Statistics of peaks of Gaussian random fields
International Nuclear Information System (INIS)
Bardeen, J.M.; Bond, J.R.; Kaiser, N.; Szalay, A.S.; Stanford Univ., CA; California Univ., Berkeley; Cambridge Univ., England; Fermi National Accelerator Lab., Batavia, IL)
1986-01-01
A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of upcrossing points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima. 67 references
A note on moving average models for Gaussian random fields
DEFF Research Database (Denmark)
Hansen, Linda Vadgård; Thorarinsdottir, Thordis L.
The class of moving average models offers a flexible modeling framework for Gaussian random fields with many well known models such as the Matérn covariance family and the Gaussian covariance falling under this framework. Moving average models may also be viewed as a kernel smoothing of a Lévy...... basis, a general modeling framework which includes several types of non-Gaussian models. We propose a new one-parameter spatial correlation model which arises from a power kernel and show that the associated Hausdorff dimension of the sample paths can take any value between 2 and 3. As a result...
Yan, Yuan
2017-07-13
Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.
Yan, Yuan; Genton, Marc G.
2017-01-01
Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.
GAUSSIAN RANDOM FIELD: PHYSICAL ORIGIN OF SERSIC PROFILES
International Nuclear Information System (INIS)
Cen, Renyue
2014-01-01
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.
Ding, Jian; Li, Li
2018-06-01
We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.
International Nuclear Information System (INIS)
Bertschinger, E.
1987-01-01
Path integrals may be used to describe the statistical properties of a random field such as the primordial density perturbation field. In this framework the probability distribution is given for a Gaussian random field subjected to constraints such as the presence of a protovoid or supercluster at a specific location in the initial conditions. An algorithm has been constructed for generating samples of a constrained Gaussian random field on a lattice using Monte Carlo techniques. The method makes possible a systematic study of the density field around peaks or other constrained regions in the biased galaxy formation scenario, and it is effective for generating initial conditions for N-body simulations with rare objects in the computational volume. 21 references
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 ...
Directory of Open Access Journals (Sweden)
Pablo Gregori
2014-03-01
Full Text Available This paper represents a survey of recent advances in modeling of space or space-time Gaussian Random Fields (GRF, tools of Geostatistics at hand for the understanding of special cases of noise in image analysis. They can be used when stationarity or isotropy are unrealistic assumptions, or even when negative covariance between some couples of locations are evident. We show some strategies in order to escape from these restrictions, on the basis of rich classes of well known stationary or isotropic non negative covariance models, and through suitable operations, like linear combinations, generalized means, or with particular Fourier transforms.
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.
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.
Multi-fidelity Gaussian process regression for prediction of random fields
International Nuclear Information System (INIS)
Parussini, L.; Venturi, D.; Perdikaris, P.; Karniadakis, G.E.
2017-01-01
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.
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).
A novel approach to assess the treatment response using Gaussian random field in PET
Energy Technology Data Exchange (ETDEWEB)
Wang, Mengdie [Department of Biomedical Engineering, Tsinghua University, Beijing 100084, China and Center for Advanced Medical Imaging Science, Division of Nuclear Medicine and Molecular Imaging, Massachusetts General Hospital, Boston, Massachusetts 02114 (United States); Guo, Ning [Center for Advanced Medical Imaging Science, Division of Nuclear Medicine and Molecular Imaging, Massachusetts General Hospital, Boston, Massachusetts 02114 (United States); Hu, Guangshu; Zhang, Hui, E-mail: hzhang@mail.tsinghua.edu.cn, E-mail: li.quanzheng@mgh.harvard.edu [Department of Biomedical Engineering, Tsinghua University, Beijing 100084 (China); El Fakhri, Georges; Li, Quanzheng, E-mail: hzhang@mail.tsinghua.edu.cn, E-mail: li.quanzheng@mgh.harvard.edu [Center for Advanced Medical Imaging Science, Division of Nuclear Medicine and Molecular Imaging, Massachusetts General Hospital, Boston, Massachusetts 02114 and Department of Radiology, Harvard Medical School, Boston, Massachusetts 02115 (United States)
2016-02-15
Purpose: The assessment of early therapeutic response to anticancer therapy is vital for treatment planning and patient management in clinic. With the development of personal treatment plan, the early treatment response, especially before any anatomically apparent changes after treatment, becomes urgent need in clinic. Positron emission tomography (PET) imaging serves an important role in clinical oncology for tumor detection, staging, and therapy response assessment. Many studies on therapy response involve interpretation of differences between two PET images, usually in terms of standardized uptake values (SUVs). However, the quantitative accuracy of this measurement is limited. This work proposes a statistically robust approach for therapy response assessment based on Gaussian random field (GRF) to provide a statistically more meaningful scale to evaluate therapy effects. Methods: The authors propose a new criterion for therapeutic assessment by incorporating image noise into traditional SUV method. An analytical method based on the approximate expressions of the Fisher information matrix was applied to model the variance of individual pixels in reconstructed images. A zero mean unit variance GRF under the null hypothesis (no response to therapy) was obtained by normalizing each pixel of the post-therapy image with the mean and standard deviation of the pretherapy image. The performance of the proposed method was evaluated by Monte Carlo simulation, where XCAT phantoms (128{sup 2} pixels) with lesions of various diameters (2–6 mm), multiple tumor-to-background contrasts (3–10), and different changes in intensity (6.25%–30%) were used. The receiver operating characteristic curves and the corresponding areas under the curve were computed for both the proposed method and the traditional methods whose figure of merit is the percentage change of SUVs. The formula for the false positive rate (FPR) estimation was developed for the proposed therapy response
Inflation in random Gaussian landscapes
Energy Technology Data Exchange (ETDEWEB)
Masoumi, Ali; Vilenkin, Alexander; Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2017-05-01
We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations n {sub s} and its running α {sub s} . These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.
Cheraghalizadeh, Jafar; Najafi, Morteza N.; Mohammadzadeh, Hossein
2018-05-01
The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize the correlations between the MNPs we have used the Ising model with an artificial temperature T that controls the number of MNPs as well as their correlations. In the T → 0 limit, one retrieves the Gaussian free field (GFF), and in the finite temperature the problem is equivalent to a GFF in iso-potential islands. The problem is argued to be equivalent to a scale-invariant random surface with some critical exponents which vary with T and correspondingly are correlation-dependent. Two type of observables have been considered: local and global quantities. We have observed that the MNPs soften the random potential and reduce its statistical fluctuations. This softening is observed in the local as well as the geometrical quantities. The correlation function of the electrostatic and its total variance are observed to be logarithmic just like the GFF, i.e. the roughness exponent remains zero for all temperatures, whereas the proportionality constants scale with T - T c . The fractal dimension of iso-potential lines ( D f ), the exponent of the distribution function of the gyration radius ( τ r ), and the loop lengths ( τ l ), and also the exponent of the loop Green function x l change in terms of T - T c in a power-law fashion, with some critical exponents reported in the text. Importantly we have observed that D f ( T) - D f ( T c ) 1/√ ξ( T), in which ξ( T) is the spin correlation length in the Ising model.
ANALYSIS AND VALIDATION OF GRID DEM GENERATION BASED ON GAUSSIAN MARKOV RANDOM FIELD
Directory of Open Access Journals (Sweden)
F. J. Aguilar
2016-06-01
Full Text Available Digital Elevation Models (DEMs are considered as one of the most relevant geospatial data to carry out land-cover and land-use classification. This work deals with the application of a mathematical framework based on a Gaussian Markov Random Field (GMRF to interpolate grid DEMs from scattered elevation data. The performance of the GMRF interpolation model was tested on a set of LiDAR data (0.87 points/m2 provided by the Spanish Government (PNOA Programme over a complex working area mainly covered by greenhouses in Almería, Spain. The original LiDAR data was decimated by randomly removing different fractions of the original points (from 10% to up to 99% of points removed. In every case, the remaining points (scattered observed points were used to obtain a 1 m grid spacing GMRF-interpolated Digital Surface Model (DSM whose accuracy was assessed by means of the set of previously extracted checkpoints. The GMRF accuracy results were compared with those provided by the widely known Triangulation with Linear Interpolation (TLI. Finally, the GMRF method was applied to a real-world case consisting of filling the LiDAR-derived DSM gaps after manually filtering out non-ground points to obtain a Digital Terrain Model (DTM. Regarding accuracy, both GMRF and TLI produced visually pleasing and similar results in terms of vertical accuracy. As an added bonus, the GMRF mathematical framework makes possible to both retrieve the estimated uncertainty for every interpolated elevation point (the DEM uncertainty and include break lines or terrain discontinuities between adjacent cells to produce higher quality DTMs.
Efficient 3D porous microstructure reconstruction via Gaussian random field and hybrid optimization.
Jiang, Z; Chen, W; Burkhart, C
2013-11-01
Obtaining an accurate three-dimensional (3D) structure of a porous microstructure is important for assessing the material properties based on finite element analysis. Whereas directly obtaining 3D images of the microstructure is impractical under many circumstances, two sets of methods have been developed in literature to generate (reconstruct) 3D microstructure from its 2D images: one characterizes the microstructure based on certain statistical descriptors, typically two-point correlation function and cluster correlation function, and then performs an optimization process to build a 3D structure that matches those statistical descriptors; the other method models the microstructure using stochastic models like a Gaussian random field and generates a 3D structure directly from the function. The former obtains a relatively accurate 3D microstructure, but computationally the optimization process can be very intensive, especially for problems with large image size; the latter generates a 3D microstructure quickly but sacrifices the accuracy due to issues in numerical implementations. A hybrid optimization approach of modelling the 3D porous microstructure of random isotropic two-phase materials is proposed in this paper, which combines the two sets of methods and hence maintains the accuracy of the correlation-based method with improved efficiency. The proposed technique is verified for 3D reconstructions based on silica polymer composite images with different volume fractions. A comparison of the reconstructed microstructures and the optimization histories for both the original correlation-based method and our hybrid approach demonstrates the improved efficiency of the approach. © 2013 The Authors Journal of Microscopy © 2013 Royal Microscopical Society.
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.
Markov random field and Gaussian mixture for segmented MRI-based partial volume correction in PET
International Nuclear Information System (INIS)
Bousse, Alexandre; Thomas, Benjamin A; Erlandsson, Kjell; Hutton, Brian F; Pedemonte, Stefano; Ourselin, Sébastien; Arridge, Simon
2012-01-01
In this paper we propose a segmented magnetic resonance imaging (MRI) prior-based maximum penalized likelihood deconvolution technique for positron emission tomography (PET) images. The model assumes the existence of activity classes that behave like a hidden Markov random field (MRF) driven by the segmented MRI. We utilize a mean field approximation to compute the likelihood of the MRF. We tested our method on both simulated and clinical data (brain PET) and compared our results with PET images corrected with the re-blurred Van Cittert (VC) algorithm, the simplified Guven (SG) algorithm and the region-based voxel-wise (RBV) technique. We demonstrated our algorithm outperforms the VC algorithm and outperforms SG and RBV corrections when the segmented MRI is inconsistent (e.g. mis-segmentation, lesions, etc) with the PET image. (paper)
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.
Directory of Open Access Journals (Sweden)
M. Mahdian
2013-09-01
Full Text Available In recent years, the use of Polarimetric Synthetic Aperture Radar (PolSAR data in different applications dramatically has been increased. In SAR imagery an interference phenomenon with random behavior exists which is called speckle noise. The interpretation of data encounters some troubles due to the presence of speckle which can be considered as a multiplicative noise affecting all coherent imaging systems. Indeed, speckle degrade radiometric resolution of PolSAR images, therefore it is needful to perform speckle filtering on the SAR data type. Markov Random Field (MRF has proven to be a powerful method for drawing out eliciting contextual information from remotely sensed images. In the present paper, a probability density function (PDF, which is fitted well with the PolSAR data based on the goodness-of-fit test, is first obtained for the pixel-wise analysis. Then the contextual smoothing is achieved with the MRF method. This novel speckle reduction method combines an advanced statistical distribution with spatial contextual information for PolSAR data. These two parts of information are combined based on weighted summation of pixel-wise and contextual models. This approach not only preserves edge information in the images, but also improves signal-to-noise ratio of the results. The method maintains the mean value of original signal in the homogenous areas and preserves the edges of features in the heterogeneous regions. Experiments on real medium resolution ALOS data from Tehran, and also high resolution full polarimetric SAR data over the Oberpfaffenhofen test-site in Germany, demonstrate the effectiveness of the algorithm compared with well-known despeckling methods.
Directory of Open Access Journals (Sweden)
Gunter eSpöck
2015-05-01
Full Text Available Recently, Spock and Pilz [38], demonstratedthat the spatial sampling design problem forthe Bayesian linear kriging predictor can betransformed to an equivalent experimentaldesign problem for a linear regression modelwith stochastic regression coefficients anduncorrelated errors. The stochastic regressioncoefficients derive from the polar spectralapproximation of the residual process. Thus,standard optimal convex experimental designtheory can be used to calculate optimal spatialsampling designs. The design functionals ̈considered in Spock and Pilz [38] did nottake into account the fact that kriging isactually a plug-in predictor which uses theestimated covariance function. The resultingoptimal designs were close to space-fillingconfigurations, because the design criteriondid not consider the uncertainty of thecovariance function.In this paper we also assume that thecovariance function is estimated, e.g., byrestricted maximum likelihood (REML. Wethen develop a design criterion that fully takesaccount of the covariance uncertainty. Theresulting designs are less regular and space-filling compared to those ignoring covarianceuncertainty. The new designs, however, alsorequire some closely spaced samples in orderto improve the estimate of the covariancefunction. We also relax the assumption ofGaussian observations and assume that thedata is transformed to Gaussianity by meansof the Box-Cox transformation. The resultingprediction method is known as trans-Gaussiankriging. We apply the Smith and Zhu [37]approach to this kriging method and show thatresulting optimal designs also depend on theavailable data. We illustrate our results witha data set of monthly rainfall measurementsfrom Upper Austria.
Gaussian processes and constructive scalar field theory
International Nuclear Information System (INIS)
Benfatto, G.; Nicolo, F.
1981-01-01
The last years have seen a very deep progress of constructive euclidean field theory, with many implications in the area of the random fields theory. The authors discuss an approach to super-renormalizable scalar field theories, which puts in particular evidence the connections with the theory of the Gaussian processes associated to the elliptic operators. The paper consists of two parts. Part I treats some problems in the theory of Gaussian processes which arise in the approach to the PHI 3 4 theory. Part II is devoted to the discussion of the ultraviolet stability in the PHI 3 4 theory. (Auth.)
Yura, Harold T; Hanson, Steen G
2012-04-01
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 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 examples with relevance for optics are given.
Directory of Open Access Journals (Sweden)
Fermín Segovia
2017-10-01
Full Text Available 18F-DMFP-PET is an emerging neuroimaging modality used to diagnose Parkinson's disease (PD that allows us to examine postsynaptic dopamine D2/3 receptors. Like other neuroimaging modalities used for PD diagnosis, most of the total intensity of 18F-DMFP-PET images is concentrated in the striatum. However, other regions can also be useful for diagnostic purposes. An appropriate delimitation of the regions of interest contained in 18F-DMFP-PET data is crucial to improve the automatic diagnosis of PD. In this manuscript we propose a novel methodology to preprocess 18F-DMFP-PET data that improves the accuracy of computer aided diagnosis systems for PD. First, the data were segmented using an algorithm based on Hidden Markov Random Field. As a result, each neuroimage was divided into 4 maps according to the intensity and the neighborhood of the voxels. The maps were then individually normalized so that the shape of their histograms could be modeled by a Gaussian distribution with equal parameters for all the neuroimages. This approach was evaluated using a dataset with neuroimaging data from 87 parkinsonian patients. After these preprocessing steps, a Support Vector Machine classifier was used to separate idiopathic and non-idiopathic PD. Data preprocessed by the proposed method provided higher accuracy results than the ones preprocessed with previous approaches.
Vanmarcke, Erik
1983-03-01
Random variation over space and time is one of the few attributes that might safely be predicted as characterizing almost any given complex system. Random fields or "distributed disorder systems" confront astronomers, physicists, geologists, meteorologists, biologists, and other natural scientists. They appear in the artifacts developed by electrical, mechanical, civil, and other engineers. They even underlie the processes of social and economic change. The purpose of this book is to bring together existing and new methodologies of random field theory and indicate how they can be applied to these diverse areas where a "deterministic treatment is inefficient and conventional statistics insufficient." Many new results and methods are included. After outlining the extent and characteristics of the random field approach, the book reviews the classical theory of multidimensional random processes and introduces basic probability concepts and methods in the random field context. It next gives a concise amount of the second-order analysis of homogeneous random fields, in both the space-time domain and the wave number-frequency domain. This is followed by a chapter on spectral moments and related measures of disorder and on level excursions and extremes of Gaussian and related random fields. After developing a new framework of analysis based on local averages of one-, two-, and n-dimensional processes, the book concludes with a chapter discussing ramifications in the important areas of estimation, prediction, and control. The mathematical prerequisite has been held to basic college-level calculus.
Integration of non-Gaussian fields
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Mohr, Gunnar; Hoffmeyer, Pernille
1996-01-01
The limitations of the validity of the central limit theorem argument as applied to definite integrals of non-Gaussian random fields are empirically explored by way of examples. The purpose is to investigate in specific cases whether the asymptotic convergence to the Gaussian distribution is fast....... and Randrup-Thomsen, S. Reliability of silo ring under lognormal stochastic pressure using stochastic interpolation. Proc. IUTAM Symp., Probabilistic Structural Mechanics: Advances in Structural Reliability Methods, San Antonio, TX, USA, June 1993 (eds.: P. D. Spanos & Y.-T. Wu) pp. 134-162. Springer, Berlin...
DEFF Research Database (Denmark)
Yura, Harold; Hanson, Steen Grüner
2012-01-01
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...
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.
Tunnelling through a Gaussian random barrier
International Nuclear Information System (INIS)
Bezak, Viktor
2008-01-01
A thorough analysis of the tunnelling of electrons through a laterally inhomogeneous rectangular barrier is presented. The barrier height is defined as a statistically homogeneous Gaussian random function. In order to simplify calculations, we assume that the electron energy is low enough in comparison with the mean value of the barrier height. The randomness of the barrier height is defined vertically by a constant variance and horizontally by a finite correlation length. We present detailed calculations of the angular probability density for the tunnelled electrons (i.e. for the scattering forwards). The tunnelling manifests a remarkably diffusive character if the wavelength of the electrons is comparable with the correlation length of the barrier
DEFF Research Database (Denmark)
Frier, Christian; Sørensen, John Dalsgaard
2005-01-01
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...... 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....... As an example a bridge pier in a marine environment is considered and the results are given in terms of the distribution of the time for initialization of corrosion...
Perturbative Gaussianizing transforms for cosmological fields
Hall, Alex; Mead, Alexander
2018-01-01
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.
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.
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.
Discretisation Schemes for Level Sets of Planar Gaussian Fields
Beliaev, D.; Muirhead, S.
2018-01-01
Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic compact manifolds. Our work is motivated by questions about the geometry of such random functions, in particular relating to the structure of their nodal and level sets. We study four discretisation schemes that extract information about level sets of planar Gaussian fields. Each scheme recovers information up to a different level of precision, and each requires a maximum mesh-size in order to be valid with high probability. The first two schemes are generalisations and enhancements of similar schemes that have appeared in the literature (Beffara and Gayet in Publ Math IHES, 2017. https://doi.org/10.1007/s10240-017-0093-0; Mischaikow and Wanner in Ann Appl Probab 17:980-1018, 2007); these give complete topological information about the level sets on either a local or global scale. As an application, we improve the results in Beffara and Gayet (2017) on Russo-Seymour-Welsh estimates for the nodal set of positively-correlated planar Gaussian fields. The third and fourth schemes are, to the best of our knowledge, completely new. The third scheme is specific to the nodal set of the random plane wave, and provides global topological information about the nodal set up to `visible ambiguities'. The fourth scheme gives a way to approximate the mean number of excursion domains of planar Gaussian fields.
Super-resolving random-Gaussian apodized photon sieve.
Sabatyan, Arash; Roshaninejad, Parisa
2012-09-10
A novel apodized photon sieve is presented in which random dense Gaussian distribution is implemented to modulate the pinhole density in each zone. The random distribution in dense Gaussian distribution causes intrazone discontinuities. Also, the dense Gaussian distribution generates a substantial number of pinholes in order to form a large degree of overlap between the holes in a few innermost zones of the photon sieve; thereby, clear zones are formed. The role of the discontinuities on the focusing properties of the photon sieve is examined as well. Analysis shows that secondary maxima have evidently been suppressed, transmission has increased enormously, and the central maxima width is approximately unchanged in comparison to the dense Gaussian distribution. Theoretical results have been completely verified by experiment.
Linear velocity fields in non-Gaussian models for large-scale structure
Scherrer, Robert J.
1992-01-01
Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.
Partial summations of stationary sequences of non-Gaussian random variables
DEFF Research Database (Denmark)
Mohr, Gunnar; Ditlevsen, Ove Dalager
1996-01-01
The distribution of the sum of a finite number of identically distributed random variables is in many cases easily determined given that the variables are independent. The moments of any order of the sum can always be expressed by the moments of the single term without computational problems...... 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)....... lognormal variables or polynomials of standard Gaussian variables. The dependency structure is induced by specifying the autocorrelation structure of the sequence of standard Gaussian variables. Particularly useful polynomials are the Winterstein approximations that distributionally fit with non...
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.
Generation of correlated finite alphabet waveforms using gaussian random variables
Ahmed, Sajid; Alouini, Mohamed-Slim; Jardak, Seifallah
2016-01-01
Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.
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.
Area of isodensity contours in Gaussian and non-Gaussian fields
International Nuclear Information System (INIS)
Ryden, B.S.
1988-01-01
The area of isodensity contours in a smoothed density field can be measured by the contour-crossing statistic N1, the number of times per unit length that a line drawn through the density field pierces an isodensity contour. The contour-crossing statistic distinguishes between Gaussian and non-Gaussian fields and provides a measure of the effective slope of the power spectrum. The statistic is easy to apply and can be used on pencil beams and slices as well as on a three-dimensional field. 10 references
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...
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...
Xu, Ganggang; Genton, Marc G.
2016-01-01
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.
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.
A characterization of Markovian homogeneous multicomponent Gaussian fields
International Nuclear Information System (INIS)
Ekhaguere, G.O.S.
1980-01-01
Necessary and sufficient conditions are given for a certain class of homogeneous multicomponent Gaussian generalized stochastic fields to possess a Markov property equivalent to Nelson's. The class of Markov fields so characterized has a as a cubclass the class of Markov fields which lead by Nelson's Reconstruction Theorem to some covariant (free) quantum fields. (orig.)
Some Metric Properties of Planar Gaussian Free Field
Goswami, Subhajit
In this thesis we study the properties of some metrics arising from two-dimensional Gaussian free field (GFF), namely the Liouville first-passage percolation (Liouville FPP), the Liouville graph distance and an effective resistance metric. In Chapter 1, we define these metrics as well as discuss the motivations for studying them. Roughly speaking, Liouville FPP is the shortest path metric in a planar domain D where the length of a path P is given by ∫Pe gammah(z)|dz| where h is the GFF on D and gamma > 0. In Chapter 2, we present an upper bound on the expected Liouville FPP distance between two typical points for small values of gamma (the near-Euclidean regime). A similar upper bound is derived in Chapter 3 for the Liouville graph distance which is, roughly, the minimal number of Euclidean balls with comparable Liouville quantum gravity (LQG) measure whose union contains a continuous path between two endpoints. Our bounds seem to be in disagreement with Watabiki's prediction (1993) on the random metric of Liouville quantum gravity in this regime. The contents of these two chapters are based on a joint work with Jian Ding. In Chapter 4, we derive some asymptotic estimates for effective resistances on a random network which is defined as follows. Given any gamma > 0 and for eta = {etav}v∈Z2 denoting a sample of the two-dimensional discrete Gaussian free field on Z2 pinned at the origin, we equip the edge ( u, v) with conductance egamma(etau + eta v). The metric structure of effective resistance plays a crucial role in our proof of the main result in Chapter 4. The primary motivation behind this metric is to understand the random walk on Z 2 where the edge (u, v) has weight egamma(etau + etav). Using the estimates from Chapter 4 we show in Chapter 5 that for almost every eta, this random walk is recurrent and that, with probability tending to 1 as T → infinity, the return probability at time 2T decays as T-1+o(1). In addition, we prove a version of subdiffusive
Energy Technology Data Exchange (ETDEWEB)
Wang, Yuan-Mei; Li, Jun-Gang, E-mail: jungl@bit.edu.cn; Zou, Jian
2017-06-15
Highlights: • Adaptive measurement strategy is used to detect the presence of a magnetic field. • Gaussian Ornstein–Uhlenbeck noise and non-Gaussian noise have been considered. • Weaker magnetic fields may be more easily detected than some stronger ones. - Abstract: By using the adaptive measurement method we study how to detect whether a weak magnetic field is actually present or not under Gaussian noise and non-Gaussian noise. We find that the adaptive measurement method can effectively improve the detection accuracy. For the case of Gaussian noise, we find the stronger the magnetic field strength, the easier for us to detect the magnetic field. Counterintuitively, for non-Gaussian noise, some weaker magnetic fields are more likely to be detected rather than some stronger ones. Finally, we give a reasonable physical interpretation.
Gaussian random bridges and a geometric model for information equilibrium
Mengütürk, Levent Ali
2018-03-01
The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.
International Nuclear Information System (INIS)
Tsuchida, Takahiro; Kimura, Koji
2015-01-01
Equivalent non-Gaussian excitation method is proposed to obtain the moments up to the fourth order of the response of systems under non-Gaussian random excitation. The excitation is prescribed by the probability density and power spectrum. Moment equations for the response can be derived from the stochastic differential equations for the excitation and the system. However, the moment equations are not closed due to the nonlinearity of the diffusion coefficient in the equation for the excitation. In the proposed method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by the second-order polynomial. In order to demonstrate the validity of the method, a linear system to non-Gaussian excitation with generalized Gaussian distribution is analyzed. The results show the method is applicable to non-Gaussian excitation with the widely different kurtosis and bandwidth. (author)
Entropy of level-cut random Gaussian structures at different volume fractions.
Marčelja, Stjepan
2017-10-01
Cutting random Gaussian fields at a given level can create a variety of morphologically different two- or several-phase structures that have often been used to describe physical systems. The entropy of such structures depends on the covariance function of the generating Gaussian random field, which in turn depends on its spectral density. But the entropy of level-cut structures also depends on the volume fractions of different phases, which is determined by the selection of the cutting level. This dependence has been neglected in earlier work. We evaluate the entropy of several lattice models to show that, even in the cases of strongly coupled systems, the dependence of the entropy of level-cut structures on molar fractions of the constituents scales with the simple ideal noninteracting system formula. In the last section, we discuss the application of the results to binary or ternary fluids and microemulsions.
Entropy of level-cut random Gaussian structures at different volume fractions
Marčelja, Stjepan
2017-10-01
Cutting random Gaussian fields at a given level can create a variety of morphologically different two- or several-phase structures that have often been used to describe physical systems. The entropy of such structures depends on the covariance function of the generating Gaussian random field, which in turn depends on its spectral density. But the entropy of level-cut structures also depends on the volume fractions of different phases, which is determined by the selection of the cutting level. This dependence has been neglected in earlier work. We evaluate the entropy of several lattice models to show that, even in the cases of strongly coupled systems, the dependence of the entropy of level-cut structures on molar fractions of the constituents scales with the simple ideal noninteracting system formula. In the last section, we discuss the application of the results to binary or ternary fluids and microemulsions.
Topological recursion for Gaussian means and cohomological field theories
Andersen, J. E.; Chekhov, L. O.; Norbury, P.; Penner, R. C.
2015-12-01
We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich-Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M g,s disc (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M g,1 for all g in three ways: using the refined Harer-Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.
International Nuclear Information System (INIS)
Tsuchida, Takahiro; Kimura, Koji
2016-01-01
Equivalent non-Gaussian excitation method is proposed to obtain the response moments up to the 4th order of dynamic systems under non-Gaussian random excitation. The non-Gaussian excitation is prescribed by the probability density and the power spectrum, and is described by an Ito stochastic differential equation. Generally, moment equations for the response, which are derived from the governing equations for the excitation and the system, are not closed due to the nonlinearity of the diffusion coefficient in the equation for the excitation even though the system is linear. In the equivalent non-Gaussian excitation method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by a quadratic polynomial. In numerical examples, a linear system subjected to nonGaussian excitations with bimodal and Rayleigh distributions is analyzed by using the present method. The results show that the method yields the variance, skewness and kurtosis of the response with high accuracy for non-Gaussian excitation with the widely different probability densities and bandwidth. The statistical moments of the equivalent non-Gaussian excitation are also investigated to describe the feature of the method. (paper)
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.
A programmable Gaussian random pulse generator for automated performance measurements
International Nuclear Information System (INIS)
Abdel-Aal, R.E.
1989-01-01
This paper describes a versatile random signal generator which produces logic pulses with a Gaussian distribution for the pulse spacing. The average rate at the pulse generator output can be software-programmed, which makes it useful in performing automated measurements of dead time and CPU time performance of data acquisition systems and modules over a wide range of data rates. Hardware and software components are described and data on the input-output characteristics and the statistical properties of the pulse generator are given. Typical applications are discussed together with advantages over using radioactive test sources. Results obtained from an automated performance run on a VAX 11/785 data acquisition system are presented. (orig.)
Generating Correlated QPSK Waveforms By Exploiting Real Gaussian Random Variables
Jardak, Seifallah; Ahmed, Sajid; Alouini, Mohamed-Slim
2012-01-01
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.
Yeung, Chuck
2018-06-01
The assumption that the local order parameter is related to an underlying spatially smooth auxiliary field, u (r ⃗,t ) , is a common feature in theoretical approaches to non-conserved order parameter phase separation dynamics. In particular, the ansatz that u (r ⃗,t ) is a Gaussian random field leads to predictions for the decay of the autocorrelation function which are consistent with observations, but distinct from predictions using alternative theoretical approaches. In this paper, the auxiliary field is obtained directly from simulations of the time-dependent Ginzburg-Landau equation in two and three dimensions. The results show that u (r ⃗,t ) is equivalent to the distance to the nearest interface. In two dimensions, the probability distribution, P (u ) , is well approximated as Gaussian except for small values of u /L (t ) , where L (t ) is the characteristic length-scale of the patterns. The behavior of P (u ) in three dimensions is more complicated; the non-Gaussian region for small u /L (t ) is much larger than that in two dimensions but the tails of P (u ) begin to approach a Gaussian form at intermediate times. However, at later times, the tails of the probability distribution appear to decay faster than a Gaussian distribution.
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.
Non-gaussianity from the trispectrum and vector field perturbations
International Nuclear Information System (INIS)
Valenzuela-Toledo, Cesar A.; Rodriguez, Yeinzon
2010-01-01
We use the δN formalism to study the trispectrum T ζ of the primordial curvature perturbation ζ when the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, τ NL , is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f NL , and the level of statistical anisotropy in the power spectrum, g ζ . Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on τ NL from WMAP, for generic inflationary models, is done.
Non-gaussianity from the trispectrum and vector field perturbations
Energy Technology Data Exchange (ETDEWEB)
Valenzuela-Toledo, Cesar A., E-mail: cavalto@ciencias.uis.edu.c [Escuela de Fisica, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga (Colombia); Rodriguez, Yeinzon, E-mail: yeinzon.rodriguez@uan.edu.c [Escuela de Fisica, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga (Colombia); Centro de Investigaciones, Universidad Antonio Narino, Cra 3 Este 47A-15, Bogota D.C. (Colombia)
2010-03-01
We use the deltaN formalism to study the trispectrum T{sub z}eta of the primordial curvature perturbation zeta when the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, tau{sub NL}, is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f{sub NL}, and the level of statistical anisotropy in the power spectrum, g{sub z}eta. Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on tau{sub NL} from WMAP, for generic inflationary models, is done.
Hessian eigenvalue distribution in a random Gaussian landscape
Yamada, Masaki; Vilenkin, Alexander
2018-03-01
The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential minima. In particular, the stability of vacua and the dynamics of slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues. The Hessian eigenvalue distribution has been studied earlier, using the saddle point approximation, in the leading order of 1/ N expansion, where N is the dimensionality of the landscape. This approximation, however, is insufficient for the small eigenvalue end of the spectrum, where sub-leading terms play a significant role. We extend the saddle point method to account for the sub-leading contributions. We also develop a new approach, where the eigenvalue distribution is found as an equilibrium distribution at the endpoint of a stochastic process (Dyson Brownian motion). The results of the two approaches are consistent in cases where both methods are applicable. We discuss the implications of our results for vacuum stability and slow-roll inflation in the landscape.
EVOLUTION OF THE MAGNETIC FIELD LINE DIFFUSION COEFFICIENT AND NON-GAUSSIAN STATISTICS
Energy Technology Data Exchange (ETDEWEB)
Snodin, A. P. [Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800 (Thailand); Ruffolo, D. [Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400 (Thailand); Matthaeus, W. H. [Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 (United States)
2016-08-20
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.
Initial conditions for slow-roll inflation in a random Gaussian landscape
Energy Technology Data Exchange (ETDEWEB)
Masoumi, Ali; Vilenkin, Alexander; Yamada, Masaki, E-mail: ali@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: Masaki.Yamada@tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2017-07-01
In the landscape perspective, our Universe begins with a quantum tunneling from an eternally-inflating parent vacuum, followed by a period of slow-roll inflation. We investigate the tunneling process and calculate the probability distribution for the initial conditions and for the number of e-folds of slow-roll inflation, modeling the landscape by a small-field one-dimensional random Gaussian potential. We find that such a landscape is fully consistent with observations, but the probability for future detection of spatial curvature is rather low, P ∼ 10{sup −3}.
Non-Gaussianity from self-ordering scalar fields
International Nuclear Information System (INIS)
Figueroa, Daniel G.; Caldwell, Robert R.; Kamionkowski, Marc
2010-01-01
The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and provide a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges k 1 ≅2k 2 ≅2k 3 ) as opposed to the local-model bispectrum, which peaks for squeezed triangles (k 1 ≅k 2 >>k 3 ), and the equilateral bispectrum, which peaks at k 1 ≅k 2 ≅k 3 . We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit.
Non-Gaussian statistics, classical field theory, and realizable Langevin models
International Nuclear Information System (INIS)
Krommes, J.A.
1995-11-01
The direct-interaction approximation (DIA) to the fourth-order statistic Z ∼ left-angle λψ 2 ) 2 right-angle, where λ is a specified operator and ψ is a random field, is discussed from several points of view distinct from that of Chen et al. [Phys. Fluids A 1, 1844 (1989)]. It is shown that the formula for Z DIA already appeared in the seminal work of Martin, Siggia, and Rose (Phys. Rev. A 8, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sd. 28, 145 (1971)] and Kraichnan [J. Fluid Mech. 41, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections (''spurious vertices'') is described. It is shown how to derive an improved representation, that realizes cumulants through O(ψ 4 ), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation Z DIA M to Z DIA is derived. Both Z DIA and Z DIA M incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example
Gaussian random-matrix process and universal parametric correlations in complex systems
International Nuclear Information System (INIS)
Attias, H.; Alhassid, Y.
1995-01-01
We introduce the framework of the Gaussian random-matrix process as an extension of Dyson's Gaussian ensembles and use it to discuss the statistical properties of complex quantum systems that depend on an external parameter. We classify the Gaussian processes according to the short-distance diffusive behavior of their energy levels and demonstrate that all parametric correlation functions become universal upon the appropriate scaling of the parameter. The class of differentiable Gaussian processes is identified as the relevant one for most physical systems. We reproduce the known spectral correlators and compute eigenfunction correlators in their universal form. Numerical evidence from both a chaotic model and weakly disordered model confirms our predictions
Holographic non-Gaussianities in general single-field inflation
Energy Technology Data Exchange (ETDEWEB)
Isono, Hiroshi [Department of Physics, Faculty of Science,Chulalongkorn University, Bangkok 10330 (Thailand); Noumi, Toshifumi [Department of Physics and Jockey Club Institute for Advanced Study,Hong Kong University of Science and Technology (Hong Kong); Department of Physics,Kobe University, Kobe 657-8501 (Japan); Shiu, Gary [Department of Physics and Jockey Club Institute for Advanced Study,Hong Kong University of Science and Technology (Hong Kong); Department of Physics, University of Wisconsin-Madison,Madison, WI 53706 (United States); Wong, Sam S.C.; Zhou, Siyi [Department of Physics and Jockey Club Institute for Advanced Study,Hong Kong University of Science and Technology (Hong Kong)
2016-12-07
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 (∂{sub μ}ϕ∂{sup μ}ϕ){sup 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-consistent setup which reproduces a red tilted power spectrum, as well as all possible bispectrum shapes in the slow-roll regime.
The Gaussian streaming model and convolution Lagrangian effective field theory
Energy Technology Data Exchange (ETDEWEB)
Vlah, Zvonimir [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94306 (United States); Castorina, Emanuele; White, Martin, E-mail: zvlah@stanford.edu, E-mail: ecastorina@berkeley.edu, E-mail: mwhite@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States)
2016-12-01
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.
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...
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.
Gaussian width bounds with applications to arithmetic progressions in random settings
J. Briët (Jop); S. Gopi (Sivakanth)
2017-01-01
textabstractMotivated by two problems on arithmetic progressions (APs)—concerning large deviations for AP counts in random sets and random differences in Szemer´edi’s theorem— we prove upper bounds on the Gaussian width of the image of the n-dimensional Boolean hypercube under a mapping ψ : Rn →
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...
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...
Probability distribution for the Gaussian curvature of the zero level surface of a random function
Hannay, J. H.
2018-04-01
A rather natural construction for a smooth random surface in space is the level surface of value zero, or ‘nodal’ surface f(x,y,z) = 0, of a (real) random function f; the interface between positive and negative regions of the function. A physically significant local attribute at a point of a curved surface is its Gaussian curvature (the product of its principal curvatures) because, when integrated over the surface it gives the Euler characteristic. Here the probability distribution for the Gaussian curvature at a random point on the nodal surface f = 0 is calculated for a statistically homogeneous (‘stationary’) and isotropic zero mean Gaussian random function f. Capitalizing on the isotropy, a ‘fixer’ device for axes supplies the probability distribution directly as a multiple integral. Its evaluation yields an explicit algebraic function with a simple average. Indeed, this average Gaussian curvature has long been known. For a non-zero level surface instead of the nodal one, the probability distribution is not fully tractable, but is supplied as an integral expression.
MINIMUM ENTROPY DECONVOLUTION OF ONE-AND MULTI-DIMENSIONAL NON-GAUSSIAN LINEAR RANDOM PROCESSES
Institute of Scientific and Technical Information of China (English)
程乾生
1990-01-01
The minimum entropy deconvolution is considered as one of the methods for decomposing non-Gaussian linear processes. The concept of peakedness of a system response sequence is presented and its properties are studied. With the aid of the peakedness, the convergence theory of the minimum entropy deconvolution is established. The problem of the minimum entropy deconvolution of multi-dimensional non-Gaussian linear random processes is first investigated and the corresponding theory is given. In addition, the relation between the minimum entropy deconvolution and parameter method is discussed.
Frydel, Derek; Ma, Manman
2016-06-01
Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, h_{λ}(r,r^{'}), in which interactions λu(r,r^{'}) are gradually switched on as λ changes from 0 to 1. The function h_{λ}(r,r^{'}) is then obtained from the inhomogeneous Ornstein-Zernike equation and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. The two equations do not yet constitute a closed set. In the present work we use the closure c_{λ}(r,r^{'})≈-λβu(r,r^{'}), known as the random-phase approximation (RPA). We demonstrate that the RPA is identical with the variational Gaussian approximation derived within the field-theoretical framework, originally derived and used for charged particles. We apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.
Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices
Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan; Gross, Sam; Hills, Gage; Hornstein, Michael; Lakkam, Milinda; Lee, Jason; Li, Jian; Liu, Linxi; Sing-Long, Carlos; Marx, Mike; Mittal, Akshay; Monajemi, Hatef; No, Albert; Omrani, Reza; Pekelis, Leonid; Qin, Junjie; Raines, Kevin; Ryu, Ernest; Saxe, Andrew; Shi, Dai; Siilats, Keith; Strauss, David; Tang, Gary; Wang, Chaojun; Zhou, Zoey; Zhu, Zhen
2013-01-01
In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions. PMID:23277588
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.
Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory
International Nuclear Information System (INIS)
Pato, Mauricio P; Oshanin, Gleb
2013-01-01
We study the probability distribution function P (β) n (w) of the Schmidt-like random variable w = x 2 1 /(∑ j=1 n x 2 j /n), where x j , (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 (β) (w)∼√((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. (paper)
Coupling the Gaussian Free Fields with Free and with Zero Boundary Conditions via Common Level Lines
Qian, Wei; Werner, Wendelin
2018-06-01
We point out a new simple way to couple the Gaussian Free Field (GFF) with free boundary conditions in a two-dimensional 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 zero-level lines (these signs are alternating for the zero-boundary GFF) in order to obtain a free boundary GFF. Constructions and couplings of the free boundary GFF and its level lines via soups of reflected Brownian loops and their clusters are also discussed. Such considerations show for instance that in a domain with an axis of symmetry, if one looks at the overlay of a single usual Conformal Loop Ensemble CLE3 with its own symmetric image, one obtains the CLE4-type collection of level lines of a GFF with mixed zero/free boundary conditions in the half-domain.
Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile
Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.
2012-09-01
Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.
International Nuclear Information System (INIS)
Itzykson, C.
1983-10-01
We review the formulation of field theory and statistical mechanics on a Poissonian random lattice. Topics discussed include random geometry, the construction of field equations for arbitrary spin, the free field spectrum and the question of localization illustrated in the one dimensional case
Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices
Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan
2012-01-01
In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the ...
Zhang, Hong; Hou, Rui; Yi, Lei; Meng, Juan; Pan, Zhisong; Zhou, Yuhuan
2016-07-01
The accurate identification of encrypted data stream helps to regulate illegal data, detect network attacks and protect users' information. In this paper, a novel encrypted data stream identification algorithm is introduced. The proposed method is based on randomness characteristics of encrypted data stream. We use a l1-norm regularized logistic regression to improve sparse representation of randomness features and Fuzzy Gaussian Mixture Model (FGMM) to improve identification accuracy. Experimental results demonstrate that the method can be adopted as an effective technique for encrypted data stream identification.
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.
Bell inequalities for random fields
Energy Technology Data Exchange (ETDEWEB)
Morgan, Peter [Physics Department, Yale University, CT 06520 (United States)
2006-06-09
The assumptions required for the derivation of Bell inequalities are not satisfied for random field models in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical two point particle models. Classical random field models that explicitly include the effects of quantum fluctuations on measurement are possible for experiments that violate Bell inequalities.
Bell inequalities for random fields
Morgan, Peter
2004-01-01
The assumptions required for the derivation of Bell inequalities are not usually satisfied for random fields in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical two point particle models. Classical random field models that explicitly include the effects of quantum fluctuations on measurement are possible for experiments that violate Bell inequalities.
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.
Ellis, Jeremy
On temporal, spatial and spectral scales which are small enough, all fields are fully polarized. In the optical regime, however, instantaneous fields can rarely be examined, and, instead, only average quantities are accessible. The study of polarimetry is concerned with both the description of electromagnetic fields and the characterization of media a field has interacted with. The polarimetric information is conventionally presented in terms of second order field correlations which are averaged over the ensemble of field realizations. Motivated by the deficiencies of classical polarimetry in dealing with specific practical situations, this dissertation expands the traditional polarimetric approaches to include higher order field correlations and the description of fields fluctuating in three dimensions. In relation to characterization of depolarizing media, a number of fourth-order correlations are introduced in this dissertation. Measurements of full polarization distributions, and the subsequent evaluation of Stokes vector element correlations and Complex Degree of Mutual Polarization demonstrate the use of these quantities for material discrimination and characterization. Recent advancements in detection capabilities allow access to fields near their sources and close to material boundaries, where a unique direction of propagation is not evident. Similarly, there exist classical situations such as overlapping beams, focusing, or diffusive scattering in which there is no unique transverse direction. In this dissertation, the correlation matrix formalism is expanded to describe three dimensional electromagnetic fields, providing a definition for the degree of polarization of such a field. It is also shown that, because of the dimensionality of the problem, a second parameter is necessary to fully describe the polarimetric properties of three dimensional fields. Measurements of second-order correlations of a three dimensional field are demonstrated, allowing the
Wilhelm, Jan; Seewald, Patrick; Del Ben, Mauro; Hutter, Jürg
2016-12-13
We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring [Formula: see text] operations and [Formula: see text] memory. The method is based on the resolution of the identity (RI) with the overlap metric, a reformulation of RI-RPA in the Gaussian basis, imaginary time, and imaginary frequency integration techniques, and the use of sparse linear algebra. Additional memory reduction without extra computations can be achieved by an iterative scheme that overcomes the memory bottleneck of canonical RPA implementations. We report a massively parallel implementation that is the key for the application to large systems. Finally, cubic-scaling RPA is applied to a thousand water molecules using a correlation-consistent triple-ζ quality basis.
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].
New Results on the Sum of Two Generalized Gaussian Random Variables
Soury, Hamza; Alouini, Mohamed-Slim
2016-01-01
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 [1].
Super-Gaussian transport theory and the field-generating thermal instability in laser–plasmas
International Nuclear Information System (INIS)
Bissell, J J; Ridgers, C P; Kingham, R J
2013-01-01
Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser–plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal (anomalous Nernst) magnetic field advection up gradients in the electron number density n e , which we associate with a novel heat-flow q n ∝∇n e . Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ, in which case the Nernst effect is reduced by a factor of five, the ∇T e × ∇n e field generation mechanism by ∼30% (where T e is the electron temperature), and the diffusive and Righi–Leduc heat-flows by ∼80 and ∼90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux q n are checked against kinetic simulation using the Vlasov–Fokker–Planck code impact, and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic analysis. Given such strong inhibition of transport at low χ, we consider the impact of IB on the seeding and evolution of magnetic fields (in otherwise un-magnetized conditions) by examining the well-known field-generating thermal instability in the light of super-Gaussian transport theory (Tidman and Shanny 1974 Phys. Fluids 12 1207). Estimates based on conditions in an inertial confinement fusion (ICF) hohlraum suggest that super-Gaussian effects can reduce the growth-rate of the instability by ≳80%. This result may be important for ICF experiments, since by increasing the strength of IB heating it would appear possible to inhibit the spontaneous generation of large magnetic fields. (paper)
Super-Gaussian transport theory and the field-generating thermal instability in laser-plasmas
Bissell, J. J.; Ridgers, C. P.; Kingham, R. J.
2013-02-01
Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser-plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal (anomalous Nernst) magnetic field advection up gradients in the electron number density ne, which we associate with a novel heat-flow qn∝∇ne. Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ, in which case the Nernst effect is reduced by a factor of five, the ∇Te × ∇ne field generation mechanism by ˜30% (where Te is the electron temperature), and the diffusive and Righi-Leduc heat-flows by ˜80 and ˜90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux qn are checked against kinetic simulation using the Vlasov-Fokker-Planck code impact, and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic analysis. Given such strong inhibition of transport at low χ, we consider the impact of IB on the seeding and evolution of magnetic fields (in otherwise un-magnetized conditions) by examining the well-known field-generating thermal instability in the light of super-Gaussian transport theory (Tidman and Shanny 1974 Phys. Fluids 12 1207). Estimates based on conditions in an inertial confinement fusion (ICF) hohlraum suggest that super-Gaussian effects can reduce the growth-rate of the instability by ≳80%. This result may be important for ICF experiments, since by increasing the strength of IB heating it would appear possible to inhibit the spontaneous generation of large magnetic fields.
Signed zeros of Gaussian vector fields - density, correlation functions and curvature
Foltin, G
2003-01-01
We calculate correlation functions of the (signed) density of zeros of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann Cartan or Riemannian manifold. As an application, we discuss one- and two-point functions. The zeros of a two-dimensional Gaussian vector field model the distribution of topological defects in the high-temperature phase of two-dimensional systems with orientational degrees of freedom, such as superfluid films, thin superconductors and liquid crystals.
Subquantum nonlocal correlations induced by the background random field
Energy Technology Data Exchange (ETDEWEB)
Khrennikov, Andrei, E-mail: Andrei.Khrennikov@lnu.s [International Center for Mathematical Modelling in Physics and Cognitive Sciences, Linnaeus University, Vaexjoe (Sweden); Institute of Information Security, Russian State University for Humanities, Moscow (Russian Federation)
2011-10-15
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).
Subquantum nonlocal correlations induced by the background random field
International Nuclear Information System (INIS)
Khrennikov, Andrei
2011-01-01
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).
Tian, Yuzhen; Guo, Jin; Wang, Rui; Wang, Tingfeng
2011-09-12
In order to research the statistical properties of Gaussian beam propagation through an arbitrary thickness random phase screen for adaptive optics and laser communication application in the laboratory, we establish mathematic models of statistical quantities, which are based on the Rytov method and the thin phase screen model, involved in the propagation process. And the analytic results are developed for an arbitrary thickness phase screen based on the Kolmogorov power spectrum. The comparison between the arbitrary thickness phase screen and the thin phase screen shows that it is more suitable for our results to describe the generalized case, especially the scintillation index.
Self-consistent field theory of protein adsorption in a non-Gaussian polyelectrolyte brush
Biesheuvel, P.M.; Leermakers, F.A.M.; Stuart, M.A.C.
2006-01-01
To describe adsorption of globular protein molecules in a polyelectrolyte brush we use the strong-stretching approximation of the Edwards self-consistent field equation, combined with corrections for a non-Gaussian brush. To describe chemical potentials in this mixture of (globular) species of
Non-Gaussianities in a two-field generalization of natural inflation
Riquelme M., Simon
2018-04-01
We describe a two-field model that generalizes natural inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spontaneously broken, and the radial mode is dynamical. We analyze how the dynamics fundamentally depends on the mass of the radial mode and calculate/estimate the non-Gaussianities arising from such a scenario.
Czech Academy of Sciences Publication Activity Database
Arkhipov, Ie.I.; Peřina, Jan; Peřina, J.; Miranowicz, A.
2016-01-01
Roč. 94, č. 1 (2016), 1-15, č. článku 013807. ISSN 2469-9926 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : two-mode Gaussian fields * optical parametric processes Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.925, year: 2016
International Nuclear Information System (INIS)
Wu, Jinghe; Guo, Kangxian; Liu, Guanghui
2014-01-01
Polaron effects on nonlinear optical rectification in asymmetrical Gaussian potential quantum wells are studied by the effective mass approximation and the perturbation theory. The numerical results show that nonlinear optical rectification coefficients are strongly dependent on the barrier hight V 0 of the Gaussian potential quantum wells, the range L of the confinement potential and the electric field F. Besides, the numerical results show that no matter how V 0 , L and F change, taking into consideration polaron effects, the optical rectification coefficients χ 0 (2) get greatly enhanced.
PHYSICS OF NON-GAUSSIAN FIELDS AND THE COSMOLOGICAL GENUS STATISTIC
International Nuclear Information System (INIS)
James, J. Berian
2012-01-01
We report a technique to calculate the impact of distinct physical processes inducing non-Gaussianity on the cosmological density field. A natural decomposition of the cosmic genus statistic into an orthogonal polynomial sequence allows complete expression of the scale-dependent evolution of the topology of large-scale structure, in which effects including galaxy bias, nonlinear gravitational evolution, and primordial non-Gaussianity may be delineated. The relationship of this decomposition to previous methods for analyzing the genus statistic is briefly considered and the following applications are made: (1) the expression of certain systematics affecting topological measurements, (2) the quantification of broad deformations from Gaussianity that appear in the genus statistic as measured in the Horizon Run simulation, and (3) the study of the evolution of the genus curve for simulations with primordial non-Gaussianity. These advances improve the treatment of flux-limited galaxy catalogs for use with this measurement and further the use of the genus statistic as a tool for exploring non-Gaussianity.
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...
Excursion probabilities of non-homogeneous Gaussian scalar fields based on maxima considerations
DEFF Research Database (Denmark)
Nielsen, Michael Havbro Faber; Rackwitz, R.
1988-01-01
Many uncertain natural or technical phenomena are most realistically described by random fields. A typical example of a random field is the load effect in a floor slab which is loaded by a spatially distributed gravity load. Other examples of random fields include the sea-level around off-shore p...
International Nuclear Information System (INIS)
Lian-Huang, Li; Fu-Yuan, Guo
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
Numerical solution of second-order stochastic differential equations with Gaussian random parameters
Directory of Open Access Journals (Sweden)
Rahman Farnoosh
2014-07-01
Full Text Available In this paper, we present the numerical solution of ordinary differential equations (or SDEs, from each orderespecially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysisfor second-order equations in specially case of scalar linear second-order equations (damped harmonicoscillators with additive or multiplicative noises. Making stochastic differential equations system from thisequation, it could be approximated or solved numerically by different numerical methods. In the case oflinear stochastic differential equations system by Computing fundamental matrix of this system, it could becalculated based on the exact solution of this system. Finally, this stochastic equation is solved by numericallymethod like E.M. and Milstein. Also its Asymptotic stability and statistical concepts like expectationand variance of solutions are discussed.
A brain MRI bias field correction method created in the Gaussian multi-scale space
Chen, Mingsheng; Qin, Mingxin
2017-07-01
A pre-processing step is needed to correct for the bias field signal before submitting corrupted MR images to such image-processing algorithms. This study presents a new bias field correction method. The method creates a Gaussian multi-scale space by the convolution of the inhomogeneous MR image with a two-dimensional Gaussian function. In the multi-Gaussian space, the method retrieves the image details from the differentiation of the original image and convolution image. Then, it obtains an image whose inhomogeneity is eliminated by the weighted sum of image details in each layer in the space. Next, the bias field-corrected MR image is retrieved after the Υ correction, which enhances the contrast and brightness of the inhomogeneity-eliminated MR image. We have tested the approach on T1 MRI and T2 MRI with varying bias field levels and have achieved satisfactory results. Comparison experiments with popular software have demonstrated superior performance of the proposed method in terms of quantitative indices, especially an improvement in subsequent image segmentation.
Generating functionals for quantum field theories with random potentials
International Nuclear Information System (INIS)
Jain, Mudit; Vanchurin, Vitaly
2016-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). 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 and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.
Delpueyo, D.; Balandraud, X.; Grédiac, M.
2013-09-01
The aim of this paper is to present a post-processing technique based on a derivative Gaussian filter to reconstruct heat source fields from temperature fields measured by infrared thermography. Heat sources can be deduced from temperature variations thanks to the heat diffusion equation. Filtering and differentiating are key-issues which are closely related here because the temperature fields which are processed are unavoidably noisy. We focus here only on the diffusion term because it is the most difficult term to estimate in the procedure, the reason being that it involves spatial second derivatives (a Laplacian for isotropic materials). This quantity can be reasonably estimated using a convolution of the temperature variation fields with second derivatives of a Gaussian function. The study is first based on synthetic temperature variation fields corrupted by added noise. The filter is optimised in order to reconstruct at best the heat source fields. The influence of both the dimension and the level of a localised heat source is discussed. Obtained results are also compared with another type of processing based on an averaging filter. The second part of this study presents an application to experimental temperature fields measured with an infrared camera on a thin plate in aluminium alloy. Heat sources are generated with an electric heating patch glued on the specimen surface. Heat source fields reconstructed from measured temperature fields are compared with the imposed heat sources. Obtained results illustrate the relevancy of the derivative Gaussian filter to reliably extract heat sources from noisy temperature fields for the experimental thermomechanics of materials.
Non-Gaussianity at tree and one-loop levels from vector field perturbations
International Nuclear Information System (INIS)
Valenzuela-Toledo, Cesar A.; Rodriguez, Yeinzon; Lyth, David H.
2009-01-01
We study the spectrum P ζ and bispectrum B ζ of the primordial curvature perturbation ζ 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 ζ and (or) in B ζ ] and vice versa. 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 ζ . 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.
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-Gaussian path integration in self-interacting scalar field theories
International Nuclear Information System (INIS)
Kaya, Ali
2004-01-01
In self-interacting scalar field theories kinetic expansion is an alternative way of calculating the generating functional for Green's functions where the zeroth order non-Gaussian path integral becomes diagonal in x-space and reduces to the product of an ordinary integral at each point which can be evaluated exactly. We discuss how to deal with such functional integrals and propose a new perturbative expansion scheme which combines the elements of the kinetic expansion with the usual perturbation theory techniques. It is then shown that, when the cutoff dependences of the bare parameters in the potential are chosen to have a well defined non-Gaussian path integral without the kinetic term, the theory becomes trivial in the continuum limit
International Nuclear Information System (INIS)
Freitas Naiff, Danilo de; Silveira, Paulo R.; Pereira, Claudio M.N.A.
2017-01-01
This article proposes an approach for determination of radiation dose pro le in a radiation-susceptible environment, aiming to guide an autonomous robot in acting on those environments, reducing the human exposure to dangerous amount of dose. The approach consists of an active learning method based on information entropy reduction, using log-normally warped Gaussian Process (GP) as surrogate model, resulting in non-linear online regression with sequential measurements. Experiments with simulated radiation dose fields of varying complexity were made, and results showed that the approach was effective in reconstruct the eld with high accuracy, through relatively few measurements. The technique was also shown some robustness in presence measurement noise, present in real measurements, by assuming Gaussian noise. (author)
Energy Technology Data Exchange (ETDEWEB)
Freitas Naiff, Danilo de; Silveira, Paulo R.; Pereira, Claudio M.N.A., E-mail: danilonai1992@poli.ufrj.br, E-mail: paulo@lmp.ufrj.br, E-mail: cmnap@ien.gov.br [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil); Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil)
2017-11-01
This article proposes an approach for determination of radiation dose pro le in a radiation-susceptible environment, aiming to guide an autonomous robot in acting on those environments, reducing the human exposure to dangerous amount of dose. The approach consists of an active learning method based on information entropy reduction, using log-normally warped Gaussian Process (GP) as surrogate model, resulting in non-linear online regression with sequential measurements. Experiments with simulated radiation dose fields of varying complexity were made, and results showed that the approach was effective in reconstruct the eld with high accuracy, through relatively few measurements. The technique was also shown some robustness in presence measurement noise, present in real measurements, by assuming Gaussian noise. (author)
Electron acceleration by longitudinal electric field of a gaussian laser beam
International Nuclear Information System (INIS)
Takeuchi, Satoshi; Sugihara, Ryo; Shimoda, Koichi.
1991-11-01
It is shown that the longitudinal electric field of a transverse magnetic mode of a Gaussian laser beam accelerates an electron to an ultra-relativistic energy. The electron is captured and accelerated in a length of the order of the Rayleigh range. The ultimate energy increment of the electron with a single laser beam is given by the product of transverse field intensity and the beam waist, and can be of the order of 100MeV. This fact implies that a multi-stage acceleration enables TeV-order-acceleration in a length of a few kilometers with the present state of the art. (author)
Primordial non-Gaussianities in single field inflationary models with non-trivial initial states
Energy Technology Data Exchange (ETDEWEB)
Bahrami, Sina; Flanagan, Éanna É., E-mail: sb933@cornell.edu, E-mail: eef3@cornell.edu [Department of Physics, Cornell University, Ithaca, NY 14853 (United States)
2014-10-01
We compute the non-Gaussianities that arise in single field, slow roll inflationary models arising from arbitrary homogeneous initial states, as well as subleading contributions to the power spectrum. Non Bunch-Davies vacuum initial states can arise if the transition to the single field, slow roll inflation phase occurs only shortly before observable modes left the horizon. They can also arise from new physics at high energies that has been integrated out. Our general result for the bispectrum exhibits several features that were previously seen in special cases.
Addendum to foundations of multidimensional wave field signal theory: Gaussian source function
Directory of Open Access Journals (Sweden)
Natalie Baddour
2018-02-01
Full Text Available Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.
Addendum to foundations of multidimensional wave field signal theory: Gaussian source function
Baddour, Natalie
2018-02-01
Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011)], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.
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.
International Nuclear Information System (INIS)
Pal, Suvajit; Sinha, Sudarson Sekhar; Ganguly, Jayanta; Ghosh, Manas
2013-01-01
Highlights: • The excitation kinetics of impurity doped quantum dot has been investigated. • The dot is subject to Gaussian white noise. • External oscillatory field is also applied. • Noise strength and field intensity fabricate the kinetics. • Role of dopant location has also been analyzed. - Abstract: We investigate the excitation kinetics of a repulsive impurity doped quantum dot initiated by simultaneous application of Gaussian white noise and external sinusoidal field. We have considered both additive and multiplicative noise (in Stratonovich sense). The combined influences of noise strength (ζ) and the field intensity (∊) have been capsuled by invoking their ratio (η). The said ratio and the dopant location have been found to fabricate the kinetics in a delicate way. Moreover, the influences of additive and multiplicative nature of the noise on the excitation kinetics have been observed to be widely different. The investigation reveals emergence of maximization/minimization and saturation in the excitation kinetics as a result of complex interplay between η and the dopant coordinate (r 0 ). The present investigation is believed to provide some useful insights in the functioning of mesoscopic devices where noise plays some significant role
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
Non-Gaussianity in two-field inflation beyond the slow-roll approximation
Energy Technology Data Exchange (ETDEWEB)
Jung, Gabriel; Tent, Bartjan van, E-mail: gabriel.jung@th.u-psud.fr, E-mail: bartjan.van-tent@th.u-psud.fr [Laboratoire de Physique Théorique (UMR 8627), CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bâtiment 210, 91405 Orsay Cedex (France)
2017-05-01
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 Δ f {sub NL}{sup local}=1. We derive an alternative formulation of the previously derived integral expression for f {sub 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 {sub NL} and the observational constraints on the spectral index n {sub s} . In the case of the sum of two monomial potentials and a constant we explicitly show in which small region of parameter space this is possible, and we show how to construct such a model. Finally, the new general expression for f {sub NL} also allows us to prove that for the sum potential the explicit expressions derived within the slow-roll approximation remain valid even when the slow-roll approximation is broken during the turn of the field trajectory (as long as only the ε slow-roll parameter remains small).
Non-Gaussianity and statistical anisotropy from vector field populated inflationary models
Dimastrogiovanni, Emanuela; Matarrese, Sabino; Riotto, Antonio
2010-01-01
We present a review of vector field models of inflation and, in particular, of the statistical anisotropy and non-Gaussianity predictions of models with SU(2) vector multiplets. Non-Abelian gauge groups introduce a richer amount of predictions compared to the Abelian ones, mostly because of the presence of vector fields self-interactions. Primordial vector fields can violate isotropy leaving their imprint in the comoving curvature fluctuations zeta at late times. We provide the analytic expressions of the correlation functions of zeta up to fourth order and an analysis of their amplitudes and shapes. The statistical anisotropy signatures expected in these models are important and, potentially, the anisotropic contributions to the bispectrum and the trispectrum can overcome the isotropic parts.
Vanishing of local non-Gaussianity in canonical single field inflation
Bravo, Rafael; Mooij, Sander; Palma, Gonzalo A.; Pradenas, Bastián
2018-05-01
We study the production of observable primordial local non-Gaussianity in two opposite regimes of canonical single field inflation: attractor (standard single field slow-roll inflation) and non attractor (ultra slow-roll inflation). In the attractor regime, the standard derivation of the bispectrum's squeezed limit using co-moving coordinates gives the well known Maldacena's consistency relation fNL = 5 (1‑ns) / 12. On the other hand, in the non-attractor regime, the squeezed limit offers a substantial violation of this relation given by fNL = 5/2. In this work we argue that, independently of whether inflation is attractor or non-attractor, the size of the observable primordial local non-Gaussianity is predicted to be fNLobs = 0 (a result that was already understood to hold in the case of attractor models). To show this, we follow the use of the so-called Conformal Fermi Coordinates (CFC), recently introduced in the literature. These coordinates parametrize the local environment of inertial observers in a perturbed FRW spacetime, allowing one to identify and compute gauge invariant quantities, such as n-point correlation functions. Concretely, we find that during inflation, after all the modes have exited the horizon, the squeezed limit of the 3-point correlation function of curvature perturbations vanishes in the CFC frame, regardless of the inflationary regime. We argue that such a cancellation should persist after inflation ends.
Directory of Open Access Journals (Sweden)
Ronghui ZHENG
2017-12-01
Full Text Available A control method for Multi-Input Multi-Output (MIMO non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multi-output kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well. Keywords: Cross spectra, Kurtosis control, Multi-input multi-output, Non-Gaussian, Random vibration test
A generalized non-Gaussian consistency relation for single field inflation
Bravo, Rafael; Mooij, Sander; Palma, Gonzalo A.; Pradenas, Bastián
2018-05-01
We show that a perturbed inflationary spacetime, driven by a canonical single scalar field, is invariant under a special class of coordinate transformations together with a field reparametrization of the curvature perturbation in co-moving gauge. This transformation may be used to derive the squeezed limit of the 3-point correlation function of the co-moving curvature perturbations valid in the case that these do not freeze after horizon crossing. This leads to a generalized version of Maldacena's non-Gaussian consistency relation in the sense that the bispectrum squeezed limit is completely determined by spacetime diffeomorphisms. Just as in the case of the standard consistency relation, this result may be understood as the consequence of how long-wavelength modes modulate those of shorter wavelengths. This relation allows one to derive the well known violation to the consistency relation encountered in ultra slow-roll, where curvature perturbations grow exponentially after horizon crossing.
International Nuclear Information System (INIS)
Vyas, Manan; Kota, V.K.B.
2010-01-01
For m fermions in Ω number of single particle orbitals, each fourfold degenerate, we introduce and analyze in detail embedded Gaussian unitary ensemble of random matrices generated by random two-body interactions that are SU(4) scalar [EGUE(2)-SU(4)]. Here the SU(4) algebra corresponds to the Wigner's supermultiplet SU(4) symmetry in nuclei. Embedding algebra for the EGUE(2)-SU(4) ensemble is U(4Ω) contains U(Ω) x SU(4). Exploiting the Wigner-Racah algebra of the embedding algebra, analytical expression for the ensemble average of the product of any two m particle Hamiltonian matrix elements is derived. Using this, formulas for a special class of U(Ω) irreducible representations (irreps) {4 r , p}, p = 0, 1, 2, 3 are derived for the ensemble averaged spectral variances and also for the covariances in energy centroids and spectral variances. On the other hand, simplifying the tabulations of Hecht for SU(Ω) Racah coefficients, numerical calculations are carried out for general U(Ω) irreps. Spectral variances clearly show, by applying Jacquod and Stone prescription, that the EGUE(2)-SU(4) ensemble generates ground state structure just as the quadratic Casimir invariant (C 2 ) of SU(4). This is further corroborated by the calculation of the expectation values of C 2 [SU(4)] and the four periodicity in the ground state energies. Secondly, it is found that the covariances in energy centroids and spectral variances increase in magnitude considerably as we go from EGUE(2) for spinless fermions to EGUE(2) for fermions with spin to EGUE(2)-SU(4) implying that the differences in ensemble and spectral averages grow with increasing symmetry. Also for EGUE(2)-SU(4) there are, unlike for GUE, non-zero cross-correlations in energy centroids and spectral variances defined over spaces with different particle numbers and/or U(Ω) [equivalently SU(4)] irreps. In the dilute limit defined by Ω → ∞, r >> 1 and r/Ω → 0, for the {4 r , p} irreps, we have derived analytical
Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.
de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos
2011-01-01
In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.
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 ...
Avendaño-Valencia, Luis David; Fassois, Spilios D.
2017-12-01
The problem of vibration-based damage diagnosis in structures characterized by time-dependent dynamics under significant environmental and/or operational uncertainty is considered. A stochastic framework consisting of a Gaussian Mixture Random Coefficient model of the uncertain time-dependent dynamics under each structural health state, proper estimation methods, and Bayesian or minimum distance type decision making, is postulated. The Random Coefficient (RC) time-dependent stochastic model with coefficients following a multivariate Gaussian Mixture Model (GMM) allows for significant flexibility in uncertainty representation. Certain of the model parameters are estimated via a simple procedure which is founded on the related Multiple Model (MM) concept, while the GMM weights are explicitly estimated for optimizing damage diagnostic performance. The postulated framework is demonstrated via damage detection in a simple simulated model of a quarter-car active suspension with time-dependent dynamics and considerable uncertainty on the payload. Comparisons with a simpler Gaussian RC model based method are also presented, with the postulated framework shown to be capable of offering considerable improvement in diagnostic performance.
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.
Fano resonance of the ultrasensitve optical force excited by Gaussian evanescent field
International Nuclear Information System (INIS)
Yang, Yang; Li, Jiafang; Li, Zhi-Yuan
2015-01-01
In this paper, we study the angle-dependent Fano-like optical force spectra of plasmonic Ag nanoparticles, which exhibit extraordinary transformation from Lorentzian resonance to Fano resonance when excited by a Gaussian evanescent wave. We systematically analyze the behavior of this asymmetric scattering induced optical force under different conditions and find that this Fano interference-induced force is ultrasensitive to the excitation wavelength, incident angle and particle size, as well as the core–shell configuration, which could be useful for wavelength- and angle-dependent size-selective optical manipulation. The origin of this Fano resonance is further identified as the interference between the two adjacent-order multipolar plasmonic modes excited in the Ag particle under the excitation of an inhomogeneously distributed evanescent field. (paper)
Phase statistics in non-Gaussian scattering
International Nuclear Information System (INIS)
Watson, Stephen M; Jakeman, Eric; Ridley, Kevin D
2006-01-01
Amplitude weighting can improve the accuracy of frequency measurements in signals corrupted by multiplicative speckle noise. When the speckle field constitutes a circular complex Gaussian process, the optimal function of amplitude weighting is provided by the field intensity, corresponding to the intensity-weighted phase derivative statistic. In this paper, we investigate the phase derivative and intensity-weighted phase derivative returned from a two-dimensional random walk, which constitutes a generic scattering model capable of producing both Gaussian and non-Gaussian fluctuations. Analytical results are developed for the correlation properties of the intensity-weighted phase derivative, as well as limiting probability densities of the scattered field. Numerical simulation is used to generate further probability densities and determine optimal weighting criteria from non-Gaussian fields. The results are relevant to frequency retrieval in radiation scattered from random media
On the ability to discriminate Gaussian-noise tokens or random tone-burst complexes
Goossens, T.L.J.; Par, van de S.L.J.D.E.; Kohlrausch, A.G.
2008-01-01
This study investigated factors that influence a listeners' ability to discriminate Gaussian-noise stimuli in a same-different discrimination paradigm. The first experiment showed that discrimination ability increased with bandwidth for noise durations up to 100 ms. Duration had a nonmonotonic
Efficient Training Methods for Conditional Random Fields
National Research Council Canada - National Science Library
Sutton, Charles A
2008-01-01
.... In this thesis, I investigate efficient training methods for conditional random fields with complex graphical structure, focusing on local methods which avoid propagating information globally along the graph...
Solvation in atomic liquids: connection between Gaussian field theory and density functional theory
Directory of Open Access Journals (Sweden)
V. Sergiievskyi
2017-12-01
Full Text Available For the problem of molecular solvation, formulated as a liquid submitted to the external potential field created by a molecular solute of arbitrary shape dissolved in that solvent, we draw a connection between the Gaussian field theory derived by David Chandler [Phys. Rev. E, 1993, 48, 2898] and classical density functional theory. We show that Chandler's results concerning the solvation of a hard core of arbitrary shape can be recovered by either minimising a linearised HNC functional using an auxiliary Lagrange multiplier field to impose a vanishing density inside the core, or by minimising this functional directly outside the core — indeed a simpler procedure. Those equivalent approaches are compared to two other variants of DFT, either in the HNC, or partially linearised HNC approximation, for the solvation of a Lennard-Jones solute of increasing size in a Lennard-Jones solvent. Compared to Monte-Carlo simulations, all those theories give acceptable results for the inhomogeneous solvent structure, but are completely out-of-range for the solvation free-energies. This can be fixed in DFT by adding a hard-sphere bridge correction to the HNC functional.
Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
International Nuclear Information System (INIS)
Al-Saidi, W.A.; Zhang Shiwei; Krakauer, Henry
2006-01-01
We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with the system size as a low power. A QMC approach with auxiliary fields, in principle, allows an exact solution of the Schroedinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few millihartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled cluster with single and double excitations and with noniterative triples [CCSD(T)]. For stretched bonds in H 2 O, our method exhibits a better overall accuracy and a more uniform behavior than CCSD(T)
International Nuclear Information System (INIS)
Hassan, W.; Blodgett, M.
2006-01-01
Shot peening is the primary surface treatment used to create a uniform, consistent, and reliable sub-surface compressive residual stress layer in aero engine components. A by-product of the shot peening process is random surface roughness that can affect the measurements of the resulting residual stresses and therefore impede their NDE assessment. High frequency eddy current conductivity measurements have the potential to assess these residual stresses in Ni-base super alloys. However, the effect of random surface roughness is expected to become significant in the desired measurement frequency range of 10 to 100 MHz. In this paper, a new Multi-Gaussian (MG) auto-correlation function is proposed for modeling the resulting pseudo-random rough profiles. Its use in the calculation of the Apparent Eddy Current Conductivity (AECC) loss due to surface roughness is demonstrated. The numerical results presented need to be validated with experimental measurements
Supplementary Material for: Tukey g-and-h Random Fields
Xu, Ganggang; Genton, Marc G.
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.
Zhu, Wuming; Trickey, S B
2017-12-28
In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic (B field) confinement. However, the best available a priori procedure for composing highly accurate AGTO sets for atoms in a strong B field [W. Zhu et al., Phys. Rev. A 90, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in B fields that allow identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary B field. For the hydrogen iso-electronic sequence, a set depends on B field strength, nuclear charge, and orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C (1 ≤ Z ≤ 6) and ions Li + , Be + , and B + , in a wide B field range (0 ≤ B ≤ 2000 a.u.), show an accuracy better than a few μhartree for single-electron systems and a few hundredths to a few mHs for multi-electron atoms. The relative errors are similar for different atoms and ions in a large B field range, from a few to a couple of tens of millionths, thereby confirming rather uniform accuracy across the nuclear charge Z and B field strength values. Residual basis set errors are two to three orders of magnitude smaller than the electronic correlation energies in multi-electron atoms, a signal of the usefulness of the new AGTO basis sets in correlated wavefunction or density functional calculations for atomic and molecular systems in an external strong B
Zhu, Wuming; Trickey, S. B.
2017-12-01
In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic (B field) confinement. However, the best available a priori procedure for composing highly accurate AGTO sets for atoms in a strong B field [W. Zhu et al., Phys. Rev. A 90, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in B fields that allow identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary B field. For the hydrogen iso-electronic sequence, a set depends on B field strength, nuclear charge, and orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C (1 ≤ Z ≤ 6) and ions Li+, Be+, and B+, in a wide B field range (0 ≤ B ≤ 2000 a.u.), show an accuracy better than a few μhartree for single-electron systems and a few hundredths to a few mHs for multi-electron atoms. The relative errors are similar for different atoms and ions in a large B field range, from a few to a couple of tens of millionths, thereby confirming rather uniform accuracy across the nuclear charge Z and B field strength values. Residual basis set errors are two to three orders of magnitude smaller than the electronic correlation energies in multi-electron atoms, a signal of the usefulness of the new AGTO basis sets in correlated wavefunction or density functional calculations for atomic and molecular systems in an external strong B field.
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
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
Vacuum instability in a random electric field
International Nuclear Information System (INIS)
Krive, I.V.; Pastur, L.A.
1984-01-01
The reaction of the vacuum on an intense spatially homogeneous random electric field is investigated. It is shown that a stochastic electric field always causes a breakdown of the boson vacuum, and the number of pairs of particles which are created by the electric field increases exponentially in time. For the choice of potential field in the form of a dichotomic random process we find in explicit form the dependence of the average number of pairs of particles on the time of the action of the source of the stochastic field. For the fermion vacuum the average number of pairs of particles which are created by the field in the lowest order of perturbation theory in the amplitude of the random field is independent of time
Uniqueness conditions for finitely dependent random fields
International Nuclear Information System (INIS)
Dobrushin, R.L.; Pecherski, E.A.
1981-01-01
The authors consider a random field for which uniqueness and some additional conditions guaranteeing that the correlations between the variables of the field decrease rapidly enough with the distance between the values of the parameter occur. The main result of the paper states that in such a case uniqueness is true for any other field with transition probabilities sufficiently close to those of the original field. Then they apply this result to some ''degenerate'' classes of random fields for which one can check this condition of correlation to decay, and thus obtain some new conditions of uniqueness. (Auth.)
Gaussian point count statistics for families of curves over a fixed finite field
Kurlberg, Par; Wigman, Igor
2010-01-01
We produce a collection of families of curves, whose point count statistics over F_p becomes Gaussian for p fixed. In particular, the average number of F_p points on curves in these families tends to infinity.
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...
International Nuclear Information System (INIS)
Smirnov, V.N.; Strokovskii, G.A.
1994-01-01
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
Random Assignment: Practical Considerations from Field Experiments.
Dunford, Franklyn W.
1990-01-01
Seven qualitative issues associated with randomization that have the potential to weaken or destroy otherwise sound experimental designs are reviewed and illustrated via actual field experiments. Issue areas include ethics and legality, liability risks, manipulation of randomized outcomes, hidden bias, design intrusiveness, case flow, and…
Solitons in a random force field
International Nuclear Information System (INIS)
Bass, F.G.; Konotop, V.V.; Sinitsyn, Y.A.
1985-01-01
We study the dynamics of a soliton of the sine-Gordon equation in a random force field in the adiabatic approximation. We obtain an Einstein-Fokker equation and find the distribution function for the soliton parameters which we use to evaluate its statistical characteristics. We derive an equation for the averaged functions of the soliton parameters. We determine the limits of applicability of the delta-correlated in time random field approximation
Generalized Whittle-Matern random field as a model of correlated fluctuations
International Nuclear Information System (INIS)
Lim, S C; Teo, L P
2009-01-01
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
Suppression of thermal noise in a non-Markovian random velocity field
International Nuclear Information System (INIS)
Ueda, Masahiko
2016-01-01
We study the diffusion of Brownian particles in a Gaussian random velocity field with short memory. By extending the derivation of an effective Fokker–Planck equation for the Lanvegin equation with weakly colored noise to a random velocity-field problem, we find that the effect of thermal noise on particles is suppressed by the existence of memory. We also find that the renormalization effect for the relative diffusion of two particles is stronger than that for single-particle diffusion. The results are compared with those of molecular dynamics simulations. (paper: classical statistical mechanics, equilibrium and non-equilibrium)
Extreme of random field over rectangle with application to concrete rupture stresses
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2000-01-01
to time consuming simulation procedures. This paperrevives a conceptually simple approach that gives surprisingly good results in particular for wide band typesof random processes and fields. The closed form formulas obtained for smooth Gaussian fieldsover rectangles contain size effects both with respect...... to the area of the rectangle and the side lengths of therectangle. Published rupture stress data for plain concrete beams illustrate the applicability of the derivedclosed form extreme value distributions as models for distributions of rupture stresses related to weakest linkmechanisms....
Anomalous diffusion and Levy random walk of magnetic field lines in three dimensional turbulence
International Nuclear Information System (INIS)
Zimbardo, G.; Veltri, P.; Basile, G.; Principato, S.
1995-01-01
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, δB∼B 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 left-angle Δx 2 i right-angle ∝s α with α>1 and α<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 (α 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 1995 American Institute of Physics
Energy Technology Data Exchange (ETDEWEB)
Li, Yu-Bin; Cai, Yi-Fu [CAS Key Laboratory for Researches in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Chinese Academy of Sciences, Hefei, Anhui 230026 (China); Quintin, Jerome [Department of Physics, McGill University, 3600 rue University, Montréal, QC, H3A 2T8 (Canada); Wang, Dong-Gang, E-mail: lyb2166@mail.ustc.edu.cn, E-mail: jquintin@physics.mcgill.ca, E-mail: wdgang@strw.leidenuniv.nl, E-mail: yifucai@ustc.edu.cn [Leiden Observatory, Leiden University, 2300 RA Leiden (Netherlands)
2017-03-01
We extend the matter bounce scenario to a more general theory in which the background dynamics and cosmological perturbations are generated by a k -essence scalar field with an arbitrary sound speed. When the sound speed is small, the curvature perturbation is enhanced, and the tensor-to-scalar ratio, which is excessively large in the original model, can be sufficiently suppressed to be consistent with observational bounds. Then, we study the primordial three-point correlation function generated during the matter-dominated contraction stage and find that it only depends on the sound speed parameter. Similar to the canonical case, the shape of the bispectrum is mainly dominated by a local form, though for some specific sound speed values a new shape emerges and the scaling behaviour changes. Meanwhile, a small sound speed also results in a large amplitude of non-Gaussianities, which is disfavored by current observations. As a result, it does not seem possible to suppress the tensor-to-scalar ratio without amplifying the production of non-Gaussianities beyond current observational constraints (and vice versa). This suggests an extension of the previously conjectured no-go theorem in single field nonsingular matter bounce cosmologies, which rules out a large class of models. However, the non-Gaussianity results remain as a distinguishable signature of matter bounce cosmology and have the potential to be detected by observations in the near future.
Aziz-Aghchegala, V. L.; Mughnetsyan, V. N.; Kirakosyan, A. A.
2018-02-01
The effect of interdiffusion and magnetic field on confined states of electron and heavy hole as well as on interband absorption spectrum in a Ga1-xAlxAs/GaAs Gaussian-shaped double quantum ring are investigated. It is shown that both interdiffusion and magnetic field lead to the change of the charge carriers' quantum states arrangement by their energies. The oscillating behavior of the electron ground state energy as a function of magnetic field induction gradually disappears with the increase of diffusion parameter due to the enhanced tunneling of electron to the central region of the ring. For the heavy hole the ground state energy oscillations are not observable in the region of the values of magnetic field induction B = 0 - 10 T . For considered transitions both the magnetic field and the interdiffusion lead to a blue-shift of the absorption spectrum and to decreasing of the absorption intensity. The obtained results indicate on the opportunity of purposeful manipulation of energy states and absorption spectrum of a Gaussian-shaped double quantum ring by means of the post growth annealing and the external magnetic field.
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...
International Nuclear Information System (INIS)
Akıncı, Ümit
2012-01-01
The effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of the Ising nanowire has been investigated with effective field theory with correlations. Gaussian distribution has been chosen as a random magnetic field distribution. The variation of the phase diagrams with that distribution parameters has been obtained and some interesting results have been found such as disappearance of the reentrant behavior and first order transitions which appear in the case of discrete distributions. Also for single and double Gaussian distributions, ground state magnetizations for different distribution parameters have been determined which can be regarded as separate partially ordered phases of the system. - Highlights: ► We give the phase diagrams of the Ising nanowire under the continuous randomly distributed magnetic field. ► Ground state magnetization values obtained. ► Different partially ordered phases observed.
Acoustic radiation force on a multilayered sphere in a Gaussian standing field
Wang, Haibin; Liu, Xiaozhou; Gao, Sha; Cui, Jun; Liu, Jiehui; He, Aijun; Zhang, Gutian
2018-03-01
We develop a model for calculating the radiation force on spherically symmetric multilayered particles based on the acoustic scattering approach. An expression is derived for the radiation force on a multilayered sphere centered on the axis of a Gaussian standing wave propagating in an ideal fluid. The effects of the sound absorption of the materials and sound wave on acoustic radiation force of a multilayered sphere immersed in water are analyzed, with particular emphasis on the shell thickness of every layer, and the width of the Gaussian beam. The results reveal that the existence of particle trapping behavior depends on the choice of the non-dimensional frequency ka, as well as the shell thickness of each layer. This study provides a theoretical basis for the development of acoustical tweezers in a Gaussian standing wave, which may benefit the improvement and development of acoustic control technology, such as trapping, sorting, and assembling a cell, and drug delivery applications. Project supported by National Key R&D Program (Grant No. 2016YFF0203000), the National Natural Science Foundation of China (Grant Nos. 11774167 and 61571222), the Fundamental Research Funds for the Central Universities of China (Grant No. 020414380001), the Key Laboratory of Underwater Acoustic Environment, Institute of Acoustics, Chinese Academy of Sciences (Grant No. SSHJ-KFKT-1701), and the AQSIQ Technology R&D Program of China (Grant No. 2017QK125).
Markov Random Fields on Triangle Meshes
DEFF Research Database (Denmark)
Andersen, Vedrana; Aanæs, Henrik; Bærentzen, Jakob Andreas
2010-01-01
In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process label...
Digital servo control of random sound fields
Nakich, R. B.
1973-01-01
It is necessary to place number of sensors at different positions in sound field to determine actual sound intensities to which test object is subjected. It is possible to determine whether specification is being met adequately or exceeded. Since excitation is of random nature, signals are essentially coherent and it is impossible to obtain true average.
Extremes of random fields over arbitrary domains with application to concrete rupture stresses
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2004-01-01
function class is studied for Gaussian processes in earlier works by the author and it has been obtained explicitly for Gaussian fields on rectangular domains in the plane. Simulation studies show that rather good predictions are obtained for sufficiently smooth wide band Gaussian processes and fields...
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
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......, 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...... different software packages available in animal breeding. The examples showed the possibility of the proposed method to alter both the mean and (co)variance of the prior distributions with currently available software packages through the use of an extended data file and a user-supplied (co)variance matrix....
Post-Gaussian Effective Potential of Double sine-Gordon Field
International Nuclear Information System (INIS)
Cai Weiran; Lou Senyue
2005-01-01
In the framework of the functional integral formalism, we calculate the effective potential of the double sine-Gordon (DsG) model up to the second order with an optimized expansion and the Coleman's normal-ordering prescription. Within the range of convergence, we make a comparison among the classical and the effective potential of the first and second order. The numerical analysis shows that the DsG post-Gaussian EP possesses some fine global properties and makes a substantial and a concordant quantum correction to the features of the classical potential.
An efficient estimator for Gibbs random fields
Czech Academy of Sciences Publication Activity Database
Janžura, Martin
2014-01-01
Roč. 50, č. 6 (2014), s. 883-895 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GBP402/12/G097 Institutional support: RVO:67985556 Keywords : Gibbs random field * efficient estimator * empirical estimator Subject RIV: BA - General Mathematics Impact factor: 0.541, year: 2014 http://library.utia.cas.cz/separaty/2015/SI/janzura-0441325.pdf
Gaussian processes for machine learning.
Seeger, Matthias
2004-04-01
Gaussian processes (GPs) are natural generalisations of multivariate Gaussian random variables to infinite (countably or continuous) index sets. GPs have been applied in a large number of fields to a diverse range of ends, and very many deep theoretical analyses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level with special emphasis on characteristics relevant in machine learning. It draws explicit connections to branches such as spline smoothing models and support vector machines in which similar ideas have been investigated. Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible non-parametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of uncertainties in our predictions and generic model selection procedures cast as nonlinear optimization problems. Their main drawback of heavy computational scaling has recently been alleviated by the introduction of generic sparse approximations.13,78,31 The mathematical literature on GPs is large and often uses deep concepts which are not required to fully understand most machine learning applications. In this tutorial paper, we aim to present characteristics of GPs relevant to machine learning and to show up precise connections to other "kernel machines" popular in the community. Our focus is on a simple presentation, but references to more detailed sources are provided.
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...
International Nuclear Information System (INIS)
Arnal, R.S.; Martin, G.V.; Gonzalez, J.L.M.-C.
1988-01-01
This paper studies the local vibrations of reactor components driven by Gaussian coloured and white forces, when nonlinear vibrations arise. We study also the important problem of noise sources, modelization and the noise propagation through the neutron field using the discrete ordinates transport theory. Finally, we study the effect of the neutron field upon the PSD (power spectral density) of the noise source and we analyse the problem of fitting neutron noise experimental data to perform pattern recognition analysis. (author)
Role of random electric fields in relaxors
Phelan, Daniel; Stock, Christopher; Rodriguez-Rivera, Jose A.; Chi, Songxue; Leão, Juscelino; Long, Xifa; Xie, Yujuan; Bokov, Alexei A.; Ye, Zuo-Guang; Ganesh, Panchapakesan; Gehring, Peter M.
2014-01-01
PbZr1–xTixO3 (PZT) and Pb(Mg1/3Nb2/3)1–xTixO3 (PMN-xPT) are complex lead-oxide perovskites that display exceptional piezoelectric properties for pseudorhombohedral compositions near a tetragonal phase boundary. In PZT these compositions are ferroelectrics, but in PMN-xPT they are relaxors because the dielectric permittivity is frequency dependent and exhibits non-Arrhenius behavior. We show that the nanoscale structure unique to PMN-xPT and other lead-oxide perovskite relaxors is absent in PZT and correlates with a greater than 100% enhancement of the longitudinal piezoelectric coefficient in PMN-xPT relative to that in PZT. By comparing dielectric, structural, lattice dynamical, and piezoelectric measurements on PZT and PMN-xPT, two nearly identical compounds that represent weak and strong random electric field limits, we show that quenched (static) random fields establish the relaxor phase and identify the order parameter. PMID:24449912
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.
DEFF Research Database (Denmark)
Dimitrov, Nikolay Krasimirov; Natarajan, Anand
2017-01-01
We demonstrate a method for incorporating wind velocity measurements from multiple-point scanning lidars into threedimensional wind turbulence time series serving as input to wind turbine load simulations. Simulated lidar scanning patterns are implemented by imposing constraints on randomly gener...
Gao, Xian; Kobayashi, Tsutomu; Yamaguchi, Masahide; Yokoyama, Jun'ichi
2011-11-18
We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in 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 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 detection experiments.
Dynamics of the Random Field Ising Model
Xu, Jian
The Random Field Ising Model (RFIM) is a general tool to study disordered systems. Crackling noise is generated when disordered systems are driven by external forces, spanning a broad range of sizes. Systems with different microscopic structures such as disordered mag- nets and Earth's crust have been studied under the RFIM. In this thesis, we investigated the domain dynamics and critical behavior in two dipole-coupled Ising ferromagnets Nd2Fe14B and LiHoxY 1-xF4. With Tc well above room temperature, Nd2Fe14B has shown reversible disorder when exposed to an external transverse field and crosses between two universality classes in the strong and weak disorder limits. Besides tunable disorder, LiHoxY1-xF4 has shown quantum tunneling effects arising from quantum fluctuations, providing another mechanism for domain reversal. Universality within and beyond power law dependence on avalanche size and energy were studied in LiHo0.65Y0.35 F4.
Nonlinear field theories and non-Gaussian fluctuations for near-critical many-body systems
International Nuclear Information System (INIS)
Tuszynski, J.A.; Dixon, J.M.; Grundland, A.M.
1994-01-01
This review article outlines a number of efforts made over the past several decades to understand the physics of near critical many-body systems. Beginning with the phenomenological theories of Landau and Ginzburg the paper discusses the two main routes adopted in the past. The first approach is based on statistical calculations while the second investigates the underlying nonlinear field equations. In the last part of the paper we outline a generalisation of these methods which combines classical and quantum properties of the many-body systems studied. (orig.)
Unmixing hyperspectral images using Markov random fields
International Nuclear Information System (INIS)
Eches, Olivier; Dobigeon, Nicolas; Tourneret, Jean-Yves
2011-01-01
This paper proposes a new spectral unmixing strategy based on the normal compositional model that exploits the spatial correlations between the image pixels. The pure materials (referred to as endmembers) contained in the image are assumed to be available (they can be obtained by using an appropriate endmember extraction algorithm), while the corresponding fractions (referred to as abundances) are estimated by the proposed algorithm. Due to physical constraints, the abundances have to satisfy positivity and sum-to-one constraints. The image is divided into homogeneous distinct regions having the same statistical properties for the abundance coefficients. The spatial dependencies within each class are modeled thanks to Potts-Markov random fields. Within a Bayesian framework, prior distributions for the abundances and the associated hyperparameters are introduced. A reparametrization of the abundance coefficients is proposed to handle the physical constraints (positivity and sum-to-one) inherent to hyperspectral imagery. The parameters (abundances), hyperparameters (abundance mean and variance for each class) and the classification map indicating the classes of all pixels in the image are inferred from the resulting joint posterior distribution. To overcome the complexity of the joint posterior distribution, Markov chain Monte Carlo methods are used to generate samples asymptotically distributed according to the joint posterior of interest. Simulations conducted on synthetic and real data are presented to illustrate the performance of the proposed algorithm.
Analysis of the anomalous mean-field like properties of Gaussian core model in terms of entropy
Nandi, Manoj Kumar; Maitra Bhattacharyya, Sarika
2018-01-01
Studies of the Gaussian core model (GCM) have shown that it behaves like a mean-field model and the properties are quite different from standard glass former. In this work, we investigate the entropies, namely, the excess entropy (Sex) and the configurational entropy (Sc) and their different components to address these anomalies. Our study corroborates most of the earlier observations and also sheds new light on the high and low temperature dynamics. We find that unlike in standard glass former where high temperature dynamics is dominated by two-body correlation and low temperature by many-body correlations, in the GCM both high and low temperature dynamics are dominated by many-body correlations. We also find that the many-body entropy which is usually positive at low temperatures and is associated with activated dynamics is negative in the GCM suggesting suppression of activation. Interestingly despite the suppression of activation, the Adam-Gibbs (AG) relation that describes activated dynamics holds in the GCM, thus suggesting a non-activated contribution in AG relation. We also find an overlap between the AG relation and mode coupling power law regime leading to a power law behavior of Sc. From our analysis of this power law behavior, we predict that in the GCM the high temperature dynamics will disappear at dynamical transition temperature and below that there will be a transition to the activated regime. Our study further reveals that the activated regime in the GCM is quite narrow.
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.
Random source generating far field with elliptical flat-topped beam profile
International Nuclear Information System (INIS)
Zhang, Yongtao; Cai, Yangjian
2014-01-01
Circular and rectangular multi-Gaussian Schell-model (MGSM) sources which generate far fields with circular and rectangular flat-topped beam profiles were introduced just recently (Sahin and Korotkova 2012 Opt. Lett. 37 2970; Korotkova 2014 Opt. Lett. 39 64). In this paper, a random source named an elliptical MGSM source is introduced. An analytical expression for the propagation factor of an elliptical MGSM beam is derived. Furthermore, an analytical propagation formula for an elliptical MGSM beam passing through a stigmatic ABCD optical system is derived, and its propagation properties in free space are studied. It is interesting to find that an elliptical MGSM source generates a far field with an elliptical flat-topped beam profile, being qualitatively different from that of circular and rectangular MGSM sources. The ellipticity and the flatness of the elliptical flat-topped beam profile in the far field are determined by the initial coherence widths and the beam index, respectively. (paper)
Gaussian Random Fields Methods for Fork-Join Network with Synchronization Constraints
2014-12-22
substantial efforts were dedicated to the study of the max-plus recursions [21, 3, 12]. More recently, Atar et al. [2] have studied a fork-join...feedback and NES, Atar et al. [2] show that a dynamic priority discipline achieves throughput optimal- ity asymptotically in the conventional heavy...2011) Patient flow in hospitals: a data-based queueing-science perspective. Submitted to Stochastic Systems, 20. [2] R. Atar , A. Mandelbaum and A
Magnetic field line random walk in non-axisymmetric turbulence
International Nuclear Information System (INIS)
Tautz, R.C.; Lerche, I.
2011-01-01
Including a random component of a magnetic field parallel to an ambient field introduces a mean perpendicular motion to the average field line. This effect is normally not discussed because one customarily chooses at the outset to ignore such a field component in discussing random walk and diffusion of field lines. A discussion of the basic effect is given, indicating that any random magnetic field with a non-zero helicity will lead to such a non-zero perpendicular mean motion. Several exact analytic illustrations are given of the effect as well as a simple numerical illustration. -- Highlights: → For magnetic field line random walk all magnetic field components are important. → Non-vanishing magnetic helicity leads to mean perpendicular motion. → Analytically exact stream functions illustrate that the novel transverse effect exists.
On plasma stability under anisotropic random electric field influence
International Nuclear Information System (INIS)
Rabich, L.N.; Sosenko, P.P.
1987-01-01
The influence of anisotropic random field on plasma stability is studied. The thresholds and instability increments are obtained. The stabilizing influence of frequency missmatch and external magnetic field is pointed out
Simulation of random walks in field theory
International Nuclear Information System (INIS)
Rensburg, E.J.J. van
1988-01-01
The numerical simulation of random walks is considered using the Monte Carlo method previously proposed. The algorithm is tested and then generalised to generate Edwards random walks. The renormalised masses of the Edwards model are calculated and the results are compared with those obtained from a simple perturbation theory calculation for small values of the bare coupling constant. The efficiency of this algorithm is discussed and compared with an alternative approach. (author)
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...
The potts chain in a random field: an exact solution
International Nuclear Information System (INIS)
Riera, R.; Chaves, C.M.G.F.; Santos, Raimundo R. dos.
1984-01-01
An exact solution is presented for the one-dimensional q-state Potts model in a quenched random field. The ferromagnetic phase is unstable against any small random field perturbation. The correlation function and the Edwards-Anderson order parameter Q are discussed. For finite q only the phase with Q ≠ 0 is present. (Author) [pt
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...
Kastelein, Ronald A; Wensveen, Paul J; Hoek, Lean; Au, Whitlow W L; Terhune, John M; de Jong, Christ A F
2009-09-01
A psychoacoustic behavioral technique was used to determine the critical ratios (CRs) of two harbor porpoises for tonal signals with frequencies between 0.315 and 150 kHz, in random Gaussian white noise. The masked 50% detection hearing thresholds were measured using a "go/no-go" response paradigm and an up-down staircase psychometric method. CRs were determined at one masking noise level for each test frequency and were similar in both animals. For signals between 0.315 and 4 kHz, the CRs were relatively constant at around 18 dB. Between 4 and 150 kHz the CR increased gradually from 18 to 39 dB ( approximately 3.3 dB/octave). Generally harbor porpoises can detect tonal signals in Gaussian white noise slightly better than most odontocetes tested so far. By combining the mean CRs found in the present study with the spectrum level of the background noise levels at sea, the basic audiogram, and the directivity index, the detection threshold levels of harbor porpoises for tonal signals in various sea states can be calculated.
Xin, Wei; Zhao, Yu-Wei; Sudu; Eerdunchaolu
2018-05-01
Considering Hydrogen-like impurity and the thickness effect, the eigenvalues and eigenfunctions of the electronic ground and first exited states in a quantum dot (QD) are derived by using the Lee-Low-Pins-Pekar variational method with the harmonic and Gaussian potentials as the transverse and longitudinal confinement potentials, respectively. A two-level system is constructed on the basis of those two states, and the electronic quantum transition affected by an electromagnetic field is discussed in terms of the two-level system theory. The results indicate the Gaussian potential reflects the real confinement potential more accurately than the parabolic one; the influence of the thickness of the QD on the electronic transition probability is interesting and significant, and cannot be ignored; the electronic transition probability Γ is influenced significantly by some physical quantities, such as the strength of the electron-phonon coupling α, the electric-field strength F, the magnetic-field cyclotron frequency ωc , the barrier height V0 and confinement range L of the asymmetric Gaussian potential, suggesting the transport and optical properties of the QD can be manipulated further though those physical quantities.
Energy Technology Data Exchange (ETDEWEB)
Eley, John G.; Hogstrom, Kenneth R.; Matthews, Kenneth L.; Parker, Brent C.; Price, Michael J. [Department of Physics and Astronomy, Louisiana State University and Agricultural and Mechanical College, 202 Nicholson Hall, Tower Drive, Baton Rouge, Louisiana 70803-4001 (United States); Department of Physics and Astronomy, Louisiana State University and Agricultural and Mechanical College, 202 Nicholson Hall, Tower Drive, Baton Rouge, Louisiana 70803-4001 (United States) and Mary Bird Perkins Cancer Center, 4950 Essen Lane, Baton Rouge, Louisiana 70809-3482 (United States); Department of Physics and Astronomy, Louisiana State University and Agricultural and Mechanical College, 202 Nicholson Hall, Tower Drive, Baton Rouge, Louisiana 70803-4001 (United States); Department of Physics and Astronomy, Louisiana State University and Agricultural and Mechanical College, 202 Nicholson Hall, Tower Drive, Baton Rouge, Louisiana 70803-4001 (United States) and Mary Bird Perkins Cancer Center, 4950 Essen Lane, Baton Rouge, Louisiana 70809-3482 (United States)
2011-12-15
Purpose: The purpose of this work was to investigate the potential of discrete Gaussian edge feathering of the higher energy electron fields for improving abutment dosimetry in the planning volume when using an electron multileaf collimator (eMLC) to deliver segmented-field electron conformal therapy (ECT). Methods: A discrete (five-step) Gaussian edge spread function was used to match dose penumbras of differing beam energies (6-20 MeV) at a specified depth in a water phantom. Software was developed to define the leaf eMLC positions of an eMLC that most closely fit each electron field shape. The effect of 1D edge feathering of the higher energy field on dose homogeneity was computed and measured for segmented-field ECT treatment plans for three 2D PTVs in a water phantom, i.e., depth from the water surface to the distal PTV surface varied as a function of the x-axis (parallel to leaf motion) and remained constant along the y-axis (perpendicular to leaf motion). Additionally, the effect of 2D edge feathering was computed and measured for one radially symmetric, 3D PTV in a water phantom, i.e., depth from the water surface to the distal PTV surface varied as a function of both axes. For the 3D PTV, the feathering scheme was evaluated for 0.1-1.0-cm leaf widths. Dose calculations were performed using the pencil beam dose algorithm in the Pinnacle{sup 3} treatment planning system. Dose verification measurements were made using a prototype eMLC (1-cm leaf width). Results: 1D discrete Gaussian edge feathering reduced the standard deviation of dose in the 2D PTVs by 34, 34, and 39%. In the 3D PTV, the broad leaf width (1 cm) of the eMLC hindered the 2D application of the feathering solution to the 3D PTV, and the standard deviation of dose increased by 10%. However, 2D discrete Gaussian edge feathering with simulated eMLC leaf widths of 0.1-0.5 cm reduced the standard deviation of dose in the 3D PTV by 33-28%, respectively. Conclusions: A five-step discrete Gaussian edge
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...
Random wave fields and scintillated beams
CSIR Research Space (South Africa)
Roux, FS
2009-01-01
Full Text Available F. Stef Roux CSIR National Laser Centre PO Box 395, Pretoria 0001, South Africa CSIR National Laser Centre – p.1/29 Contents . Scintillated beams and adaptive optics . Detecting a vortex — Shack-Hartmann . Remove optical vortices . Random vortex... beam. CSIR National Laser Centre – p.3/29 Weak scintillation If the scintillation is weak the resulting phase function of the optical beam is still continuous. Such a weakly scintillated beam can be corrected by an adaptive optical system. CSIR National...
The random field Blume-Capel model revisited
Santos, P. V.; da Costa, F. A.; de Araújo, J. M.
2018-04-01
We have revisited the mean-field treatment for the Blume-Capel model under the presence of a discrete random magnetic field as introduced by Kaufman and Kanner (1990). The magnetic field (H) versus temperature (T) phase diagrams for given values of the crystal field D were recovered in accordance to Kaufman and Kanner original work. However, our main goal in the present work was to investigate the distinct structures of the crystal field versus temperature phase diagrams as the random magnetic field is varied because similar models have presented reentrant phenomenon due to randomness. Following previous works we have classified the distinct phase diagrams according to five different topologies. The topological structure of the phase diagrams is maintained for both H - T and D - T cases. Although the phase diagrams exhibit a richness of multicritical phenomena we did not found any reentrant effect as have been seen in similar models.
New constraints on modelling the random magnetic field of the MW
Energy Technology Data Exchange (ETDEWEB)
Beck, Marcus C.; Nielaba, Peter [Department of Physics, University of Konstanz, Universitätsstr. 10, D-78457 Konstanz (Germany); Beck, Alexander M.; Dolag, Klaus [University Observatory Munich, Scheinerstr. 1, D-81679 Munich (Germany); Beck, Rainer [Max Planck Institute for Radioastronomy, Auf dem Hügel 69, D-53121 Bonn (Germany); Strong, Andrew W., E-mail: marcus.beck@uni-konstanz.de, E-mail: abeck@usm.uni-muenchen.de, E-mail: rbeck@mpifr-bonn.mpg.de, E-mail: dolag@usm.uni-muenchen.de, E-mail: aws@mpe.mpg.de, E-mail: peter.nielaba@uni-konstanz.de [Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, D-85748 Garching (Germany)
2016-05-01
We extend the description of the isotropic and anisotropic random component of the small-scale magnetic field within the existing magnetic field model of the Milky Way from Jansson and Farrar, by including random realizations of the small-scale component. Using a magnetic-field power spectrum with Gaussian random fields, the NE2001 model for the thermal electrons and the Galactic cosmic-ray electron distribution from the current GALPROP model we derive full-sky maps for the total and polarized synchrotron intensity as well as the Faraday rotation-measure distribution. While previous work assumed that small-scale fluctuations average out along the line-of-sight or which only computed ensemble averages of random fields, we show that these fluctuations need to be carefully taken into account. Comparing with observational data we obtain not only good agreement with 408 MHz total and WMAP7 22 GHz polarized intensity emission maps, but also an improved agreement with Galactic foreground rotation-measure maps and power spectra, whose amplitude and shape strongly depend on the parameters of the random field. We demonstrate that a correlation length of 0≈22 pc (05 pc being a 5σ lower limit) is needed to match the slope of the observed power spectrum of Galactic foreground rotation-measure maps. Using multiple realizations allows us also to infer errors on individual observables. We find that previously-used amplitudes for random and anisotropic random magnetic field components need to be rescaled by factors of ≈0.3 and 0.6 to account for the new small-scale contributions. Our model predicts a rotation measure of −2.8±7.1 rad/m{sup 2} and 04.4±11. rad/m{sup 2} for the north and south Galactic poles respectively, in good agreement with observations. Applying our model to deflections of ultra-high-energy cosmic rays we infer a mean deflection of ≈3.5±1.1 degree for 60 EeV protons arriving from CenA.
The use of random walk in field theory
International Nuclear Information System (INIS)
Brydges, D.
1984-01-01
Ferromagnetic spin systems and gauge theories where the gauge group is topologically a sphere, e.g. Z 2 , U(1) and SU(2) are related to the theory of random walk and random surfaces respectively. I survey some applications of this theme to the phi 4 field theories. (orig.)
Anomalous transport in fluid field with random waiting time depending on the preceding jump length
International Nuclear Information System (INIS)
Zhang Hong; Li Guo-Hua
2016-01-01
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. (paper)
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).
Yurinsky, Vadim Vladimirovich
1995-01-01
Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
Estimators for local non-Gaussianities
International Nuclear Information System (INIS)
Creminelli, P.; Senatore, L.; Zaldarriaga, M.
2006-05-01
We study the Likelihood function of data given f NL for the so-called local type of non-Gaussianity. In this case the curvature perturbation is a non-linear function, local in real space, of a Gaussian random field. We compute the Cramer-Rao bound for f NL and show that for small values of f NL the 3- point function estimator saturates the bound and is equivalent to calculating the full Likelihood of the data. However, for sufficiently large f NL , the naive 3-point function estimator has a much larger variance than previously thought. In the limit in which the departure from Gaussianity is detected with high confidence, error bars on f NL only decrease as 1/ln N pix rather than N pix -1/2 as the size of the data set increases. We identify the physical origin of this behavior and explain why it only affects the local type of non- Gaussianity, where the contribution of the first multipoles is always relevant. We find a simple improvement to the 3-point function estimator that makes the square root of its variance decrease as N pix -1/2 even for large f NL , asymptotically approaching the Cramer-Rao bound. We show that using the modified estimator is practically equivalent to computing the full Likelihood of f NL given the data. Thus other statistics of the data, such as the 4-point function and Minkowski functionals, contain no additional information on f NL . In particular, we explicitly show that the recent claims about the relevance of the 4-point function are not correct. By direct inspection of the Likelihood, we show that the data do not contain enough information for any statistic to be able to constrain higher order terms in the relation between the Gaussian field and the curvature perturbation, unless these are orders of magnitude larger than the size suggested by the current limits on f NL . (author)
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......, and second to study stochastic constructions and simulation techniques, which should provide a useful basis for discussing the statistical aspects in future work. The paper also discusses some examples of α-permanental random fields....
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...
ANALYTIC WORD RECOGNITION WITHOUT SEGMENTATION BASED ON MARKOV RANDOM FIELDS
Coisy, C.; Belaid, A.
2004-01-01
In this paper, a method for analytic handwritten word recognition based on causal Markov random fields is described. The words models are HMMs where each state corresponds to a letter; each letter is modelled by a NSHPHMM (Markov field). Global models are build dynamically, and used for recognition
Random walks, critical phenomena, and triviality in quantum field theory
International Nuclear Information System (INIS)
Fernandez, R.; Froehlich, J.; Sokal, A.D.
1992-01-01
The subject of this book is equilibrium statistical mechanics - in particular the theory of critical phenomena - and quantum field theory. A general review of the theory of critical phenomena in spin systems, field theories, and random-walk and random-surface models is presented. Among the more technical topics treated in this book, the central theme is the use of random-walk representations as a tool to derive correlation inequalities. The consequences of these inequalities for critical-exponent theory and the triviality question in quantum field theory are expounded in detail. The book contains some previously unpublished results. It addresses both the researcher and the graduate student in modern statistical mechanics and quantum field theory. (orig.)
International Nuclear Information System (INIS)
Steinbrecher, Gyoergy; Weyssow, B.
2004-01-01
The extreme heavy tail and the power-law decay of the turbulent flux correlation observed in hot magnetically confined plasmas are modeled by a system of coupled Langevin equations describing a continuous time linear randomly amplified stochastic process where the amplification factor is driven by a superposition of colored noises which, in a suitable limit, generate a fractional Brownian motion. An exact analytical formula for the power-law tail exponent β is derived. The extremely small value of the heavy tail exponent and the power-law distribution of laminar times also found experimentally are obtained, in a robust manner, for a wide range of input values, as a consequence of the (asymptotic) self-similarity property of the noise spectrum. As a by-product, a new representation of the persistent fractional Brownian motion is obtained
International Nuclear Information System (INIS)
Zimbardo, G.
2005-01-01
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
The intermittency of vector fields and random-number generators
Kalinin, A. O.; Sokoloff, D. D.; Tutubalin, V. N.
2017-09-01
We examine how well natural random-number generators can reproduce the intermittency phenomena that arise in the transfer of vector fields in random media. A generator based on the analysis of financial indices is suggested as the most promising random-number generator. Is it shown that even this generator, however, fails to reproduce the phenomenon long enough to confidently detect intermittency, while the C++ generator successfully solves this problem. We discuss the prospects of using shell models of turbulence as the desired generator.
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.
Phase transitions in the random field Ising model in the presence of a transverse field
Energy Technology Data Exchange (ETDEWEB)
Dutta, A.; Chakrabarti, B.K. [Saha Institute of Nuclear Physics, Bidhannagar, Calcutta (India); Stinchcombe, R.B. [Saha Institute of Nuclear Physics, Bidhannagar, Calcutta (India); Department of Physics, Oxford (United Kingdom)
1996-09-07
We have studied the phase transition behaviour of the random field Ising model in the presence of a transverse (or tunnelling) field. The mean field phase diagram has been studied in detail, and in particular the nature of the transition induced by the tunnelling (transverse) field at zero temperature. Modified hyper-scaling relation for the zero-temperature transition has been derived using the Suzuki-Trotter formalism and a modified 'Harris criterion'. Mapping of the model to a randomly diluted antiferromagnetic Ising model in uniform longitudinal and transverse field is also given. (author)
Huang, N. E.; Long, S. R.; Bliven, L. F.; Tung, C.-C.
1984-01-01
On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared with a series of carefully controlled laboratory observations, and good agreement is noted. Furthermore, the laboratory wind wave field observations indicate that the capillary or capillary-gravity waves may not be the dominant components in determining the total roughness of the wave field. Thus, the analytic results, though derived specifically for the gravity waves, may have more general applications.
MCEM algorithm for the log-Gaussian Cox process
Delmas, Celine; Dubois-Peyrard, Nathalie; Sabbadin, Regis
2014-01-01
Log-Gaussian Cox processes are an important class of models for aggregated point patterns. They have been largely used in spatial epidemiology (Diggle et al., 2005), in agronomy (Bourgeois et al., 2012), in forestry (Moller et al.), in ecology (sightings of wild animals) or in environmental sciences (radioactivity counts). A log-Gaussian Cox process is a Poisson process with a stochastic intensity depending on a Gaussian random eld. We consider the case where this Gaussian random eld is ...
Polarization dynamics and polarization time of random three-dimensional electromagnetic fields
International Nuclear Information System (INIS)
Voipio, Timo; Setaelae, Tero; Shevchenko, Andriy; Friberg, Ari T.
2010-01-01
We investigate the polarization dynamics of random, stationary three-dimensional (3D) electromagnetic fields. For analyzing the time evolution of the instantaneous polarization state, two intensity-normalized polarization autocorrelation functions are introduced, one based on a geometric approach with the Poincare vectors and the other on energy considerations with the Jones vectors. Both approaches lead to the same conclusions on the rate and strength of the polarization dynamics and enable the definition of a polarization time over which the state of polarization remains essentially unchanged. For fields obeying Gaussian statistics, the two correlation functions are shown to be expressible in terms of quantities characterizing partial 3D polarization and electromagnetic coherence. The 3D degree of polarization is found to have the same meaning in the 3D polarization dynamics as the usual two-dimensional (2D) degree of polarization does with planar fields. The formalism is demonstrated with several examples, and it is expected to be useful in applications dealing with polarization fluctuations of 3D light.
Gaussian vs non-Gaussian turbulence: impact on wind turbine loads
DEFF Research Database (Denmark)
Berg, Jacob; Natarajan, Anand; Mann, Jakob
2016-01-01
taking into account the safety factor for extreme moments. Other extreme load moments as well as the fatigue loads are not affected because of the use of non-Gaussian turbulent inflow. It is suggested that the turbine thus acts like a low-pass filter that averages out the non-Gaussian behaviour, which......From large-eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non-Gaussian counterpart. Time series from the two...
Infinite conditional random fields for human behavior analysis
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja
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
Random field assessment of nanoscopic inhomogeneity of bone.
Dong, X Neil; Luo, Qing; Sparkman, Daniel M; Millwater, Harry R; Wang, Xiaodu
2010-12-01
Bone quality is significantly correlated with the inhomogeneous distribution of material and ultrastructural properties (e.g., modulus and mineralization) of the tissue. Current techniques for quantifying inhomogeneity consist of descriptive statistics such as mean, standard deviation and coefficient of variation. However, these parameters do not describe the spatial variations of bone properties. The objective of this study was to develop a novel statistical method to characterize and quantitatively describe the spatial variation of bone properties at ultrastructural levels. To do so, a random field defined by an exponential covariance function was used to represent the spatial uncertainty of elastic modulus by delineating the correlation of the modulus at different locations in bone lamellae. The correlation length, a characteristic parameter of the covariance function, was employed to estimate the fluctuation of the elastic modulus in the random field. Using this approach, two distribution maps of the elastic modulus within bone lamellae were generated using simulation and compared with those obtained experimentally by a combination of atomic force microscopy and nanoindentation techniques. The simulation-generated maps of elastic modulus were in close agreement with the experimental ones, thus validating the random field approach in defining the inhomogeneity of elastic modulus in lamellae of bone. Indeed, generation of such random fields will facilitate multi-scale modeling of bone in more pragmatic details. Copyright © 2010 Elsevier Inc. All rights reserved.
Numerical solution of field theories using random walks
International Nuclear Information System (INIS)
Barnes, T.; Daniell, G.J.
1985-01-01
We show how random walks in function space can be employed to evaluate field theoretic vacuum expectation values numerically. Specific applications which we study are the two-point function, mass gap, magnetization and classical solutions. This technique offers the promise of faster calculations using less computer memory than current methods. (orig.)
Energy conservation law for randomly fluctuating electromagnetic fields
International Nuclear Information System (INIS)
Gbur, G.; Wolf, E.; James, D.
1999-01-01
An energy conservation law is derived for electromagnetic fields generated by any random, statistically stationary, source distribution. It is shown to provide insight into the phenomenon of correlation-induced spectral changes. The results are illustrated by an example. copyright 1999 The American Physical Society
The dilute random field Ising model by finite cluster approximation
International Nuclear Information System (INIS)
Benyoussef, A.; Saber, M.
1987-09-01
Using the finite cluster approximation, phase diagrams of bond and site diluted three-dimensional simple cubic Ising models with a random field have been determined. The resulting phase diagrams have the same general features for both bond and site dilution. (author). 7 refs, 4 figs
Miranda, Rodrigo A.; Schelin, Adriane B.; Chian, Abraham C.-L.; Ferreira, José L.
2018-03-01
In a recent paper (Chian et al., 2016) it was shown that magnetic reconnection at the interface region between two magnetic flux ropes is responsible for the genesis of interplanetary intermittent turbulence. The normalized third-order moment (skewness) and the normalized fourth-order moment (kurtosis) display a quadratic relation with a parabolic shape that is commonly observed in observational data from turbulence in fluids and plasmas, and is linked to non-Gaussian fluctuations due to coherent structures. In this paper we perform a detailed study of the relation between the skewness and the kurtosis of the modulus of the magnetic field |B| during a triple interplanetary magnetic flux rope event. In addition, we investigate the skewness-kurtosis relation of two-point differences of |B| for the same event. The parabolic relation displays scale dependence and is found to be enhanced during magnetic reconnection, rendering support for the generation of non-Gaussian coherent structures via rope-rope magnetic reconnection. Our results also indicate that a direct coupling between the scales of magnetic flux ropes and the scales within the inertial subrange occurs in the solar wind.
Limit theorems for functionals of Gaussian vectors
Institute of Scientific and Technical Information of China (English)
Hongshuai DAI; Guangjun SHEN; Lingtao KONG
2017-01-01
Operator self-similar processes,as an extension of self-similar processes,have been studied extensively.In this work,we study limit theorems for functionals of Gaussian vectors.Under some conditions,we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.
Magnetic field correlations in random flow with strong steady shear
International Nuclear Information System (INIS)
Kolokolov, I. V.; Lebedev, V. V.; Sizov, G. A.
2011-01-01
We analyze the magnetic kinematic dynamo in a conducting fluid where a stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field correlation functions are examined, and their growth rates and scaling behavior are established. General assertions are illustrated by the explicit solution of a model where the velocity field is short-correlated in time.
Correlation diagnostics of random spatially nonuniform optical fields
International Nuclear Information System (INIS)
Angel'skii, O.V.
1992-01-01
This review examines some questions concerning the capabilities of interference and polarization-interference correlation diagnostics of the amplitude-phase characteristics of random optical fields for the purpose of identifying these fields and then studying the corresponding objects. The diagnostics of random phase objects is discussed separately in the case in which the phase dispersion of the inhomogeneities is less than and greater than one. The outlook is promising for the use of the correlation dimensionality of chaos in a field as a diagnostic parameter. It is also shown that the use of interference principles for a parallel processing of large data files can substantially increase the speed of processing systems. 32 refs., 8 figs
Nonstationary random acoustic and electromagnetic fields as wave diffusion processes
International Nuclear Information System (INIS)
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-hat 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 not separable, as a result of nonstationarity. A general solution of the Fokker-Planck equation is obtained in integral form, together with explicit closed-form solutions for several asymptotic cases. The findings extend known results on statistics and distributions of quasi-stationary ideal random fields (pure diffusions), which are retrieved as special cases
Wen, Xian-Huan; Gómez-Hernández, J. Jaime
1998-03-01
The macrodispersion of an inert solute in a 2-D heterogeneous porous media is estimated numerically in a series of fields of varying heterogeneity. Four different random function (RF) models are used to model log-transmissivity (ln T) spatial variability, and for each of these models, ln T variance is varied from 0.1 to 2.0. The four RF models share the same univariate Gaussian histogram and the same isotropic covariance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme values (both high and low) are spatially uncorrelated. The other three models are non-multi-Gaussian: model B with high connectivity of high extreme values, model C with high connectivity of low extreme values, and model D with high connectivities of both high and low extreme values. Residence time distributions (RTDs) and macrodispersivities (longitudinal and transverse) are computed on ln T fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RTDs and macrodispersivities for the multi-Gaussian model are in good agreement with analytically derived values using first-order theories for log-transmissivity variance up to 2.0. The results from the non-multi-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when ln T variance is small. RTDs in non-multi-Gaussian realizations with high connectivity at high extreme values display earlier breakthrough than in multi-Gaussian realizations, whereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian realizations are, in general, larger than
Kant, Niti; Rajput, Jyoti; Singh, Arvinder
2018-03-01
This paper presents a scheme of electron energy enhancement by employing frequency - chirped lowest order axicon focussed radially polarised (RP) laser pulse in vacuum under the influence of wiggler magnetic field. Terawatt RP laser can be focussed down to ∼5μm by an axicon optical element, which produces an intense longitudinal electric field. This unique property of axicon focused Gaussian RP laser pulse is employed for direct electron acceleration in vacuum. A linear frequency chirp increases the time duration of laser-electron interaction, whereas, the applied magnetic wiggler helps in improving the strength of ponderomotive force v→ ×B→ and periodically deflects electron in order to keep it traversing in the accelerating phase up to longer distance. Numerical simulations have been carried out to investigate the influence of laser, frequency chirp and magnetic field parameters on electron energy enhancement. It is noticed that an electron from rest can be accelerated up to GeV energy under optimized laser and magnetic field parameters. Significant enhancement in the electron energy gain of the order of 11.2 GeV is observed with intense chirped laser pulse in the presence of wiggler magnetic field of strength 96.2 kG.
Statistical analysis of the ratio of electric and magnetic fields in random fields generators
Serra, R.; Nijenhuis, J.
2013-01-01
In this paper we present statistical models of the ratio of random electric and magnetic fields in mode-stirred reverberation chambers. This ratio is based on the electric and magnetic field statistics derived for ideal reverberation conditions. It provides a further performance indicator for
Tachyon mediated non-Gaussianity
International Nuclear Information System (INIS)
Dutta, Bhaskar; Leblond, Louis; Kumar, Jason
2008-01-01
We describe a general scenario where primordial non-Gaussian curvature perturbations are generated in models with extra scalar fields. The extra scalars communicate to the inflaton sector mainly through the tachyonic (waterfall) field condensing at the end of hybrid inflation. These models can yield significant non-Gaussianity of the local shape, and both signs of the bispectrum can be obtained. These models have cosmic strings and a nearly flat power spectrum, which together have been recently shown to be a good fit to WMAP data. We illustrate with a model of inflation inspired from intersecting brane models.
A ferromagnetic chain in a random weak field
Avgin, I.
1996-10-01
The harmonic magnon modes in a Heisenberg ferromagnetic chain in a random weak field are studied. The Lyapunov exponent for the uniform ( k = 0) mode is computed using the coherent potential approximation (CPA) in the weak-disorder limit. The CPA results are compared with the numerical and weak-disorder expansions of various random systems. We have found that the inverse localization length and the integrated density of states have anomalous power law behaviour as reported earlier. The CPA also reproduces the dispersion law for the same system, calculated by Pimentel and Stinchcombe using the real space renormalization scaling technique. A brief comment is also made for the uniform weak-field case.
Random field Ising chain and neutral networks with synchronous dynamics
International Nuclear Information System (INIS)
Skantzos, N.S.; Coolen, A.C.C.
2001-01-01
We first present an exact solution of the one-dimensional random-field Ising model in which spin-updates are made fully synchronously, i.e. in parallel (in contrast to the more conventional Glauber-type sequential rules). We find transitions where the support of local observables turns from a continuous interval into a Cantor set and we show that synchronous and sequential random-field models lead asymptotically to the same physical states. We then proceed to an application of these techniques to recurrent neural networks where 1D short-range interactions are combined with infinite-range ones. Due to the competing interactions these models exhibit phase diagrams with first-order transitions and regions with multiple locally stable solutions for the macroscopic order parameters
Efficient approximation of random fields for numerical applications
Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus
2015-01-01
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.
On the Tsallis Entropy for Gibbs Random Fields
Czech Academy of Sciences Publication Activity Database
Janžura, Martin
2014-01-01
Roč. 21, č. 33 (2014), s. 59-69 ISSN 1212-074X R&D Projects: GA ČR(CZ) GBP402/12/G097 Institutional research plan: CEZ:AV0Z1075907 Keywords : Tsallis entropy * Gibbs random fields * phase transitions * Tsallis entropy rate Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2014/SI/janzura-0441885.pdf
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.
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.
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)
International Nuclear Information System (INIS)
Ovchinnikov, O. S.; Jesse, S.; Kalinin, S. V.; Bintacchit, P.; Trolier-McKinstry, S.
2009-01-01
An approach for the direct identification of disorder type and strength in physical systems based on recognition analysis of hysteresis loop shape is developed. A large number of theoretical examples uniformly distributed in the parameter space of the system is generated and is decorrelated using principal component analysis (PCA). The PCA components are used to train a feed-forward neural network using the model parameters as targets. The trained network is used to analyze hysteresis loops for the investigated system. The approach is demonstrated using a 2D random-bond-random-field Ising model, and polarization switching in polycrystalline ferroelectric capacitors.
Directory of Open Access Journals (Sweden)
Wangchao Lou
Full Text Available Developing an efficient method for determination of the DNA-binding proteins, due to their vital roles in gene regulation, is becoming highly desired since it would be invaluable to advance our understanding of protein functions. In this study, we proposed a new method for the prediction of the DNA-binding proteins, by performing the feature rank using random forest and the wrapper-based feature selection using forward best-first search strategy. The features comprise information from primary sequence, predicted secondary structure, predicted relative solvent accessibility, and position specific scoring matrix. The proposed method, called DBPPred, used Gaussian naïve Bayes as the underlying classifier since it outperformed five other classifiers, including decision tree, logistic regression, k-nearest neighbor, support vector machine with polynomial kernel, and support vector machine with radial basis function. As a result, the proposed DBPPred yields the highest average accuracy of 0.791 and average MCC of 0.583 according to the five-fold cross validation with ten runs on the training benchmark dataset PDB594. Subsequently, blind tests on the independent dataset PDB186 by the proposed model trained on the entire PDB594 dataset and by other five existing methods (including iDNA-Prot, DNA-Prot, DNAbinder, DNABIND and DBD-Threader were performed, resulting in that the proposed DBPPred yielded the highest accuracy of 0.769, MCC of 0.538, and AUC of 0.790. The independent tests performed by the proposed DBPPred on completely a large non-DNA binding protein dataset and two RNA binding protein datasets also showed improved or comparable quality when compared with the relevant prediction methods. Moreover, we observed that majority of the selected features by the proposed method are statistically significantly different between the mean feature values of the DNA-binding and the non DNA-binding proteins. All of the experimental results indicate that
Kota, V K B; Chavda, N D; Sahu, R
2006-04-01
Interacting many-particle systems with a mean-field one-body part plus a chaos generating random two-body interaction having strength lambda exhibit Poisson to Gaussian orthogonal ensemble and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and strength functions with transition points marked by lambda = lambda c and lambda = lambda F, respectively; lambda F > lambda c. For these systems a theory for the matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with lambda > lambda F, in terms of orbital occupation numbers, level densities, and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using a bivariate-t distribution, the theory extends below from the Gaussian regime to the BW regime up to lambda = lambda c. This is well tested in numerical calculations for 6 spinless fermions in 12 single-particle states.
International Nuclear Information System (INIS)
Zimbardo, Gaetano
2005-01-01
Plasma transport in the presence of turbulence depends on a variety of parameters such as the fluctuation level, δB/B 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 0 = B 0 e z and a Fourier representation for magnetic fluctuations, which includes wavectors oblique with respect to B 0 . The energy density spectrum is a power law, and in k space it is described by the correlation lengths l x , l y , l z , which quantify the anisotropy of turbulence. For magnetic field lines, transport perpendicular to the background field depends on the Kubo number R (δB/B 0 ) (l z /l x ). For small Kubo numbers, R 0 , or the ratio l z /l 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, δB/B 0 ≅ 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 z /l x ≤ 1, with a Levy random walk (superdiffusion) along the magnetic field and subdiffusion in the perpendicular directions. Conversely, for l z /l x > 1 normal Gaussian diffusion is found. A possible expression for generalized double diffusion is discussed
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.
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.
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.
Gaussian limit of compact spin systems
International Nuclear Information System (INIS)
Bellissard, J.; Angelis, G.F. de
1981-01-01
It is shown that the Wilson and Wilson-Villain U(1) models reproduce, in the low coupling limit, the gaussian lattice approximation of the Euclidean electromagnetic field. By the same methods it is also possible to prove that the plane rotator and the Villain model share a common gaussian behaviour in the low temperature limit. (Auth.)
Phase conjugation with random fields and with deterministic and random scatterers
International Nuclear Information System (INIS)
Gbur, G.; Wolf, E.
1999-01-01
The theory of distortion correction by phase conjugation, developed since the discovery of this phenomenon many years ago, applies to situations when the field that is conjugated is monochromatic and the medium with which it interacts is deterministic. In this Letter a generalization of the theory is presented that applies to phase conjugation of partially coherent waves interacting with either deterministic or random weakly scattering nonabsorbing media. copyright 1999 Optical Society of America
Statistical mechanics and stability of random lattice field theory
International Nuclear Information System (INIS)
Baskaran, G.
1984-01-01
The averaging procedure in the random lattice field theory is studied by viewing it as a statistical mechanics of a system of classical particles. The corresponding thermodynamic phase is shown to determine the random lattice configuration which contributes dominantly to the generating function. The non-abelian gauge theory in four (space plus time) dimensions in the annealed and quenched averaging versions is shown to exist as an ideal classical gas, implying that macroscopically homogeneous configurations dominate the configurational averaging. For the free massless scalar field theory with O(n) global symmetry, in the annealed average, the pressure becomes negative for dimensions greater than two when n exceeds a critical number. This implies that macroscopically inhomogeneous collapsed configurations contribute dominantly. In the quenched averaging, the collapse of the massless scalar field theory is prevented and the system becomes an ideal gas which is at infinite temperature. Our results are obtained using exact scaling analysis. We also show approximately that SU(N) gauge theory collapses for dimensions greater than four in the annealed average. Within the same approximation, the collapse is prevented in the quenched average. We also obtain exact scaling differential equations satisfied by the generating function and physical quantities. (orig.)
Deep recurrent conditional random field network for protein secondary prediction
DEFF Research Database (Denmark)
Johansen, Alexander Rosenberg; Sønderby, Søren Kaae; Sønderby, Casper Kaae
2017-01-01
Deep learning has become the state-of-the-art method for predicting protein secondary structure from only its amino acid residues and sequence profile. Building upon these results, we propose to combine a bi-directional recurrent neural network (biRNN) with a conditional random field (CRF), which...... of the labels for all time-steps. We condition the CRF on the output of biRNN, which learns a distributed representation based on the entire sequence. The biRNN-CRF is therefore close to ideally suited for the secondary structure task because a high degree of cross-talk between neighboring elements can...
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
Rotating quantum Gaussian packets
International Nuclear Information System (INIS)
Dodonov, V V
2015-01-01
We study two-dimensional quantum Gaussian packets with a fixed value of mean angular momentum. This value is the sum of two independent parts: the ‘external’ momentum related to the motion of the packet center and the ‘internal’ momentum due to quantum fluctuations. The packets minimizing the mean energy of an isotropic oscillator with the fixed mean angular momentum are found. They exist for ‘co-rotating’ external and internal motions, and they have nonzero correlation coefficients between coordinates and momenta, together with some (moderate) amount of quadrature squeezing. Variances of angular momentum and energy are calculated, too. Differences in the behavior of ‘co-rotating’ and ‘anti-rotating’ packets are shown. The time evolution of rotating Gaussian packets is analyzed, including the cases of a charge in a homogeneous magnetic field and a free particle. In the latter case, the effect of initial shrinking of packets with big enough coordinate-momentum correlation coefficients (followed by the well known expansion) is discovered. This happens due to a competition of ‘focusing’ and ‘de-focusing’ in the orthogonal directions. (paper)
International Nuclear Information System (INIS)
McFadden, Paul; Skenderis, Kostas
2011-01-01
We investigate the non-Gaussianity of primordial cosmological perturbations within our recently proposed holographic description of inflationary universes. We derive a holographic formula that determines the bispectrum of cosmological curvature perturbations in terms of correlation functions of a holographically dual three-dimensional non-gravitational quantum field theory (QFT). This allows us to compute the primordial bispectrum for a universe which started in a non-geometric holographic phase, using perturbative QFT calculations. Strikingly, for a class of models specified by a three-dimensional super-renormalisable QFT, the primordial bispectrum is of exactly the factorisable equilateral form with f NL equil. = 5/36, irrespective of the details of the dual QFT. A by-product of this investigation is a holographic formula for the three-point function of the trace of the stress-energy tensor along general holographic RG flows, which should have applications outside the remit of this work
Trapping, percolation, and anomalous diffusion of particles in a two-dimensional random field
International Nuclear Information System (INIS)
Avellaneda, M.; Apelian, C.; Elliott, F. Jr.
1993-01-01
The authors analyze the advection of particles in a velocity field with Hamiltonian H(x,y) = bar V 1 y-bar V 2 x + W 1 (y) - W 2 (x), where W i , i=1,2, are random functions with stationary, independent increments. In the absence of molecular diffusion, the particle dynamics are sensitive to the streamline topology, which depends on the mean-to-fluctuations ratio p=max(|bar V 1 |/bar U;|bar V 2 |/bar U), with bar U = [|W' 1 | 2 ] 1/2 = rms fluctuations. The model is exactly solvable for p≥1 and well suited for Monte Carlo simulations for all p. Statistics are considered of streamlines for p=0, deriving power laws for the escape probability and the length of escaping trajectories for a box of size L much-gt 1. Also obtained is a characterization of the statistical topography of the Hamiltonian. The large-scale transport is studied of advected particles with p > 0. For 0 -v/2 [x(t) - (x(t))] and t -v/2 [y(t) - (y(t))]. The large-scale motions are Fickian (v=1) or superdiffusive (v=3/2) with a non-Gaussian coarse-grained probability, according to the direction of the mean velocity relative to the underlying lattice. These results are obtained analytically for p≥1 and extended to the regime 0 1 , bar V 2 ) for which stagnation regions in the flow exist. The results are compared with existing predictions on the topology of streamlines based on percolation theory and with mean-field calculations of effective diffusivities. 29 refs., 15 figs., 7 tabs
Some continual integrals from gaussian forms
International Nuclear Information System (INIS)
Mazmanishvili, A.S.
1985-01-01
The result summary of continual integration of gaussian functional type is given. The summary contains 124 continual integrals which are the mathematical expectation of the corresponding gaussian form by the continuum of random trajectories of four types: real-valued Ornstein-Uhlenbeck process, Wiener process, complex-valued Ornstein-Uhlenbeck process and the stochastic harmonic one. The summary includes both the known continual integrals and the unpublished before integrals. Mathematical results of the continual integration carried in the work may be applied in the problem of the theory of stochastic process, approaching to the finding of mean from gaussian forms by measures generated by the pointed stochastic processes
Quantum Coherence and Random Fields at Mesoscopic Scales
International Nuclear Information System (INIS)
Rosenbaum, Thomas F.
2016-01-01
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.
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.
Large deviations for Gaussian processes in Hoelder norm
International Nuclear Information System (INIS)
Fatalov, V R
2003-01-01
Some results are proved on the exact asymptotic representation of large deviation probabilities for Gaussian processes in the Hoeder norm. The following classes of processes are considered: the Wiener process, the Brownian bridge, fractional Brownian motion, and stationary Gaussian processes with power-law covariance function. The investigation uses the method of double sums for Gaussian fields
Conditional Random Fields for Morphological Analysis of Wireless ECG Signals
Natarajan, Annamalai; Gaiser, Edward; Angarita, Gustavo; Malison, Robert; Ganesan, Deepak; Marlin, Benjamin
2015-01-01
Thanks to advances in mobile sensing technologies, it has recently become practical to deploy wireless electrocardiograph sensors for continuous recording of ECG signals. This capability has diverse applications in the study of human health and behavior, but to realize its full potential, new computational tools are required to effectively deal with the uncertainty that results from the noisy and highly non-stationary signals collected using these devices. In this work, we present a novel approach to the problem of extracting the morphological structure of ECG signals based on the use of dynamically structured conditional random field (CRF) models. We apply this framework to the problem of extracting morphological structure from wireless ECG sensor data collected in a lab-based study of habituated cocaine users. Our results show that the proposed CRF-based approach significantly out-performs independent prediction models using the same features, as well as a widely cited open source toolkit. PMID:26726321
Random fields, topology, and the Imry-Ma argument.
Proctor, Thomas C; Garanin, Dmitry A; Chudnovsky, Eugene M
2014-03-07
We consider an n-component fixed-length order parameter interacting with a weak random field in d=1, 2, 3 dimensions. Relaxation from the initially ordered state and spin-spin correlation functions are studied on lattices containing hundreds of millions of sites. At n ≤ d the presence of topological defects leads to strong metastability and glassy behavior, with the final state depending on the initial condition. At n=d+1, when topological structures are nonsingular, the system possesses a weak metastability. At n>d+1, when topological objects are absent, the final, lowest-energy state is independent of the initial condition. It is characterized by the exponential decay of correlations that agrees quantitatively with the theory based upon the Imry-Ma argument.
Baryon-to-dark matter ratio from random angular fields
International Nuclear Information System (INIS)
McDonald, John
2013-01-01
We consider the baryon-to-dark matter ratio in models where the dark matter and baryon densities depend on angular fields θ d and θ b according to ρ d ∝θ d α and ρ b ∝θ b β , with all values of θ d and θ b being equally probable in a given randomly-selected domain. Under the assumption that anthropic selection depends primarily on the baryon density in galaxies at spherical collapse, we show that the probability density function for the baryon-to-dark matter ratio r = Ω B /Ω DM is purely statistical in nature and is independent of anthropic selection. We compute the probability density function for r as a function of α and β and show that the observed value of the baryon-to-dark matter ratio, r ≈ 1/5, is natural in this framework
Cover estimation and payload location using Markov random fields
Quach, Tu-Thach
2014-02-01
Payload location is an approach to find the message bits hidden in steganographic images, but not necessarily their logical order. Its success relies primarily on the accuracy of the underlying cover estimators and can be improved if more estimators are used. This paper presents an approach based on Markov random field to estimate the cover image given a stego image. It uses pairwise constraints to capture the natural two-dimensional statistics of cover images and forms a basis for more sophisticated models. Experimental results show that it is competitive against current state-of-the-art estimators and can locate payload embedded by simple LSB steganography and group-parity steganography. Furthermore, when combined with existing estimators, payload location accuracy improves significantly.
A Markov random field approach for microstructure synthesis
International Nuclear Information System (INIS)
Kumar, A; Nguyen, L; DeGraef, M; Sundararaghavan, V
2016-01-01
We test the notion that many microstructures have an underlying stationary probability distribution. The stationary probability distribution is ubiquitous: we know that different windows taken from a polycrystalline microstructure are generally ‘statistically similar’. To enable computation of such a probability distribution, microstructures are represented in the form of undirected probabilistic graphs called Markov Random Fields (MRFs). In the model, pixels take up integer or vector states and interact with multiple neighbors over a window. Using this lattice structure, algorithms are developed to sample the conditional probability density for the state of each pixel given the known states of its neighboring pixels. The sampling is performed using reference experimental images. 2D microstructures are artificially synthesized using the sampled probabilities. Statistical features such as grain size distribution and autocorrelation functions closely match with those of the experimental images. The mechanical properties of the synthesized microstructures were computed using the finite element method and were also found to match the experimental values. (paper)
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...
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.
Clustering, randomness, and regularity in cloud fields. 4. Stratocumulus cloud fields
Lee, J.; Chou, J.; Weger, R. C.; Welch, R. M.
1994-07-01
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 (>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.
Gaussian entanglement revisited
Lami, Ludovico; Serafini, Alessio; Adesso, Gerardo
2018-02-01
We present a novel approach to the separability problem for Gaussian quantum states of bosonic continuous variable systems. We derive a simplified necessary and sufficient separability criterion for arbitrary Gaussian states of m versus n modes, which relies on convex optimisation over marginal covariance matrices on one subsystem only. We further revisit the currently known results stating the equivalence between separability and positive partial transposition (PPT) for specific classes of Gaussian states. Using techniques based on matrix analysis, such as Schur complements and matrix means, we then provide a unified treatment and compact proofs of all these results. In particular, we recover the PPT-separability equivalence for: (i) Gaussian states of 1 versus n modes; and (ii) isotropic Gaussian states. In passing, we also retrieve (iii) the recently established equivalence between separability of a Gaussian state and and its complete Gaussian extendability. Our techniques are then applied to progress beyond the state of the art. We prove that: (iv) Gaussian states that are invariant under partial transposition are necessarily separable; (v) the PPT criterion is necessary and sufficient for separability for Gaussian states of m versus n modes that are symmetric under the exchange of any two modes belonging to one of the parties; and (vi) Gaussian states which remain PPT under passive optical operations can not be entangled by them either. This is not a foregone conclusion per se (since Gaussian bound entangled states do exist) and settles a question that had been left unanswered in the existing literature on the subject. This paper, enjoyable by both the quantum optics and the matrix analysis communities, overall delivers technical and conceptual advances which are likely to be useful for further applications in continuous variable quantum information theory, beyond the separability problem.
Discriminative Random Field Models for Subsurface Contamination Uncertainty Quantification
Arshadi, M.; Abriola, L. M.; Miller, E. L.; De Paolis Kaluza, C.
2017-12-01
Application of flow and transport simulators for prediction of the release, entrapment, and persistence of dense non-aqueous phase liquids (DNAPLs) and associated contaminant plumes is a computationally intensive process that requires specification of a large number of material properties and hydrologic/chemical parameters. Given its computational burden, this direct simulation approach is particularly ill-suited for quantifying both the expected performance and uncertainty associated with candidate remediation strategies under real field conditions. Prediction uncertainties primarily arise from limited information about contaminant mass distributions, as well as the spatial distribution of subsurface hydrologic properties. Application of direct simulation to quantify uncertainty would, thus, typically require simulating multiphase flow and transport for a large number of permeability and release scenarios to collect statistics associated with remedial effectiveness, a computationally prohibitive process. The primary objective of this work is to develop and demonstrate a methodology that employs measured field data to produce equi-probable stochastic representations of a subsurface source zone that capture the spatial distribution and uncertainty associated with key features that control remediation performance (i.e., permeability and contamination mass). Here we employ probabilistic models known as discriminative random fields (DRFs) to synthesize stochastic realizations of initial mass distributions consistent with known, and typically limited, site characterization data. Using a limited number of full scale simulations as training data, a statistical model is developed for predicting the distribution of contaminant mass (e.g., DNAPL saturation and aqueous concentration) across a heterogeneous domain. Monte-Carlo sampling methods are then employed, in conjunction with the trained statistical model, to generate realizations conditioned on measured borehole data
Zhang, Hua; Harter, Thomas; Sivakumar, Bellie
2006-06-01
examined, the third moment of the traveltime pdf varies from negatively skewed to strongly positively skewed. We also show that the Markov chain approach may give significantly different traveltime distributions when compared to the more commonly used Gaussian random field approach, even when the first- and second-order moments in the geostatistical distribution of the lnK field are identical. The choice of the appropriate geostatistical model is therefore critical in the assessment of nonpoint source transport, and uncertainty about that choice must be considered in evaluating the results.
Gaussian statistics for palaeomagnetic vectors
Love, J.J.; Constable, C.G.
2003-01-01
With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to
Gaussian statistics for palaeomagnetic vectors
Love, J. J.; Constable, C. G.
2003-03-01
With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimodal) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to
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.
A Markov Random Field Groupwise Registration Framework for Face Recognition.
Liao, Shu; Shen, Dinggang; Chung, Albert C S
2014-04-01
In this paper, we propose a new framework for tackling face recognition problem. The face recognition problem is formulated as groupwise deformable image registration and feature matching problem. The main contributions of the proposed method lie in the following aspects: (1) Each pixel in a facial image is represented by an anatomical signature obtained from its corresponding most salient scale local region determined by the survival exponential entropy (SEE) information theoretic measure. (2) Based on the anatomical signature calculated from each pixel, a novel Markov random field based groupwise registration framework is proposed to formulate the face recognition problem as a feature guided deformable image registration problem. The similarity between different facial images are measured on the nonlinear Riemannian manifold based on the deformable transformations. (3) The proposed method does not suffer from the generalizability problem which exists commonly in learning based algorithms. The proposed method has been extensively evaluated on four publicly available databases: FERET, CAS-PEAL-R1, FRGC ver 2.0, and the LFW. It is also compared with several state-of-the-art face recognition approaches, and experimental results demonstrate that the proposed method consistently achieves the highest recognition rates among all the methods under comparison.
Pose-invariant face recognition using Markov random fields.
Ho, Huy Tho; Chellappa, Rama
2013-04-01
One of the key challenges for current face recognition techniques is how to handle pose variations between the probe and gallery face images. In this paper, we present a method for reconstructing the virtual frontal view from a given nonfrontal face image using Markov random fields (MRFs) and an efficient variant of the belief propagation algorithm. In the proposed approach, the input face image is divided into a grid of overlapping patches, and a globally optimal set of local warps is estimated to synthesize the patches at the frontal view. A set of possible warps for each patch is obtained by aligning it with images from a training database of frontal faces. The alignments are performed efficiently in the Fourier domain using an extension of the Lucas-Kanade algorithm that can handle illumination variations. The problem of finding the optimal warps is then formulated as a discrete labeling problem using an MRF. The reconstructed frontal face image can then be used with any face recognition technique. The two main advantages of our method are that it does not require manually selected facial landmarks or head pose estimation. In order to improve the performance of our pose normalization method in face recognition, we also present an algorithm for classifying whether a given face image is at a frontal or nonfrontal pose. Experimental results on different datasets are presented to demonstrate the effectiveness of the proposed approach.
Branched flow and caustics in random media with magnetic fields
Metzger, Jakob; Fleischmann, Ragnar; Geisel, Theo
2009-03-01
Classical particles as well as quantum mechanical waves exhibit complex behaviour when propagating through random media. One of the dominant features of the dynamics in correlated, weak disorder potentials is the branching of the flow. This can be observed in several physical systems, most notably in the electron flow in two-dimensional electron gases [1], and has also been used to describe the formation of freak waves [2]. We present advances in the theoretical understanding and numerical simulation of classical branched flows in magnetic fields. In particular, we study branching statistics and branch density profiles. Our results have direct consequences for experiments which measure transport properties in electronic systems [3].[1] e.g. M. A. Topinka et al., Nature 410, 183 (2001), M. P. Jura et al., Nature Physics 3, 841 (2007)[2] E. J. Heller, L. Kaplan and A. Dahlen, J. Geophys. Res., 113, C09023 (2008)[3] J. J. Metzger, R. Fleischmann and T. Geisel, in preparation
Infinite hidden 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), which is a nonparametric model based on hierarchical Dirichlet processes and is capable of automatically learning the optimal number of hidden states for a classification task. We show how we learn the model hyperparameters with an effective Markov-chain Monte Carlo sampling technique, and we explain the process that underlines our iHCRF model with the Restaurant Franchise Rating Agencies analogy. We show that the iHCRF is able to converge to a correct number of represented hidden states, and outperforms the best finite HCRFs--chosen via cross-validation--for the difficult tasks of recognizing instances of agreement, disagreement, and pain. Moreover, the iHCRF manages to achieve this performance in significantly less total training, validation, and testing time.
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.
Markov random field based automatic image alignment for electron tomography.
Amat, Fernando; Moussavi, Farshid; Comolli, Luis R; Elidan, Gal; Downing, Kenneth H; Horowitz, Mark
2008-03-01
We present a method for automatic full-precision alignment of the images in a tomographic tilt series. Full-precision automatic alignment of cryo electron microscopy images has remained a difficult challenge to date, due to the limited electron dose and low image contrast. These facts lead to poor signal to noise ratio (SNR) in the images, which causes automatic feature trackers to generate errors, even with high contrast gold particles as fiducial features. To enable fully automatic alignment for full-precision reconstructions, we frame the problem probabilistically as finding the most likely particle tracks given a set of noisy images, using contextual information to make the solution more robust to the noise in each image. To solve this maximum likelihood problem, we use Markov Random Fields (MRF) to establish the correspondence of features in alignment and robust optimization for projection model estimation. The resulting algorithm, called Robust Alignment and Projection Estimation for Tomographic Reconstruction, or RAPTOR, has not needed any manual intervention for the difficult datasets we have tried, and has provided sub-pixel alignment that is as good as the manual approach by an expert user. We are able to automatically map complete and partial marker trajectories and thus obtain highly accurate image alignment. Our method has been applied to challenging cryo electron tomographic datasets with low SNR from intact bacterial cells, as well as several plastic section and X-ray datasets.
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.
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. PsycINFO Database Record (c) 2014 APA, all rights reserved.
Gaussian free turbulence: structures and relaxation in plasma models
International Nuclear Information System (INIS)
Gruzinov, A.V.
1993-01-01
Free-turbulent relaxation in two-dimensional MHD, the degenerate Hasegawa-Mima equation and a two-dimensional microtearing model are studied. The Gibbs distributions of these three systems can be completely analyzed, due to the special structure of their invariants and due to the existence of ultraviolet catastrophe. The free-turbulent field is seen to be a sum of a certain coherent structure (statistical attractor) and Gaussian random noise. Two-dimensional current layers are shown to be statistical attractors in 2D MHD. (author)
The mean field theory in EM procedures for blind Markov random field image restoration.
Zhang, J
1993-01-01
A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing.
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.
CSIR Research Space (South Africa)
Roux, FS
2009-01-01
Full Text Available , t0)} = P(du, dv) {FR{g(u, v, t0)}} Replacement: u→ du = t− t0 i2 ∂ ∂u′ v → dv = t− t0 i2 ∂ ∂v′ CSIR National Laser Centre – p.13/30 Differentiation i.s.o integration Evaluate the integral over the Gaussian beam (once and for all). Then, instead... . Gaussian beams with vortex dipoles CSIR National Laser Centre – p.2/30 Gaussian beam notation Gaussian beam in normalised coordinates: g(u, v, t) = exp ( −u 2 + v2 1− it ) u = xω0 v = yω0 t = zρ ρ = piω20 λ ω0 — 1/e2 beam waist radius; ρ— Rayleigh range ω ω...
Clustering, randomness, and regularity in cloud fields: 2. Cumulus cloud fields
Zhu, T.; Lee, J.; Weger, R. C.; Welch, R. M.
1992-12-01
During the last decade a major controversy has been brewing concerning the proper characterization of cumulus convection. The prevailing view has been that cumulus clouds form in clusters, in which cloud spacing is closer than that found for the overall cloud field and which maintains its identity over many cloud lifetimes. This "mutual protection hypothesis" of Randall and Huffman (1980) has been challenged by the "inhibition hypothesis" of Ramirez et al. (1990) which strongly suggests that the spatial distribution of cumuli must tend toward a regular distribution. A dilemma has resulted because observations have been reported to support both hypotheses. The present work reports a detailed analysis of cumulus cloud field spatial distributions based upon Landsat, Advanced Very High Resolution Radiometer, and Skylab data. Both nearest-neighbor and point-to-cloud cumulative distribution function statistics are investigated. The results show unequivocally that when both large and small clouds are included in the cloud field distribution, the cloud field always has a strong clustering signal. The strength of clustering is largest at cloud diameters of about 200-300 m, diminishing with increasing cloud diameter. In many cases, clusters of small clouds are found which are not closely associated with large clouds. As the small clouds are eliminated from consideration, the cloud field typically tends towards regularity. Thus it would appear that the "inhibition hypothesis" of Ramirez and Bras (1990) has been verified for the large clouds. However, these results are based upon the analysis of point processes. A more exact analysis also is made which takes into account the cloud size distributions. Since distinct clouds are by definition nonoverlapping, cloud size effects place a restriction upon the possible locations of clouds in the cloud field. The net effect of this analysis is that the large clouds appear to be randomly distributed, with only weak tendencies towards
Gaussian operations and privacy
International Nuclear Information System (INIS)
Navascues, Miguel; Acin, Antonio
2005-01-01
We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in [Navascues et al. Phys. Rev. Lett. 94, 010502 (2005)]. Then, we prove that a generalized version of this protocol does not allow one to distill a secret key out of bound entangled Gaussian states
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.
An application of random field theory to analysis of electron trapping sites in disordered media
International Nuclear Information System (INIS)
Hilczer, M.; Bartczak, W.M.
1993-01-01
The potential energy surface in a disordered medium is considered a random field and described using the concepts of the mathematical theory of random fields. The preexisting traps for excess electrons are identified with certain regions of excursion (extreme regions) of the potential field. The theory provides an analytical method of statistical analysis of these regions. Parameters of the cavity-averaged potential field, which are provided by computer simulation of a given medium, serve as input data for the analysis. The statistics of preexisting traps are obtained for liquid methanol as a numerical example of the random field method. 26 refs., 6 figs
Czech Academy of Sciences Publication Activity Database
Kaprálová-Žďánská, Petra Ruth; Šmydke, Jan; Civiš, S.
2013-01-01
Roč. 139, č. 10 (2013), s. 104314 ISSN 0021-9606 R&D Projects: GA AV ČR IAAX00100903; GA MŠk(CZ) ME10046; GA ČR GAP205/11/0571 Institutional support: RVO:68378271 Keywords : Gaussian distribution * helium * oscillator strengths * quantum chemistry * rotational states * Rydberg states * two-photon processes Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 3.122, year: 2013
Galaxy bias and primordial non-Gaussianity
Energy Technology Data Exchange (ETDEWEB)
Assassi, Valentin; Baumann, Daniel [DAMTP, Cambridge University, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Schmidt, Fabian, E-mail: assassi@ias.edu, E-mail: D.D.Baumann@uva.nl, E-mail: fabians@MPA-Garching.MPG.DE [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching (Germany)
2015-12-01
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation.
Galaxy bias and primordial non-Gaussianity
International Nuclear Information System (INIS)
Assassi, Valentin; Baumann, Daniel; Schmidt, Fabian
2015-01-01
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation
Mitri, F G; Fellah, Z E A
2014-01-01
The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z(R). Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere's resonance frequencies for kw₀≤1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force. Copyright © 2013 Elsevier B.V. All rights reserved.
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....
Reduction of the Random Variables of the Turbulent Wind Field
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.
2012-01-01
.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......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...... 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...
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian U...
Additivity properties of a Gaussian channel
International Nuclear Information System (INIS)
Giovannetti, Vittorio; Lloyd, Seth
2004-01-01
The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Renyi entropies at the output of a channel. The conjecture is proven true for all Renyi entropies of integer order greater than two in a class of Gaussian bosonic channel where the input signal is randomly displaced or where it is coupled linearly to an external environment
Electron traps in polar liquids. An application of the formalism of the random field theory
International Nuclear Information System (INIS)
Hilczer, M.; Bartczak, W.M.
1992-01-01
The potential energy surface in a disordered medium is described, using the concepts of the mathematical theory of random fields. The statistics of trapping sites (the regions of an excursion of the random field) is obtained for liquid methanol as a numerical example of the theory. (author). 15 refs, 4 figs
A test for stationarity of spatio-temporal random fields on planar and spherical domains
Jun, Mikyoung; Genton, Marc G.
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
Specific heat of the Ising linear chain in a Random field
International Nuclear Information System (INIS)
Silva, P.R.; Sa Barreto, F.C. de
1984-01-01
Starting from correlation identities for the Ising model the effect of a random field on the one dimension version of the model is studied. Explicit results for the magnetization, the two-particle correlation function and the specific heat are obtained for an uncorrelated distribution of the random fields. (Author) [pt
Smooth random surfaces from tight immersions?
International Nuclear Information System (INIS)
Baillie, C.F.; Johnston, D.A.
1994-01-01
We investigate actions for dynamically triangulated random surfaces that consist of a Gaussian or area term plus the modulus of the Gaussian curvature and compare their behavior with both Gaussian plus extrinsic curvature and ''Steiner'' actions
Global mean-field phase diagram of the spin-1 Ising ferromagnet in a random crystal field
Borelli, M. E. S.; Carneiro, C. E. I.
1996-02-01
We study the phase diagram of the mean-field spin-1 Ising ferromagnet in a uniform magnetic field H and a random crystal field Δi, with probability distribution P( Δi) = pδ( Δi - Δ) + (1 - p) δ( Δi). We analyse the effects of randomness on the first-order surfaces of the Δ- T- H phase diagram for different values of the concentration p and show how these surfaces are affected by the dilution of the crystal field.
Diffusion in the kicked quantum rotator by random corrections to a linear and sine field
International Nuclear Information System (INIS)
Hilke, M.; Flores, J.C.
1992-01-01
We discuss the diffusion in momentum space, of the kicked quantum rotator, by introducing random corrections to a linear and sine external field. For the linear field we obtain a linear diffusion behavior identical to the case with zero average in the external field. But for the sine field, accelerator modes with quadratic diffusion are found for particular values of the kicking period. (orig.)
Nonclassicality by Local Gaussian Unitary Operations for Gaussian States
Directory of Open Access Journals (Sweden)
Yangyang Wang
2018-04-01
Full Text Available A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 -mode Gaussian states and an estimate of N for ( n + m -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.
Metastability of Reversible Random Walks in Potential Fields
Landim, C.; Misturini, R.; Tsunoda, K.
2015-09-01
Let be an open and bounded subset of , and let be a twice continuously differentiable function. Denote by the discretization of , , and denote by the continuous-time, nearest-neighbor, random walk on which jumps from to at rate . We examine in this article the metastable behavior of among the wells of the potential F.
Learning conditional Gaussian networks
DEFF Research Database (Denmark)
Bøttcher, Susanne Gammelgaard
This paper considers conditional Gaussian networks. The parameters in the network are learned by using conjugate Bayesian analysis. As conjugate local priors, we apply the Dirichlet distribution for discrete variables and the Gaussian-inverse gamma distribution for continuous variables, given...... a configuration of the discrete parents. We assume parameter independence and complete data. Further, to learn the structure of the network, the network score is deduced. We then develop a local master prior procedure, for deriving parameter priors in these networks. This procedure satisfies parameter...... independence, parameter modularity and likelihood equivalence. Bayes factors to be used in model search are introduced. Finally the methods derived are illustrated by a simple example....
Phase diagram and tricritical behavior of an metamagnet in uniform and random fields
International Nuclear Information System (INIS)
Liang Yaqiu; Wei Guozhu; Xu Xiaojuan; Song Guoli
2010-01-01
A two-sublattice Ising metamagnet in both uniform and random fields is studied within the mean-field approach based on Bogoliubov's inequality for the Gibbs free energy. We show that the qualitative features of the phase diagrams are dependent on the parameters of the model and the uniform field values. The tricritical point and reentrant phenomenon can be observed on the phase diagram. The reentrance is due to the competition between uniform and random interactions.
Critical behavior in a random field classical Heisenberg model for amorphous systems
International Nuclear Information System (INIS)
Albuquerque, Douglas F. de; Alves, Sandro Roberto L.; Arruda, Alberto S. de
2005-01-01
By using the differential operator technique and the effective field theory scheme, the critical behavior of amorphous classical Heisenberg ferromagnet of spin-1/2 in a random field is studied. The phase diagram in the T-H and T-α planes on a simple cubic lattice for a cluster with two spins is obtained. Tricritical points, reentrant phenomena and influence of the random field and amorphization on the transition temperature are discussed
Random errors in the magnetic field coefficients of superconducting magnets
International Nuclear Information System (INIS)
Herrera, J.; Hogue, R.; Prodell, A.; Wanderer, P.; Willen, E.
1985-01-01
Random errors in the multipole magnetic coefficients of superconducting magnet have been of continuing interest in accelerator research. The Superconducting Super Collider (SSC) with its small magnetic aperture only emphasizes this aspect of magnet design, construction, and measurement. With this in mind, we present a magnet model which mirrors the structure of a typical superconducting magnet. By taking advantage of the basic symmetries of a dipole magnet, we use this model to fit the measured multipole rms widths. The fit parameters allow us then to predict the values of the rms multipole errors expected for the SSC dipole reference design D, SSC-C5. With the aid of first-order perturbation theory, we then give an estimate of the effect of these random errors on the emittance growth of a proton beam stored in an SSC. 10 refs., 6 figs., 2 tabs
Charged Particle Diffusion in Isotropic Random Magnetic Fields
Energy Technology Data Exchange (ETDEWEB)
Subedi, P.; Matthaeus, W. H.; Chuychai, P.; Parashar, T. N.; Chhiber, R. [Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716 (United States); Sonsrettee, W. [Faculty of Engineering and Technology, Panyapiwat Institute of Management, Nonthaburi 11120 (Thailand); Blasi, P. [INAF/Osservatorio Astrofisico di Arcetri, Largo E. Fermi, 5—I-50125 Firenze (Italy); Ruffolo, D. [Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400 (Thailand); Montgomery, D. [Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755 (United States); Dmitruk, P. [Departamento de Física Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria, 1428 Buenos Aires (Argentina); Wan, M. [Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055 (China)
2017-03-10
The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider the diffusion of charged particles in fully three-dimensional isotropic turbulent magnetic fields with no mean field, which may be pertinent to many astrophysical situations. We identify different ranges of particle energy depending upon the ratio of Larmor radius to the characteristic outer length scale of turbulence. Two different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. The theoretical results are compared to those from computer simulations, showing good agreement.
AUTONOMOUS GAUSSIAN DECOMPOSITION
Energy Technology Data Exchange (ETDEWEB)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Heiles, Carl [Radio Astronomy Lab, UC Berkeley, 601 Campbell Hall, Berkeley, CA 94720 (United States); Hennebelle, Patrick [Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp-CNRS-Université Paris Diderot, F-91191 Gif-sur Yvette Cedex (France); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville, Socorro, NM 87801 (United States); Dickey, John, E-mail: rlindner@astro.wisc.edu [University of Tasmania, School of Maths and Physics, Private Bag 37, Hobart, TAS 7001 (Australia)
2015-04-15
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
Bounded Gaussian process regression
DEFF Research Database (Denmark)
Jensen, Bjørn Sand; Nielsen, Jens Brehm; Larsen, Jan
2013-01-01
We extend the Gaussian process (GP) framework for bounded regression by introducing two bounded likelihood functions that model the noise on the dependent variable explicitly. This is fundamentally different from the implicit noise assumption in the previously suggested warped GP framework. We...... with the proposed explicit noise-model extension....
AUTONOMOUS GAUSSIAN DECOMPOSITION
International Nuclear Information System (INIS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-01-01
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes
Quantum information with Gaussian states
International Nuclear Information System (INIS)
Wang Xiangbin; Hiroshima, Tohya; Tomita, Akihisa; Hayashi, Masahito
2007-01-01
Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright Gaussian light and weak Gaussian light. Extending the existing results of quantum information with discrete quantum states to the case of continuous variable quantum states is an interesting theoretical job. The quantum Gaussian states play a central role in such a case. We review the properties and applications of Gaussian states in quantum information with emphasis on the fundamental concepts, the calculation techniques and the effects of imperfections of the real-life experimental setups. Topics here include the elementary properties of Gaussian states and relevant quantum information device, entanglement-based quantum tasks such as quantum teleportation, quantum cryptography with weak and strong Gaussian states and the quantum channel capacity, mathematical theory of quantum entanglement and state estimation for Gaussian states
Külske, C
2003-01-01
We derive useful general concentration inequalities for functions of Gibbs fields in the uniqueness regime. We also consider expectations of random Gibbs measures that depend on an additional disorder field, and prove concentration w.r.t the disorder field. Both fields are assumed to be in the uniqueness regime, allowing in particular for non-independent disorder field. The modification of the bounds compared to the case of an independent field can be expressed in terms of constants that resemble the Dobrushin contraction coefficient, and are explicitly computable. On the basis of these inequalities, we obtain bounds on the deviation of a diffraction pattern created by random scatterers located on a general discrete point set in the Euclidean space, restricted to a finite volume. Here we also allow for thermal dislocations of the scatterers around their equilibrium positions. Extending recent results for independent scatterers, we give a universal upper bound on the probability of a deviation of the random sc...
Body fixed frame, rigid gauge rotations and large N random fields in QCD
International Nuclear Information System (INIS)
Levit, S.
1995-01-01
The ''body fixed frame'' with respect to local gauge transformations is introduced. Rigid gauge ''rotations'' in QCD and their Schroedinger equation are studied for static and dynamic quarks. Possible choices of the rigid gauge field configuration corresponding to a non-vanishing static colormagnetic field in the ''body fixed'' frame are discussed. A gauge invariant variational equation is derived in this frame. For large number N of colors the rigid gauge field configuration is regarded as random with maximally random probability distribution under constraints on macroscopic-like quantities. For the uniform magnetic field the joint probability distribution of the field components is determined by maximizing the appropriate entropy under the area law constraint for the Wilson loop. In the quark sector the gauge invariance requires the rigid gauge field configuration to appear not only as a background but also as inducing an instantaneous quark-quark interaction. Both are random in the large N limit. (orig.)
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...
Cross-covariance functions for multivariate random fields based on latent dimensions
Apanasovich, T. V.; Genton, M. G.
2010-01-01
The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable
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...
Quantum beamstrahlung from gaussian bunches
International Nuclear Information System (INIS)
Chen, P.
1987-08-01
The method of Baier and Katkov is applied to calculate the correction terms to the Sokolov-Ternov radiation formula due to the variation of the magnetic field strength along the trajectory of a radiating particle. We carry the calculation up to the second order in the power expansion of B tau/B, where tau is the formation time of radiation. The expression is then used to estimate the quantum beamstrahlung average energy loss from e + e - bunches with gaussian distribution in bunch currents. We show that the effect of the field variation is to reduce the average energy loss from previous calculations based on the Sokolov-Ternov formula or its equivalent. Due to the limitation of our method, only an upper bound of the reduction is obtained. 18 refs
Convergence of posteriors for discretized log Gaussian Cox processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus Plenge
2004-01-01
In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations...... when the cell sizes of the discretization tends to zero. The effect of discretization is studied in a data example....
Diffusion of charged particles in strong large-scale random and regular magnetic fields
International Nuclear Information System (INIS)
Mel'nikov, Yu.P.
2000-01-01
The nonlinear collision integral for the Green's function averaged over a random magnetic field is transformed using an iteration procedure taking account of the strong random scattering of particles on the correlation length of the random magnetic field. Under this transformation the regular magnetic field is assumed to be uniform at distances of the order of the correlation length. The single-particle Green's functions of the scattered particles in the presence of a regular magnetic field are investigated. The transport coefficients are calculated taking account of the broadening of the cyclotron and Cherenkov resonances as a result of strong random scattering. The mean-free path lengths parallel and perpendicular to the regular magnetic field are found for a power-law spectrum of the random field. The analytical results obtained are compared with the experimental data on the transport ranges of solar and galactic cosmic rays in the interplanetary magnetic field. As a result, the conditions for the propagation of cosmic rays in the interplanetary space and a more accurate idea of the structure of the interplanetary magnetic field are determined
Chimera states in Gaussian coupled map lattices
Li, Xiao-Wen; Bi, Ran; Sun, Yue-Xiang; Zhang, Shuo; Song, Qian-Qian
2018-04-01
We study chimera states in one-dimensional and two-dimensional Gaussian coupled map lattices through simulations and experiments. Similar to the case of global coupling oscillators, individual lattices can be regarded as being controlled by a common mean field. A space-dependent order parameter is derived from a self-consistency condition in order to represent the collective state.
Improving the gaussian effective potential: quantum mechanics
International Nuclear Information System (INIS)
Eboli, O.J.P.; Thomaz, M.T.; Lemos, N.A.
1990-08-01
In order to gain intuition for variational problems in field theory, we analyze variationally the quantum-mechanical anharmonic oscillator [(V(x)sup(k) - sub(2) x sup(2) + sup(λ) - sub(4) λ sup(4)]. Special attention is paid to improvements to the Gaussian effective potential. (author)
Restoration of dimensional reduction in the random-field Ising model at five dimensions
Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas
2017-04-01
The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D equality at all studied dimensions.
Gaussian discriminating strength
Rigovacca, L.; Farace, A.; De Pasquale, A.; Giovannetti, V.
2015-10-01
We present a quantifier of nonclassical correlations for bipartite, multimode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in Farace et al., [New J. Phys. 16, 073010 (2014), 10.1088/1367-2630/16/7/073010]. As the latter the new measure exploits the quantum Chernoff bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam splitter a factorized two-mode thermal state. For these density matrices, we study how nonclassical correlations are related with the entanglement present in the system and with its total photon number.
Kinetic Theory of Electronic Transport in Random Magnetic Fields
Lucas, Andrew
2018-03-01
We present the theory of quasiparticle transport in perturbatively small inhomogeneous magnetic fields across the ballistic-to-hydrodynamic crossover. In the hydrodynamic limit, the resistivity ρ generically grows proportionally to the rate of momentum-conserving electron-electron collisions at large enough temperatures T . In particular, the resulting flow of electrons provides a simple scenario where viscous effects suppress conductance below the ballistic value. This new mechanism for ρ ∝T2 resistivity in a Fermi liquid may describe low T transport in single-band SrTiO3 .
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...
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.
A Gaussian graphical model approach to climate networks
International Nuclear Information System (INIS)
Zerenner, Tanja; Friederichs, Petra; Hense, Andreas; Lehnertz, Klaus
2014-01-01
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
Replica field theory for a polymer in random media
International Nuclear Information System (INIS)
Goldschmidt, Yadin Y.
2000-01-01
In this paper we revisit the problem of a (non-self-avoiding) polymer chain in a random medium which was previously investigated by Edwards and Muthukumar (EM) [J. Chem. Phys. 89, 2435 (1988)]. As noticed by Cates and Ball (CB) [J. Phys. (France) 49, 2009 (1988)] there is a discrepancy between the predictions of the replica calculation of EM and the expectation that in an infinite medium the quenched and annealed results should coincide (for a chain that is free to move) and a long polymer should always collapse. CB argued that only in a finite volume one might see a ''localization transition'' (or crossover) from a stretched to a collapsed chain in three spatial dimensions. Here we carry out the replica calculation in the presence of an additional confining harmonic potential that mimics the effect of a finite volume. Using a variational scheme with five variational parameters we derive analytically for d -1/(4-d) ∼(g ln V) -1/(4-d) , where R is the radius of gyration, g is the strength of the disorder, μ is the spring constant associated with the confining potential, and V is the associated effective volume of the system. Thus the EM result is recovered with their constant replaced by ln V as argued by CB. We see that in the strict infinite volume limit the polymer always collapses, but for finite volume a transition from a stretched to a collapsed form might be observed as a function of the strength of the disorder. For d V ' ∼exp(g 2/(2-d) L (4-d)/(2-d) ) the annealed results are recovered and R∼(Lg) 1/(d-2) , where L is the length of the polymer. Hence the polymer also collapses in the large L limit. The one-step replica symmetry breaking solution is crucial for obtaining the above results. (c) 2000 The American Physical Society
First steps towards a state classification in the random-field Ising model
International Nuclear Information System (INIS)
Basso, Vittorio; Magni, Alessandro; Bertotti, Giorgio
2006-01-01
The properties of locally stable states of the random-field Ising model are studied. A map is defined for the dynamics driven by the field starting from a locally stable state. The fixed points of the map are connected with the limit hysteresis loops that appear in the classification of the states
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
Depth images have granted new possibilities to computer vision researchers across the field. A prominent task is scene understanding and segmentation on which the present work is concerned. In this paper, we present a procedure combining well known methods in a unified learning framework based on...
International Nuclear Information System (INIS)
Braginsky, V.B.; Kardashev, N.S.; Polnarev, A.G.; Novikov, I.D.
1989-12-01
Propagation of an electromagnetic wave in the field of gravitational waves is considered. Attention is given to the principal difference between the electromagnetic wave propagation in the field of random gravitational waves and the electromagnetic wave propagation in a medium with a randomly-inhomogeneous refraction index. It is shown that in the case of the gravitation wave field the phase shift of an electromagnetic wave does not increase with distance. The capability of space radio interferometry to detect relic gravitational waves as well as gravitational wave bursts of non cosmological origin are analyzed. (author). 64 refs, 2 figs
International Nuclear Information System (INIS)
Liu Shixiong; Guo Hong; Liu Mingwei; Wu Guohua
2004-01-01
Propagation characteristics of focused Gaussian beam (FoGB) and fundamental Gaussian beam (FuGB) propagating in vacuum are investigated. Based on the Fourier transform and the angular spectral analysis, the transverse component and the second-order approximate longitudinal component of the electric field are obtained in the paraxial approximation. The electric field components, the phase velocity and the group velocity of FoGB are compared with those of FuGB. The spot size of FoGB is also discussed
Interconversion of pure Gaussian states requiring non-Gaussian operations
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2015-01-01
We analyze the conditions under which local operations and classical communication enable entanglement transformations between bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found [G. Giedke et al., Quant. Inf. Comput. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 ×2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other.
Kernel-Correlated Lévy Field Driven Forward Rate and Application to Derivative Pricing
International Nuclear Information System (INIS)
Bo Lijun; Wang Yongjin; Yang Xuewei
2013-01-01
We propose a term structure of forward rates driven by a kernel-correlated Lévy random field under the HJM framework. The kernel-correlated Lévy random field is composed of a kernel-correlated Gaussian random field and a centered Poisson random measure. We shall give a criterion to preclude arbitrage under the risk-neutral pricing measure. As applications, an interest rate derivative with general payoff functional is priced under this pricing measure
Kernel-Correlated Levy Field Driven Forward Rate and Application to Derivative Pricing
Energy Technology Data Exchange (ETDEWEB)
Bo Lijun [Xidian University, Department of Mathematics (China); Wang Yongjin [Nankai University, School of Business (China); Yang Xuewei, E-mail: xwyangnk@yahoo.com.cn [Nanjing University, School of Management and Engineering (China)
2013-08-01
We propose a term structure of forward rates driven by a kernel-correlated Levy random field under the HJM framework. The kernel-correlated Levy random field is composed of a kernel-correlated Gaussian random field and a centered Poisson random measure. We shall give a criterion to preclude arbitrage under the risk-neutral pricing measure. As applications, an interest rate derivative with general payoff functional is priced under this pricing measure.
Analysis of multi-species point patterns using multivariate log Gaussian Cox processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus; Guan, Yongtao; Jalilian, Abdollah
Multivariate log Gaussian Cox processes are flexible models for multivariate point patterns. However, they have so far only been applied in bivariate cases. In this paper we move beyond the bivariate case in order to model multi-species point patterns of tree locations. In particular we address t...... of the data. The selected number of common latent fields provides an index of complexity of the multivariate covariance structure. Hierarchical clustering is used to identify groups of species with similar patterns of dependence on the common latent fields.......Multivariate log Gaussian Cox processes are flexible models for multivariate point patterns. However, they have so far only been applied in bivariate cases. In this paper we move beyond the bivariate case in order to model multi-species point patterns of tree locations. In particular we address...... the problems of identifying parsimonious models and of extracting biologically relevant information from the fitted models. The latent multivariate Gaussian field is decomposed into components given in terms of random fields common to all species and components which are species specific. This allows...
Simple form for the Gaussian equations in curved space
International Nuclear Information System (INIS)
Mazzitelli, F.D.; Paz, J.P.
1988-01-01
We show that the variational Gaussian equations for λphi 4 theory in an arbitrary background gravitational field admit a simple form, which allows the use of a Schwinger-DeWitt-type expansion in order to renormalize them
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.
Properties of a random bond Ising chain in a magnetic field
International Nuclear Information System (INIS)
Landau, D.P.; Blume, M.
1976-01-01
The Ising chain with random bonds in a magnetic field H = -Σ/sub i/J/sub i/sigma/sub i/sigma/sub i + l/ - hΣ/sub i/sigma/sub i/, where J/sub i/ = +- 1 at random, and Σ/sub i/J/sub i/ = 0, represents a model of a magnetic glass, or of heteropolymer melting. Calculations of the thermodynamic properties of the chain as a function of field strength and temperature have been performed by Monte Carlo techniques. These results are compared with perturbation calculations for small and large values of h/T. The Monte Carlo results show, in agreement with the perturbation calculations, that the field-induced magnetization is generally smaller for the random bond model than for a chain of noninteracting spins. As T → 0 the magnetization approaches the result for noninteracting spins
Random errors in the magnetic field coefficients of superconducting quadrupole magnets
International Nuclear Information System (INIS)
Herrera, J.; Hogue, R.; Prodell, A.; Thompson, P.; Wanderer, P.; Willen, E.
1987-01-01
The random multipole errors of superconducting quadrupoles are studied. For analyzing the multipoles which arise due to random variations in the size and locations of the current blocks, a model is outlined which gives the fractional field coefficients from the current distributions. With this approach, based on the symmetries of the quadrupole magnet, estimates are obtained of the random multipole errors for the arc quadrupoles envisioned for the Relativistic Heavy Ion Collider and for a single-layer quadrupole proposed for the Superconducting Super Collider
Quantum Information Protocols with Gaussian States of Light
DEFF Research Database (Denmark)
Jacobsen, Christian Scheffmann
and hardware for secure quantum key distribution. These technologies directly exploit quantum effects, and indeed this is where they offer advantages to classical products. This thesis deals with the development and implementation of quantum information protocols that utilize the rather inexpensive resource......Quantum cryptography is widely regarded as the most mature field within the context of quantum information in the sense that its application and development has produced companies that base their products on genuine quantum mechanical principles. Examples include quantum random number generators...... of Gaussian states. A quantum information protocol is essentially a sequence of state exchanges between some number of parties and a certain ordering of quantum mechanical unitary operators performed by these parties. An example of this is the famous BB84 protocol for secret key generation, where photons...
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.
Accelerating Sequential Gaussian Simulation with a constant path
Nussbaumer, Raphaël; Mariethoz, Grégoire; Gravey, Mathieu; Gloaguen, Erwan; Holliger, Klaus
2018-03-01
Sequential Gaussian Simulation (SGS) is a stochastic simulation technique commonly employed for generating realizations of Gaussian random fields. Arguably, the main limitation of this technique is the high computational cost associated with determining the kriging weights. This problem is compounded by the fact that often many realizations are required to allow for an adequate uncertainty assessment. A seemingly simple way to address this problem is to keep the same simulation path for all realizations. This results in identical neighbourhood configurations and hence the kriging weights only need to be determined once and can then be re-used in all subsequent realizations. This approach is generally not recommended because it is expected to result in correlation between the realizations. Here, we challenge this common preconception and make the case for the use of a constant path approach in SGS by systematically evaluating the associated benefits and limitations. We present a detailed implementation, particularly regarding parallelization and memory requirements. Extensive numerical tests demonstrate that using a constant path allows for substantial computational gains with very limited loss of simulation accuracy. This is especially the case for a constant multi-grid path. The computational savings can be used to increase the neighbourhood size, thus allowing for a better reproduction of the spatial statistics. The outcome of this study is a recommendation for an optimal implementation of SGS that maximizes accurate reproduction of the covariance structure as well as computational efficiency.
Gibbs perturbations of a two-dimensional gauge field
International Nuclear Information System (INIS)
Petrova, E.N.
1981-01-01
Small Gibbs perturbations of random fields have been investigated up to now for a few initial fields only. Among them there are independent fields, Gaussian fields and some others. The possibility for the investigation of Gibbs modifications of a random field depends essentially on the existence of good estimates for semiinvariants of this field. This is the reason why the class of random fields for which the investigation of Gibbs perturbations with arbitrary potential of bounded support is possible is rather small. The author takes as initial a well-known model: a two-dimensional gauge field. (Auth.)
How Gaussian can our Universe be?
Cabass, G.; Pajer, E.; Schmidt, F.
2017-01-01
Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of kl2/ks2, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × (ns-1).
How Gaussian can our Universe be?
Energy Technology Data Exchange (ETDEWEB)
Cabass, G. [Physics Department and INFN, Università di Roma ' ' La Sapienza' ' , P.le Aldo Moro 2, 00185, Rome (Italy); Pajer, E. [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); Schmidt, F., E-mail: giovanni.cabass@roma1.infn.it, E-mail: e.pajer@uu.nl, E-mail: fabians@mpa-garching.mpg.de [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)
2017-01-01
Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of k {sub ℓ}{sup 2}/ k {sub s} {sup 2}, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × ( n {sub s}−1).
Study of Landau spectrum for a two-dimensional random magnetic field
International Nuclear Information System (INIS)
Furtlehner, C.
1997-01-01
This thesis deals with the two-dimensional problem of a charged particle coupled to a random magnetic field. Various situations are considered, according to the relative importance of the mean value of field and random component. The last one is conceived as a distribution of magnetic impurities (punctual vortex), having various statistical properties (local or non-local correlations, Poisson distribution, etc). The study of this system has led to two distinct situations: - the case of the charged particle feeling the influence of mean field that manifests its presence in the spectrum of broadened Landau levels; - the disordered situation in which the spectrum can be distinguished from the free one only by a low energy Lifshits behaviour. Additional properties are occurring in the limit of 'strong' mean field, namely a non-conventional low energy behaviour (in contrast to Lifshits behaviour) which was interpreted in terms of localized states. (author)
International Nuclear Information System (INIS)
Perez, J.F.; Pontin, L.F.; Segundo, J.A.B.
1985-01-01
Using a method proposed by van Hemmen the free energy of the Curie-Weiss version of the site-dilute antiferromagnetic Ising model is computed, in the presence of an uniform magnetic field. The solution displays an exact correspondence between this model and the Curie-Weiss version of the Ising model in the presence of a random magnetic field. The phase diagrams are discussed and a tricritical point is shown to exist. (Author) [pt
Palm distributions for log Gaussian Cox processes
DEFF Research Database (Denmark)
Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus Plenge
2017-01-01
This paper establishes a remarkable result regarding Palm distributions for a log Gaussian Cox process: the reduced Palm distribution for a log Gaussian Cox process is itself a log Gaussian Cox process that only differs from the original log Gaussian Cox process in the intensity function. This new...... result is used to study functional summaries for log Gaussian Cox processes....
On the unlikeliness of multi-field inflation: bounded random potentials and our vacuum
International Nuclear Information System (INIS)
Battefeld, Diana; Battefeld, Thorsten; Schulz, Sebastian
2012-01-01
Based on random matrix theory, we compute the likelihood of saddles and minima in a class of random potentials that are softly bounded from above and below, as required for the validity of low energy effective theories. Imposing this bound leads to a random mass matrix with non-zero mean of its entries. If the dimensionality of field-space is large, inflation is rare, taking place near a saddle point (if at all), since saddles are more likely than minima or maxima for common values of the potential. Due to the boundedness of the potential, the latter become more ubiquitous for rare low/large values respectively. Based on the observation of a positive cosmological constant, we conclude that the dimensionality of field-space after (and most likely during) inflation has to be low if no anthropic arguments are invoked, since the alternative, encountering a metastable deSitter vacuum by chance, is extremely unlikely
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...
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
Bayesian structure learning for Markov Random Fields with a spike and slab prior
Chen, Y.; Welling, M.; de Freitas, N.; Murphy, K.
2012-01-01
In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of disadvantages such as the inability to assess model uncertainty and
Joint modeling of ChIP-seq data via a Markov random field model
Bao, Yanchun; Vinciotti, Veronica; Wit, Ernst; 't Hoen, Peter A C
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
Random model of two-level atoms interacting with electromagnetic field
International Nuclear Information System (INIS)
Kireev, A.N.; Meleshko, A.N.
1983-12-01
A phase transition has been studied in a random system of two-level atoms interacting with an electromagnetic field. It is shown that superradiation can arise when there is short-range order in a spin-subsystem. The existence of long-range order is irrelevant for this phase transition
The limiting behavior of the estimated parameters in a misspecified random field regression model
DEFF Research Database (Denmark)
Dahl, Christian Møller; Qin, Yu
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 n...
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 mom...
Geometry of Gaussian quantum states
International Nuclear Information System (INIS)
Link, Valentin; Strunz, Walter T
2015-01-01
We study the Hilbert–Schmidt measure on the manifold of mixed Gaussian states in multi-mode continuous variable quantum systems. An analytical expression for the Hilbert–Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert–Schmidt measure. (paper)
Coupé, Christophe
2018-01-01
As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM), which address grouping of observations, and generalized linear mixed-effects models (GLMM), which offer a family of distributions for the dependent variable. Generalized additive models (GAM) are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS). We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for 'difficult' variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships. Relying on GAMLSS, we
Directory of Open Access Journals (Sweden)
Christophe Coupé
2018-04-01
Full Text Available As statistical approaches are getting increasingly used in linguistics, attention must be paid to the choice of methods and algorithms used. This is especially true since they require assumptions to be satisfied to provide valid results, and because scientific articles still often fall short of reporting whether such assumptions are met. Progress is being, however, made in various directions, one of them being the introduction of techniques able to model data that cannot be properly analyzed with simpler linear regression models. We report recent advances in statistical modeling in linguistics. We first describe linear mixed-effects regression models (LMM, which address grouping of observations, and generalized linear mixed-effects models (GLMM, which offer a family of distributions for the dependent variable. Generalized additive models (GAM are then introduced, which allow modeling non-linear parametric or non-parametric relationships between the dependent variable and the predictors. We then highlight the possibilities offered by generalized additive models for location, scale, and shape (GAMLSS. We explain how they make it possible to go beyond common distributions, such as Gaussian or Poisson, and offer the appropriate inferential framework to account for ‘difficult’ variables such as count data with strong overdispersion. We also demonstrate how they offer interesting perspectives on data when not only the mean of the dependent variable is modeled, but also its variance, skewness, and kurtosis. As an illustration, the case of phonemic inventory size is analyzed throughout the article. For over 1,500 languages, we consider as predictors the number of speakers, the distance from Africa, an estimation of the intensity of language contact, and linguistic relationships. We discuss the use of random effects to account for genealogical relationships, the choice of appropriate distributions to model count data, and non-linear relationships
MULTITEMPORAL CROP TYPE CLASSIFICATION USING CONDITIONAL RANDOM FIELDS AND RAPIDEYE DATA
Directory of Open Access Journals (Sweden)
T. Hoberg
2012-09-01
Full Text Available The task of crop type classification with multitemporal imagery is nowadays often done applying classifiers that are originally developed for single images like support vector machines (SVM. These approaches do not model temporal dependencies in an explicit way. Existing approaches that make use of temporal dependencies are in most cases quite simple and based on rules. Approaches that integrate temporal dependencies to statistical models are very rare and at an early stage of development. Here our approach CRFmulti, based on conditional random fields (CRF, should make a contribution. Conditional random fields consider context knowledge among neighboring primitives in the same way as Markov random fields (MRF do. Furthermore conditional random fields handle the feature vectors of the neighboring primitives and not only the class labels. Additional to taking spatial context into account, we present an approach for multitemporal data processing where a temporal association potential has been integrated to the common CRF approach to model temporal dependencies. The classification works on pixel ‐level using spectral image features, whereas all available single images are taken separately. For our experiments a high resolution RapidEye satellite data set of 2010 consisting of 4 images made during the whole vegetation period from April to October is taken. Six crop type categories are distinguished, namely grassland, corn, winter crop, rapeseed, root crops and other crops. To evaluate the potential of the new conditional random field approach the classification result is compared to a manual reference on pixel‐ and on object‐level. Additional a SVM approach is applied under the same conditions and should serve as a benchmark.
Cosmological information in Gaussianized weak lensing signals
Joachimi, B.; Taylor, A. N.; Kiessling, A.
2011-11-01
Gaussianizing the one-point distribution of the weak gravitational lensing convergence has recently been shown to increase the signal-to-noise ratio contained in two-point statistics. We investigate the information on cosmology that can be extracted from the transformed convergence fields. Employing Box-Cox transformations to determine optimal transformations to Gaussianity, we develop analytical models for the transformed power spectrum, including effects of noise and smoothing. We find that optimized Box-Cox transformations perform substantially better than an offset logarithmic transformation in Gaussianizing the convergence, but both yield very similar results for the signal-to-noise ratio. None of the transformations is capable of eliminating correlations of the power spectra between different angular frequencies, which we demonstrate to have a significant impact on the errors in cosmology. Analytic models of the Gaussianized power spectrum yield good fits to the simulations and produce unbiased parameter estimates in the majority of cases, where the exceptions can be traced back to the limitations in modelling the higher order correlations of the original convergence. In the ideal case, without galaxy shape noise, we find an increase in the cumulative signal-to-noise ratio by a factor of 2.6 for angular frequencies up to ℓ= 1500, and a decrease in the area of the confidence region in the Ωm-σ8 plane, measured in terms of q-values, by a factor of 4.4 for the best performing transformation. When adding a realistic level of shape noise, all transformations perform poorly with little decorrelation of angular frequencies, a maximum increase in signal-to-noise ratio of 34 per cent, and even slightly degraded errors on cosmological parameters. We argue that to find Gaussianizing transformations of practical use, it will be necessary to go beyond transformations of the one-point distribution of the convergence, extend the analysis deeper into the non
Controllable gaussian-qubit interface for extremal quantum state engineering.
Adesso, Gerardo; Campbell, Steve; Illuminati, Fabrizio; Paternostro, Mauro
2010-06-18
We study state engineering through bilinear interactions between two remote qubits and two-mode gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.
3D vector distribution of the electro-magnetic fields on a random gold film
Canneson, Damien; Berini, Bruno; Buil, Stéphanie; Hermier, Jean-Pierre; Quélin, Xavier
2018-05-01
The 3D vector distribution of the electro-magnetic fields at the very close vicinity of the surface of a random gold film is studied. Such films are well known for their properties of light confinement and large fluctuations of local density of optical states. Using Finite-Difference Time-Domain simulations, we show that it is possible to determine the local orientation of the electro-magnetic fields. This allows us to obtain a complete characterization of the fields. Large fluctuations of their amplitude are observed as previously shown. Here, we demonstrate large variations of their direction depending both on the position on the random gold film, and on the distance to it. Such characterization could be useful for a better understanding of applications like the coupling of point-like dipoles to such films.
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....
Resource theory of non-Gaussian operations
Zhuang, Quntao; Shor, Peter W.; Shapiro, Jeffrey H.
2018-05-01
Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.
Manoussakis, G.; Delikaraoglou, D.
2011-01-01
In this paper we form relations for the determination of the elements of the E\\"otv\\"os matrix of the Earth's normal gravity field. In addition a relation between the Gauss curvature of the normal equipotential surface and the Gauss curvature of the actual equipotential surface both passing through the point P is presented. For this purpose we use a global Cartesian system (X, Y, Z) and use the variables X, and Y to form a local parameterization a normal equipotential surface to describe its ...
Scaled unscented transform Gaussian sum filter: Theory and application
Luo, Xiaodong
2010-05-01
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]). In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel. As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to
Non-Gaussian conductivity fluctuations in semiconductors
International Nuclear Information System (INIS)
Melkonyan, S.V.
2010-01-01
A theoretical study is presented on the statistical properties of conductivity fluctuations caused by concentration and mobility fluctuations of the current carriers. It is established that mobility fluctuations result from random deviations in the thermal equilibrium distribution of the carriers. It is shown that mobility fluctuations have generation-recombination and shot components which do not satisfy the requirements of the central limit theorem, in contrast to the current carrier's concentration fluctuation and intraband component of the mobility fluctuation. It is shown that in general the mobility fluctuation consist of thermal (or intraband) Gaussian and non-thermal (or generation-recombination, shot, etc.) non-Gaussian components. The analyses of theoretical results and experimental data from literature show that the statistical properties of mobility fluctuation and of 1/f-noise fully coincide. The deviation from Gaussian statistics of the mobility or 1/f fluctuations goes hand in hand with the magnitude of non-thermal noise (generation-recombination, shot, burst, pulse noises, etc.).
Frisch, H.; Anusha, L. S.; Sampoorna, M.; Nagendra, K. N.
2009-07-01
Context: The Hanle effect is used to determine weak turbulent magnetic fields in the solar atmosphere, usually assuming that the angular distribution is isotropic, the magnetic field strength constant, and that micro-turbulence holds, i.e. that the magnetic field correlation length is much less than a photon mean free path. Aims: To examine the sensitivity of turbulent magnetic field measurements to these assumptions, we study the dependence of Hanle effect on the magnetic field correlation length, its angular, and strength distributions. Methods: We introduce a fairly general random magnetic field model characterized by a correlation length and a magnetic field vector distribution. Micro-turbulence is recovered when the correlation length goes to zero and macro-turbulence when it goes to infinity. Radiative transfer equations are established for the calculation of the mean Stokes parameters and they are solved numerically by a polarized approximate lambda iteration method. Results: We show that optically thin spectral lines and optically very thick ones are insensitive to the correlation length of the magnetic field, while spectral lines with intermediate optical depths (around 10-100) show some sensitivity to this parameter. The result is interpreted in terms of the mean number of scattering events needed to create the surface polarization. It is shown that the single-scattering approximation holds good for thin and thick lines but may fail for lines with intermediate thickness. The dependence of the polarization on the magnetic field vector probability density function (PDF) is examined in the micro-turbulent limit. A few PDFs with different angular and strength distributions, but equal mean value of the magnetic field, are considered. It is found that the polarization is in general quite sensitive to the shape of the magnetic field strength PDF and somewhat to the angular distribution. Conclusions: The mean field derived from Hanle effect analysis of
Handbook of Gaussian basis sets
International Nuclear Information System (INIS)
Poirier, R.; Kari, R.; Csizmadia, I.G.
1985-01-01
A collection of a large body of information is presented useful for chemists involved in molecular Gaussian computations. Every effort has been made by the authors to collect all available data for cartesian Gaussian as found in the literature up to July of 1984. The data in this text includes a large collection of polarization function exponents but in this case the collection is not complete. Exponents for Slater type orbitals (STO) were included for completeness. This text offers a collection of Gaussian exponents primarily without criticism. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Zaim, N.; Zaim, A., E-mail: ah_zaim@yahoo.fr; Kerouad, M., E-mail: kerouad@fs-umi.ac.ma
2017-02-15
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 J{sub s} 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. - Highlights: • Phase diagrams of a ferromagnetic nanowire are examined by the Monte Carlo simulation. • Different types of the phase diagrams are obtained. • The effect of the random crystal field on the hysteresis loops is studied. • Single, double and para hysteresis regions are explicitly determined.
International Nuclear Information System (INIS)
Yu, Jie; Chen, Kuilin; Mori, Junichi; Rashid, Mudassir M.
2013-01-01
Optimizing wind power generation and controlling the operation of wind turbines to efficiently harness the renewable wind energy is a challenging task due to the intermittency and unpredictable nature of wind speed, which has significant influence on wind power production. A new approach for long-term wind speed forecasting is developed in this study by integrating GMCM (Gaussian mixture copula model) and localized GPR (Gaussian process regression). The time series of wind speed is first classified into multiple non-Gaussian components through the Gaussian mixture copula model and then Bayesian inference strategy is employed to incorporate the various non-Gaussian components using the posterior probabilities. Further, the localized Gaussian process regression models corresponding to different non-Gaussian components are built to characterize the stochastic uncertainty and non-stationary seasonality of the wind speed data. The various localized GPR models are integrated through the posterior probabilities as the weightings so that a global predictive model is developed for the prediction of wind speed. The proposed GMCM–GPR approach is demonstrated using wind speed data from various wind farm locations and compared against the GMCM-based ARIMA (auto-regressive integrated moving average) and SVR (support vector regression) methods. In contrast to GMCM–ARIMA and GMCM–SVR methods, the proposed GMCM–GPR model is able to well characterize the multi-seasonality and uncertainty of wind speed series for accurate long-term prediction. - Highlights: • A novel predictive modeling method is proposed for long-term wind speed forecasting. • Gaussian mixture copula model is estimated to characterize the multi-seasonality. • Localized Gaussian process regression models can deal with the random uncertainty. • Multiple GPR models are integrated through Bayesian inference strategy. • The proposed approach shows higher prediction accuracy and reliability
International Nuclear Information System (INIS)
Artaud, J.F.
1994-01-01
The main themes of this thesis are: review of superconductivity principles; critical current in a random orientation magnetic field; the MHD model applied to superconductors (with comprehensive calculation of the field in a plate type conductor); the magnetization created by a variation of a random orientation magnetic field; the electric field in a superconductor in steady or quasi-steady state (MHD displacement, pinning and thermal effects). 145 figs., 166 refs
Random walk loop soups and conformal loop ensembles
van de Brug, T.; Camia, F.; Lis, M.
2016-01-01
The random walk loop soup is a Poissonian ensemble of lattice loops; it has been extensively studied because of its connections to the discrete Gaussian free field, but was originally introduced by Lawler and Trujillo Ferreras as a discrete version of the Brownian loop soup of Lawler and Werner, a
Endogenous fields enhanced stochastic resonance in a randomly coupled neuronal network
International Nuclear Information System (INIS)
Deng, Bin; Wang, Lin; Wang, Jiang; Wei, Xi-le; Yu, Hai-tao
2014-01-01
Highlights: • We study effects of endogenous fields on stochastic resonance in a neural network. • Stochastic resonance can be notably enhanced by endogenous field feedback. • Endogenous field feedback delay plays a vital role in stochastic resonance. • The parameters of low-passed filter play a subtle role in SR. - Abstract: Endogenous field, evoked by structured neuronal network activity in vivo, is correlated with many vital neuronal processes. In this paper, the effects of endogenous fields on stochastic resonance (SR) in a randomly connected neuronal network are investigated. The network consists of excitatory and inhibitory neurons and the axonal conduction delays between neurons are also considered. Numerical results elucidate that endogenous field feedback results in more rhythmic macroscope activation of the network for proper time delay and feedback coefficient. The response of the network to the weak periodic stimulation can be notably enhanced by endogenous field feedback. Moreover, the endogenous field feedback delay plays a vital role in SR. We reveal that appropriately tuned delays of the feedback can either induce the enhancement of SR, appearing at every integer multiple of the weak input signal’s oscillation period, or the depression of SR, appearing at every integer multiple of half the weak input signal’s oscillation period for the same feedback coefficient. Interestingly, the parameters of low-passed filter which is used in obtaining the endogenous field feedback signal play a subtle role in SR
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.
Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces
International Nuclear Information System (INIS)
Khrennikov, Andrei
2010-01-01
One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical random fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.
Analysis of family-wise error rates in statistical parametric mapping using random field theory.
Flandin, Guillaume; Friston, Karl J
2017-11-01
This technical report revisits the analysis of family-wise error rates in statistical parametric mapping-using random field theory-reported in (Eklund et al. []: arXiv 1511.01863). Contrary to the understandable spin that these sorts of analyses attract, a review of their results suggests that they endorse the use of parametric assumptions-and random field theory-in the analysis of functional neuroimaging data. We briefly rehearse the advantages parametric analyses offer over nonparametric alternatives and then unpack the implications of (Eklund et al. []: arXiv 1511.01863) for parametric procedures. Hum Brain Mapp, 2017. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.
Random crystal field effects on the integer and half-integer mixed-spin system
Yigit, Ali; Albayrak, Erhan
2018-05-01
In this work, we have focused on the random crystal field effects on the phase diagrams of the mixed spin-1 and spin-5/2 Ising system obtained by utilizing the exact recursion relations (ERR) on the Bethe lattice (BL). The distribution function P(Di) = pδ [Di - D(1 + α) ] +(1 - p) δ [Di - D(1 - α) ] is used to randomize the crystal field.The phase diagrams are found to exhibit second- and first-order phase transitions depending on the values of α, D and p. It is also observed that the model displays tricritical point, isolated point, critical end point and three compensation temperatures for suitable values of the system parameters.
The phase diagrams of a ferromagnetic thin film in a random magnetic field
Energy Technology Data Exchange (ETDEWEB)
Zaim, N.; Zaim, A., E-mail: ah_zaim@yahoo.fr; Kerouad, M., E-mail: m.kerouad@fs-umi.ac.ma
2016-10-07
In this paper, the magnetic properties and the phase diagrams of a ferromagnetic thin film with a thickness N in a random magnetic field (RMF) are investigated by using the Monte Carlo simulation technique based on the Metropolis algorithm. The effects of the RMF and the surface exchange interaction on the critical behavior are studied. A variety of multicritical points such as tricritical points, isolated critical points, and triple points are obtained. It is also found that the double reentrant phenomenon can appear for appropriate values of the system parameters. - Highlights: • Phase diagrams of a ferromagnetic thin film are examined by the Monte Carlo simulation. • The effect of the random magnetic field on the magnetic properties is studied. • Different types of the phase diagrams are obtained. • The dependence of the magnetization and susceptibility on the temperature are investigated.
Theoretical analysis of non-Gaussian heterogeneity effects on subsurface flow and transport
Riva, Monica; Guadagnini, Alberto; Neuman, Shlomo P.
2017-04-01
Much of the stochastic groundwater literature is devoted to the analysis of flow and transport in Gaussian or multi-Gaussian log hydraulic conductivity (or transmissivity) fields, Y(x)=ln\\func K(x) (x being a position vector), characterized by one or (less frequently) a multiplicity of spatial correlation scales. Yet Y and many other variables and their (spatial or temporal) increments, ΔY, are known to be generally non-Gaussian. One common manifestation of non-Gaussianity is that whereas frequency distributions of Y often exhibit mild peaks and light tails, those of increments ΔY are generally symmetric with peaks that grow sharper, and tails that become heavier, as separation scale or lag between pairs of Y values decreases. A statistical model that captures these disparate, scale-dependent distributions of Y and ΔY in a unified and consistent manner has been recently proposed by us. This new "generalized sub-Gaussian (GSG)" model has the form Y(x)=U(x)G(x) where G(x) is (generally, but not necessarily) a multiscale Gaussian random field and U(x) is a nonnegative subordinator independent of G. The purpose of this paper is to explore analytically, in an elementary manner, lead-order effects that non-Gaussian heterogeneity described by the GSG model have on the stochastic description of flow and transport. Recognizing that perturbation expansion of hydraulic conductivity K=eY diverges when Y is sub-Gaussian, we render the expansion convergent by truncating Y's domain of definition. We then demonstrate theoretically and illustrate by way of numerical examples that, as the domain of truncation expands, (a) the variance of truncated Y (denoted by Yt) approaches that of Y and (b) the pdf (and thereby moments) of Yt increments approach those of Y increments and, as a consequence, the variogram of Yt approaches that of Y. This in turn guarantees that perturbing Kt=etY to second order in σYt (the standard deviation of Yt) yields results which approach those we obtain
Quantum Field Theory of Black-Swan Events
Kleinert, H.
2014-05-01
Free and weakly interacting particles are described by a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. They describe Gaussian random walks with collisions. By contrast, the fields of strongly interacting particles are governed by effective actions, whose extremum yields fractional field equations. Their particle orbits perform universal Lévy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong windgusts, monster or rogue waves, earthquakes, and financial crashes. While earthquakes may destroy entire cities, the latter have the potential of devastating entire economies.
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...
Prediction of the spatial occurrence of fire induced spalling in concrete slabs using random fields
Directory of Open Access Journals (Sweden)
Van Coile R.
2013-09-01
Full Text Available As the loss of concrete cover can significantly influence the reliability of concrete elements during fire, spalling should be taken into account when performing reliability calculations. However, the occurrence and spatial variation of spalling are highly uncertain. A first step towards a probabilistic analysis of spalling is made by combining existing deterministic models with a stochastic representation of the concrete tensile strength and by using random fields to model the tensile strength spatial variation.
Application of the random field theory in PET imaging - injection dose optimization
Czech Academy of Sciences Publication Activity Database
Dvořák, Jiří; Boldyš, Jiří; Skopalová, M.; Bělohlávek, O.
2013-01-01
Roč. 49, č. 2 (2013), s. 280-300 ISSN 0023-5954 R&D Projects: GA MŠk 1M0572 Institutional support: RVO:67985556 Keywords : random field theory * Euler characteristic * PET imaging * PET image quality Subject RIV: BD - Theory of Information Impact factor: 0.563, year: 2013 http://library.utia.cas.cz/separaty/2013/ZOI/boldys-0397176.pdf
Boruch, R F; Mcsweeny, A J; Soderstrom, E J
1978-11-01
This bibliography lists references to over 300 field experiments undertaken in schools, hospitals, prisons, and other social settings, mainly in the U.S. The list is divided into 10 major categories corresponding to the type of program under examination. They include: criminal and civil justice programs, mental health, training and education, mass media, information collection, utilization, commerce and industry, welfare, health, and family planning. The main purpose of the bibliography is to provide evidence on feasibility and scope of randomized field tests, since despite their advantages, it is not always clear from managerial, political, and other constraints on research that they can be mounted. Dates of publications range from 1944 to 1978.
Statistical Shape Modelling and Markov Random Field Restoration (invited tutorial and exercise)
DEFF Research Database (Denmark)
Hilger, Klaus Baggesen
This tutorial focuses on statistical shape analysis using point distribution models (PDM) which is widely used in modelling biological shape variability over a set of annotated training data. Furthermore, Active Shape Models (ASM) and Active Appearance Models (AAM) are based on PDMs and have proven...... deformation field between shapes. The tutorial demonstrates both generative active shape and appearance models, and MRF restoration on 3D polygonized surfaces. ''Exercise: Spectral-Spatial classification of multivariate images'' From annotated training data this exercise applies spatial image restoration...... using Markov random field relaxation of a spectral classifier. Keywords: the Ising model, the Potts model, stochastic sampling, discriminant analysis, expectation maximization....
A Unified 3D Mesh Segmentation Framework Based on Markov Random Field
Z.F. Shi; L.Y. Lu; D. Le; X.M. Niu
2012-01-01
3D Mesh segmentation has become an important research field in computer graphics during the past decades. Many geometry based and semantic oriented approaches for 3D mesh segmentation has been presented. In this paper, we present a definition of mesh segmentation according to labeling problem. Inspired by the Markov Random Field (MRF) based image segmentation, we propose a new framework of 3D mesh segmentation based on MRF and use graph cuts to solve it. Any features of 3D mesh can be integra...
Lifetime, turnover time, and fast magnetic field regeneration in random flows
International Nuclear Information System (INIS)
Tanner, S. E. M.
2007-01-01
The fast dynamo is thought to be relevant in the regeneration of magnetic fields in astrophysics where the value of the magnetic Reynolds number (Rm) is immense. The fast dynamo picture is one in which chaotic flows provide a mechanism for the stretching of magnetic field lines. Furthermore, a cascade of energy down to small scales results in intermittent regions of a small-scale, intense magnetic field. Given this scenario it is natural to invoke the use of kinematic random flows in order to understand field regeneration mechanisms better. Here a family of random flows is used to study the effects that L, the lifetime of the cell, and τ, the turnover time of the cell, may have on magnetic field regeneration. Defining the parameter Γ=L/τ, it has been varied according to Γ>1, Γ<1, Γ∼O(1). In the kinematic regime, dynamo growth rates and Lyapunov exponents are examined at varying values of Rm. The possibility of fast dynamo action is considered. In the nonlinear regime, magnetic and kinetic energies are examined. Results indicate that there does appear to be a relationship between Γ and dynamo efficiency. In particular, the most efficient dynamos seem to operate at lower values of Γ
Earl, James A.
1992-01-01
When charged particles spiral along a large constant magnetic field, their trajectories are scattered by any random field components that are superposed on the guiding field. If the random field configuration embodies helicity, the scattering is asymmetrical with respect to a plane perpendicular to the guiding field, for particles moving into the forward hemisphere are scattered at different rates from those moving into the backward hemisphere. This asymmetry gives rise to new terms in the transport equations that describe propagation of charged particles. Helicity has virtually no impact on qualitative features of the diffusive mode of propagation. However, characteristic velocities of the coherent modes that appear after a highly anisotropic injection exhibit an asymmetry related to helicity. Explicit formulas, which embody the effects of helicity, are given for the anisotropies, the coefficient diffusion, and the coherent velocities. Predictions derived from these expressions are in good agreement with Monte Carlo simulations of particle transport, but the simulations reveal certain phenomena whose explanation calls for further analytical work.
Hong, Liang
2013-10-01
The availability of high spatial resolution remote sensing data provides new opportunities for urban land-cover classification. More geometric details can be observed in the high resolution remote sensing image, Also Ground objects in the high resolution remote sensing image have displayed rich texture, structure, shape and hierarchical semantic characters. More landscape elements are represented by a small group of pixels. Recently years, the an object-based remote sensing analysis methodology is widely accepted and applied in high resolution remote sensing image processing. The classification method based on Geo-ontology and conditional random fields is presented in this paper. The proposed method is made up of four blocks: (1) the hierarchical ground objects semantic framework is constructed based on geoontology; (2) segmentation by mean-shift algorithm, which image objects are generated. And the mean-shift method is to get boundary preserved and spectrally homogeneous over-segmentation regions ;(3) the relations between the hierarchical ground objects semantic and over-segmentation regions are defined based on conditional random fields framework ;(4) the hierarchical classification results are obtained based on geo-ontology and conditional random fields. Finally, high-resolution remote sensed image data -GeoEye, is used to testify the performance of the presented method. And the experimental results have shown the superiority of this method to the eCognition method both on the effectively and accuracy, which implies it is suitable for the classification of high resolution remote sensing image.
Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin
2018-02-01
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.
Directory of Open Access Journals (Sweden)
Jaewook Jung
2016-12-01
Full Text Available Railways have been used as one of the most crucial means of transportation in public mobility and economic development. For safe railway operation, the electrification system in the railway infrastructure, which supplies electric power to trains, is an essential facility for stable train operation. Due to its important role, the electrification system needs to be rigorously and regularly inspected and managed. This paper presents a supervised learning method to classify Mobile Laser Scanning (MLS data into ten target classes representing overhead wires, movable brackets and poles, which are key objects in the electrification system. In general, the layout of the railway electrification system shows strong spatial regularity relations among object classes. The proposed classifier is developed based on Conditional Random Field (CRF, which characterizes not only labeling homogeneity at short range, but also the layout compatibility between different object classes at long range in the probabilistic graphical model. This multi-range CRF model consists of a unary term and three pairwise contextual terms. In order to gain computational efficiency, MLS point clouds are converted into a set of line segments to which the labeling process is applied. Support Vector Machine (SVM is used as a local classifier considering only node features for producing the unary potentials of the CRF model. As the short-range pairwise contextual term, the Potts model is applied to enforce a local smoothness in the short-range graph; while long-range pairwise potentials are designed to enhance the spatial regularities of both horizontal and vertical layouts among railway objects. We formulate two long-range pairwise potentials as the log posterior probability obtained by the naive Bayes classifier. The directional layout compatibilities are characterized in probability look-up tables, which represent the co-occurrence rate of spatial relations in the horizontal and vertical
Wang, Hui; Wellmann, Florian; Verweij, Elizabeth; von Hebel, Christian; van der Kruk, Jan
2017-04-01
Lateral and vertical spatial heterogeneity of subsurface properties such as soil texture and structure influences the available water and resource supply for crop growth. High-resolution mapping of subsurface structures using non-invasive geo-referenced geophysical measurements, like electromagnetic induction (EMI), enables a characterization of 3D soil structures, which have shown correlations to remote sensing information of the crop states. The benefit of EMI is that it can return 3D subsurface information, however the spatial dimensions are limited due to the labor intensive measurement procedure. Although active and passive sensors mounted on air- or space-borne platforms return 2D images, they have much larger spatial dimensions. Combining both approaches provides us with a potential pathway to extend the detailed 3D geophysical information to a larger area by using remote sensing information. In this study, we aim at extracting and providing insights into the spatial and statistical correlation of the geophysical and remote sensing observations of the soil/vegetation continuum system. To this end, two key points need to be addressed: 1) how to detect and recognize the geometric patterns (i.e., spatial heterogeneity) from multiple data sets, and 2) how to quantitatively describe the statistical correlation between remote sensing information and geophysical measurements. In the current study, the spatial domain is restricted to shallow depths up to 3 meters, and the geostatistical database contains normalized difference vegetation index (NDVI) derived from RapidEye satellite images and apparent electrical conductivities (ECa) measured from multi-receiver EMI sensors for nine depths of exploration ranging from 0-2.7 m. The integrated data sets are mapped into both the physical space (i.e. the spatial domain) and feature space (i.e. a two-dimensional space framed by the NDVI and the ECa data). Hidden Markov Random Fields (HMRF) are employed to model the
Scalable Gaussian Processes and the search for exoplanets
CERN. Geneva
2015-01-01
Gaussian Processes are a class of non-parametric models that are often used to model stochastic behavior in time series or spatial data. A major limitation for the application of these models to large datasets is the computational cost. The cost of a single evaluation of the model likelihood scales as the third power of the number of data points. In the search for transiting exoplanets, the datasets of interest have tens of thousands to millions of measurements with uneven sampling, rendering naive application of a Gaussian Process model impractical. To attack this problem, we have developed robust approximate methods for Gaussian Process regression that can be applied at this scale. I will describe the general problem of Gaussian Process regression and offer several applicable use cases. Finally, I will present our work on scaling this model to the exciting field of exoplanet discovery and introduce a well-tested open source implementation of these new methods.
Imprint of primordial non-Gaussianity on dark matter halo profiles
Energy Technology Data Exchange (ETDEWEB)
Dizgah, Azadeh Moradinezhad; Dodelson, Scott; Riotto, Antonio
2013-09-01
We study the impact of primordial non-Gaussianity on the density profile of dark matter halos by using the semi-analytical model introduced recently by Dalal {\\it et al.} which relates the peaks of the initial linear density field to the final density profile of dark matter halos. Models with primordial non-Gaussianity typically produce an initial density field that differs from that produced in Gaussian models. We use the path-integral formulation of excursion set theory to calculate the non-Gaussian corrections to the peak profile and derive the statistics of the peaks of non-Gaussian density field. In the context of the semi-analytic model for halo profiles, currently allowed values for primordial non-Gaussianity would increase the shapes of the inner dark matter profiles, but only at the sub-percent level except in the very innermost regions.
Gaussian Process-Mixture Conditional Heteroscedasticity.
Platanios, Emmanouil A; Chatzis, Sotirios P
2014-05-01
Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an alternative approach based on methodologies widely used in the field of statistical machine learning. Specifically, we propose a novel nonparametric Bayesian mixture of Gaussian process regression models, each component of which models the noise variance process that contaminates the observed data as a separate latent Gaussian process driven by the observed data. This way, we essentially obtain a Gaussian process-mixture conditional heteroscedasticity (GPMCH) model for volatility modeling in financial return series. We impose a nonparametric prior with power-law nature over the distribution of the model mixture components, namely the Pitman-Yor process prior, to allow for better capturing modeled data distributions with heavy tails and skewness. Finally, we provide a copula-based approach for obtaining a predictive posterior for the covariances over the asset returns modeled by means of a postulated GPMCH model. We evaluate the efficacy of our approach in a number of benchmark scenarios, and compare its performance to state-of-the-art methodologies.
The quantum transverse spin-2 Ising model with a bimodal random-field in the pair approximation
International Nuclear Information System (INIS)
Canko, O.; Albayrak, E.; Keskin, M.
2005-01-01
In this paper, we have investigated the bimodal random-field spin-2 Ising system in a transverse field by combining the pair approximation with the discretized path-integral representation. The exact equations for the second-order phase transition lines and tricritical points are obtained in terms of the random field H, the transverse field G and the coordination number z. It is found that there are some critical values for H and G where the tricritical points disappear for given z. We have also observed that the system presents reentrant behavior which may be caused by the quantum effects and randomness. The phase diagram with respect to the random field and the second-order phase transition temperature are studied extensively for given values of the transverse field and the coordination number
Scaled unscented transform Gaussian sum filter: Theory and application
Luo, Xiaodong; Moroz, Irene M.; Hoteit, Ibrahim
2010-01-01
the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form
Bansal, Ravi; Peterson, Bradley S
2018-06-01
Identifying regional effects of interest in MRI datasets usually entails testing a priori hypotheses across many thousands of brain voxels, requiring control for false positive findings in these multiple hypotheses testing. Recent studies have suggested that parametric statistical methods may have incorrectly modeled functional MRI data, thereby leading to higher false positive rates than their nominal rates. Nonparametric methods for statistical inference when conducting multiple statistical tests, in contrast, are thought to produce false positives at the nominal rate, which has thus led to the suggestion that previously reported studies should reanalyze their fMRI data using nonparametric tools. To understand better why parametric methods may yield excessive false positives, we assessed their performance when applied both to simulated datasets of 1D, 2D, and 3D Gaussian Random Fields (GRFs) and to 710 real-world, resting-state fMRI datasets. We showed that both the simulated 2D and 3D GRFs and the real-world data contain a small percentage (<6%) of very large clusters (on average 60 times larger than the average cluster size), which were not present in 1D GRFs. These unexpectedly large clusters were deemed statistically significant using parametric methods, leading to empirical familywise error rates (FWERs) as high as 65%: the high empirical FWERs were not a consequence of parametric methods failing to model spatial smoothness accurately, but rather of these very large clusters that are inherently present in smooth, high-dimensional random fields. In fact, when discounting these very large clusters, the empirical FWER for parametric methods was 3.24%. Furthermore, even an empirical FWER of 65% would yield on average less than one of those very large clusters in each brain-wide analysis. Nonparametric methods, in contrast, estimated distributions from those large clusters, and therefore, by construct rejected the large clusters as false positives at the nominal
The propagation of charged particles in a focussing magnetic field with random components
International Nuclear Information System (INIS)
Pauls, H.L.
1993-01-01
Boltzmann's equation which describes the evolution of the particle distribution function in a focussing magnetic field with finite helicity, is solved by expanding the distribution function in terms of orthogonal focussing eigenfunctions. The present work advances upon previous work by carrying the expansion of the particle distribution function to a higher order (Ν=7 compared to Ν=3), the adding of magnetic helicity, and the injection of a delta function instead of a Gaussian as initial distribution. Results from this model compare very well with those from other known numerical models, provided that a time constraint, which is a direct consequence of the truncation of the eigenfunction expansion, is satisfied. This model, which gives the solution of Boltzmann's equation to a very high degree of accuracy, is used to evaluate the densities predicted by three lower order (and hence easier to implement) models. Two of these models, where the anisotropic component of the distribution function is approximated to first and second order respectively, follow from the Born approximation technique, while the third follows from a truncated eigenfunction expansion of the particle distribution function. It is shown that the latter two models, which include the effect of the dispersion of the so-called coherent pulses, give a better description of the isotropic density than the model which ignores the effect. The main use of this dispersionless model is that it provides a zeroth order approximation to the speed of the coherent pulses in the presence of helicity and focussing. When the dispersion in the pulse is small, its speed is shown to be predicted quite well by this simple model. (author). 67 refs
Vector solution for the mean electromagnetic fields in a layer of random particles
Lang, R. H.; Seker, S. S.; Levine, D. M.
1986-01-01
The mean electromagnetic fields are found in a layer of randomly oriented particles lying over a half space. A matrix-dyadic formulation of Maxwell's equations is employed in conjunction with the Foldy-Lax approximation to obtain equations for the mean fields. A two variable perturbation procedure, valid in the limit of small fractional volume, is then used to derive uncoupled equations for the slowly varying amplitudes of the mean wave. These equations are solved to obtain explicit expressions for the mean electromagnetic fields in the slab region in the general case of arbitrarily oriented particles and arbitrary polarization of the incident radiation. Numerical examples are given for the application to remote sensing of vegetation.
Information geometry of Gaussian channels
International Nuclear Information System (INIS)
Monras, Alex; Illuminati, Fabrizio
2010-01-01
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).
Detectability of the effect of Inflationary non-Gaussianity on halo bias
Verde, Licia
2009-01-01
We consider the description of the clustering of halos for physically-motivated types of non-Gaussian initial conditions. In particular we include non-Gaussianity of the type arising from single field slow-roll, multi fields, curvaton (local type), higher-order derivative-type (equilateral), vacuum-state modifications (enfolded-type) and horizon-scale GR corrections type. We show that large-scale halo bias is a very sensitive tool to probe non-Gaussianity, potentially leading, for some planned surveys, to a detection of non-Gaussianity arising from horizon-scale GR corrections.
Directory of Open Access Journals (Sweden)
Mingjie Wang
2016-01-01
Full Text Available For the frequency response analysis of acoustic field with random and interval parameters, a nonintrusive uncertain analysis method named Polynomial Chaos Response Surface (PCRS method is proposed. In the proposed method, the polynomial chaos expansion method is employed to deal with the random parameters, and the response surface method is used to handle the interval parameters. The PCRS method does not require efforts to modify model equations due to its nonintrusive characteristic. By means of the PCRS combined with the existing interval analysis method, the lower and upper bounds of expectation, variance, and probability density function of the frequency response can be efficiently evaluated. Two numerical examples are conducted to validate the accuracy and efficiency of the approach. The results show that the PCRS method is more efficient compared to the direct Monte Carlo simulation (MCS method based on the original numerical model without causing significant loss of accuracy.
Transverse spin correlations of the random transverse-field Ising model
Iglói, Ferenc; Kovács, István A.
2018-03-01
The critical behavior of the random transverse-field Ising model in finite-dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization-group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in d =1 ,2 , and 3 dimensions. At the critical point an algebraic decay of the form ˜r-ηt is found, with a decay exponent being approximately ηt≈2 +2 d . In d =1 the results are related to dimer-dimer correlations in the random antiferromagnetic X X chain and have been tested by numerical calculations using free-fermionic techniques.
CMB constraints on running non-Gaussianity
Oppizzi, Filippo; Liguori, Michele; Renzi, Alessandro; Arroja, Frederico; Bartolo, Nicola
2017-01-01
We develop a complete set of tools for CMB forecasting, simulation and estimation of primordial running bispectra, arising from a variety of curvaton and single-field (DBI) models of Inflation. We validate our pipeline using mock CMB running non-Gaussianity realizations and test it on real data by obtaining experimental constraints on the $f_{\\rm NL}$ running spectral index, $n_{\\rm NG}$, using WMAP 9-year data. Our final bounds (68\\% C.L.) read $-0.3< n_{\\rm NG}
Gaussian entanglement distribution via satellite
Hosseinidehaj, Nedasadat; Malaney, Robert
2015-02-01
In this work we analyze three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme, the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the tradeoff between space-based engineering complexity and the rate of ground-station entanglement generation.
Non-gaussianity versus nonlinearity of cosmological perturbations.
Verde, L
2001-06-01
Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.
Revisiting non-Gaussianity from non-attractor inflation models
Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei
2018-05-01
Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition—such as in the case of smooth transition or some sharp transition scenarios—the Script O(1) local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.
Automatic Recognition of Chinese Personal Name Using Conditional Random Fields and Knowledge Base
Directory of Open Access Journals (Sweden)
Chuan Gu
2015-01-01
Full Text Available According to the features of Chinese personal name, we present an approach for Chinese personal name recognition based on conditional random fields (CRF and knowledge base in this paper. The method builds multiple features of CRF model by adopting Chinese character as processing unit, selects useful features based on selection algorithm of knowledge base and incremental feature template, and finally implements the automatic recognition of Chinese personal name from Chinese document. The experimental results on open real corpus demonstrated the effectiveness of our method and obtained high accuracy rate and high recall rate of recognition.
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
Online forum discussions often contain vast amounts of questions that are the focuses of discussions. Extracting contexts and answers together with the questions will yield not only a coherent forum summary but also a valuable QA knowledge base. In this paper, we propose a general framework based...... 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....
A heuristic for the distribution of point counts for random curves over a finite field.
Achter, Jeffrey D; Erman, Daniel; Kedlaya, Kiran S; Wood, Melanie Matchett; Zureick-Brown, David
2015-04-28
How many rational points are there on a random algebraic curve of large genus g over a given finite field Fq? We propose a heuristic for this question motivated by a (now proven) conjecture of Mumford on the cohomology of moduli spaces of curves; this heuristic suggests a Poisson distribution with mean q+1+1/(q-1). We prove a weaker version of this statement in which g and q tend to infinity, with q much larger than g. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
International Nuclear Information System (INIS)
Watanabe, Shuichi; Kudo, Hiroyuki; Saito, Tsuneo
1993-01-01
In this paper, we propose a new reconstruction algorithm based on MAP (maximum a posteriori probability) estimation principle for emission tomography. To improve noise suppression properties of the conventional ML-EM (maximum likelihood expectation maximization) algorithm, direct three-dimensional reconstruction that utilizes intensity correlations between adjacent transaxial slices is introduced. Moreover, to avoid oversmoothing of edges, a priori knowledge of RI (radioisotope) distribution is represented by using a doubly-stochastic image model called the compound Gauss-Markov random field. The a posteriori probability is maximized by using the iterative GEM (generalized EM) algorithm. Computer simulation results are shown to demonstrate validity of the proposed algorithm. (author)
Light absorption in disordered semiconductors with a random coulomb-type field
International Nuclear Information System (INIS)
Arbuzov, Yu.D.; Evdokimov, V.M.; Kolenkin, M.Yu.
1988-01-01
A method is proposed for the formulation of an asymptotic series for the light absorption coefficient in disordered semiconductors with a random field of the Coulomb type. It is shown that the series is obtained by expanding the exponent of an exponential function in powers of a parameter proportional to (E g - ℎω) -1/3 , where E g is the band gap of the semiconductor, and ℎω is the photon energy. The first three terms of the series are calculated in explicit form
Colour and rotation invariant textural features based on Markov random fields
Czech Academy of Sciences Publication Activity Database
Vácha, Pavel; Haindl, Michal; Suk, Tomáš
2011-01-01
Roč. 32, č. 6 (2011), s. 771-779 ISSN 0167-8655 R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/0593 Grant - others:GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10750506 Keywords : Image modelling * colour texture * Illumination invariance * Markov random field * rotation invariance Subject RIV: BD - Theory of Information Impact factor: 1.034, year: 2011 http://library.utia.cas.cz/separaty/2011/RO/vacha-0357314.pdf
International Nuclear Information System (INIS)
Kiskis, J.; Narayanan, R.; Vranas, P.
1993-01-01
The authors study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments, the authors show that the critical exponent v describing the vanishing of the physical mass at the critical point is equal to v θ /d w , where d w is the Hausdorff dimension of the walk, and v θ = var-phi, where var-phi is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is var-phi/v for O(N) models. 3 refs
Typed Linear Chain Conditional Random Fields and Their Application to Intrusion Detection
Elfers, Carsten; Horstmann, Mirko; Sohr, Karsten; Herzog, Otthein
Intrusion detection in computer networks faces the problem of a large number of both false alarms and unrecognized attacks. To improve the precision of detection, various machine learning techniques have been proposed. However, one critical issue is that the amount of reference data that contains serious intrusions is very sparse. In this paper we present an inference process with linear chain conditional random fields that aims to solve this problem by using domain knowledge about the alerts of different intrusion sensors represented in an ontology.
Sharp Trapping Boundaries in the Random Walk of Interplanetary Magnetic Field Lines
Ruffolo, D.; Chuychai, P.; Meechai, J.; Pongkitiwanichkul, P.; Kimpraphan, N.; Matthaeus, W. H.; Rowlands, G.
2004-05-01
Although magnetic field lines in space are believed to undergo a diffusive random walk in the long-distance limit, observed dropouts of solar energetic particles, as well as computer simulations, indicate sharply defined filaments in which interplanetary magnetic field lines have been temporarily trapped. We identify mechanisms that can explain such sharp boundaries in the framework of 2D+slab turbulence, a model that provides a good explanation of solar wind turbulence spectra and the parallel transport of solar energetic particles. Local trapping boundaries (LTBs) are empirically defined as trajectories of 2D turbulence where the mean 2D field is a local maximum. In computer simulations, the filaments (or ``islands'' in the two dimensions perpendicular to the mean field) that are most resistant to slab diffusion correspond closely to the mathematically defined LTBs, that is, there is a mathematical prescription for defining the trapping regions. Furthermore, we provide computational evidence and a theoretical explanation that strong 2D turbulence can inhibit diffusion due to the slab component. Therefore, while these filaments are basically defined by the small-scale topology of 2D turbulence, there can be sharp trapping boundaries where the 2D field is strongest. This work was supported by the Thailand Research Fund, the Rachadapisek Sompoj Fund of Chulalongkorn University, and NASA Grant NAG5-11603. G.R. thanks Mahidol University for its hospitality and the Thailand Commission for Higher Education for travel support.
Local features with large spiky non-Gaussianities during inflation
International Nuclear Information System (INIS)
Abolhasani, Ali Akbar; Firouzjahi, Hassan; Khosravi, Shahram; Sasaki, Misao
2012-01-01
We provide a dynamical mechanism to generate localized features during inflation. The local feature is due to a sharp waterfall phase transition which is coupled to the inflaton field. The key effect is the contributions of waterfall quantum fluctuations which induce a sharp peak on the curvature perturbation which can be as large as the background curvature perturbation from inflaton field. Due to non-Gaussian nature of waterfall quantum fluctuations a large spike non-Gaussianity is produced which is narrowly peaked at modes which leave the Hubble radius at the time of phase transition. The large localized peaks in power spectrum and bispectrum can have interesting consequences on CMB anisotropies
Random eigenvalue problems revisited
Indian Academy of Sciences (India)
statistical distributions; linear stochastic systems. 1. ... dimensional multivariate Gaussian random vector with mean µ ∈ Rm and covariance ... 5, the proposed analytical methods are applied to a three degree-of-freedom system and the ...... The joint pdf ofω1 andω3 is however close to a bivariate Gaussian density function.
Experimental vibroacoustic testing of plane panels using synthesized random pressure fields.
Robin, Olivier; Berry, Alain; Moreau, Stéphane
2014-06-01
The experimental reproduction of random pressure fields on a plane panel and corresponding induced vibrations is studied. An open-loop reproduction strategy is proposed that uses the synthetic array concept, for which a small array element is moved to create a large array by post-processing. Three possible approaches are suggested to define the complex amplitudes to be imposed to the reproduction sources distributed on a virtual plane facing the panel to be tested. Using a single acoustic monopole, a scanning laser vibrometer and a baffled simply supported aluminum panel, experimental vibroacoustic indicators such as the Transmission Loss for Diffuse Acoustic Field, high-speed subsonic and supersonic Turbulent Boundary Layer excitations are obtained. Comparisons with simulation results obtained using a commercial software show that the Transmission Loss estimation is possible under both excitations. Moreover and as a complement to frequency domain indicators, the vibroacoustic behavior of the panel can be studied in the wave number domain.
Magnetic field line random walk in two-dimensional dynamical turbulence
Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.
2017-08-01
The field line random walk (FLRW) of magnetic turbulence is one of the important topics in plasma physics and astrophysics. In this article, by using the field line tracing method, the mean square displacement (MSD) of FLRW is calculated on all possible length scales for pure two-dimensional turbulence with the damping dynamical model. We demonstrate that in order to describe FLRW with the damping dynamical model, a new dimensionless quantity R is needed to be introduced. On different length scales, dimensionless MSD shows different relationships with the dimensionless quantity R. Although the temporal effect affects the MSD of FLRW and even changes regimes of FLRW, it does not affect the relationship between the dimensionless MSD and dimensionless quantity R on all possible length scales.
Baumgarten, Daniel; Eichardt, Roland; Crevecoeur, Guillaume; Supriyanto, Eko; Haueisen, Jens
2013-01-01
Biomedical applications of magnetic nanoparticles require a precise knowledge of their biodistribution. From multi-channel magnetorelaxometry measurements, this distribution can be determined by means of inverse methods. It was recently shown that the combination of sequential inhomogeneous excitation fields in these measurements is favorable regarding the reconstruction accuracy when compared to homogeneous activation . In this paper, approaches for the determination of activation sequences for these measurements are investigated. Therefor, consecutive activation of single coils, random activation patterns and families of m-sequences are examined in computer simulations involving a sample measurement setup and compared with respect to the relative condition number of the system matrix. We obtain that the values of this condition number decrease with larger number of measurement samples for all approaches. Random sequences and m-sequences reveal similar results with a significant reduction of the required number of samples. We conclude that the application of pseudo-random sequences for sequential activation in the magnetorelaxometry imaging of magnetic nanoparticles considerably reduces the number of required sequences while preserving the relevant measurement information.
Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure
International Nuclear Information System (INIS)
Yang Xuhua; Sun Bao; Wang Bo; Sun Youxian
2010-01-01
Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to explore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus Transport Networks (BTNs) evolution model with random overlapping clique structure, which gives a possible explanation for the observed exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-field theory, we analyze the BTNs model and prove that this model has the character of exponential distribution of the connectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with the statistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponential distribution of the connectivities, and their exponents have same order of magnitude, which show the availability of the analytical result of this paper. (general)
Non-Gaussianity from tachyonic preheating in hybrid inflation
International Nuclear Information System (INIS)
Barnaby, Neil; Cline, James M.
2007-01-01
In a previous work we showed that large non-Gaussianities and nonscale-invariant distortions in the cosmic microwave background power spectrum can be generated in hybrid inflation models, due to the contributions of the tachyon (waterfall) field to the second order curvature perturbation. Here we clarify, correct, and extend those results. We show that large non-Gaussianity occurs only when the tachyon remains light throughout inflation, whereas n=4 contamination to the spectrum is the dominant effect when the tachyon is heavy. We find constraints on the parameters of warped-throat brane-antibrane inflation from non-Gaussianity. For F-term and D-term inflation models from supergravity, we obtain nontrivial constraints from the spectral distortion effect. We also establish that our analysis applies to complex tachyon fields
The Multivariate Gaussian Probability Distribution
DEFF Research Database (Denmark)
Ahrendt, Peter
2005-01-01
This technical report intends to gather information about the multivariate gaussian distribution, that was previously not (at least to my knowledge) to be found in one place and written as a reference manual. Additionally, some useful tips and tricks are collected that may be useful in practical ...
On Gaussian conditional independence structures
Czech Academy of Sciences Publication Activity Database
Lněnička, Radim; Matúš, František
2007-01-01
Roč. 43, č. 3 (2007), s. 327-342 ISSN 0023-5954 R&D Projects: GA AV ČR IAA100750603 Institutional research plan: CEZ:AV0Z10750506 Keywords : multivariate Gaussian distribution * positive definite matrices * determinants * gaussoids * covariance selection models * Markov perfectness Subject RIV: BA - General Mathematics Impact factor: 0.552, year: 2007
Dynamical effects and the critical behavior of random-field systems (invited)
International Nuclear Information System (INIS)
Shapir, Y.
1985-01-01
A variety of phenomena is observed experimentally in random-field (RF) systems realized by the application of an external field to diluted antiferromagnets. At low temperatures, infinitely long hysteretic effects are manifested by the history dependence of the final states: long-range order is observed if the field is applied after cooling, while domain states are reached when field cooled. While no indications for critical fluctuations are detected in 2-D systems, scaling behavior, for both the correlation length and the specific heat, is observed in 3-D systems over an intermediate range of temperatures. The related critical properties seem to be well described by the corresponding ones in the 2-D pure Ising model. The renormalization-group approach, which yields for the equilibrium critical exponents their values of the pure model in d-2 dimensions, is reviewed. A generalization of the dimensional-reduction approach, which accounts self-consistently for renormalized responses of the RF system, is presented. The dynamical effects are implicitly incorporated through the variation in the critical response between the local and the global regimes, associated with short- and long-time scales, respectively. In both regimes the lower critical dimension is found to be d = 2 in accordance with stability arguments. The short-time critical behavior indicates a dimensional reduction by one for the 3-D thermal exponents, in agreement with the experimental results
Dynamical effects and the critical behavior of random-field systems
International Nuclear Information System (INIS)
Shapir, Y.
1985-01-01
A variety of phenomena is observed experimentally in random-field (RF) systems realized by the application of an external field to diluted antiferromagnets. At low temperatures, infinitely long hysteretic effects are manifested by the history dependence of the final states: long-range order is observed if the field is applied after cooling, while domain states are reached when field cooled. While no indications for critical fluctuations are detected in 2-D systems, scaling behavior, for both the correlation length and the specific heat, is observed in 3-D systems over an intermediate range of temperatures. The related critical properties seem to be well described by the corresponding ones in the 2-D pure Ising model. The renormalization-group approach, which yields for the equilibrium critical exponents their values of the pure model in d-2 dimensions, is reviewed. A generalization of the dimensional-reduction approach, which accounts self-consistently for renormalized responses of the RF system, is presented. The dynamical effects are implicitly incorporated through the variation in the critical response between the local and the global regimes, associated with short- and long-time scales, respectively. In both regimes the lower critical dimension is found to be d = 2 in accordance with stability arguments. The short-time critical behavior indicates a dimensional reduction by one for the 3-D thermal exponents, in agreement with the experimental results. 37 references
The time-dependent relativistic mean-field theory and the random phase approximation
International Nuclear Information System (INIS)
Ring, P.; Ma, Zhong-yu; Van Giai, Nguyen; Vretenar, D.; Wandelt, A.; Cao, Li-gang
2001-01-01
The Relativistic Random Phase Approximation (RRPA) is derived from the Time-Dependent Relativistic Mean-Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative-energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac-sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the αh-configurations with the ph-configurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the nonrelativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained
Connectivity ranking of heterogeneous random conductivity models
Rizzo, C. B.; de Barros, F.
2017-12-01
To overcome the challenges associated with hydrogeological data scarcity, the hydraulic conductivity (K) field is often represented by a spatial random process. The state-of-the-art provides several methods to generate 2D or 3D random K-fields, such as the classic multi-Gaussian fields or non-Gaussian fields, training image-based fields and object-based fields. We provide a systematic comparison of these models based on their connectivity. We use the minimum hydraulic resistance as a connectivity measure, which it has been found to be strictly correlated with early time arrival of dissolved contaminants. A computationally efficient graph-based algorithm is employed, allowing a stochastic treatment of the minimum hydraulic resistance through a Monte-Carlo approach and therefore enabling the computation of its uncertainty. The results show the impact of geostatistical parameters on the connectivity for each group of random fields, being able to rank the fields according to their minimum hydraulic resistance.
White Gaussian Noise - Models for Engineers
Jondral, Friedrich K.
2018-04-01
This paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.
Wetting and layering transitions of a spin-1/2 Ising model in a random transverse field
International Nuclear Information System (INIS)
Bahmad, L.; Benyoussef, A.; El-Kenz, A.; Ez-Zahraouy, H.
2000-09-01
The effect of a random transverse field (RTF) on the wetting and layering transitions of a spin-1/2 Ising model, in the presence of bulk and surface fields, is studied within an effective field theory by using the differential operator technique. Indeed, the dependencies of the wetting temperature and wetting transverse field on the probability of the presence of a transverse field are established. For specific values of the surface field we show the existence of a critical probability p, above which wetting and layering transitions disappear. (author)
Analytic matrix elements with shifted correlated Gaussians
DEFF Research Database (Denmark)
Fedorov, D. V.
2017-01-01
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.......Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics....
Gaussian process regression analysis for functional data
Shi, Jian Qing
2011-01-01
Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dime
Palacios, Julia A; Minin, Vladimir N
2013-03-01
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method. Copyright © 2013, The International Biometric Society.
Reproducing kernel Hilbert spaces of Gaussian priors
Vaart, van der A.W.; Zanten, van J.H.; Clarke, B.; Ghosal, S.
2008-01-01
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described
Lifting Primordial Non-Gaussianity Above the Noise
Welling, Yvette; Woude, Drian van der; Pajer, Enrico
2016-01-01
Primordial non-Gaussianity (PNG) in Large Scale Structures is obfuscated by the many additional sources of non-linearity. Within the Effective Field Theory approach to Standard Perturbation Theory, we show that matter non-linearities in the bispectrum can be modeled sufficiently well to strengthen
An approximate fractional Gaussian noise model with computational cost
Sø rbye, Sigrunn H.; Myrvoll-Nilsen, Eirik; Rue, Haavard
2017-01-01
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood
Cross-covariance functions for multivariate random fields based on latent dimensions
Apanasovich, T. V.
2010-02-16
The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable and computationally feasible classes of cross-covariance functions in closed form. We focus on spatio-temporal cross-covariance functions that can be nonseparable, asymmetric and can have different covariance structures, for instance different smoothness parameters, in each component. We discuss estimation of these models and perform a small simulation study to demonstrate our approach. We illustrate our methodology on a trivariate spatio-temporal pollution dataset from California and demonstrate that our cross-covariance performs better than other competing models. © 2010 Biometrika Trust.
Document page structure learning for fixed-layout e-books using conditional random fields
Tao, Xin; Tang, Zhi; Xu, Canhui
2013-12-01
In this paper, a model is proposed to learn logical structure of fixed-layout document pages by combining support vector machine (SVM) and conditional random fields (CRF). Features related to each logical label and their dependencies are extracted from various original Portable Document Format (PDF) attributes. Both local evidence and contextual dependencies are integrated in the proposed model so as to achieve better logical labeling performance. With the merits of SVM as local discriminative classifier and CRF modeling contextual correlations of adjacent fragments, it is capable of resolving the ambiguities of semantic labels. The experimental results show that CRF based models with both tree and chain graph structures outperform the SVM model with an increase of macro-averaged F1 by about 10%.
Finite nucleus Dirac mean field theory and random phase approximation using finite B splines
International Nuclear Information System (INIS)
McNeil, J.A.; Furnstahl, R.J.; Rost, E.; Shepard, J.R.; Department of Physics, University of Maryland, College Park, Maryland 20742; Department of Physics, University of Colorado, Boulder, Colorado 80309)
1989-01-01
We calculate the finite nucleus Dirac mean field spectrum in a Galerkin approach using finite basis splines. We review the method and present results for the relativistic σ-ω model for the closed-shell nuclei 16 O and 40 Ca. We study the convergence of the method as a function of the size of the basis and the closure properties of the spectrum using an energy-weighted dipole sum rule. We apply the method to the Dirac random-phase-approximation response and present results for the isoscalar 1/sup -/ and 3/sup -/ longitudinal form factors of 16 O and 40 Ca. We also use a B-spline spectral representation of the positive-energy projector to evaluate partial energy-weighted sum rules and compare with nonrelativistic sum rule results
Adaptive Markov Random Fields for Example-Based Super-resolution of Faces
Stephenson, Todd A.; Chen, Tsuhan
2006-12-01
Image enhancement of low-resolution images can be done through methods such as interpolation, super-resolution using multiple video frames, and example-based super-resolution. Example-based super-resolution, in particular, is suited to images that have a strong prior (for those frameworks that work on only a single image, it is more like image restoration than traditional, multiframe super-resolution). For example, hallucination and Markov random field (MRF) methods use examples drawn from the same domain as the image being enhanced to determine what the missing high-frequency information is likely to be. We propose to use even stronger prior information by extending MRF-based super-resolution to use adaptive observation and transition functions, that is, to make these functions region-dependent. We show with face images how we can adapt the modeling for each image patch so as to improve the resolution.
Zhang, Y.; Li, F.; Zhang, S.; Hao, W.; Zhu, T.; Yuan, L.; Xiao, F.
2017-09-01
In this paper, Statistical Distribution based Conditional Random Fields (STA-CRF) algorithm is exploited for improving marginal ice-water classification. Pixel level ice concentration is presented as the comparison of methods based on CRF. Furthermore, in order to explore the effective statistical distribution model to be integrated into STA-CRF, five statistical distribution models are investigated. The STA-CRF methods are tested on 2 scenes around Prydz Bay and Adélie Depression, where contain a variety of ice types during melt season. Experimental results indicate that the proposed method can resolve sea ice edge well in Marginal Ice Zone (MIZ) and show a robust distinction of ice and water.
A Coupled Hidden Markov Random Field Model for Simultaneous Face Clustering and Tracking in Videos
Wu, Baoyuan
2016-10-25
Face clustering and face tracking are two areas of active research in automatic facial video processing. They, however, have long been studied separately, despite the inherent link between them. In this paper, we propose to perform simultaneous face clustering and face tracking from real world videos. The motivation for the proposed research is that face clustering and face tracking can provide useful information and constraints to each other, thus can bootstrap and improve the performances of each other. To this end, we introduce a Coupled Hidden Markov Random Field (CHMRF) to simultaneously model face clustering, face tracking, and their interactions. We provide an effective algorithm based on constrained clustering and optimal tracking for the joint optimization of cluster labels and face tracking. We demonstrate significant improvements over state-of-the-art results in face clustering and tracking on several videos.
Evaluating Consumer m-Health Services for Promoting Healthy Eating: A Randomized Field Experiment.
Kato-Lin, Yi-Chin; Padman, Rema; Downs, Julie; Abhishek, Vibhanshu
2015-01-01
Mobile apps have great potential to deliver promising interventions to engage consumers and change their health-related behaviors, such as healthy eating. Currently, the interventions for promoting healthy eating are either too onerous to keep consumers engaged or too restrictive to keep consumers connected with healthcare professionals. In addition, while social media allows individuals to receive information from many sources, it is unclear how peer support interacts with professional support in the context of such interventions. This study proposes and evaluates three mobile-enabled interventions to address these challenges. We examine their effects on user engagement and food choices via a 4-month randomized field experiment. Mixed models provide strong evidence of the positive effect of image-based dietitian support and negative effects of peer support, and moderate evidence of the positive effects of mobile-based visual diary, highlighting the value of mobile apps for delivering advanced interventions to engage users and facilitate behavior change.
Liu, Dan; Liu, Xuejun; Wu, Yiguang
2018-04-24
This paper presents an effective approach for depth reconstruction from a single image through the incorporation of semantic information and local details from the image. A unified framework for depth acquisition is constructed by joining a deep Convolutional Neural Network (CNN) and a continuous pairwise Conditional Random Field (CRF) model. Semantic information and relative depth trends of local regions inside the image are integrated into the framework. A deep CNN network is firstly used to automatically learn a hierarchical feature representation of the image. To get more local details in the image, the relative depth trends of local regions are incorporated into the network. Combined with semantic information of the image, a continuous pairwise CRF is then established and is used as the loss function of the unified model. Experiments on real scenes demonstrate that the proposed approach is effective and that the approach obtains satisfactory results.
Sign Language Recognition with the Kinect Sensor Based on Conditional Random Fields
Directory of Open Access Journals (Sweden)
Hee-Deok Yang
2014-12-01
Full Text Available Sign language is a visual language used by deaf people. One difficulty of sign language recognition is that sign instances of vary in both motion and shape in three-dimensional (3D space. In this research, we use 3D depth information from hand motions, generated from Microsoft’s Kinect sensor and apply a hierarchical conditional random field (CRF that recognizes hand signs from the hand motions. The proposed method uses a hierarchical CRF to detect candidate segments of signs using hand motions, and then a BoostMap embedding method to verify the hand shapes of the segmented signs. Experiments demonstrated that the proposed method could recognize signs from signed sentence data at a rate of 90.4%.
Directory of Open Access Journals (Sweden)
Dan Liu
2018-04-01
Full Text Available This paper presents an effective approach for depth reconstruction from a single image through the incorporation of semantic information and local details from the image. A unified framework for depth acquisition is constructed by joining a deep Convolutional Neural Network (CNN and a continuous pairwise Conditional Random Field (CRF model. Semantic information and relative depth trends of local regions inside the image are integrated into the framework. A deep CNN network is firstly used to automatically learn a hierarchical feature representation of the image. To get more local details in the image, the relative depth trends of local regions are incorporated into the network. Combined with semantic information of the image, a continuous pairwise CRF is then established and is used as the loss function of the unified model. Experiments on real scenes demonstrate that the proposed approach is effective and that the approach obtains satisfactory results.
Adaptive Markov Random Fields for Example-Based Super-resolution of Faces
Directory of Open Access Journals (Sweden)
Stephenson Todd A
2006-01-01
Full Text Available Image enhancement of low-resolution images can be done through methods such as interpolation, super-resolution using multiple video frames, and example-based super-resolution. Example-based super-resolution, in particular, is suited to images that have a strong prior (for those frameworks that work on only a single image, it is more like image restoration than traditional, multiframe super-resolution. For example, hallucination and Markov random field (MRF methods use examples drawn from the same domain as the image being enhanced to determine what the missing high-frequency information is likely to be. We propose to use even stronger prior information by extending MRF-based super-resolution to use adaptive observation and transition functions, that is, to make these functions region-dependent. We show with face images how we can adapt the modeling for each image patch so as to improve the resolution.
Birkelund, Gunn Elisabeth; Chan, Tak Wing; Ugreninov, Elisabeth; Midtbøen, Arnfinn H; Rogstad, Jon
2018-01-24
Terrorist attacks are known to influence public opinion. But do they also change behaviour? We address this question by comparing the results of two identical randomized field experiments on ethnic discrimination in hiring that we conducted in Oslo. The first experiment was conducted before the 2011 terrorist attacks in Norway; the second experiment was conducted after the attacks. In both experiments, applicants with a typical Pakistani name were significantly less likely to get a job interview compared to those with a typical Norwegian name. But the ethnic gap in call-back rates were very similar in the two experiments. Thus, Pakistanis in Norway still experienced the same level of discrimination, despite claims that Norwegians have become more positive about migrants after the far-right, anti-migrant terrorist attacks of 2011. © London School of Economics and Political Science 2018.
High energy X-ray phase and dark-field imaging using a random absorption mask.
Wang, Hongchang; Kashyap, Yogesh; Cai, Biao; Sawhney, Kawal
2016-07-28
High energy X-ray imaging has unique advantage over conventional X-ray imaging, since it enables higher penetration into materials with significantly reduced radiation damage. However, the absorption contrast in high energy region is considerably low due to the reduced X-ray absorption cross section for most materials. Even though the X-ray phase and dark-field imaging techniques can provide substantially increased contrast and complementary information, fabricating dedicated optics for high energies still remain a challenge. To address this issue, we present an alternative X-ray imaging approach to produce transmission, phase and scattering signals at high X-ray energies by using a random absorption mask. Importantly, in addition to the synchrotron radiation source, this approach has been demonstrated for practical imaging application with a laboratory-based microfocus X-ray source. This new imaging method could be potentially useful for studying thick samples or heavy materials for advanced research in materials science.
Hidden State Conditional Random Field for Abnormal Activity Recognition in Smart Homes
Directory of Open Access Journals (Sweden)
Yu Tong
2015-03-01
Full Text Available As the number of elderly people has increased worldwide, there has been a surge of research into assistive technologies to provide them with better care by recognizing their normal and abnormal activities. However, existing abnormal activity recognition (AAR algorithms rarely consider sub-activity relations when recognizing abnormal activities. This paper presents an application of the Hidden State Conditional Random Field (HCRF method to detect and assess abnormal activities that often occur in elderly persons’ homes. Based on HCRF, this paper designs two AAR algorithms, and validates them by comparing them with a feature vector distance based algorithm in two experiments. The results demonstrate that the proposed algorithms favorably outperform the competitor, especially when abnormal activities have same sensor type and sensor number as normal activities.
International Nuclear Information System (INIS)
Ryutova, M.
1990-08-01
Effects of strong and random inhomogeneities of the magnetic fields, plasma density, and temperature in the solar atmosphere on the properties of magnetoacoustic waves of arbitrary amplitudes are studied. The procedure which allows one to obtain the averaged equation containing the nonlinearity of a wave, dispersion properties of a system, and dissipative effects is described. It is shown that depending on the statistical properties of the medium, different scenarios of wave propagation arise: in the predominance of dissipative effects the primary wave is damped away in the linear stage and the efficiency of heating due to inhomogeneities is much greater than that in homogeneous medium. Depending on the interplay of nonlinear and dispersion effects, the process of heating can be afforded through the formation of shocks or through the storing of energy in a system of solitons which are later damped away. Our computer simulation supports and extends the above theoretical investigations. In particular the enhanced dissipation of waves due to the strong and random inhomogeneities is observed and this is more pronounced for shorter waves
Virial expansion for almost diagonal random matrices
Yevtushenko, Oleg; Kravtsov, Vladimir E.
2003-08-01
Energy level statistics of Hermitian random matrices hat H with Gaussian independent random entries Higeqj is studied for a generic ensemble of almost diagonal random matrices with langle|Hii|2rangle ~ 1 and langle|Hi\
Large non-Gaussianity from two-component hybrid inflation
International Nuclear Information System (INIS)
Byrnes, Christian T.; Choi, Ki-Young; Hall, Lisa M.H.
2009-01-01
We study the generation of non-Gaussianity in models of hybrid inflation with two inflaton fields, (2-brid inflation). We analyse the region in the parameter and the initial condition space where a large non-Gaussianity may be generated during slow-roll inflation which is generally characterised by a large f NL , τ NL and a small g NL . For certain parameter values we can satisfy τ NL >> f NL 2 . The bispectrum is of the local type but may have a significant scale dependence. We show that the loop corrections to the power spectrum and bispectrum are suppressed during inflation, if one assume that the fields follow a classical background trajectory. We also include the effect of the waterfall field, which can lead to a significant change in the observables after the waterfall field is destabilised, depending on the couplings between the waterfall and inflaton fields
Schweiner, Frank; Laturner, Jeanine; Main, Jörg; Wunner, Günter
2017-11-01
Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) have analytical formulas for the level spacing distribution function been derived within random matrix theory. We investigate arbitrary crossovers in the triangle between all three statistics. To this aim we propose an according formula for the level spacing distribution function depending on two parameters. Comparing the behavior of our formula for the special cases of P→GUE, P→GOE, and GOE→GUE with the results from random matrix theory, we prove that these crossovers are described reasonably. Recent investigations by F. Schweiner et al. [Phys. Rev. E 95, 062205 (2017)2470-004510.1103/PhysRevE.95.062205] have shown that the Hamiltonian of magnetoexcitons in cubic semiconductors can exhibit all three statistics in dependence on the system parameters. Evaluating the numerical results for magnetoexcitons in dependence on the excitation energy and on a parameter connected with the cubic valence band structure and comparing the results with the formula proposed allows us to distinguish between regular and chaotic behavior as well as between existent or broken antiunitary symmetries. Increasing one of the two parameters, transitions between different crossovers, e.g., from the P→GOE to the P→GUE crossover, are observed and discussed.
Perturbative corrections for approximate inference in gaussian latent variable models
DEFF Research Database (Denmark)
Opper, Manfred; Paquet, Ulrich; Winther, Ole
2013-01-01
Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact b...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....
Polarization coupling of vector Bessel–Gaussian beams
International Nuclear Information System (INIS)
Takeuchi, Ryushi; Kozawa, Yuichi; Sato, Shunichi
2013-01-01
We report polarization coupling of radial and azimuthal electric field components of a vector light beam as predicted by the fact that the vector Helmholtz equation is expressed as coupled differential equations in cylindrical coordinates. To clearly observe the polarization variation of a beam as it propagates, higher order transverse modes of a vector Bessel–Gaussian beam were generated by a gain distribution modulation technique, which created a narrow ring-shaped gain region in a Nd:YVO 4 crystal. The polarization coupling was confirmed by the observation that the major polarization component of a vector Bessel–Gaussian beam alternates between radial and azimuthal components along with the propagation. (paper)
Gaussian-state entanglement in a quantum beat laser
International Nuclear Information System (INIS)
Tahira, Rabia; Ikram, Manzoor; Nha, Hyunchul; Zubairy, M. Suhail
2011-01-01
Recently quantum beat lasers have been considered as a source of entangled radiation [S. Qamar, F. Ghafoor, M. Hillery, and M. S. Zubairy, Phys. Rev. A 77, 062308 (2008)]. We investigate and quantify the entanglement of this system when the initial cavity modes are prepared in a Gaussian two-mode state, one being a nonclassical state and the other a thermal state. It is investigated how the output entanglement varies with the nonclassicality of the input Gaussian state, thermal noise, and the strength of the driving field.
Ensemble of Neural Network Conditional Random Fields for Self-Paced Brain Computer Interfaces
Directory of Open Access Journals (Sweden)
Hossein Bashashati
2017-07-01
Full Text Available Classification of EEG signals in self-paced Brain Computer Interfaces (BCI is an extremely challenging task. The main diﬃculty stems from the fact that start time of a control task is not defined. Therefore it is imperative to exploit the characteristics of the EEG data to the extent possible. In sensory motor self-paced BCIs, while performing the mental task, the user’s brain goes through several well-defined internal state changes. Applying appropriate classifiers that can capture these state changes and exploit the temporal correlation in EEG data can enhance the performance of the BCI. In this paper, we propose an ensemble learning approach for self-paced BCIs. We use Bayesian optimization to train several different classifiers on different parts of the BCI hyper- parameter space. We call each of these classifiers Neural Network Conditional Random Field (NNCRF. NNCRF is a combination of a neural network and conditional random field (CRF. As in the standard CRF, NNCRF is able to model the correlation between adjacent EEG samples. However, NNCRF can also model the nonlinear dependencies between the input and the output, which makes it more powerful than the standard CRF. We compare the performance of our algorithm to those of three popular sequence labeling algorithms (Hidden Markov Models, Hidden Markov Support Vector Machines and CRF, and to two classical classifiers (Logistic Regression and Support Vector Machines. The classifiers are compared for the two cases: when the ensemble learning approach is not used and when it is. The data used in our studies are those from the BCI competition IV and the SM2 dataset. We show that our algorithm is considerably superior to the other approaches in terms of the Area Under the Curve (AUC of the BCI system.
The Stochastic Galerkin Method for Darcy Flow Problem with Log-Normal Random
Czech Academy of Sciences Publication Activity Database
Beres, Michal; Domesová, Simona
2017-01-01
Roč. 15, č. 2 (2017), s. 267-279 ISSN 1336-1376 R&D Projects: GA MŠk LQ1602 Institutional support: RVO:68145535 Keywords : Darcy flow * Gaussian random field * Karhunen-Loeve decomposition * polynomial chaos * Stochastic Galerkin method Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics http://advances.utc.sk/index.php/AEEE/article/view/2280
General Galilei Covariant Gaussian Maps
Gasbarri, Giulio; Toroš, Marko; Bassi, Angelo
2017-09-01
We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we consider translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined by Nimmrichter and Hornberger [Phys. Rev. Lett. 110, 16 (2013)].
Gaussian Embeddings for Collaborative Filtering
Dos Santos , Ludovic; Piwowarski , Benjamin; Gallinari , Patrick
2017-01-01
International audience; Most collaborative ltering systems, such as matrix factorization, use vector representations for items and users. Those representations are deterministic, and do not allow modeling the uncertainty of the learned representation, which can be useful when a user has a small number of rated items (cold start), or when there is connict-ing information about the behavior of a user or the ratings of an item. In this paper, we leverage recent works in learning Gaussian embeddi...
Non-Gaussian Methods for Causal Structure Learning.
Shimizu, Shohei
2018-05-22
Causal structure learning is one of the most exciting new topics in the fields of machine learning and statistics. In many empirical sciences including prevention science, the causal mechanisms underlying various phenomena need to be studied. Nevertheless, in many cases, classical methods for causal structure learning are not capable of estimating the causal structure of variables. This is because it explicitly or implicitly assumes Gaussianity of data and typically utilizes only the covariance structure. In many applications, however, non-Gaussian data are often obtained, which means that more information may be contained in the data distribution than the covariance matrix is capable of containing. Thus, many new methods have recently been proposed for using the non-Gaussian structure of data and inferring the causal structure of variables. This paper introduces prevention scientists to such causal structure learning methods, particularly those based on the linear, non-Gaussian, acyclic model known as LiNGAM. These non-Gaussian data analysis tools can fully estimate the underlying causal structures of variables under assumptions even in the presence of unobserved common causes. This feature is in contrast to other approaches. A simulated example is also provided.
Continuous-variable quantum teleportation with non-Gaussian resources
International Nuclear Information System (INIS)
Dell'Anno, F.; De Siena, S.; Albano, L.; Illuminati, F.
2007-01-01
We investigate continuous variable quantum teleportation using non-Gaussian states of the radiation field as entangled resources. We compare the performance of different classes of degaussified resources, including two-mode photon-added and two-mode photon-subtracted squeezed states. We then introduce a class of two-mode squeezed Bell-like states with one-parameter dependence for optimization. These states interpolate between and include as subcases different classes of degaussified resources. We show that optimized squeezed Bell-like resources yield a remarkable improvement in the fidelity of teleportation both for coherent and nonclassical input states. The investigation reveals that the optimal non-Gaussian resources for continuous variable teleportation are those that most closely realize the simultaneous maximization of the content of entanglement, the degree of affinity with the two-mode squeezed vacuum, and the, suitably measured, amount of non-Gaussianity
Primordial non-Gaussian features from DBI Galileon inflation
International Nuclear Information System (INIS)
Choudhury, Sayantan; Pal, Supratik
2015-01-01
We have studied primordial non-Gaussian features of a model of potential-driven single field DBI Galileon inflation. We have computed the bispectrum from the three-point correlation function considering all possible cross correlations between the scalar and tensor modes of the proposed setup. Further, we have computed the trispectrum from a four-point correlation function considering the contribution from contact interaction, and scalar and graviton exchange diagrams in the in-in picture. Finally we have obtained the non-Gaussian consistency conditions from the four-point correlator, which results in partial violation of the Suyama-Yamaguchi four-point consistency relation. This further leads to the conclusion that sufficient primordial non-Gaussianities can be obtained from DBI Galileon inflation. (orig.)
Non-Gaussian signatures arising from warm inflation driven by geometric tachyon
International Nuclear Information System (INIS)
Bhattacharjee, Anindita; Deshamukhya, Atri
2014-01-01
In a warm inflationary scenario, the initial seeds of density perturbation arise from thermal fluctuations of the inflaton field. These fluctuations in principle have Gaussian distribution. In a Gaussian distribution the density perturbation can be expressed as the two point correlation function. Thus if in an inflationary model the density perturbation is expressed as correlation function of order higher than two, these fluctuations are non-Gaussian in nature. A simple inflationary model containing single scalar field, slow roll, canonical kinetic term and vacuum initial state can produce a tiny amount of non-Gaussianity which are very small to be detected by any experiment. Non-Gaussianity can also arise in inflationary models containing multiple scalar fields. For an inflationary scenario with single scalar field, non-Gaussianity can be expressed in terms of bi-spectrum however for multi field Inflation, it is expressed in terms of trispectrum etc. In this piece of work, the warm inflationary scenario, driven by a D3 brane due to the presence of a stack of k coincident NS 5 branes is considered and the non-Gaussian effects in such an inflationary scenario has been analysed by measuring the bispectrum of the gravitational field fluctuations generated during the warm inflation in strong dissipative regime. The bi-spectrum of the Inflation is expressed in terms of the parameter f NL and it is seen that the value of f NL parameter lies well within the limit observed by WMAP7
Lauterbach, S.; Fina, M.; Wagner, W.
2018-04-01
Since structural engineering requires highly developed and optimized structures, the thickness dependency is one of the most controversially debated topics. This paper deals with stability analysis of lightweight thin structures combined with arbitrary geometrical imperfections. Generally known design guidelines only consider imperfections for simple shapes and loading, whereas for complex structures the lower-bound design philosophy still holds. Herein, uncertainties are considered with an empirical knockdown factor representing a lower bound of existing measurements. To fully understand and predict expected bearable loads, numerical investigations are essential, including geometrical imperfections. These are implemented into a stand-alone program code with a stochastic approach to compute random fields as geometric imperfections that are applied to nodes of the finite element mesh of selected structural examples. The stochastic approach uses the Karhunen-Loève expansion for the random field discretization. For this approach, the so-called correlation length l_c controls the random field in a powerful way. This parameter has a major influence on the buckling shape, and also on the stability load. First, the impact of the correlation length is studied for simple structures. Second, since most structures for engineering devices are more complex and combined structures, these are intensively discussed with the focus on constrained random fields for e.g. flange-web-intersections. Specific constraints for those random fields are pointed out with regard to the finite element model. Further, geometrical imperfections vanish where the structure is supported.
Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data
Directory of Open Access Journals (Sweden)
Ji Hoon Ryoo
2017-08-01
Full Text Available As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet growth modeling with non-Gaussian data is somewhat limited when considering the transformed expectation of the response via a linear predictor as a functional form of explanatory variables. In this study, we introduce a fractional polynomial model (FPM that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. The results clearly show the efficiency and flexibility of the FPM for such applications.
IMPLEMENTATION OF THE MARKOV RANDOM FIELD FOR URBAN LAND COVER CLASSIFICATION OF UAV VHIR DATA
Directory of Open Access Journals (Sweden)
Jati Pratomo
2016-10-01
Full Text Available The usage of Unmanned Aerial Vehicle (UAV has grown rapidly in various fields, such as urban planning, search and rescue, and surveillance. Capturing images from UAV has many advantages compared with satellite imagery. For instance, higher spatial resolution and less impact from atmospheric variations can be obtained. However, there are difficulties in classifying urban features, due to the complexity of the urban land covers. The usage of Maximum Likelihood Classification (MLC has limitations since it is based on the assumption of the normal distribution of pixel values, where, in fact, urban features are not normally distributed. There are advantages in using the Markov Random Field (MRF for urban land cover classification as it assumes that neighboring pixels have a higher probability to be classified in the same class rather than a different class. This research aimed to determine the impact of the smoothness (λ and the updating temperature (Tupd on the accuracy result (κ in MRF. We used a UAV VHIR sized 587 square meters, with six-centimetre resolution, taken in Bogor Regency, Indonesia. The result showed that the kappa value (κ increases proportionally with the smoothness (λ until it reaches the maximum (κ, then the value drops. The usage of higher (Tupd has resulted in better (κ although it also led to a higher Standard Deviations (SD. Using the most optimal parameter, MRF resulted in slightly higher (κ compared with MLC.
Field-controlled randomness of colloidal paths on a magnetic bubble lattice
International Nuclear Information System (INIS)
Jungnickel, C; Fischer, Th M; Khattari, Z; Johansen, T H
2011-01-01
Paramagnetic colloidal particles move in the potential energy landscape of a magnetically modulated bubble lattice of a magnetic garnet film. The modulation causes the energy minima to alternate between positions above the centres of the bubbles and interstitial positions. The particles deterministically follow the time-dependent positions of the energy minima until the minima become unstable in one or several directions and allow the particles to hop to a new minimum. We control the time delay between instabilities of the minima in alternative directions by the angle of the external magnetic field with the crystallographic directions of the bubble lattice. When the time delay is large, the particles deterministically hop to the next minimum along the direction that becomes unstable first. When the time delay is short, diffusion of the particle in the marginal potential randomizes the choice of the hopping directions or the choice of the transport network. Gradual changes of the external field direction from 0 0 to 30 0 lead to a continuous crossover from a deterministic to a fully stochastic path of the colloids.
Gong, Zheng; Chen, Tianrun; Ratilal, Purnima; Makris, Nicholas C
2013-11-01
An analytical model derived from normal mode theory for the accumulated effects of range-dependent multiple forward scattering is applied to estimate the temporal coherence of the acoustic field forward propagated through a continental-shelf waveguide containing random three-dimensional internal waves. The modeled coherence time scale of narrow band low-frequency acoustic field fluctuations after propagating through a continental-shelf waveguide is shown to decay with a power-law of range to the -1/2 beyond roughly 1 km, decrease with increasing internal wave energy, to be consistent with measured acoustic coherence time scales. The model should provide a useful prediction of the acoustic coherence time scale as a function of internal wave energy in continental-shelf environments. The acoustic coherence time scale is an important parameter in remote sensing applications because it determines (i) the time window within which standard coherent processing such as matched filtering may be conducted, and (ii) the number of statistically independent fluctuations in a given measurement period that determines the variance reduction possible by stationary averaging.
Multilayer Markov Random Field models for change detection in optical remote sensing images
Benedek, Csaba; Shadaydeh, Maha; Kato, Zoltan; Szirányi, Tamás; Zerubia, Josiane
2015-09-01
In this paper, we give a comparative study on three Multilayer Markov Random Field (MRF) based solutions proposed for change detection in optical remote sensing images, called Multicue MRF, Conditional Mixed Markov model, and Fusion MRF. Our purposes are twofold. On one hand, we highlight the significance of the focused model family and we set them against various state-of-the-art approaches through a thematic analysis and quantitative tests. We discuss the advantages and drawbacks of class comparison vs. direct approaches, usage of training data, various targeted application fields and different ways of Ground Truth generation, meantime informing the Reader in which roles the Multilayer MRFs can be efficiently applied. On the other hand we also emphasize the differences between the three focused models at various levels, considering the model structures, feature extraction, layer interpretation, change concept definition, parameter tuning and performance. We provide qualitative and quantitative comparison results using principally a publicly available change detection database which contains aerial image pairs and Ground Truth change masks. We conclude that the discussed models are competitive against alternative state-of-the-art solutions, if one uses them as pre-processing filters in multitemporal optical image analysis. In addition, they cover together a large range of applications, considering the different usage options of the three approaches.
Funaki, Tadahisa
2016-01-01
Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book. Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ∇φ-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers. Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hyd...
Simuta-Champo, R.; Herrera-Zamarrón, G. S.
2010-01-01
The Monte Carlo technique provides a natural method for evaluating uncertainties. The uncertainty is represented by a probability distribution or by related quantities such as statistical moments. When the groundwater flow and transport governing equations are solved and the hydraulic conductivity field is treated as a random spatial function, the hydraulic head, velocities and concentrations also become random spatial functions. When that is the case, for the stochastic simulation of groundw...
Random-field Potts model for the polar domains of lead magnesium niobate and lead scandium tantalate
Energy Technology Data Exchange (ETDEWEB)
Qian, H.; Bursill, L.A
1997-06-01
A random filed Potts model is used to establish the spatial relationship between the nanoscale distribution of charges chemical defects and nanoscale polar domains for the perovskite-based relaxor materials lead magnesium niobate (PMN) and lead scandium tantalate (PST). The random fields are not set stochastically but are determined initially by the distribution of B-site cations (Mg, Nb) or (Sc, Ta) generated by Monte Carlo NNNI-model simulations for the chemical defects. An appropriate random field Potts model is derived and algorithms developed for a 2D lattice. It is shown that the local fields are strongly correlated with the chemical domain walls and that polar domains as a function of decreasing temperature is simulated for the two cases of PMN and PST. The dynamics of the polar clusters is also discussed. 33 refs., 9 figs.
Transverse eV Ion Heating by Random Electric Field Fluctuations in the Plasmasphere
Artemyev, A. V.; Mourenas, D.; Agapitov, O. V.; Blum, L.
2017-01-01
Charged particle acceleration in the Earth inner magnetosphere is believed to be mainly due to the local resonant wave-particle interaction or particle transport processes. However, the Van Allen Probes have recently provided interesting evidence of a relatively slow transverse heating of eV ions at distances about 2-3 Earth radii during quiet times. Waves that are able to resonantly interact with such very cold ions are generally rare in this region of space, called the plasmasphere. Thus, non-resonant wave-particle interactions are expected to play an important role in the observed ion heating. We demonstrate that stochastic heating by random transverse electric field fluctuations of whistler (and possibly electromagnetic ion cyclotron) waves could explain this weak and slow transverse heating of H+ and O+ ions in the inner magnetosphere. The essential element of the proposed model of ion heating is the presence of trains of random whistler (hiss) wave packets, with significant amplitude modulations produced by strong wave damping, rapid wave growth, or a superposition of wave packets of different frequencies, phases, and amplitudes. Such characteristics correspond to measured characteristics of hiss waves in this region. Using test particle simulations with typical wave and plasma parameters, we demonstrate that the corresponding stochastic transverse ion heating reaches 0.07-0.2 eV/h for protons and 0.007-0.015 eV/h for O+ ions. This global temperature increase of the Maxwellian ion population from an initial Ti approx. 0.3 eV could potentially explain the observations.
Fetal MEG evoked response latency from beamformer with random field theory.
McCubbin, J; Vrba, J; Murphy, P; Temple, J; Eswaran, H; Lowery, C L; Preissl, H
2010-01-01
Analysis of fetal magnetoencephalographic brain recordings is restricted by low signal to noise ratio (SNR) and non-stationarity of the sources. Beamformer techniques have been applied to improve SNR of fetal evoked responses. However, until now the effect of non-stationarity was not taken into account in detail, because the detection of evoked responses is in most cases determined by averaging a large number of trials. We applied a windowing technique to improve the stationarity of the data by using short time segments recorded during a flash-evoked study. In addition, we implemented a random field theory approach for more stringent control of false-positives in the statistical parametric map of the search volume for the beamformer. The search volume was based on detailed individual fetal/maternal biometrics from ultrasound scans and fetal heart localization. Average power over a sliding window within the averaged evoked response against a randomized average background power was used as the test z-statistic. The significance threshold was set at 10% over all members of a contiguous cluster of voxels. There was at least one significant response for 62% of fetal and 95% of newborn recordings with gestational age (GA) between 28 and 45 weeks from 29 subjects. We found that the latency was either substantially unchanged or decreased with increasing GA for most subjects, with a nominal rate of about -11 ms/week. These findings support the anticipated neurophysiological development, provide validation for the beamformer model search as a methodology, and may lead to a clinical test for fetal cognitive development.
A statistical theory on the turbulent diffusion of Gaussian puffs
International Nuclear Information System (INIS)
Mikkelsen, T.; Larsen, S.E.; Pecseli, H.L.
1982-12-01
The relative diffusion of a one-dimensional Gaussian cloud of particles is related to a two-particle covariance function in a homogeneous and stationary field of turbulence. A simple working approximation is suggested for the determination of this covariance function in terms of entirely Eulerian fields. Simple expressions are derived for the growth of the puff's standard deviation for diffusion times that are small compared to the integral time scale of the turbulence. (Auth.)
Inflation with a graceful exit in a random landscape
International Nuclear Information System (INIS)
Pedro, F.G.; Westphal, A.
2016-11-01
We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N<<10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Inflation with a graceful exit in a random landscape
Energy Technology Data Exchange (ETDEWEB)
Pedro, F.G. [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica y Inst. de Fisica Teorica UAM/CSIC; Westphal, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2016-11-15
We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N<<10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.
Stable Lévy motion with inverse Gaussian subordinator
Kumar, A.; Wyłomańska, A.; Gajda, J.
2017-09-01
In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.
Mean-field Ensemble Kalman Filter
Law, Kody
2015-01-07
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Polewski, Przemyslaw; Yao, Wei; Heurich, Marco; Krzystek, Peter; Stilla, Uwe
2018-06-01
In this study, we present a method for improving the quality of automatic single fallen tree stem segmentation in ALS data by applying a specialized constrained conditional random field (CRF). The entire processing pipeline is composed of two steps. First, short stem segments of equal length are detected and a subset of them is selected for further processing, while in the second step the chosen segments are merged to form entire trees. The first step is accomplished using the specialized CRF defined on the space of segment labelings, capable of finding segment candidates which are easier to merge subsequently. To achieve this, the CRF considers not only the features of every candidate individually, but incorporates pairwise spatial interactions between adjacent segments into the model. In particular, pairwise interactions include a collinearity/angular deviation probability which is learned from training data as well as the ratio of spatial overlap, whereas unary potentials encode a learned probabilistic model of the laser point distribution around each segment. Each of these components enters the CRF energy with its own balance factor. To process previously unseen data, we first calculate the subset of segments for merging on a grid of balance factors by minimizing the CRF energy. Then, we perform the merging and rank the balance configurations according to the quality of their resulting merged trees, obtained from a learned tree appearance model. The final result is derived from the top-ranked configuration. We tested our approach on 5 plots from the Bavarian Forest National Park using reference data acquired in a field inventory. Compared to our previous segment selection method without pairwise interactions, an increase in detection correctness and completeness of up to 7 and 9 percentage points, respectively, was observed.
Self-consistent Random Phase Approximation applied to a schematic model of the field theory
International Nuclear Information System (INIS)
Bertrand, Thierry
1998-01-01
The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum
Directory of Open Access Journals (Sweden)
P. M. A. Diaz
2016-06-01
Full Text Available This paper presents a method to estimate the temporal interaction in a Conditional Random Field (CRF based approach for crop recognition from multitemporal remote sensing image sequences. This approach models the phenology of different crop types as a CRF. Interaction potentials are assumed to depend only on the class labels of an image site at two consecutive epochs. In the proposed method, the estimation of temporal interaction parameters is considered as an optimization problem, whose goal is to find the transition matrix that maximizes the CRF performance, upon a set of labelled data. The objective functions underlying the optimization procedure can be formulated in terms of different accuracy metrics, such as overall and average class accuracy per crop or phenological stages. To validate the proposed approach, experiments were carried out upon a dataset consisting of 12 co-registered LANDSAT images of a region in southeast of Brazil. Pattern Search was used as the optimization algorithm. The experimental results demonstrated that the proposed method was able to substantially outperform estimates related to joint or conditional class transition probabilities, which rely on training samples.
Tao, R.; Tang, H.
Chocolate is one of the most popular food types and flavors in the world. Unfortunately, at present, chocolate products contain too much fat, leading to obesity. For example, a typical molding chocolate has various fat up to 40% in total and chocolate for covering ice cream has fat 50 -60%. Especially, as children are the leading chocolate consumers, reducing the fat level in chocolate products to make them healthier is important and urgent. While this issue was called into attention and elaborated in articles and books decades ago and led to some patent applications, no actual solution was found unfortunately. Why is reducing fat in chocolate so difficult? What is the underlying physical mechanism? We have found that this issue is deeply related to the basic science of soft matters, especially to their viscosity and maximally random jammed (MRJ) density φx. All chocolate productions are handling liquid chocolate, a suspension with cocoa solid particles in melted fat, mainly cocoa butter. The fat level cannot be lower than 1-φxin order to have liquid chocolate to flow. Here we show that that with application of an electric field to liquid chocolate, we can aggregate the suspended particles into prolate spheroids. This microstructure change reduces liquid chocolate's viscosity along the flow direction and increases its MRJ density significantly. Hence the fat level in chocolate can be effectively reduced. We are looking forward to a new class of healthier and tasteful chocolate coming to the market soon. Dept. of Physics, Temple Univ, Philadelphia, PA 19122.
Zhao, Chao; Jiang, Jingchi; Guan, Yi; Guo, Xitong; He, Bin
2018-05-01
Electronic medical records (EMRs) contain medical knowledge that can be used for clinical decision support (CDS). Our objective is to develop a general system that can extract and represent knowledge contained in EMRs to support three CDS tasks-test recommendation, initial diagnosis, and treatment plan recommendation-given the condition of a patient. We extracted four kinds of medical entities from records and constructed an EMR-based medical knowledge network (EMKN), in which nodes are entities and edges reflect their co-occurrence in a record. Three bipartite subgraphs (bigraphs) were extracted from the EMKN, one to support each task. One part of the bigraph was the given condition (e.g., symptoms), and the other was the condition to be inferred (e.g., diseases). Each bigraph was regarded as a Markov random field (MRF) to support the inference. We proposed three graph-based energy functions and three likelihood-based energy functions. Two of these functions are based on knowledge representation learning and can provide distributed representations of medical entities. Two EMR datasets and three metrics were utilized to evaluate the performance. As a whole, the evaluation results indicate that the proposed system outperformed the baseline methods. The distributed representation of medical entities does reflect similarity relationships with respect to knowledge level. Combining EMKN and MRF is an effective approach for general medical knowledge representation and inference. Different tasks, however, require individually designed energy functions. Copyright © 2018 Elsevier B.V. All rights reserved.
Ben Daya, Ibrahim; Chen, Albert I H; Shafiee, Mohammad Javad; Wong, Alexander; Yeow, John T W
2017-09-06
The row-column method received a lot of attention for 3-D ultrasound imaging. By reducing the number of connections required to address the 2-D array and therefore reducing the amount of data to handle, this addressing method allows for real time 3-D imaging. Row-column still has its limitations: the issues of sparsity, speckle noise inherent to ultrasound, the spatially varying point spread function, and the ghosting artifacts inherent to the row-column method must all be taken into account when building a reconstruction framework. In this research, we build on a previously published system and propose an edge-guided, compensated row-column ultrasound imaging system that incorporates multilayered edge-guided stochastically fully connected conditional random fields to address the limitations of the row-column method. Tests carried out on simulated and real row-column ultrasound images show the effectiveness of our proposed system over other published systems. Visual assessment show our proposed system's potential at preserving edges and reducing speckle. Quantitative analysis shows that our proposed system outperforms previously published systems when evaluated with metrics such as Peak Signal-to-Noise Ratio, Coefficient of Correlation, and Effective Number of Looks. These results show the potential of our proposed system as an effective tool for enhancing 3-D row-column imaging.
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Hoffmann Nico
2016-09-01
Full Text Available Intraoperative thermal neuroimaging is a novel intraoperative imaging technique for the characterization of perfusion disorders, neural activity and other pathological changes of the brain. It bases on the correlation of (sub-cortical metabolism and perfusion with the emitted heat of the cortical surface. In order to minimize required computational resources and prevent unwanted artefacts in subsequent data analysis workflows foreground detection is a important preprocessing technique to differentiate pixels representing the cerebral cortex from background objects. We propose an efficient classification framework that integrates characteristic dynamic thermal behaviour into this classification task to include additional discriminative features. The first stage of our framework consists of learning this representation of characteristic thermal time-frequency behaviour. This representation models latent interconnections in the time-frequency domain that cover specific, yet a priori unknown, thermal properties of the cortex. In a second stage these features are then used to classify each pixel’s state with conditional random fields. We quantitatively evaluate several approaches to learning high-level features and their impact to the overall prediction accuracy. The introduction of high-level features leads to a significant accuracy improvement compared to a baseline classifier.
Pécot, Thierry; Bouthemy, Patrick; Boulanger, Jérôme; Chessel, Anatole; Bardin, Sabine; Salamero, Jean; Kervrann, Charles
2015-02-01
Image analysis applied to fluorescence live cell microscopy has become a key tool in molecular biology since it enables to characterize biological processes in space and time at the subcellular level. In fluorescence microscopy imaging, the moving tagged structures of interest, such as vesicles, appear as bright spots over a static or nonstatic background. In this paper, we consider the problem of vesicle segmentation and time-varying background estimation at the cellular scale. The main idea is to formulate the joint segmentation-estimation problem in the general conditional random field framework. Furthermore, segmentation of vesicles and background estimation are alternatively performed by energy minimization using a min cut-max flow algorithm. The proposed approach relies on a detection measure computed from intensity contrasts between neighboring blocks in fluorescence microscopy images. This approach permits analysis of either 2D + time or 3D + time data. We demonstrate the performance of the so-called C-CRAFT through an experimental comparison with the state-of-the-art methods in fluorescence video-microscopy. We also use this method to characterize the spatial and temporal distribution of Rab6 transport carriers at the cell periphery for two different specific adhesion geometries.
Oriented Markov random field based dendritic spine segmentation for fluorescence microscopy images.
Cheng, Jie; Zhou, Xiaobo; Miller, Eric L; Alvarez, Veronica A; Sabatini, Bernardo L; Wong, Stephen T C
2010-10-01
Dendritic spines have been shown to be closely related to various functional properties of the neuron. Usually dendritic spines are manually labeled to analyze their morphological changes, which is very time-consuming and susceptible to operator bias, even with the assistance of computers. To deal with these issues, several methods have been recently proposed to automatically detect and measure the dendritic spines with little human interaction. However, problems such as degraded detection performance for images with larger pixel size (e.g. 0.125 μm/pixel instead of 0.08 μm/pixel) still exist in these methods. Moreover, the shapes of detected spines are also distorted. For example, the "necks" of some spines are missed. Here we present an oriented Markov random field (OMRF) based algorithm which improves spine detection as well as their geometric characterization. We begin with the identification of a region of interest (ROI) containing all the dendrites and spines to be analyzed. For this purpose, we introduce an adaptive procedure for identifying the image background. Next, the OMRF model is discussed within a statistical framework and the segmentation is solved as a maximum a posteriori estimation (MAP) problem, whose optimal solution is found by a knowledge-guided iterative conditional mode (KICM) algorithm. Compared with the existing algorithms, the proposed algorithm not only provides a more accurate representation of the spine shape, but also improves the detection performance by more than 50% with regard to reducing both the misses and false detection.
Influence of Averaging Preprocessing on Image Analysis with a Markov Random Field Model
Sakamoto, Hirotaka; Nakanishi-Ohno, Yoshinori; Okada, Masato
2018-02-01
This paper describes our investigations into the influence of averaging preprocessing on the performance of image analysis. Averaging preprocessing involves a trade-off: image averaging is often undertaken to reduce noise while the number of image data available for image analysis is decreased. We formulated a process of generating image data by using a Markov random field (MRF) model to achieve image analysis tasks such as image restoration and hyper-parameter estimation by a Bayesian approach. According to the notions of Bayesian inference, posterior distributions were analyzed to evaluate the influence of averaging. There are three main results. First, we found that the performance of image restoration with a predetermined value for hyper-parameters is invariant regardless of whether averaging is conducted. We then found that the performance of hyper-parameter estimation deteriorates due to averaging. Our analysis of the negative logarithm of the posterior probability, which is called the free energy based on an analogy with statistical mechanics, indicated that the confidence of hyper-parameter estimation remains higher without averaging. Finally, we found that when the hyper-parameters are estimated from the data, the performance of image restoration worsens as averaging is undertaken. We conclude that averaging adversely influences the performance of image analysis through hyper-parameter estimation.
Zhang, Xueliang; Xiao, Pengfeng; Feng, Xuezhi
2017-09-01
It has been a common idea to produce multiscale segmentations to represent the various geographic objects in high-spatial resolution remote sensing (HR) images. However, it remains a great challenge to automatically select the proper segmentation scale(s) just according to the image information. In this study, we propose a novel way of information fusion at object level by combining hierarchical multiscale segmentations with existed thematic information produced by classification or recognition. The tree Markov random field (T-MRF) model is designed for the multiscale combination framework, through which the object type is determined as close as the existed thematic information. At the same time, the object boundary is jointly determined by the thematic labels and the multiscale segments through the minimization of the energy function. The benefits of the proposed T-MRF combination model include: (1) reducing the dependence of segmentation scale selection when utilizing multiscale segmentations; (2) exploring the hierarchical context naturally imbedded in the multiscale segmentations. The HR images in both urban and rural areas are used in the experiments to show the effectiveness of the proposed combination framework on these two aspects.
Analysis of tree stand horizontal structure using random point field methods
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O. P. Sekretenko
2015-06-01
Full Text Available This paper uses the model approach to analyze the horizontal structure of forest stands. The main types of models of random point fields and statistical procedures that can be used to analyze spatial patterns of trees of uneven and even-aged stands are described. We show how modern methods of spatial statistics can be used to address one of the objectives of forestry – to clarify the laws of natural thinning of forest stand and the corresponding changes in its spatial structure over time. Studying natural forest thinning, we describe the consecutive stages of modeling: selection of the appropriate parametric model, parameter estimation and generation of point patterns in accordance with the selected model, the selection of statistical functions to describe the horizontal structure of forest stands and testing of statistical hypotheses. We show the possibilities of a specialized software package, spatstat, which is designed to meet the challenges of spatial statistics and provides software support for modern methods of analysis of spatial data. We show that a model of stand thinning that does not consider inter-tree interaction can project the size distribution of the trees properly, but the spatial pattern of the modeled stand is not quite consistent with observed data. Using data of three even-aged pine forest stands of 25, 55, and 90-years old, we demonstrate that the spatial point process models are useful for combining measurements in the forest stands of different ages to study the forest stand natural thinning.
A Joint Land Cover Mapping and Image Registration Algorithm Based on a Markov Random Field Model
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Apisit Eiumnoh
2013-10-01
Full Text Available Traditionally, image registration of multi-modal and multi-temporal images is performed satisfactorily before land cover mapping. However, since multi-modal and multi-temporal images are likely to be obtained from different satellite platforms and/or acquired at different times, perfect alignment is very difficult to achieve. As a result, a proper land cover mapping algorithm must be able to correct registration errors as well as perform an accurate classification. In this paper, we propose a joint classification and registration technique based on a Markov random field (MRF model to simultaneously align two or more images and obtain a land cover map (LCM of the scene. The expectation maximization (EM algorithm is employed to solve the joint image classification and registration problem by iteratively estimating the map parameters and approximate posterior probabilities. Then, the maximum a posteriori (MAP criterion is used to produce an optimum land cover map. We conducted experiments on a set of four simulated images and one pair of remotely sensed images to investigate the effectiveness and robustness of the proposed algorithm. Our results show that, with proper selection of a critical MRF parameter, the resulting LCMs derived from an unregistered image pair can achieve an accuracy that is as high as when images are perfectly aligned. Furthermore, the registration error can be greatly reduced.
A Deep-Structured Conditional Random Field Model for Object Silhouette Tracking.
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Mohammad Javad Shafiee
Full Text Available In this work, we introduce a deep-structured conditional random field (DS-CRF model for the purpose of state-based object silhouette tracking. The proposed DS-CRF model consists of a series of state layers, where each state layer spatially characterizes the object silhouette at a particular point in time. The interactions between adjacent state layers are established by inter-layer connectivity dynamically determined based on inter-frame optical flow. By incorporate both spatial and temporal context in a dynamic fashion within such a deep-structured probabilistic graphical model, the proposed DS-CRF model allows us to develop a framework that can accurately and efficiently track object silhouettes that can change greatly over time, as well as under different situations such as occlusion and multiple targets within the scene. Experiment results using video surveillance datasets containing different scenarios such as occlusion and multiple targets showed that the proposed DS-CRF approach provides strong object silhouette tracking performance when compared to baseline methods such as mean-shift tracking, as well as state-of-the-art methods such as context tracking and boosted particle filtering.