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Random Fields by Erik Vanmarcke

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1Random Dynamics And Thermodynamic Limits For Polygonal Markov Fields In The Plane

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We construct random dynamics on collections of non-intersecting planar contours, leaving invariant the distributions of length- and area-interacting polygonal Markov fields with V-shaped nodes. The first of these dynamics is based on the dynamic construction of consistent polygonal fields, as presented in the original articles by Arak (1982) and Arak and Surgailis (1989, 1991), and it provides an easy-to-implement Metropolis-type simulation algorithm. The second dynamics leads to a graphical construction in the spirit of Fernandez, Ferrari and Garcia (1998,2002) and it yields a perfect simulation scheme in a finite window from the infinite-volume limit. This algorithm seems difficult to implement, yet its value lies in that it allows for theoretical analysis of thermodynamic limit behaviour of length-interacting polygonal fields. The results thus obtained include the uniqueness and exponential $\alpha$-mixing of the thermodynamic limit of such fields in the low temperature region, in the class of infinite-volume Gibbs measures without infinite contours. Outside this class we conjecture the existence of an infinite number of extreme phases breaking both the translational and rotational symmetries

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2Active Sterile Neutrino Conversions In A Supernova With Random Magnetic Fields

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{Large enough random magnetic fields may affect in an important way neutrino conversion rates, even in the case where neutrinos have zero transition magnetic moments. We consider their effect in the case of active to sterile \neu conversions in a supernova and show that for KeV neutrino masses these limits may overcome those derived for the case of zero magnetic field.}

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3Integral Operators Basic In Random Fields Estimation Theory

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The paper deals with the basic integral equation of random field estimation theory by the criterion of minimum of variance of the error estimate. This integral equation is of the first kind. The corresponding integra$ operator over a bounded domain $\Omega $ in ${\Bbb R}^{n}$ is weakly singular. This operator is an isomorphism between appropriate Sobolev spaces. This is proved by a reduction of the integral equ$ an elliptic boundary value problem in the domain exterior to $\Omega .$ Extra difficulties arise due to the fact that the exterior boundary value problem should be solved in the Sobolev spaces of negative order.

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4Gaussian Fluctuation For The Number Of Particles In Airy, Bessel, Sine And Other Determinantal Random Point Fields

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We prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the Gaussian fluctuation of the number of particles in random point fields with determinantal correlation functions. As another corollary of Costin-Lebowitz Theorem we prove CLT for the empirical distribution function of the eigenvalues of random matrices from classical compact groups.

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  • Title: ➤  Gaussian Fluctuation For The Number Of Particles In Airy, Bessel, Sine And Other Determinantal Random Point Fields
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5Controlling Dispersion Forces Between Small Particles With Artificially Created Random Light Fields

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Appropriate combinations of laser beams can be used to trap and manipulate small particles with "optical tweezers" as well as to induce significant "optical binding" forces between particles. These interaction forces are usually strongly anisotropic depending on the interference landscape of the external fields. This is in contrast with the familiar isotropic, translationally invariant, van der Waals and, in general, Casimir-Lifshitz interactions between neutral bodies arising from random electromagnetic waves generated by equilibrium quantum and thermal fluctuations. Here we show, both theoretically and experimentally, that dispersion forces between small colloidal particles can also be induced and controlled using artificially created fluctuating light fields. Using optical tweezers as gauge, we present experimental evidence for the predicted isotropic attractive interactions between dielectric microspheres induced by laser-generated, random light fields. These light induced interactions open a path towards the control of translationally invariant interactions with tuneable strength and range in colloidal systems.

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6Laws Of The Single Logarithm For Delayed Sums Of Random Fields

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We extend a law of the single logarithm for delayed sums by Lai to delayed sums of random fields. A law for subsequences, which also includes the one-dimensional case, is obtained in passing.

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7Asymptotic Normality For Deconvolution Kernel Density Estimators From Random Fields

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The paper discusses the estimation of a continuous density function of the target random field $X_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ which is contaminated by measurement errors. In particular, the observed random field $Y_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ is such that $Y_{\bf{i}}=X_{\bf{i}}+\epsilon_{\bf{i}}$, where the random error $\epsilon_{\bf{i}}$ is from a known distribution and independent of the target random field. Compared to the existing results, the paper is improved in two directions. First, the random vectors in contrast to univariate random variables are investigated. Second, a random field with a certain spatial interactions instead of i. i. d. random variables is studied. Asymptotic normality of the proposed estimator is established under appropriate conditions.

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8Moderate Deviations For Random Fields And Random Complex Zeroes

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Moderate deviations for random complex zeroes are deduced from a new theorem on moderate deviations for random fields.

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9Random Fields Of Multivariate Test Statistics, With Applications To Shape Analysis

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Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are nonzero using classical multivariate statistics evaluated at each point. The problem is to find the $P$-value of the maximum of such a random field of test statistics. We approximate this by the expected Euler characteristic of the excursion set. Our main result is a very simple method for calculating this, which not only gives us the previous result of Cao and Worsley [Ann. Statist. 27 (1999) 925--942] for Hotelling's $T^2$, but also random fields of Roy's maximum root, maximum canonical correlations [Ann. Appl. Probab. 9 (1999) 1021--1057], multilinear forms [Ann. Statist. 29 (2001) 328--371], $\bar{\chi}^2$ [Statist. Probab. Lett 32 (1997) 367--376, Ann. Statist. 25 (1997) 2368--2387] and $\chi^2$ scale space [Adv. in Appl. Probab. 33 (2001) 773--793]. The trick involves approaching the problem from the point of view of Roy's union-intersection principle. The results are applied to a problem in shape analysis where we look for brain damage due to nonmissile trauma.

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10Higher Order Markov Random Fields For Independent Sets

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It is well-known that if one samples from the independent sets of a large regular graph of large girth using a pairwise Markov random field (i.e. hardcore model) in the uniqueness regime, each excluded node has a binomially distributed number of included neighbors in the limit. In this paper, motivated by applications to the design of communication networks, we pose the question of how to sample from the independent sets of such a graph so that the number of included neighbors of each excluded node has a different distribution of our choosing. We observe that higher order Markov random fields are well-suited to this task, and investigate the properties of these models. For the family of so-called reverse ultra log-concave distributions, which includes the truncated Poisson and geometric, we give necessary and sufficient conditions for the natural higher order Markov random field which induces the desired distribution to be in the uniqueness regime, in terms of the set of solutions to a certain system of equations. We also show that these Markov random fields undergo a phase transition, and give explicit bounds on the associated critical activity, which we prove to exhibit a certain robustness. For distributions which are small perturbations around the binomial distribution realized by the hardcore model at critical activity, we give a description of the corresponding uniqueness regime in terms of a simple polyhedral cone. Our analysis reveals an interesting non-monotonicity with regards to biasing towards excluded nodes with no included neighbors. We conclude with a broader discussion of the potential use of higher order Markov random fields for analyzing independent sets in graphs.

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11Fourier Coefficients Of Invariant Random Fields On Homogeneous Spaces Of Compact Groups

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Let $T$ be a random field invariant under the action of a compact group $G$. In the line of previous work we investigate properties of the Fourier coefficients as orthogonality and Gaussianity. In particular we give conditions ensuring that independence of the random Fourier coefficients implies Gaussianity. As a consequence, in general, it is not possible to simulate a non-Gaussian invariant random field through its Fourier expansion using independent coefficients.

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12On The Rank Of Random Matrices Over Finite Fields

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A novel lower bound is introduced for the full rank probability of random finite field matrices, where a number of elements with known location are identically zero, and remaining elements are chosen independently of each other, uniformly over the field. The main ingredient is a result showing that constraining additional elements to be zero cannot result in a higher probability of full rank. The bound then follows by "zeroing" elements to produce a block-diagonal matrix, whose full rank probability can be computed exactly. The bound is shown to be at least as tight and can be strictly tighter than existing bounds.

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13Measuring Directionality In Random Fields Using The Monogenic Signal

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Analyzing directional structures in images is important in many applications since one-dimensional patterns often correspond to important features such as object contours or trajectories. Most of the work on this topic has dealt with deterministic images; so far, little research has been performed on analyzing directionality in random fields. In this paper, we propose a measure to quantify the degree of directionality in random fields. This measure can be used to construct statistical tests for the presence of directional structure. Our measure is based on the monogenic signal, which enables a unique decomposition of a 2D signal into local amplitude, local orientation, and local phase. We investigate the second-order statistical properties of the monogenic signal for isotropic, anisotropic, and unidirectional random fields. We analyze our measure of directionality for finite-size sample images, and determine a threshold to distinguish between unidirectional and non-unidirectional random fields.

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14Dynamic Fluctuations In Unfrustrated Systems: Random Walks, Scalar Fields And The Kosterlitz-Thouless Phase

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We study analytically the distribution of fluctuations of the quantities whose average yield the usual two-point correlation and linear response functions in three unfrustrated models: the random walk, the $d$ dimensional scalar field and the 2d XY model. In particular we consider the time dependence of ratios between composite operators formed with these fluctuating quantities which generalize the largely studied fluctuation-dissipation ratio, allowing us to discuss the relevance of the effective temperature notion beyond linear order. The behavior of fluctuations in the aforementioned solvable cases is compared to numerical simulations of the 2d clock model with $p=6,12$ states.

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15Detecting Sparse Cone Alternatives For Gaussian Random Fields, With An Application To FMRI

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Our problem is to find a good approximation to the P-value of the maximum of a random field of test statistics for a cone alternative at each point in a sample of Gaussian random fields. These test statistics have been proposed in the neuroscience literature for the analysis of fMRI data allowing for unknown delay in the hemodynamic response. However the null distribution of the maximum of this 3D random field of test statistics, and hence the threshold used to detect brain activation, was unsolved. To find a solution, we approximate the P-value by the expected Euler characteristic (EC) of the excursion set of the test statistic random field. Our main result is the required EC density, derived using the Gaussian Kinematic Formula.

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16MRFalign: Protein Homology Detection Through Alignment Of Markov Random Fields.

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This article is from PLoS Computational Biology , volume 10 . Abstract Sequence-based protein homology detection has been extensively studied and so far the most sensitive method is based upon comparison of protein sequence profiles, which are derived from multiple sequence alignment (MSA) of sequence homologs in a protein family. A sequence profile is usually represented as a position-specific scoring matrix (PSSM) or an HMM (Hidden Markov Model) and accordingly PSSM-PSSM or HMM-HMM comparison is used for homolog detection. This paper presents a new homology detection method MRFalign, consisting of three key components: 1) a Markov Random Fields (MRF) representation of a protein family; 2) a scoring function measuring similarity of two MRFs; and 3) an efficient ADMM (Alternating Direction Method of Multipliers) algorithm aligning two MRFs. Compared to HMM that can only model very short-range residue correlation, MRFs can model long-range residue interaction pattern and thus, encode information for the global 3D structure of a protein family. Consequently, MRF-MRF comparison for remote homology detection shall be much more sensitive than HMM-HMM or PSSM-PSSM comparison. Experiments confirm that MRFalign outperforms several popular HMM or PSSM-based methods in terms of both alignment accuracy and remote homology detection and that MRFalign works particularly well for mainly beta proteins. For example, tested on the benchmark SCOP40 (8353 proteins) for homology detection, PSSM-PSSM and HMM-HMM succeed on 48% and 52% of proteins, respectively, at superfamily level, and on 15% and 27% of proteins, respectively, at fold level. In contrast, MRFalign succeeds on 57.3% and 42.5% of proteins at superfamily and fold level, respectively. This study implies that long-range residue interaction patterns are very helpful for sequence-based homology detection. The software is available for download at http://raptorx.uchicago.edu/download/. A summary of this paper appears in the proceedings of the RECOMB 2014 conference, April 2–5.

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17Relativistic Diffusive Motion In Random Electromagnetic Fields

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We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature \beta^{-1}=mc^{2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).

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18Gradient Tree Boosting For Training Conditional Random Fields

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We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature \beta^{-1}=mc^{2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).

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19Bell Inequalities For Random Fields

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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.

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20Eight-potential-well Order-disorder Ferroelectric Model And Effects Of Random Fields

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An eight-potential-well order-disorder ferroelectric model was presented and the phase transition was studied under the mean-field approximation. It was shown that the two-body interactions are able to account for the first-order and the second order phase transitions. With increasing the random fields in the system, a first-order phase transition is transformed into a second-order phase transition, and furthermore, a second-order phase transition is inhibited. However, proper random fields can promote the spontaneous appearance of a first-order phase transition by increasing the overcooled temperature. The connections of the model with relaxors were discussed.

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21DTIC ADA612906: Gradient Boosting For Conditional Random Fields

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In this paper, we present a gradient boosting algorithm for tree-shaped conditional random fields (CRF). Conditional random fields are an important class of models for accurate structured prediction, but effective design of the feature functions is a major challenge when applying CRF models to real world data. Gradient boosting, which can induce and select functions, is a natural candidate solution for the problem. However, it is non-trivial to derive gradient boosting algorithms for CRFs, due to the dense Hessian matrices introduced by variable dependencies. We address this challenge by deriving a Markov Chain mixing rate bound to quantify the dependencies, and introduce a gradient boosting algorithm that iteratively optimizes an adaptive upper bound of the objective function. The resulting algorithm induces and selects features for CRFs via functional space optimization, with provable convergence guarantees. Experimental results on three real world datasets demonstrate that the mixing rate based upper bound is effective for training CRFs with non-linear potentials.

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22NASA Technical Reports Server (NTRS) 20000120209: Possible Statistics Of Two Coupled Random Fields: Application To Passive Scalar

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We use the relativity postulate of scale invariance to derive the similarity transformations between two coupled scale-invariant random elds at different scales. We nd the equations leading to the scaling exponents. This formulation is applied to the case of passive scalars advected i) by a random Gaussian velocity field; and ii) by a turbulent velocity field. In the Gaussian case, we show that the passive scalar increments follow a log-Levy distribution generalizing Kraichnan's solution and, in an appropriate limit, a log-normal distribution. In the turbulent case, we show that when the velocity increments follow a log-Poisson statistics, the passive scalar increments follow a statistics close to log-Poisson. This result explains the experimental observations of Ruiz et al. about the temperature increments.

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23Dynamic Models And Nonlinear Filtering Of Wave Propagation In Random Fields

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In this paper, a general model of wireless channels is established based on the physics of wave propagation. Then the problems of inverse scattering and channel prediction are formulated as nonlinear filtering problems. The solutions to the nonlinear filtering problems are given in the form of dynamic evolution equations of the estimated quantities. Finally, examples are provided to illustrate the practical applications of the proposed theory.

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24Electron-ion-ion Coincidence Experiments For Photofragmentation Of Polyatomic Molecules Using Pulsed Electric Fields: Treatment Of Random Coincidences

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In molecular photofragmentation processes by soft X-rays, a number of ionic fragments can be produced, each having a different abundance and correlation with the emitted electron kinetic energy. For investigating these fragmentation processes, electron-ion and electron-ion-ion coincidence experiments, in which the kinetic energy of electrons are analyzed using an electrostatic analyzer while the mass of the ions is analyzed using a pulsed electric field, are very powerful. For such measurements, however, the contribution of random coincidences is substantial and affects the data in a non-trivial way. Simple intuitive subtraction methods cannot be applied. In the present paper, we describe these electron-ion and electron-ion-ion coincidence experiments together with a subtraction method for the contribution from random coincidences. We provide a comprehensive set of equations for the data treatment, including equations for the calculation of error-bars. We demonstrate the method by applying it to the fragmentation of free CF$_3$SF$_5$ molecules.

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25Change-Point Detection And Bootstrap For Hilbert Space Valued Random Fields

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The problem of testing for the presence of epidemic changes in random fields is investigated. In order to be able to deal with general changes in the marginal distribution, a Cram\'er-von Mises type test is introduced which is based on Hilbert space theory. A functional central limit theorem for $\rho$-mixing Hilbert space valued random fields is proven. In order to avoid the estimation of the long-run variance and obtain critical values, Shao's dependent wild bootstrap method is adapted to this context. For this, a joint functional central limit theorem for the original and the bootstrap sample is shown. Finally, the theoretic results are supplemented by a short simulation study.

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26Pathwise Taylor Expansions For Itô Random Fields

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In this paper we study the {\it pathwise stochastic Taylor expansion}, in the sense of our previous work \cite{Buckdahn_Ma_02}, for a class of It\^o-type random fields in which the diffusion part is allowed to contain both the random field itself and its spatial derivatives. Random fields of such an "self-exciting" type particularly contains the fully nonlinear stochastic PDEs of curvature driven diffusion, as well as certain stochastic Hamilton-Jacobi-Bellman equations. We introduce the new notion of "$n$-fold" derivatives of a random field, as a fundamental device to cope with the special self-exciting nature. Unlike our previous work \cite{Buckdahn_Ma_02}, our new expansion can be defined around any random time-space point $(\t,\xi)$, where the temporal component $\t$ does not even have to be a stopping time. Moreover, the exceptional null set is independent of the choice of the random point $(\t,\xi)$. As an application, we show how this new form of pathwise Taylor expansion could lead to a different treatment of the stochastic characteristics for a class of fully nonlinear SPDEs whose diffusion term involves both the solution and its gradient, and hence lead to a definition of the {\it stochastic viscosity solution} for such SPDEs, which is new in the literature.

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27Gibbs Random Fields And Markov Random Fields With Constraints

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It was shown many times in the literature that a Markov random field is equivalent to a Gibbs random field when all realizations of the field have non-zero probabilities; the proofs are rather complicated. A simpler proof, which is based directly on simple probability theory, is presented. Furthermore, it is shown that the equivalence is still valid when there are constraints (zero probability realizations) of any type. The equivalence extends to infinite size random fields, as well.

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28A Functional Central Limit Theorem For Integrals Of Stationary Mixing Random Fields

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We prove a functional central limit theorem for integrals $\int_W f(X(t))\, dt$, where $(X(t))_{t\in\mathbb{R}^d}$ is a stationary mixing random field and the stochastic process is indexed by the function $f$, as the integration domain $W$ grows in Van Hove-sense. We discuss properties of the covariance function of the asymptotic Gaussian process.

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29Motion In Random Fields - An Application To Stock Market Data

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A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-scale field show characteristics similar to those found in empirical studies of stock market data. Specifically, short-term returns have a non-Gaussian distribution, with super-diffusive volatility, and a fast-decaying correlation function. The correlation function of the absolute value of returns decays as a power-law, and the returns distribution converges towards Gaussian over long times. Some important characteristics of empirical data are not, however, reproduced by the model, notably the scaling of tails of the cumulative distribution function of returns.

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30Multi-colour Random Fields With Polygonal Realisations

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We introduce a class of random fields that can be understood as discrete versions of multi-colour polygonal fields built on regular linear tessellations. We focus fir st on consistent polygonal fields, for which we show Markovianity and solvability by means of a dynamic representation. This representation forms the basis for new sampling techniques for Gibbsian modifications of such fields, a class which cove rs lattice based random fields. A flux based modification is applied to the extracti on of the field tracks network from a SAR image of a rural area.

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31Persistent Homology For Random Fields And Complexes

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We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices, and, in most detail, the algebraic topology of the excursion sets of random fields.

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32Properties Of Quick Simulation Random Fields

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Herein, we introduce and study a new class of discrete random fields designed for quick simulation and covariance inference under inhomogeneous condition. Simulation of these correlated fields can be done in a single pass instead of relying on multi-pass convergent methods like the Gibbs Sampler or other Markov Chain Monte Carlo methods. The fields are constructed directly from specified marginal probability mass functions and covariances between nearby sites. The proposition on which the construction is based establishes when and how it is possible to simplify the conditional probabilities of each site given the other sites in a manner that makes simulation quite feasible yet maintains desired marginal probabilities and covariances between sites. Special cases of these correlated fields have been deployed successfully in data authentication, object detection and image generation. The limitations that must be imposed on the covariances and marginal probabilities in order for the algorithm to work are studied. What's more, a necessary and sufficient condition that guarantees the permutation property of correlated random fields are investigated. In particular, Markov random fields as a subclass of correlated random fields are derived by a general and natural condition. Consequently, a direct and flexible single pass algorithm for simulating Markov random fields follows.

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33Telescoping Recursive Representations And Estimation Of Gauss-Markov Random Fields

Herein, we introduce and study a new class of discrete random fields designed for quick simulation and covariance inference under inhomogeneous condition. Simulation of these correlated fields can be done in a single pass instead of relying on multi-pass convergent methods like the Gibbs Sampler or other Markov Chain Monte Carlo methods. The fields are constructed directly from specified marginal probability mass functions and covariances between nearby sites. The proposition on which the construction is based establishes when and how it is possible to simplify the conditional probabilities of each site given the other sites in a manner that makes simulation quite feasible yet maintains desired marginal probabilities and covariances between sites. Special cases of these correlated fields have been deployed successfully in data authentication, object detection and image generation. The limitations that must be imposed on the covariances and marginal probabilities in order for the algorithm to work are studied. What's more, a necessary and sufficient condition that guarantees the permutation property of correlated random fields are investigated. In particular, Markov random fields as a subclass of correlated random fields are derived by a general and natural condition. Consequently, a direct and flexible single pass algorithm for simulating Markov random fields follows.

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34Neutrino Conversions In Solar Random Magnetic Fields

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We consider the effect of a random magnetic field in the convective zone of the Sun superimposed to a regular magnetic field on resonant neutrino spin-flavour oscillations. We argue for the existence of a field of strongly chaotic nature at the bottom of the convective zone. In contrast to previous attempts we employ in addition a model motivated regular twisting magnetic field profile. In this scenario electron antineutrinos are produced through cascades like $\nu_{eL}\to \nu_{\mu L}\to \tilde{\nu}_{eR}$, The expected signals in the different experiments (SK,GALLEX-SAGE, Homestake) are obtained as a function of the level of noise, regular magnetic field and neutrino mixing parameters. Previous results obtained for small mixing and ad-hoc regular magnetic profiles are reobtained. We confirm the strong suppression for large part of the parameter space of the $\tilde{\nu}_{eR}$-flux for high energy boron neutrinos in agreement with present data of the SK experiment. We find that MSW regions ($\Delta m^2\approx 10^{-5}$ eV$^2$, both small and large mixing solutions) are stable up to very large levels of noise (P=0.7-0.8) but they are acceptable from the point of view of antineutrino production only for moderate levels of it ($P\approx 0.95$). For strong noise and reasonable regular magnetic field, any parameter region $(\Delta m^2, \sin^2 2\theta)$ is excluded. As a consequence, we are allowed to reverse the problem and to put limits on r.m.s field strength and transition magnetic moments by demanding a particle physics solution to the SNP under this scenario.

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35Quasi-Elastic Scattering, Random Fields And Phonon-coupling Effects In PbMg1/3Nb2/3O3

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The low-energy part of the vibration spectrum in PbMg$_{1/3}$Nb$_{2/3}$O$_3$ (PMN) relaxor ferroelectric has been studied by neutron scattering above and below the Burns temperature, T$_d$. The transverse acoustic and the lowest transverse optic phonons are strongly coupled and we have obtained a model for this coupling. We observe that the lowest optic branch is always underdamped. A resolution-limited central peak and quasi-elastic scattering appear in the vicinity of the Burns temperature. It is shown that it is unlikely that the quasi-elastic scattering originates from the combined effects of coupling between TA and TO phonons with an increase of the damping of the TO phonon below T$_d$. The quasi-elastic scattering has a peak as a function of temperature close to the peak in the dielectric constant while the intensity of the central peak scattering increases strongly below this temperature. These results are discussed in terms of a random field model for relaxors.

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36Control Of Spatially Structured Random Processes And Random Fields With Applications

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xi, 261 p. ; 25 cm

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37An Approach To Complete Convergence Theorems For Dependent Random Fields Via Application Of Fuk Nagaev Inequality

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Let $\{ X_{\bf n}, {\bf n}\in \mathbb{N}^d \}$ be a random field i.e. a family of random variables indexed by $\mathbb{N}^d $, $d\ge 2$. Complete convergence, convergence rates for non identically distributed, negatively dependent and martingale random fields are studied by application of Fuk-Nagaev inequality. The results are proved in asymmetric convergence case i.e. for the norming sequence equal $n_1^{\alpha_1}\cdot n_2^{\alpha_2}\cdot\ldots\cdot n_d^{\alpha_d}$, where $(n_1,n_2,\ldots, n_d)=\mathbf{n} \in \mathbb{N}^d$ and $\min\limits_{1\leq i \leq d}\alpha_i \geq \frac{1}{2}.$

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38Ensemble Inequivalence In The Ferromagnetic P-spin Model In Random Fields

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We study the effect that randomness has on long-range interacting systems by using the ferromagnetic Ising model with $p$-body interactions in random fields. The case with p=2 yields a phase diagram similar to that of previously studied models and shows known features that inequivalence of the canonical and microcanonical ensembles brings with it, for example negative specific heat in a narrow region of the phase diagram. When p>2, however, the canonical phase diagram is completely different from the microcanonical one. The temperature does not necessarily determine the microcanonical phases uniquely, and thus the ferromagnetic and paramagnetic phases are not separated in such a region of a conventional phase diagram drawn with the temperature and field strength as the axes. Below a certain value of the external field strength, part of the ferromagnetic phase has negative specific heat. For large values of the external field strength the ergodicity is broken before the phase transition occurs for p>2. Moreover, for p>2, the Maxwell construction cannot be derived in a consistent manner and therefore, in contrast to previous cases with negative specific heat, the Maxwell construction does not bridge the gap between the ensembles.

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39Hölder Regularity For Operator Scaling Stable Random Fields

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We investigate the sample paths regularity of operator scaling alpha-stable random fields. Such fields were introduced as anisotropic generalizations of self-similar fields and satisfy a scaling property for a real matrix E. In the case of harmonizable operator scaling random fields, the sample paths are locally H\"{o}lderian and their H\"{o}lder regularity is characterized by the eigen decomposition with respect to E. In particular, the directional H\"{o}lder regularity may vary and is given by the eigenvalues of E. In the case of moving average operator scaling random alpha-stable random fields, with 0

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40NASA Technical Reports Server (NTRS) 20160013853: On The Calculation Of Uncertainty Statistics With Error Bounds For CFD Calculations Containing Random Parameters And Fields

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This chapter discusses the ongoing development of combined uncertainty and error bound estimates for computational fluid dynamics (CFD) calculations subject to imposed random parameters and random fields. An objective of this work is the construction of computable error bound formulas for output uncertainty statistics that guide CFD practitioners in systematically determining how accurately CFD realizations should be approximated and how accurately uncertainty statistics should be approximated for output quantities of interest. Formal error bounds formulas for moment statistics that properly account for the presence of numerical errors in CFD calculations and numerical quadrature errors in the calculation of moment statistics have been previously presented in [8]. In this past work, hierarchical node-nested dense and sparse tensor product quadratures are used to calculate moment statistics integrals. In the present work, a framework has been developed that exploits the hierarchical structure of these quadratures in order to simplify the calculation of an estimate of the quadrature error needed in error bound formulas. When signed estimates of realization error are available, this signed error may also be used to estimate output quantity of interest probability densities as a means to assess the impact of realization error on these density estimates. Numerical results are presented for CFD problems with uncertainty to demonstrate the capabilities of this framework.\n\n\n\n\n

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41NASA Technical Reports Server (NTRS) 19870001019: Can Stochastic, Dissipative Wave Fields Be Treated As Random Walk Generators

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A suggestion by Meek et al. (1985) that the gravity wave field be viewed as stochastic, with significant nonlinearities, is applied to calculate diffusivities. The purpose here is to calculate the diffusivity for stochastic wave model and compare it with previous diffusivity estimates. The researchers do this for an idealized case in which the wind velocity changes but slowly, and for which saturation is the principal mechanism by which wave energy is lost. A related calculation was given in a very brief way (Weinstock, 1976), but the approximations were not fully justified, nor were the physical pre-suppositions clearly explained. The observations of Meek et al. (1985) have clarified the pre-suppositions for the researchers and provided a rationalization and improvement of the approximations employed.

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42DTIC ADA342713: Random Fields Governed By Stochastic Partial Differential Equations And Their Applications To Oceanography

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An effective method of estimating transport parameters from tracer observations was developed based on the maximum likelihood approach in stochastic partial differential equations. Different classes of statistical estimators for near surface velocities and turbulence parameters have been studied. A complete error analysis for the method of moments was performed. Hamiltonian theory of wave turbulence was extended to the oceanic Rossby waves.

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43Gaussian Fields And Random Packing

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Consider sequential packing of unit balls in a large cube, as in the Renyi car-parking model, but in any dimension and with Poisson input. We show after suitable rescaling that the spatial distribution of packed balls tends to that of a Gaussian field in the thermodynamic limit. We prove analogous results for related applied models, including ballistic deposition and spatial birth-growth models.

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44An Invariance Principle For Stationary Random Fields Under Hannan's Condition

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We establish an invariance principle for a general class of stationary random fields indexed by $\mathbb Z^d$, under Hannan's condition generalized to $\mathbb Z^d$. To do so we first establish a uniform integrability result for stationary orthomartingales, and second we establish a coboundary decomposition for certain stationary random fields. At last, we obtain an invariance principle by developing an orthomartingale approximation. Our invariance principle improves known results in the literature, and particularly we require only finite second moment.

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45Intrusion Detection Using Conditional Random Fields

Intrusion detection systems have become a key component in ensuring the safety of systems and networks. This paper introduces the probabilistic approach called Conditional Random Fields (CRF) for detecting network based intrusions. In this paper, we have shown results for the issue of accuracy using CRFs. It is demonstrated that high attack detection accuracy can be achieved by using Conditional Random Fields. Experimental results on the benchmark KDD’99 intrusion data set show the importance of proposed system. The improvement in attack detection accuracy is very high for Probe, Denial of Service, U2R and R2L attacks.

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46Microsoft Research Video 150895: Semantic Segmentation Using Higher-Order Markov Random Fields

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Many scene understanding tasks are formulated as a labelling problem that tries to assign a label to each pixel of an image, that may correspond to different object classes such as car, grass or sky, or to depths or to intensity after denoising. These labelling problems are typically formulated as a pairwise Random Field, modelling the dependencies of labels of pairs of variables in the local neighborhoods. However, these pairwise models are very restricted in their expressivity and can not induce desired complex structures in the output labelling. In this work we propose global structured formulation beyond pairwise models, that can combine features over multiple scales and enforce globally consistent label-set in the resulting labelling. We show that this complex model can still be learnt and optimised efficiently. Proposed method has been tested on several semantic segmentation data sets, where it gets (close to) state-of-the-art results. We then show how multiple random field models can be formulated jointly across different domains. We demonstrate the usefulness of this model on the problem of joint semantic segmentation and dense 3D stereo reconstruction and show that this approach significantly outperforms existing methods for street scenes. The complete source code is publicly available at http://cms.brookes.ac.uk/staff/PhilipTorr/ale.htm ©2011 Microsoft Corporation. All rights reserved.

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47Bigram Feature Extraction And Conditional Random Fields Model To Improve Text Classification Clinical Trial Document

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In the field of health and medicine, there is a very important term known as clinical trials. Clinical trials are a type of activity that studies how the safest way to treat patients is. These clinical trials are usually written in unstructured free text which requires translation from a computer. The aim of this paper is to classify the texts of cancer clinical trial documents consisting of unstructured free texts taken from cancer clinical trial protocols. The proposed algorithm is conditional random Fields and bigram features. A new classification model from the cancer clinical trial document text is proposed to compete with other methods in terms of precision, recall, and f-1 score. The results of this study are better than the previous results, namely 88.07 precision, 88.05 recall and f-1 score 88.06.

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48NASA Technical Reports Server (NTRS) 19740018067: The Diffusive Idealization Of Charged Particle Transport In Random Magnetic Fields

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The transport of charged particles diffusing in a random magnetic field parallel to a relatively large guiding field is presented. The same coefficient of diffusion is obtained by three methods. Two corrections must be added to the expression in which the diffusive flux is proportional to the gradient of the density. Explicit expressions are given for a characteristic time and a characteristic length which describe the corrections. The well known divergence of the coefficient of diffusion, which is implied by the quasilinear analysis of pitch angle scattering, does not occur if the scattering rate is finite at 90 deg pitch angle. This effect is illustrated by formulas which give the coefficient of diffusion when the quasilinear expression is perturbed by a variable amount of isotropic scattering.

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49Exponents Of Operator Self-similar Random Fields

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If X(c^E t) and c^H X(t) have the same finite-dimensional distributions for some linear operators E and H, we say that the random vector field X(t) is operator self-similar. The exponents E and H are not unique in general, due to symmetry. This paper characterizes the possible set of range exponents H for a given domain exponent, and conversely, the set of domain exponents E for a given range exponent.

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50Modeling And Recursive Estimation Of Two Dimensional Random Fields And Applications To Target Detection.

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ADA045179

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