuchs, Douglas; Cirino, Paul T.; FLETCHER, JACK M.
2008-01-01
The major purposes of this study were to assess the efficacy of tutoring to remediate 3rd-grade computational deficits and to explore whether remediation is differentially efficacious depending on whether students experience mathematics difficulty alone or concomitantly with reading difficulty. At 2 sites, 127 students were stratified on mathematics difficulty status and randomly assigned to 4 conditions: word recognition (control) tutoring or 1 of 3 computation tutoring conditions: fact retr...
Preventing Youth Violence and Dropout: A Randomized Field Experiment
Sara Heller; Harold A. Pollack; Roseanna Ander; Jens Ludwig
2013-01-01
Improving the long-term life outcomes of disadvantaged youth remains a top policy priority in the United States, although identifying successful interventions for adolescents - particularly males - has proven challenging. This paper reports results from a large randomized controlled trial of an intervention for disadvantaged male youth grades 7-10 from high-crime Chicago neighborhoods. The intervention was delivered by two local non-profits and included regular interactions with a pro-social ...
Ruban, V P
2015-01-01
The nonlinear dynamics of an obliquely oriented wave packet at sea surface is studied both analytically and numerically for various initial parameters of the packet, in connection with the problem of oceanic rogue waves. In the framework of Gaussian variational ansatz applied to the corresponding (1+2D) hyperbolic nonlinear Schr\\"odinger equation, a simplified Lagrangian system of differential equations is derived, which determines the evolution of coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description for the process of nonlinear spatio-temporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system is integrated in quadratures, which fact allows us to understand qualitative differences between the linear and nonlinear regimes of the focusing of wave packet. Comparison of the Gaussian model predictions with results of direct numerical simulation of fully nonlinear long-cres...
Kang; Ih; Kim; Kim
2000-03-01
In this study, a new prediction method is suggested for sound transmission loss (STL) of multilayered panels of infinite extent. Conventional methods such as random or field incidence approach often given significant discrepancies in predicting STL of multilayered panels when compared with the experiments. In this paper, appropriate directional distributions of incident energy to predict the STL of multilayered panels are proposed. In order to find a weighting function to represent the directional distribution of incident energy on the wall in a reverberation chamber, numerical simulations by using a ray-tracing technique are carried out. Simulation results reveal that the directional distribution can be approximately expressed by the Gaussian distribution function in terms of the angle of incidence. The Gaussian function is applied to predict the STL of various multilayered panel configurations as well as single panels. The compared results between the measurement and the prediction show good agreements, which validate the proposed Gaussian function approach.
Segmentation of RGB-D indoor scenes by stacking random forests and conditional random fields
DEFF Research Database (Denmark)
Thøgersen, Mikkel; Guerrero, Sergio Escalera; Gonzàlez, Jordi;
2016-01-01
on stacked classifiers; the benefits are two fold: on one hand, the system scales well to consider different types of complex features and, on the other hand, the use of stacked classifiers makes the performance of the proposed technique more accurate. The proposed method consists of a random forest using...... a stacked random forest which gives the final predictions. The model is tested on the renown NYU-v2 dataset and the recently available SUNRGBD dataset. The approach shows that simple multimodal features with the power of using multi-class multi-scale stacked sequential learners (MMSSL) can achieve slight...
Autonomous Gaussian Decomposition
Lindner, Robert R; Murray, Claire E; Stanimirović, Snežana; Babler, Brian L; Heiles, Carl; Hennebelle, Patrick; Goss, W M; Dickey, John
2014-01-01
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21cm absorption spectra from the 21cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the HI line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the up...
Broadcasting Correlated Gaussians
Bross, Shraga; Tinguely, Stephan
2007-01-01
We consider the transmission of a bi-variate Gaussian source over a one-to-two power-limited Gaussian broadcast channel. Receiver 1 observes the transmitted signal corrupted by Gaussian noise and wishes to estimate the first component of the source. Receiver 2 observes the transmitted signal in larger Gaussian noise and wishes to estimate the second component. We seek to characterize the pairs of mean squared-error distortions that are simultaneously achievable at the two receivers. Our result is that below a certain SNR-threshold an "uncoded scheme" that sends a linear combination of the source components is optimal. The SNR-theshold can be expressed as a function of the source correlation and the distortion at Receiver 1.
Hammouda, Boualem
2014-01-01
It is common practice to assume that Bragg scattering peaks have Gaussian shape. The Gaussian shape function is used to perform most instrumental smearing corrections. Using Monte Carlo ray tracing simulation, the resolution of a realistic small-angle neutron scattering (SANS) instrument is generated reliably. Including a single-crystal sample with large d-spacing, Bragg peaks are produced. Bragg peaks contain contributions from the resolution function and from spread in the sample structure. Results show that Bragg peaks are Gaussian in the resolution-limited condition (with negligible sample spread) while this is not the case when spread in the sample structure is non-negligible. When sample spread contributes, the exponentially modified Gaussian function is a better account of the Bragg peak shape. This function is characterized by a non-zero third moment (skewness) which makes Bragg peaks asymmetric for broad neutron wavelength spreads. PMID:26601025
Development of a Random Field Model for Gas Plume Detection in Multiple LWIR Images.
Energy Technology Data Exchange (ETDEWEB)
Heasler, Patrick G.
2008-09-30
This report develops a random field model that describes gas plumes in LWIR remote sensing images. The random field model serves as a prior distribution that can be combined with LWIR data to produce a posterior that determines the probability that a gas plume exists in the scene and also maps the most probable location of any plume. The random field model is intended to work with a single pixel regression estimator--a regression model that estimates gas concentration on an individual pixel basis.
Learning conditional Gaussian networks
DEFF Research Database (Denmark)
Bøttcher, Susanne Gammelgaard
This paper considers conditional Gaussian networks. The parameters in the network are learned by using conjugate Bayesian analysis. As conjugate local priors, we apply the Dirichlet distribution for discrete variables and the Gaussian-inverse gamma distribution for continuous variables, given...... independence, parameter modularity and likelihood equivalence. Bayes factors to be used in model search are introduced. Finally the methods derived are illustrated by a simple example....
Semiparametric Gaussian copula classification
Zhao, Yue; Wegkamp, Marten
2014-01-01
This paper studies the binary classification of two distributions with the same Gaussian copula in high dimensions. Under this semiparametric Gaussian copula setting, we derive an accurate semiparametric estimator of the log density ratio, which leads to our empirical decision rule and a bound on its associated excess risk. Our estimation procedure takes advantage of the potential sparsity as well as the low noise condition in the problem, which allows us to achieve faster convergence rate of...
Filling transitions on rough surfaces: inadequacy of Gaussian surface models
Dufour, Renaud; Herminghaus, Stephan
2015-01-01
We present numerical studies of wetting on various topographic substrates, including random topographies. We find good agreement with recent predictions based on an analytical interface-displacement-type theory \\cite{Herminghaus2012, Herminghaus2012a}. The phase diagrams are qualitatively as predicted, but differently in this study the critical points are found to lie within the physical parameter range (i.e., at positive contact angle) in all cases studied. Notably, it is corroborated that Gaussian random surfaces behave qualitatively different from all non-Gaussian topographies investigated, exhibiting a qualitatively different phase diagram. This shows that Gaussian random surfaces must be used with great care in the context of wetting phenomena.
Test particle transport in perturbed magnetic fields in tokamaks
de Rover, M.; Schilham, A.M.R.; Montvai, A.; Cardozo, N. J. L.
1999-01-01
Numerical calculations of magnetic field line trajectories in a tokamak are used to investigate the common hypotheses that (i) field lines in a chaotic field make a Gaussian random walk and (ii) that the poloidal component of the magnetic field is uniform in regions with a chaotic magnetic field. Bo
Rare-event Analysis and Computational Methods for Stochastic Systems Driven by Random Fields
2014-12-29
random elliptic differential equations . The equation has been employed to describe physics systems in areas as diverse as material science, fluid...probabilities associated with random fields and the associated random elliptic differential equations . The equation has been employed to describe physics...Received Paper 1.00 3.00 4.00 Gongjun Xu, Guang Lin, Jingchen Liu. Rare-Event Simulation for the Stochastic Korteweg--de Vries Equation , SIAM/ASA
On Closely Coupled Dipoles in a Random Field
DEFF Research Database (Denmark)
Andersen, Jørgen Bach; Vincent, L.
2006-01-01
Reception of partially correlated fields by two closely coupled electrical dipoles is discussed as a function of load impedances and open-circuit correlations. Two local maxima of the power may be achieved for two different load impedances, but in those cases the output correlations are high...
Average Number of Coherent Modes for Pulse Random Fields
Lazaruk, A M; Lazaruk, Alexander M.; Karelin, Nikolay V.
1997-01-01
Some consequences of spatio-temporal symmetry for the deterministic decomposition of complex light fields into factorized components are considered. This enables to reveal interrelations between spatial and temporal coherence properties of wave. An estimation of average number of the decomposition terms is obtained in the case of statistical ensemble of light pulses.
Institute of Scientific and Technical Information of China (English)
Erhan Albayrak
2013-01-01
The spin-1 Blume-Capel model with transverse Ω and longitudinal external magnetic fields h,in addition to a longitudinal random crystal field D,is studied in the mean-field approximation.It is assumed that the crystal field is either turned on with probability p or turned off with probability 1-p on the sites of a square lattice.Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ =-Ω/J and p at zero h.Thus,the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.
Thermodynamical Properties of Spin-3/2 Ising Model in a Longitudinal Random Field with Crystal Field
Institute of Scientific and Technical Information of China (English)
LIANG Ya-Qiu; WEI Guo-Zhu; ZHANG Hong; SONG Guo-Li
2004-01-01
A theoretical study of a spin-3/2 Ising model in a longitudinal random field with crystal field is studiedby using of the effective-field theory with correlations. The phase diagrams and the behavior of the tricritical point areinvestigated numerically for the honeycomb lattice when the randorm field is bimodal. In particular, the specific heatand the internal energy are examined in detail for the system with a crystal-field constant in the critical region wherethe ground-state configuration may change from the spin-3/2 state to the spin-1/2 state. We find many interestingphenomena in the system.
Modulation of electromagnetic fields by a depolarizer of random polarizer array
DEFF Research Database (Denmark)
Ma, Ning; Hanson, Steen Grüner; Wang, Wei
2016-01-01
The statistical properties of the electric fields with random changes of the polarization state in space generated by a depolarizer are investigated on the basis of the coherence matrix. The depolarizer is a polarizer array composed of a multitude of contiguous square cells of polarizers with ran......The statistical properties of the electric fields with random changes of the polarization state in space generated by a depolarizer are investigated on the basis of the coherence matrix. The depolarizer is a polarizer array composed of a multitude of contiguous square cells of polarizers...... with randomly distributed polarization angles, where the incident fields experience a random polarization modulation after passing through the depolarizer. The propagation of the modulated electric fields through any quadratic optical system is examined within the framework of the complex ABCD matrix to show...
Initialization of Markov Random Field Clustering of Large Remote Sensing Images
Tran, T.N.; Wehrens, H.R.M.J.; Hoekman, D.H.; Buydens, L.M.C.
2005-01-01
Markov random field (MRF) clustering, utilizing both spectral and spatial interpixel dependency information, often improves classification accuracy for remote sensing images, such as multichannel polarimetric synthetic aperture radar (SAR) images. However, it is heavily sensitive to initial conditio
Active sterile neutrino conversions in a supernova with random magnetic fields
Pastor, S; Valle, José W F; Pastor, S; Semikoz, V; Valle, Jose W F
1995-01-01
{Large enough random magnetic fields may affect in an important way neutrino conversion rates, even in the case where neutrinos have zero transition magnetic moments. We consider their effect in the case of active to sterile \
Continuous Markov Random Fields for Robust Stereo Estimation
Yamaguchi, Koichiro; McAllester, David; Urtasun, Raquel
2012-01-01
In this paper we present a novel slanted-plane MRF model which reasons jointly about occlusion boundaries as well as depth. We formulate the problem as the one of inference in a hybrid MRF composed of both continuous (i.e., slanted 3D planes) and discrete (i.e., occlusion boundaries) random variables. This allows us to define potentials encoding the ownership of the pixels that compose the boundary between segments, as well as potentials encoding which junctions are physically possible. Our approach outperforms the state-of-the-art on Middlebury high resolution imagery as well as in the more challenging KITTI dataset, while being more efficient than existing slanted plane MRF-based methods, taking on average 2 minutes to perform inference on high resolution imagery.
DEFF Research Database (Denmark)
Wang, W.; Hanson, Steen Grüner; Miyamoto, Y.;
2005-01-01
We present the first direct experimental evidence of the local properties of optical vortices in a random laser speckle field. We have observed the Berry anisotropy ellipse describing the anisotropic squeezing of phase lines close to vortex cores and quantitatively verified the Dennis angular...... momentum rule for its phase. Some statistics associated with vortices, such as density, anisotropy ellipse eccentricity, and its relation to zero crossings of real and imaginary parts of the random field, are also investigated by experiments....
Phase Diagrams and Tricritical Behaviour of the Spin-2 Ising Model in a Longitudinal Random Field
Institute of Scientific and Technical Information of China (English)
LIANG Ya-Qiu; WEI Guo-Zhu; ZHANG Qi; SONG Guo-Li
2004-01-01
@@ Within the framework of the effective-field theory with correlations, we study the ferromagnetic spin-2 randomfield Ising model (RFIM) in the presence of a crystal field on honeycomb (z = 3), square (z = 4) and simple cubic (z = 6) lattices. The effects of the crystal field and the longitudinal random field on the phase diagrams are investigated. Some characteristic features of the phase diagrams, such as the tricritical phenomena, reentrant phenomena and existence of two tricritical points, are found.
Revisiting Boltzmann learning: parameter estimation in Markov random fields
DEFF Research Database (Denmark)
Hansen, Lars Kai; Andersen, Lars Nonboe; Kjems, Ulrik
1996-01-01
This article presents a generalization of the Boltzmann machine that allows us to use the learning rule for a much wider class of maximum likelihood and maximum a posteriori problems, including both supervised and unsupervised learning. Furthermore, the approach allows us to discuss regularization...... and generalization in the context of Boltzmann machines. We provide an illustrative example concerning parameter estimation in an inhomogeneous Markov field. The regularized adaptation produces a parameter set that closely resembles the “teacher” parameters, hence, will produce segmentations that closely reproduce...
Random walk study of electron motion in helium in crossed electromagnetic fields
Englert, G. W.
1972-01-01
Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.
Arnaut, L R
2006-01-01
Using a TE/TM decomposition for an angular plane-wave spectrum of free random electromagnetic waves and matched boundary conditions, we derive the probability density function for the energy density of the vector electric field in the presence of a semi-infinite isotropic medium. The theoretical analysis is illustrated with calculations and results for good electric conductors and for a lossless dielectric half-space. The influence of the permittivity and conductivity on the intensity, random polarization, statistical distribution and standard deviation of the field is investigated, both for incident plus reflected fields and for refracted fields. External refraction is found to result in compression of the fluctuations of the random field.
Metastable minima of the Heisenberg spin glass in a random magnetic field
Sharma, Auditya; Yeo, Joonhyun; Moore, M. A.
2016-11-01
We have studied zero-temperature metastable minima in classical m -vector component spin glasses in the presence of m -component random fields for two models, the Sherrington-Kirkpatrick (SK) model and the Viana-Bray (VB) model. For the SK model we have calculated analytically its complexity (the log of the number of minima) for both the annealed case where one averages the number of minima before taking the log and the quenched case where one averages the complexity itself, both for fields above and below the de Almeida-Thouless (AT) field, which is finite for m >2 . We have done numerical quenches starting from a random initial state (infinite temperature state) by putting spins parallel to their local fields until there is no further decrease of the energy and found that in zero field it always produces minima that have zero overlap with each other. For the m =2 and m =3 cases in the SK model the final energy reached in the quench is very close to the energy Ec at which the overlap of the states would acquire replica symmetry-breaking features. These minima have marginal stability and will have long-range correlations between them. In the SK limit we have analytically studied the density of states ρ (λ ) of the Hessian matrix in the annealed approximation. Despite the fact that in the presence of a random field there are no continuous symmetries, the spectrum extends down to zero with the usual √{λ } form for the density of states for fields below the AT field. However, when the random field is larger than the AT field, there is a gap in the spectrum, which closes up as the AT field is approached. The VB model behaves differently and seems rather similar to studies of the three-dimensional Heisenberg spin glass in a random vector field.
Optimizing Electromagnetically Induced Transparency Signals with Laguerre-Gaussian Beams
Holtfrerich, Matthew; Akin, Tom; Krzyzewski, Sean; Marino, Alberto; Abraham, Eric
2016-05-01
We have performed electromagnetically induced transparency in ultracold Rubidium atoms using a Laguerre-Gaussian laser mode as the control beam. Laguerre-Gaussian modes are characterized by a ring type transverse intensity profile and carry intrinsic orbital angular momentum. This angular momentum carried by the control beam can be utilized in optical computing applications which is unavailable to the more common Gaussian laser field. Specifically, we use a Laguerre-Gaussian control beam with a Gaussian probe to show that the linewidth of the transmission spectrum can be narrowed when compared to a Gaussian control beam that has the same peak intensity. We present data extending this work to compare control fields in both the Gaussian and Laguerre-Gaussian modes with constant total power. We have made efforts to find the optical overlap that best minimizes the transmission linewidth while also maintaining signal contrast. This was done by changing the waist size of the control beam with respect to the probe. The best results were obtained when the waist of a Laguerre-Gaussian control beam is equal to the waist of the Gaussian probe resulting in narrow linewidth features.
A dissipative random velocity field for fully developed fluid turbulence
Pereira, Rodrigo M; Chevillard, Laurent
2015-01-01
We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectory. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model depending on a single free parameter $\\gamma$ that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments (i.e. the structure functions), including the intermittent corrections, and the existence of energy transfers across scales. We quantify the dependence of these basic properties of turbulent flows on the free...
Deblured Gaussian Blurred Images
Al-amri, Salem Saleh; D, Khamitkar S
2010-01-01
This paper attempts to undertake the study of Restored Gaussian Blurred Images. by using four types of techniques of deblurring image as Wiener filter, Regularized filter, Lucy Richardson deconvlutin algorithm and Blind deconvlution algorithm with an information of the Point Spread Function (PSF) corrupted blurred image with Different values of Size and Alfa and then corrupted by Gaussian noise. The same is applied to the remote sensing image and they are compared with one another, So as to choose the base technique for restored or deblurring image.This paper also attempts to undertake the study of restored Gaussian blurred image with no any information about the Point Spread Function (PSF) by using same four techniques after execute the guess of the PSF, the number of iterations and the weight threshold of it. To choose the base guesses for restored or deblurring image of this techniques.
CRITICAL BEHAVIOR OF S-3／2 ISING MODEL IN RANDOM LONGITUDINAL AND TRANSVERSE FIELDS
Institute of Scientific and Technical Information of China (English)
宋为基
1995-01-01
The phase diagrams and the other crtical properties of S-3/2 Ising model in random longitudinal and transverse fields(RLIM) are dicussed with the approximate scheme combined by mean-field renormalization group theory(MFRG) and the discretized path-integral representation(DPIR).
A Remark on the Lifshitz Tail for Schrödinger Operator with Random Magnetic Field
Indian Academy of Sciences (India)
Shu Nakamura
2002-02-01
In this note, we consider the Lifshitz singularity for Schrödinger operator with ergodic random magnetic field. A key estimate is an energy bound for magnetic Schrödinger operators as discussed in Nakamura [8]. Here we remove a technical assumption in [8], namely, the uniform boundedness of the magnetic field.
Scheerlinck, N.; Verboven, P.; Stigter, J.D.; Baerdenmaeker, de J.; Impe, van J.F.; Nicolai, B.A.
2000-01-01
A first-order perturbation algorithm for the computation of mean values and variances of transient temperature and moisture fields during coupled heat and mass transfer problems with random field parameters has been developed and implemented. The algorithm is based on the Galerkin finite-element dis
Mean-field theory of random-site q-state Potts models
van Enter, Aernout; Hemmen, Jan Leonard van; Pospiech, C.
1988-01-01
A class of random-site mean-field Potts models is introduced and solved exactly. The bifurcation properties of the resulting mean-field equations are analysed in detail. Particular emphasis is put on the relation between the solutions and the underlying symmetries of the model. It turns out that, in
Relaxation oscillations in a laser with a Gaussian mirror.
Mossakowska-Wyszyńska, Agnieszka; Witoński, Piotr; Szczepański, Paweł
2002-03-20
We present an analysis of the relaxation oscillations in a laser with a Gaussian mirror by taking into account the three-dimensional spatial field distribution of the laser modes and the spatial hole burning effect. In particular, we discuss the influence of the Gaussian mirror peak reflectivity and a Gaussian parameter on the damping rate and frequency of the relaxation oscillation for two different laser structures, i.e., with a classically unstable resonator and a classically stable resonator.
Spectra for the product of Gaussian noises
Kish, L B; Gingl, Z; Granqvist, C G
2012-01-01
Products of Gaussian noises often emerge as the result of non-linear detection techniques or as a parasitic effect, and their proper handling is important in many practical applications, including in fluctuation-enhanced sensing, indoor air or environmental quality monitoring, etc. We use Rice's random phase oscillator formalism to calculate the power density spectra variance for the product of two Gaussian band-limited white noises with zero-mean and the same bandwidth W. The ensuing noise spectrum is found to decrease linearly from zero frequency to 2W, and it is zero for frequencies greater than 2W. Analogous calculations performed for the square of a single Gaussian noise confirm earlier results. The spectrum at non-zero frequencies, and the variance of the square of a noise, is amplified by a factor two as a consequence of correlation effects between frequency products. Our analytic results is corroborated by computer simulations.
Firmani, C
2013-01-01
In order to attain a statistical description of the evolution of cosmic density fluctuations in agreement with results from the numerical simulations, we introduce a probability conditional formalism (CF) based on an inventory of isolated overdense regions in a density random field. This formalism is a useful tool for describing at the same time the mass function (MF) of dark haloes, their mass aggregation histories (MAHs) and merging rates (MRs). The CF focuses on virialized regions in a self-consistent way rather than in mass elements, and it offers an economical description for a variety of random fields. Within the framework of the CF, we confirm that, for a Gaussian field, it is not possible to reproduce at the same time the MF, MAH, and MR of haloes, both for a constant and moving barrier. Then, we develop an inductive method for constraining the cumulative conditional probability from a given halo MF description, and thus, using the CF, we calculate the halo MAHs and MRs. By applying this method to the...
Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures
DEFF Research Database (Denmark)
Beermann, Jonas; Bozhevolnyi, Sergey I.; Coello, Victor
2006-01-01
Nonlinear microscopy of localized field enhancements in random metal nanostructures with a tightly focused laser beam scanning over a sample surface is modeled by making use of analytic representations of the Green dyadic in the near- and far-field regions, with the latter being approximated...... by the part describing the scattering via excitation of surface plasmon polaritons. The developed approach is applied to scanning second-harmonic (SH) microscopy of small gold spheres placed randomly on a gold surface. We calculate self-consistent fundamental harmonic (FH) and SH field distributions...
Magnetic properties of a transverse spin- Ising model with random longitudinal field
Liang, Ya-Qiu; Wei, Guo-Zhu; Song, Guo-Li
2004-12-01
Within the framework of the effective-field theory with correlations, a spin- transverse Ising model in the longitudinal random-field on a honeycomb lattice is studied. The phase diagrams and the behavior of the tricritical point are examined. The possible re-entrance phenomena displayed by the system due to the competition effects that occur for the appropriate ranges of the random and transverse field are investigated. The longitudinal and transverse magnetizations, the longitudinal quadrupolar moments and internal energy are given numerically for a honeycomb lattice (z = 3).
Phase diagram of the classical Heisenberg model in a trimodal random field distribution
Santos-Filho, A.; Albuquerque, D. F. de; Santos-Filho, J. B.; Batista, T. S. Araujo
2016-11-01
The classical spin 1 / 2 Heisenberg model on a simple cubic lattice, with fluctuating bond interactions between nearest neighbors and in the presence of a random magnetic field, is investigated by effective field theory based on two-spin cluster. The random field is drawn from the asymmetric and anisotropic trimodal probability distribution. The fluctuating bond is extracted from the symmetric and anisotropic bimodal probability. We estimate the transition temperatures, and the phase diagram in the Tc- h, Tc- p and Tc - α planes. We observe that the temperature of the tricritical point decreases with the increase of disorder in exchange interactions until the system ceases to display tricritical behavior. The disorder of the interactions and reentrant phenomena depends on the trimodal distribution of the random field.
Institute of Scientific and Technical Information of China (English)
李阔湖; 宋月丽; 姚东永; 景东山
2012-01-01
运用边界元素法把圆形高斯镜平凹腔的自再现模的衍射积分方程转化为有限阶矩阵方程.计算了谐振腔在理想情况和高斯反射率平面输出镜倾斜情况下基模的场强分布、相位分布和本征值.研究表明,腔镜倾斜使激光场模式分布沿发生倾斜的方向向镜边缘偏移,而且在腔镜倾斜较严重时模式分布发生畸变,不再是对称的拉盖尔-高斯基模分布.基模本征值随倾斜角增大而变小,光束远场分布变差.减小高斯分布反射率的膜斑半径,则能减弱因倾斜引起的模式畸变.%By means of boundary finite-element method, the field distributions and eigenvalues of the fundamental mode of the plano-concave resonator with a tilted Gaussian-reflectivity plane mirror are calculated and discussed. The results show that the laser mode moves along the direction of the mirror tilting. When the tilt angle of the mirror is big e-nough, the mode is distorted, no longer with a Laguerre-Gaussian distribution. Furthermore, following the increasing of the tilt angle, the far field distributions become bad, and the eigenvalue decrease. By decreasing the characteristic radius of the Gaussian-reflectivity, the distortion of the mode that is induced by the mirror tilting is decreased.
Non-Gaussianity of Racetrack Inflation Models
Institute of Scientific and Technical Information of China (English)
SUN Cheng-Yi; ZHANG De-Hai
2007-01-01
In this paper, we use the result in [C.Y. Sun and D.H. Zhang, arXiv:astro-ph/0510709] to calculate the non-Gaussianity of the racetrack models in[J.J. Blanco-Pillado, et al., JHEP 0411 (2004) 063; arXiv:hep-th/0406230]and [J.J. Blanco-Pillado, et al., arXiv:hep-th/0603129]. The two models give different non-Gaussianities. Both of them are reasonable. However, we find that, for multi-field inflationary models with the non-trivial metric of the field space,the condition of the slow-roll cannot guarantee small non-Gaussianities.
Trofimov, M Yu; Kozitskiy, S B
2015-01-01
An adiabatic mode Helmholtz equation for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the crosswedge benchmark and proved an excellent agreement with the source images method.
AUTONOMOUS GAUSSIAN DECOMPOSITION
Energy Technology Data Exchange (ETDEWEB)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Heiles, Carl [Radio Astronomy Lab, UC Berkeley, 601 Campbell Hall, Berkeley, CA 94720 (United States); Hennebelle, Patrick [Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp-CNRS-Université Paris Diderot, F-91191 Gif-sur Yvette Cedex (France); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville, Socorro, NM 87801 (United States); Dickey, John, E-mail: rlindner@astro.wisc.edu [University of Tasmania, School of Maths and Physics, Private Bag 37, Hobart, TAS 7001 (Australia)
2015-04-15
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
Gaussian fluctuations in chaotic eigenstates
Srednicki, M A; Srednicki, Mark; Stiernelof, Frank
1996-01-01
We study the fluctuations that are predicted in the autocorrelation function of an energy eigenstate of a chaotic, two-dimensional billiard by the conjecture (due to Berry) that the eigenfunction is a gaussian random variable. We find an explicit formula for the root-mean-square amplitude of the expected fluctuations in the autocorrelation function. These fluctuations turn out to be O(\\hbar^{1/2}) in the small \\hbar (high energy) limit. For comparison, any corrections due to scars from isolated periodic orbits would also be O(\\hbar^{1/2}). The fluctuations take on a particularly simple form if the autocorrelation function is averaged over the direction of the separation vector. We compare our various predictions with recent numerical computations of Li and Robnik for the Robnik billiard, and find good agreement. We indicate how our results generalize to higher dimensions.
Non-gaussian CMBR angular power spectra
Magueijo, J
1995-01-01
In this paper we show how the prediction of CMBR angular power spectra C_l in non-Gaussian theories is affected by a cosmic covariance problem, that is (C_l,C_{l'}) correlations impart features on any observed C_l spectrum which are absent from the average C^l spectrum. Therefore the average spectrum is rendered a bad observational prediction, and two new prediction strategies, better adjusted to these theories, are proposed. In one we search for hidden random indices conditional to which the theory is released from the correlations. Contact with experiment can then be made in the form of the conditional power spectra plus the random index distribution. In another approach we apply to the problem a principal component analysis. We discuss the effect of correlations on the predictivity of non-Gaussian theories. We finish by showing how correlations may be crucial in delineating the borderline between predictions made by non-Gaussian and Gaussian theories. In fact, in some particular theories, correlations may ...
Institute of Scientific and Technical Information of China (English)
程红伟; 陶俊勇; 蒋瑜; 陈循
2014-01-01
Aiming at the difficulty in deriving mathematical expressions of amplitude probability density functions of non-Gaussian vibrations,a Gaussian mixture model-based probability density function (PDF ) was proposed for non-Gaussian vibration signals.The estimation of higher-order moments of a non-Gaussian vibration process was obtained with sample time histories.Based on the quantitative relations between the even order moments of a given Gaussian process, combining with a secorld order Gaussian mixture model,an equation set for achieving the parameters of each Gaussian component in the Gaussian mixture model was established.Based on the obtained weighting factors and variances of Gaussian components,the mathematical model of non-Gaussian probability density function was then achieved.The examples of simulated signals and measured signals verified the validity of the presented method.%针对非高斯振动信号的幅值概率密度函数难以用数学模型表述的问题，提出了基于高斯混合模型的非高斯概率密度函数表示方法。首先，基于时域样本信号得到非高斯振动信号的高阶矩估计值。其次，基于高斯随机过程偶次高阶矩之间的定量关系，结合二阶高斯混合模型建立方程组，求解得到混合模型中每个高斯分量的方差和权值。然后，将各高斯分量的权值和方差代入高斯混合模型，得到适用于对称非高斯振动信号的幅值概率密度函数。最后，通过仿真信号和实测振动信号，验证了该方法的有效性和适用性。
Effects of the random field on the magnetic behavior of nanowires with core/shell morphology
Energy Technology Data Exchange (ETDEWEB)
Zaim, A., E-mail: ah_zaim@yahoo.fr [Laboratoire Physique des Matériaux et Modélisation des Systèmes (LP2MS), Unité Associée au CNRST-URAC: 08, Faculty of Sciences, University Moulay Ismail, B.P. 11201, Zitoune, Meknes (Morocco); Kerouad, M., E-mail: kerouad@fs-umi.ac.ma [Laboratoire Physique des Matériaux et Modélisation des Systèmes (LP2MS), Unité Associée au CNRST-URAC: 08, Faculty of Sciences, University Moulay Ismail, B.P. 11201, Zitoune, Meknes (Morocco); Boughrara, M. [Laboratoire Physique des Matériaux et Modélisation des Systèmes (LP2MS), Unité Associée au CNRST-URAC: 08, Faculty of Sciences, University Moulay Ismail, B.P. 11201, Zitoune, Meknes (Morocco)
2013-04-15
We have used the effective field theory based on probability distribution method to investigate the hysteresis behavior of the magnetic nanowires with core/shell morphology in a random magnetic field. The hysteresis curves are obtained for different values of the random magnetic field, both ferromagnetic and antiferromagnetic couplings between the shell and the core are considered. A number of characteristic behaviors are find, such as the existence of double or triple hysteresis loops for appropriate values of the system parameters affected by the random magnetic field, temperature, and interfacial coupling. -- Highlights: ► The hysteresis behavior of the Ising nanowires has been studied by EFT. ► The effects of the random field on the hysteresis loops have been examined. ► The hysteresis loops are obtained for different values of the interfacial coupling constant. ► The triple hysteresis loops occur for the larger antiferromagnetic coupling constant. ► The dependence of the coercive field on the temperature is investigated.
Stochastic structure formation in random media
Klyatskin, V. I.
2016-01-01
Stochastic structure formation in random media is considered using examples of elementary dynamical systems related to the two-dimensional geophysical fluid dynamics (Gaussian random fields) and to stochastically excited dynamical systems described by partial differential equations (lognormal random fields). In the latter case, spatial structures (clusters) may form with a probability of one in almost every system realization due to rare events happening with vanishing probability. Problems involving stochastic parametric excitation occur in fluid dynamics, magnetohydrodynamics, plasma physics, astrophysics, and radiophysics. A more complicated stochastic problem dealing with anomalous structures on the sea surface (rogue waves) is also considered, where the random Gaussian generation of sea surface roughness is accompanied by parametric excitation.
The limiting behavior of the estimated parameters in a misspecified random field regression model
DEFF Research Database (Denmark)
Dahl, Christian Møller; Qin, Yu
convenient new uniform convergence results that we propose. This theory may have applications beyond those presented here. Our results indicate that classical statistical inference techniques, in general, works very well for random field regression models in finite samples and that these models succesfully......This paper examines the limiting properties of the estimated parameters in the random field regression model recently proposed by Hamilton (Econometrica, 2001). Though the model is parametric, it enjoys the flexibility of the nonparametric approach since it can approximate a large collection...... of nonlinear functions and it has the added advantage that there is no "curse of dimensionality."Contrary to existing literature on the asymptotic properties of the estimated parameters in random field models our results do not require that the explanatory variables are sampled on a grid. However...
Randomness in highly reflective silver nanoparticles and their localized optical fields
Naruse, Makoto; Yasuda, Hideki; Tate, Naoya; Ohtsu, Motoichi; Naya, Masayuki
2014-01-01
Reflection of near-infrared light is important for preventing heat transfer in energy saving applications. A large-area, mass-producible reflector that contains randomly distributed disk-shaped silver nanoparticles and that exhibits high reflection at near-infrared wavelengths was demonstrated. Although resonant coupling between incident light and the nanostructure of the reflector plays some role, what is more important is the geometrical randomness of the nanoparticles, which serves as the origin of a particle-dependent localization and hierarchical distribution of optical near-fields in the vicinity of the nanostructure. Here we show and clarified the unique optical near-field processes associated with the randomness seen in experimentally fabricated silver nanostructures by adapting a rigorous theory of optical near-fields based on an angular spectrum and detailed electromagnetic calculations.
A test for stationarity of spatio-temporal random fields on planar and spherical domains
Jun, Mikyoung
2012-01-01
A formal test for weak stationarity of spatial and spatio-temporal random fields is proposed. We consider the cases where the spatial domain is planar or spherical, and we do not require distributional assumptions for the random fields. The method can be applied to univariate or to multivariate random fields. Our test is based on the asymptotic normality of certain statistics that are functions of estimators of covariances at certain spatial and temporal lags under weak stationarity. Simulation results for spatial as well as spatio-temporal cases on the two types of spatial domains are reported. We describe the results of testing the stationarity of Pacific wind data, and of testing the axial symmetry of climate model errors for surface temperature using the NOAA GFDL model outputs and the observations from the Climate Research Unit in East Anglia and the Hadley Centre.
Experimental realization of random-field Ising ferromagnetism in a molecular magnet
Sarachik, Myriam P.
2011-03-01
The longitudinal magnetic susceptibility of single crystals of the molecular magnet Mn 12 -acetate obeys a Curie-Weiss law, indicating a transition to a ferromagnetic phase at ~ 0.9 K [1,2]. With increasing magnetic field applied transverse to the easy axis, a marked change is observed in the temperature dependence of the susceptibility, with a considerably more rapid suppression of the Curie-Weiss temperature than predicted by mean-field theory for an ordered single crystal. Our results can instead be fit by a Hamiltonian for a random-field Ising ferromagnet in a transverse magnetic field, where the randomness derives from the intrinsic distribution of locally tilted magnetic easy axes known to exist in Mn 12 -acetate crystals. Mn 12 -ac and other single molecule magnets may thus serve as clean model systems for the study of random field ferromagnetism where the random fields are controllable and considerably larger than typical hyperfine fields. This discovery promises to enable widespread and convenient experimental study of magnetism in a random field in a broad class of new materials. Work performed by and in collaboration with: Bo Wen, and Lin Bo, Physics Dept. City College of New York, CUNY (funded by NSF-DMR-0451605), P. Subedi and A. D. Kent, Physics Dept., NYU, (funded by NSF-DMR-0506946 and ARO-W911NF-08-1-0364) Y. Yeshurun, Physics Dept., Bar Ilan U, (funded by Deutsche Forschungsgemeinschaft), A. J. Millis, Physics Dept. Columbia U. (funded by DMR DMR-0705847), C. Lampropoulos and G. Christou, Chemistry Dept., U. of Florida (funded by NSF -CHE-0910472). Funding provided by NSF award DMR-0451605.
Energy Technology Data Exchange (ETDEWEB)
Grigoriev, K S; Makarov, Vladimir A; Perezhogin, I A; Potravkin, N N [Department of Physics, M.V. Lomonosov Moscow State University (Russian Federation)
2011-11-30
We have analysed the conditions for the appearance of polarisation singularities in the second-harmonic beam cross section arising in the case of reflection of a uniformly elliptically polarised Gaussian beam at the fundamental frequency from the surface of an isotropic gyrotropic medium. It is shown that there are elliptical polarisation states of the incident light at which the cross section of the second-harmonic reflected beam contains either one or two C lines and either two, or one, or none L lines [the loci of the points where the propagating radiation is circularly (C) or linearly (L) polarised].The formulas determining the conditions for the occurrence of L and C lines and specifying their orientation in the plane of the cross-section of the second-harmonic beam are obtained.
The Gaussian entropy of fermionic systems
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav, E-mail: T.Prokopec@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Schmidt, Michael G., E-mail: M.G.Schmidt@thphys.uni-heidelberg.de [Institut fuer Theoretische Physik, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany); Weenink, Jan, E-mail: J.G.Weenink@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands)
2012-12-15
We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of these correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence and classicalization. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields. - Highlights: Black-Right-Pointing-Pointer We construct the Gaussian density operator for relativistic fermionic systems. Black-Right-Pointing-Pointer The Gaussian entropy of relativistic fermionic systems is described in terms of 2-point correlators. Black-Right-Pointing-Pointer We explicitly show the growth of entropy for fermionic fields mixing with a thermal fermionic environment.
Dynamics of Crowd Behaviors: From Complex Plane to Quantum Random Fields
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
The following sections are included: * Complex Plane Dynamics of Crowds and Groups * Introduction * Complex-Valued Dynamics of Crowd and Group Behaviors * Kähler Geometry of Crowd and Group Dynamics * Computer Simulations of Crowds and Croups Dynamics * Braids of Agents' Behaviors in the Complex Plane * Hilbert-Space Control of Crowds and Groups Dynamics * Quantum Random Fields: A Unique Framework for Simulation, Optimization, Control and Learning * Introduction * Adaptive Quantum Oscillator * Optimization and Learning on Banach and Hilbert Spaces * Appendix * Complex-Valued Image Processing * Linear Integral Equations * Riemann-Liouville Fractional Calculus * Rigorous Geometric Quantization * Supervised Machine-Learning Methods * First-Order Logic and Quantum Random Fields
THE DECISION OF THE OPTIMAL PARAMETERS IN MARKOV RANDOM FIELDS OF IMAGES BY GENETIC ALGORITHM
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper introduces the principle of genetic algorithm and the basic method of solving Markov random field parameters.Focusing on the shortcomings in present methods,a new method based on genetic algorithms is proposed to solve the parameters in the Markov random field.The detailed procedure is discussed.On the basis of the parameters solved by genetic algorithms,some experim ents on classification of aerial images are given.Experimental results show that the proposed method is effective and the classification results are satisfactory.
The limiting behavior of the estimated parameters in a misspecified random field regression model
DEFF Research Database (Denmark)
Dahl, Christian Møller; Qin, Yu
, as a consequence the random field model specification introduces non-stationarity and non-ergodicity in the misspecified model and it becomes non-trivial, relative to the existing literature, to establish the limiting behavior of the estimated parameters. The asymptotic results are obtained by applying some...... convenient new uniform convergence results that we propose. This theory may have applications beyond those presented here. Our results indicate that classical statistical inference techniques, in general, works very well for random field regression models in finite samples and that these models succesfully...
Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure
DEFF Research Database (Denmark)
Rønn-Nielsen, Anders; Jensen, Eva B. Vedel
We consider a continuous, infinitely divisible random field in R d , d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields we compute the asymptotic probability that the excursion set a...... at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure...
Carbon nanotube field emitters on KOVAR substrate modified by random pattern
Energy Technology Data Exchange (ETDEWEB)
Park, Seol Ah; Song, Eun-Ho; Kang, Byung Hyun; Ju, Byeong-Kwon, E-mail: bkju@korea.ac.kr [Korea University, Display and Nanosystem Laboratory, College of Engineering (Korea, Republic of)
2015-07-15
We investigated the field emission characteristics of patterned carbon nanotubes (CNTs) on KOVAR substrates with different surface morphologies. The substrate with a micro-sized random pattern was fabricated through chemical wet etching, whereas the substrate with a nano-sized random pattern was formed by surface roughening process of polymer and chemical wet etching. The field emission characteristics of these substrates were the compared with those of non-treated substrates. It was clearly revealed that the field emission characteristics of CNTs were influenced by the surface morphology of the cathode substrate. When the surface of cathode was modified by random pattern, the modified substrate provided a large surface area and a wider print area. Also, the modified surface morphology of the cathode provided strong adhesion between the CNT paste and the cathode. Particularly, the substrate with the nano-sized random pattern showed that the turn-on field value decreases and the field enhancement factor value improves as compared with non-treated substrate.
A Gaussian graphical model approach to climate networks
Energy Technology Data Exchange (ETDEWEB)
Zerenner, Tanja, E-mail: tanjaz@uni-bonn.de [Meteorological Institute, University of Bonn, Auf dem Hügel 20, 53121 Bonn (Germany); Friederichs, Petra; Hense, Andreas [Meteorological Institute, University of Bonn, Auf dem Hügel 20, 53121 Bonn (Germany); Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn (Germany); Lehnertz, Klaus [Department of Epileptology, University of Bonn, Sigmund-Freud-Straße 25, 53105 Bonn (Germany); Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn (Germany); Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn (Germany)
2014-06-15
Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.
Gaussian quantum marginal problem
Eisert, J; Sanders, B C; Tyc, T
2007-01-01
The quantum marginal problem asks what local spectra are consistent with a given state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn) and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of ...
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
Trofimov, M. Yu.; Zakharenko, A. D.; Kozitskiy, S. B.
2016-10-01
A mode parabolic equation in the ray centered coordinates for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the ASA wedge benchmark and proved an excellent agreement with the source images method in the case of cross-slope propagation. But in the cases of wave propagation at some angles to the cross-slope direction an account of mode interaction becomes necessary.
Trap split with Laguerre-Gaussian beams
Hamideh Kazemi, Seyedeh; Ghanbari, Saeed; Mahmoudi, Mohammad
2017-08-01
We present a convenient and effective way to generate a novel phenomenon of trapping, named ‘trap split’, in a conventional four-level double-Λ atomic system, driven by four femtosecond Laguerre-Gaussian laser pulses. We find that trap split can always be achieved when atoms are trapped by such laser pulses, as compared to Gaussian ones. This feature is enabled by the interaction of the atomic system and the Laguerre-Gaussian laser pulses with zero intensity in the center. A further advantage of using Laguerre-Gaussian laser pulses is the insensitivity to fluctuation in the intensity of the lasers in such a way that the separation between the traps remains constant. Moreover, it is demonstrated that the suggested scheme with Laguerre-Gaussian laser pulses can form optical traps with spatial sizes that are not limited by the wavelength of the laser, and can, in principle, become smaller than the wavelength of light. This work would greatly facilitate the trapping and manipulating of particles and the generation of trap split. It may also suggest the possibility of extension into new research fields, such as micro-machining and biophysics.
Gaussian entanglement in the turbulent atmosphere
Bohmann, M.; Semenov, A. A.; Sperling, J.; Vogel, W.
2016-07-01
We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a nontrivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.
Disorder fingerprint: Intensity distributions in the near field of random media
Naraghi, R. Rezvani; Sukhov, S.; Dogariu, A.
2016-11-01
The structural morphology of complex dielectric media determines their functionalities by driving the statistical properties of the electromagnetic fields. Our controlled experiments and full electromagnetic calculations that go beyond common dipolar approximations demonstrate that the specific characteristics of disorder lead to non-Rayleigh statistics of detected intensity, which can be directly accessed in the near field of random media and can be unambiguously related to the short-range correlations of disorder.
Quintin, Jerome; Cai, Yi-Fu; Brandenberger, Robert H
2015-01-01
Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the non-trivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter $f_{\\mathrm{NL}}$ (which is of order unity bef...
Bessel-Gaussian entanglement; presentation
CSIR Research Space (South Africa)
Mclaren, M
2013-07-01
Full Text Available GAUSSIAN BEAM LAGUERRE-GAUSSIAN BEAM 15 Page 5 Higher-order Bessel-Gaussian beams carry OAM Page 6 © CSIR 2013 www.csir.co.za Generating Bessel-Gaussian beams using spatial light modulators (SLMs) Blazed axicon Binary axicon... stream_source_info McLaren_2013.pdf.txt stream_content_type text/plain stream_size 2915 Content-Encoding UTF-8 stream_name McLaren_2013.pdf.txt Content-Type text/plain; charset=UTF-8 Bessel-Gaussian entanglement M. Mc...
Using Conditional Random Fields to Extract Contexts and Answers of Questions from Online Forums
DEFF Research Database (Denmark)
Ding, Shilin; Cong, Gao; Lin, Chin-Yew;
2008-01-01
on Conditional Random Fields (CRFs) to detect the contexts and answers of questions from forum threads. We improve the basic framework by Skip-chain CRFs and 2D CRFs to better accommodate the features of forums for better performance. Experimental results show that our techniques are very promising....
Kernel conditional ordinal random fields for temporal segmentation of facial action units
Rudovic, Ognjen; Pavlovic, Vladimir; Pantic, Maja
2012-01-01
We consider the problem of automated recognition of temporal segments (neutral, onset, apex and offset) of Facial Action Units. To this end, we propose the Laplacian-regularized Kernel Conditional Ordinal Random Field model. In contrast to standard modeling approaches to recognition of AUs’ temporal
Using Conditional Random Fields to Extract Contexts and Answers of Questions from Online Forums
DEFF Research Database (Denmark)
Ding, Shilin; Cong, Gao; Lin, Chin-Yew
2008-01-01
on Conditional Random Fields (CRFs) to detect the contexts and answers of questions from forum threads. We improve the basic framework by Skip-chain CRFs and 2D CRFs to better accommodate the features of forums for better performance. Experimental results show that our techniques are very promising....
van Kasteren, T.L.M.; Noulas, A.K.; Kröse, B.J.A.; Smit, G.J.M.; Epema, D.H.J.; Lew, M.S.
2008-01-01
Conditional Random Fields are a discriminative probabilistic model which recently gained popularity in applications that require modeling nonindependent observation sequences. In this work, we present the basic advantages of this model over generative models and argue about its suitability in the do
Separate Training for Conditional Random Fields Using Co-occurrence Rate Factorization
Zhu, Zhemin; Hiemstra, Djoerd; Apers, Peter M.G.; Wombacher, Andreas
2012-01-01
The standard training method of Conditional Random Fields (CRFs) is very slow for large-scale applications. As an alternative, piecewise training divides the full graph into pieces, trains them independently, and combines the learned weights at test time. In this paper, we present separate training
A Central Limit Theorem for the Volumes of High Excursions of Stationary Associated Random Fields
Directory of Open Access Journals (Sweden)
Vadim Demichev
2015-05-01
Full Text Available We prove that under certain conditions the excursion sets volumes of stationary positively associated random fields converge after rescaling to the normal distribution as the excursion level and the size of the observation window grow. In addition, we provide a number of examples.
Modelling Distributed Shape Priors by Gibbs Random Fields of Second Order
Flach, Boris
2011-01-01
We analyse the potential of Gibbs Random Fields for shape prior modelling. We show that the expressive power of second order GRFs is already sufficient to express simple shapes and spatial relations between them simultaneously. This allows to model and recognise complex shapes as spatial compositions of simpler parts.
Joint modeling of ChIP-seq data via a Markov random field model
Bao, Yanchun; Vinciotti, Veronica; Wit, Ernst; 't Hoen, Peter A C
2014-01-01
Chromatin ImmunoPrecipitation-sequencing (ChIP-seq) experiments have now become routine in biology for the detection of protein-binding sites. In this paper, we present a Markov random field model for the joint analysis of multiple ChIP-seq experiments. The proposed model naturally accounts for spat
Random fields of initial out of straightness leading to column buckling
DEFF Research Database (Denmark)
Kala, Zdeněk; Valeš, Jan; Jönsson, Jeppe
2017-01-01
The elastic load-carrying capacity and buckling trajectory of steel columns under compression with open and hollow cross-sections, whose axis is curved by spatial random fields, are studied in the article. As a result of the spatial curvature of the axis the cross-sections are subjected to compre...
Exponential Distribution for the Occurrence of Rare Patterns in Gibbsian Random Fields
Abadi, M.; Chazottes, J.-R.; Redig, F.; Verbitskiy, E.
2004-01-01
We study the distribution of the occurrence of rare patterns in sufficiently mixing Gibbs random fields on the lattice Z^d, d ≥ 2. A typical example is the high temperature Ising model. This distribution is shown to converge to an exponential law as the size of the pattern diverges. Our analysis not
Modulation of electromagnetic fields by a depolarizer of random polarizer array
DEFF Research Database (Denmark)
Ma, Ning; Hanson, Steen Grüner; Wang, Wei
2016-01-01
The statistical properties of the electric fields with random changes of the polarization state in space generated by a depolarizer are investigated on the basis of the coherence matrix. The depolarizer is a polarizer array composed of a multitude of contiguous square cells of polarizers with ran...
High Performance Ambipolar Field-Effect Transistor of Random Network Carbon Nanotubes
Bisri, Satria Zulkarnaen; Gao, Jia; Derenskyi, Vladimir; Gomulya, Widianta; Iezhokin, Igor; Gordiichuk, Pavlo; Herrmann, Andreas; Loi, Maria Antonietta
2012-01-01
Ambipolar field-effect transistors of random network carbon nanotubes are fabricated from an enriched dispersion utilizing a conjugated polymer as the selective purifying medium. The devices exhibit high mobility values for both holes and electrons (3 cm(2)/V.s) with a high on/off ratio (10(6)). The
Information Extraction from Research Papers based on Conditional Random Field Model
Directory of Open Access Journals (Sweden)
Zhu Shuxin
2013-01-01
Full Text Available With the increasing use of CiteSeer academic search engines, the accuracy of such systems has become more and more important. The paper adopts the improved particle swarm optimization algorithm for training conditional random field model and applies it into the research papers’ title and citation retrieval. The improved particl swarm optimization algorithm brings the particle swarm aggregation to prevent particle swarm from being plunged into local convergence too early, and uses the linear inertia factor and learning factor to update particle rate. It can control algorithm in infinite iteration by the iteration between particle relative position change rate. The results of which using the standard research papers’ heads and references to evaluate the trained conditional random field model shows that compared with traditionally conditional random field model and Hidden Markov Model, the conditional random field model ,optimized and trained by improved particle swarm, has been better ameliorated in the aspect of F1 mean error and word error rate.
Is Bonferroni correction more sensitive than Random Field Theory for most fMRI studies?
Tierney, Tim M; Carmichael, David W
2016-01-01
Random Field Theory has been used in the fMRI literature to address the multiple comparisons problem. The method provides an analytical solution for the computation of precise p-values when its assumptions are met. When its assumptions are not met the thresholds generated by Random Field Theory can be more conservative than Bonferroni corrections, which are arguably too stringent for use in fMRI. As this has been well documented theoretically it is surprising that a majority of current studies (~80%) would not meet the assumptions of Random Field Theory and therefore would have reduced sensitivity. Specifically most data is not smooth enough to meet the good lattice assumption. Current studies smooth data on average by twice the voxel size which is rarely sufficient to meet the good lattice assumption. The amount of smoothing required for Random Field Theory to produce accurate p-values increases with image resolution and decreases with degrees of freedom. There is no rule of thumb that is valid for all study...
Primordial Non-Gaussianity and Reionization
Lidz, Adam; Adshead, Peter; Dodelson, Scott
2013-01-01
The statistical properties of the primordial perturbations contain clues about the origins of those fluctuations. Although the Planck collaboration has recently obtained tight constraints on primordial non-gaussianity from cosmic microwave background measurements, it is still worthwhile to mine upcoming data sets in effort to place independent or competitive limits. The ionized bubbles that formed at redshift z~6-20 during the Epoch of Reionization are seeded by primordial overdensities, and so the statistics of the ionization field at high redshift are related to the statistics of the primordial field. Here we model the effect of primordial non-gaussianity on the reionization field. The epoch and duration of reionization are affected as are the sizes of the ionized bubbles, but these changes are degenerate with variations in the properties of the ionizing sources and the surrounding intergalactic medium. A more promising signature is the power spectrum of the spatial fluctuations in the ionization field, whi...
Magalhaes, S. G.; Zimmer, F. M.; Coqblin, B.
2012-12-01
We study here the influence of a random applied magnetic field on the competition between the Kondo effect, the spin glass phase and a ferromagnetic order in disordered cerium systems such as CeNi1-xCux. The model used here takes an intrasite Kondo coupling and an intersite random coupling; both the intersite random coupling and the random magnetic field are described within the Sherrington-Kirkpatrick model and the one-step replica symmetry breaking procedure is also used here. We present phase diagrams giving Temperature versus the Kondo exchange parameter and the random magnetic field makes decrease particularly the importance of the spin glass and ferromagnetic phases.
On Non-Parametric Field Estimation using Randomly Deployed, Noisy, Binary Sensors
Wang, Ye
2007-01-01
We consider the problem of reconstructing a deterministic data field from binary quantized noisy observations of sensors randomly deployed over the field domain. Our focus is on the extremes of lack of control in the sensor deployment, arbitrariness and lack of knowledge of the noise distribution, and low-precision and unreliability in the sensors. These adverse conditions are motivated by possible real-world scenarios where a large collection of low-cost, crudely manufactured sensors are mass-deployed in an environment where little can be assumed about the ambient noise. We propose a simple estimator that reconstructs the entire data field from these unreliable, binary quantized, noisy observations. Under the assumption of a bounded amplitude field, we prove almost sure and mean-square convergence of the estimator to the actual field as the number of sensors tends to infinity. For fields with bounded-variation, Sobolev differentiable, or finite-dimensionality properties, we derive specific mean squared error...
Phase Diagram and Tricritical Behavior of a Spin-2 Transverse Ising Model in aRandom Field
Institute of Scientific and Technical Information of China (English)
LIANGYa-Qiu; WEIGuo-Zhu; SONGLi-Li; SONGGuo-Li; ZANGShu-Liang
2004-01-01
The phase diagrams of a spin-2 transverse Ising model with a random field on honeycomb, square, and simple-cubic lattices, respectively, are investigated within the framework of an effective-field theory with correlations.We find the behavior of the tricritical point and the reentrant phenomenon for the system with any coordination number z, when the applied random field is bimodal. The behavior of the tricritical point is also examined as a function of applied transverse field. The reentrant phenomenon comes from the competition between the transverse field and the random field.
Exact Partition Function for the Random Walk of an Electrostatic Field
Directory of Open Access Journals (Sweden)
Gabriel González
2017-01-01
Full Text Available The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either ±σ is obtained. We find the electrostatic energy of the system and show that it can be analyzed through generalized Dyck paths. The relation between the electrostatic field and generalized Dyck paths allows us to sum overall possible electrostatic field configurations and is used for obtaining the partition function of the system. We illustrate our results with one example.
Directory of Open Access Journals (Sweden)
Xiaofeng Sun
2017-08-01
Full Text Available As an intermediate step between raw remote sensing data and digital maps, remote sensing data classification has been a challenging and long-standing problem in the remote sensing research community. In this work, an automated and effective supervised classification framework is presented for classifying high-resolution remote sensing data. Specifically, the presented method proceeds in three main stages: feature extraction, classification, and classified result refinement. In the feature extraction stage, both multispectral images and 3D geometry data are used, which utilizes the complementary information from multisource data. In the classification stage, to tackle the problems associated with too many training samples and take full advantage of the information in the large-scale dataset, a random forest (RF ensemble learning strategy is proposed by combining several RF classifiers together. Finally, an improved fully connected conditional random field (FCCRF graph model is employed to derive the contextual information to refine the classification results. Experiments on the ISPRS Semantic Labeling Contest dataset show that the presented 3-stage method achieves 86.9% overall accuracy, which is a new state-of-the-art non-CNN (convolutional neural networks-based classification method.
The van Hemmen model and effect of random crystalline anisotropy field
Energy Technology Data Exchange (ETDEWEB)
Morais, Denes M. de [Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, Mato Grosso (Brazil); Godoy, Mauricio, E-mail: mgodoy@fisica.ufmt.br [Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, Mato Grosso (Brazil); Arruda, Alberto S. de, E-mail: aarruda@fisica.ufmt.br [Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, Mato Grosso (Brazil); Silva, Jonathas N. da [Universidade Estadual Paulista, 14800-901, Araraquara, São Paulo (Brazil); Ricardo de Sousa, J. [Instituto Nacional de Sistemas Complexos, Departamento de Fisica, Universidade Federal do Amazona, 69077-000, Manaus, Amazonas (Brazil)
2016-01-15
In this work, we have presented the generalized phase diagrams of the van Hemmen model for spin S=1 in the presence of an anisotropic term of random crystalline field. In order to study the critical behavior of the phase transitions, we employed a mean-field Curie–Weiss approach, which allows calculation of the free energy and the equations of state of the model. The phase diagrams obtained here displayed tricritical behavior, with second-order phase transition lines separated from the first-order phase transition lines by a tricritical point. - Highlights: • Several phase diagrams are obtained for the model. • The influence of the random crystalline anisotropy field on the model is investigated. • Three ordered (spin-glass, ferromagnetic and mixed) phases are found. • The tricritical behavior is examined.
Controlling dispersion forces between small particles with artificially created random light fields
Bruegger, Georges; Scheffold, Frank; Saenz, Juan Jose
2015-01-01
Appropriate combinations of laser beams can be used to trap and manipulate small particles with "optical tweezers" as well as to induce significant "optical binding" forces between particles. These interaction forces are usually strongly anisotropic depending on the interference landscape of the external fields. This is in contrast with the familiar isotropic, translationally invariant, van der Waals and, in general, Casimir-Lifshitz interactions between neutral bodies arising from random electromagnetic waves generated by equilibrium quantum and thermal fluctuations. Here we show, both theoretically and experimentally, that dispersion forces between small colloidal particles can also be induced and controlled using artificially created fluctuating light fields. Using optical tweezers as gauge, we present experimental evidence for the predicted isotropic attractive interactions between dielectric microspheres induced by laser-generated, random light fields. These light induced interactions open a path towards...
Maximizing Entropy of Pickard Random Fields for 2x2 Binary Constraints
DEFF Research Database (Denmark)
Søgaard, Jacob; Forchhammer, Søren
2014-01-01
This paper considers the problem of maximizing the entropy of two-dimensional (2D) Pickard Random Fields (PRF) subject to constraints. We consider binary Pickard Random Fields, which provides a 2D causal finite context model and use it to define stationary probabilities for 2x2 squares, thus...... allowing us to calculate the entropy of the field. All possible binary 2x2 constraints are considered and all constraints are categorized into groups according to their properties. For constraints which can be modeled by a PRF approach and with positive entropy, we characterize and provide statistics...... of the maximum PRF entropy. As examples, we consider the well known hard square constraint along with a few other constraints....
Field quality control of an earth dam: random versus purposive sampling
Energy Technology Data Exchange (ETDEWEB)
Kotzias, P.C.; Stamatopoulos, A.C.
1996-08-01
Two sampling operations, the random and purposive techniques, for field quality control of an earth dam were presented. Each technique was analyzed and their similarities and differences were compared. Each took into consideration the attributes or variables such as strength, temperature, slump, air content, density, and water content. The purposive operation needed much less field sampling and testing than the random operation. The advantages and disadvantages of each technique were described. It was concluded that both techniques could be used individually or jointly on the same project as long as the extent of the application, with all rules and underlying assumptions, were recognized for each case and were strictly adhered to in the field. 19 refs., 4 tabs., 2 figs.
Certified Randomness from a Two-Level System in a Relativistic Quantum Field
Thinh, Le Phuc; Martin-Martinez, Eduardo
2016-01-01
Randomness is an indispensable resource in modern science and information technology. Fortunately, an experimentally simple procedure exists to generate randomness with well-characterized devices: measuring a quantum system in a basis complementary to its preparation. Towards realizing this goal one may consider using atoms or superconducting qubits, promising candidates for quantum information processing. However, their unavoidable interaction with the electromagnetic field affects their dynamics. At large time scales, this can result in decoherence. Smaller time scales in principle avoid this problem, but may not be well analysed under the usual rotating wave and single-mode approximation (RWA and SMA) which break the relativistic nature of quantum field theory. Here, we use a fully relativistic analysis to quantify the information that an adversary with access to the field could get on the result of an atomic measurement. Surprisingly, we find that the adversary's guessing probability is not minimized for ...
Levitation of Extended States in a Random Magnetic Field with a Finite Mean
Institute of Scientific and Technical Information of China (English)
LIU Wen-Sheng; LEI Xiao-Lin
2004-01-01
We study the localization properties of electrons in a two-dimensional system in a random magnetic field B(r) = Bo + δB(r) with the average Bo and the amplitude of the magnetic field fluctuations δB. The localization length of the system is calculated by using the finite-size scaling method combined with the transfer-matrix technique.Inthe case of weak δB, we find that the random magnetic field system is equivalent to the integer quantum Hall effect system, namely, the energy band splits into a series of disorder broadened Landau bands, at the centers of which states are extended with the localization length exponent v = 2.34 ± 0.02. With increasing δB, the extended states float up in energy, which is similar to the levitation scenario proposed for the integer quantum Hall effect.
Zaim, N.; Zaim, A.; Kerouad, M.
2017-02-01
In this work, the magnetic behavior of the cylindrical nanowire, consisting of a ferromagnetic core of spin-1 atoms surrounded by a ferromagnetic shell of spin-1 atoms is studied in the presence of a random crystal field interaction. Based on Metropolis algorithm, the Monte Carlo simulation has been used to investigate the effects of the concentration of the random crystal field p, the crystal field D and the shell exchange interaction Js on the phase diagrams and the hysteresis behavior of the system. Some characteristic behaviors have been found, such as the first and second-order phase transitions joined by tricritical point for appropriate values of the system parameters, triple and isolated critical points can be also found. Depending on the Hamiltonian parameters, single, double and para hysteresis regions are explicitly determined.
The Stochastic Galerkin Method for Darcy Flow Problem with Log-Normal Random Field Coefficients
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Michal Beres
2017-01-01
Full Text Available This article presents a study of the Stochastic Galerkin Method (SGM applied to the Darcy flow problem with a log-normally distributed random material field given by a mean value and an autocovariance function. We divide the solution of the problem into two parts. The first one is the decomposition of a random field into a sum of products of a random vector and a function of spatial coordinates; this can be achieved using the Karhunen-Loeve expansion. The second part is the solution of the problem using SGM. SGM is a simple extension of the Galerkin method in which the random variables represent additional problem dimensions. For the discretization of the problem, we use a finite element basis for spatial variables and a polynomial chaos discretization for random variables. The results of SGM can be utilised for the analysis of the problem, such as the examination of the average flow, or as a tool for the Bayesian approach to inverse problems.
Predictors of Consent in a Randomized Field Study in Child Welfare.
McDonald, Tom; Bhattarai, Jackie; Akin, Becci
2017-01-01
Randomized controlled trials (RCTs) are often viewed as the "gold standard" for proving the efficacy and effectiveness of new interventions. However, some are skeptical of the generalizability of the findings that RCTs produce. The characteristics of those willing to participate in research studies have the potential to affect the generalizability of its findings. This study examined factors that could influence consent among families recruited to participate in a randomized field trial in a real-world child welfare setting. This study tested the Parent Management Training Oregon Model for children in foster care with serious emotional disturbance. It employed a post-randomization consent design, whereby the entire sample of eligible participants, not just those who are willing to consent to randomization, are included in the sample. Initial eligibility assessment data and data from the federally mandated reporting system for public child welfare agencies provided the pool of potential predictors of consent. Bivariate and multivariate analyses were conducted to identify statistically significant predictors of consent. Being a dual reunification family was the most significant factor in predicting consent. Unmarried individuals, younger, female parents, cases where parental incarceration was the reason for removal and cases where the removal reason was not due to their children's behavioral problem(s) were also more likely to participate. As one of the first research studies to examine predictors of consent to a randomized field study in child welfare settings, results presented here can act as a preliminary guide for conducting RCTs in child welfare settings.
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian...... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...
Dynamic attack zone of air-to-air missile after being launched in random wind field
Institute of Scientific and Technical Information of China (English)
Hui Yaoluo; Nan Ying; Chen Shaodong; Ding Quanxin; Wu Shengliang
2015-01-01
A new concept is presented for air-to-air missile which is dynamic attack zone after being launched in random wind field. This new concept can be used to obtain the 4-dimensional (4-D) information regarding the dynamic envelope of an air-to-air missile at any flight time aimed at different flight targets considering influences of random wind, in the situation of flight fighters coop-erated with missiles fighting against each other. Based on an air-to-air missile model, some typical cases of dynamic attack zone after being launched in random wind field were numerically simulated. Compared with the simulation results of traditional dynamic envelope, the properties of dynamic attack zone after being launched are as follows. The 4-D dynamic attack zone after being launched is inside traditional maximum dynamic envelope, but its forane boundary is usually not inside tra-ditional no-escape dynamic envelope;Traditional dynamic attack zone can just be reliably used at launch time, while dynamic envelope after being launched can be reliably and accurately used dur-ing any flight antagonism time. Traditional envelope is a special case of dynamic envelope after being launched when the dynamic envelope is calculated at the launch time;the dynamic envelope after being launched can be influenced by the random wind field.
Approximately achieving Gaussian relay network capacity with lattice codes
Ozgur, Ayfer
2010-01-01
Recently, it has been shown that a quantize-map-and-forward scheme approximately achieves (within a constant number of bits) the Gaussian relay network capacity for arbitrary topologies. This was established using Gaussian codebooks for transmission and random mappings at the relays. In this paper, we show that the same approximation result can be established by using lattices for transmission and quantization along with structured mappings at the relays.
Axial distribution of Gaussian beam limited by a hard-edged aperture
Institute of Scientific and Technical Information of China (English)
Shuyun Teng(滕树云); Liren Liu(刘立人); Zhu Luan(栾竹); Lingyu Wan(万玲玉)
2004-01-01
In this letter, the axial distribution of Gaussian beam limited by a hard-edged aperture is studied. We theoretically analyze the axial diffraction of Gaussian beam limited by a hard-edged aperture, and give the simpler formulas of the axial diffraction intensities of Gaussian beam in Fresnel diffraction field and Fraunhofer diffraction field. The corresponding numerical calculation of axial diffraction intensity distribution of Gaussian beam with different wave waist is provided and the evolution of the diffraction distribution with the wave waist of Gaussian beam is explained. As the especial cases of the truncated Gaussian beam,the Gaussian beam in free space and the parallel light limited by the aperture are discussed too, and the system parameters of the truncated Gaussian beam which can cause it to equal to these cases are given.The theoretical results conform to the numerical analysis.
On Polynomial Lieb-Robinson Bounds for the XY Chain in a Decaying Random Field
Gebert, Martin; Lemm, Marius
2016-08-01
We consider the isotropic XY quantum spin chain in a random external field in the z direction, with single site distributions given by i.i.d. random variables times the critical decaying envelope j^{-1/2}. Our motivation is the study of many-body localization. We investigate transport properties in terms of polynomial Lieb-Robinson (PLR) bounds. We prove a zero-velocity PLR bound for large disorder strength λ and for small λ we show a partial converse, which suggests the existence of a transition to non-trivial transport in the model.
Random pinning glass transition: hallmarks, mean-field theory and renormalization group analysis.
Cammarota, Chiara; Biroli, Giulio
2013-03-28
We present a detailed analysis of glass transitions induced by pinning particles at random from an equilibrium configuration. We first develop a mean-field analysis based on the study of p-spin spherical disordered models and then obtain the three-dimensional critical behavior by the Migdal-Kadanoff real space renormalization group method. We unveil the important physical differences with the case in which particles are pinned from a random (or very high temperature) configuration. We contrast the pinning particles approach to the ones based on biasing dynamical trajectories with respect to their activity and on coupling to equilibrium configurations. Finally, we discuss numerical and experimental tests.
Randomized Field Trials and Internal Validity: Not So Fast My Friend.
Directory of Open Access Journals (Sweden)
James H. McMillan
2007-12-01
Full Text Available The purpose of this article is to summarize eight potential threats to internal validity that occur with randomized field trial (RFT studies. Depending on specific contextual factors, RFTs do not necessarily result in strong internal validity. Of particular concern is whether the unit of random assignment is the same as the number of replications of the intervention, threats as a result of local history, and subject effects. The eight threats are described, with suggestions for providing adequate monitoring to know if they rise to the level of likely or plausible threat to internal validity.
Transmission loss between single-mode Gaussian antennas.
Perlot, Nicolas; Rohde, Michael
2016-08-22
We analytically derive a set of formulas for the transmission loss in vacuum between antennas that send and receive single-mode Gaussian beams. We relate our results to standard far-field link budget parameters.
基于高斯随机球的小天体三维建模方法研究%Small Body Shape Modeling Based on Gaussian Random Sphere Hypothesis
Institute of Scientific and Technical Information of China (English)
陈建清; 崔祜涛; 崔平远
2013-01-01
Small body shape has played an important role in the planning of deep space mission to a small body.Considering the numbers and precision,the real solar system small body shapes were constructed before they couldn't satisfy the present requirements.Based on the Gaussian random sphere hypothesis,a small body shape modeling method was proposed.By sorting the surface points into levels,new points completely depended on their higher-level neighbors and specified through fractal theory.Surface features such as craters and rocks were analyzed,and then the addition methods of these two kinds of characters were described.Finally,a set of simulated images based on the constructed shape model were used to illustrate the efficiency of the modeling method.%小天体形状及其相应的光学数据在小天体探测任务规划中有着重要作用,地面已有的实际小天体模型数量、精度有限,难以满足应用要求.针对小天体的不规则形状,在整体形状大致符合高斯随机球的假设条件下,建立初始的虚拟形状模型；为满足不同精度的应用要求,利用数据分层的思想,采用她表细节结构分形插值的方法添加新的表面点,逐步提高模型精度；通过对天体表面的陨石坑、岩石特性进行分析,根据现有的天体表面地形特征分布特性,添加小天体表面的地形特征,进而构建出完整的天体形状模型.论文最后对模型结果进行了图像仿真,并作了进一步的应用分析.
Scaled unscented transform Gaussian sum filter: theory and application
Luo, Xiaodong; Hoteit, Ibrahim
2010-01-01
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlyi...
Using Geometrical Properties for Fast Indexation of Gaussian Vector Quantizers
Directory of Open Access Journals (Sweden)
Vassilieva EA
2007-01-01
Full Text Available Vector quantization is a classical method used in mobile communications. Each sequence of samples of the discretized vocal signal is associated to the closest -dimensional codevector of a given set called codebook. Only the binary indices of these codevectors (the codewords are transmitted over the channel. Since channels are generally noisy, the codewords received are often slightly different from the codewords sent. In order to minimize the distortion of the original signal due to this noisy transmission, codevectors indexed by one-bit different codewords should have a small mutual Euclidean distance. This paper is devoted to this problem of index assignment of binary codewords to the codevectors. When the vector quantizer has a Gaussian structure, we show that a fast index assignment algorithm based on simple geometrical and combinatorial considerations can improve the SNR at the receiver by 5dB with respect to a purely random assignment. We also show that in the Gaussian case this algorithm outperforms the classical combinatorial approach in the field.
Non-Gaussian entanglement swapping
Dell'Anno, F; Nocerino, G; De Siena, S; Illuminati, F
2016-01-01
We investigate the continuous-variable entanglement swapping protocol in a non-Gaussian setting, with non- Gaussian states employed either as entangled inputs and/or as swapping resources. The quality of the swapping protocol is assessed in terms of the teleportation fidelity achievable when using the swapped states as shared entangled resources in a teleportation protocol. We thus introduce a two-step cascaded quantum communication scheme that includes a swapping protocol followed by a teleportation protocol. The swapping protocol is fed by a general class of tunable non-Gaussian states, the squeezed Bell states, which, by means of controllable free parameters, allows for a continuous morphing from Gaussian twin beams up to maximally non-Gaussian squeezed number states. In the realistic instance, taking into account the effects of losses and imperfections, we show that as the input two-mode squeezing increases, optimized non-Gaussian swapping resources allow for a monotonically increasing enhancement of the ...
3D morphology of a random field from its 2D cross-section
Makarenko, Irina; Shukurov, Anvar
2014-01-01
We show that both aspect ratios of randomly oriented triaxial ellipsoids (representing isosurfaces of an isotropic 3D random field) can be determined from a single 2D cross-section of their sample using the probability distribution of the filamentarity F of the structures seen in the cross-section (F=0 for a circle and F=1 for a line). The probability distribution of F has a robust form with a sharp maximum and truncation that are sensitive to the ellipsoids' aspect ratios. We show that the aspect ratios of triaxial ellipsoids with randomly distributed dimensions can still be recovered from the probability distribution of F. This method is applicable to many shape recognition and classification problems, here illustrated with neutral hydrogen density in the turbulent interstellar medium of the Milky Way. The gas distribution is shown to be filamentary with the mean axis ratio 1:2:20.
Yang, Yongchao; Sun, Peng; Nagarajaiah, Satish; Bachilo, Sergei M.; Weisman, R. Bruce
2017-07-01
Structural damage is typically a local phenomenon that initiates and propagates within a limited area. As such high spatial resolution measurement and monitoring is often needed for accurate damage detection. This requires either significantly increased costs from denser sensor deployment in the case of global simultaneous/parallel measurements, or increased measurement time and labor in the case of global sequential measurements. This study explores the feasibility of an alternative approach to this problem: a computational solution in which a limited set of randomly positioned, low-resolution global strain measurements are used to reconstruct the full-field, high-spatial-resolution, two-dimensional (2D) strain field and rapidly detect local damage. The proposed approach exploits the implicit low-rank and sparse data structure of the 2D strain field: it is highly correlated without many edges and hence has a low-rank structure, unless damage-manifesting itself as sparse local irregularity-is present and alters such a low-rank structure slightly. Therefore, reconstruction of the full-field, high-spatial-resolution strain field from a limited set of randomly positioned low-resolution global measurements is modeled as a low-rank matrix completion framework and damage detection as a sparse decomposition formulation, enabled by emerging convex optimization techniques. Numerical simulations on a plate structure are conducted for validation. The results are discussed and a practical iterative global/local procedure is recommended. This new computational approach should enable the efficient detection of local damage using limited sets of strain measurements.
Optimization by Estimation of Distribution with DEUM Framework Based on Markov Random Fields
Institute of Scientific and Technical Information of China (English)
Siddhartha Shakya; John McCall
2007-01-01
This paper presents a Markov random field (MRP) approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields (DEUM). DEUM is a subclass of estimation of distribution algorithms (EDAs) where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are: 1) use of MRF models, 2) fitness modeling approach to estimating the parameter of the model and 3) Monte Carlo approach to sampling from the model.
Estimation of random fields from network observations. Technical report No. 26
Energy Technology Data Exchange (ETDEWEB)
Cabannes, A F
1979-06-01
When one has observed a random field Z at some points and recorded its values (network observations), a natural problem is to estimate Z at points where there are no observations. This dissertation deals first with this problem in an abstract setting, in m dimensions; later, it considers the estimation of a spatial two-dimensional random field. The problem then is one of constructing an estimated map of Z over a geographic area. For a given network of stations the quality of a map depends on the method of estimation. But for the given method of estimation the quality of a map depends on the choice of locations for the stations. This is the problem of network design. Both the study of methods of estimation and the problem of network design are addressed. 16 figures. (RWR)
A Study and Comparative Analysis of Conditional Random Fields for Intrusion Detection
Directory of Open Access Journals (Sweden)
Deepa Guleria
2012-07-01
Full Text Available Intrusion detection systems are an important component of defensive measures protecting computer systems and networks from abuse. Intrusion detection plays one of the key roles in computer security techniques and is one of the prime areas of research. Due to complex and dynamic nature of computer networks and hacking techniques, detecting malicious activities remains a challenging task for security experts, that is, currently available defense systems suffer from low detection capability and high number of false alarms. An intrusion detection system must reliably detect malicious activities in a network and must perform efficiently to cope with the large amount of network traffic. In this paper we study the Machine Learning and data mining techniques to solve Intrusion Detection problems within computer networks and compare the various approaches with conditional random fields and address these two issues of Accuracy and Efficiency using Conditional Random Fields and Layered Approach.
A Modified FCM Classifier Constrained by Conditional Random Field Model for Remote Sensing Imagery
Directory of Open Access Journals (Sweden)
WANG Shaoyu
2016-12-01
Full Text Available Remote sensing imagery has abundant spatial correlation information, but traditional pixel-based clustering algorithms don't take the spatial information into account, therefore the results are often not good. To this issue, a modified FCM classifier constrained by conditional random field model is proposed. Adjacent pixels' priori classified information will have a constraint on the classification of the center pixel, thus extracting spatial correlation information. Spectral information and spatial correlation information are considered at the same time when clustering based on second order conditional random field. What's more, the global optimal inference of pixel's classified posterior probability can be get using loopy belief propagation. The experiment shows that the proposed algorithm can effectively maintain the shape feature of the object, and the classification accuracy is higher than traditional algorithms.
Multipole invariants and non-Gaussianity
Land, K; Land, Kate; Magueijo, Joao
2004-01-01
We propose a framework for separating the information contained in the CMB multipoles, $a_{\\ell m}$, into its algebraically independent components. Thus we cleanly separate information pertaining to the power spectrum, non-Gaussianity and preferred axis effects. The formalism builds upon the recently proposed multipole vectors (Copi, Huterer & Starkman 2003; Schwarz & al 2004; Katz & Weeks 2004), and we elucidate a few features regarding these vectors, namely their lack of statistical independence for a Gaussian random process. In a few cases we explicitly relate our proposed invariants to components of the $n$-point correlation function (power spectrum, bispectrum). We find the invariants' distributions using a mixture of analytical and numerical methods. We also evaluate them for the co-added WMAP first year map.
Features of randomized electric-field assisted domain inversion in lithium tantalate
Stivala, Salvatore; Curcio, Luciano; Oliveri, Roberto L; Busacca, Alessandro C; Assanto, Gaetano; 10.1364/OE.19.025780
2012-01-01
We report on bulk and guided-wave second-harmonic generation via random Quasi-Phase-Matching in Lithium Tantalate. By acquiring the far-field profiles at several wavelengths, we extract statistical information on the distribution of the quadratic nonlinearity as well as its average period, both at the surface and in the bulk of the sample. By investigating the distribution in the two regions we demonstrate a non-invasive approach to the study of poling dynamics.
Magnetoresistance of a two-dimensional electron gas in a random magnetic field
DEFF Research Database (Denmark)
Smith, Anders; Taboryski, Rafael Jozef; Hansen, Luise Theil
1994-01-01
We report magnetoresistance measurements on a two-dimensional electron gas made from a high-mobility GaAs/AlxGa1-xAs heterostructure, where the externally applied magnetic field was expelled from regions of the semiconductor by means of superconducting lead grains randomly distributed on the surf...... on the surface of the sample. A theoretical explanation in excellent agreement with the experiment is given within the framework of the semiclassical Boltzmann equation. © 1994 The American Physical Society...
Ilic, Velimir M; Todorovic, Branimir T; Stankovic, Miomir S
2010-01-01
The paper proposes a new recursive algorithm for the exact computation of the linear chain conditional random fields gradient. The algorithm is an instance of the Entropy Message Passing (EMP), introduced in our previous work, and has the purpose to enhance memory efficiency when applied to long observation sequences. Unlike the traditional algorithm based on the forward and the backward recursions, the memory complexity of our algorithm does not depend on the sequence length, having the same computational complexity as the standard algorithm.